Research Collection. Indexical Architecture: Prominent positions, applications and the Web. Doctoral Thesis. ETH Library

Transcription

1 Research Collection Doctoral Thesis Indexical Architecture: Prominent positions, applications and the Web Author(s): Orozco Esquivel, Jorge Publication Date: 2017 Permanent Link: Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library

2 DISS. ETH NO INDEXICAL ARCHITECTURE Prominent positions, applications and the Web Jorge Orozco Esquivel

3

4 DISS. ETH NO INDEXICAL ARCHITECTURE Prominent positions, applications and the Web A thesis submitted to attain the degree of DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich) presented by JORGE OROZCO ESQUIVEL Arch., Universidad Michoacana de San Nicolás de Hidalgo, México MAA, Universitat Politècnica de Catalunya, Barcelona MAS ETH ARCH/CAAD, ETH Zurich born on citizen of México accepted on the recommendation of Prof. Dr. Ludger Hovestadt, examiner Prof. Dr. Vera Bühlmann, co-examiner Assoc. Prof. Philippe Morel, co-examiner 2017

5

6 ABSTRACT This dissertation deals with the abundance of online information in architecture. It looks at this novel phenomenon with prominent contemporary architects, bringing forward the phenomenon s implications in relation to their and others positions in architecture. Assuming that these implications present the necessity of articulating architecture addressing the abundance of online information, it looks at three prominent online applications, seeking a rather abstract operational, philosophical, and mathematical understanding of what they do and how they do it. It further discusses the relevance of articulating architecture in terms similar to those of the online information, and shows the feasibility of putting together applications to talk to the web communities that circulate information ad infinitum. This dissertation is divided into three chapters. First, it presents three talks with a number of contemporary architects who, on the one hand, affirm and engage with the idea that global conditions influence the tradition of architecture, and on the other, celebrate the interplays between architecture and computers. By placing their positions next to various phenomena observable by anyone with a computer online, talks about the global network of computers emerge, rendering apparent these positions capacities and limits to articulating architecture in terms of the online information. It further looks at three prominent applications on the global network web search engines, content sharing platforms, and online translations that in the last decade have shown ways to create new stabilities meters and values rooted in an indexical characterization and operation of online information. In order to construct an abstract understanding of these applications, this dissertation puts together universal talks around them with voices of prominent positions in philosophy and contributions in mathematics. These talks give the foundations to articulate architecture in terms similar to those of the information circulating on the global network free from specificity and capable of having pre-specific talks. It finally presents three applications with which to talk to different web communities e.g., Tumblr, Wikimedia Commons, swiss-architects. With these applications, the architect positions him-herself in the middle of the infinite circulation of information and addresses the community in a personal and lively manner. These applications show that in order to ask architectural questions to web communities or to talk on the global network architecture itself needs to be thought of and articulated free from specificity. This basic research aims to present a consistent understanding of the abundance of online information, as this promises in turn a vivid and capacious understanding of architecture. 5

7 ZUSAMMENFASSUNG Die vorliegende Dissertation erörtert die Fülle von Online-Informationen in der Architektur. Es sieht dieses neuartige Phänomen im Kontext prominenter zeitgenössischer Architekten und legt die Implikationen des Phänomens in Bezug auf ihre und andere Positionen in der Architektur vor. Unter der Annahme, dass diese Implikationen die Notwendigkeit hervorrufen, die Architektur als Adressat dieser Fülle von Online-Informationen zu artikulieren, werden drei prominente Online- Anwendungen innerhalb eines eher abstrakten, operativen, philosophischen und mathematischen Verständnisses dessen, was sie tun und wie sie es tun, betrachtet. Diese Dissertation diskutiert die Relevanz der Artikulation von Architektur in ähnlicher Weise wie der von Online-Informationen und zeigt die Möglichkeit der Zusammenstellung von Anwendungen welche mit Web-Communities kommunizieren. Diese Dissertation ist in drei Kapitel unterteilt. Zuerst werden drei Gespräche mit einer Reihe von zeitgenössischen Architekten präsentiert, die einerseits die Vorstellung, dass globale Bedingungen die Tradition der Architektur beeinflussen, bekräftigen und sich mit dieser Idee auseinandersetzen, sowie das Zusammenspiel von Architektur und Computern verfolgen. Durch das Platzieren dieser Positionen neben verschiedenen Phänomenen, die von Jedermann mit einem onlinefähigen Computer beobachtbar sind, tauchen Gespräche über das globale Netzwerk von Computern auf, welche die Kapazitäten und Grenzen dieser Positionen, die Architektur in Bezug auf die unendliche Zirkulation von Online Informationen zu artikulieren, sichtbar macht. Die Arbeit geht weiteres auf drei prominente Anwendungen des globalen Netzwerks ein - Web- Suchmaschinen, Content-Sharing-Plattformen und Online-Übersetzungen - welche im letzten Jahrzehnt gezeigt haben, wie man neue Stabilitäten - Meter und Werte - in einer indexikalischen Charakterisierung und Bedienung von Online- Informationen verankert. Um ein abstraktes Verständnis dieser Anwendungen zu konstruieren, vereint diese Dissertation universelle Gespräche mit Stimmen von herausragenden Positionen in der Philosophie und in der Mathematik. Diese universellen Gespräche bilden die Grundlagen, um die Architektur in einer ähnlicher Weise wie die Informationen, die in den globalen Netzwerken zirkulieren, zu artikulieren - frei von Spezifität und in der Lage, vor-spezifische Gespräche zu führen. Abschliessend werden drei Applikationen, mit denen man mit verschiedenen Web-Communities kommunizieren kann wie z. B. Tumblr, Wikimedia Commons, Schweizer Architekten - präsentiert. Mit diesen Anwendungen positioniert sich der Architekt mitten in der unendlichen Zirkulation von Informationen und adressiert die Gemeinschaft auf eine persönliche und lebendige Art und Weise. Diese Anwendungen zeigen, dass, um architektonische Fragen an Web-Communities zu stellen - oder um über das globale Netzwerk zu sprechen, die Architektur selbst frei von Spezifität gedacht und artikuliert werden muss. 6

8 Diese Dissertation zielt darauf ab, ein umfassendes Verständnis der Fülle von Online- Informationen darzustellen, da dies ein lebendiges und umfangreiches Architekturverständnis verspricht. 7

9 ACKNOWLEDGMENTS I would like to express my sincere gratitude to Prof. Dr. Ludger Hovestadt for his trust in my intuition and for his uninterrupted support over the course of the past several years; to Prof. Dr. Vera Bühlmann for sharing with me her richness in thought and for her patience as I tried to grasp it. Over the past seven years, their thinking has influenced me in ways that I never imagined. I would also like to thank my co-supervisor Ass. Prof. Philippe Morel for his provocative questions that, early on in my studies, cast new shadows when things looked disturbingly clear. I am proud to have been a member of the Chair for CAAD, and would like to thank the whole group for their sense of community in particular to those with whom I started this journey and took our discussions beyond the ETH, to other nations, continents and fantastic places. I am especially grateful to Katia for being Ariadne, Theseus and the Minotaur. 8

10 CONTENTS ABSTRACT 5 ZUSAMMENFASSUNG 6 ACKNOWLEDGMENTS 8 INTRODUCTION 13 THE GLOBAL NETWORK 13 INFORMATION AD INFINITUM 14 DIGITAL LITERACY 14 ALL THE ANSWERS 15 INDEXICALITY 15 INTERPLAYS 16 STABILITIES 16 THE DOUBLE-SLIT EXPERIMENT 17 TO TALK 18 MANNERS OF TALK 18 THIS WORK SPECIFIC TALKS BETWEEN ARCHITECTS ABOUT THE WEB INTRODUCTION THE GLOBAL NETWORK Index Architecture Being Digital The Second Digital Turn in Architecture The Architect Is Dead The Digital World Remarks Typical Plan Globalization Elements of Architecture The Generic City Junkspace Remarks THE ABUNDANCE OF INFORMATION ON THE GLOBAL NETWORK The Dialectic of the Pragmatic and the Aesthetic Arguing for Elegance The Autopoiesis of Architecture Parametricist Manifesto Parametric Diagrams Remarks Toward an Understanding of Form in Architecture Architecture as a Second Language Diagram: An Original Scene of Writing Remarks The Alphabet and the Algorithm 90 9

11 Remarks THE WAYS TO OPERATE THE INFORMATION S INFINITE CIRCULATION The Architecture Machine Soft Architecture Machines Remarks Notes on the Synthesis of Form The Determination of Components of an Indian Village A City Is Not a Tree Linguistic Talks Remarks Architectural Curvilinearity Blobs Animate Form Remarks Earth Moves Towards a Non-Standard Mode of Production Remarks REMARKS PRE-SPECIFIC TALKS BETWEEN ARCHITECTS AND WEB 157 COMMUNITIES 2.1 INTRODUCTION STOPWATCH Movement I Movement II Movement III Movement IV Remarks MIND PALACE Movement I Movement II Movement III Remarks PENTECOST Movement I Movement II Movement III Movement IV Remarks REMARKS UNIVERSAL TALKS ABOUT PROMINENT WEB APPLICATIONS INTRODUCTION WEB SEARCH ENGINES Weaving the Web The Anatomy of a Large-Scale Hypertextual Web Search Engine Markov Chains The Strange Theory of Light and Matter

12 3.2.5 Of Reasoning in General CONTENT SHARING PLATFORMS Cinematic Time and the Question of Malaise Theory of the Quasi-Object Information and Thinking A Mathematical Theory of Communication Pentecost Remarks Self-Organized Formation of Topologically Correct Featured Maps ONLINE TRANSLATIONS Course in General Linguistics Syntactic Structures Aspects of the Theory of Syntax Continuity and Irrational Numbers Statistical Machine Translation REMARKS 285 OVERALL REMARKS AND DISCUSSION 287 THIS WORK 287 PRE-SPECIFIC ARCHITECTURE IN THE CONTINUUM 287 FUTURE APPLICATIONS 288 REFERENCES 289 APPENDIX 293 CURRICULUM VITAE

13

14 INTRODUCTION THE GLOBAL NETWORK When we refer to the concept of computing today, we do not refer to a single computer anymore, but to a network of computers talking to each other without interruption. Even when the origins of computer networks 1 can be indexed not very far from the origins of computers, 2 it was the burst of the dot-com bubble in 2000 that changed the understanding of computers from symbolic machines to an infrastructure for applications: the global network. 3 The global network is decoupled from the ground as it introduces ways to think, articulate, and construct objects of the world decoupled from limited resources 4 ; therefore, it engenders new stabilities meters and values categorically different from those coupled to the ground. This setup opens up new scenarios for architecture 5 from which the turn from limited resources to an abundance of information is at the foundation of this work. 1 See the Wikipedia entry of the Semi-Automatic Ground Environment (SAGE) from 1958, and the Advanced Research Projects Agency Network (ARPANET) from See Norbert Wiener s Cybernetics: Or Control and Communication in the Animal and the Machine (1948) and Claude Shannon s A Mathematical Theory of Communication (1948). 3 For an extended characterization of the global network see Cultivating the Generic (Hovestadt 2013). 4 A characterization of the global network is: a system of interconnected computers circulating electrical impulses. With the invention of photovoltaics, electricity comes from outside the world, from the sun. For an extended argument see A Genius Planet (Hovestadt, Buehlmann, Michael 2017). 5 For these scenarios see Beyond the Grid (Hovestadt 2010). 13

15 INFORMATION AD INFINITUM The global network accommodates any application with very few requirements. Due to its availability, open-collaboration drive, and capacity to accommodate multimedia content, the World Wide Web is today the most known and used set of protocols of communication online. The web accommodates hundreds of billions of documents 6, and further presents a novel way to talk and share online. It engenders communities that circulate information ad infinitum, making it ubiquitous and alive. Through the web and its communities, we visit the buildings in our neighborhood, 7 review the latest commissions all around the world, and are up to date with the development of many projects. Traditional magazines become computational, and we read all of their corpus on the web images, projects, theories, critiques, and manifestoes, all online. Furthermore, with projects like Google Books, we access an index of thousands of architectural books, and with one click, we download them to our device or buy them from Amazon. DIGITAL LITERACY The circulation on the web is not only changing the scope of what we can learn but also how we learn it. We see how Massive Open Online Courses 8 (MOOC) are re-articulating models of education. They are being taught by prominent European and US institutions in many disciplines and to students all around the world; the fundamental requirement is to have access to a computer online. These courses further challenge the values placed on educational institutions, celebrating that to study an object and to acquire mastership 9 is decoupled from the how. 10 Architects also learn on the web the basics of the generic software used in an average architectural studio Vectorworks, Revit, grasshopper, 11 Vray, and Photoshop. 12 For physical models, 3D printing technology is offered at low cost, on a desk size device, and most of the time ready to plug and play. 13 Specifically for us, architects with an interest in the global network and its applications, the web itself presents a way to learn how web documents and web applications are put together. It presents tutored views of the instrumentality. We find detailed instructions for installation and examples, and when there is a question, communities like Stack Overflow or Github are there to collaborate with. Thanks to an open-source drive, the programming languages, integrated 6 From How Search Works by Google at (accessed ). 7 See (accessed ). 8 Coursera is one of the most prominent MOOC communities. It offers over 2,000 courses from over 100 educational institutions, including EPFL and the University of Zurich. For a full lists see (accessed ). 9 For an articulation of mastership see What Are Masterpieces and Why Are There so Few of Them? (Stein 1936). 10 A contemporary example is Vitalik Buterin. Vitalik is a computer programmer who dropped out the University of Waterloo to co-found Ethereum, the second most valued cryptocurrency today. See (accessed ). 11 See Grasshopper tutorials online at (accessed ). 12 See Lynda online at (accessed ) for Vectorworks and Revit. See YouTube for Vray and Photoshop tutorials. 13 For a 3D printing service in your neighborhood and 3D printer reviews see (accessed ). 14

16 development environments, and libraries are there for us to learn. 14 ALL THE ANSWERS The applications running on the global network are prominent due to the influence they have in society today 15 and the economic value that we put on them. 16 These applications see the information they circulate as a new primal source from which new values need to be constructed with new instrumentality. 17 In order to construct an image of this phenomenon, we think of a web application that gathers people with a shared interest e.g., Ricardo, Airbnb, Flickr, Fiverr. The primal source is any answer that a community member may give, and the application itself is a kind of interrogator. A good application asks the community relevant questions, where are you going to?, what are you interested in?, how did you like your meal?, and the members answer any answer is a good answer, as it is primal source. In turn, the application, from its vast primal source and novel instrumentality, gives back to the member relevant information. The more interesting the questions are, the more answers they get; the more answers they get and the more sophisticated their instruments are the more interesting questions they ask. This phenomenon seems to create a scenario where the main challenge is to ask relevant questions because any answer is already in the primal source, and the principle instrumentality to operate it is available on the web. Interestingly enough, this circular understanding of an online application is explicitly rendered on the web. Udacity, a MOOC community, offers courses to teach the instrumentality to operate primal sources with the promise of developing prominent online applications and becoming a prominent interrogator. INDEXICALITY What happens when making a web search is the same everywhere? When a user has a question, and assumes that an answer is somewhere in a web document, a query is presented to a web search engine. The search engine presents back, in a fraction of a second, a short list of web documents in which most probably an answer will be found. The user clicks, ending the event, or comes back to the list to click again. A look with care at this phenomenon shows that it is a re-articulation of search as an action, as it would be impossible to select a few documents out of billions, so fast and with such 14 For an extended argument on Digital Literacy see Coding as Literacy Metalithikum IV (Buehlmann, Hovestadt, Moosavi 2015). 15 Facebook has 2 billion monthly active users [en.wikipedia.org/wiki/facebook (accessed 23.8)] and the analysis of Facebook data has been significantly used in political agendas, as seen in Ich habe nur gezeigt, dass es die Bombe gibt. Der Psychologe Michal Kosinski hat eine Methode entwickelt, um Menschen anhand ihres Verhaltens auf Facebook minutiös zu analysieren. Und verhalf so Donald Trump mit zum Sieg at (accessed ). 16 For example, Instagram was bought by Facebook in 2012 for approximately 1B USD [ (accessed )] when the company was 13 computer scientists. See Who Owns the Future? (Lanier 2014). 17 Instrumentality as in programming paradigms. The state of the art are those around Machine Learning. 15

17 confidence, if they were paper documents, for example. There is at its foundations a new way of thinking of and operating documents. A search engine characterizes a web document by its neighborhood, by the documents that point to it the document is what its pointers say it is. And it is operated in the same way: The document is measured, selected, and arranged by its pointers, by its neighborhood the web is indexically characterized and operated as a vivid corpus, as documents appear and disappear without interruption. For a search engine, a document is never fully defined, never fixed; it is thought of and treated as alive. It is the user who fixes, who defines answers, not the application. We will see in chapter 3 that an indexical characterization and operation is an invariant property of the online applications across the global network. INTERPLAYS The first interplays between architecture and computers in the 1970s were brought to such scale and credibility that today architectural applications and research around the world can be indexed by them 18 : robotic arms, virtual reality, internet of things. The modeling tools indexed by these interplays challenge long term architectural notions, e.g., style and aesthetics (chapter ); complexity and continuity (chapter 1.4); authorship and originality (chapter ); scale and resolution 19. When we agree that the applications on the global network have the capacity to address architectural questions that architecture can be thought of and treated as information on the web we see categorical differences between the applications indexed by the well established interplays and the applications on the global network. For example, in the way architecture is articulated specific (chapter 1) vs pre-specific (chapter 2); operated logical (chapter ) vs indexical (chapter 2 and 3); and measured linguistic (1.4.7) vs probabilistic (chapter 2 and 3). Even when addressing all these categorical questions at once can be seen as an act of discontinuity or disruption for the tradition (chapter 1.3.8), we nevertheless see an interest in our contemporaries on them (chapter ), arguments for their exploration, 20 academic research, 21 and applications at the urban scale. 22 STABILITIES The influence of global conditions to the tradition of architecture is identified by our contemporary architects (chapter 1.2). Rem Koolhaas, for example, recognizes a global 18 See figure See Digital Grotesque by Michael Hansmeyer and Benjamin Dillenburger, 2013 at (accessed ). 20 As seen in Computation or Revolution where Philippe Morel (2014) explores the instrumentality of the global network in the context of robotic fabrication. 21 See Pre-Specific Modeling Computational machines in coexistence with urban data streams (Moosavi 2015) and Towards Communication in CAAD Spectral Characterisation and Modelling with Conjugate Symbolic Domains (Marincic 2017). 22 For many examples, see (accessed ). 16

18 condition and its influence in cities and buildings. In a retrospective gesture, he calls it the Generic City (chapter ), and its products, Junkspace (chapter ). Other contemporaries further argue that other global conditions had a significant influence on the tradition of architecture. 23 During the Renaissance, for example, Alberti re-articulated the notion of the architect and architecture (chapter ). Alberti placed great emphasis on authorship (the architect); the medium (the drawings); and the instrumentality (grids and scales). In this line of argumentation and looking at the established influence that Vitruvius De Architectura had on Alberti s De Re Aedificatoria 24 we hypothetically place another global condition: the Roman Empire. Vitruvius 25 wrote De Architectura as a treatise on architecture, as the unique book for the planning and building of cities and artifacts all over the (Roman) world. An invariant to these global conditions is that they happened when influences and the reach of actions extended over the world and new stabilities needed to be introduced. In the Roman Empire, the tradition of building was re-articulated from speech to text, instructions to build Rome were written in a book, and Rome was built all over the world. During the Renaissance, medieval drawings on a printing press (figure 1.35) would not liberate the architect from presence, and Vitruvius constructed drawings and instruments with which to claim authorship, even when he was off-site. Since globalization a physical infrastructure and its logistics covering the whole world took place, any architect is available, any material is one flight away, and any decision is one phone call away. If Koolhaas identified what happens to architecture when a physical infrastructure is at its peak, we want to discuss what would happen when the digital infrastructure the global network reaches its peak. THE DOUBLE-SLIT EXPERIMENT The double-slit experiment tells us that the mere act of observing changes the behavior of our reality. On a quantum level, when electrons are projected onto a screen over an intermediate object with two slits, the screen on the back shows the electrons interference pattern, a wavelike behavior. 26 But, in the same setup, when we measure the path of the electron; that is, when we observe which slit it went through, the electron changes to a particle-like behavior, projecting on the back screen the negative of the intermediate object like a stenciled drawing and not an interference pattern. Physicists conclude today that observing a bit of matter changes the way it behaves. What this experiment tells us about the nature of reality and the relationship of a researcher to that being researched is that when a bit of matter behaves like a wave of potentials, and any path is possible before observation in the case of the experiment, an electron can go through both slits or through none, through only the first, or through the second we are presented with 23 See Architecture in the age of printing: orality, writing, typography, and printed images in the history of architectural theory (Carpo 2001). 24 The second sentence in the De Re Aedificatoria s entry in Wikipedia mentions it. See (accessed ). 25 See Ten Books On Architecture (Vitruvius 1914). 17

19 a scenario where reality cannot be fully held. Where either we celebrate and navigate the probabilities of an event to occur, or we cancel its possibilities and celebrate the paradoxes that a measured event entails. Physics today is about the first scenario, and the work of Richard Feynman 27 is a prominent example. He shows a way to precisely measure the probability of a quantum event to occur (chapter 3.2.4), and like him, most of the positions and applications presented in chapter 3 are within the same paradigm. Similarly, this work characterizes the abundance of information on the web as an object of study full of potentials in architecture, and further deals with the probability of events to occur before engaging with it in a paradoxical reality. TO TALK Given our paradigm, a systematic enquiry that we see appropriate for this research is indexed by the act of talking. To talk about an object is an indexical act, as it points out the object without aiming for its definition. It celebrates that an object is never complete in its characterization, that it is kept as a wave of potentials. It invites us to open things up without necessarily closing them up, to pursue certain arguments and leave others on hold, to stress positions, pause, and go back to previous thoughts. To talk is a personal and vivid act. A successful talk does not require an in-depth understanding of what is discussed, nor does it necessarily follow established strategies for successful research e.g., focusing on the social and cultural circumstances that are contemporaneous to an object-study, so as to present an exhaustive description and analysis that can cast new light on the object of study. 28 In a successful talk, knowledge is constructed by the circulation of the object of discussion, by engaging with it repetitively and from different positions. Despite the informality that talking implies in the broader context of this work, this self-confident characterization of talk toward the construction of knowledge, does not exclude the seriousness and rigorousness required to address our object of study. MANNERS OF TALK This work presents three different manners of talking: specific, pre-specific, 29 and universal. The specific talks are those we have with our contemporary architects. These do not try to answer specific questions, nor do they conclude with definitions. They present arguments around the object of discussion, and stress their positions and views, aiming at a consistent understanding of the object. To this goal, this chapter gives an extensive voice (quotations) to the contemporaries. 26 As shown by Thomas Young in See QED: The Strange Theory of Light and Matter (Feynman 1985). 28 For this and other strategies in architectural research see Architectural Research Methods (Groat & Wang 2013). 29 The concept Pre-specific was introduced by Bühlmann and Wiedmer (2008) in the context of information-based designs in Pre-Specifics. Some comparatistic investigations on research in art and design. 18

20 The pre-specific talks are those that we have with a web community through custom-made applications. They deal with the abundance of information decoupled from logics and rationality but nevertheless in a personal and lively manner. They are held in probabilities. When placed in relation to the other two talks, we can in short say that a pre-specific talk is one decision away from becoming a specific talk. The universal talks are those decoupled from a specific context, but nevertheless always linked to the prominent online applications in retrospective, and to architecture in prospective. They aim to be a third, a common ground where abstract understandings of the applications as well as more capacious articulations of architecture, indexed by these understandings, can be constructed. THIS WORK This basic research presents a consistent understanding of our object of study. It provides the means of answering important architectural questions (practical and theoretical) that arise in our contemporary global condition, though without giving a complete specific answer to them. 30 It consists of three chapters. The first chapter presents three specific talks with a number of contemporary architects about (1) the global network; (2) the abundance of information on the global network; and (3) the ways to operate this abundance. We will see how their prominent positions hold on when placed next to the phenomena that any architect can observe by having a computer online i.e., doing a web search, searching for the fastest route between two places, or streaming a song or TV show. The second chapter presents three pre-specific talks with different web communities e.g., Tumblr, Wikimedia Commons, swiss-architects. It discusses the capacities and promises of thinking and articulating architecture in terms similar to these communities articulation of information, i.e., free from specifications (chapter 3.2.1). It further shows the feasibility of putting together applications by a non-expert in programming. This chapter focuses on the 'what' can be done, rather than the 'how' it is done. It is written in a non-conventional way for a PhD dissertation, with the purpose of placing great emphasis on the promises of thinking and articulating architecture free from specifications. The third and final chapter presents three universal talks about three prominent online applications: web search engines, content sharing platforms, and online translations. They are universal as they abstract from an architectural context and point toward philosophy and mathematics, seeking an abstract understanding of the applications, so as to construct an understanding from the position of an architect. At last, overall remarks and discussions are presented. 30 See a characterization and the importance of basic research in Science the Endless Frontier by Vannevar Bush (1945). 19

21

22 Chapter 1. SPECIFIC TALKS BETWEEN ARCHITECTS ABOUT THE WEB

23

24 1.1 INTRODUCTION The abundance of online information presents a new and capacious setup that is already rearticulating the objects of the world. 1 The influence of this setup in architecture is not explicit yet; it is not fully present and cannot be addressed in retrospective. Furthermore, to talk with a prominent architect about it from a position that can be seen as a challenge to the foundations of his prominency can estrange us from the community. We nevertheless do it. In the following talks with our contemporaries, we don't necessarily agree with them on the articulations and values that they present. We recognize, though, the influence of their positions and want to make this a work of continuity and not of disruption. The positions presented here are prominent due to their influence in academia and praxis. They show an all-round characterization of the contemporary architect they teach, they write, they build, they are mediatic and go beyond architecture. We recognize that many were left behind, 2 but as this work celebrates, they are all online and ready to talk. The architects presented here can be categorized into two groups. Those who recognize and articulate that global conditions affect the tradition of architecture, or address questions that we see directly linked to the global condition. And those who celebrate interplays between architecture and computers, either by articulating architecture or by constructing artifacts. Each talk is seen as a neighborhood with different voices, including ours, which will discuss phenomena observable by anyone with access to a web browser, and will further place emphasis on the ways that the objects in architecture and on the web are articulated, operated, and measured. 1 See for example how the news gets to us or how we travel and do tourism. Both using mobile apps to address different communities and get services. 2 For example, the prominent work of the Pritzker Architecture Prize 2004, Zaha Hadid, as an architect and artist, both in academia at the University of Applied Arts in Vienna and praxis at the London-based studio named after her building projects all around the world. 23

25

26 1.2 THE GLOBAL NETWORK This talk is about the recognition of the global network and the phenomena that it engenders. It gives voice to a number of contemporary architects who recognize it and articulate their potentials and implications to architecture. Different voices are heard, and their engagement or awareness varies. While all are architects, not all care equally about architecture and computers. We start by talking about our work and its relation to Bernard Tschumi s or better, the absence of it. We consider this relevant since the titles may be read similarly, but we have no intention to be connected to it in any significant way. 25

27 [1/10] Index Architecture education, praxis, multi-culture, ideas, cross-fertilization Figure 1.1: Explanatory chart of the book Index Architecture by Bernard Tschumi (2003). Bernard Tschumi, as Dean of the Graduate School of Architecture at Columbia University in New York City, has published Index Architecture, A Columbia Book of Architecture. It is a contribution that aims to present the ideas that occurred, within a ten year span, between practice and education. He calls it an index because it is not presented as a summary per se, but rather as a pointer to a cross-fertilization of ideas. Through our work, intuitive similarities to Tschumi s work will vanish. We start by saying that our work is about today s global condition in relation to an architecture that is not fully here yet, hence is out of practice, and finds the concept of indexicality promising, philosophically and operationally, to address the present and future architecture. Tschumi recognizes a global condition in architecture that other contemporaries would call globalization or the generic. At the end of the 20th century, the international architectural scene began to undergo an important change. A new culture, reflecting the contemporary age and its networks of information and mass media images, emerged in opposition to the contextualist and historicist morphologies prevalent during the 1980s. (Tschumi 2003:6a) This condition s influence on architecture, and specifically on architectural education, is very present; the question for Tschumi is if education can push back or have a voice on its own that can influence practice. Could a school, by definition an institution in which knowledge is transmitted, become a place for generating new forms of architectural thought? Instead of being influenced by 26

28 the world of practice, in the way that architectural academies traditionally have followed the teachings of masters from the Beaux Arts to Le Corbusier and others, could a school directly address the culture of its time and influence practice itself? (Ibid.:6a) And if so, what does it look like? He asks. How could the School generate an architecture culture that would not be reductive, representing the stylistic or intellectual approach of a single interest group or perspective, but instead reflect and thrive on differences of opinion and conflicting points of view? (Ibid.) For over ten years, Tschumi s strategy was to give voice and authority to young practitioners mostly in New York and educators; for example, Stan Allen, Karen Bausman, Jeffrey Kipnis, Greg Lynn, Reiser + Umemoto. We invited young architects whose relatively limited practical experience was counterbalanced by boundless talent and energy. We asked them to teach what they knew or wanted to know about. Each studio critic was given sufficient authority and means to pursue his or her ambitions so that a multi-culture of competing ideas, discussions, and polemics would result. (Ibid.) The index emerges as a strategy to talk about the results of the studios as well as their leaders. It is further complemented by interviews and other documents. Instead of attempting to translate the School's contribution to this developing culture into a chronology or a treatise on education, we decided to document these conversations, topics, and polemics in the form of an index. Like an index, this book does not summarize or inclusively represent, but rather points to or indicates a cross-fertilization of ideas between theory and practice and between education and the world of making. (Ibid.:7a) What remained in the book were the studios central ideas, definitions, condensations and short answers. We began by reading the studio briefs from the early 1990s onward. Subsequently, the studio briefs were examined and edited down to their central ideas. The result was a document encapsulating each critic s teaching and practice. (Ibid.) Our interest in the index and indexicality is categorically different; it is philosophical and operational. We are interested in addressing questions like, where is the meaning of an object when it is indexed? Or, what kind of abilities do we gain when we operate just the indexes instead of the object itself? These questions will be addressed operationally in chapter two and philosophically in chapter three. What follows are the voices of four contemporaries explicitly talking about the global network or about the phenomena that it engenders. We start with Nicolas Negroponte, a pioneer in interplays between architecture and information technology. 27

29 [2/10] Being Digital bits, atoms, information, accessibility, computers, communities Figure 1.2: Wired Magazine cover, November In the National Bestseller book Being Digital, Nicolas Negroponte presents a series of stories around Move Bits, Not Atoms, which was the name of his monthly column at Wired Magazine from 1993 to The book presents an optimist view on societies becoming digital. It is full of personal stories and analogies that forecast the implications of a switch from analog to digital. To move bits, not atoms refers to the way traditional objects are treated when they become computational; for example, the switch from vinyl records to mp3 files, or from paper books to pdf format. These re-articulations are Negroponte s main focus, to predict what happens when societies are, or become, digital. World trade has traditionally consisted of exchanging atoms. In the case of Evian water, we were shipping a large, heavy, and inert mass, slowly, painfully, and expensively, across thousands of miles, over a period of many days. When you go through customs you declare your atoms, not your bits. (Negroponte 1995:4) What we see is that the re-articulation of traditional objects within the global network gives them the instant ability to be globally available. The methodical movement of recorded music as pieces of plastic, like the slow human handling of most information in the form of books, magazines, newspapers, and videocassettes, is about to become the instantaneous and inexpensive transfer of electronic data that move at the speed of light. In this form, the information can become universally accessible. (Ibid.) Computers are here to stay; the change from bits to atoms is irrevocable and unstoppable. They will take up part of our daily lives, intimately. This phenomenon is bringing computers so close to societies to the point that they have become a fundamental part of them. Computing is not about computers any more. It is about living. The giant central 28

30 computer, the so-called mainframe, has been almost universally replaced by personal computers. (Ibid.:6) He presents a lot of predictions that today are realities, e.g., the emergence of social networks, the popularization of a digital nomadic lifestyle, and the security issues that living a life codependent on computers may imply. As we interconnect ourselves, many of the values of a nationstate will give way to those of both larger and smaller electronic communities. We will socialize in digital neighborhoods in which physical space will be irrelevant and time will play a different role. (Ibid.:7) The next decade will see cases of intellectual property abuse and invasion of our privacy. We will experience digital vandalism, software piracy, and data thievery. Worst of all, we will witness the loss of many jobs to wholly automated systems, which will soon change the white-collar workplace to the same degree that it has already transformed the factory floor. The notion of lifetime employment at one job as already started to disappear. (Ibid.:227) These predictions are founded on what he likes doing most: telling stories that place computing in a central and active role in societies. And that is what they are: stories drawn from years of inventing new systems for computer graphics, human communications, and interactive multimedia. (Ibid.:7) When talking about the future, Negroponte is optimistic, as we are, but for reasons irrelevant to this work. The control bits of that digital future are more than ever before in the hands of the young. Nothing could make me happier. (Ibid.:231) In a very similar line of argumentation, Negroponte gives in 2014 a TED talk entitled, A 30-year History of the Future 1, where he celebrates some of his predictions that have turned into reality today. Similar to this book, we missed the significant insights or indexes of his stories, something comparable within our framework. The foundations of his work seem to be somewhere else. 1 See (accessed ). 29

31 [3/10] The Second Digital Turn in Architecture computer, science, big data, classification, sorting, searching, spline, voxel Figure 1.3: Vienna OMV Corporation. Greg Lynn FORM Mario Carpo binds together a number of interplays of architecture and IT in the book, The Digital Turn in Architecture (Carpo 2013). As its name suggests, this talk is about the sequel. In a 2015 lecture at The University of New South Wales, Sydney, entitled The Second Digital Turn in Architecture: Computation, Simulation, Optimization, and the Style of Big Data, Carpo presents his account of the abundance of digitized information available to us all any time and anywhere, on the ways it is operated, and its implications for architecture. He affirms that the concept of computing today gives up to logics and cause and effect relations. Today, on the contrary, in my opinion, something else is happening. More and more we do not use computers to imitate old stuff, or to replicate all science. We re starting to use computers in a new way. In a sense, we re learning to let computers work in their own way, even when we cannot understand what they do. This is not a post-human science fiction. Not at all; this new kind of science is already all around us. It is already part of our daily life, and you know how it all started? It started with Gmail. (Carpo 2015) Google s mail application, Gmail, showed him first what this new computing is about. Specifically, when he recognized that sorting s is no longer crucial to finding them. The exact opposite condition is true when searching for snail mail, for example. This new sorting or better, the lack of sorting is the ability he considers a game-changer. There is another much more practical reason why we sort, or classify things, in daily life as opposed to philosophy: We put things in specific places following some order so we know where to look for our stuff when we need it. Now Google is training us to leave documents unsorted because digital search is now so fast that there is no need to manually pre-sort documents. Using Gmail we are all learning this new digital art most outstanding, most miraculous, most supernatural of all digital arts the art of finding stuff without knowing where it is. (Ibid.) For Carpo, the main difference between humans and computers, is the ability to keep things 30

32 aligned in memory. He argues that there is just so much memory that humans can operate. And again, that the exact opposite is true for computers; hence, computers don t need to sort, because they can allocate big data in their memory. Why do we need sorting and Google doesn t? Because there is only so much information our mind can process at any given time, so when data get too big, we must make them smaller. So we have to drop some or we find a way to compress data. (Ibid.) Big data is all around us, and computers do not need to compress data in order to operate it, Carpo argues. Today data is so plentiful and cheap that there is no need to spend additional time and labor to sort of compress. Today, computers can keep data just as they can all of them or almost all of them almost forever and almost for free. If data costs nothing, or almost nothing, then all data compression technology we use are useless If you think of it, almost all technologies we use are still based to some extent on the old technical need to compress data to make them smaller. (Ibid.) Interesting enough for us, a good number of file types online are all about compression: audio, images, videos, text. We furthermore see that a decentralized internet, i.e., online services based on mobile devices instead of server farms, will be possible only when data compression reaches a bench. 2 Despite these different understandings, we recognize like Carpo that modern science is being challenged by the abundance of information, but for different reasons that we will discuss in chapter three. But the same also applies to most of modern science. Modern science, all of it, based as it was on formalization, on mathematical abstraction, always hardwired for small data, and with today s big data, as someone has already noticed, we can do away with most of it. Today in many cases, Google can already replace science. (Ibid.) He gives a couple of examples that in his understanding show the impacts of this phenomenon. First are the digital-design tools to model splines, curved surfaces, and blobs. Calculus is also the ultimate small data technology because it compresses an infinite number of points, all the points that belong to this curve or surface, into a single short notation. Let s assume that we can have access to unlimited zero cost data storage and data processing. In that case, we could easily eliminate any synthetic mathematical notation of that figure and simply record instead a very long log, the list of the position in space of many points of that line, as many as necessary. (Ibid.) Big data seems to be for him a cause of voxelization in computer-aided design. For Carpo, small data is to splines what big data is to voxels. 2 See Pied Piper s New Internet Isn t Just Possible It s Almost Here at (accessed ). 31

33 This is one reason why some of today s digital designers already discarded the small data calculus based spline that was so important for the digital style of the 90s and have started to use big data and computation to engage somehow with the messy discreetness of nature as is, its pristine raw state, without the mediation of elegant streamlined mathematical notations. The messy point clouds and volumetric units of design and calculation that result from these processes are today increasingly shown, their apparently disjointed and fragmentary stage, and the style resulting from this mode of composition is often called voxelization. (Ibid.) Figure 1.4: ICD/ITKE Research Pavilion 2010, Stuttgart University. 3 His second example is on digitally designed architectural artifacts that do not follow traditional design methods to measure their forces, as these methods simply don t apply. See figure 1.4. It was calculated in a new way, using in a sense a new scientific approach. In this case, the designers built first a digital model of the structure they had in mind, and they tested it on the screen, in simulation using finite element analysis until it broke. Then they tricked the model a little, randomly, and they tested it again, until it broke again, and again [ ]. In the end the designer found one model on the screen that didn t break, the one they chose and built. (Ibid.) Carpo argues that digital simulation combined with a trial and error method that iterates processes ad infinitum is an example of big data in architecture. Using digital simulation, we can search and find form more effectively today than any artisan ever could. In traditional scientific terms, this mode of design is perfectly stupid because we didn t use any science to design. Think of what we did not do. The traditional formulas of structural engineering establish causal relationships between loads, forms, and stresses. By the causality they express, these formulas provide some understanding 3 Figure: Institute for Computational Design (ICD) and the Institute of Building Structures and Structural Design (ITKE). 32

34 of the physical phenomena they describe, and they have a meaning which we think is true to nature. This meaningfulness is visible in all the masterpieces of modern structural engineering. But we did not use any of that to build this structure, for example, so when we look at it, we do not have the faintest idea of how and why it stands up. Nobody knows, least of all its designers, and yet it stands up. Using digital simulations, we know in advance it will, which is why we can build it. (Ibid.) There is a new kind of science driven by big data that is not based on arguments that are logically valid nor in cause and effect relations, Carpo argues. We agree and see in Google Maps a big-data-driven application. From A to B, a user is always faster than the optimum, and he does not know why. This is what I mean by a new kind of science. Computers can already predict things that modern science cannot explain and our mind cannot understand. In some cases, computers can already tell us what is going to happen but they won t tell us why, because computers don t do that. Prediction without causation, that is not magic; it is the way computers work. And the way we must let them work if we want to take advantage of their power. (Ibid.) He finalizes the lecture by pointing out a direction with which we sympathize but which is out of the scope of this work: What would an architectural artifact that reflects an understating of this phenomenon look like? This is the technical logic of today s digital tools, and if we use these tools we end up working this way. That is probably inevitable, but that s only the easy part. Then the difficult part comes. If on top of that, as designers we also manage to invent and create new shapes and forms that express, interpret, critique, or exult the logic of the tools that we are using and the spirit of the game we re playing, which is in fact the new technical logic of our time, then as designers we shall have done our job. (Ibid.) Despite the fundamental indexes missing in his lecture like the implications of the distributed and arbitrary source of the data, the mathematical or philosophical concepts at the foundations of the applications that learn from this data, or the new values created by these applications and the misleading technological characterizations in Carpo s lecture, we agree with a rearticulation of the concept of computing that gives up to logics and cause and effect relations, and with the importance to the tradition of architecture to engage with these questions. 33

35 [4/10] The Architect Is Dead artificial intelligence, competency, society, complexity, intelligence, judgment Figure 1.5: Pix2Pix autofill image with AI. 4 In a discussion table at the AA, students discussed the advent of artificial intelligence and the role of computers in everyday life, and asked Patrik Schumacher if we are witnessing the end of architecture s transcendence in man, and if so, who should hold primacy on the concern of building: man, machine, or both. His position is in general optimistic but not very insightful, and he nevertheless affirms a change in the role of the architect and in the tradition itself. There s an evolving role of the architect, but there s also a very long-term stability of the core competency of the architect, which you could find in Alberti as much as you can find it today, which is the ordering of social processes and creating the specialization for the good society on the level of the city, individual, household (Schumacher 2016) For him, the change is on the level of the competencies that the architect has today, and what these competencies imply to the production of architectural artifacts. He recognizes a similar phenomenon to the one we are experiencing now, when at the time of Alberti, drawings became not thick architecture. Alberti had a lot more other things in there. There was the construction knowledge, engineering, embedded in there, and what we witness in the 19th and particularly 20th centuries seem to look in many ways an erosion of the full scope of competencies that the architect had. A lot of people are puzzling people who can only think in terms of tangible, physical results. What I m emphasizing on that point is that no, what we have to concentrate on is the competency of ordering social processes. We have to focus in on what that means; it means organization elements, but it also means seeing the built environment. We have to look at the communicative capacity, through its phenomenology. (Ibid.) Schumacher projects architecture to society, and measures it by its influence on society and by how architecture responds to the complexity of societal elements. Therefore, AI presents no challenge to architecture today for him, but recognizes fear from society. 4 Figure: Dami Lee 2017 at (accessed ). 34

36 We very much work through appearances. A lot of people are worrying, are we just becoming decorators? That s totally missing the point of the essential social functionality. (Ibid.) For Schumacher, societies are complex, and they get more complex by the day; they lose their grasp on some things, they change, they are re-articulated. The changes can be seen in the societal stratum, he argues. The division of labor is progressing and moving forward in all domains of life, and as our lives become more complex, societies become richer and more intricate, [ ] we need to grasp what really is the role of the architect essentially. (Ibid.) What he proposes is to keep up with the phenomenon without elaborating, an optimistic gesture. There s no need to feel afraid, we should see this as an opportunity, he says. But in the contemporary complexity, we have to all tool-up, to cope with the new complexity of the contemporary world. To do that well, all have to be tooled-up, like the engineers and contractors and everybody. We need to embrace that. That s not a disempowerment which takes over our skills or pushes us aside, but it s empowering us to concentrate again in our key intelligence, guiding a process where a lot of the judgement has been found to the machines, and some of the decision-making also based on premises we set. So we re moving; we re migrating from the moment that we actually sit down and make individual decisions about this column here, that corner there. No, we pull back and have set up systems, in particular evolutionary design systems, genetic algorithms that just got us to that metalevel of key setup, defining criteria of success and letting agents roll out decisions. We re left with we re drowning in, of course, software experts, and we may be just selecting various design systems. We orchestrate them, sequence them, but then we also of course evaluate results and make selections and other things, eminent for authorship. (Ibid.) His time is up. Are we witnessing the end of architecture s transcendence in man with the advent of AI? Scrap that thesis, and embrace the world of Artificial Intelligence. (Ibid.) Schumacher presents an attitude towards our phenomenon at hand; it is optimistic and in general inviting to engage with our questions, to look for new stabilities and get empowered again. It is just an attitude, though, and now his long lasting interest seems to be somewhere else he just edited Parametricism 2.0: Rethinking Architecture s Agenda for the 21st Century (Schumacher 2016b), where he celebrates over 15 years of the avant-garde architecture and design movement that encompasses all design disciplines, from urban design to fashion: Parametricism. 35

37 [5/10] The Digital World countryside, city, infrastructure, Amazon, Tesla, server farms, robot playground Figure 1.6: The 1 million sq. ft. Amazon Fulfillment Center in San Bernardino, California. 5 In the context of the 15th Venice Biennale of Architecture, 2016, Rem Koolhaas discussed at Meetings on Architecture his interest in the digital world and its implications in the non-urban condition that he argues is being changed drastically by Amazon, Tesla, and the server farms. To talk about the digital world, Koolhaas looks at the physical infrastructure of the digital infrastructure. We read this position as an invitation to look down to the ground in order to talk about the new abilities and values that we gain by being decoupled from the ground. I am particularly fascinated by the manifestations of the digital world outside the cities. Maybe not only the digital world but also the world of Amazon, the world of distribution centers, the world of fulfillment centers [ ] and the world of server farms. (Koolhaas 2016) The footprints of such industrial artifacts impress Koolhaas, both by their dimensions and their location. The infrastructure is now so enormous in such an incredible scale that the idea of even putting them in cities is completely impossible. [ ] A battery factory of Tesla which is one mile long and maybe 1.5 miles wide. Completely flat entity. It is simply there; there is no effort to understand it beyond its physical presence there. There s also an Amazon fulfillment center of previously unknown dimensions. (Ibid.) Koolhaas suggests we look at this phenomenon and try to integrate it to the philosophy and praxis of architecture. What I find fascinating is to consider whether architecture should continue to ignore it is happening but has nothing to do with us, or whether we re challenged to find a symbolic purpose, make some kind of effort to make it an accessible part of the world s repertoire, and if so, how we can do it. 5 Figure: Saul Gonzalez 2013 from (accessed ). 36

38 The question is not only whether architecture has evolved to play in a kind of digestion of this world, therefore in the digestion of the digital world and try to find symbols to express it in symbolic terms. (Ibid.) A sharp diagnosis: These new infrastructures are slightly mediocre, suggesting that there is room for exploration and improvement from the perspective of an architect. And many of these new structures are very close to being in those terms sublime even though they are actually just unfortunately slightly mediocre. (Ibid.) He talks about these impressive-in-scale artifacts and puts them next to a city, a ground of comparison and speculation. The other fascinating thing is that these buildings are all absolutely enormous, but they have a very minimal number of inhabitants. They are largely automated, largely robotized so they have a very interesting situation that the territory is as big as a metropolis but the number of inhabitants is perhaps one percent of a metropolis, yet there is outside space, there is space that I hesitate to call public space because there s barely public to inhabit it, maybe some cars in the morning. (Ibid.) Figure 1.7: Facebook s Arctic server farm, Sweden. 6 Koolhaas speculates on what can be learned from this physical infrastructure. At this is early point in the 21st century we begin to really see some contours of how it will eventually develop, how do we design and define a public realm in these situations, and is it for instance, could we gain architecture initiative by simply embracing these abstractions, embracing even their lack of inhabitation and go back to an architecture which is very radical, really stark, which is not beige, an architecture which is not handicap access, an arch that can be really pure, stark inhabited and amazing. (Ibid.) And on the new programs that spaces should accommodate. Sooner or later we will have to establish a relationship with the robotized world. Do robots need free time, for instance, or do robots need to play? Or do we need to imagine a 6 Figure: Facebook 2016 at (accessed ). 37

39 playground were humans and robots interact in free time or in the factory? (Ibid.) His closing remarks: Let s not forget the countryside, where the digital world is happening. 7 This is what I think is one dimension of the countryside which I would say is no longer the countryside but is a form of high organization of the countryside to support realities that we continue to call urban but which are actually transforming the countryside in a way which is more radical than our cities are currently changing. (Ibid.) Remarks We see an interest in our contemporaries to talk about our object at hand, about how it may impact the tradition of architecture. When we listen to them we feel a very distant scenario, from another epoch even, but when we turn our heads and start looking around with care, we see it everywhere around us. Our contemporaries are open, yes, but we do not perceive engagement. We do not want to put them aside, though, for we recognize their work and influence, and we want to talk to them and figure things out. What follows now, and until the end of this chapter, is the voices of these and other contemporary architects who recognize a global condition and affirm that changes in it affect the tradition of architecture. These views do not necessarily include concepts of computing, but we nevertheless see that they articulate relevant questions to today s global condition. We will start with Rem Koolhaas, whose beginnings as an architect are indexed by articulating the world as a fully urbanized totality. 7 A more insightful view of the new values introduced by these farms is presented in Computational Intelligence: The Grid as Post-Human Network (Morel 2006). 38

40 [6/10] Typical Plan repetition, population, indeterminacy, quantity Figure 1.8: 120 West St., Rem Koolhaas 9 sees in Manhattan s skyscrapers an architecture of undetermined repetition. It has at its foundations a celebrated technology, i.e., light bulbs, elevators, escalators, air conditioners. This architecture finds its value and stability not in fixed grounds of content, but in the indeterminacy and multiplicity, i.e., undetermined functionality repeated n times. For him, the typical plan is a phenomenon of modernity in America. Typical Plan is an American invention. It is zero-degree architecture, architecture stripped of all traces of uniqueness and specificity. It belongs to the New World. (Koolhaas 1993:335) It is a new architecture introduced and mastered by skyscraper designers and builders. These buildings are icons of Manhattan s society and technology of the time. From the late 19th century to the early 1970s, there is an American century in which Typical Plan is developed from the primitive loft type (ruthless creation of floor space through the sheer multiplication of a given site) via early masterpieces of smooth space like the RCA Building (1933) its escalators, its elevators, the Zen-like serenity of its office suites to provisional culminations such as the Exxon Building (1971) and the World Trade Center ( ). Together they represent evidence of the discovery and subsequent mastery of a new architecture (often proclaimed but never realized at the scale of Typical Plan). (Ibid.:336) 8 Figure: from (Koolhaas 1993). 9 Rem Koolhaas is an architect, architectural theorist, urbanist, and professor at Harvard University. In his early ages he practiced as a film writer and journalist. He wrote Delirious New York, a career boost, at age of 34. He is the co-founder of OMA (The Office for Metropolitan Architecture) and AMO, the research counterpart. Koolhaas won a Pritzker Price in 2000, and does not seem to be interested in concepts of computing. He recognizes and celebrates oxymorons and paradoxes in architecture. 39

41 Figure 1.9: 1251 Avenue of the Americas, As a modernist building, its value is functional, and it accommodates any activity of a modern society. The ambition of Typical Plan is to create new territories for the smooth unfolding of new processes, in this case, ideal accommodation for business. The architects of Typical Plan understood the secret of business: the office building represents the first totally abstract program it does not demand a particular architecture, its only function is to let its occupants exist. Business can invade any architecture. Out of this indeterminacy Typical Plan generates character. (Ibid.:337) As a typical object, it exists only in populations of the same. The bigger the count, the more stable it gets. Typical Plan implies repetition it is the nth plan: to be typical, there must be many and indeterminacy: to be typical, it must be sufficiently undefined. It presumes the presence of 10 Figure: from (Koolhaas 1993). 40

42 many others, but at the same time suggests that their exact number is of no importance. (Ibid.:342) This architecture celebrates the moment just before functional determinacy; it stays forever undetermined. Architecture is monstrous in the way in which each choice leads to the reduction of possibility. It implies a regime of either/or decisions often claustrophobic, even for the architect. All other architecture preempts the future; Typical Plan by making no choices postpones it, keeps it open forever. (Ibid.:344) A typical plan s absence of content presents no opportunity for intellectual discussion. It is what it is, and its stability and value can be indexed by quantities of the same. Typical Plan is a quantum leap that provokes a conceptual leap: an absence of content in quantities that overwhelm, or simply preempt, intellectual speculation. (Ibid.:345) For Koolhaas, a typical plan is from a certain ideology, and in Europe, it is reduced to a faceless place for slavery. There are no Typical Plans in Europe. the one really new architectural subject this century has introduced has been endlessly denigrated in the name of ideology its occupants slaves, its environment faceless, its accumulations ugly. Europe has suffered from a catastrophic failure to accommodate to think the one typology whose emergence was architecturally and urbanistically irresistible. Typical Plan has been forced underground, condemned to the status of parasite devouring larger and larger sections of historical substance, invading whole centers or exiled to the periphery. (Ibid.:348) A typical plan in Europe does not celebrate its technological foundations. On the contrary, nature is always better: natural light, and low-rise buildings. There is no value in the critical mass, nor in the undetermined repetition. The European office is thin, as thin as its more historic substance. The European needs daylight and air, even though a simple extrapolation of the square meters involved reveals that this need will destroy the very decor that reassures him of his historical status. Where the American office assembles a critical mass, the European office dismantles it, simply because the things that happen in an office are supposed to be bad ; we like our badness in small doses. (Ibid.:349) When looking with care at Manhattan, Koolhaas is able to grasp hundreds of undifferentiated floor-plans and see a typical plan that builds a million people island. Today, in our global condition, we are able to grasp thousands of differentiated floor-plans from many cities. What we see is the invert of what Koolhaas sees: one floor-plan that is indexed by thousands of differentiated floor-plans. This is the kind of setup that we will explore in chapter 3. 41

43 [7/10] Globalization collaboration, hybrid, compound, unforeseeable, contamination, recombination, catastrophe Fig 1.10: The Seagram Building, Manhattan, Koolhaas recognizes in Globalization the new architecture of a global condition. He talks about the phenomenon that his contemporaries would say took place before 12 : projects and buildings decouple from the ground and their reach of action increases; they travel fast. When this phenomena occur, traditions are overseen and chaos is introduced, pushed-in until it becomes a new nature. Architecture behaves like one global totality, information flows in new ways, boundaries are re-articulated, and multilingual talks proliferate. Globalization engenders a new architecture. the UN was a building that an American could never have thought and a European could never have built. It was a collaboration, not only between two architects, but between cultures; a cross-fertilization between Europe and America produced a hybrid that could not have existed without their mating, however unenthusiastic. (Koolhaas 1993b:363) In globalization, time-space is not an obstacle when talking about design and construction. They can be a few meters away or antipodes; it s the same. Some of Paul Rudolph s most impossible megastructural speculations for New York [ ] stand, 25 years after their initial conception, marooned among the palms in Singapore. (Ibid.:364) This new condition challenges local traditions. An alien object lands on a village and chaos is introduced. A megapolis talks to a village, a village to a city, a city to city, and new discussions emerge. 11 Figure: (accessed ). 42

44 There is an Aldo Rossi building in Fukuoka, the deep south of Japan. In pictures it looks like a caricature red Persian travertine facades hermetically closed, overblown copper roofline. Beyond Florida, there is an entire Michael Graves World in Japan more than 40 projects, from skyscrapers to city halls for small villages, mimetic devices for a culture unfamiliar with the initial sources, belated signs of a public domain they never had, and never will have. (Ibid.) Japanese architects talk proudly about chaos: Tokyo is rapidly becoming a cliché; its very resistance to organization gives it an unforeseen glamour that paradoxically threatens to promote it to the status of model. The ultimate oxymoron: chaos as project. Injected into the bloodstream of architecture, its effects will be felt in Mexico, Africa, Paris, Lagos, anywhere. After all the imports, finally an export. (Ibid.:365) Figure 1.11: Il Palazzo, Fukuoka, Koolhaas recognizes that the phenomenon is a new order where new stabilities need to be articulated, and the old ones are let go. Once in the new order, we can talk to each other. The question is, what should we talk about? We are by now blasé about these instances of transcontinental conception, but it is revealing to restore them to the status of geopolitical alchemy: architecture as compound, unforeseeable contaminations and recombinations triggered by the ever-expanding volume of architectural traffic, the architectonic deposit of globalization architecture cut loose from its moorings. (Ibid.) Koolhaas diagnosis is not smooth; rather, it is rough. Projects on this mountain of the refused are all: 1. ugly (still an issue at architectural juries); See The Alphabet and the Algorithm by Mario Carpo, Figure: Morris Adjmi Architects (accessed ). 43

45 2. big, if not colossal; 3. planned for tabula rasa conditions (the original sin of modernism in Europe, now the norm everywhere else); 4. complex montages of program almost Roman in their richness: pools, libraries, concert halls, universities, embedded in throbbing connective tissue of boutiques, malls, entertainment, atriums. They suggest a programmatic renewal, the discovery of a (new) collective; but at the last moment the ingredients curdle, and somehow dissociate; 5. produced by architects not remotely connected to the context for which their works are intended an ignorance that leads to a new purism ; 6. repeating a single module of invention to its breaking point: this systematic exhaustion of inspiration perversely generates a condition of hyperbolized identity. (Ibid.:366) catastrophic: architecture stretched, pushed beyond its own impossibility to the point of breakdown the return of Babel. (Ibid.:367) Figure 1.12: Resorts World Sentosa, Singapore, For him, globalization is a major challenge for the tradition of architecture, and the over-twothousand-years-old questions remain. Globalization destabilizes and redefines both the way architecture is produced and that which architecture produces. Architecture is no longer patient transaction between known quantities that share cultures, no longer the manipulation of established possibilities, no longer a possible judgment in rational terms of investment and return, no longer something experienced in person by the public of critics. Globalization lends virtuality to real buildings, keeps them indigestible, forever fresh. (Ibid.) In the novel global stage, new things are possible. Ideas and matter are decoupled from the ground; they are one second away, one flight away. Characters talk to each other, about the old world, about themselves. It is a drama. This Babel: The Sequel contains the promise of a new architectural system; it establishes episodes of a global enterprise: an infrastructural project to change the world, its aim a 14 Figure: Michael Graves Architecture & Design (accessed ). 44

46 montage of maximum possibility collected from any point, lifted from any context, pilfered from any ideology. It promises the final installment of the Promethean soap opera. (Ibid.:368) Koolhaas characterization feels still very present today. Even when today s global condition is not quite the same as the global condition he is talking about, still we recognize invariances, and we see that some things remain. Are these re-articulations an everlasting condition of the world? Should we identify and fight their catastrophic consequences, or should we learn to construct new stabilities within them? Our position is clear: let us learn. [8/10] Elements of Architecture floor, door, wall, ceiling, toilet, audit, complexity, tradition, conservation Figure 1.13: Toilets, at Elements of Architecture at the Venice Biennale. 15 Koolhaas was the director of the 14th Venice Biennale of Architecture and the curator of its main exhibition, Elements of Architecture. Here, he defines 15 universal elements of architecture and further presents extensive stories around each one of them from the beginning of time until today, and sometimes the future. He suggests that identifying and celebrating the universal elements of architecture will assure the future of architecture. A modernization of architectural thinking. Elements of Architecture, an exhibition of a new body of knowledge in the Central Pavilion exploring the often overlooked but universally familiar elements of architecture used by any architect, anywhere, anytime: the floor, the door, the wall, the ceiling, the toilet, etc By focusing on the history of each element, architecture is revealed as an amalgamation of very ancient and some current components. Their interaction is not well understood; by 15 Figure: Nico Saieh (accessed ). 45

47 looking at them under a microscope, unsuspected (hi)stories and qualities emerge. (Koolhaas 2014:17) For him, to have such research together, presents an opportunity to reflect on the tradition of architecture, on its past, present, and future. Together, these exhibitions and events perform an audit of architecture, asking: What do we have? How did we get here? What can we do, and where do we go from here? (Ibid.) Figure 1.14: 15-volume catalogue of more than 2,000 pages. 16 Each of the fifteen elements of architecture carries a history of its own. And they are revealed in the exhibition. Just as science has recently shown that all of us carry inner Neanderthal genes, each element, too, carries long strands of junk DNA that dates from time immemorial. (Ibid.:193) A closer and more detailed look at these elements shows how complex architecture has increasingly become through the centuries, he argues. The fact that elements change independently, according to different cycles and economies, and for different reasons, turns each architectural project into a complex collage of the archaic and the current, of the standard and the unique, of mechanical smoothness and bricolage a complexity revealed in its full extent only by looking at its constituent parts under a microscope. (Ibid.) And it is in the details of architecture s elements where Koolhaas finds the stability to address the whole tradition and suggest that if we are to continue, a look at these elements is necessary. Here, we present micronarratives revealed by focusing systematically on the scale of the detail of the fragment. We uncover not a single, unified history of architecture, but the multiple histories, origins, contaminations, similarities, and differences of these very ancient elements and how they evolved into their current iterations through technological advances, regulatory requirements, and new digital regimes. (Ibid.) Koolhaas recognizes that the phenomena of a digital era will be part of the tradition of architecture. He does not seem very optimistic about it, though, suggesting that information technology mostly follows obsessive feelings. 16 Figure: designboom (accessed ). 46

48 Onto this still largely unexplored and unfinished chapter is now grafted a digital era, which offers drastically improved levels of control to feed our obsessive need for security and comfort, though we have not even begun to confront the constantly expanding vastness of its potential dark side (Ibid.) He acknowledges the great influence of technology on architecture throughout his writings. In Delirious NY, for example, Koolhaas celebrates the elevator, light bulb, and air conditioning as being at the foundations of a new global architecture (Koolhaas 1978). It is interesting then for us that he does not reflect on today s global condition; on the concept of computation, it is perfectly left behind the exhibition. My obsession with elements has been to assure that elements such as the escalator have never really been incorporated in either the ideology or theory of architecture and that now with the new digital intersections, the risk is that architecture is simple incapable of thinking of its entire repertoire and that s what I hope will be one of the outcomes of this exhibition, a modernization of the core of architecture and architecture thinking itself. (Koolhaas 2014b) Koolhaas' gesture rendered in the exhibition is to stop and reflect, to take a moment and modernize architecture, he says. We see it more as a gesture of conservation, though, a taxonomy of architectural elements. We imagine Koolhaas gesture as going to the bookshelf, opening an encyclopedia, searching for door, and reading the entry in detail. What we would be interested in doing is opening the etymology dictionary, searching for door, and putting together a definition that will empower our concept of door to do marvelous things, like talk to my favorite Tarantino movies, for example. This scenario is possible with today s computing and the abundance of online information. [9/10] The Generic City generic, renewal, contradiction, tabula rasa, big, fast, beautiful It is not extremely difficult not to have identity but it is extremely difficult the knowing not having identity. One might say it is impossible but that it is not impossible is proved by the existence of master-pieces which are just that. They are knowing that there is no identity and producing while identity is not. Gertrude Stein 1936 The Generic City is an explicit recognition of the last decades global condition indexed by the physical infrastructure covering the world and its influence in architecture. The Generic City has 47

49 at its center a city s identity. Koolhaas characterizes architecture as one, as a global totality, and he addresses its looks and the abilities of its particular condition. A generic city is everywhere and decoupled from local traditions but rooted nevertheless in the ground. It is open; people can talk to each other; everybody is welcome. What follows is a small essay in two parts where we think about today s global condition indexed by a digital infrastructure and its global network of computers from Koolhaas perspective. They invite us to think about the habitable spaces online in relation to those coupled to the ground. What is it about social media and content sharing platforms that makes us feel we know them all? Sign up, , password, click, welcome! The home button points to a space to talk about anything; your-face button points to a space to talk about you. What happened before our arrival? It doesn t matter we have to catch up. Is the contemporary city like the contemporary airport all the same? Is it possible to theorize this convergence? And if so, to what ultimate configuration is it aspiring? Convergence is possible only at the price of shedding identity. That is usually seen as a loss. But at the scale at which it occurs, it must mean something. What if we are witnessing a global liberation movement: down with character! What is left after identity is stripped? The Generic? (Koolhaas 1994:1248) Let us think of a paper magazine as social media s predecessor. It gathers the voices and interests of a community. It is always there, ready to talk to you about the same, but differently. The stronger identity, the more it imprisons, the more it resists expansion, interpretation, renewal, contradiction. Identity becomes like a lighthouse fixed, overdetermined: it can change its position or the pattern it emits only at the cost of destabilizing navigation. (Ibid.) To have a voice in a paper magazine, you must have a recognized influence in the community. That, or pass through several checkpoints towards the center, formats, peer-reviews. They get tougher as you reach the core. Identity centralizes; it insists on an essence, a point. Its tragedy is given in simple geometric terms. As the sphere of influence expands, the area characterized by the center becomes larger and larger, hopelessly diluting both the strength and the authority of the core; inevitably the distance between center and circumference increases to the breaking point. (Ibid.) There are people at the center keeping the magazine s values, the community s values. Many things depend on them. They oversee it all. In our concentric programming (author spent part of his youth in Amsterdam, city of ultimate centrality) the insistence on the center as the core of value and meaning, font of all significance, is doubly destructive not only is the ever increasing volume of dependencies an ultimately intolerable strain, it also means that the center has to be constantly maintained, i.e., modernized. As the most important place, it paradoxically 48

50 has to be, at the same time, the most old and the most new, the most fixed and the most dynamic; it undergoes the most intense and constant adaptation, which is then compromised and complicated by the fact that it has to be an unacknowledged transformation, invisible to the naked eye. (Ibid.:1249) Social media and content sharing platforms are different from their predecessor, even when they both talk to communities. Social media has no center, no most important place or value keepers. It is easy and fast to be part of and to have a voice. It is always the right size. The Generic City is the city liberated from the captivity of center, from the straitjacket of identity. The Generic City breaks with this destructive cycle of dependency: it is nothing but a reflection of present need and present ability. It is the city without history. It is big enough for everybody. It is easy. It does not need maintenance. If it gets too small it just expands. If it gets old it just self-destructs and renews. It is equally exciting or unexciting everywhere. It is superficial like a Hollywood studio lot, it can produce a new identity every Monday morning. (Ibid.) A community exists only because people are part of it, because there s something that needs to be told, something that needs to circulate. A community to share power tools? It s there. A community to review Soviet films? It s there. The Generic City is always founded by people on the move, poised to move on. This explains the insubstantiality of their foundations. Like the flakes that are suddenly formed in a clear liquid by joining two chemical substances, eventually to accumulate in an uncertain heap on the bottom, the collision or confluence of two migrations Cuban emigres going north and Jewish retirees going south, for instance, both ultimately on their way someplace else establishes, out of the blue, a settlement. A Generic City is born. (Ibid.:1252) There are always new spaces opening up. Is this category too broad? No problem, make a new one. Comments, messages, and hashtags ad infinitum. Nobody is watching, everyone is watching. Housing is not a problem. It has either been completely solved or totally left to chance; in the first case it is legal, in the second illegal ; in the first case, towers or, usually, slabs (at the most, 15 meters deep), in the second (in perfect complementarity) a crust of improvised hovels. (Ibid.:1253) There is no necessity for conservation, nor for re-articulation. Talks are deleted, moved, copy/pasted, contaminated. All Generic Cities issue from the tabula rasa; if there was nothing, now they are there; if there was something, they have replaced it. They must, otherwise they would be historic. (Ibid.) A community s platform is promptly put online. Layouts are chosen from an array of versions. Which one to choose if all of them are possible? The one that looks better across devices, of 49

51 course. The architecture of the Generic City is by definition beautiful. Built at incredible speed, and conceived at even more incredible pace, there is an average of 27 aborted versions for every realized but that is not quite the term structure. (Ibid.:1260) They are done by thousands of designers and software engineers ready to get involved in any project; yes is more and they are not enough. Front-end libraries, back-end libraries, color schemes, database schemes, icons, they are always ready. There is no time to lose. They are prepared in the 10,000 architectural offices nobody has ever heard of, each vibrant with fresh inspiration. Presumably more modest than their well known colleagues, these offices are bonded by a collective awareness that something is wrong with architecture that can only be rectified through their efforts. They are the ones who design without any hesitation. They assemble, from 1,001 sources, with savage precision, more riches than any genius ever could. (Ibid.:1261) They are communities of snip-snap. A new idea? What about something like when Airbnb meets Tinder for a Periscope-like audience? Let s do it. The style of choice is postmodern, and will always remain so. Postmodernism is the only movement that has succeeded in connecting the practice of architecture with the practice of panic. Postmodernism is not a doctrine based on a highly civilized reading of architectural history but a method, a mutation in professional architecture that produces results fast enough to keep pace with the Generic City's development. (Ibid.:1262) Everyone is welcome to an online community everyone but boredom. Maxim Gorky speaks in relation to Coney Island of varied boredom. He clearly intends the term as an oxymoron. Variety cannot be boring. Boredom cannot be varied. But the infinite variety of the Generic City comes close, at least, to making variety normal: banalized, in a reversal of expectation, it is repetition that has become unusual, therefore, potentially, daring, exhilarating. But that is for the 21st century. (Ibid.) And what about the products of modernization, what Koolhaas calls Junkspace? What would be the products of our global network? Are there any? 50

52 [10/10] Junkspace modernization, continuity, exploitation, design, creativity, escalation, masterpieces Figure 1.14b: Flic, a smart button that crowdfunded 1M on Indiegogo. 17 Here is an interesting hypothesis: Startups are the new Junkspace. These products of the global network are meant to be global and have an impact on the world. They are crowdfunded by the totality, send to the totality, and care about the totality while doing so. Global blessings. The built (more about that later) product of modernization is not modern architecture but Junkspace. Junkspace is what remains after modernization has run its course, or, more precisely, what coagulates while modernization is in progress, its fallout. Modernization had a rational program: to share the blessings of science, universally. (Koolhaas 2002:175) They incorporate the newest hardware, because the newest is always cheaper, smaller, and faster. The final version of a product has more sensors, the newest actuator, connects to the cloud, and will be delivered by a drone. Continuity is the essence of junkspace; it exploits any invention that enables expansion, deploys the infrastructure of seamlessness: escalator, air-conditioning, sprinkler, fire shutter, hot-air curtain. (Ibid.) The simplest design is the goal. Scandinavian is never wrong. Friendly lines, friendly colors, functional. It is likewise presented: simple narrative, simple diagrams, plain color t-shirt, friendly female voice-over. Smile. Junkspace thrives on design, but design dies in Junkspace. There is no form, only proliferation Regurgitation is the new creativity; instead of creation, we horror, cherish, and embrace manipulation. (Ibid.:177) They are crowdfunded by tens of communities. Their mission is to empower people and unite them around ideas that matter to them and together make those ideas come to life B 17 See Figure: from (both accessed ). 18 See (accessed ). 51

53 dollars pledged to one community, and counting. 19 Junkspace sheds architectures like a reptile sheds skins, is reborn every Monday morning. In previous building, materiality was based on a final state that could only be modified at the expense of partial destruction. At the exact moment that our culture has abandoned repetition and regularity as repressive, building materials have become more and more modular, unitary, and standardized; substance now comes predigitized. (Ibid.:178) There is always a campaign to support. Choose your category: games, art, design, technology. More than 60% die trying 20, but that does not kill the spirit. While whole millennia worked in favor of permanence, axialities, relationships, and proportion, the program of Junkspace is escalation. Instead of development, it offers entropy. Because it is endless, it always leaks somewhere in Junkspace; in the worst case, monumental ashtrays catch intermittent drops in a gray broth. (Ibid.) Users determine what to do with the product; startups give the power back to the user. Here is a super empowering glow-in-the-dark-plastic button 21 to send a panic alarm to a person you trust or to put food in your cat s bowl. Junkspace is post existential; it makes you uncertain where you are, obscures where you go, undoes where you were. Who do you think you are? Who do you want to be? (Ibid.:182) The products are environmentally friendly, powered by green technology, and delivered in biodegradable and recyclable packages. They combine nature, science, and art. Junkspace knows all your emotions, all our desires. It is the interior of Big Brother s belly. It preempts people s sensations. It comes with a sound track, smell, captions; it blatantly proclaims how it wants to be read: rich, stunning, cool, huge, abstract, minimal, historical. (Ibid.:183) For every product sold, a part of it is sent to charities. Or even better, the crowdfunding is directly for a charity. 22 Junkspace pretends to unite, but it actually splinters. It creates communities not out of shared interest or free association, but of identical statistics and unavoidable demographics, an opportunistic weave of vested interest. Each man, woman, and child is individually targeted, tracked, split off from the rest. (Ibid.) Startups are developed by young enthusiasts called Digital Nomads who chose entrepreneurship over employment. The promise is that you can build a startup while traveling to 19 See (accessed ). 20 See (accessed ). 21 See and its second crowdfunding campaign at (accessed ). 22 See (accessed ). 52

54 20 countries 23 and raising 1M dollars. 24 A shortage of masters has not stopped a proliferation of masterpieces. Masterpiece has become a definitive sanction, a semantic space that saves the object from criticism, leaves its qualities unproven, its performance untested, its motives unquestioned. Masterpiece is no longer an inexplicable fluke, a roll of the dice, but a consistent typology: its mission to intimidate, most of its exterior surfaces bent, huge percentages of its square footage dysfunctional, its centrifugal components barely held together by the pull of the atrium, dreading the imminent arrival of forensic accounting. (Ibid.:184) Digital Nomads are location free, moving from city to city. Nevertheless, they are online all the time, 25 uploading source code in JavaScript, downloading libraries in Python, translating web documents to English or messages to Indonesian. Languages are not a problem. Globalization turns language into Junkspace. We are stuck in a speech-doldrums. The ubiquity of English is Pyrrhic: now that we all speak it, nobody remembers its use. The collective bastardization of English is our most impressive achievement; we have broken its back with ignorance, accent, slang, jargon, tourism, outsourcing, and multitasking. (Ibid.:186) Remarks From these talks, we affirm that we are living in the global condition described by Koolhaas, and that it has become ever more digital, as traditional objects become computational, as they are re-articulated. We don t see any e-junkspace in architecture, but nevertheless the setup is here. And that is one of our major challenges, or advantages, during this work; we will be talking about the present and future of architecture, and not about a diagnosis in the light of the global network. 23 See (accessed ). 24 See (accessed ). 25 Google Fi is one of the basic and most popular services for Digital Nomads. Google Fi is a global SIM card that gives you LTE speed in over 135 different countries. See (accessed ). 53

55

56 1.3 THE ABUNDANCE OF INFORMATION ON THE GLOBAL NETWORK As we presented in the previous talk, some contemporary architects explicitly recognize the global network as a condition that is influencing architecture, and we placed emphasis on the absence of consistent arguments that could cast a shadow over our at this point intuitive understanding of the global network. Here, we will talk about the information s infinite circulation on the global network, and how it may impact their current understanding of architecture and its artifacts. We will see how these architects talk about an overwhelming complexity that threatens our society, and how they find stability by claiming territories, building enclosures, and establishing authority within its walls. In their understanding, information can only come from within, from the experts, and any other talk from the outside is irrelevant. To consider a streamline from infinity to their position would only challenge their stability. We will also see how they talk about such a scenario, and how they agree that it presents a problem for the establishment, and how, despite this recognition, they engage with this question and formalize inclusion machines to talk about the infinite information that is coming from their architectural artifacts. Finally, we will talk about how the contemporary ways of computer-aided design and production raise ontological questions that are relevant when talking about information-streams. These questions revolve around the origins of architectural artifacts and the true authors of an architectural design. We start with Patrick Schumacher. 55

57 [1/9] The Dialectic of the Pragmatic and the Aesthetic exploration, extrapolation, urban fabric, environment, poetic sensibility, cause-effect Figure 1.15: Datatown, MVRDV In a lecture delivered at the AA, London, in 1997, Patrik Schumacher 2 talked about the aesthetics of data-scapes. He placed next to each other the pragmatism and the aesthetic excitement of the data-scape approach. We think of this moment as Schumacher s reaction to his colleagues and students exploration of the abilities and potentials of having real-time measurements of tangible and intuitive things of the world, i.e., light conditions, air and noise pollution, and such. For us, this phenomenon can only happen within a global network, but Schumacher s arguments focus on the aesthetics of the explorations, and not on the phenomenon itself. The notion of 'datascapes' conceives architectural form as the translation of certain determining parameter or 'data'. The notion may be understood analytically interpreting existing urban formations as well as describing hypothetical design experiments based on selective extrapolations testing the quantitative or qualitative limits of the respective selected parameters. Those parameters describe certain performance criteria of the urban fabric, like density, light-conditions, ventilation, visual penetration, structural limits, traffic flows, institutional use patterns etc. (Schumacher 1997) The novel availability of the data-streams and the visualization tools encourage the architect to articulate their impacts, and further project them as architectural artifacts. The spirit of these experiments is explorative rather than pragmatic. They are trying to turn design-constraints into design-engines testing what form architecture might take if one 1 Figure: mvrdv 1999 at (accessed ). 2 Patrik Schumacher is an architect of theories, manifestoes, concepts, buildings, writings, interviews, lectures; aesthetics, elegance, avant-garde, parametricism. He has built and designed over 950 projects with Zaha Hadid Architects, spread around 44 countries [see Zaha s world online at zaha-hadid.com/archive/#zha-world (accessed )]. Dubai, Saudi Arabia, Armenia, NY. An architect of presence, he teaches at the AA School of Architecture. Big numbers, impressive answers, but to our surprise, we find difficulties in sympathizing with his questions. They are around enclosure, centrality, specialization, authority, the global network s negative. We nevertheless recognize that there is no one else today arguing for architecture and computing like he is. 56

58 really gives up all aesthetic prejudice and just follows the morphological thrust of certain selected functional parameters, ready to take it as it comes and the stranger it comes the better. (Ibid.) Data-scapes present a new kind of graphics for architectural design and new ways to address the real-time measurements of well known phenomena, all around the world. Aesthetic judgement is delayed but in the end remains the ultimate ground of contestation for the high cultural institution of Architecture. Data-scaping offers its own aesthetic sensibility, expressing an urge for the new, a readiness for the unfamiliar. Abstract and synthetic environments are offered as the next human habitat. (Ibid.) For Schumacher, data-scapes construct cause-effect relations between that which is measured and its materialization, and leave other relevant architectural qualities behind. Nevertheless the polemic and ideological importance of the data-scape approach rests in the rebuttal of purely aesthetically driven discourses (like minimalism). The reaffirmed 'functionalism' of data-scaping starts with the rejection of poetic sensibility and artistic intuition as points of departure for architectural and urban design. The aesthetic judgement of cities and buildings is rational in as much as it operates as an immediate intuitive appreciation of performativity, short-circuiting first hand comparative experience or extended analysis. Aesthetic judgement thus represents an economical substitute for experience. It depends on a tradition that disseminates accumulated experience via extrinsic and dogmatic rules. This dogmatism is the virtue as well as the limit of aesthetically condensed intelligence. (Ibid.) Figure 1.16: Digital Avalanche in City of London. AA Diploma Project They are seen by Schumacher as an imposition of new values and measures for architecture based on aesthetics. This gesture that, for him, is not alien to the tradition of architecture. For instance: The Vitruvian or Palladian regime of proportions represents a condensation of accumulated building experience, allowing for the 'blind' design of sound stonestructures. The classical orders are regulating column-height to width-ratios, spans, foundations, minimum roof-angles for drainage etc. The Palladian rules concerning room proportions guarantee certain standards of day-lighting and air-volume. Any such rule- 57

59 system embodies an economy of performance as well as an economy of design effort. Those regimes are as it were dogmatized data-scapes. (Ibid.) The interest in data-scapes is motivated by promised abilities to challenge and re-articulate our building technologies. The promise is to be materialized. With the development of society and the availability of new building technologies (reinforced concrete, steel etc.) the classical aesthetic regime lost its rationality and became a fetter upon the further development of the built environment. (Ibid.) For Schumacher, data-scapes are not much more than an aesthetic discourse motivated by a new phenomenon that lacks reflection on the logics of modernization and its influence on the way societies absorb it and evolve. But any extended reliance on aesthetic judgement creates the idealist illusion that the well-designed can be identified and ascertained aesthetically beyond the limits of a specific historical period an illusion the profession is still infested with. The point is not to start with 'nice ideas' or fantasies of the beautiful in order to suffer their inevitable corruption (quite pathetic), but to find beauty within the logic of modernization and the social relations this process throws or allows us into, like high density, mobility, diversity, anonymity...etc. The point is to construct, and aesthetisize the latest possibilities of the development of social productivity. (Ibid.) [2/9] Arguing for Elegance avant-garde, mainstream, progress, complexity, problem, solution Figure 1.17: Studio Zaha Hadid at the University of Applied Arts Vienna 2008/09. 4 Patrik Schumacher also looks at the elegance of today s computational models, and considers that they show a necessity to re-articulate this concept. For him, the challenge of the computational models is to bring their elegance from a superficial to a deeper and holistic architecture from an elegant avant-garde movement to an elegant nature. 3 4 Figure: Yufei Li 2015 from (accessed ). Figure: Milan Suchanek 2008/9 from (Hadid 2011). 58

60 We have reached the final stages of the current cycle of avant-gardist innovation: folds and blobs are heading mainstream. What else should be the destiny and purpose of the avant-garde? Its function is to advance the development of the discipline. Avant-garde and mainstream are two complementing sides of a single evolution: architectural progress. (Schumacher 2007:30) To be mainstream and elegant goes hand-in-hand, according to Schumacher. Elegance is an asset in architecture, and the current theoretical emptiness of it presents a liability. He sees it as an opportunity. The immediate appeal of elegance is certainly an asset in the push towards the mainstream. The current theoretical emptiness of elegance is also an asset rather than a liability. (Ibid.) Therefore, a theory of elegance: The elegance being referred to is not the elegance of minimalism. Minimalist elegance thrives on simplicity. The elegance being promoted here instead thrives on complexity, and achieves a visual reduction of an underlying complexity that is thereby sublated rather than eliminated. Elegance thus articulates complexity. (Ibid.) Elegance happens by how the architectural artifact is articulated and how it relates to the contemporary society. If elegance is to articulate complexity, it must have its own means to measure it as an object of the world, as an object of a specific society. This new theory of elegance in contemporary architecture has two distinct components: 1 descriptive: the elaboration of a descriptive language that provides the resources to distinguish and characterise the style in question and the particular agenda of its refinement. 2 argumentative: the stipulation of form function relationships and the formulation of hypotheses about the social efficacy and pertinence of elegant architecture in the context of contemporary societal challenges. (Ibid.) Elegance is in complex solutions. We also talk about an elegant solution to a complex problem. In fact only if the problem is complex and difficult does the solution deserve the attribute elegant. (Ibid.) And complexity in architecture is twofold. On one hand, we have the social interaction, and on the other, the spatial configuration. Two parallel applications of the concept of complexity need to be distinguished in our domain of reference: the underlying complexity of the institutional arrangements and lifeprocesses on the one hand needs to be distinguished from the complexity of the spatial arrangements and architectural forms that help to organise and articulate those lifeprocesses on the other hand. elegance facilitates orientation within a spatial complex arrangement and thus ensures 59

61 the legibility of a complex social formation. Again, elegance articulates complexity. (Ibid.:31) The computational models that Schumacher constructs facilitate an architectural elegance. Elegance is computed, computing elegance. Current digital modelling tools are able to facilitate integrative effects: lofting, spline networks, soft bodies, working with force fields and so on. There is an inevitable, powerful relationship between the new digital tools (such as animation software), compositional tropes and stylistic characteristics. In fact, it has become increasingly easy to achieve abstract sketch designs (surfaces) that satisfy these terms and thereby achieve the measure of elegance defined here. However, surface compositions are only the first sketchy step in the design of an elegant architecture. (Ibid.:32) But this computed elegance has not achieved a level of full implementation, yet. As of today, elegance is superficial and is lacking deepness in its construction. The next obvious challenge is to go beyond pure surfaces and to elaborate structural systems that are compatible with this ambition for continuous differentiation, perhaps even enhancing the overall effect of integrated complexity. (Ibid.) Placing the concept of elegance in line with the tradition of architecture, Schumacher looks at Alberti s account on beauty. The notion of elegance promoted here still gives a certain relevance to Leon Battista Alberti s criterion of beauty: you can neither add nor subtract without destroying the harmony achieved. Except in the case of contemporary elegance, the overall composition lacks this sense of perfect closure that is implied in Alberti s conception. (Ibid.:33) The difference between Alberti s beauty and Schumacher s elegance is the movement from ordering principles to integrative flows. Alberti focused on key ordering principles, such as symmetry and proportion, which were seen as integrating the various parts into a whole by means of setting the parts into definite relations of relative position and proportion in analogy to the human figure. Our current idea of organic integration does not rely on fixed ideal types. Neither does it presuppose any proportional system, nor does it privilege symmetry. Instead, the parts or subsystems mutually inflect and adapt to each other, achieving integration via various modes of spatial interlocking, soft transitions at the boundaries between parts, morphological affiliation and so on. (Ibid.) Schumacher s principle of elegance: do not add or subtract without elaborate inflections, mediations or inter-articulations. While the classical concept of preordained perfection has been abandoned, there remains a strong sense of increasing tightness and stringency, even approaching a sense of 60

62 internal necessity, as the network of compositional relations is elaborated and tightened. (Ibid.) Figure 1.18: Capital Hill Residence, Zaha Hadid Architects Everyday societal life gets more complex, and elegance is a way to describe the results of a complex design problem, Schumacher argues. The overriding headline here is: Orientation within complex organisations. Contemporary architectural briefs are marked by a demand for more complex and simultaneous programmatic provisions to be organised within more complex urban contexts. Elegance as defined here signifies this capacity to articulate complex life-processes in a way that can maintain overall comprehension, legibility and continuous orientation within the composition. Complex organisational relations of overlapping or interpenetrating domains can be articulated and made legible so that a complex order is perceived rather than allowing the complexity to appear as disorder. (Ibid.:35) Elegance is compared with the concept of orientation in space. Space used to be simple containers; now, with the concept of computing, spaces get complex and, if spacial orientation is not altered, elegance remains. Traditionally, spatial orientation has been operating primarily on the basis of relations of inclusion or containment the Russian doll principle of nesting domains. Spatial position is defined as a series of relations of containments: continent, country, region, city, district, neighbourhood, estate, building, floor, apartment, room. Each domain has a clear boundary and is fully contained within a larger domain with an equally crisp boundary. This is how one knows where one is at any time. A change of position implies the crossing of a boundary. Orientation is traditionally further supported if the domains can be identified with easily recognisable platonic/geometric figures such as circles, squares or rectangles. Domains and figures are ideally kept separate. It should be obvious that the scope of this system of ordering is limited. (Ibid.) 61

63 For Schumacher, elegance is measured by its spatial complexity, and spatial complexity is achieved by computation. A radically different, alternative mode of ordering and orientation is afforded by the principles of elegance discussed above. Here, figures and domains need not sustain platonic simplicity because their deformation no longer spells the break down of order, but the lawful inscription of information. Figures/domains do not have to remain neatly separated because we have developed lawful rules of mutual inflection, and lawful rules of gradual transformation. (Ibid.) Orientation in a complex, lawfully differentiated field affords navigation along vectors of transformation for example, a morphing trajectory rather than snapping from position to position via boundary crossings. In the extreme case of a pure field condition, both bounded domains and identifiable figures have in fact disappeared and orientation along reference objects and bounded/nested domains is fully replaced by the navigation of lawfully modulated field qualities such as density, directionality, agitation in the field and so on, affording inferences and anticipations. (Ibid.:36) [3/9] The Autopoiesis of Architecture system, autonomy, differentiation, communication, self-reference, enclosure, specialization Figure 1.19: Architecture as pattern of continuously transforming components. Zaha Hadid Architects, Randers Art Museum Competition, London Schumacher finds in a social theory a stable and fertile ground for his most prominent theory The Autopoiesis of Architecture and for its core concept in relation to computing Parametricism. In order to continue the tradition of architecture, he argues that he needs to look at its link to society and measure its impact on it. In order to understand such a complex concept, i.e., society, it is necessary to decompose it, to differentiate its parts and to model the 5 Figure: Zaha Hadid Architects (accessed ). 62

64 ways in which these parts talk to each other and formalize it. Architecture is seen by Schumacher as an autonomous system of communications. Society is a system, and architecture is its autonomous subsystem. The tendency towards architectural autonomy might be understood as a moment of an overall societal process of differentiation, whereby social communication fragments into a series of autonomous domains the economy, politics, the legal system, science, art etc. establishing self-referentially closed subsystems within society. Each of these autonomous discourses contributes, in its specific way, to the overall social process. But this overall social process society does no longer have any control centre over and above the various increasingly autonomous communication systems. The differentiated discourses establish their own sovereign independence with respect to their underlying values, performance criteria, programmes and priorities. In this sense the various subsystems operate selfreferentially. (Schumacher 2002) This is a characterization of the modern society, our society, the one that succeeded the medieval society. Any attempt to reduce all value systems to one a form of regressive totalitarianism could only serve to blunt the operative complexity achieved by the co-evolution of the self-enclosed discursive systems with catastrophic consequences. (Ibid.) Schumacher s theory has at its foundations the general theory of the social systems of Niklas Luhmann, a prominent German sociologist of the 20c who wrote more than 70 books and nearly 400 scholarly articles. 6 This sketch of a society as a communication process without centre and without binding self-representation is based on Niklas Luhmann s theory of functionally differentiated society. According to Luhmann this internally differentiated system of communication works, because the process of differentiation follows a functional logic, crystallising selfreferentially closed, but structurally coupled, function systems. Luhmann s theory of modern society as a functionally differentiated society is embedded in his general theory of social systems. The problem of systems theory, the constitution, maintainance and evolution of continuous (rather than stable) systems within changing environments is also the problem of Luhmann s sociology. (Ibid.) Regarding one of the core concepts in this theory of Schumacher s, the concept of autopoiesis refers to a system capable of reproducing and maintaining itself. Autopoeisis defines biological life-processes as the circular self-reproduction of recursive processes that constitute a unity of interaction (the system) within a domain of interaction (the environment). The environment is not assumed to be given as the same for all 6 See Luhmann and his numbers at 63

65 organisms but each organism occupies a peculiar niche in accordance with its peculiar mode of life, sensitivity and responsiveness. Each system thus determines what counts as its relevant environment, i.e. which differences make a difference versus those aspects that remain indifferent. (Ibid.) Autopoiesis of architecture, seen from a systems theory perspective, needs to talk to the other sub-systems of the society. It needs to be differentiated but capable of importing concepts and ideas. An oxymoron: openness through closure. Differentiation can not be the full story. Obviously autonomy and self-referential closure can not imply hermetic isolation. Luhmann posits the formula: openess through closure. This formula poses the task of continuous adaptation of the system to the relevant changes it distinguishes within its environment. This process of adaptation in turn implies self-referential autonomy for the system with respect to the task of organising its response. The impact of the environment does not pervade and directly determine the system. (Ibid.) Schumacher distinguishes between two types of communication that happen in society, internal and external communication. communication within a given subsystem of society and communication between different subsystems. Within a given system communications are constituted recursively within a shared conceptual framework or horizon of understanding. Across system boundaries communications do not share the same horizon and are therefore not understood in the same specific and elaborate way. Here communication can only rely on the rather simple, common denominator of colloquial understanding. (Ibid.) Figure 1.20: Avilion Triflow Taps, Zaha Hadid Architects. 7 7 Figure: (accessed ). 64

66 Between architecture, and let us say, computer science, Schumacher says that we can only have small talks, that we can only irritate each other because we re specialists in our own subsystem and we don t share the view of the overall system. Across the boundary lies the environment which remains an unpredictable source of irritation, because the various specialized discourses are not mutually mastered and thus remain largely intransparent with respect to each other. Specialized communication is thus contrasted with irritation. (Ibid.) But external irritation is not the same as internal communication; internal communication shares the expertise, hence the history and validation of the subsystem. The outside irritates, the inside validates. It s an experts talk. This notion of external irritation is not only distinguished from internal communication, but is then sharply contrasted with any notion of external determination. This contrast focuses on two aspects: What can or can not become an irritation for a system depends first of all upon the historically elaborated structure of the system. Secondly the responsive behavior of the autopoeitic system is specified by its peculiar sensitivity (information processing apparatus) and its current momentary/historical state. (Ibid.) He elaborates on the validity and necessity of his arguments by pointing out the validity and necessity of Luhmann s arguments. The dispute within architecture about its degree of autonomy might be clarified and assessed within the framework of Luhmann s theory of social autopoeisis. Architecture s autonomy within society does not imply indifference to society. Rather it is a necessary mode of contributing to society with sufficient flexibility and sophistication. Contemporary society is far too complex and too dynamic to establish clear and fixed hierarchies of values/priorities that would in turn allow the societal division of labor to be conceived as chains of instruction, whereby centrally/democratically set purposes are to be fulfilled by the various appointed function systems. (Ibid.) If society, with all its complexity, can be seen through the lenses of systems theory, architecture also can. Architecture too can only appoint itself, and define its own purposes, both with respect to the identification of the most urgent architecturally relevant social problems and with respect to the appropriate selection of architectural means to tackle such problems. However architecture, like all the other subsystems of society, is doing this under risky conditions of mutual interdependence. Failure to self-organise effective responses leads to irrelevance and spells extinction. (Ibid.) And systems have always been there. They are part of history, he says, suggesting that there is no need to re-articulate the concept. The autopoeitic system, as a complex, historically evolving system, always uses time and involves whole series of events into its responses, so that simple, predictable one-to-one 65

67 correlations between environmental impacts and system responses are out of the question. (Ibid.) Figure 1.21: One North Masterplan, Zaha Hadid Architects When the system is complex, it can never be directly influenced. There cannot be a one-to-one correlation, nevertheless causation may exist. With respect to architecture, any attempt to establish immediate and determinate correlations between architecture as a discipline, with its current analytic/synthetic procedures on the one hand and its social environment on the other hand, is as futile as the related attempt to determine fixed one-to-one relations between functions and forms. A mark of the self-referential closure of architecture is that design decisions are tightly knit to their kind and only obliquely/indirectly, i.e. en bloc, refer to external demands and circumstances. Design decisions always refer to other design decisions which in turn are embedded in the extensive chain and network of architectural discourse. (Ibid.) Society is too complex, and the only way to find stability as an architect is by making theories; in other words, stability comes with clear views of the world. The network of implications is too complex. Any architectural response has to involve whole networks of design decisions on the basis of architectural (theoretical) principles. This is a measure of the sophistication of architecture, it can not be bullied into a knee-jerk response. This is the raison d être of autopoeitic closure. (Ibid.) Schumacher s solution: The more complex society gets, the more we need to close up our subsystems; the more we need to become specialists, be more specific, go in depth, close our borders. The more complex the societal environment the more autonomous the more selective 8 Figure: (accessed ). 66

68 and specific must every social system operate in order to cope with the various, often contradictory demands that challenge the respective social system. (Ibid.) [4/9] Parametricist Manifesto style, innovation, adaptation, science, fields, lawful Figure 1.22: Heydar Aliyev Centre, Zaha Hadid Architects In today s society, computers are everywhere, and internally, in the sub-system called architecture, digital architectural models are present in different, unorganized ways, Schumacher argues. Contrary to us, he does not celebrate this phenomenon. He rather tries to bring everything to an order, as he presents Parametricism as the all-reaching umbrella that covers any model of architecture today. Architecture finds itself at the mid-point of an ongoing cycle of innovative adaptation retooling the discipline and adapting the architectural and urban environment to the socioeconomic era of post-fordism. (Schumacher 2008) Computing is the tool to operate and control complex societies, at any scale. The key issues that avant-garde architecture and urbanism should be addressing can be summarized in the slogan: organising and articulating the increased complexity of postfordist society. The task is to develop an architectural and urban repertoire that is geared up to create complex, polycentric urban and architectural fields which are densely layered and continuously differentiated. (Ibid.) Computers are everywhere. They present a new order of general nature. Architecture is no exception; digital models are everywhere. For Schumacher, this phenomenon in architecture is called parametricism. 9 Figure: (accessed ). 67

69 The contemporary architectural style that has achieved pervasive hegemony within the contemporary architectural avant-garde can be best understood as a research programme based upon the parametric paradigma. We propose to call this style: Parametricism. Parametricism is the great new style after modernism. Postmodernism and Deconstructivism have been transitional episodes that ushered in this new, long wave of research and innovation. (Ibid.) Parametricism starts as an avant-garde movement, but it drives towards becoming the style of today s society. Avant-garde styles might be interpreted and evaluated in analogy to new scientific paradigms, affording a new conceptual framework, and formulating new aims, methods and values. Thus a new direction for concerted research work is established. My thesis is therefore: Styles are design research programmes. (Ibid.) For Schumacher, the insistence of solving everything with the same style might me compared to Newton s insistence on explaining the universe with the same principles. Each style has its hard core of principles and a characteristic way of tackling design problems/tasks. Avant-garde architecture produces manifestos: paradigmatic expositions of a new style s unique potential, not buildings that are balanced to function in all respects. There can be neither verification, nor final refutation merely on the basis of its built results. (Ibid.) But parametricism is as valuable as its tools and the masters of the tools. The current stage of advancement within parametricism relates as much to the continuous advancement of the attendant computational design technologies as it is due to the designer s realization of the unique formal and organizational opportunities that are afforded. Parametricism can only exist via sophisticated parametric techniques. (Ibid.) Figure 1.23: Beijing New Airport Terminal Building, Zaha Hadid Architects. 10 Parametricism happens to be the style of today s complex society, and it is already so highly integrated to architecture that it has become a new nature. 10 Figure: (accessed ). 68

70 Parametricism emerges from the creative exploitation of parametric design systems in view of articulating increasingly complex social processes and institutions. It is the sense of organized (law-governed) complexity that assimilates parametricist works to natural systems, where all forms are the result of lawfully interacting forces. Just like natural systems, parametricist compositions are so highly integrated that they cannot be easily decomposed into independent subsystems a major point of difference in comparison with the modern design paradigm of clear separation of functional subsystems. (Ibid.) For Schumacher, parametricism comes after modernism. Its contribution is radical, namely the turn from spaces to fields, and from discrete elements to continuous bodies. Modernism was founded on the concept of space. Parametricism differentiates fields. Fields are full, as if filled with a fluid medium. We might think of liquids in motion, structured by radiating waves, laminal flows, and spiraling eddies. Swarms have also served as paradigmatic analogues for the field-concept. We would like to think of swarms of buildings that drift across the landscape. Or we might think of large continuous interiors like open office landscapes or big exhibition halls of the kind used for trade fairs. Such interiors are visually infinitely deep and contain various swarms of furniture coalescing with the dynamic swarms of human bodies. There are no platonic, discrete figures with sharp outlines. Within fields only the global and regional field qualities matter: biases, drifts, gradients, and perhaps even conspicuous singularities like radiating centres. Deformation does no longer spell the breakdown of order but the lawful inscription of information. (Ibid.) Parametricism: an analogy with the contemporary city. Orientation in a complex, lawfully differentiated field affords navigation along vectors of transformation. The contemporary condition of arriving in a metropolis for the first time, without prior hotel arrangements, without a map, might instigate this kind of fieldnavigation. Imagine there are no more landmarks to hold on, no axis to follow and no more boundaries to cross. Contemporary architecture aims to construct new logics the logic of fields that gear up to organize and articulate the new level of dynamism and complexity of contemporary society. (Ibid.) 69

71 [5/9] Parametric Diagrams abstraction, efficiency, drawings, ordinary, extraordinary, metric, parametric, sophistication Figure 1.24: Deleuzian Diagrammatic Processes: Field-directionalities, Zaha Hadid Architects Getting into a bit more detail with the all encompassing theory of architecture by Schumacher, and its style, Parametricism, we look at how he relates it to the tradition of drawing and architecture, and to semiotics. Here, Schumacher elaborates on the idea of his parametric diagrams. A diagram is a type of representation that is characterised by a high level of abstraction. The representation focuses on very specific aspects of the represented entity. These isolated aspects can then be grasped and manipulated with a high degree of efficiency. (Schumacher 2010:260) He makes a basic classification of diagrams, ordinary and extra-ordinary. I would like to talk of ordinary diagrams, if the relationship between the abstract diagram and the concrete entity represented is unproblematic because it is fixed through built-in routine assumptions. (Ibid.) Schumacher recognizes Durand as a master of diagrams due to his mechanics of composition. Durand was perhaps the first to introduce a diagrammatic process within architecture. He proposed a 'mechanics of composition, made easy and efficient by using gridded paper upon which a series of basic elements such as walls and columns could be combined following the rules of alignment, regularity and symmetry to form standard building parts such as porches, vestibules and rooms, which in turn could be combined into various whole buildings, again following the rules of alignment, regularity and symmetry. (Ibid.) The advancements in building technology broke with classical restrictions of geometric configuration in architecture. The advent of the 20th century saw a massive increase in building tasks. Architectural 70

72 composition finally shook off the classical restrictions of global geometric prefiguration, symmetry and proportion. The compositional process could now proceed from inside out, with nearly total openness with respect to the final configuration. (Ibid.:261) Looking back at architecture, Schumacher sees that modernism also re-articulated the way we do drawings as hierarchical types. Since the refoundation of the discipline in the early 1920s, the architect's design world has thus been a singular and stable system of hierarchically scaled line drawings. From the scale-less (topological) sketch to the working drawings, this world distributes nothing but outlines and boundaries. Everything is about the distribution of horizontal and vertical planes. The meaning of each drawing resides in its position and role in the chain of translation from one drawing to the next (more detailed) drawing, and from there to the construction process and the building itself. (Ibid.) Ordinary diagrams are opposed to extra-ordinary diagrams in terms of what they symbolize. Ordinary diagrams are agreed upon, while extra-ordinary are open-ended. The concept of an ordinary diagram that is firmly lodged in a routine practice is the model against which the extra-ordinary diagram is defined. The extra-ordinary diagram is a diagram in the sense that Deleuze distinguishes diagrams from representations. A Deleuzian (extra-ordinary) diagram is an abstract machine that is valued precisely because its downstream implications are totally open. (Ibid.) Avant-garde, in general, operates extra-ordinary diagrams. At least from the mid-1980s to the late 1990s, virtually all avant-garde design efforts were conducted through such Deleuzian 'diagrammatic' processes. Such design processes are as open-ended as they are unpredictable. (Ibid.:262) Ordinary and extra-ordinary diagrams are orthogonal to the metric and parametric, hence they are not mutually exclusive categories, and operate orthogonal to each other, so that each side of each distinction can be combined with each side of the other distinction. (Ibid.) A second distinction is that of the metric and parametric diagrams, which is concerned with the internal constitution of the diagram. Parametric diagrams emerged as extra-ordinary diagrams as animation. From the mid-1990s parametric diagrams started to emerge, first in the form of animations. These were extra-ordinary parametric diagrams with in open-ended design research explorations. Today most of us have switched to work with ordinary parametric diagrams, that is to say we know in advance what we are aiming for. (Ibid.) Schumacher thinks of parametricism as the new nature introduced by the ubiquity of computers in architecture. 11 Figure: (accessed ). 71

73 Parametric diagrams rely on digital technology. The first generation of parametric diagrams entered architecture via the use of animation software allowing for versioning and intuitive form-finding by means of the continuous deformation of topologically defined surfaces or by means of inverse kinematic constructs. (Ibid.:264) Parametric diagrams are self-categorizable, as their nature is explicit. The stability or recognisable self-identity of parametric diagrams against the backdrop of shifting parameter inputs rests on the powerful possibility to 'link' or 'associate' parameters by defining correlations (dependencies) between them. (Ibid.) Figure 1.25: Network script accentuates undulated surface Maren Klasing & Martin Krcha, Masterclass Hadid, University of Applied Arts, Vienna. 12 A more elaborate characterization of the diagram by Schumacher, or how they come into being. In principle, any conceivable network of relations between a given set of element attributes can be constructed. Scripting languages started to open the hood and allowed us to be creative on the molecular and even the atomic level. On the other hand, there is no principled limit (except computational limits) to taking (or building) dynamic 'primitives', or complex components, and building up complexity by associating whole swarms of them, then correlating different swarms, and so on: the demiurge-like freedom to link any parameter/property of any object with arbitrary parameters/properties of any or all other objects within the model (as long as circularity is avoided). The realisation of this ability to set up whole chains of dependencies and the creative challenge to conceive such functions as the quasi-laws of nature of a new artificial universe was the moment at which I was first struck by the enormous potential power of parametric design for the organisation and articulation of social complexity as both static and dynamic condition. (Ibid.) In the last decade, parametric diagrams have moved from extra-ordinary diagrams to ordinary diagrams, from avant-garde to mainstream. Since the contemporary avant-garde has moved from a revolutionary stage to a cumulative stage of design research at least since 2000 the parametric diagrams employed transformed from extra-ordinary to ordinary parametric diagrams. This shift 12 Figure: Ibid. 72

74 from extra-ordinary to ordinary parametrics often goes hand in hand with a more rigorous employment of computationally advanced design techniques such as scripting (in Mel Script or RhinoScript) and parametric modelling (with tools such as Generative Components or Design Project). (Ibid.:266) The move from extra-ordinary to ordinary parametric diagrams are both important towards architectural progress, he finalizes. Extra-ordinary parametric diagramming is not obsolete, and it might continue to take place on the highest level of technical sophistication. It is precisely the richness of this new world of associative design that still demands and rewards open-ended (extraordinary) diagrammatic design explorations into the abstract world of relational logics without a preconceived path of translation into the design-world where parametric models offer concrete solutions to clearly stated design problems. (Ibid.) Figure 1.26: Adidas Originals Superstar Supershell in Collaboration with Pharrell Williams, Zaha Hadid Architects Remarks In The Autopoiesis of Architecture: A New Framework for Architecture, Schumacher (2011) put together a 1,200 page book in two volumes, dedicated to the 2014 Pritzker Architecture Prize, Zaha Hadid. It is a groundbreaking, benchmark book where he presents 60 theses on architecture. Clear, strong, sharp, each thesis is undoubted, defined, and worked out with a precision that a white coat scientist would celebrate. It explains everything there is to know about the current state of our tradition. It is impressive because it seems to be the philosophical negative of the global condition that we celebrate in this work. On the global network there are no unique truths or fixed definitions, and all-encompassing gestures seem authoritarian. On the global network, borders are re-articulated: politics, genders, meters, values, currencies. There are no enclosed systems because we celebrate that we can all 13 Figure: (accessed ). 73

75 be connected and that we can all talk to each other. The global network does not define objects; it characterizes them from many indexes. Foundations are in motion, origins are everywhere, and what is measured is probabilities. Political stabilities on the global network are not constructed by theories or manifestoes, but rather by affirming infinity and articulating meters that are rooted in a symbolization within probability space by meters that are outside linguistic understandings, outside right and wrong, beautiful or ugly. These are the meters we celebrate from the online applications, those that we are trying to cultivate and further show in chapter 2. [6/9] Toward an Understanding of Form in Architecture critic, design, communication, idea, concept, function, structure, technics, form, movement Figure 1.27: House I, Eisenman Peter Eisenman 15 discusses form in architecture in this document from He argues that architecture in general can be thought of in terms of form, regardless of style. Hence, the promise of such discussion is to establish a common ground to articulate architecture as a 14 Figure: (accessed ). 15 Peter Eisenman does not talk about architecture and computing. Nevertheless, his work addresses questions that interest us. Throughout his writings, he seems to be interested in articulating an architecture beyond form or physical experience, an architecture that is open to interpretations and tells non-linear and rich stories full of indexes pointing from outside the artifact s temporality and form. He considers himself a mentor of Rem Koolhaas, with whom he is utterly direct and honest [1]. He was born in New Jersey, U.S., and is considered one of the New York Five [2]. Eisenman is Professor in Practice at the Yale School of Architecture and is recognized by his extensive writing and award winning buildings all around the world. [1] See an interview in the context of the Venice Biennale of Architecture, 2014 at (accessed ). [2] See (accessed ). 74

76 totality in times when the society is becoming overwhelming and no significant order can be found anymore. I am putting forth a few ideas that may help clarify the relationship of form to any architecture. It will be my contention that formal considerations are basic to all architecture regardless of style, and that they alone can help us to develop an agreed language both for criticism and for design. (Eisenman 1963:3) His initial assumption is that any architectural artifact communicates the author s ideas. Communication must be clear and sharp, and must address fundamental elements of architecture. Initially the essence of any creative act can be thought of as the communication of an original idea from its author, through a means of expression, to a receiver. The means of expression must be such as to transmit the original intention as clearly and fully as possible to the receiving mind. All of these elements contribute to the architectural equation, and I shall name them as concept, or intent, function, structure, technics, form. (Ibid.) For Eisenman, the lack of clarity when addressing one of these five elements, or their absence at all, is what causes an architecture of confusion. And he believed that today (1963), more than ever, order needed to be established since society had become so overwhelming. The uncoordinated or non-rational invoking of this or that element is a root cause of the architectural confusion that all too often confronts us. we must establish a basic priority in architecture which is evolved from the dialectic between relative and absolute ends. The proposing of this priority is of critical importance today since our social, economic, and technological environment has become so overwhelmingly distended that no significant order can be perceived by the individual. (Ibid.:4) Eisenman presents a definition of architecture that places form as its most important element. His definition stands out from his contemporaries by presenting a different articulation of form in architecture. my contention will be that architecture is in essence the giving of form (itself an element) to intent, function, structure, and technics. In stating this I raise form to a position of primacy in the hierarchy of elements. To claim supremacy for form in this way is to adopt an original standpoint, despite the fact that all academic and rationalist thinking well into this century would have placed formal considerations above all others. (Ibid.:5) The initial assumption for Eisenman s argument is that there are two types of form, ideal and real, or in terms of communication models, the form-message on the sender s side and on the receiver s side. If this position is to be sustained we must first make a vitally important subdivision of the general category form into two types generic and specific. By generic form I here 75

77 mean form thought of in a Platonic sense, as a definable entity with its own inherent laws. By specific form, on the other hand, I mean the actual physical configuration realized as a result of a specific intent and function. (Ibid.) For Eisenman, the specific form is the architectural artifact, that which communicates the author s ideas, i.e., the synthesis of intent, function, structure, and technics. The specific form is unique and of less importance than a generic form. The same conclusion is reached when we consider the much-canvassed form-function interrelationship. Since no one function can do more than suggest a specific form (i.e., it cannot determine it); in other words, since there is no one form for any function, specific form can be considered to be of a relative nature (relative, that is, to a particular interpretation of a program) and therefore of a lesser degree of importance in the hierarchy than generic form. (Ibid.) Figure 1.28: House II, Eisenman For Eisenman, intent is the very initial idea that leads toward the specific form, i.e., to build a temple, the architect should have an idea or concept of temple. All specific form in architecture is conceived initially from the critique of two of the elements, intent and function A further definition of intent will perhaps substantiate the point: the word is here used to mean the primary conception of a thing. Hence the close association between intent and function; we must always have the concept of something before we can envisage a function for it. (Ibid.:6) Even when an architect s initial ideas can be thought of as semiotic signs, Eisenman suggests not to confuse them with an arbitrary symbolization of the world in which the specific form (the artifact) will exist. One must also be careful not to confuse symbolic function with intent. Symbolic function is the representation of a transcendental idea. In architecture the inherent difficulty that 76

78 arises here is that the types of specific form in common use change with each succeeding age, and therefore their meaning as symbols tends to be different for each generation. (Ibid.) To elaborate on the idea of specific and generic form in relation to intent and function, and to semantic predefinitions and symbolizations of the world, Eisenman continues with the example of the concept of dome in a temple. A religious leader might think of this same structure in its mystical connotations and its relation to church liturgy. A psychologist might think of its sexual associations, and so on. These are all types of responses to the percept dome as a specific form. But there is also a range of responses to the concept dome which are of a generic nature. A dome is centroidal. It is equally expansive in all directions. It suggests centrifugal motion. These are formal absolutes, although of course they must be realized in terms of the particular problem before we can say that we have the proper specific form, the actual shape of dome, appropriate to the specific circumstances. It is only when we establish a specific form from utilitarian function that we can, by analyzing the properties inherent in the generic form, test their relevance to the specific conditions. (Ibid.:7) Eisenman uses the skeleton and the ligaments metaphorically to talk about the structure and the technics of an architectural artifact. Structure may be thought of as the bones, veins, and arteries of any building. It is the framework for the translation of intent and function into physical reality. If structure is the skeleton, then technics are the ligaments of any building. (Ibid.:8) For Eisenman, the challenge of structure is to have an understanding between the structural economy and the scale, so to accommodate the maximum number of specific functions. The rest seems to be established by the form s intent and function. Decisions as to structural form are thus seen to be derived ultimately from generic form. There is no limitation arguable from the other elements which can dictate whether a column is to be round, square, cruciform, rectilinear, etc. (Ibid.) For Eisenman, architecture is experienced visually. Such appreciation should aggregate a conceptual clarity, and that s architecture s goal. To understand architectural form we must introduce the notion of movement and postulate that an experience of architecture is the sum of a large number of experiences, each one of them apprehended visually (as well as through other senses), but accumulated over a much longer time span than is required for the initial appreciation of a pictorial work, and building up into a conceptual, not a perceptual, whole. Since this whole is conceptual it must have a clarity of concept; and therefore its argument must be 16 Figure: (accessed ). 77

79 intellectually as well as visually comprehensible. (Ibid.:9) To argue for a clarity of form seems to belong to another paradigm, as he sees unfortunate a lack of clarity or of a logic-based synthetic approach. Our paradigm revolves about the probable and the unknown. The need for formal clarity and unmistakable reference to some well-understood archetypal solid thereby becomes still more urgent, since the person experiencing it must be able to hold in his visual and somatic memory at the end of the process everything which has impinged upon it since the beginning. Only an architectural logic based on generic form can achieve this; nevertheless it cannot be too strongly emphasized that the end product can only be a synthesis of form with all the other elements of the equation. (Ibid.) Figure 1.29: House III, Eisenman This is how Eisenman discusses form in architecture beyond aesthetics or styles. It aims to establish an architectural logic based on form. This clearly demonstrates that the giving of form is far more than the making of shapes, or the creation of beautiful or aesthetically pleasing objects in themselves. But rather it is the presentation of an order, whether it be directed toward the clarity of concept and function of a specific building, or toward the clarity of the relationship between the individual building and the total environment. Form is therefore specific yet at the same time general. It is architecture's particular means of expressing intent and accommodating function, and it is its general means for creating an ordered environment. (Ibid.) In Eisenman s work we see an architecture characterized as a synthesis of form. It is not the synthesis from the analysis of a deep structure, but rather the synthesis of double-articulated elements: intent-function and structure-technics. These two elements address the ideal and the real, the generic and specific, semantic definitions and symbolizations of the world. 17 Figure: (accessed ). 78

80 [7/9] Architecture as a Second Language text, structure, traces, dislocation, multi valencies, time-space, narrative, author, source, meaning Figure 1.30: Dorothy Vallens played by Isabella Rossellini, David Lynch Eisenman elaborates an interesting argument on dislocating multi valencies. He presents text as a code to articulate architecture free from fixed ontologies, semantic pre-definitions, and causal relations. With text, Eisenman aims to dislocate a singular time in architecture, i.e., to include any time-space to the articulation of an architectural artifact. It resonates with our, at this time intuitive, understanding and interest in the index. Eisenman s dislocation of time-space and our indexicality seems to be addressing similar questions around fixed definitions and understandings of an object. Eisenman presents text as a handy structure to challenge established architectural narratives. Text goes ad infinitum. For the purpose of this discussion a more specific use of the term text, which incorporates two recent developments, will be used. In the first of these developments, text is not so much the representation of a narrative but rather the representation of the structure of the form of the narrative. In the second, text is no longer something complete, enclosed in a book or its margins, it is a differential network. A fabric of traces referring endlessly to something other than itself. (Eisenman 1988:227) Eisenman s interest is in discussing how the idea of an infinite text can challenge established readings of architecture. What do these developments of the idea of text mean for architecture? What is an architectural text and how can it inform a strategy for dislocation? (Ibid.) To talk about text in architecture seems to be unnatural to the tradition. In text, time and space do not necessarily match; in an architectural artifact, time and space can only match. Architecture, because of its presence, its here and now, its time and space specificity, was traditionally seen as necessarily univocal. Thus, it would be resistant to the 18 Figure: Still frame from Blue Velvet. 79

81 dislocating multi valency of text. The implications for an architecture of texts would be the same as that of the second language, in other words, non-originary and unnatural. (Ibid.:228) Eisenman takes film as an exemplary medium for time-space mismatch. Film is the master medium of dislocation. Since the terms of the natural in architecture have always been thought to be the specificity of time and place, it might be useful to examine this textuality, the dislocation of time and place, in another medium. Film is a discourse that is constantly impacted by a second language. Film is the sine qua non of a dislocated place and time because it always has at least two times and two places: the actual time and place of watching, and the narrative time and place. (Ibid.) Specifically, the movie Blue Velvet by David Lynch renders his argument into film, and gives direction for possible answers. For example, in David Lynch's film Blue Velvet, the story, but not the text, is about an average young American couple in a small town in North Carolina in the fifties and their adventures related to a bizarre murder in the town. In fact it is about the dislocation or the dissolution of narrative time in film seen as a natural or first language. All of the icons which are used in this film in a seemingly innocuous and straightforward way set up a condition whereby the space of narrative time in the film is dissolved. (Ibid.) The scene described links to different temporalities. Time is dislocated, references are crisscrossed, linearity and causality are given up. This is accomplished particularly, though not exclusively, through the soundtrack. For example, the lead song, Blue Velvet, is from 1951, when it was sung by Tony Bennett. It was restylized by a group called the Statues in 1960, and that version was covered by Bobby Vinton in 1963 (which is the version used in the film). So there is already a first temporal dislocation in the soundtrack itself. In the film, the star, Isabella Rosselini, sings the same song in a nightclub over a microphone which is certainly of a 1940's vintage, if not earlier. (Ibid.) In this example, the film s image of sound is dislocated. Blue Velvet is textual in that one of its intrinsic image components, sound, is not about the film's narrative structure of a time and place in the fifties. The complex and intentional tissue of superpositions of future and past create a temporal dislocation. (Ibid.) He argues that this other text of the movie is relevant to architecture due to its aesthetic value and the dislocation of time-space it presents. The dislocation of narrative time in Blue Velvet is exemplary for the case of text in architecture for two reasons: because it illustrates another text in an aesthetic medium, but more importantly, because of its dislocation of the concept of an internal time or time of narrative. (Ibid.:229) 80

82 Figure 1.31: The Project of Campo Marzio, Eisenman and Yale University School of Architecture Architecture is bad at telling linear stories, and architecture s continuity is somewhere else, Eisenman argues. Architecture, unlike literature or film, has never had the capacity to contain or display a linear or internal time. This has problematized the concept of an architectural text. (Ibid.) Architecture as a Second Language addresses the following question: How could time be introduced in architecture itself, if an artifact can only explicitly display a single temporal dimension? [ ] architecture as text does not reside in the aesthetic or functional presence of the object, but rather as a state of between. Therefore, textual time can be introduced into architecture to produce an architecture which dislocates not only the memory of internal time but all the aspects of presence, origin, place, scale, and so forth. (Ibid.) These questions challenge well established concepts of origin and authorship in architecture. They open up meanings and interpretations, leaving interpretation to whoever reads the text. A dislocating architecture confronts originary or authorial value; it does not represent an original source or imagery or figuration; nor does it represent the uses of an object or even an outside discourse. Dislocating architecture displays its multiple meanings by representing the various relationships between other texts, between an architectural text and other texts. (Ibid.) A dislocating event brings up the question of origin. A dislocating text is always a second language. (Ibid.) For Eisenman, whatever is called a natural reading of architecture today was an authoritative gesture yesterday. Any interpretation of a text which is thought to be natural to the discourse of architecture can be called a text of authority, that is, given correctness and value by architecture itself. 81

83 Architecture is constantly writing texts of authority without realizing that it is engaging in this activity. (Ibid.:230) And architects write texts claiming that it is the correct way to read artifacts, or in some cases, the correct way to read the tradition itself. Representation is a false authority that suggests some sort of correct truthful relationship between the object of architecture and what it is signifying. The idea that the classical orders or a functional type is natural to architecture is an example of the representation of presence. (Ibid.) And this is the difference with a dislocating text: It challenges any pre-text by presenting an alternate text, vast, fast, and full of indexes. The dislocating text attacks the terms by which presence is represented, that is, that origin, beauty, function, truth are natural (i. e., authentic) and not conventional to architecture. The dislocating text does not deny function or beauty but denies their authority and thus shifts the perception of them. (Ibid.) Origins then are set in motion. A dislocating text in architecture confronts this idea of originary (or what is thought to be the originary) or authorial value; i.e., that there is a correct way to read the object. A dislocating text is or represents the various relationships between these other texts. In this sense, text is always a strategy which seems to be dislocating and thus a second language. (Ibid.) A dislocating text for Eisenman, in a nutshell: In a dislocating text the object is seen and read as different, as between its abstract and necessary object being and some known iconic form, which in its iconicity contains the traditional architectural text. Dislocating texts refuse any single authoritative reading. They do not appeal to the logic of grammar or the reason of truth. Their truth is constantly in flux. Although they are directed, they are authorless. They are directed in the sense that they suggest a way of reading which seems to be internal to the object. But, at the same time, they deflect any single reading. (Ibid.) For Eisenman, the text is the code for articulation and exchange, a general equivalent for an economy of architectural readings. Text is then perhaps a term that can be used for any and all strategies and conditions which dislocate architecture from its authorial or natural condition of being; that is, the detaching of what architecture looks like from the need to represent function, shelter, meaning, and so forth. (Ibid.) What does a dislocated text of an architectural artifact look like for Eisenman? The Romeo and Juliet project for the castles of the same name outside of Vicenza in Montecchio for the Venice Biennale 1986, because of its already having in place an other 82

84 text, that is, the play by the same name, presented an ideal opportunity to present an architectural text that was no longer guaranteed by the tradition of architecture. (Ibid.:231) Eisenman s setup places architecture in-between interpretations. It stays open. Most importantly, the received system of meaning, i.e., the cultural significance of a form, is denied without denying the form, but now the forms in themselves have neither transcendental nor a priori meanings. They are cut off from the authority of their former singular significance. The architecture is between the signs. (Ibid.:232) How come this idea is not discussed? How come it s not in the air? Eisenman asks himself. The question is why the idea of text in general, and more specifically, a dislocating text, has been resisted or repressed in architecture. Perhaps because this idea of text removes the restraint of morality, that is, the responsibility of form to the traditions of architecture. (Ibid.:233) His answer, in short: because it is disruptive. Therefore, the idea of a text between is necessarily dislocating. It does violence to the former celebrations of architecture as an object of desire (of an aesthetic pleasure); as a reification of man (anthropomorphism and human scale); as an object of value (truth, origin, and metaphoric meaning). Such a between text is not place specific, time specific, or scale specific. It does not symbolize use, shelter, or structure. Its aesthetic and history are other. Its dislocation takes place between the conventional and natural. Thus, what is being violated is the maintenance of the system as a whole. (Ibid.) This is Eisenman s question for architects: how to dislocate time? We see in indexicality the ability to articulate architecture, its artifacts included, decoupled form a linearity of time and space. An indexical architecture celebrates its implicit and explicit links, not imposing readings, but rather engendering readings. We think that an indexical architecture s stability is rooted in this indeterminacy, in probabilities and ratios. The next two chapters will return to this question. 83

85 [8/9] Diagram: An Original Scene of Writing ideogram, value, meaning, explanation, analysis, generation, representation, interiority Figure 1.32: Church of the year 2000, Eisenman Eisenman presents the diagram as a generative device that unveils an architecture s interiority. We read this as the formalization of the concept of text in architecture discussed in Architecture as a Second Language (chapter 1.3.8). When compared to text, diagrams are more familiar to architecture, and even when they do not follow fixed scale, proportion, or aesthetic, they are also capable of indexing the events of the world, for instance. We think of a diagram not as a generative device, as Eisenman proposes, but rather as a moment of condensation that comes from an infinite circulation of information that is outside the object. Eisenman re-articulates the concept of diagram so to bring new light to the tradition of architecture. He reviews some characterizations of diagrams in architecture. Generically, a diagram is a graphic shorthand. Though it is an ideogram, it is not necessarily an abstraction. It is a representation of something in that it is not the thing itself. In this sense, it cannot help but be embodied. It can never be free of value or meaning, even when it attempts to express relationships of formation and their processes. At the same time, a diagram is neither a structure nor an abstraction of structure. While it explains relationships in an architectural object, it is not isomorphic with it. (Eisenman 1999:27) For Eisenman, the diagram in architecture is a device that can be used in two ways, for analysis or generation. In the latter, Eisenman sees a way to articulate what he calls architecture s interiority. In architecture the diagram is historically understood in two ways: as an explanatory or analytical device and as a generative device. In an analytical role, the diagram represents in a different way from a sketch or a plan of a building. As a generative device in a process of design, the diagram is also a form of representation. But unlike traditional forms of representation, the diagram as a generator is a mediation between a palpable 19 Figure: (accessed ). 84

86 object, a real building, and what can be called architecture's interiority. (Ibid.) There are some historical traces for Eisenman that point to this understanding of the diagram. He looks at the lines on a paper, that layer by layer and all together generate a diagram that can be distinguished from, let s say, the construction plan. In many of these drawings from late Gothic architecture to the Renaissance the overlay does not actually take all of the diagrammatic imprint, only partial traces of it. The quality of the ink on the page changes where it runs over the diagram as opposed to the places where the diagram is actually part of the plan of the building. (Ibid.:28) The architecture s interiority, Eisenman argues, manifests itself through these diagrams. Diagrams are indexes of past events and present chance. These lines are the trace of an intermediary condition (that is, the diagram) that exists between what can be called the anteriority and the interiority of architecture; the summation of its history as well as the projects that could exist are indexed in the traces and the actual building. (Ibid.) An example of such a diagrammatic process in history. As Kurt Forster notes, in the late Gothic, for example, there is a diagrammatic process that leads the schematic articulation of foliage on column capitals to change from a stylized or conventional nature with bilateral symmetries to a more naturalistic, free-form nature. Such a process differs from the straightforward manipulation of geometry that was the tradition in Gothic leaf capitals. (Ibid.) The diagram is not the artifact nor the construction drawings; it is that moment in-between. Here the diagram acts neither as geometry nor as the existent capital. It is a trace or phantom, which acts between something which can be called the interiority of architecture and the specific capital; between some explicit geometric formation which is then transformed by the diagram or intermediary process onto a result. (Ibid.:29) Eisenman places his diagram next to philosophical and psychoanalytical accounts. The first challenge for Eisenman s diagrams is introduced by Deleuze, who thinks of the diagram as a perpetual entropic state from which any taxonomic gesture defeats its purpose. The second point that Deleuze makes is that the diagram is different from structure. The classical architectural idea of a diagram exhibits a belief in structure as something that is hierarchical, static, and has a point of origin. Deleuze says that a diagram is a supple set of relationships between forces. It forms unstable physical systems that are in a perpetual disequilibrium. (Ibid.) A diagram is for Deleuze an abstract machine that extends itself ad infinitum and oscillates between that which Eisenman would call the history and the probability of an architectural artifact. a diagram is no longer an auditory or visual archive, but a map, a cartography that is 85

87 coextensive with the whole social field. It is an abstract machine. (Deleuze 1988:30) This abstract machine is defined by its functioning in unformed matter, as a series of processes that are neither mechanical nor organic. The diagram then is both form and matter, the visible and the articulable. (Ibid.:30) And this is the gap that Eisenman wants to close with the diagram, i.e., he wants to materialize the history and chance of an architectural artifact. Diagrams for Deleuze do not attempt to bridge the gap between these pairs, but rather attempt to widen it, to open the gap to other unformed matters and functions which will become formed. Diagrams, then, form visible matter and formalize articulable functions. (Ibid.) Figure 1.33: Virtual House, Eisenman Eisenman finds in Derrida s ideas on writing and memory, an argumentation that aligns with his notion of the diagram as the object in-between. For Derrida, writing is initially a condition of repressed memory. The repression of writing is also the repression of that which threatens presence, and since architecture is the sine qua non of the metaphysics of presence, anything that threatens presence would be presumed to be repressed in architecture's interiority. In this sense, architecture's anteriority and interiority can be seen as a sum of repressions. (Ibid.:31) Writing is a mnemonic device that can be compared to an architectural plan, but the traces of writing are what concerns Eisenman. Because it is there, in the traces, where the interiority is exposed. In architecture, literal notations can produce a plan but they have nothing to do with the diagram, because a plan is a literal mnemonic device. A plan is a finite condition of writing, but the traces of writing suggest many different plans. This is the idea of the trace that is important for any concept of the diagram, because unlike a plan, traces are neither fully 20 Figure: (accessed ). 86

88 structural presences nor motivated signs. Rather, traces suggest potential relationships, which may both generate and emerge from previously repressed or unarticulated figures. But traces in themselves re not generative, transformative, or even critical. (Ibid.:32) Freud s concept of the Mystic Writing Pad (1925) is also placed in line with Eisenman s diagram. They both operate similarly, as devices for layering in a generative process. The architectural diagram, like the Mystic Writing Pad, can be conceived of as a series of surfaces or layers which are both constantly regenerated and at the same time capable of retaining multiple series of traces. (Ibid.:33) The diagram is understood as the visible of the articulable. In this context, architecture becomes more than that which is seen or which is present; it is no longer entirely a representation or an illustration of presence. Rather, architecture can be a re-presentation of this intervening apparatus called the diagram. In this sense, the diagram could be understood to exist before the anteriority and the interiority of architecture. It exists as the potential space of writing, a writing which supplements the idea of an interiority before perception. (Ibid.:34) His conclusion: The diagram is an intermediary condition, an agent. The diagram acts as an agency which focuses the relationship between an authorial subject, an architectural object, and a receiving subject; it is the strata that exist between them. (Ibid.:35) For Eisenman, the diagram runs forever, but never fully automated. It is about overcoming the architect s repression, making it both a rational and mystical generation. The diagrammatic process will never run without some psychical input from a subject. The diagram cannot reproduce from within these psychical conditions. The diagram does not generate in and of itself. It opens up the repression that limits a generative and transformative capacity, a repression that is constituted in both the anteriority of architecture and in the subject. The diagram does not in itself contain a process of overcoming repression. Rather, the diagram enables an author to overcome and access the history of the discourse while simultaneously overcoming his or her own psychical resistance to such an act. Here, the diagram takes on the distancing of the subjectauthor. It becomes both rational and mystical, a strange superposition of the two. (Ibid.) We see in Eisenman s gesture an attempt to formalize that which is not visible in an architectural artifact as a production process. He is trying to materialize, specify, taxonomize, all the indexes or the dislocations that come from an artifact. In this same line of argumentation as Eisenman, we index Bernard Tschumi s and Daniel Libeskind s work. Bernard Tschumi presents a number of drawings that propose to transcribe an architectural representation of reality. He argues that the drawings explicit purpose is to transcribe things normally removed from conventional architectural representation, namely the complex relationship between spaces and their use; between the set and the script; between 87

89 type and program ; between objects and events (Tschumi 1994:7). For him, the origin of architecture is a reality already in existence and generally excluded. He further talks about the operations that can be performed to this reality, for which he proposes to break it down into three different words: of objects, of movements, and of events (Ibid.:8). Such categorization makes easy its analysis, transformation, and symbolization as a reality s drawn-architectural representation. He presents some of these drawings in The Manhattan Transcripts (1994). Figure 1.34: Greater Columbus Convention Center, Eisenman As an explicit rendering of the inclusion of the kind of phenomenon just discussed by Eisenman and Tschumi, Daniel Libeskind presents the Three Lessons in Architecture: The Machines (1985). An installation that consists of three large machines for the public to create and interpret architecture. The three machines propose a fundamental recollection and a retrieval of the historical destiny of architecture; a singular, if unexpected, homecoming (Libeskind 1985). Once the machines are in motion, he argues, the arrangements appear ready for interpretation from (1) the architecture s techne, or an almost forgotten (medieval) process of building ; (2) a historical program, or that which can still be remembered in architecture ; and (3) an industrialized poetic of architecture. For Libeskind, the symbolization of an existing reality to poetry as well as the symbolization of the tradition of architecture are literally set in motion by a subject to generate and interpret architecture Remarks Eisenman shows in his writings an interest in what can be articulated beyond architecture s physical experience, beyond elegance, beauty, or style. He talks about form as a synthesis towards the communication of an author s ideas. He is interested in the circulation of these ideas, and sees in the text a very helpful code for their economy. We see Eisenman s concept of 88

90 text as an affirmation and celebration of infinity. He thinks of it as a fabric of traces that endlessly points to something outside itself. Celebrating infinity is to celebrate what he calls multi valencies, multiple lines joining points, multiple reasons created from infinity. To place next to each other a metaphysics of architecture and film is interesting for us as well. To be able as a spectator to identify indexes to other time-space in a scene or in architecture while at the same time knowing that there are infinitely more indexes that we cannot see, and that the ones that we do see may be different from those that the spectator next to us perceives, and that we are all able to talk about them, resonates with our work. He warns us that these ideas can be seen as disruptive, though, because if we celebrate them, origins start appearing without control, foundations are put in motion, truths multiply each other, doubt is introduced, spaces open up, centralities vanish, everybody becomes an expert, and authoritarian theories lose their grip. In short, our old meters and values just don t do the trick anymore. We see that. We also see that we can learn from the global network to construct new stabilities, because the applications on the global network do it all the time, and what we can tell so far is that they are all rooted within the probability space. This is our intuition at this point, but it will be graspable towards the end of this work. Eisenman talked about celebrating infinity 20 years ago, and since he has been building and teaching since then, we would expect his artifacts to be discussed like he does, but instead what we see is architects like Charles Jencks talking about them as post-modern artifacts (Jencks 2002). An open question: Did Eisenman renounce to his ideas, or are we just not able to see them? We introduce now a voice that recognizes the power of authorship and origins in architecture, Mario Carpo s. He claims that technology is challenging these concepts, and furthermore, that this challenge is a reason to worry. 21 Figure: (accessed ). 89

91 [9/9] The Alphabet and the Algorithm modernity, authorship, original, copy, standardization, variability, hand-making, digital-making Figure 1.35: Medieval architectural practice. 22 Mario Carpo 23 places computer-aided design tools in line with the tradition of architecture from the Renaissance until today. He argues in his book that the main challenges that computers present today are around the origins and standardization of architectural artifacts, i.e., who and where is the author? What is an original artifact and what is its copy? And, how does the mass production of variability challenge the established economies of scale based on identicality? This work will trace the rise of some aspects of modernity that have marked the history of Western architecture. They all relate to one key practice of modernity: the making of identical copies of nature, art, objects, and media objects of all sorts. (Carpo 2011:ix) This chronicle situates today s computational tools in architecture within the ambit of a centuries-old tradition, with all of its twists and turns, of which the digital represents the most recent. Technologies change rapidly new technologies in particular. (Ibid.:xi) He identifies two important moments in the tradition of architecture that index the current established notions of authorship and mass production, notions that are directly challenged 22 Figure: Laon cathedral tower, ink on vellum, from Villard de Honnecourt, Ms. fr , folio 10. Cliché Bibliothèque nationale de France, Paris. 23 Mario Carpo is an architectural historian, professor at the University College, London. He specializes in the history of architectural theory and history of cultural technologies, with a focus on the classical tradition and contemporary digital design theory [1]. He has written several books and articles, many of them in Italian with no available translation, and has held over 18 different positions as educator. He holds a Dr.Arch., PhD., and HDR titles. Carpo is a traditional educator who is non-traditionally concerned with contemporary interplays of architecture and computing. [1] See Wikipedia s entry on him at 90

92 today by digital design tools. Two instances of identicality were crucial to the shaping of architectural modernity. The first was Leon Battista Alberti s invention of architectural design. In Alberti s theory, a building is the identical copy of the architect s design; with Alberti s separation in principle between design and making came the modern definition of the architect as an author, in the humanistic sense of the term. After Alberti s cultural revolution, the second wave of identical copies in architecture came with the industrial revolution, and the mass production of identical copies from mechanical master models, matrixes, imprints, or molds. Industrial standardization generates economies of scale so long as all items in a series are the same. (Ibid.:x) The power of the author and the copy comes to an end when the digital design and production tools directly challenge the power of the identical, which is at the core of the mass production of artifacts. The modern power of the identical came to an end with the rise of digital technologies. All that is digital is variable, and digital variability goes counter to all the postulates of identicality that have informed the history of Western cultural technologies for the last five centuries. In architecture this means the end of notational limitations, of industrial standardization, and, more generally, of the Albertian and authorial way of building by design. (Ibid.) The values that we look for in our artifacts are pretty much indexed by their production tools and techniques. With every introduction of novel tools, the values of the objects also change. In the world of hand-making that preceded the machine-made environment, imitation and visual similarity were the norm, replication and visual identicality were the exception. And in the digital world that is now rapidly overtaking the mechanical world, visual identicality is quickly becoming irrelevant. (Ibid.:3) Carpo sees his story rendered in the changes that money has had throughout history. We think of these changes as those discussed with Negroponte: traditional objects become computational objects that are constantly re-articulated, i.e., industrial objects today are becoming computational, as before handcrafted objects became industrial. these monetary examples illustrate three paradigms of visual identification, essentially related to three different ways of making things. The signature, the banknote, and the credit card: when objects are handmade, as a signature is, variability in the processes of production generates differences and similarities between copies, and identification is based on visual resemblance; when objects are machine-made, as a banknote is, massproduced, exactly repeatable mechanical imprints generate standardized products, and identification is based on visual identicality; when objects are digitally made, as are the latest machine-readable or chip-based credit cards, identification is based on the recognition of hidden patterns, on computational algorithms, or on other nonvisual features. (Ibid.:4) 91

93 Automated variability is a new condition presented by digital technologies, Carpo argues. Variability can now become a part of an automated design and production chain. Indeed, this is what the most alert users of digital technologies have been doing for the last fifteen years or so artists and technologists as well as entrepreneurs and capitalists. (Ibid.:7) As an example, Carpo suggests looking at the personalized ads on our web browsers. As is well known, various features of many web pages are now automatically customized based on what the page makers know of each individual page user. This is why the advertising (and increasingly, the content) which appears on some of the most popular web sites differs based on the computer, the browser, network, or protocol we use to access those pages, and varies according to the time of day, the geographical location of the user, and a number of other arcane factors that are well-protected trade secrets. (Ibid.:8) The phenomenon presented by Carpo, in a nutshell: So it seems, to sum up, that in the long duration of historical time the age of massproduced, standardized, mechanical, and identical copies should be seen as an interlude, and a relatively brief one sandwiched between the age of hand-making, which preceded it, and the digital age that is now replacing it. Hand-making begets variations, as does digital making; but the capacity to design and mass-produce serial variations (or differentiality) is specific to the present digital environment. (Ibid.:10) The massive variability is the new normal. Massive variability is not special anymore. Unlimited visual variability, however, may entail a loss of visual relevance: signs that change too often or too randomly may mean less, individually taken, and may in the end lose all meaning. (Ibid.) For Carpo, the tradition of architecture cannot be addressed without technology. Technology has always influenced the ways to design and build. So it is just expected that this new technology will also influence how to think and take actions. The history of architecture features a conflation of different technological timelines. Built architecture depends on the production of material objects (bricks, nails, iron beams, etc.), hence its modern history is linked to the traditional chronology of the industrial revolution. On the other hand, architectural design is a purely informational operation, and its processes are defined by a specific range of cultural and media technologies. For centuries the classical tradition was based on the recording, transmission, and imitation of architectural models. In turn, this tradition, or transmission, was and still is dependent on the media technologies that are available, at any given point in time, to record a trace of such models and to transmit them across space and time. (Ibid.:12) Architecture and the identical copy: a timeline that shows how it took time for architecture to adopt the industrial revolution and to think about industrialized artifacts. Throughout the nineteenth century, most architects either ignored or reacted against the 92

94 new technologies of industrial mass production. Then came the pioneers of modern architecture, and their wakeup call. As Le Corbusier and others began to claim in the early twenties, mechanization was changing the world, and architecture had to rise to the challenge. Architects should invent new architectural forms, made to measure for the new tools of mechanical mass production; and town planners should invent new urban forms, made to measure for the new tools of mechanical mass transportation. (Ibid.:13) The emergence of printed books had a remarkable influence on architecture. Well before the industrial revolution, however, another mechanical revolution had already changed the history of architecture. Printed books are a quintessentially industrial product. They are mass-produced. Mass production generates economies of scale, which makes them cheaper than manuscript copies. (Ibid.) The phenomena that Carpo is describing is not exclusive to architecture. Another revolution happened with the printing press, one that facilitated the production of architectural drawings. Before the invention of print, manual copies of drawings were famously untrustworthy, and as a result, images were seldom used, or altogether avoided, whenever precise copies were required. In such cases, nonvisual media (alphabetical or alphanumerical) were deemed safer. (Ibid.) With the new media for communication, architectural drawings were available everywhere and their reach of action increased. An architectural revolution. The advent of print reversed this relationship between text and images. All printed images in the same print run are notionally the same, for all and in all places. Both the makers and the users of images were quick to realize that, thanks to print, technical information could be recorded and safely transmitted in new visual formats. And a new architectural theory soon developed, made to measure for this new technical condition. (Ibid.:14) Carpo thinks of the Renaissance method as the first international style. The most successful spin-off of this media revolution was the new method of the Renaissance architectural orders the first international style in the history of world architecture. (Ibid.) Figure 1.36: Albrecht Dürer in The Painter's Manual, Along with the availability of mass produced identical images and projects, the modes of use are also distributed. A sort of instructions book. As it happens, at the very moment printed images were revolutionizing the transmission of 93

95 architectural models, another media revolution was crucially changing the way architects work. the project documents that Renaissance architects produced in growing numbers and forwarded to increasingly distant building sites a physical distance that went hand in hand with the growing intellectual and social estrangement between architects and builders. (Ibid.:15) The only technological innovation in Renaissance project drawings may well have been their very invention or the invention of their mode of use. (Ibid.:16) A new phenomenon occurred; the architect is now absent from the building site, but still claims authorship over the building even when the artifact is never experienced by the author or has no awareness of its existence. The traditional view, which attributes to early modern humanism the invention of the modern architect, and of his new professional role, rests upon some famous narratives: Brunelleschi s legendary struggle for the recognition of his role as the sole conceiver and master of a major building program; Alberti s radical claim that architects should be not makers but designers, and his definition of a modern notational system of scaled architectural drawings in plan and elevation that were the indispensable means to this end. (Ibid.:16) It was Alberti who conceived this humanist view of the modern architect. Along with the drawings, the notation tools to communicate the author's project were equally necessary. Alberti s distinction between building and design (lineamenta) is spelled out in various but unequivocal terms in the first, second, and ninth books of De re aedificatoria, and it is one of the foundational principles of his entire architectural theory. His new geometrical definition of architectural project drawings (and models) provided a consistent set of notational tools suited to his new, allographic way of building. (Ibid.:20) In this understanding, Alberti is not only the author of the drawings, but also the author of the building, as long as he is satisfied with its execution, as long as it is identical. An original, autographic work (for example, a painting made and signed by the artist s hand) is the unmediated making of its author. But in the Albertian, allographic way of building the only work truly made by the author is the design of the building not the building itself, which by definition is made by others. The only way for Alberti to claim an extension of authorship, so to speak, from the drawing to the building was to require that the building and its design should be seen as perfectly identical. (Ibid.:22) Alberti's theory in a nutshell, from Carpo s story: Alberti s entire architectural theory is predicated on the notational sameness between design and building, implying that drawings can, and must, be identically translated into three-dimensional objects. In Alberti s theory, the design of a building is the original, and the building is its copy. (Ibid.:26) The new notational tools always point to a scale-consistent model, even when the 94

96 measurements are not always given. Construction drawings generally contain some precalculated measurements in the form of digits inscribed in the drawing. All measurements that are not given as numbers, however, are shown only analogically by the length of segments drawn to a given scale. (Ibid.:30) This introduces a new kind of dependency between the model and the building, i.e., if it cannot be modeled, it cannot be built. If all that is built is built from notations, and if the drawings (or models) must contain all of the necessary data for an object to be built identically to its design, it follows that in most cases what can be built is determined by what can be drawn and measured in drawings. (Ibid.:31) These are the limits of the Renaissance model, a two-dimensional and handmade medium. This notational bottleneck was the inevitable companion of all allographic architecture from its very start. Forms that are difficult to draw and measure used to be difficult or impossible to build by notation. (Ibid.) One of the main differences with computer models is that three-dimensional models can be done from the beginning, avoiding the condition of two-dimensions in order to be built. Early in the history of computer-aided design (the actual chronology varies with the development and releases of specific families of software) architects started to realize that, even though a computer screen is two-dimensional, all three-dimensional forms visualized through it may exist in a computational three-dimensional space right from the start. (Ibid.:33) Architectural artifacts can be produced directly from the computer, i.e., artifacts are directly printed from 3D models. By bridging the gap between design and production, this mode of digital making also reduces the limits that previously applied under the notational regimes of descriptive and predescriptive geometries, and this may well mean the end of the notational bottleneck that was the uninvited guest of architectural design throughout most of its early modern and modern history. (Ibid.) This phenomenon challenges established notions of the economies of scale, Carpo argues. Artifacts are mass produced without being similar. The capacity to mass-produce series of nonidentical items led to a new range of theoretical and practical issues. The idea of nonstandard seriality, as this mode of production is often called, was already inherent in the original definitions of the objectile, but its economic implications were not. In its simplest formulation, the theory of nonstandard seriality posits that economies of scale are irrelevant in digital production processes. In a digital production process, standardization is no longer a money-saver. Likewise, 95

97 customization is no longer a money-waster. (Ibid.:41) Today, variations in mass production come at no extra cost. Nonstandard seriality, in turn, already contains the seeds of a potentially different authorial approach. As digital fabrication processes invite endless design variations (within given technical limits), and promise to deliver them at no extra cost, the question inevitably arises as to who is going to design them all. (Ibid.:42) Carpo's main question: Who is the author in this digital setup? The old authorial paradigm was predicated upon mechanical indexicality, and on the mark of authorship that mechanical reproduction carried over from archetypes to identical copies. The rise of architectural authorship may have been following the same trajectory. If this is the case, then chances are that, with the transition from mechanical to digital technologies, and from identical to variable reproductions, a recast of architectural agency will also be inevitable. In fact, the trend may already have started. (Ibid.:44) For Carpo, the reversal of the Albertian paradigm, authorship, gives us ground to worry about. We have reason to worry about, and possibly lament, the forthcoming demise of traditional architectural authorship. The recent spasms of authorial conceit (always an indelible part of the architect s trade, but recently risen to unprecedented levels) further reinforce the perception of an incipient crisis. (Ibid.:47) He finds in Cache-Deleuze s concept of the objectile ideas that may point to a re-articulation of the author. the objectile is not an object but an algorithm a parametric function which may determine an infinite variety of objects, all different (one for each set of parameters) yet all similar (as the underlying function is the same for all). (Ibid.:40) But even if Carpo agrees that an author today is not the author of an object but of the objectile, he claims that the 'real' author is still out there and needs to be found. The objectile is to an object what a mathematical function (a script or notation) is to a family of curves, or the Aristotelian form is to an Aristotelian event: in Aristotelian terms, the objectile is a generic object. The theory of the objectile also implies that the object itself (or the specific object) should fall outside the scope of design (much as the Aristotelian event falls outside the domain of science), since both the object and the event are seen as essentially variable entities. But insofar as the objectile is, technically, an open-ended algorithm, and a generative, incomplete notation, the objectile s designer will authorize some general norms to determine aspects common to a range of variable and individual events. Evidently, in an open-sourced environment, the algorithmic code itself may be open to aleatoric, nonauthorial variations, but this does not alter the bigger picture. Seen in terms of a genus-species hierarchy, objects are ontologically specific, whereas the objectile is the general category to which they belong. Hence the objectile s designer is a general, or perhaps a generic, author. This is not an unprecedented 96

98 authorial model. It was in use for centuries, before Alberti came by. (Ibid.:47) Remarks Mario Carpo is one of the few historians who engages with the contemporary events around digital technology in architecture. He places in line the interplays of architecture and computers with the history of architecture. We agree, to a certain extent, with his diagnosis of the computeraided design tools' impact on 'key' questions in architecture, who is an author, what is an original object, what is its copy. But we further see that these questions are not asked by the global network and its online applications in a simple look at Wikipedia, Github, or more generally the MIT Media Lab, we won t find the author of an entry or a project as a celebrated figure. Nevertheless, that these questions are not there does not mean that they should not be asked. We see in content sharing platforms and social networks that information circulates ad infinitum, and that origins are in constant circulation. Origins are arbitrarily indexed; 'zeros' are everywhere. Despite this phenomenon, that in Carpo's understanding is at the foundations of 'modern' architecture, the digital objects that accommodate such a setup are in perfect stability, and furthermore, new values are emerging from them. This is our understanding as users on the global network and as architects. The question is turned: What kind of architecture would emerge if we affirm that origins are in infinite motion? This question is addressed in the next two chapters. 97

99

100 1.4 THE WAYS TO OPERATE THE INFORMATION S INFINITE CIRCULATION In the last talk we discussed how the abundance of information on the global network and its circulation ad infinitum may affect our contemporaries understandings of architecture, and saw that their understanding of information significantly differs from the global network s, and that any overlap would only threaten their positions. Here we will see how architects recognize infinite objects and relations in architecture and cities and how they address them. They create rule-based scenarios in order to understand and react accordingly in complex situations. When faced with a complex problem, they construct stabilities by analyzing their components and synthesizing their solutions. They argue that a deep understanding of the problem is the way to face complexity. We will also see how they try to smooth out the differences that a complex object may engender, so to operate complexity without getting over it. 99

101 [1/10] The Architecture Machine computer-aided design, artificial intelligence, learn, understand, react, rules, complexity Figure 1.37: Google Ngram Viewer showing the occurrences in a corpus of books of Media Lab, Rem Koolhaas, Patrik Schumacher, from For Nicolas Negroponte 1, Artificial Intelligence should be at the foundations of any interplay between architecture and computers. He recognizes that society perceives the concept of computing with certain skepticism its origins are indexed by titles like Cybernetics: Or Control and Communication in the Animal and the Machine (Wiener 1948), for example and presents in The Architecture Machine an optimistic scenario that aims to humanize computers. Computer-aided design cannot occur without machine intelligence and would be dangerous without it. In our culture an intelligent machine is immediately assumed to be a bad machine. As soon as intelligence is ascribed to the artificial, some people believe that the artifact will become evil and strip us of our humanistic values. (Negroponte 1970:1) One of Negroponte s main focuses is to make computers aware of our environment. To humanize computers is to bring them closer to our everyday life, to show them what being human is about. And in terms of architecture, to make them aware of what is important for design. Why ask a machine to learn, to understand, to associate courses with goals, to be selfimproving, to be ethical in short, to be intelligent? The answer is the underlying postulate of an architecture machine. A design machine must have an artificial intelligence because any design procedure, set of rules, or truism is tenuous, of not subversive, when used out of context or regardless of context. It follows that a mechanism must recognize and understand the context before carrying out an operation. (Ibid.) 1 Nicolas Negroponte is the founder of the Massachusetts Institute of Technology s Media Lab. He is a trained architect but also a tech visionary. He is the first investor of Wired Magazine where he wrote a monthly column for several years and founder of One Laptop Per Child Association. His early interplays between architecture and computers with the MIT s Media Lab are still very vivid today in academia and emerging technologies. 100

102 But to program computers to understand the environment is only one part of the story, because they should also be able to perform accordingly and operate in the understood environment. Intelligence is a behavior. It implies the capacity to add to, delete from, and use stored information. What makes this behavior unique and particularly difficult to emulate in machines is its extreme dependence on context: time, locality, culture, mood, and so forth. (Ibid.) For Negroponte, the establishment of clear rules is a fundamental starting point. To this we say that rules are not natural, as we make and agree on these rules so we can talk to each other. Even when we make our own rules, they are not necessarily embedded in human activities. In the past when only humans were involved in the design process, the absence of resolute rules was not critical. Being an adaptable species, we have been able to treat each problem as a new situation, a new context. But machines at this point in time are not very adaptable and are prone to encourage repetition in process and repetition in product. (Ibid.:3) Figure 1.38: Trick automation feigning to write, draw and calculate, made by Leon Joly (c. 1855). This already presents a problem in Negroponte s analogy between the designers and computers awareness of the environment. We say that one of our greatest abilities as humans is to communicate with each other on the go, beyond explicit rules. Ironically, though it is now difficult for a machine to have adaptable methods, machines can be employed in a manner that treats pieces of information individually and in detail. Human designers cannot do this; they cannot accommodate the particular, instead the accommodate the general. (Ibid.) A spectrum of abilities and potentials of the interplays between computers and architecture is presented by Negroponte. He tries to build bridges between designers and computers, around many questions. The problem is therefore twofold: first, architects cannot handle large-scale problems for they are too complex; second, architects ignore small-scale problems for they are too particular and individual. Architects do not appear to be well trained to look at the whole urban scene; nor are they apparently skilled at observing the needs of the particular, the family, the individual. (Ibid.) 101

103 There are two main research directions that he presents in this book. In one, the architect talks to a form-maker computer. In the other, activities that are traditionally given to the architect are passed directly to the consumer who, with the aid of a computer, performs them. Our bias towards localized information implies two directions for the proposed relationship between designer and machine. The first is a do-it-yourselfism, where consumer becomes producer and dweller becomes designer. (Ibid.:5) The second direction presupposes the architect to be the prime interpreter between physical form and human needs. (Ibid.:7) Negroponte imagines that an interesting interplay between computers and design takes advantage of the computer s ability to draw. With computers, we can go from drawings to holographies, he envisions. Today, interesting examples can be seen in the pop and hip-hop culture, i.e., bringing to life dead artists like Tupac or Michael Jackson and performing to hundreds of thousands. 2 The computer is a natural medium for the mass production of perspective images. At first, numerically controlled plotters were employed to draw perspectives at hundreds of small increments along a path. These drawings were then filmed with animation procedures to produce a cartoon of moving figures (Fetter, 1964), a general procedure more cumbersome than any previous method. (Ibid.:31) What we now call virtual reality is envisioned and explored by Negroponte in this book. An early commercial application is Nintendo s Virtual Boy in the mid 1990s. Today it is still being explored as virtual reality and augmented reality, with products like Oculus Rift or Google Cardboard. Further efforts will eventually allow three-dimensional displays to be joined with wandlike devices. Ivan Sutherland is creating a machine that gives the illusion of actually walking around and within visual models. The device is a helmet mounted with two eyeglass-size cathode-ray tubes (with prisms) that permit stereoscopic images to be transformed in accordance with the head position of the wearer. (Ibid.:37) When talking about big scale problems, such as urban, Negroponte envisions computers helping humans to address complexity and generate solutions. Today, software like City Engine can be put in this line. In the urban context the complexity of these forces often surpasses human comprehension. A machine, meanwhile, could procreate forms that respond to many hereto unmanageable dynamics. (Ibid.:39) He further classifies design problems in two ways. One, where the solution space of the problem is vast, and its opposite, where the solution space is limited, both difficult to solve. There are two distinct types of generated solution: one accommodates underconstrained problems; the other works within overconstrained situations. The underconstrained 2 See Coachella Festival in California, 2012 and the Billboard Music Awards,

104 situation (rare in architecture) has a large set of possible solutions. The criteria are satisfied by many alternatives. These alternatives must then be evaluated by the architect using intuitive means, selection criteria he either does not understand or has never presented to the machine. In the overconstrained problem, the generating mechanism is presented with great amounts of factional criteria that no form can completely satisfy. The generating mechanism searches for a solution that best relaxes the constraints, a point of greatest happiness and least friction. The resulting form is a status of criteria compromise where the constraints least antagonize one another. (Ibid.) The simulation of events aids the designer in solving a problem by playing with the environment s rules, without changing the environment itself, he argues. The simulation of events can benefit the architect in two ways. If the designer does not fully understand the behavioral aspects of an event, he can play with rules and regulations, searching for recognizable activity patterns. (Ibid.:47) Figure 1.39: A preliminary output from the Children s Hospital Project of the Leo A. Daly Company, Architects. The 134 activities are given minimal interrelationships. While talking with a particular designer, the program implicitly develops functional relationships through trial and error, punishment and reward. Over time the system should improve. 3 3 Figure: from (Negroponte 1970). 103

105 The Emergence and Design Group 4 explores this hypothesis. The group focuses on agents of design driven by simple behavioral rules that cause a fascinating phenomenon. The second design application, pretesting, assumes the rules are correct. Whether empirical or experimental, simulations are no better than their underlying rules, whether the rules are provided by the man or by the machine. If the simulation model is correct, a designer or a machine can observe the performance of an environment, a specific context. (Ibid.) Negroponte recognizes that to characterize our environment requires a lot of data. The idea of a software for data management follows. Today, database management system (DBMS) is the standard for any large-scale computer application, whether implemented locally or on the global network. Census data, site descriptions, transportation statistics, activity constraints, economic criteria, and material specifications are all part of the bulky dossier of design information necessary for any urban design project. The information burden is fantastic. An architect's role in urban design requires a complex information supply with characteristics of retrieval, labeling, and interassociation. But machines are good at this. (Ibid.:51) Negroponte explores the idea of bring computers to our homes, closer to our domestic affairs. The concept of Internet of Things can be placed in line here. Today, our home appliances gain great operability when connected to the global network. A fridge can order products when running low on stock; sensors and cameras can talk to a mobile phone and send updates, for example. Granting machines in the home, each urbanite could intimately involve himself with the design of his own physical environment by (in effect) conversing with his own needs. Or, another way of thinking of the interaction is that everybody would be talking to the architect, not explicitly but implicitly, via a machine-to-machine interchange. (Ibid.:55) Negroponte thinks to discretize, store, and learn from the events of the world. This idea is at the foundations of Machine Learning, a subfield of computer science closely linked to AI, and that we will explore in chapter 2. Each event is either a temporal or sequential occurrence; together they constitute part of a process. A sequential response of one protagonist is generated by the previous event in the dialogue, usually on the behalf of the other. A sequential event is a reply. It can be the reply to a facial expression or the answer to a question. What is important, however, is that not only is one actor responding but he can assume that the other is listening and probably is aware of the context. In other words, a sequential episode assumes the reply of one (intelligent) system and the attention of the other system a chain of chronologically ordered incidents. (Ibid.:59) 4 See Michael Weinstock 2004,

106 He actually presents some specifics of the Machine Learning scenario, and looking at state of the art online applications today, we recognize them around us. You never actually told the machine that you were interested in lepidoptera, but the machine is finding out from experience. It contains, that is, a learning model which stores, measures, sorts and computes the probabilities of your interests, reactions and ways of thinking. It is learning about you all right, and will soon be giving you extra information about butterflies. (Ibid.:64) There are three sources for such unsolicited comments. First, you could previously have stated very specifically that all soap trays must drain water. The criterion is specific. A second way, at the other extreme of complexity, is through direct experience and realworld observation. A third method, more realizable in the near future, is through deduction. (Ibid.) Finally, gaming is also another scenario where computers are of great help to model the world and learn from their simple but rich rules. Games provide a happy vehicle for studying methods of simulating certain aspects of intellectual behavior; happy because they are fun, and happy because they reduce the problem to one of manageable proportions. Games are a learning device for both people and machines. (Ibid.:67) [2/10] Soft Architecture Machines design process, learning, language, artificial intelligence, models, human behavior, anthropomorphism Figure 1.40: SEEK, part of the SOFTWARE exhibit at the Jewish Museum, New York, September 16-November 8,

107 Its purpose was to show how a machine handled a mismatch between its model of the world and the real world in this case five hundred two-inch metal-plated cubes. The mismatch was created by a colony of gerbils whose activity constantly disturbed the strictly rectilinear arrangement called for by the machine s model. 5 In Soft Architecture Machines, Nicolas Negroponte reports on a number of experiments carried out by the Architecture Machine Group at MIT. Negroponte s main argument is rendered in the organization of this book. As this research is carried out, he says, the architect should become less and less relevant to the tradition of architecture. And this suggests that at the peak of AI there is an anthropomorphic machine. Each chapter removes the architect and his design function more and more from the design process; the limit of this progression is giving the physical environment the ability to design itself, to be knowledgeable, and to have an autogenic existence. The general assumption is that in most cases the architect is an unnecessary and cumbersome (and even detrimental) middleman between individual, constantly changing needs and the continuous incorporation of these needs into the built environment. The architect's primary functions, I propose, will be served well and served best by computers. In this sense the book is about a new kind of architecture without architects (and even without surrogate architects). (Negroponte 1975:1) This expulsion of the architect from architecture can only happen on the basis of the advancements of AI, he argues. As previously discussed, AI should give computers the ability to recognize their environment and act accordingly, in this case towards the design and production of architectural artifacts, and even towards the ability to reflect on the implication of their actions to architecture s tradition. The field is still small and ill defined (as even the name suggests), and can be roughly characterized by two contrasting approaches to achieving a machine intelligence. One approach is to attempt to embed knowledge directly (both facts and methods for manipulating those facts) into a computer, in some sense to capitalize upon the time we, as humans collectively, have taken to learn these facts. The other route is to understand and to impart to machines the learning process itself (which includes learning how to learn and, more important, the desire to learn) with the notion that machines could subsequently mature in a manner not dissimilar to that of humans. (Ibid.:35) Just as in the theories of machine control, communication is at its foundations. AI cannot happen without models of language and meaning that can present to the computers the ability to communicate with each other and with humans. Negroponte further points out what he believes to be problems with the lack of progress on the matter. We can see here that his diagnosis suggests getting out from structuralist paradigms in language. I propose that present theories of language, whether in artificial intelligence or in the few instances of computer-aided architecture, show no reason to be more productive than the automatic translation efforts of the late 1950s and early 1960s. I believe that the 5 Figure: from (Negroponte 1975). 106

108 inadequacies result from two failures: (1) our lack of understanding of meaning and our insistence on searching for it in the language itself; (2) our treatment of language from the point of view of an external observer overseeing a conversation (usually through a single channel). (Ibid.:39) Negroponte sees in computing an opportunity to re-articulate the concept of modeling in architecture. He recognizes two main activities in which computers can be of great help. Only recently, with the advent of computers, has it become practicable to model human behavior (as well as physical states) in intellectual activities. As such, computer modeling has become extremely important to (1) test hypotheses and (2) simulate events. In each case, it is necessary to describe some states and some transitions. It is precisely the description process that can both legitimize and confuse the modeling procedure. (Ibid.:43) He further develops a categorization of models according to their ability to discretize and render the environment. There exist three general classes of models; each contains very particular biases toward how we observe that slice of the world and how we represent it. To facilitate discussion, I am calling the three models aggregate, essence, and reality. (Ibid.) The most common model is a causal model, where the world is discretized and modeled by the aggregated human knowledge. We could say that this model can be an aggregate of the laws of physics, for example. The aggregate model is the most common. It is epitomized in the family of Dynamics, which I mention as an example because it has been implemented with great care and expertise. However, the aggregate model is also found frequently in game playing, in picture processing and recognition, and in most exercises of artificial intelligence. The general characteristic of the aggregate model is the decomposition of events to be modeled into many unambiguous causalities, using human insights and expertise to achieve the proper compartmentalization. (Ibid.:44) Figure 1.41: Face and machine contour taken from Kelly (1970). 6 There is also the abstract model that is put together by a symbolization of the events of the environment. 6 Figure: from (Negroponte 1975). 107

109 The essence model, on the other hand, makes no attempt to account for the whole through detail. It is quite specifically an abstraction, one that permits us to exercise more global processes in terms of our interpretations of their salient features. Models of the design process are often of this kind, the caricature being the homely analyze-synthesizetest model. (Ibid.) The last category is of full-scale models, i.e., why to model the city, if we can use the city as a model of itself? Rather than model a chunk of the world, use that chunk of the world for a model of itself. In other words, instead of modeling a city, use the city as a model of itself. The architectural counterpart is, in some sense, found in the use of full-scale models. This kind of model may appear to be simply a play on words. However, it acknowledges a device that we, as humans, use all the time in our daily activities and rarely consider viable for machines. That is using the world as memory. It allows us to attach whatever symbols we wish, apply whatever metaphors we like, and ascribe very personal meanings. (Ibid.:45) So far, Negroponte talks about the directions to take in order to have effective communication between computers and humans, as well as the kind of models of the world that are best to operate for an intelligent machine. For a computer to acquire intelligence will it have to look like me, be about six feet tall, have two arms, two eyes, and an array of humanlike apparatus? I believe that the question is not ludicrous; on the contrary, it is one of the cruxes of the dilemma in which many of us find ourselves. It is clear that computers need a wide variety of sensory channels and a host of effectors in order to witness and manipulate aspects of the world, particularly those we use daily in our metaphors. (Ibid.:48) Negroponte s intuition of what is left to achieve is that humans learn the environment with our senses; it is through them that we receive, store, and process information, and with our bodily organs that we act accordingly. It is so obvious that our interfaces, that is, our bodies, are intimately related to learning and to how we learn, that one point of departure in artificial intelligence is to concentrate specifically on the interfaces. (Ibid.) Therefore, if the machine could have the chance to experience the world as we do, then they would be as intelligent as we are, he says. Our experiments are based on the hope that if machines are given the faculty for sophisticated interactions with the real world (people, places, pictures, and so forth), they can learn to develop their own design methods and methodologies, perhaps better than our own. (Negroponte 1970c and d) For Negroponte, anthropomorphism is at the answer for a truly intelligent machine. 108

110 The initial question, however, remains unanswered. Does a machine have to possess a body like my own and be able to experience personally behaviors like my own in order to share in what we call intelligent behavior? While it may seem absurd, I believe the answer is yes. (Negroponte 1975:49) Remarks Nicolas Negroponte is one of the first architects to bring interplays between architecture and computers to such scale and credibility. The influence of the Media Lab is present all around the world today: robotic arms putting bricks together, smart materials reacting and talking to the environment, bionics enhancing our physical abilities; the list goes on. 7 There is no trace of overwhelm anywhere. We see an immediate mediation to the vast corpus of predictions. His contribution is of no doubt. Nevertheless, we see fundamental differences between his interplays and today s global condition. For Negroponte, the ability to understand the world and react accordingly is at the foundations of AI. He talks about rule based logics, cause-effect relations, strict control, but, if we look at the global network today, we can see that there is no understanding, nor will to understand the information that circulates, and still operations can be done, like finding a needle in a haystack, i.e., finding one web document in billions that will tell us something we may find interesting. We see a discrepancy there. Furthermore, Negroponte argues for the architect s dissolution towards progress. And again, if we look at the global network, we can see that the online applications are just as good as the people using them. Let us take Google Maps as an example. This application will tell us, live, the fastest route from A to B in Zürich. It works because Zürichers use it a lot, and it would not be the same situation in a city that does not use it. In our current understanding of the global network, the dissolution seems an oxymoron, but most importantly, in a permanent position that we want to take in relation with computers, the dissolution of the role of the architect in architecture just seems uninteresting to explore. 7 See MIT s Media Lab website at (accessed ). 109

111 [3/10] Notes on the Synthesis of Form complexity, design, order, organization, form, function, mathematics, logic, clarity, analysis, synthesis Figure 1.42: 21 specific requirements. 8 In this early book, Christopher Alexander 9 affirms complexity in the design problems and presents a methodology for the analysis and synthesis of solutions. In Notes on the Synthesis of Form, he presents a view of the world based on the recognition of components and the relations between them. It sharply defines a problem, whatever it may be, so as to facilitate its operation. These notes are about the process of design; the process of inventing physical things which display new physical order, organization, form, in response to function. (Alexander 1964:1) For Alexander, the world has become too complex to understand, and things happen too fast. To solve a problem superficially is simple, but a closer look reveals its real complexity. Designers lose control over their work and come up with arbitrary solutions without stable grounds. With the aid of mathematics, logic, and computers, control is to be re-claimed. This is Alexander s background and motivation. Today functional problems are becoming less simple all the time. But designers rarely confess their inability to solve them. Instead, when a designer does not understand a problem clearly enough to find the order it really calls for, he falls back on some arbitrarily 8 Figure: See Alexander (1964). 9 Christopher Alexander is emeritus professor at the University of California, Berkeley. Born in Vienna, raised and educated in England, he holds degrees in mathematics and architecture. At age of 26 he wrote his PhD thesis titled Notes on the Synthesis of Form (1964), which, along with A Pattern Language (1977), became his most famous contributions to the interplays of architecture and computers. We can characterize Alexander as a pioneer theorist and designer who implements analysis and synthesis of problems and bridges architecture and computer science to an engineering level. He is the father of the Pattern Language movement in computer science [1] design patterns is the most significant emerging area in the field of object-oriented technology. More than stressing his contributions in mathematics or computer science, we are interested in talking about how he models and operates what he calls complexity in architecture and design. [1] Pattern Languages of Programs (PLoP) conference is a premier event for pattern authors and pattern enthusiasts to gather, discuss, and learn more about patterns and software development. See (accessed ). Its purpose is to develop and refine the art of software design patterns. See (accessed ). 110

112 chosen formal order. The problem, because of its complexity, remains unsolved. (Ibid.) At the same time that the problems increase in quantity, complexity, and difficulty, they also change faster than before. In the past even after the intellectual upheaval of the Renaissance the individual designer would stand to some extent upon the shoulders of his predecessors. (Ibid.:4) As time goes on the designer gets more and more control over the process of design. But as he does so, his efforts to deal with the increasing cognitive burden actually make it harder and harder for the real causal structure of the problem to express itself in this process. (Ibid.:73) When Alexander looks around carefully, he sees that the designed objects are not properly organized, and thinks of it as a symptom of the lack of control caused by the absence of proper methods to solve complex problems. The intuitive resolution of contemporary design problems simply lies beyond a single individual's integrative grasp. Of course there are no definite limits to this grasp (especially in view of the rare cases where an exceptional talent breaks all bounds). But if we look at the lack of organization and lack of clarity of the forms around us, it is plain that their design has often taxed their designer's cognitive capacity well beyond the limit. (Ibid.:5) For Alexander, to address complexity it is first necessary to look at mathematics specifically set theory and to logic, in order to construct a problem s abstract structures. The analysis of such structures is potentially exhausting so computing becomes handy. Mathematics, in the popular view, deals with magnitude. Designers recognize, correctly, that calculations of magnitude only have strictly limited usefulness in the invention of form. What they do not realize, however, is that modern mathematics deals at least as much with questions of order and relations as with questions of magnitude. it can be a very powerful tool indeed if it is used to explore the conceptual order and pattern which a problem presents to its designer. (Ibid.:6) While it is true that a great deal of what is generally understood to be logic is concerned with deduction, logic, in the widest sense, refers to something far more general. It is concerned with the form of abstract structures, and is involved the moment we make pictures of reality and then seek to manipulate these pictures so that we may look further into the reality itself. It is the business of logic to invent purely artificial structures of elements and relations. (Ibid.:8) One consequence of looking at logic in these terms is that it will change the way we understand a problem. It will take us from a superficial and simple view to a deep and exposed view, from which there is no way back, and further analysis seems inevitable, Alexander says. The use of logical structures to represent design problems has an important consequence. It brings with it the loss of innocence. A logical picture is easier to criticize 111

113 than a vague picture since the assumptions it is based on are brought out into the open. Its increased precision gives us the chance to sharpen our conception of what the design process involves. (Ibid.) But before the creation of models of mathematics and logic to solve a problem, the designer should have a clear understanding of what is at stake in a given situation. The following argument is based on the assumption that physical clarity cannot be achieved in a form until there is first some programmatic clarity in the designer's mind and actions; and that for this to be possible, in turn, the designer must first trace his design problem to its earliest functional origins and be able to find some sort of pattern in them. I shall try to outline a general way of stating design problems which draws attention to these functional origins, and makes their pattern reasonably easy to see. (Ibid.:15) Figure 1.43: models of context-form relations. 10 The concept of fitness is at the foundations of Alexander s synthesis. Fitness is the action and binary meter of bringing two things that are different by nature together. It is based on the idea that every design problem begins with an effort to achieve fitness between two entities: the form in question and its context. The form is the solution to the problem; the context defines the problem. (Ibid.) Alexander s main challenge at this point is to test and evaluate all the fitnesses that together make a problem complex. 10 Figure: Christopher Alexander (Alexander 1964). 112

114 There is as yet no theory of ensembles capable of expressing a unitary description of the varied phenomena we encounter in the urban context of a dwelling, for example, or in a sonata, or a production cycle. Yet we certainly need a way of evaluating the fit of a form which does not rely on the experiment of actually trying the form out in the real world context. (Ibid.:20) There are two ideal conditions that Alexander envisions to explore and evaluate fitness, and both are impossible. The experiment of putting a prototype form in the context itself is the real criterion of fit. A complete unitary description of the demands made by the context is the only fully adequate nonexperimental criterion. The first is too expensive, the second is impossible: so what shall we do? (Ibid.:21) Alexander s strategy is to double articulate the act of putting elements together, i.e., the fitness. In a way, he is giving up control of the environment but claims total control over the form. Fitness does not focus on giving the solution to a problem, but on bringing the overall misfits to zero, to create a global stability. If we divide an ensemble into form and context, the fit between them may be regarded as an orderly condition of the ensemble, subject to disturbance in various ways, each one a potential misfit. The task of design is not to create form which meets certain conditions, but to create such an order in the ensemble that all the variables take the value 0 [misfits don t occur]. The form is simply that part of the ensemble over which we have control. It is only through the form that we can create order in the ensemble. (Ibid.:27) The binary evaluation of a misfit 1 or 0 transforms Alexander s problem into a selection problem of hierarchical structure, from which rules of operation and selection are described. To solve a problem by selection, two things are necessary: 1. It must be possible to generate a wide enough range of possible alternative solutions symbolically. 2. It must be possible to express all the criteria for solution in terms of the same symbolism. Whenever these two conditions are met, we may compare symbolically generated alternatives with one another by testing them against the criteria, until we find one which is satisfactory, or the one which is the best. (Ibid.:74) At this point, Alexander elaborates on the articulation of the problem and its levels of abstraction, and further introduces the mathematical models to operate the problem as the formal picture of a mental picture. This third picture [Figure 1.43] is built out of mathematical entities called sets. A set, just as its name suggests, is any collection of things whatever, without regard to common 113

115 properties, and has no internal structure until it is given one. (Ibid.:78) He sees in set theory a way to freely formalize elements and their relations. Something that designers intuitively do when addressing a program. The great power and beauty of the set, as an analytical tool for design problems, is that its elements can be as various as they need be, and do not have to be restricted only to requirements which can be expressed in quantifiable form. (Ibid.:79) An example: in the design of a house, the set M may contain the need for individual solitude, the need for rapid construction, the need for family comfort, the need for easy maintenance, as well as such easily quantifiable requirements as the need for low capital cost and efficiency of operation. Indeed, M may contain any requirement at all. (Ibid.) These requirements are the individual conditions which must be met at the form-context boundary, in order to prevent misfit. The field structure of this form-context boundary, in so far as the designer is aware of it, it is also not hard to describe. (Ibid.:80) Alexander s set theoretical model of context and form is then applied to a graph structure. We represent the interactions by associating with M a second set L, of non-directed, signed, one-dimensional elements called links, where each link joins two elements of M, and contains no other elements of M. (Ibid.) The complex problem is modeled as a graph. The nodes are the unique components of the complex system, and the edges their relations. A graph is the result of a proper analysis of a complex problem. The two sets M and L together define a structure known as a linear graph or topological 1-complex, which we shall refer to as G(M,L), or simply G for short. (Ibid.) Figure 1.44: A typical linear graph. 11 Once analysis is done, synthesis follows. To find the unique components of a problem as well as their internal relationships based on their requirements is the first phase for Alexander s synthesis of form. 11 Figure: Christopher Alexander (Alexander 1964). 114

116 Finding the right design program for a given problem is the first phase of the design process. It is, if we like, the analytical phase of the process. This first phase of the process must of course be followed by the synthetic phase, in which a form is derived from the program. We shall call this synthetic phase the realization of the program. (Ibid.:84) What follows is to introduce a method to make a tree of sets of requirements into complex diagrams. These diagrams will be further discussed in the next subchapter of this thesis, where we will have a closer look at Alexander s implementation of his methodology. The starting point of analysis is the requirement. The end product of analysis is a program, which is a tree of sets of requirements. The starting point of synthesis is the diagram. The end product of synthesis is the realization of the problem, which is a tree of diagrams. The program is made by decomposing a set of requirements into successively smaller subsets. The realization is made by making small diagrams and putting them together as the program directs, to get more and more complex diagrams. (Ibid.) For Alexander, the relations between the components of the problem are arbitrary, but nevertheless they are evaluated locally. the set M consists of all those possible kinds of misfit which might occur between the form and the context To be exact, each element of M is a variable which can be in one of two states: fit and misfit. It is important to remember that the state of this variable depends on the entire ensemble. We cannot decide whether a misfit has occurred either by looking at the form alone, or by looking at the context alone. Misfit is a condition of the ensemble as a whole, which comes from the unsatisfactory interaction of the form and context. (Ibid.:96) Not all of the relations between elements have universal measures. There are concepts like comfort that cannot be pinned down and measured as area of work, for example. A design problem is not an optimization problem. In other words, it is not a problem of meeting any one requirement or any function of a number of requirements in the best possible way (though we may sometimes speak loosely as though it were, and may actually try to optimize one or two things like cost or construction time). (Ibid.:99) But still, the unquantifiable variables should be personally evaluated as a fit or a misfit. We shall treat a property of the ensemble (quantifiable or not), as an acceptable misfit variable, provided we can associate with it an unambiguous way of dividing all possible forms into two classes: those for which we agree that they fit or meet the requirement, which we describe by saying that the variable takes the value 0, and those for which we do not agree, which therefore fail to meet the requirement, and for which the variable is assigned the value 1. (Ibid.:100) For Alexander, to establish a connection between variables is a cause-effect relation. Instead of just looking for statistical connections between variables, we may try to find causal relations between them. (Ibid.:108) 115

117 The causality upon which Alexander is basing his methodology does not include the concept of computing. It relies on the designer, on his knowledge and expertise. It is a personal decision. The search for causal relations of this sort cannot be mechanically experimental or statistical; it requires interpretation: to practice it we must adopt the same kind of common sense that we have to make use of all the time in the inductive part of science. We shall say that two variables interact if and only if the designer can find some reason (or conceptual model) which makes sense to him and tells him why they should do so. (Ibid.:109) The construction of M and L is as well a personal decision. The graph G(M,L) follows the designers knowledge, intuition, and ability to symbolize the problem and the world around it. Again, as with the definition of the variables, this introduces a personal bias, and reminds us that L, like M, is a picture of the way the designer sees the problem, not an objective description of the problem itself. (Ibid.) For Alexander, one of the main advantages of the discretization of a complex problem is that small subproblems are solved toward the solution of the whole. Small solutions, if put together properly, will become complex solutions. If we are to solve the problem M by working our way through the program, solving various subproblems separately, it must obviously be possible to put the resulting diagrams together somehow when we have them. (Ibid.:122) In hierarchical systems, there are clear paths for navigation; the top reaches the bottom in various steps, and the other way around. This gives Alexander the idea of control and operation. The global is operated through the local. The organization of any complex physical object is hierarchical. It is true that, if we wish, we may dismiss this observation as an hallucination caused by the way the human brain, being disposed to see in terms of articulations and hierarchies, perceives the world. On the whole, though, there are good reasons to believe in the hierarchical subdivision of the world as an objective feature of reality. (Ibid.:129) The synthesized diagram should render the structural stability modeled by Alexander in the linear graph. The hierarchical composition of these diagrams will then lead to a physical object whose structural hierarchy is the exact counterpart of the functional hierarchy established during the analysis of the problem; as the program clarifies the component sources of the form's structure, so its realization, in parallel, will actually begin to define the form's physical components and their hierarchical organization. (Ibid.:131) This is Alexander s methodology with some detail. We look now at how he implements it to solve a complex design problem. In a paper presented in a conference a year before the publication of this book, he goes into the practical details of analysis and synthesis. 116

118 [4/10] The Determination of Components of an Indian Village structure, system, problem, adaptation, set theory, graph theory, diagrams, analysis, synthesis Figure 1.45: The entire village. 12 Alexander understands the phenomena of the world by the analysis of their basic components and interrelations. He argues that the objects of nature are intelligible, regardless of their complexity, by a closer look at their underlying structure. He presents here an application of his own methodology. We sometimes forget how deeply the nature of an object is determined by the nature of its components. The difference between graphite and diamond is very largely caused by the difference in the structure of their component building blocks. Both are pure carbon. (Alexander 1963:34) This structural view applies to the city and to architecture. For this analysis, he follows a generic understanding of a city. Now think of an example from architecture. If you ask anyone to name the pieces a city is made of, he will tell you that it is made of houses, streets, factories, offices and parks, and so on. When we ask what it is that makes each one of these macro-components what it is, we see that, just as the component plates of graphite are themselves made up of carbon atoms, so each component of the city is really a collection of smaller elements, and that each gets its character from the way these smaller elements are grouped. (Ibid.) When we agree with this characterization of the city and architecture, we know almost everything that is needed about its structure, he argues. To change the city, it is necessary to change its components. If you once agree that houses, streets, parks, and offices, are the proper components of the city (as you have already done, usually, when you even begin to use some systematic method), then there is really very little choice open to you about the city structure. Systematic techniques, just because they need to operate on known units, usually beg the real question of design, and so achieve little more than a second rate designer does. 117

119 The fundamental change which a structure undergoes at the hands of a great designer, who is able to redistribute its functions altogether, cannot take place if its components stay the same. (Ibid.:35) In this paper, as the title suggests, Alexander s task is to determine the components of a small city, a village. Due to its complexity, the answer to this problem is beyond intuition, and intuition is of little or no help here. Let us now discuss the special nature of the city problem. A city is a live structure, not a dead one. That is, it is a loose assemblage or aggregate of components, which is all the time being added to, and changed. (Ibid.) The city is alive, and older than the designer. Its traces can go way back in time and its future may as well be vastly extended. Nevertheless, it is the designer s object of study and may be the greatest challenge of this setup. The form of a city cannot bear the same relation to its needs, as a designed object does. Since the life of the city is always much greater than the life-span of any one pattern of needs, the needs of the city change constantly and unpredictably throughout its lifetime. (Ibid.) It is this unforeseen future of the city that causes Alexander to give up control over the totality. The city is not a whole but a number of connected components. we must devote our attention to the development of what we might call a selforganizing city structure which, apart from meeting present needs, is by nature able to adapt easily to any changes in the pattern of needs whatever, foreseen or unforeseen. (Ibid.:36) Due to this self-organization, the ability of the city to change and adapt goes beyond the designer s work. To look at the city not as a whole but as interconnected components gives the designer the ability to differentiate and keep control over new components introduced and over old components that are replaced, without endangering the functionality of the totality. The city is a live assembly or aggregate of components. The problem of city design is not to design the city as a whole, but really to establish a kit of components out of which such a growing, ever-changing aggregate can be built up. These components will be determined by two properties which the aggregate system must have if it is to maintain its functional efficiency while expanding and changing to meet new needs and circumstances. The first property concerns the addition of new components to the system. The second concerns the modification and replacement of components already in the system. (Ibid.) A city grows, and new components are needed to keep its proper function; hence, new components need to be added up. 12 Figure: Christopher Alexander (Alexander 1963). 118

120 I will deal first with the addition of new components. It is very certain that we cannot develop all the components of the city simultaneously. We do not have the money, nor the power, nor would it be desirable to cause such an upheaval in the city's life, nor does this correspond to the realities of a city's growth. The city develops gradually. (Ibid.) Figure 1.46: Some of the requirements and relations of the village. 13 Alexander s first axiom aims to apply changes while maintaining the city s stability. We cannot add unregulated quantities of elements to a developing structure, but only certain well-integrated units which bear a proper relation to the presently functioning whole. And we cannot change or replace arbitrarily chosen pieces of a functioning whole, but again, only units which are sufficiently well-integrated to function as units or components of the whole. (Ibid.:37) The other situation that Alexander focuses on is what happens when existing components become functionally obsolete or old, to the point that they need to be replaced. The second kind of development which shapes the city, is the modification of the existing fabric as the system encounters new internal needs, and tries to adapt them. (Ibid.) An example of such a setup: Suppose a new kind of centrally distributed piped heat for dwellings becomes commercially feasible. With the city organized as it is today, it would be impossible to install this new piped heat in existing neighbourhoods, because of all the roads and gardens which would have to be dug up. In other words, the installation of piped heat 13 Figure: Christopher Alexander (Alexander 1963). 119

121 calls for modification of so many of the existing components (dwellings, gardens, streets), that it simply cannot take place. In all these cases, instead of the city adapting to the changing way of life, it is the people who bear the brunt of the adaptation by having to carry out new activities in obsolete surroundings. (Ibid.) Alexander argues that things fail when adding or replacing components if the analysis and synthesis is wrong by conception. Failure is due to the lack of a clear understanding of the underlaying structure of the city. This failure of adaptation on the part of the city is not caused by the faulty design of the components. You cannot improve it by building better roads or better houses or better parks. The real trouble lies with the root choice of the components; the functions they represent, though perhaps independent to some extent, are not independent enough. What we require, ideally, are components which are so independent, functionally, that every new need and new situation which occurs, only demands change or modification in one of the existing components, instead of all of them. (Ibid.:38) Alexander s second axiom aims to define components as functionally and physically independent as possible. The general statement of this principle, which will allow the city to adapt rapidly to future changes, is my second axiom. If a changing system in contact with a changing environment is to maintain its adaptation to that environment, it must have the property that every one of its subsystems with an independent function is also given so much physical independence as an isolable component, that the inertia of those components which for the time being require no modification, does not make it impossible to modify those other components which do need to be changed. (Ibid.) Following these two axioms, the components must have two properties. To satisfy the first axiom, the components must be functionally compact that is, each must operate as a unit. And to satisfy the second axiom, the components must be highly independent of one another, functionally. (Ibid.) Now to the determination of components: It rests on the assumption that each component of a physical structure represents what we might call a 'coming together' of a number of functional requirements. (Ibid.) A street is the coming together of the need for circulation space, the need for access to houses, the need for light and air between buildings, the need for somewhere to bury services, the need to lead off excess water during rainstorms. All these requirements, because they have similar physical implications, together define the linear component of the city which we call a street. (Ibid.:39) There is a cause-effect relation between the functional needs and the determination of its components, and the success of the design can be evaluated by how these relations are 120

122 identified and mapped into the system. A less homely way of putting this is to say that each component of the physical city comes into being to deal with some specific subset or subsystem of requirements in its environment. If we want the components to have the kind of independence and unity described above, the way to ensure this is to put them in 1-1 correspondence with the most independent subsystems of their environment. (Ibid.) To start identifying the requirements which may influence the physical shape of the village, Alexander suggests three sources. The list which follows includes requirements of every conceivable kind: (1) all those which are explicitly felt by villagers themselves as needs, (2) all those which are called for by national and regional economy and social purpose, and (3) all those already satisfied implicitly in the present village (which are required, though not felt as needs by anybody). Each requirement must be clearly enough defined for it to be decidable in principle in an actual village, whether the requirement is satisfied or not. (Ibid.) Once the requirements are there, the relations need to be identified. Secondly, in order to examine the system properties of the set of requirements, we must decide, for each pair of requirements, whether they are dependent or not. (Ibid.) And again, Alexander s analysis of the components and their relations are rendered in a linear graph. If we think of the requirements as points, and of the dependences between requirements as links, then the set of requirements and the set of links together define a linear graph (or topological1-complex). This serves as a complete structural description of the functional environment which contains the village and calls it into being. (Ibid.:40) And this is the promise that Alexander sees in set theory and graphs, to model and operate an underlying structure of a complex system. The beauty of this description is that we can now give it a mathematical interpretation, compatible with the real-world facts, though nonetheless artificial, which suggests criteria for decomposing the system of requirements into subsystems, and these themselves into further subsystems, in such a way that each subsystem contains a set of requirements very densely connected internally, yet as far as possible independent of the requirements in other subsystems. (Ibid.) Alexander introduces two functions. The first defines two sets of variables that can be thought of as independent systems. Subsets are defined iteratively afterwards. The first function is derived from the problem of establishing components as wellintegrated units. It is a measure of the information transited by one set of variables to the other. If we partition the variables in such a way as to minimize this function, we get subsystems 121

123 which are informationally as independent as possible. (Ibid.:41) The second function is about having the lesser impact to the whole when introducing new components to the system. The second function is derived from the problem of having new needs affect no more than one component at a time. Suppose that in the future some new need arises, not at present represented in the set of variables. If the present city is to adapt to this new need successfully, we should hope that only one of the existing city's components need be modified in response to the new need. We can then express the total probability of a new requirement being linked to just one subsystem, not to both, for any division of the existing requirements into two subsystems. (Ibid.) What follows is a detailed analysis and synthesis of the village (ibid.:42-55). The application of Alexander s method requires a considerable amount of computation and manipulation, something that challenges the human capabilities or will; therefore, he used an IBM 7090 computer (Ibid.:33). 1. The diagram I have shown for the entire village is only one way of putting the components together. There are many ways of doing it. The way they fit together in any actual case will depend on local peculiarities of site and population. (Ibid.:55) 2. It is not at all necessary that these components be introduced into an existing village structure all at once. In fact, although the components do function well in company with one another, each one of the twelve is capable of being introduced into the fabric of an existing village by itself. It is just this that I mean by calling these components the proper units of development. (Ibid.: 56) The results of such analysis are not computer generated see figure He presents a number of handmade possible solutions. There is no one solution, nor a fixed order for the chosen solution to be implemented. It seems that to achieve a solution, a political layer should be added. 122

124 [5/10] A City Is Not a Tree natural, artificial, inner nature, ordering principle, semi-lattice, tree, complexity, mental act Figure 1.47: A semi-lattice structure and tree structure, respectively. 14 Alexander presents in this award winning article 15 another articulation on cities. Even when he does not contradict himself, he presents a punctual distinction with his previous understanding of a city. In a way, this articulation feels more appropriate to a city of a global condition. Alexander recognizes the limits of trying to model and operate complexity. He starts by making an interesting categorization of cities: there are cities that follow design, and those that do not, Figure: Christopher Alexander (Alexander 1966). It was selected as one of the 1965 Kaufmann International Design Awards (Alexander 1966). 123

125 i.e., are spontaneous cities. I want to call those cities which have arisen more or less spontaneously over many, many years natural cities. And I shall call those cities and parts of cities which have been deliberately created by designers and planners artificial cities. (Alexander 1966) The adjective artificial in Alexander s characterization of a city connotes failure. An artificial city seems to lose to an ancient city. The problem is that we do not know the reason of a successful natural city. It is more and more widely recognised today that there is some essential ingredient missing from artificial cities. When compared with ancient cities that have acquired the patina of life, our modern attempts to create cities artificially are, from a human point of view, entirely unsuccessful. (Ibid.) The motivation of this article is to construct reason and articulate the inner nature of a natural city. The problem these designers have tried to face is real. It is vital that we discover the property of old towns which gave them life, and get it back into our own artificial cities. These designers fail to put new life into the city, because they merely imitate the appearance of the old, its concrete substance: they fail to unearth its inner nature. (Ibid.) The difference between these two categories can be boiled down to their different ways of organization. What is the inner nature, the ordering principle, which distinguishes the artificial city from the natural city? You will have guessed from the first paragraph what I believe this ordering principle to be. I believe that a natural city has the organisation of a semi-lattice; but that when we organise a city artificially, we organise it as a tree. (Ibid.) And however their organization may be, a city is a system: a tree or a semi-lattice. Both the tree and the semi-lattice are ways of thinking about how a large collection of many small systems goes to make up a large and complex system. More generally, they are both names for structures of sets. When the elements of a set belong together because they co-operate or work together somehow, we call the set of elements a system. (Ibid.) Alexander recognizes that everything is connected, giving an insightful example of this view. Other examples of systems in the city are: the set of particles which go to make up a building; the set of particles which go to make up a human body; the cars on the freeway, plus the people in them, plus the freeway they are driving on; two friends on the phone, plus the telephones they hold, plus the telephone line connecting them; Telegraph Hill with all its buildings, services and inhabitants; the chain of Rexall drug stores; the physical elements of San Francisco that fall under the administrative authority of City Hall; everything within the physical boundary of San Francisco, plus all the people who visit the 124

126 city regularly and contribute to its development (like Bob Hope or the president of Arthur D. Little), plus all the major sources of economic welfare which supply the city with its wealth; the dog next door, plus my garbage can, plus the garbage out of my garbage can which he lives on; the San Francisco chapter of the John Birch Society. (Ibid.) And to be in line with his understanding of a system, Alexander argues that there are inner forces in a city bringing things together that need to be unveiled. Each one of these is a set of elements made coherent and co-operative by some sort of inner binding forces. And each one, just like the traffic light-newsrack system, has a physically fixed part which we think of as a unit of the city. (Ibid.) The semi-lattice and the tree organization in a nutshell: The semi-lattice axiom goes like this: A collection of sets forms a semi-lattice if and only if, when two overlapping sets belong to the collection, then the set of elements common to both also belongs to the collection. The tree axiom states: A collection of sets forms a tree if, and only if, for any two sets that belong to the collection, either one is wholly contained in the other, or else they are wholly disjoint. (Ibid.) For Alexander, a semi-lattice accommodates a bigger number of connections, if compared with the tree; hence, it is a complex model. It is not merely the overlap which makes the distinction between the two important. Still more important is the fact that the semi-lattice is potentially a much more complex and subtle structure than a tree. We may see just how much more complex a semi-lattice can be than a tree in the following fact: a tree based on 20 elements can contain at most 19 further subsets of the 20, while a semi-lattice based on the same 20 elements can contain more than one million different subsets. (Ibid.) And the promise is that we can model the city in its totality with a semi-lattice. This enormously greater variety is an index of the great structural complexity a semi-lattice can have when compared with the structural simplicity of a tree. It is this lack of structural complexity, characteristic of trees, which is crippling our conceptions of the city. (Ibid.) Alexander continues building his argument by presenting a number of cities that can be recognized as belonging to a tree structure, i.e., an artificial city. He names a few. Columbia, Maryland, Community Research and Development Inc.Greenbelt, Maryland, Clerence Stein Greater London plan (1943), Abercrombie and Forshaw Tokyo plan, Kenzo Tange Mesa City, Paolo Soleri Chandigarh (1951), by Le Corbusier Brazilia, Lucio Costa Communitas, Pervical and Paul Goodman The Nature of Cities, Hilberseimer. The units of which an artificial city is made up are always organised to form a tree. (Ibid.) And presents different metaphors for a tree and a semi-lattice. 125

127 The structural simplicity of trees is like the compulsive desire for neatness and order that insists that the candlesticks on a mantelpiece be perfectly straight and perfectly symmetrical about the centre. The semi-lattice, by comparison, is the structure of a complex fabric; it is the structure of living things - of great paintings and symphonies. (Ibid.) For Alexander, a semi-lattice does not represent a structural loss of order or rigidity; on the contrary, it presents a way to model more complex structures. It must be emphasised, lest the orderly mind shrink in horror from anything that is not clearly articulated and categorised in tree form, that the ideas of overlap, ambiguity, multiplicity of aspect, and the semi-lattice, are not less orderly than the rigid tree, but more so. They represent a thicker, tougher, more subtle and more complex view of structure. (Ibid.) As designers, we need to think the living city is a semi-lattice. In the worst trees, the units which do appear fail to correspond to any living reality; and those real systems, whose existence actually makes the city live, have been provided with no physical receptacle. (Ibid.) Previous designers have thought differently maybe even he, himself, thought differently and the result is a city that does not properly accommodate the necessities of a living city. Another favourite concept of the CIAM theorists and others is the separation of recreation from everything else. This has crystallised in our real cities in the form of playgrounds. The playground, asphalted and fenced in, is nothing but a pictorial acknowledgement of the fact that play exists as an isolated concept in our minds. It has nothing to do with the life of play itself. (Ibid.) An example of desirable and successful events in a natural city: Play itself, the play that children practise, goes on somewhere different everyday. One day it may be indoors, another day in a friendly gas station, another day in a derelict building, another day down by the river, another day on a construction site which has been abandoned for the weekend. In a natural city this is what happens. Play takes place in a thousand places it fills the interstices of adult life. As they play, children become full of their surroundings. How can a child become filled with his surroundings in a fenced enclosure? He can't. In a semilattice, he can; in a tree, he can't. (Ibid.) But when did we start thinking in tree-like structures? he asks. The tree though so neat and beautiful as a mental device, though it offers such a simple and clear way of dividing a complex entity into units does not describe correctly the actual structure of naturally occurring cities, and does not describe the structure of the cities which we need. (Ibid.) 126

128 Alexander s hypothesis of the origins of tree-like cities points to an old designer s habit to envision things as trees in their minds, due to the inability to perceive complexity in its totality as a mental image. I shall try to convince you that it is for this second reason that trees are being proposed and built as cities that it is because designers, limited as they must be by the capacity of the mind to form intuitively accessible structures, cannot achieve the complexity of the semi-lattice in a single mental act. (Ibid.) It is just impossible, he says, to grasp the complexity of a system in a single moment. And the only way to articulate this complexity is with tree-like structures. You cannot bring the semi-lattice structure into a visualisable form for a single mental act. In a single mental act you can only visualise a tree. This is the problem we face as designers. While we are not, perhaps, necessarily occupied with the problem of total visualisation in a single mental act, the principle is still the same. The tree is accessible mentally, and easy to deal with. The semi-lattice is hard to keep before the mind's eye, and therefore hard to deal with. (Ibid.) Any articulation of a city will aways be a tree-like structure, Alexander says. It is for this reason because the mind's first function is to reduce the ambiguity and overlap in a confusing situation, and because, to this end, it is endowed with a basic intolerance for ambiguity that structures like the city, which do require overlapping sets within them, are nevertheless persistently conceived as trees. (Ibid.) But when we agree on Alexander s characterization, a practical question arises: Is it even possible to model a city as a semi-lattice structure? You are no doubt wondering, by now, what a city looks like which is a semi-lattice, but not a tree. I must confess that I cannot yet show you plans or sketches. It is not enough merely to make a demonstration of overlap the overlap must be the right overlap. (Ibid.) He seems to believe so, and to be working on it. The work of trying to understand just what overlap the modern city requires, and trying to put this required overlap into physical and plastic terms, is still going on. Until the work is complete, there is no point in presenting facile sketches of ill thought out structure. (Ibid.) And he finalizes: For the human mind, the tree is the easiest vehicle for complex thoughts. But the city is not, cannot, and must not be a tree. The city is a receptacle for life. If the receptacle severs the overlap of the strands of life within it, because it is a tree, it will be like a bowl full of razor blades on edge, ready to cut up whatever is entrusted to it. In such a receptacle life will be cut to pieces. If we make cities which are trees, they will cut our life within to pieces. (Ibid.) We are not aware of Alexander presenting the semi-lattice diagram that he promised. What he 127

129 did present, though, was A Pattern Language (1977), yet another methodology for building and planning. The difference that we see with the work discussed here is that he seems to renounce understanding the inner structure of a city as a whole, but not understanding the inner structure of its events. A pattern describes a problem which occurs over and over again in our environment, and then describes the core of the solution to that problem, in such a way that you can use this solution a million times over, without ever doing the same way twice (Alexander 1977:x). A pattern presents the nature of the relation between problems and solutions, and each solution capture[s] the invariant property common to all places which succeed in solving the problem (Ibid.:xiv). He argues that each town or city must have their own pattern language, and that it should be put together by the people living in the city. Alexander presents a language as a system of generic solutions to architectural and urban problems Linguistic Talks Christopher Alexander is not the only contemporary who makes analogies between architecture and language. A number of architects present clear views on architecture that seem to be influenced by the philosophical approaches to language of the early 20c. They celebrate the analogies between language and architecture (Jencks 1981); identify languages, vocabularies, and grammars in traditional architectural objects; and present methods to create language-like structures to design and build. For a number of architects, talking about architecture as a language allows for different degrees of both expression and verification. John Summerson (1964) in The Classical Language of Architecture is interested in the nature and use of language in classical buildings. A classical building is one whose decorative elements derive directly or indirectly from the architectural vocabulary of the ancient world the classical world as it is often called: these elements are easily recognizable, as for example columns of five standard varieties, applied in standard ways; standard ways of treating door and window openings and gable ends and standard runs of mouldings applicable to all these things (Ibid.:7). He suggests that an architectural artifact can be analyzed and further understood by identifying its vocabulary and the meaning of its elements. Summerson uses the vocabulary as a measure to determine if, and how well, a building speaks a particular language. Another example is Bruno Zevi, who explicitly follows Summerson s interest. He published The Modern Language of Architecture (Zevi 1978), in which he argues that architects necessarily communicate, and that design requires the vocabulary, the grammar, and the syntax of a language. Zevi s goal is to establish a series of invariables in the modern language of architecture, based on the most significant and challenging buildings (Ibid.:5). He identifies and analyses seven invariables in modern buildings: listing as design methodology; asymmetry and dissonance; anti-perspective three-dimensionality; the syntax of four-dimensional 128

130 decomposition; cantilever, shell, and membrane structures; space in time; and, reintegration of building, city, and landscape. The validity of these variables, he says, should be tested on drawings and on architectural artifacts, and these invariables should further equip architects to speak architecture, rather than talk about architecture. Today, Eisenman still discusses architecture in terms of language. When asked about Koolhaas Elements of Architecture, he replied, If architecture is to be considered a language, elements don t matter. So for me what s missing [from the show], purposely missing, is the grammatic (Eisenman 2014). What we find interesting in these understandings of architecture is that they analyze architectural artifacts and synthesize their hidden structure, inner nature, or ordering principles just like we see Alexander does. This requires a deep understanding of its elements and their relations. And in turn, the synthesized rules, patterns, or grammars aim to validate the use of a specific language in architecture as for Alexander it is validating his design process. To characterize architecture in linguistic terms seems to promise the insertion of subjectivity into architecture while keeping a structural talk. To be expressive while providing at the same time the means to validate such expression Remarks We see in Alexander s work that for him architecture is about solving complex problems. In order to solve a complex problem, he first needs to have a deep understanding of it its inner structure should be understood. Throughout his work we can see his struggles when trying to understand, model, and operate complexity, and we see a peek in A City Is Not a Tree, where he exposes the limits of his own methods by affirming infinity. He recognizes that there can be infinite components in a whole, infinite ways for these components to talk to each other, and infinite ways for people to talk to these components, and that an architect has just so much to say. From there on, we see how he gradually relaxes this idea. We see his book, The Timeless Way of Building (Alexander 1979), as a poem to the city. As late Alexander, we are interested in talking about architecture while affirming infinity, but not in terms of full understandings, inner natures, synthesized rules, or patterns. A look with care to prominent online applications on the global network shows that there is no room for analysis and synthesis, not in Alexander s terms. When using Foursquare in a first-time visit to a city, for example, it will suggest to us a place to eat. We can move around in the city and talk to it and have a joyful meal without a prior analysis of the city, restaurants, or customs. The suggestions are based on observations of past meals, and not on a full understanding of the meal or the city itself. This would present a major challenge for Alexander, because the global network seems to have turned around his view of the world. Online applications seem to see any phenomenon as 129

131 a solution to a problem. In this new setup, the question is: How can we articulate good questions, if we have any answers? [6/10] Architectural Curvilinearity complexity, smoothness, vicissitude, continuity, mixing, blending, pliant Figure 1.48: Blobwall by Greg Lynn. 16 In Architectural Curvilinearity: The Folded, the Pliant, and the Supple, Greg Lynn 17 presents a plane to discuss his interplays of curvilinear forms. His main assumption is that buildings and cities are complex and that he needs to smooth out their differences and contradictions, for which the computed forms are a fundamental part. Lynn celebrates the characterization of architecture and cities as rough systems. For the last two decades, beginning with Robert Venturi s Complexity and Contradiction in Architecture, and Colin Rowe and Fred Koetter s Collage City, and continuing through 16 Figure: (accessed ). 17 Greg Lynn is an architect and designer. He was honored with the American Academy of Arts and Letters Architecture Award in Forbes magazine named Lynn one of the ten most influential living architects in 2005, and in 1999 Time Magazine named him one of 100 of the most innovative people in the world for the 21st century. He was named a 2010 Fellow of United States Artists (USA). His work is in the permanent collections of the Art Institute of Chicago, the San Francisco Museum of Modern Art, the Museum of Modern Art in New York City, and the Canadian Center for Architecture in Montreal [1]. He is Professor of Architecture at the UCLA School of the Arts and Architecture and at the University of Applied Arts Vienna. He hosts the Greg Lynn Show at the Canadian Center for Architecture (CAA)[2]. Lynn is the author of several books where he reflects on the implications of the computer-aided design tools and their specific models in architecture and arts. His work reflects an interest in computer generated form based on calculus. [1] See his profile at the UCLA website at (accessed 2017). [2] See the show online at (accessed ). 130

132 Mark Wigley and Philip Johnson s Deconstructivist Architecture, architects have been primarily concerned with the production of heterogeneous, fragmented and conflicting formal systems. (Lynn 1993) Two main works give Lynn the stability to construct the plane for his interplays in architecture. Both Venturi and Wigley argue for the deployment of discontinuous, fragmented, heterogeneous and diagonal formal strategies based on the incongruities, juxtapositions and oppositions within specific sites and programmes. These disjunctions result from a logic which tends to identify the potential contradictions between dissimilar elements. (Ibid.) Lynn argues that the question of complexity in architecture is relevant today due the advent of computer-aided design tools, finding the answer in smoothness. In response to architecture s discovery of complex, disparate, differentiated and heterogeneous cultural and formal contexts, two options have been dominant; either conflict and contradiction or unity and reconstruction. Presently, an alternative smoothness is being formulated that may escape these dialectically opposed strategies. (Ibid.) Lynn s smoothness in a nutshell: Smooth mixtures are made up of disparate elements which maintain their integrity while being blended within a continuous field of other free elements. Smoothing does not eradicate differences but incorporates free intensities through fluid tactics of mixing and blending. Smooth mixtures are not homogeneous and therefore cannot be reduced. For the first time perhaps, complexity might be aligned with neither unity nor contradiction but with smooth, pliant mixture. Both pliancy and smoothness provide an escape from the two camps which would either have architecture break under the stress of difference or stand firm. Pliancy allows architecture to become involved in complexity through flexibility. Pliancy implies first an internal flexibility and second a dependence on external forces for self-definition. If there is a single effect produced in architecture by folding, it will be the ability to integrate unrelated elements within a new continuous mixture. (Ibid.) For Lynn, architecture is about having all contingent events connected in one operable and encompassing form. Unlike an architecture of contradictions, superpositions and accidental collisions, pliant systems are capable of engendering unpredicted connections with contextual, cultural, programmatic, structural and economic contingencies by vicissitude. (Ibid.) Lynn s understanding of vicissitude: Vicissitude is a quality of being mutable or changeable in response to both favourable and 131

133 unfavourable situations that occur by chance. Vicissitudinous events result from events that are neither arbitrary nor predictable but seem to be accidental. These events are made possible by a collision of internal motivations with external forces. (Ibid.) And how a viscous space would look. Viscous space would exhibit a related cohesive stability in response to adjacent pressures and a stickiness or adhesion to adjacent elements. Viscous relations such as these are not reducible to any single or holistic organisation. (Ibid.) This is the setup to discuss a computed curvilinearity capable of opposing the arbitrary values and meanings that emerge from architecture and cities. The contradictory architecture of the last two decades has evolved primarily from highly differentiated, heterogeneous contexts within which conflicting, contradictory and discontinuous buildings were sited. An alternative involvement with heterogeneous contexts could be affiliated, compliant and continuous. In both Learning from Las Vegas and Deconstructivist Architecture, urban contexts provided rich sites of difference. These differences are presently being exploited for their ability to engender multiple lines of local connections rather than lines of conflict. These affiliations are not predictable by any contextual orders but occur by vicissitude. Here, urban fabric has no value or meaning beyond the connections that are made within it. (Ibid.) For Lynn, the form of a city should be the effect of the city s internal logic. We ask him, how can we bring a city s own logics to form? How can we think of this curvilinear form beyond a computer calculated function? These folded, pliant and supple forms of urbanism are neither in deference to nor in defiance of their contexts but exploit them by turning them within their own twisted and curvilinear logics. To become complicated is to be involved in multiple complex, intricate connections. Where Post-Modernism and Deconstructivism resolve external influences of programme, use, economy and advertising through contradiction, compliancy involves these external forces by knotting, twisting, bending and folding them within form. (Ibid.) Indexes pointing to our answers can be found in other fields and industries that have proven to be valuable to our society. The morphing effects used in the contemporary advertising and film industry may already have something in common with recent developments in architecture. These mere images have concrete influences on space, form, politics and culture. (Ibid.) The form that Lynn is talking about can be seen in the film industry and in his architectural artifacts. A similar comparison might be made between the liquid mercury man in the film 132

134 Terminator 2 and the Peter Lewis House by Frank Gehry and Philip Johnson. The Hollywood special effects sequences allow the actor to both become and disappear into virtually any form. The horror of the film results not from ultra-violence, but from the ability of the antagonist to pass through and occupy the grids of floors, prison bars and other actors. (Ibid.) For Lynn, the novelty lies in the curvilinearity s ability to (a) connect two fixed forms that have no apparent common ground and (b) create a form in-between. Computer technology is capable of constructing intermediate images between any two fixed points resulting in a smooth transformation. These smooth effects calculate with probability the interstitial figures between fixed figures. (Ibid.) Going through a number of projects, Lynn finds his ideas rendered in specific typologies. So far in architecture, Deleuze s, Cobb s, Eisenman s and Hoberman s discourse inherits dominant typologies of organisation into which new elements are folded. Within these activities of folding it is perhaps more important to identify those new forms of local organisation and occupation which inhabit the familiar types of the Latin cross church, the siedlung, the office tower and the stadium, rather than the disturbances visited on those old forms of organisation. (Ibid.) Lynn sees in these artifacts the concepts he has been discussing. And exalts the abilities that he argues for. Despite the differences between these practices, they share a sensibility that resists cracking or breaking in response to external pressures. These tactics and strategies are all compliant to, complicated by, and complicit with external forces in manners which are: submissive, suppliant, adaptable, contingent, responsive, fluent, and yielding through involvement and incorporation. The formal affinities of these projects result from their pliancy and ability to deform in response to particular contingencies. (Ibid.) 133

135 [7/10] Blobs complexity, polysurface, difference, repetition, interaction, multiplicity, influence Figure 1.49: Recycled Toy Furniture by Greg Lynn. 18 Greg Lynn presents in Blobs a theory of complexity. It places great emphasis on complex geometry and sees special-effects software as helpful tools to model it. The origins of the blob as a concept can be indexed by this industry. Lynn recognizes that the concept of complexity has been a starting point for architectural theory in the last years, and his theory is no exception. In the last three decades, if one word could be identified as having a primary effect on architectural theory and design, that word would most likely be complexity. The meaning of the term complexity has varied widely, yet its use as a vehicle for launching new ideas in architecture has been consistent. (Lynn 1995:157) Lynn presents a theory of complexity in architecture that does not engage with a concept of identity that is characterized by the singular or the plural, but by the in-between. In order to develop a theory of complexity that is not founded on the contradiction of differences it is necessary to reconceptualize identity as neither reducing toward primitives nor emerging towards wholes. A theory of complexity that abandons either the single or the multiple in favor of a series of continuous multiplicities and singularities is one way of escaping the definition of identity through dialectic contradiction. one approach to a theory of complexity might be to develop a notion of the composite or the assemblage which is understood as neither multiple nor single, neither internally contradictory nor a unified. Complexity involves the fusion of multiple and different systems into an assemblage which behaves as a singularity while remaining irreducible to any single simple organization. (Ibid.:161) Lynn s account of complexity does not escape being characterized as discrete components interconnected. 18 Figure: Dezeen 2008 at (accessed ). 134

136 The terms multiplicity and singularity both describe a linked assemblage of discrete components, although in two ways. The first is a provisional composition that exhibits a collective identity or a singularity. The second is a provisionally unified composition that exhibits its own internal diversification or a multiplicity. Singularity and multiplicity are mutually constituative terms as one that is internally multiple is termed a multiplicity and many that are aggregated into an assemblage are termed a singularity. (Ibid.:162) Geometric complexity is argued to be achieved by a top-down and bottom-up approach, both being a failure in Lynn s understanding. He nevertheless thinks it is strictly necessary to develop a model of complex geometry. Both reductive and emergent theories of complexity contain geometric assumptions. A theory of iterative reduction through variation emerges from a top-down elimination of complexity towards a simple geometric type. On the other hand, the formation of a higher level dynamical or structurally stable type through emergence is implied by a bottom-up development of complexity from a simple collection of types. Both assumptions are inadequate to describe the relationships within a continuously differentiated multiplicity. Nevertheless, in order to develop a theory of complexity, it is necessary to develop an abstract model of its relations, a task for which geometry has been invoked throughout the history of philosophy. (Ibid.) Lynn looks for the geometrical model that can be the third between complexity and contradiction. The question remains, if complexity and contradiction were characterized by the conflict of geometric systems, what is the implicit spatial model with which one can measure a complex relationship that is not reducible to either the contradiction of the many or the wholistic unity of one. (Ibid.) Lynn s quest points to the blob. Widely popular today in the special effects industry. A class of topological geometric types for modeling complex aggregates that exhibits the qualities of multiplicity and singularity outlined above has recently been developed. The most interesting example of these topological types are isomorphic polysurfaces or what in the special effects and animation industry are referred to as meta-clay, meta-ball or blob models. (Ibid.:163) Lynn s characterization of a blob, in a nutshell: For example, in their blob modeling package, objects are defined by monad-like primitives with internal forces of attraction and mass. Unlike a conventional geometric primitive such as a sphere, these objects are defined with a center, a surface area, a mass relative to other objects and importantly by two types of fields of influence. These meta-ball primitives are surrounded by halos of influence. (Ibid.:164) A blob is both singular and plural. This is what differentiates the blob from the previous models of complex geometry presented by Lynn. 135

137 From the perspective of the unified surface it is a singularity (as it is contiguous but not reducible to a single order) and from the perspective of the constituent components it is a multiplicity (as it is composed of disparate components that are put into a complex relation). (Ibid.) What follows in Lynn s theory of complexity is the incorporation of time. Along with an abstract geometrical model or typology, the primary component of any complex organization is temporal development. (Ibid.:165) It is through repetition that primitive geometric models become complex models. Iterative differentiation is necessary for the development of a theory of complexity that integrates time, suggesting a repetition with difference, or iteration, that is proliferative rather than reductive. Such a theory of complex organization in architecture would incorporate temporal variation within the development of alternative geometric types. (Ibid.) Each iteration aggregates the influence of the exterior. Iteration does not aim to reduce or aggregate but to make the interactions part of itself, part of the blob. In this model, simplicity and complexity coexist and influence each other. In the case of the isomorphic polysurfaces, a low number of interacting components and/or a stable relationship of those components over time leads to a global form that is more simple and stable and less complex and unstable. The qualification of their organization as more or less simple as opposed to reducible and as more or less stable rather than static is a crucial distinction. A high number of components and/or a gradual or abrupt change in relative position of those components over time leads to a global form that is more complex and unstable and less simple and stable. (Ibid.:166) An example of a simple and complex geometry in Lynn s model can be seen in the difference between a sphere and a blob, as he describes. According to this logic, there is no essential difference between a more or less spherical formation and a blob. The sphere and its provisional symmetries are merely the index of a rather low level of interactions where the blob is an index of a high degree of information in the form of differentiation between components in time. (Ibid.) Lynn s final remarks: Tell me how much a system behaves like a blob and I will tell you how complex the system is. Indeed, the sphere is exposed as a blob when it demonstrates the capacity of fluid and continuous differentiation based on interactions with neighboring forces with which it can be either inflected or fused to form higher degrees of singularity and multiplicity simultaneously. Complexity, therefore, is not only always present as potential in even the most simple or primitive of forms; but, even more so, it is measured by the degree of both continuity and difference that are copresent at any moment. This measure of complexity (the index of which is continuity and differentiation) might best be described as the degree 136

138 to which a system behaves as a blob. (Ibid.) [8/10] Animate Form virtuality, topology, time, parameters, form, field, model, shape, curvature, spline, calculus Figure 1.50: Greg Lynn, Embryological House: Size A eggs, ca Animation is a difficult concept in architecture, Lynn argues, because it challenges the established notions of motion and gravity. With the advent of computer-aided design software, it seems only necessary for Lynn to reflect on the implications of modeling a population of elements in constant influence. And to discuss what is it that makes this modeling different from its predecessors. Animation is a term that differs from, but is often confused with, motion. While motion implies movement and action, animation implies the evolution of a form and its shaping forces; it suggests animalism, animism, growth, actuation, vitality and virtuality. In its manifold implications, animation touches on many of architecture s most deeply embedded assumptions about its structure. What makes animation so problematic for architects is that they have maintained an ethics of statics in their discipline. Because of its dedication to permanence, architecture is one of the last modes of thought based on the inert. (Lynn 1999:9) Lynn argues that architectural design is always virtual because it does not deal with the fabrication of the artifact. Thus, use of the term virtual here refers to an abstract scheme that has the possibility of becoming actualized, often in a variety of possible configurations. Since architects produce drawings of buildings and not buildings themselves, architecture, more than any other discipline, is involved with the production of virtual descriptions. (Ibid.:10) But even when architects don t produce buildings, but just the possibility of their actualization, 137

139 architects are shy with regard to the explorations of space, he argues. An example: Architects do not go outside Cartesian spaces. There is one aspect of virtuality that architects have neglected, however, and that is the principle of virtual force and the differential variation it implies. Architectural form is conventionally conceived in a dimensional space of idealized stasis, defined by Cartesian fixed-point coordinates. Contemporary animation and special-effects software are just now being introduced as tools for design rather than as devices for rendering, visualization and imaging. (Ibid.:11) And this is what Lynn s design in animation is about, to explore form and shape beyond an existence in an initial condition of X, Y, and Z. animate design is defined by the co-presence of motion and force at the moment of formal conception. Force is an initial condition, the cause of both motion and the particular inflections of a form. entities are given vectorial properties before they are released into a space differentiated by gradients of force. Instead of a neutral abstract space for design, the context for design becomes an active abstract space that directs form within a current of forces that can be stored as information in the shape of the form. Rather than as a frame through which time and space pass, architecture can be modeled as a participant immersed within dynamical flows. (Ibid.) The idea of motion is not totally unique in the architectural discourse; nevertheless, there s some novelty in it. Lynn indexes a few prominent examples. Previous architectural experiments in capturing motion have involved the superimposition of simultaneous instances. The superimposition of a sequence of frames produces memory in the form of spatio-temporal simultaneity. This idea of an architecture in which time is built into form as memory has been a persistent theme throughout its history, but it was Sigfried Giedion in both Mechanization Takes Command (1948) and Space, Time, and Architecture (1941) who established these themes as the primary concern of twentieth-century architectural theory and design. (Lynn 1999:11) Another model of indexical time is associated with Colin Rowe and his disciples. In Rowe s text, Transparency: Literal and Phenomenal, co-authored with Robert Slutzky, the idea of a formal, or phenomenal, transparency is proposed along with literal transparency. Phenomenal transparency is the tracing or imprinting of a deeper formal space on a surface. (Ibid.:12) For him, these examples are still timid in the sense that they talk about static forms placed next to, on top of, or added to each other. In all of these indexical responses to time, a superimposition or sequence of static forms is put into relation such that the viewer resolves multiple states through the initiation of optical motion. (Ibid.:13) And what Lynn articulates is a modeling space of forces, where the elements evolve in shape, all 138

140 together, by constantly talking to each other about themselves and their context. The modeling of architecture in a conceptual field populated by forces and motion contrasts with these previous paradigms and technologies of formal stasis. However, statics does not hold an essential grip on architectural thinking as much as it is a lazy habit or default that architects either choose to reinforce or contradict for lack of a better model. Each of these assumptions [permanence, usefulness, typology, procession, and verticality] can be transformed once the virtual space in which architecture is conceptualized is mobilized with both time and force. (Ibid.) Lynn s modeling space challenges the importance of gravitational forces in architectural design. Buildings don t always go downwards; they can also go upwards, he says. Finally, static models underwrite the retrograde understanding of gravity as a simple, unchanging, vertical force. The relationships of structure to force and gravity are by definition multiple and interrelated, yet architects tend to reduce these issues to what is still held as a central truth: that buildings stand up vertically. (Ibid.:14) Mathematical models of motion are not the first choice for architects, nor the easiest. The algebraic tools for architecture are more generic than the tools for calculus, as the latter call for computation. architects infrequently use calculus for the design of form. The fact that architecture is so heavily dependent on mathematics for the description of space has been a stumbling block to the use of motion and flow in the design process, as these ideas require that architects draw geometries whose underlying mathematics is calculus. The tools that architects use to draw, such as adjustable triangles and compasses, are based on simple algebra. The prevalence of topological surfaces in even the simplest CAD software, along with the ability to tap the time-and-force modeling attributes of animation software, presents perhaps the first opportunity for architects to draw and sketch using calculus. (Ibid.:16) Today, the computer-aided design software to model splines and blobs is generic, and their results are easy to differentiate because they point back to their mathematical models. there are distinct formal and visual consequences of the use of computer animation. For instance, the most obvious aesthetic consequence is the shift from volumes defined by Cartesian coordinates to topological surfaces defined by U and V vector coordinates. Another obvious aesthetic byproduct of these spatial models is the predominance of deformation and transformation techniques available in a time-based system of flexible surfaces. These are not merely shapes but the expression of the mathematics of the topological medium. (Ibid.:18) He discusses the main concepts around animation that make it possible and distinguishable from other modeling techniques. There are three fundamental properties of organization in a computer that are very 139

141 different from the characteristics of inert mediums such as paper and pencil: topology, time, and parameters. (Ibid.:20) The linkages between these characteristics of time, topology, and parameters combine to establish the virtual possibilities for designing in an animate rather than static space. Each of these characteristics can be used to rethink the familiar Cartesian space of neutral equilibrium as a more active space of motion and flow. (Ibid.:25) The elements modeled in animation are topological; hence, their potentials and abilities are different from those modeled in a Cartesian space. One of the first principles of topological entities is that because they are defined with calculus they take the shape of a multiplicity; meaning they are not composed of discrete points but rather, they are composed of a continuous stream of relative values. (Ibid.:20) We look at a line next to a spline so as to characterize a spline in Lynn s context. Instead of being defined by points and centers, topology is characterized by flexible surfaces composed of splines. These splines are oriented in an opposing U and V orientation to construct surfaces composed of curve networks. Unlike lines, splines are vectors defined with direction. (Ibid.) The spline curve is unlike a line or radius in that its shape is not reducible to exact coordinates. The spline curve flows as a stream between a constellation of weighted control vertices and any position along this continuous series can only be defined relative to its position in the sequence. (Ibid.:22) Calculus is the study of constant chance; hence, time is embedded in these mathematical models. Curvature in a temporal environment is the method by which the interaction of multiple forces can be structured, analyzed, and expressed. The calculation of time as expressed through curvature is possible with calculus, which animates numerical snapshots at an infinite speed, simulating time. (Ibid.:23) Parameters are the design decisions in Lynn s modeling space. The shapes that are formed in computer-aided design are the result of decisions made using parameters. Numerical data which describe characteristics of the virtual design environment-such as temperature, gravity, and other forces-have an impact on the forms which result. (Ibid.:25) We find it interesting that modeling in animation is about elements talking to each other about themselves and their context. This introduces the idea of modeling in population and the impossibility of modeling a single element. The impossibility of modeling taxonomic elements. This possibility of an animate field opens up a more intricate relationship of form and field than has been previously possible. Rather than an entity being shaped only by its own internal definition, these topological surfaces are inflected by the field in which they are 140

142 modeled. If an entity is moved in space, its shape might change based on the position within gradient space even though the definition of the entity remains constant. (Ibid.:32) This is the setup that Lynn proposes thinking about. It requires technical abstraction and stays open to the meaning of form. The use of parameters and statistics for the design of form requires a more abstract, and often less representational origin for design. The shape of statistics, or parameters, may yield a culturally symbolic form, yet at the beginning, their role is more inchoate. (Ibid.:39) Lynn s final remarks. It is in the spirit of the abstract technical statement yet to become concrete that topologies, animation and parameter-based modeling are being explored here. In order to bring these technologies into a discipline that is defined as the site of translation from the virtual into the concrete, it is necessary that we first interrogate their abstract structure. (Ibid.:40) Remarks Greg Lynn thinks of the computer generated form as a way to smooth out complexity in architecture. His gesture is to cover with a geometrical model the differences that a city or artifacts may engender. We see this gesture in opposition to the way online applications on the global network operate. On the global network, the differences between objects are celebrated while they remain operable. The global network itself is about differences between applicationabilities; it is heterogeneous and oppositions appear, but by following a protocol, a simple handshake, they are able to remain different and talk to each other. For example, the web with its billions of documents and applications online remains operable because it follows the Hypertext Transfer Protocol (HTTP). There is no need to smooth things out with the same handshake we can talk to an entire community, to the local store, our bank, or a car. Lynn works with populations of architectural artifacts that can talk to their environment, and influence and be influenced by it. We see in the computed generated from a specificity that limits their abilities, i.e., they talk in specific measures about specific forms, like gravitational forces, or the distances between them. We are interested in exploring interplays that accommodate populations that are not necessarily of the same kind, of the same nature, and still able to talk to each other. What we experience online today are spectrums of suggestions based on previous observations something like, if you liked this color you may also like that color. We think there is no technical limitation to the arbitrary meters or measures we can construct in order to have different objects talking to each other something like, if you like this color, you may also like that texture. This is how recommendation engines operate, and we will talk about this idea in the next 141

143 chapter. [9/10] Earth Moves images, frames, chance, singularity, orography Figure 51: Pure events along a vector. 19 In Earth Moves, Bernard Cache 20 discusses infinity through the generic models engendered by his interplays between architecture and computers. He sees in the spline an index of pure events, which in turn can accommodate any vector. The same phenomenon happens in architecture, he says, because architecture is about enframing chance. This book is about the development of an arbitrary meter to measure architectural events. Topography is a primary concern in the establishment of cities. The best example may be a city that is rich in geography: Laussane. (Cache 1995:6) Cache tells stories of Laussane: Lac Léman; green plane on the hills, blue plane of the lake; the plane of the Ceinture Pichard; the Flon and the Louvre; a Gallo-Roman port; the narrow spur of the Cité. This formalist history of Lausanne should suffice to put into question the notion of urban identity. For far from expressing the nature of a place, the identity of a city is eminently variable and assumes the most diverse forms. (Ibid.:10) For Cache, there are four figures that can be said to point to Lausanne s identity. In the case of the city of Lausanne, at least four distinct figures can be counted: the perched Cité, the city of the Bourg crest, the city of the valley that stretches along the Flon, the city of the Leman slope surrounded by the Ceinture Pichardo. (Ibid.) And they can be further drawn. For each of these urban identities, a geometrical figure can be drawn: a cone for the 19 Figure: Bernard Cache (Cache 1995). 20 Bernard Cache is an architect and architectural theorist. Professor of the Laboratory of Digital Culture for Architectural Projects at EPFL, he wrote a number of books, one of them dedicated to Gilles Deleuze, and in turn, Gilles Deleuze renamed a concept of his in his book on Leibniz, The Fold (Deleuze 1993). Cache reads classical texts with the help of CAD/CAM software, while addressing questions of chance, proportion, identity, invariance. 142

144 perched city, an inclined prism for the crest city, a dihedral for the valley, and a plane that stretches toward the lake for the sloped city. A sort of cubist sculpture of the city of Lausanne could then be constructed through the combination of these four basic figures: cone, prism, dihedral, and plane. (Ibid.:11) Figure 1.52: Sculpture of Lausanne. 21 A memory device for the identity of Lausanne. This sculpture is a mnemotechnical object. One must also remember that the surface of the territory is mobile and fluid as it is given to the continual distortions of memory. (Ibid.) What Lausanne s four figures have in common is topography. On each diagram thus folded, the vector expresses a way of raising the problem of topography. The series of diagrams indicate the different ways in which this question has been posed throughout history. (Ibid.) But topography does not tell much about linear historical events that can be helpful to establish a further common ground. But very quickly, it becomes clear that this series of vectors does not translate a simple historical succession. First of all, because during each period many secondary concerns confer additional values to each of these vectors. (Ibid.:12) These surfaces can be measured against each other by looking at how objects roll down their hills. More precisely, the first four historical concerns that have been described can all be translated into gravitational terms: letting stones fall, climbing a hill, positioning oneself on the thalweg, or choosing the least inclined plane. What counts, in fact, is the reading of a territory in terms of a conjunction between two sorts of images: concrete gravitational vectors and abstract vectorial space. (Ibid.) The inflection point of the gravitational vectors and that of the arbitrary abstract vectors do not necessarily match. Each abstract vector nails down a multiplicity of concrete values, such that the historical succession of vectors appears as a sort of repetition. It s not because of any genius loci that the cathedral s spire still preserves its meaning; it is rather that the abstract vector of 21 Figure: Bernard Cache (Cache 1995). 143

145 the site still designates the Cité as a place of predilection, whether as a seat for the Vaud parliament of as the place for local festivities. (Ibid.) Even when both vectors are talking about the same, Lausanne. But even beyond repetition, one must learn to read a space of transistance that allows us to pass from one vector to another. Throughout the ages, the identity of Lausanne has not so much changed, or repeated itself, as it has lived with itself under the determination of these four sorts of vectors. The real question is then to find a solution of contiguity between these four geometrical figures; it is a question of deploying a space of transistance from one identity to another. (Ibid.:14) Traditionally, architects choose the code for their models. In this example, Cache chooses the site as a general equivalent. It is also a question of craft. In the exercise of their profession, architects can choose to ground their practice in the concept of site. The work of architecture then becomes the expression of the specificity of the site that is to be built upon. (Ibid.) To address the site in terms of its identity does not seem to provide a good ground for Cache s study. Generally, today, it no longer seems possible to think in terms of identity. Whether it refers to the identity of a place or of a self, a substantialist way of thinking seems to lead to a dead end. For as soon as one attributes a particular identity to a particular place, the only possible modes of intervention then become imitation, dissimulation, or minimalism. (Ibid.:15) For Cache, identity is always there, and addressing a place s identity brings a discourse of negation and reduction. This task of working beneath the surface of identities has been a focus of recent philosophy. For the most part, however, this sort of work has only served to renew the practices of negative theology. According to this way of thinking, language belongs to the identical, and thus any discourse that is held beneath it can only proceed through negation or reduction. In architectural theory, this gives rise to statements such as reinforce the identity of a place, which implicitly means that identity is not given and must be constructed; but in fact identity is already there, and has only to be emphasized. The specificity of a place would thus only be its unaffirmed identity. (Ibid.) Therefore, he proposes working with the concept of singularity instead. Take the concept of singularity. In mathematics, what is said to be singular is not a given point, but rather a set of points on a given curve. A point is not singular; it becomes singularized on a continuum. (Ibid.:16) For Cache, singularities of a vector are in their extremes or in the points in between. We will then retain two types of singularity. On one hand there are the extrema, the 144

146 maximum and minimum on a given curve. And on the other there are those singular points that, in relation to the extrema, figure as in-betweens. These are known as points of inflection. They are different from the extrema in that they are defined only in relation to themselves, whereas the definition of the extrema presupposes the prior choice of an axis or an orientation, that is to say of a vector. (Ibid.:17) But pure events are only found in the vector s in-between. The point of inflection, however, designates a pure event of curvature where the tangent crosses the curve; yet this event does not depend in any way on the orientation of the axes, which is why it can be said that inflection is an intrinsic singularity. (Ibid.) For Cache, these pure events or points of inflection contain the totality of possible vectors, as they precede any vector. Points of inflection are singularities in and of themselves, while they confer an indeterminacy to the rest of the curve. Preceding the vector, inflection makes of each of the points a possible extremum in relation to its inverse: virtual maxima and minima. In this way, inflection represents a totality of possibilities, as well as an openness, a receptiveness, or an anticipation. (Ibid.) Cache presents so far three different levels of reading a territory. We are thus faced with three types of images or concepts: inflections, vectors, and the geometrical figures of identity. They are three sorts of images that are superimposed in the constitution of a territory, where each refers to a different level of reading. (Ibid.) With the just discussed concepts of inflection, vectors, and geometrical figures of identity, Cache looks back at Lausanne in its pure form. We are now confronted with a very peculiar image. It is that of the inflections of the relief of Lausanne: the orographic map. This map is a pure form because on its surface no signs or markings appear at all. The orographic design is a design without destiny, a map without a plan. (Ibid.:18) What makes this image special for Cache is that it reveals the inflection points, the singularities that contain all possibilities before language, before articulation. In Cache s talk, we think of these inflection points as infinity, from which Lausanne s paradoxes and contingent events will be articulated. For the thalweg, the line where the waters gather, is the line of an equilibrium restored, a twin line around which the river that seeks its course fluctuates. But the point of imbalance, the point of incline, is the point of inflection. In planar projection, it is the area where the contour lines are concentrated. Or, under another definition, the point of inflection becomes the point of a plateau from which the contour lines diverge. These are the facts that language betrays but that orographic maps display. (Ibid.:19) 145

147 Figure 1.53: Lausanne s orographic map. 22 Cache looks at the context of an architectural image, aiming to formalize it. An architectural practice that deals with the problem of site thus brings three basic images into play: the site plan (the orographic map), the vectorial sketch (the folded diagram), and finally those geometrical figures (cone, dihedron, prism, and plane) that give a cubist appearance to any urban composition. Can we find an abstract principle that specifies the nature of this third register of images? In other words, what is the architectural in an edifice? (Ibid.:22) For Cache, architecture is about building frames. Boundaries for events to happen in the inside. We can begin to answer this question by noting that, strictly speaking, architects design frames. This can be easily verified by consulting architectural plans, which are nothing but the interlocking of frames in every dimension: plans, sections, and elevations. Cubes, nothing but cubes. (Ibid.) The frame is the architect s basic expression. The frame reduces architecture to its most basic expression and allows us to formulate a concept that derives directly from Eugène Dupréel, whose philosophy was centered entirely on the notion of frame of probability. (Ibid.) Cache presents and sympathizes with Dupréel s work on the interval, or that which separates a cause and effect relationship. Chance is something that takes place. Dupréel criticized the classical causal scheme, remarking that no value has been attributed to the interval that separates the cause from the realization of its effect. For a cause to produce an effect, this interval must be filled. For in and of themselves, the set of causes that produce an effect are only frames of probability. One never knows how the 22 Figure: Bernard Cache (Cache 1995). 146

148 interval will be filled; otherwise, everything that is known about the interval would cross over to the side of the cause, and all one would have done is to define a more restricted frame of probability. And if, by any chance, no indeterminacy remained in the interval, the cause would become identical to the effect and nothing new could happen at all. (Ibid.:23) Reality fills our frames; frames become the probability space of reality. Experimental imprecision, the occurrence of unexpected events, are the signs that reality is a hollow image and that its structure is alveolar. Intervals always remain and intercalated phenomena always slip into them, even if they finally break the frames of probability apart. (Ibid.) With this argumentation, Cache defines architecture. Architecture would be the art of introducing intervals in a territory in order to construct frames of probability. This presupposes that the architectural frame fulfill at least three functions, whatever the concrete purpose of the building might be. (Ibid.) And further presents how to proceed to do architecture following functional activities. Walls are first. The first function is that of separation. Its functional element is the wall. One must delimit an interval in which a form of life that doesn't fit a priori in its milieu will occur. (Ibid.) Separation and selection are walls and windows. The second abstract function of the frame is selection. The frame thus becomes a window that carefully selects the causes of life in order to produce ever more singular effects. The first function of the frame removed us from the territory; the second function reestablishes connections, selectively. (Ibid.:24) The second function of the frame is to select the vector that will fold the abstract line and thus designate the apexes. (Ibid.:25) The third function is about arranging the inside so things can happen. It s about cultivating the interval: the floor. Once the interval is delimited and the vector selected, this interval must be arranged in such a way as to allow the frame of probability to produce its effects. The interval is a factor of absolute uncertainty. It is the flatness of the stage that makes choreography probable, just as it is the flatness of the stadium that increases the probability of athletics. The ground plane rarefies the surface of the earth in order to allow human activities to take shape. (Ibid.:25) For Cache, the roof can be seen as nothing more than a horizontal wall with no specificity. But still, it is in the roof where we can have indexes of territorial identity. We must see that in all instances, the roof belonged to a specific formal register: the prism, the dome, the cone, the pyramid. Here we encounter once again the figures of territorial identity, as well as the crest line or apex: the figures of extrinsic singularity. 147

149 (Ibid.:26) The sloping roof then differs from the three other elements of the frame, for it is neither an interval nor a cause; it is the envelope of an effect: it is the singular becoming of a place, of the domestic as an eminent place. (Ibid.:27) The roof is of another order: it envelops an event; it is the effect of singularization. (Ibid.:28) Cache articulates architecture while keeping distance from the events it frames. And this is the point, since it is just not possible to know how the interval will be filled. This impossibility does not limit the will or ability to construct frames around it. So far, we have only spoken of abstract functions and have not considered any concrete content. We have dealt neither with form nor with the function of the edifice. This is because the notion of frame of probability presupposes that a distance or dehiscence be maintained between a frame and its content: one never knows how the interval that is marked off by the frame will be filled. (Ibid.) From this perspective, architecture is an image that needs to be filled. We are then back to thinking of form as form, which means that we take things as images, with no relation to depth, to anteriority, or to use, and even less to representation. (Ibid.:29) Therefore, architecture, design, and territorial planning are not the same. In view of this cinema of things, we can proceed to a classification and verify that, formally, a building is not the equivalent of an object or a territory. And that therefore architecture, design, and the planning of territories require different skills, though all three work with form. (Ibid.) 148

150 [10/10] Towards a Non-Standard Mode of Production form, proportion, geometry, gnomon, invariance Figure 1.54: Non-standard technical details. 23 Cache asks why it is that non-standard modes of production are not at least remotely close to the contemporary modes of production that build our world. In the journey to an answer, he touches on long lasting questions of the tradition of architecture, i.e., form, proportions, topology, projection. Cache is not presenting an interplay between architecture and computers per se, but an articulation of their implications. What does non-standard architecture look like? Under what conditions does an expression like 'nonstandard architecture' have meaning? Perhaps it is easier to begin by saying what it's not. For, if non-standard architecture were to mean generating more or less fluid surfaces which are transferred onto a battery of CAM software in order to qualify as 'buildings or rather, very expensive kinds of sculpture that no longer have any relation to the historical and social fabric of the city then we would merely be perpetuating the romantic myth of the artist-architect. Over and above any polemical intention this negative introduction should help us to define the criteria that we need to cultivate if we want to exploit the possibilities of a non-standard architecture: at stake are the questions of form, city and productivity. (Cache 2005:60) The form of these fluid surfaces and splines are the first fascination of these generic models. Let's begin with form, since (why deny it?) this is where the 'fascination' lies. The use of CAD to generate surfaces that generally cannot be designed with ruler and compass instils in architects an extraordinary feeling of power. This feeling of omnipotence may be inspired in the first instance by highly ergonomic programs such as Rhino, which make it easy to create surfaces so complex that one can no longer be certain of their spatial coherence. (Ibid.) Agent based models also present fascinating forms. The how of these forms is not intuitive or 23 Figure: OBJECTILE: Bernard Cache and Patrick Beaucé. 149

151 easily graspable, even when the agents are just following simple rules. Then there are the complex generators, such as simulators of particle movements, that we find on graphics software like Maya, Softimage and others. the simplicity of an extremely transparent interface, here the sense of power comes, on the contrary, from being able to wield tools that are so complex that the means of form-generation are outside our control, so the result materialises as if by magic a seemingly random or chance occurrence. In this respect the chaos is entirely determinist, but since we don't comprehend the algorithmic determinants, the forms are imprinted with a kind of aura conferred by their alleged randomness. (Ibid.:61) But the fascinating forms that Cache is talking about are not exclusive to computer software. Handmade surfaces can also have such an effect. A third and ultimately much more honest approach is to set aside the computer and simply twist sheets of paper a time-honoured way of mocking up a sculpture. The advantage of this process is that it creates developable surfaces, ie ones with nil curvature, in other words surfaces that are intrinsically Euclidian. (Ibid.) These are three different strategies for the same purpose. In these three strategies 'non-standard' is equated with 'original' or 'complex', but in each case we remain entrenched in the Beaux-Arts mentality that treats every architectural project as the opportunity for a work of individual creation. (Ibid.) Cache dives into the concept of form. He discusses it by looking at how two forms are compared with each other, based on their proportions. Morphè, indeed. What is form? What properties must two objects share for them to be considered to have the same form? The answer lies in a concept that is fundamental to architectural theory and geometry alike. Two objects have the same form when, independently of their size, the angles between their elements are the same and, above all, their proportions are consistent. More precisely, the preoccupation with form is fuelled by a theory of proportions that must be clearly grasped if we are to avoid the pitfalls that have ensnared architectural thinking from neo-pythagorean acoustics to the Modulor of Le Corbusier. (Ibid.:62) Proportion in geometry goes way back to the old Greeks, Cache stresses, where proportion is a crucial concept for the evaluation of any material thing. We live in a world of images and simulacra. The visible world consists merely of copies of Ideas, which are the only entities to escape the cycle of coming-into-being and passing away. Referring specifically to the plastic arts in an architectural context, Plato notes that there are two kinds of copy on the one hand good copies, which respect the proportions of the model, and on the other simulacra, or shadows and reflections which distort the proportions. The Greek for proportion is logos, the Latin ratio, which takes us to the very root of rationality and discourse. For Plato every material thing is manifestly 150

152 corrupted by its coming-into-being, to the extent that no physical model can equal the eidôs, the Idea or Form. The perfect relationship, in Plato, is the one that will convert identity into an ideal proportion: the isometric relationship of sameness, the ratio of 1:1. (Ibid.:63) A prominent example: the evaluation of two different objects and their shadows. The shadow of the pyramid varies depending on the hour, day and season, but the relationship of the pyramid to its shadow remains identical to the relationship between the gnomon planted in the ground and its own shadow these relationships are invariants by variation, entanglements of being and becoming. (Ibid.:64) A definition of architecture is helpful to Cache to see that what is at stake with the question at hand can be articulated by the Greek evaluation of different objects. What relation can this very brief sketch of the history of geometry have with the opportunities we have, right now, to create an architecture that is genuinely nonstandard? To begin with, we can retain an altogether classical definition of architecture: the ordering of space in such a manner as to ensure the greatest possible freedom for the people who collectively frequent or colonise it. (Ibid.:65) For Cache, architecture is about fixing points in space and presenting ways to orient ourselves with gnomons. Ordering means equipping a space that is not naturally habitable with fixed points (invariants) and a means of orientation, for absolute space, without any kind of structure, is scarcely more inhabitable than the hyper-grid of a totalitarian architecture. (Ibid.) To cultivate gnomonic devices is to cultivate the non-standard. We need to find mediating devices that will ensure a supple variety in the necessary invariants, since between absolute variation and total invariance there is room for a whole spectrum of invariants by variation. (Ibid.:66) Proportions in architecture is a constant invariant in its tradition. architectural thinking has always emphasised proportional invariants. Even when attempting to elaborate a universal system of industrial standardisation, Le Corbusier still went back to proportion. That he then invoked a harmonic, neo-pythagorean concept dreamt up by nineteenth-century German ideologues does not in any way diminish the relevance of the idea of proportion in architecture; on the contrary, this modern error proves just how difficult it is to conceive of architecture without proportion. Moreover, whenever the theorists of the Italian Renaissance attempted to interpret the perspective system invented by Brunelleschi in 1420, they still returned to the system of proportions, striving (in vain) to drape the projective over the similitude by establishing simple ratios between the diminishing segments of a paved area seen in perspective, even though this is a classic case of the projective biratio. (Ibid.) The novelty that Cache believes the generic tools are introducing is the ability to work with 151

153 projection and deformation to levels of fascination. This formal analysis of course needs to be refined, but the more we consider the history of architecture from the CAD-CAM angle, the more it seems to us that tradition has always integrated, albeit in varying doses, these four types of invariant: isometric, homothetic, projective and topological. What is different today is that we now have the means to challenge the implicit system of hierarchy between these different registers and to develop more sophisticated invariants, both projective and topological. (Ibid.:67) Figure 1.55: The architecture of geometry according to the Erlangen Programme (1872). So what is missing is to think of the complementary similarity and isometry of such models. what we're aiming at is a means of integrating the different registers of invariants as an alternative to the solution promoted by the current media consensus architecture is better able to order the diversity of space when it brings each of the four registers of invariant into play, deterritorialising their traditional field of application the isometry of the central plan, the similitude of a proportional architectonics, the projectivity of complex solids, and the topology of intertwining ornaments. (Ibid.:67) Cache asks, how can the fragile state of production of non-standard architecture be brought to the level of production that actually builds our world today? Since urban relationships are determined, at least in part, by the relations of production, how do we ensure that a non-standard architecture becomes a true social fact rather than a luxury item for a well-heeled clientele? How do we prevent the non-standard from collapsing into original formalism? How can we guarantee that the object will be genuinely conceived and produced as a single instance in a series? How do we integrate the architectural object into the urban fabric? To all these questions there is, in our opinion, one basic response: the productivity of the various agencies of architecture, with conception keeping pace with fabrication. From this point of view, the question of nonstandard architecture is no different from the basic problem of postindustrial societies, namely the productivity of services in general. (Ibid.:68) The way software talk to each other in a non-standard mode of production is at its foundations. 152

154 Associativeness is the principle used in software that organises the architectural project in a long chain of relationships, from the first conceptual ideas to the driving of the machines that will prefabricate the components to be assembled on site. Designing on an associative software program comes down to transforming the geometrical design into a programming language interface. (Ibid.) Cache s diagnosis: The key problem of a non-standard mode of production lies in the lack of ability to operate the information that such a mode requires. the whole difficulty of nonstandard architecture lies in the sheer quantity of data that has to be generated and manipulated in order to industrially fabricate components that are totally different to each other at a cost no greater than standardised production. (Ibid.:69) The final remarks stress the need to construct a culture of digital production in architecture. what is the point of developing highly sophisticated software unless the people who use it and architects, in particular are interested in how it works and in exploiting its potential to the full? What use is it, either, to develop an associativeness between conception and fabrication if in practice manufacturers and clients fail to establish relationships enabling them to make the most of the continuity of the flow of information? (Ibid.:71) Remarks Cache sees a vector as a meter for architectural events. For Cache, splines nail down a multiplicity of concrete values contained in a vector, and by placing architectural events along the spline, he is able to measure and differentiate them. Even when Cache does not explicitly affirm infinity, we see that chance 24 is part of Cache s understanding of architecture, regardless of the event s origin. This characterization may be not very distant from our characterization of content sharing platforms and social networks, for example. These online applications do not engage with that which is circulating, with its contents, an infinite circulation of fillings, to talk with Cache s concepts. Similar to Cache s understanding, they enframe chance; they construct a frame that accommodates information ad infinitum, and further construct their ways to measure, the meters, to navigate this infinity. A social network will present us with an index of other users from hundreds of millions that we may be interested in based on their enframings, and not on their contents. 24 chance (n.) c. 1300, "something that takes place, what happens, an occurrence" (good or bad, but more often bad), from Old French cheance "accident, chance, fortune, luck, situation, the falling of dice" (12c., Modern French chance), from Vulgar Latin *cadentia "that which falls out," a term used in dice, from neuter plural of Latin cadens, present participle of cadere "to fall," from PIE root *kad- "to lay out, fall or make fall" (see case (n.1)) at the Online Etymology Dictionary 153

155 We sympathize with Cache s interest in chance, proportion, measures, stability, invariance, and identity, and would like to take it forward, by asking, for example, what would be a proportional invariant of an architectural artifact that celebrates the infinite information that points to it? 154

156 1.5 REMARKS In the last talks, we showed prominent architectural positions next to the abundance of information and to the ways in which web applications characterize and operate it. The challenging and promising understandings were stressed, opening up questions and suggesting different positions. From these talks we affirm that the novel phenomenon has still not found a place in architecture. In order to go to the next chapter, we make a remark. The global condition in architecture is characterized as a negentropic state where everything becomes the same, everything turns to noise and nothing is distinguishable the airport being its epitome; no matter where in the world, they all feel the same, they are all the same. In this condition, local differentiations lose to globalization, and the price of being global is paid by the loss of one s identity there is no 'I' in the noise, there is just noise. If we are to think about the abundance of information as an entropic state where all the theories can be found, all the projects, manifestoes, images, regulations, software, interviews, floor plans, architects, tutorials, competitions, doors, windows, elements, lectures, and documentaries, in short, all the answers how to play and not lose to entropy? How to find an 'I' in the noise? How to work a way out from the generic while remaining global? What we will see in the next chapter is a promising way. We will see the generic as an opportunity to construct different ways to talk to it so we can position ourselves in the abundance of information, in the infinite circulation, within all the answers, and remain stable. We will be constructing an 'I' while celebrating the 'we'. 155

157

158 Chapter 2. PRE-SPECIFIC TALKS BETWEEN ARCHITECTS AND WEB COMMUNITIES

159

160 2.1 INTRODUCTION Talking to a web community is not complicated. The main requirement is to have access to a computer online; an address on a web browser is enough to start. The information circulating in the community is vast, more than a user can or wants to know about, and for which the application that engenders the community provides navigation tools news feed, messaging app, user page, diverse categories, and a box to search. These built-in tools influence the way to talk to the community, what is seen and how it is presented, to a level that it seems to bring the talk to a curated space where everything is personalized suggestions, layouts, ads with the goal of having a better conversation. What we will see next is another way the pre-specific way. We let go of the community's curated spaces, of what is thought of to be the best for us. We talk directly to the abundance of information, and we profile, characterize, and operate it, so as to address the community in a personal and lively manner. To construct an image of such scenario, we say that the architect is standing still in the middle of an infinite circulation. Information is going around her, nonstop; it gets big and small, less and more but always the right size. The architect does not move. She has a compass, a stopwatch, a gnomon, with which to address the circulation. The architect asks a question to the infinity and an answer comes back, but it is not quite an answer it is a list, a cloud, a spectrum, from which the architect has to decide what it is. The architect stays still, doesn't move. She is stable. 159

161

162 2.2 STOPWATCH Stopwatch is interested in the content sharing platform and social network Tumblr. 105 It finds fascinating how very few fixed things can engender such a big community on the web. In this community, there are so many members talking about so many different things. Stopwatch is very curious about that, and wants to talk to them all. So, it goes around, looks at all sorts of things happening in the community, and indexes them for later, non-stop. Clearly, there are too many things, as many as numbers between 1 and 2. So Stopwatch plays with different ways to model what its index so as to (1) get an idea of what the community is talking about; (2) look for interesting and strange things; (3) look at the community with a specific interest; and (4) put together personalized daily stories engendered within the community. Stopwatch is not afraid of infinity; it has its ways to move around and surf. We are friends of Stopwatch. But before we get into what it can do, we talk about the community and what is possible to do there. First of all, Tumblr is blogs, simple. Users, i.e., the community members, create blogs, as many as they want, and collect posts. Posts can be about anything: stories, photos, GIFs, TV shows, links, Spotify tracks, mp3s, videos, fashion, art, architecture. There are no pre-defined categories for a post in Tumblr. What happens when such openness to talk about the world is celebrated? In numbers, Tumblr hosts 356 million different blogs with over 151 billion posts 106, and counting See See (accessed ). 161

163 Figure 2.1: Four Tumblr blogs on a web browser. When a user connects with another user s blog, all of its posts appear in the user s Dashboard. We can think of the dashboard as a streamline coming from infinity. The number of posts flowing to the user depends on the activity of the blogs she follows, but it can be between zero and 1.2 million posts per day. 107 What can a user do in such a simple and rich setup? When something interesting appears on the dashboard, users can Like it or Reblog it to their own blog, and add a commentary if desired. To start a post, there are seven types to choose from: Text, Photo, Quote, Link, Chat, Audio, and Video. These post types are helpful to format a blog, i.e., to play with the looks of the blog on a web browser, but again, the content and commentaries of the post are totally up to the user. These two activities, post and repost, keep the posts in constant circulation; blogs are always mutating, and the whole community keeps changing. Let us go back to Stopwatch now. As mentioned before, Stopwatch likes to look at what is happening in the community. Therefore, it requests Tumblr s contents in two ways. One is just like any user would do using a web browser, 162

164 typing plus an address. 108 And two, by requesting specific data using Tumblr s API. The main difference between these two ways to talk to the community is that with the HTTP requests, Stopwatch gets what it needs plus a lot more data, much of it non-relevant for this purpose. And with the API, it gets clean, straightforward data. These two ways are pretty much complementary, since not everything Stopwatch would like to look at is available with an API request, and vice versa. The dashboard is Stopwatch s personal streamline coming from infinity. What flows is the activity of five thousand blogs it is following. Based on these blogs diversity, activity, and popularity, this collection aims to be a representative of the whole community. So, Stopwatch is constantly looking at this flow of posts and indexing each one of them without making any distinction whatsoever. On average, it requests and indexes 80,000 different posts per day. Let us have a look at what Stopwatch thinks of the community s posts, blogs, and users. Figure 2.2: Four blogs showing post-consistency. For Stopwatch, a post is whatever the community says it is. A post is characterized by its As of today, the limit for following blogs is 5,000, and the limit of posts per day per user is 250. Actually, the user does not need to type anymore, the web browser does it for him-her. 163

165 commentaries, popularity, and neighborhood. A post image, for example, can have several commentaries from one or multiple users, i.e., descriptions of the image, title, a quote, hashtags, a date, an emoji, anything. One way for Stopwatch to measure the post s popularity is by its note count or the number of times that users Liked or Reblogged it. For Stopwatch, a post s neighborhood is the aggregate of posts within the same blog. What is interesting for us is that this characterization of a post neglects any definition alien to the community, e.g., a dictionary or encyclopedic definition, or other instruments to recognize elements in an image. 109 A blog is whatever it explicitly says it is, plus the posts that it collects. Every blog has a name, a brief description of itself, and of course, a posts collection. Stopwatch sees in the blogs of this community a tendency to be consistent, i.e., posts within the same blog are similar to each other in their own terms, out of Stopwatch s scope and interest. A blog consistency is one of its assumptions. About the users: For Stopwatch, a user is her interest and behavior. Stopwatch characterizes a user by a collection of posts; for instance, one user can be characterized by the posts she likes, or by those she does not like. Or by the posts she s interested in, or by those on her blog. Similarly to a post, a user is whatever a she wants to be. And this is what Stopwatch affirms: A community that can talk ad infinitum about the events of the world without any categorical or semantical pre-definition or fixed ontologies. Where posts are whatever the community says they are, and are wherever the community wants them to be. Where all users are equally able to come, talk, and perform, or not, and go as they please. Does this sound overwhelming, boring, or pointless? Not for Stopwatch, and not for us. Let us see now what Stopwatch can do Movement I The first thing Stopwatch learned to do was to get an idea of what a lot of posts are about, without having any prior knowledge or expectation of the forthcoming. It looks at a large collection of posts and learns to recognize their similarities and differences that can be thought of as categories. Stopwatch takes a sample of posts from the Dashboard s index and creates a new index in this case, of 120,000 nonconsecutive posts. A careful look at it shows that these posts come from 325 different blogs. Stopwatch assumes that blogs in this community tend to be post-consistent, i.e., posts within the same blog are similar to each other, even when one and the same post can be in different blogs. Stopwatch characterizes each blog with the blog s own words its name, description, and the commentaries of a carelessly selected sample of its posts. Let us imagine now that each blog is one array of words; some of them have a lot to say about themselves, some not 109 There are some instruments that aim to automatically recognize what s depicted in an image. They ask questions like, is 164

166 that much; nevertheless, this is Stopwatch s plane of comparison. Stopwatch models the blogs to an n-dimensional space based on the presence or absence of words 110 imagine a matrix in which there is one row per blog and one column per unique word used to characterize the blogs, and it is filled with ones and zeros according to the presence or absence of each word per blog; simple. All the blogs now have a common plane for comparison, and they are all described in the same terms. What Stopwatch does now is look at this n-dimensional space and learn to distinguish similarities and differences between the blogs according to the words they use. A number of categories become apparent, suggesting consistencies and differences across the blogs. To visualize this phenomenon, the n-dimensional model is transformed to a two-dimensional scatter plot where each star represents a blog. Figure 2.3: one post on a web browser and on the dashboard s index. The C -like plot suggests that three different blog categories may be apparent. Figure 2.5 shows a number of images of posts carelessly selected from ten neighboring blogs from the upper arm. Similarities between these images are apparent; they suggest they are talking about architectural themes. Likewise, figure 2.6 shows images of posts from the bottom arm that are similar to each other but different from those in figure 2.5; they suggest they are posts talking about artistic themes. Figure 2.7 shows images of posts from blogs in the highly concentrated center; the figure suggests that at this moment there s no apparent distinction between them, that they are noise. Stopwatch gives us the ability to index and label blogs without any prior knowledge of the posts contents, or without any pre-definition of what architecture, art, or noise is. there a cat in the image? These instruments go with the name of Image Recognition, for example. 110 See the entry on Bag of Words on Wikipedia. 165

167 Figure 2.4: Scatter plot with 325 blogs. Due to Stopwatch s generic instrumentality, the presence or absence of a blog has a performative impact; they all influence each other. Once blogs are distinguished, indexed, and labeled, this movement can be repeated without them, and Stopwatch will render apparent new categories from what at this moment is rendered as noise. This iteration is interesting up to a certain point, after which it will tend back to noise. Nevertheless, we could say that in web communities like Tumblr, as long as blogs are constantly put together and posts constantly introduced, reblogged, and commented on, categories will always be apparent: categories ad infinitum. Stopwatch characterizes the posts in this community in their own terms; hence, similarities and differences are apparent from within. There is no outside authority defining categories, meanings, or origins. There are no fixed definitions of the contents of the community, and any attempt to do so defeats the community s purpose. In this movement, Stopwatch shows us a way to grasp its constantly circulating content without a prior understanding and without a necessary engagement with any alien or fixed pre-definition. We see here how arbitrary and consistent labels emerge. 166

168 Figure 2.5: Collage from posts within the same category, architecture. Figure 2.6: Collage from posts within the same category, art. Figure 2.7: Collage from posts within the same category. 167

169 168 Figure 2.8: A Tumblr's dashboard.

170 2.2.2 Movement II In this movement, Stopwatch looks at a learned category of blogs like the one discussed in the previous movement. It learns how they normally talk about themselves and reblogs the abnormal talks to another blog. Stopwatch presents an updated collection of posts that can be thought of as rarities, without engaging at any point with the contents of the category nor with a pre-definition of rarity. We already said that all posts in the same category are talking about the same thing; for instance, architecture, in their own terms. First, Stopwatch learns what a normal architectural talk is for each blog. For that, it goes through the blog s posts and learns the topics of their commentaries the talk Pentecost will tell us more about learning topics. Then, Stopwatch looks at the posts popularity and models them into a histogram from which it learns how popular a normal post is. This is repeated for each blog in the category, so each one has its own normal talk and normal popularity defined. There are as many normalities as blogs in the category, and there is no singular normal way to talk about architecture. Stopwatch knows that and can handle it. We celebrate it. The new talks can be put in perspective now. Figure 2.9: Stopwatch listens to the Dashboard s Index constantly. When blogs within the category at hand are 169

171 active, that is to say, they post or reblog, Stopwatch adds these posts to their topics and popularity models, and if the topic of the new posts is not normal, or when the post s popularity is not normal, the new post is considered rare and is reblogged to a blog where all the rarities are. Stopwatch collects rarities from two categories; one could be characterized as 20th and 21st century architectural artifacts from all around the world and the other as art history in Europe. Respectively they are and See figure 2.9 and Looking at Stopwatch s abilities, we can say that rareness can be learned locally, and that it is always changing. Posts in the community are in constant circulation, new posts, reposts. And blogs are constantly changing their collections. What now may be thought of as rare, later on may become normal, no problem. Stopwatch shows us here a way to keep up with these changes, with the infinite circulation in terms of rareness. Figure 2.10: (accessed ). (accessed ). 170

172 2.2.3 Movement III Stopwatch shows us in this movement how to indexically characterize a concept and make it a compass to navigate the community. It is yet another way to talk to the community, decoupled from specific definitions like those in a dictionary and general popularities like those that determine the result of a search query. Let us start with the community s search engine. By experience, we are familiar with web search engines, like Google Search. We know that whenever we ask something, the results are not randomly organized the order is determined by how popular the web document is, generally. We will talk more about it in the next chapter, but for the moment let us say that something similar applies to Tumblr s search engine. The response of a query labyrinth, for example, will be a relevant number of posts of David Bowie playing Jareth, the Goblin King in the movie Labyrinth from Why is that? Because for the community, the most popular posts with that word feature him or the movie. Out of curiosity, if we query labyrinth on DuckDuckGo, the first link is to Wikipedia s entry, and second the movie at IMDb. These search engines perform very well when dealing with general popularities, but they do not perform equally well when considering personal characterizations or popularities. Stopwatch addresses this question. Figure 2.11: A collection of posts characterizing 'labyrinth'. Now with the indexical characterization, Stopwatch shows us how a concept can be whatever we want it to be, and that this characterization can hold true when talking to the community. In this case, we initially selected one hundred posts that for us, are talking about labyrinth very personal. Stopwatch models these posts to a high dimensional space based on learned topics. The concept is not a word anymore but a number of topics learned from posts that point to our characterization of it. 171

173 Stopwatch introduces our concept to the community. It listens constantly to the dashboard, characterizing and modeling the posts that circulate. When a post is talking similarly, in terms of the topics learned from our personal characterization of a labyrinth, then the post is reblogged to a specific blog, where all similarities are collected. Our characterization of a labyrinth goes ad infinitum. The new blog that Stopwatch is constantly putting together presents a collection of posts that most probably are talking about our concept at hand. Probably, not truly. Then we can agree or disagree with it, just like with the response of a web search engine. When we agree, it is placed with the other posts that are characterizing our concept, from which Stopwatch will keep learning. Our concept is never fixed, nor are the posts that talk about it. Image search engines are very effective in part because they focus on recognizing a global definition of a concept in question. If we image search for labyrinth on Google, for example, the results will be pretty close to a dictionary s definition of a labyrinth. Or if we search for labyrinth with the Tumblr search engine, the results will be what the community says a labyrinth is. Stopwatch shows here that there are other ways to operate the contents of a community, that we can go from semantic definitions and general popularities to personal characterizations and local popularities. These movements can be thought of as pre-specific: being able to operate and talk just before fixing semantic definitions. Figure 2.12: (accessed ). 172

174 2.2.4 Movement IV In this movement, Stopwatch presents personalized daily stories based on what is happening in the community. It is an alternative way to talk to the community, decoupled from Tumblr s characterization of itself. Figure 2.13: A sample of image-posts used in the learning process of Stopwatch s movement IV. Stopwatch listens to the dashboard, non-stop let us remember that the dashboard is a personal streamline coming from infinity, built by Tumblr, and that in Stopwatch s case, it aims to be a representative of the whole community. From here, Stopwatch indexes in average 80,000 posts per day, which can be thought of as noise; there is no distinction whatsoever. Post about space, TV, memes, gifs, vacations, boring, artifacts, architecture, everything. Stopwatch then characterizes each post by its commentaries and the commentaries of the other posts within the same blog, so the same post is differentiated across the community. These 80,000 characterized posts are modeled to an n-dimensional space based on their topics. Imagine that each post is an array of words, words that are talking about the post and about the post s friends. The length of the array varies per post, of course, all the talks are different. But after modeling, each post is not an array of words anymore, but an array of numbers, and furthermore, all the arrays are of the same length. This is a matrix, and we will talk more about it as we go further. Now, from this matrix similarities and differences can be calculated by Stopwatch, because they are all numbers and they all have the same length. Stopwatch does this by itself, and it can be called clustering. 114 Now, Stopwatch has put all the posts in clusters, where similar posts stay together. What comes next is to look at these 114 See Wikipedia s entry at (accessed ). 173

175 clusters in relation to us. For that, we need to show Stopwatch a number of posts we like, and a number of posts we do not like. Stopwatch takes the posts in these two lists and characterizes and models them just as it did with the posts from the dashboard. Then Stopwatch goes back to all the clusters and starts measuring its contents against the posts that we passed along. Finally, those that are similar are re-arranged so the web browser can render them as personalized stories from the community s infinite talk. Figure 2.14: One story of many from the day before. ON PRIVACY Stopwatch moves towards privacy on the web by celebrating the noise around us. Online services make their applications more effective by storing and reasoning about the user's behavior without any further effort from the user side (chapter 3.3). The user just does her things and the application looks, learns, and suggests next steps. Let us see the Netflix Prize, 2009, 1M USD. It aimed to improve the accuracy of predictions about how much a user is going to enjoy a movie based on their movie preferences. 115 The interesting thing here is that the Netflix community, the users, had nothing to do with it, while the very first requirement is to have identified the community s interests. This 115 See (accessed ). 174

176 sometimes can be seen against the user s will to remain a private person. What Stopwatch shows us here is that we can be effective at talking to the web while keeping our behavior private as Stopwatch runs on a dedicated computer, 24/7. It looks, stores, and likes everything on our behalf. So, anyone watching has no distinct behavior to reason about; we like everything, we become noise. It is only in the privacy of a local network that, according to locally stored interests, information emerges out of the noise. Today, we ask a web search engine for distinctions between noise and information. In this movement, Stopwatch turns the question from public questions to private interest. Figure 2.15: Eight bots rendering different stories from the community Remarks Post to infinity. The count of posts and blogs on Tumblr is adding up, somedays faster than others, and it doesn t stop. We even call the dashboard a personal streamline to infinity. Stopwatch is good at it, looking, grasping, bending, wrapping. It is around us. New posts are always welcome; new blogs are interesting. Is the same post here and there? No problem, we know they are different, we celebrate they are different. Are there too many? Never. Objects are what they want to be, images, words, popularities, friendships. And it is ok, we find ways to talk. Do we want to ask a question? We do it. Do we want to understand it all? No, just the necessity to stay stable. Let us be careful not to start running around. On the web, an image is whatever we want it to be. When we ask IBM Watson what it sees in Velázquez s Las Meninas, it is 66% sure to see a little theater with female faces in it, of age 18 to 175

177 We can say that. Let us go to the other extreme. When we ask Michel Foucault what he sees in Las Meninas, he tells us he sees a void, a space with elements resembling, pointing to something that is not there. 117 We can say that as well, and we actually like it better. The difference that we want to point out here is that Foucault and many other authors is treating this masterpiece as an object that is alive, that is talking to him. He recognizes elements, as Watson does, but he is more interested in what they can do and tell, and not in what they are. And this is what we are interested in as well; the what they are is open, and we celebrate the novel abilities to keep it open, to characterize objects indexically, with as many pointers as we see sufficient, to treat them as living things so they can perform and talk to us. With the same instruments as Watson, 118 this is what Stopwatch is doing here, and it is doing it ad infinitum. Figure 2.16: Tumblr's error page and search engine on a web browser. 116 IBM Watson Developer Cloud has a demo online. We can upload any image and Watson will tell us what it sees, at (accessed ). 117 See the Introduction of The Order of Things: An Archaeology of the Human Sciences (Foucault 1970). 118 Actually, Watson implements what is called Deep Learning, Stopwatch Machine Learning. We will talk more about them in the next chapter. 176

178 2.3 MIND PALACE Mind Palace shows the operations that can be done to a large collection of objects whose origins and characterizations are fixed, and categories are human maintained. This talk is with another community, Wikimedia Commons, a community for media files online. Mind Palace places us in the center of a three-dimensional space and orchestrates the community s contents according to our interest, showing differences and similarities that were not rendered by the community. 1 Let us talk about the community first. Wikimedia Commons characterizes itself as an online media file repository that makes available public domain and freely-licensed educational media content (images, sounds, and video clips) to everyone, in their own language. 2 Like Tumblr, it is created and maintained by the community, joining is cost free, and participation can be in different forms, by contributing one s own work, translating content, improving images, completing information, moving files, and finding and reverting vandalism. The community keeps it tidy and organized. It currently hosts over 39 million files and over 125,000 media collections. 3 As its name suggests, Wikimedia Commons is part of the non-profit, multilingual, free-content Wikimedia Foundation, that includes Wikipedia, Wikinews, Wikiversity, and others. 1 This application s original idea and Movement I were developed in collaboration with Mathias Bernhard, Nikola Marincic, and Sonja Gasser in the context of the 1st Swiss Open Cultural Data Hackathon at the Swiss National Library, Bern See openglam.org/2015/03/04/first-swiss-open-cultural-data-hackathon (accessed ). 2 See (accessed ). 177

179 Figure 2.17: Collection Gugelmann rendered by the community as an alphabetical 1-dimensional array. Now, if we place this community next to Tumblr s, we can distinguish three main efforts that differentiate them. In Wikimedia Commons, (1) the authors are fixed and terms of use are granted; (2) it aims to have its contents categorized and objectively described; and (3) the subjects in the media are to be identified. In other words: ontologies are fixed, characterizations are fixed, and featured subjects are fixed. Media files are included into the community by a contributor; it can be her own work or someone else s when owning the rights and the terms of copy, use, or modification must be defined. Also, objective information such as description, date, source, and author must accompany the media file. Contributors can also create categories and sub-categories, and assign files to them. These categories are human maintained, and even when programmatic efforts to categorize content are done, they need to be evaluated by a contributor. Contributors are also asked to identify the subject on media content, i.e., if the category trees contains a number of images featuring trees, contributors may be asked to identify their botanical types. As with the previous community, the contents are sourced by making HTTP requests of web documents or by the API. The API requests are managed by MediaWiki, a community part of the Wikimedia Foundation. For this interplay, the content is sourced by personalized bots that make 3 See (accessed ). 178

180 web documents requests. 4 For the following movements, Mind Palace focuses on one category, the Collection Gugelmann. The collection holds high quality scans of a number of drawings, watercolors, and oil paintings by the Schweizer Kleinmeister that capture Swiss landscapes and characteristic genre scenes. It offers a rich insight into the landscape and culture of Switzerland from mid 18th to mid 19th century. 5 Mind Palace sources over 2,300 media files from the collection, as well as the contributor s characterization of each print the artist s name, place and date, technique, title of the print, dimensions, and a short description. Now, let us see what Mind Palace can do. Figure 2.18: Sample of images from the Collection Gugelmann Movement I In this movement, Mind Palace looks at the whole collection of images sourced from the online community and renders it in a three-dimensional space. It constantly orchestrates the 2,300 images according to our interests. It renders a navigable space where we can explore the whole collection at once and the non-linear relations between images become apparent. Relations that were difficult or impossible to perceive in a community s web document. 4 5 Complementary information was also provided by the Swiss National Library. See (accessed ). 179

181 Mind Palace models the images to an n-dimensional space. It first takes the place of print of each image, Jungfrau, Adelboden, Staubbach, and so on, and requests to Google Maps their geo coordinates, latitude and longitude. Then, their color features are extracted, RGB values. Mind Palace uses these to characterize the images, adding the contributor s entry. That is, overall, the author, technique, descriptive text, date, geo coordinates, and RGB values. Let us imagine now that each image is one array of numbers and words, over 2,500 of them. What happens now is that the words are modeled to numbers following their presence or absence. 6 What we have after this is a matrix where all the images are characterized by same-size arrays of numbers. Figure 2.19: Still from the 3-dimensional space. In order to render apparent the non-linear differences and similarities between the images, Mind Palace transforms the n-dimensional space to a three-dimensional space, where topological distances between the images are kept (chapter 3.3.7). Figure 2.17 shows the Wikimedia Common s rendering of the collection, alphabetically arranged, 200 images at a time. Figure 2.19 shows a still of the navigable space showing the over 2,300 images arranged by its similarities and differences in terms of its full characterization. We are immersed in an infinite space and explore its gravitational fields, routes, and voids, phenomena corresponding to the similarities and differences of the images (Bernhard, Marincic, Orozco 2015). At this point we can specify certain interest in terms of the images characterization, and they are re-arranged before our eyes. Let us say that we want them arranged according to their technique, or by color, geolocation, author, or a combination of them. By hovering over an image, a close up is further rendered. We see it all, change perspective, see what s here and there, all at once. 6 See Bag of Words at (accessed ). 180

182 Figure 2.20: Stills from the navigable space. 181

183 2.3.2 Movement II Movement II 7 shows us one image in different neighborhoods. Within the navigable space, Mind Palace follows our personal interest in one image and fixes it at the center of it all, and makes all the rest turn around it. For instance, figure 2.21 shows one selected image and its closest images around it, according to different arrangements. The image has different friends, according to where it is. In this movement, Mind Palace shows how one and the same image can be in different neighborhoods and always be in their right place. This rightness does not come from the image itself, but from how the neighborhood is characterized, and our sympathy towards the whole. In a masterful neighborhood, its objects are always in their right place. Figure 2.21: One and the same image in different neighborhoods Movement III This movement by Mathias Bernhard 9 adds another characterization to the images based on a custom-made composition analysis instead of thinking of each image by its author, technique, or descriptive text, as in the previous movements so to grasp what they may be depicting. When characterized and modeled in their own compositional terms, they are re-arranged into a two-dimensional space. The images with circular vignettes, upright figures, and wide landscapes 7 This movement was developed in collaboration with Mathias Bernhard and Nikola Marincic, see (Bernhard, Marinci, Orozco 2015). 8 Figure: from (Bernhard, Marinci, Orozco 2015). 9 As shown at (accessed ). 182

184 are placed next to each other, without any pre-definition of these concepts. This instrumentality 10 is often used in computer vision for object detection, but, placing it in line with Mind Palace s interests, it does not engage with definitions of what is depicted. Interpretation stays open; it is a movement to grasp and not to hold. Figure 2.22: TSNE projection to two dimensions, rearranged into a 64 x 36 grid of square tiles. 11 Figure 2.22a: The sequence for a composition analysis of one image Remarks The interest of Wikimedia Commons is to keep fixed ontologies and semantic definitions, and it is ok. Mind Palace finds ways to source it, model it, and talk to it. This community feels closer to architecture than Tumblr, as architects place value on models that are well defined; they make us feel more under control. 13 But this long-established interest does not keep us from thinking of architecture beyond norms. Norms are there, and are important; they are the establishment. We 10 For more, see Wikipedia s entry on Histogram of oriented gradients (HOG) at (accessed ). 11 Figure: Mathias Bernhard 2015 at (accessed ). 12 Figure: Mathias Bernhard (accessed ). 13 A simple web search of BIM and the IFC will show. We further discuss this in the next chapter. 183

185 don t want to break the establishment; we want to introduce new variables and countervariables, so architecture can be re-articulated in the shadow of today s global condition. 184

186 2.4 PENTECOST Every architect has his-her own definition of architecture. 1 Do we sympathize with all of them? Probably not. 'Architecture is' reflects in a way the society at the time, the big questions in the air, but also, personal interests, and probably even moods. A definition of architecture is like an elevator pitch, all in two minutes; it is 'it'. Or better, like taxonomy. It reduces an immense and rich corpus of ideas and pins it down to the wall, death. Architects are actually very good at taxonomy. Now, let us imagine another situation where we can talk about what 'architecture is' ad infinitum. No elevator pitch, no taxonomy, it stays alive. Talk after talk, after image after metaphor, after photo after project, after Tarantino, after Aztecs, after coffee, after building, after idea, after love. Interesting? Very. First question, how to recognize the beginning or the end of an idea? How to get hold of it? How to know if the talk is really about architecture? How to compare it with my talk, or her talk? Are you still talking? Pentecost likes architects, how they look, what they do, how they talk about architecture, about themselves and their projects, the images they produce and how other people talk about them. And Pentecost also likes characters from TV series, interesting lives they have. There is something about them that feels very different from those in the movies. They just feel closer, like a neighbor. 185

187 TV series are long. Seven seasons, seven years. Enough time to witness a character's mutation, winning us over or becoming unbearable. How many things they say in seven years, how many people they talk to in seven years, places, buildings, cities. We see what they see, what they care about, like and do. It feels familiar because we also do these things in seven years. Maybe there is a Tony Soprano somewhere in our city. Architects and characters have their voices on the web. They expose themselves online, their ideas, actions, friends, artifacts. People also talk about them in the social networks, and in some cases even entire communities are built around them. The new season is coming, a new building is finished, new photos of an old building, an interview, a party, a book. They all have a corpus, countable and graspable, to which we can talk. We know it, and Pentecost knows it too. THE CORPORA The applications shown so far have focused on one online community at a time. Pentecost, in an attempt to build the corpora, looks at different communities: swiss-architects.com, 2 wikia.com 3 and magicalquote.com. 4 Swiss-architects.com is a community that celebrates architecture built in Switzerland today. Over 600 Swiss offices are profiled there, including a number of their selected projects. Descriptive text, philosophy, awards, numbers, images and sometimes floor-plans. Around these, profiles of manufacturers, lists of jobs, agenda, and news. We could say that if an office has a building site in Switzerland today, its profile is most probably featured in this community. Swiss-architects is part of the world-architects network, curated and membership-based. The website is marketed globally by a Swiss company. 5 Wikia.com 6 and magicalquote.com are two communities that celebrate TV series and their characters. On Wikia, each TV series has its own subdomain, and even when they are organized differently, most of them have a reserved place for their characters and episodes. Characters are extensively characterized by their background, significance, physical appearance, personality, and even some external references. The community is open and adopts the Wikipedia model, and members can create and edit entries following pre-defined directions and standards. Magicalquote.com is a blog that collects quotes from movies, series, books, and authors. Since 2013, it has put together a relevant database for the popular taste. If there is an Emmy around the show, their characters are most probably featured here. The blog is open to access, but the entry creation or edition is closed to the community members. 1 As a very recent example online: Arch Daily recently published the article 121 Definitions of Architecture by Becky Quintal 2016, at (accessed ). 2 (accessed ). 3 (accessed ). 4 (accessed ). 5 See (accessed ). 6 Wikia, Inc., describes itself as the largest entertainment fan site in the world with more than 385,000 fan communities and a global audience of over 175 million monthly uniques. See (accessed ). 186

188 2.4.1 Movement I As its other colleagues, Pentecost sources from these communities' servers: (a) the profiles of every architectural office featured on swiss-architects, as well as their projects. That is, all texts and images available; and (b) all that is said about one particular TV character that Pentecost is into now, e.g., Elliot Alderson from Mr. Robot, both from Mr. Robot's wikia 7 and magicalquote. 8 The corpus of architects is 640 profiles, each one talking about themselves and their projects. Some offices have a lot to say, as much as 10,000 unique words, and others not much more than a couple sentences. And also, not all the offices speak English, so Pentecost translates their talks from German using Yandex Translate API. 9 On Elliot: Pentecost sources over 3,000 unique words, a combination of what he says, his quotes, and what other people say about him. For Pentecost, text is what constitutes the corpora; it is the ground of comparison. How can we know now what are they all talking about? Figure 2.23: A sourced quote in German translated to English with Yandex Translate API. Figure 2.24: Bar chart showing the number of unique words for 431 offices (accessed ). (accessed ). See (accessed ). 187

189 2.4.2 Movement II Pentecost has the combined vocabulary of the Swiss offices, as well as the vocabulary of Elliot. What follows is modeling both for similarities and difference to emerge. The starting point is knowing which office says what; that is the before implemented bag-of-words (BoW). Imagine again a matrix where the rows are the offices and the columns the words in the vocabulary, 3,344 words by 431 offices, and it is filled with ones and zeros, very scattered. The next step is to transform this model into a term frequency inverse document frequency (tf-idf) model, so that, instead of ones and zeros, Pentecost will have numbers between 0 and 1 that reflect how important a word in a document is. One of Pentecost's goals is to show what it learns the architects are talking about; if they are talking about colors, proportions, or the stars, we don t know at this point. The interesting part is that so far Pentecost only has a vocabulary that is completely defined by the Swiss offices, not by itself or us. What Pentecost can do with it is fantastic; just by counting numbers, it can construct topics that each office can directly relate to. In this case, 200. Each topic is a little bit of this word plus a little bit of that word, minus the other one. For example, topic number 7 is constructed by of the word 'school', plus of the word competition', plus of price', and so on. Interesting? Figure 2.25: Vocabularies of swiss-architects and Elliot, respectively. 188

190 Figure 2.26: Learned topics of swiss-architects and Elliot, respectively. Let us imagine the matrix again. It used to be of 3,344 columns (dimensions) by 431 rows (observations), with a lot of zeros and very few numbers from 0 to 1. Now the matrix is 200 dimensions, where each dimension is one topic, by 431 observations, where each observation is one office. The matrix is full of numbers from -1 to 1 now, because each office talks about each topic, but in different quantities. We need to remember that the topics are constructed by the offices themselves, not by us or by Pentecost. The similarities and differences between offices are in this matrix. But we cannot see them, of course, there are 86,200 numbers there, and we need Pentecost to do it for us Movement III Pentecost sourced and modeled text into a matrix full of numbers between -1 and 1, from which we would like to visualize their similarities and differences. As with its colleagues, Pentecost learns to find patters in the matrix so 200 dimensions are reduced to 2, while keeping its topological distances. This process is called non-linear dimensionality reduction. Pentecost repeats this process with the other two models it put together, the BoW and tf-idf. Figure 2.27a shows the three different models of the same speech. Offices talk to each other and position themselves on a plane according to what they are talking about; the closer they are, the more they share their talks. Now that a common plane is constructed, we can see where does Elliot place himself. 189

191 Figure 2.27: Scatter plot of three different models, BoW, tf-idf, topics. Each one showing the 431 offices. Figure 2.27a: Zoom that shows the same office in different neighborhoods Movement IV Pentecost constructs a common plane where offices move around and talk to each other. They have their own vocabulary and use it differently, so talks are not the same. Pentecost now looks at Elliot's vocabulary and compares it with the Swiss offices' talks, in this case with their topics. Once Elliot is in the plane, distances to offices can be measured. It turns out that Elliot is not an alien. Figure 2.29 shows four offices close to him and what they are talking about. The instruments Pentecost plays are very present today in fields of study that celebrate exact 190

192 as a quality. 10 At this point, recurrent questions are, what does the whole setup and results tell you? Is it true that these Swiss offices are similar to Elliot? How do you measure your success? We think those questions need to be re-articulated. To elaborate, let us go back to Elliot for a moment. We know Elliot; we have followed him for two years. We know his family members, friends, and struggles. We have an idea of what he is up to, what he says and does. We have a corpus in our heads of who he is. When we see his reaction to an extraordinary event, we could say, We did not see that coming, but it nevertheless looks like Elliot, yes, or, That is very strange, something is wrong, this makes no sense. This reasoning is founded in our corpus of Elliot, and not in a book definition. A corpus that is breathing, that is alive. And this is why we find those questions questionable ; they are questions of single paths, of single stories, of single truths. They are like fixing a point in the horizon, and walking to it; no matter what we encounter or who we talk to on the way, the point never moves, never changes, is dead. Let us try this one, do you sympathize with this setup? Do you make sense of it? Yes, we do, and that is the beauty of Pentecost and its colleagues and of the whole setup we are presenting here. We have the instruments to source and model corpora, and to construct our personal objectivity with their own measuring devices where they can talk to each other and to us. We celebrate that. Figure 2.28: Elliot Alderson on Tumblr Exact (adj.): precise, rigorous, accurate," 1530s, from Latin exactus "precise, accurate, highly finished," past participle adjective from exigere "demand, require, enforce," literally "to drive or force out," also "to finish, measure," from ex "out" (see ex-) + agere "to set in motion, drive, drive forward; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move"). Online Etymology Dictionary at (accessed ). 11 Figure: (accessed ). 191

193 192 Figure 2.29: Elliot s four closest neighboring offices.

194 2.4.5 Remarks Architecture is already tells us that architecture is an alive tradition, and it is constantly celebrated and questioned. Architecture is built, projected, imagined, discussed, lived. Nonstop. Pentecost shows us a way to build a corpus that keeps up with our personal interest in architecture. For Pentecost, there is no fundamental difference between sourcing swissarchitects or any of the other 20 national platforms in the world-architects network, or all of them. Or to source the individual web pages of each architectural office that world-architects points to. There are very few limitations today as to what can be sourced on the web. And the same applies to Elliot. These corpora grow and mutate, and they stay like this, alive, as we question or celebrate them. How we talk to the corpora is another interesting ability. Pentecost uses nonproprietary instruments the same instruments used on prominent online applications to model the corpora so they can talk to each other. As Pentecost, we have the ability to construct common grounds where models of objects of different natures can talk. Let us imagine now that we know Elliot s favorite movies and that we put together a corpus of them. All dialogues, soundtracks, stills of scenes, their interiors, landscapes, and so on. And we place it next to our corpus of architecture, but enhanced, way more enhanced. What we could see is a not-so-alien guess of the architecture Elliot would be interested in. Not the architecture that he would like, not a solution, not a prediction, but a grasp, an idea, a spectrum, a space of probabilities. These talks, like the one between architecture and Elliot s favorite movies, are what we call pre-specific. They are the talks that objects have without a precise definition or specification of that which is being discussed. They are talks before a moment of decision, but still framed by a probability space. Back to Elliot. What comes after making an idea of the architecture that he may like in terms of his favorite movies, would be for us to imagine as well. Build him an artifact, write a book about it, prepare a script for a movie? Maybe. More interesting for us, architects interested in computing, is that these next steps are not necessarily computer generated, that they can be very well outside the computer. If he wants us to work on rehabilitating an abandoned metro station so he can plot against E Corp, we will not immediately open our Processing sketchpad, Rhino and Grasshopper, or the latest script for light optimization. We could, but we don t have to. The stories we could build around such an imaginary project live outside the computer as well. These are the kind of interplays between architecture and computing that we would like to cultivate and celebrate. The ones we believe Stopwatch, Mind Palace, and Pentecost are about. 193

195

196 2.5 REMARKS The talks presented here show the capacities, potentials, and limits of articulating architecture within the abundance of information, addressing some of the questions that emerged when talking to our contemporaries, and further opening up new ones. As computer applications, they show two things: (a) the feasibility for an architect with no formal education as a computer programmer to put together applications that address information in the same terms as today s prominent online applications i.e., Google Search, Facebook, Twitter; and (b) promising and under-explored directions for future interplays between computers and architecture as our setup and instrumentality is fundamentally different from those presented in the first part of this work. Our applications are not meant to show any truth in their results as none of the online applications we will discuss next do therefore, they should be evaluated in terms decoupled from truth. That is, if we sympathize with what they are saying or not, or if the setup is adequate or inadequate. Our applications should be thought of as personal and political objects and not as natural given objects like in the previously discussed (chapter ) that are alive in the probability space, prior linguistic understandings, prior decisions, prior to an answer, prior to a specific talk. Language is celebrated outside the computers. We have seen what a pre-specific talk can say when addressing the vivid and generic ground. What we will see next is how its instruments are put together. 195

197

198 Chapter 3. UNIVERSAL TALKS ABOUT PROMINENT WEB APPLICATIONS

199

200 3.1 INTRODUCTION The following talks are not about architecture, as the web and its applications were not engendered in a community that cares about architecture, but they nevertheless index our last architectural articulations. As we will see, origins of the phenomenon we are studying are indexed by a scientific community that deeply cares about computers. Due to its ideological and legal terms the open-source drive and being of the public domain the web and its applications have influenced over the last decades other sciences, disciplines, and practices. The web became global and is talking without interruption. The applications we will talk about can be experienced by anyone with access to a web browser, from which we stress two things. First, that people s experiences are not necessarily the same. When making a web search, for example, a computer scientist and an architect may find some results more relevant than others; they care about different things, and they place values differently. And second, that an in-depth understanding of these applications can be constructed by anyone from academic papers, 1 online courses, 2 programing libraries, 3 developer's communities. 4 The following talks are not in-depth talks about prominent applications then; they rather decouple from their original context computer science. They are about what we see as architects at their foundations, philosophically and mathematically. They aim to cast shadows over them, so we can reconstruct architectural understandings and articulate them from an architectural position. To construct a vivid and capacious understanding of the objects of the world as they are thought of and treated on the global network holds the promise of rearticulating a more vivid and capacious architecture See for example Google Scholar. See for example Udacity. See for example the Python Package Index (PyPI). See for example Stack Overflow. 199

201

202 3.2 Web Search Engines The web is a novel information space within the global network. It was invented by Sir Timothy John Berners-Lee in 1989 at CERN, and by 1993 it was in the public domain. Berners-Lee s original idea was to develop a system for fast and easy sharing of documents, where anything could potentially be connected to anything. For him, an easy connection between documents was more important than the content itself. He developed one of the web s protocols based on Hypertext a text that references to other texts so one document can point to many others, with no explicit cause. The web quickly became a space for sharing and communication. Universities, museums, governmental institutions, and enthusiasts were setting up their servers, and users on their desktops were connecting as clients. Information was piling up, and keeping track of the servers and their contents became a great difficulty; human maintained indexes were just not able to cover it all. The first web search engine, as we know them today, was developed in The main contribution was to introduce a novel meter to measure the novel information space the web. A web search engine is an online application that is very good at finding documents on the web. A user presents a question and the application presents back a number of web documents in which the user most probably will find an answer. A web search engine programmatically 201

203 indexes all of the contents on the web by following the document s hypertext, then it constructs a meter to measure the popularity of the documents individually, without understanding, nor trying to understand what the document is talking about. For this meter, there are no predefined semantic, categorical, or ontological definitions on the web; objects are defined in their own terms. At the foundations of this novel meter, we find a probabilistic mathematical model, Markov Chains. A. A. Markov invented a process to make predictions for the future of the process based exclusively on its present state, independent from its past and future. What we see in this contribution is the ability to operate in the probability space any observable event, from the throw of a coin to a poem. If we are able to symbolize it, we are able to operate it. The scientific relevance of probability today can be seen in quantum physics. For almost 70 years now, Richard Feynman s theory on light and matter has held a scientific equivalence between experimentation and theory. Feynman is able to describe (almost) all the phenomena of the world, precisely, in probabilities. He introduced a code for a photon s reflection on glass, and a gnomon a witness of time to measure the probability of a photon being reflected. The web and its novel meter are based on the connections between documents the pointers and not on their contents the meaning. We can trace this observation back to the philosophy of signs. In this regard, Charles Sanders Pierce presented a number of philosophical studies on signs and meaning-making. He classified the signs for their study in three categories icons, indexes, and symbols but always included them all when talking about reasoning. He identifies and celebrates the infinite circulation of signs; for him, a sign exists only if it s interpreted, and interpretation always requires previous signs. This infinite circulation of objects also engenders another phenomenon, the impossibility of a unique way to reason about the same thing. Linking the philosophical and mathematical contributions back to the novel meter at hand, we argue that the novelty we are interested in and further implemented in the previous chapter lies in its ability to operate observable events of the world, including architecture, before a moment of decision and interpretation, and that this pre-specific moment can only happen within probabilities. All the rest is outside the computer, all the rest is with us. 202

204 [1/5] Weaving the Web web, connectivity, CERN, information, availability, internet, hypertext, markup language, HTML, HTTP, URI, document, browser, universality, protocol, decentralization Figure 3.1: Tim Berners-Lee at London 2012 Olympics Opening Ceremony. 1 In the book Weaving the Web, Sir Timothy John Berners-Lee 2 presents the short history of the web. He describes the events prior to the first successful communication between client and server, how it happened, what came after, and his vision for the web at the time. Throughout it, we will review the web s main concepts that we have discussed in the first two chapters of this work. The history, stories, and concepts of the web will unfold all together. The vision I have for the Web is about anything being potentially connected with anything. It is a vision that provides us with new freedom, and allows us to grow faster than we ever could when we were fettered by the hierarchical classification systems into which we bound ourselves. (Berners-Lee 2000:1) It started with ideas around making an information management system easy to implement and access, scalable and decentralized. I took a brief software consulting job with CERN, the famous European Particle Physics Laboratory in Geneva. That's where I wrote Enquire, my first weblike program. I wrote it in my spare time and for my personal use, and for no loftier reason than to help me remember the connections among the various people, computers, and projects at the lab. Still, the larger vision had taken firm root in my consciousness. (Ibid.:4) He thought of a new decentralized space where documents could be arbitrarily connected to each other. Suppose all the information stored on computers everywhere were linked I thought. Suppose I could program my computer to create a space in which anything could be linked to anything. All the bits of information in every computer at CERN, and on the 1 Figure: (accessed ). 2 Sir Timothy John Berners-Lee is the inventor of the World Wide Web and the director of the World Wide Web Consortium (W3C) that oversees the continued development of the web. He has received a number of awards and honors for his invention. He published Weaving the Web 10 years after the first successful communication between an HTTP client and server via the internet. 203

205 planet, would be available to me and to anyone else. There would be a single, global information space. (Ibid.) To be able to reference a document within a document, Berners-Lee would need a fixed unique address. Without trees or hierarchies, documents are equally linked to each other. Once a bit of information in that space was labeled with an address, I could tell my computer to get it. By being able to reference anything with equal ease, a computer could represent associations between things that might seem unrelated but somehow did, in fact, share a relationship. (Ibid.) The web operates through the internet. The internet is the digital infrastructure, the global network engendered by computers talking to each other following different communication protocols. Of course, the next great development in the quest for global connectivity was the Internet, a general communications infrastructure that links computers together, on top of which the Web rides. (Ibid.:6) One of his first experiments was called Enquire, which sounds like a re-articulated Rolodex. 3 In Enquire, I could type in a page of information about a person, a device, or a program. Each page was a node in the program, a little like an index card. (Ibid.:10) The interesting ability of Enquire for Berners-Lee is that it is open to intuitive links between the index cards, without any explicit rationality of its contents. I liked Enquire and made good use of it because it stored information without using structures like matrices or trees. The human mind uses these organizing structures all the time, but can also break out of them and make intuitive leaps across the boundaries those coveted random associations. (Ibid.) From this experiment, Berners-Lee seemed to have learned the importance of a connection over the content of a document. That it is not about the meaning of the words but about the links between them. Computers store information as sequences of characters, so meaning for them is certainly in the connections among characters. (Ibid.:12) The philosophy was: What matters is in the connections. It isn't the letters, it's the way they're strung together into words. It isn't the words, it's the way they're strung together into phrases. It isn't the phrases, it's the way they're strung together into a document. I imagined putting in an encyclopedia this way, then asking Tangle a question. (Ibid.:13) Enquire was not developed further, but it helped him to get his ideas about the future work clearer. 204

206 What I was looking for fell under the general category of documentation systems software that allows documents to be stored and later retrieved. (Ibid.:15) The links between documents would be implemented with hypertext: text with references to other text that the user can immediately access. 4 My vision was to somehow combine Enquire's external links with hypertext and the interconnection schemes I had developed for RPC. The system had to have one other fundamental property: It had to be completely decentralized. That would be the only way a new person somewhere could start to use it without asking for access from anyone else. (Ibid.:16) Figure 3.2: The first website by Berners-Lee on a web browser as.html and.txt. The idea of a distributed and non-hierarchical system was always present in Berners-Lee s projects. For him, documents are always to be treated equally. Hypertext would be most powerful if it could conceivably point to absolutely anything. Every node, document whatever it was called would be fundamentally equivalent in some way. Each would have an address by which it could be referenced. They would all exist together in the same space the information space. (Ibid.) Enquire had good results, but it had still the problem of getting different computers to talk to each other what is called client and server. For him, the internet was a feasible solution. The solution was to communicate indirectly over a network. The Internet is a network of networks. Its essence, though, is a set of standardized protocols conventions by which computers send data to each other. (Ibid.:18) 3 A Rolodex is a rotating file device used to store business contact information. Its name is a portmanteau word of rolling and index and desk. The Rolodex holds specially shaped index cards; the user writes or types the contact information for one person or company onto each card. The cards are notched to be able to be snapped in and out of the rotating spindle. Wikipedia entry at (accessed ). 4 See the Wikipedia entry at 205

207 Berners-Lee then started joining the discussion on the web and internet outside CERN. There was not an immediate acceptance of his ideas. It seemed that explaining the vision of the Web to people was exceedingly difficult without a Web browser in hand. People had to be able to grasp the Web in full, which meant imagining a whole world populated with Web sites and browsers. They had to sense the abstract information space that the Web could bring into being. (Ibid.:27) So, he decided to create the web on his own. My first objective was to write the Web client the program that would allow the creation, browsing, and editing of hypertext pages. It would look basically like a word processor. (Ibid.:28) There are two kinds of computers on the web, the client and the server. When we want to read ETH s home page, for example, the client is our browser, whether on our laptop or smartphone, and the server is the computer that stores the document. Servers are located in a special setup, somewhere, and next to other computers of the same kind this is the setup Koolhaas is interested in, the server farms. I still had to find a way to turn text into hypertext, though. This required being able to distinguish text that has a link from text that wasn t. I was then able to rapidly write the code for the Hypertext Transfer Protocol (HTTP), the language computers would use to communicate over the Internet, and the Universal Resource Identifier (URI), the scheme for document addresses. (Ibid.) Berners-Lee wants to establish communication between computers to share specific documents over the internet, for which protocols are needed. A protocol is like a handshake between two computers; once it is done, communication proceeds. He developed the HTTP protocol that is to be used to talk about specific documents over the internet. Along with this protocol, he also wrote about how computers would identify a document from a string of characters; that is, when we type an address in the web browser, it is mapped to a series of numbers which will point to the server that holds the document we requested. I also wrote the first Web server the software that holds Web pages on a portion of a computer and allows others to access them. Like the first client, the server actually ran on my desktop NeXT machine. Though the server was formally known as nxoc01.cern.ch (NeXT, Online Controls, 1), I registered an alias for it info.cern.ch. with the CERN computer system folks. (Ibid.:29) And this is the relevance of protocols: It is one single action that will allow two computers to talk to each other, regardless of their talk. It is a code two computers share to make any exchange. Incompatibility between computers had always been a huge pain in everyone's side, at CERN and anywhere else where they were used. (Ibid.:35) The art was to define the few basic, common rules of protocol that would allow one computer to talk to another, in such a way that when all computers everywhere did it, the 206

208 system would thrive, not break down. For the Web, those elements were, in decreasing order of importance, universal resource identifiers (URIs), the Hypertext Transfer Protocol (HTTP), and the Hypertext Markup Language (HTML). (Ibid.:36) Three handshakes are needed to communicate over the web, the URI, HTTP, and HTML. From this, everything that we do, and how we do it including the web search engines, the content sharing platforms, and online translations follows. I told people that the Web was like a market economy. In a market economy, anybody can trade with anybody, and they don't have to go to a market square to do it. (Ibid.) ON MARKUP LANGUAGES As we see with Berners-Lee, markup languages are sets of rules for describing documents that are easily readable for both humans and machines 5, something in-between. They are based on the idea that the annotations and the contents of a document should be easily differentiated. Because of their ability to freely qualify arbitrary data structures, they are used not only on the web but also across other internet protocols and software, including architectural. For example, Building Information Modeling (BIM) aims to close the gap between digital models and actual buildings by introducing a single and intelligent model to control and manage this process (Garber 2009:9). In BIM, notions of creativity and innovation happen through performance operations, cost efficiencies, and material and system simulations (Ibid.). Prominent examples of such performance include the Denver Art Museum by Daniel Libeskind (2005), completed ahead of schedule without changing orders during the construction process. Since there are different architectural softwares that implement such building models, like Revit, ArchiCAD, and Tekla, a unitary standard for communication between them is being developed by the Industry Foundation Classes (IFC) using Extensible Markup Language (XML), an open format, just like HTML. The IFC data model describes a building and construction industry data. 6 It is not only used for collaboration between BIM projects but as a general specification that facilitates interoperability in architecture, engineering, and the construction industry. By doing so, IFC attempts to create a unitary classification of all buildings. This initiative is driven by the idea that for every future building in the world, IFC develops a standardized form that can describe the building in all its detail. 7 Although XML is an open and widely used format, again, just like HTML, the IFC uses it to establish one single model. We will see that a similar phenomenon of privatization was experience by Berners-Lee during the development of the web. The web decoupled information from the territory. It is part of a digital infrastructure where new models of communication are accommodated and information flows, regardless of the specificity of its content or geo-political boundaries. The fundamental principle behind the Web was that once someone somewhere made See (accessed ). See at This idea is further developed in Beyond the Grid (Hovestadt 2010:213). 207

209 available a document, database, graphic, sound, video, or screen at some stage in an interactive dialogue, it should be accessible (subject to authorization, of course) by anyone, with any type of computer, in any country. (Berners-Lee 2000:37) At the time, there were already a number of other protocols over the internet that would give access to shared documents, but Berners-Lee s ideas around openness and easiness made it different from the rest. It is the most fundamental innovation of the Web because it is the one specification the every Web program, client or server, anywhere uses when any link is followed. Once a document had a URI, It could be posted on a server and found by a browser. (Ibid.:39) The request for a new document over a browser was implemented with the hypertext. In a web browser, a request for a new document is hidden behind a letter, word, or image. On the web, any symbolization becomes an index. Hidden behind a highlighted word that denotes a hypertext link is the destination document s URI, which tells the browser where to go to find the document. (Ibid.) This implementation stays on the back of the web browser. The ability to transform text to hypertext is embedded in the HTML. This shows us that a web browser does not render the document exactly as it is; the browser interprets the HTML document and renders it accordingly in the web browser. I never intended HTML source code (the stuff with the angle brackets) to be seen by users. A browser/editor would let a user simply view or edit the language of a page of hypertext, as if he were using a word processor. (Ibid.:42) At that point, the setup was up and running, and Berners-Lee and the team at CERN shared the code for any enthusiast with a computer to share files over the web, and anyone with a web browser would be able to read them. It was a new space ready to be built and explored. As the browsers appeared, so did new servers, with ever-increasing frequency. Occasionally, one new server would demonstrate to the community what could be done in a whole new way, and pour fresh energy into the young field. One that impressed me was a server of information about Rome during the Renaissance. The Vatican had lent a (physical) exhibit to America's Library of Congress. Some of the material in it had been photographed, scanned into a computer, and made available in the form of image files on an FTP Internet server. Then in Europe, Frans van Hoesl, who was aware of the Web, created a hypertext world of this material on a Web site. The site took the form of a virtual museum; a browser chose a wing to visit, then a corridor, then a room. (Ibid.:59) And as in unexplored territories, claims over ownership started to appear that could have changed the web in significant ways. The team put in a big effort to assure the openness, flexibility, and availability of the web. On April 30 Robert and I received a declaration, with a CERN stamp, signed by one of the directors, saying that CERN agreed to allow anybody to use the Web protocol and code 208

210 free of charge, to create a server or a browser, to give it away or sell it, without any royalty or other constraint. (Ibid.:74) These events made him realize that it was the time to take some distance from a hands on role and take more of a leadership position and work to maintain the original philosophy. I did not want to form a standards body per se, but some kind of organization that could help developers of servers and browsers reach consensus on how the Web should operate. With Mosaic picking up the ball and running single-handedly for the goal line, and more and more gopher users considering the Web, evidence was mounting that the Web could splinter into various factions some commercial, some academic; some free, some not. This would defeat the very purpose of the Web: to be a single, universal, accessible hypertext medium for sharing information. (Ibid.:76) The World Wide Web Consortium gives voice to developers and users, and sets directions for the future of the web, still today. Like the IETF, W3C would develop open technical specifications. Unlike the IETF, W3C would have a small full-time staff to help design and develop the code where necessary. Like industrial consortia, W3C would represent the power and authority of millions of developers, researchers, and users. (Ibid.:94) Berners-Lee shares with us the web s ideals, in retrospective. The Web is more a social creation than a technical one. I designed it for a social effect to help people work together and not as a technical toy. The ultimate goal of the Web is to support and improve our weblike existence in the world. (Ibid.:123) The web has shown to be crucial in engendering new ways to communicate, think of, and experience the world today. It is a big banner for the open-source model of collaboration. The essence of working together in a weblike way is that we function in groups groups of two, twenty, and twenty million. We have to learn how to do this on the Web. (Ibid.:125) Berners-Lee was heavily criticized by his decision to keep the web open. Because he, CERN, or someone else could have explicitly, and most probably heavily, monetized this invention. This did not happen; what happened was that the web became a new open space from which new values needed to emerge. Agreements on privacy are part of the greatest prerequisite for a weblike society: trust. We need to be able to trust the membership of groups, the parties engaging in e- commerce, the establishment of who owns what information, and much more. (Ibid.:126) 209

211 Figure 3.3: The Economist cover, And these new values are here, and are bigger than their predecessors. They can be seen around companies like Facebook, Amazon, Google, and many others. We see that, in a way, information is thought of as the new oil; see figure 3.3. For people to share knowledge, the Web must be a universal space across which all hypertext links can travel. I spend a good deal of my life defending this core property in one way or another. Universality must exist along several dimensions. To start with, we must be able to interlink any documents from drafts to highly polished works. (Ibid.:163) The main difference between these values is that information is thought of to be for free, while natural resources are not; those are attached to a territory with geo-political boundaries. Yes, Koolhaas is right, web servers are somewhere sitting on a field, but the value is not there, the value is not in the architectural artifact or physical infrastructure of the place. The new value is in the information that these server farms emit, receive, store, and process. The, reason we need universality on all these levels is that that's how people operate in the real world. If the World Wide Web is to represent and support the web of life, it has to enable us to operate in different ways with different groups of different sizes and scopes at different places every day: our homes, offices, schools, churches, towns, states, countries, and cultures. (Ibid.:164) We will now look at a new value that directly emerged from the web. It is a service that provides links to information on the web. By now, it has mapped all the space initiated by Berners-Lee, and without claiming it, it is one of the most economically valued and socially influential companies in the world today, Google. 210

212 [2/5] The Anatomy of a Large-Scale Hypertextual Web Search Engine web, search, document, index, crawling, hyperlink, graph, probability distribution, Markov chain, parse, sort, source Figure 3.4: Still from the ad 'Do You Yahoo!?' c Yahoo!'s human-maintained index was over-performed by an automatic source and characterization of the web. 8 In the paper, The Anatomy of a Large-Scale Hypertextual Web Search Engine, Sergey Brin and Larry Page 9 present a way to operate the novel web. What they introduce is the idea that in this new information space, control over and understanding of its contents is not necessary in order to operate it a meter rooted in the probability space is good enough to distinguish a few web documents in tens of billions. we present Google, a prototype of a large-scale search engine which makes heavy use of the structure present in hypertext. Google is designed to crawl and index the Web efficiently and produce much more satisfying search results than existing systems. Search engines index tens to hundreds of millions of web pages involving a comparable number of distinct terms. They answer tens of millions of queries every day. (Brin-Page 1998) Because of its quantity, the sourcing and indexing of the web had to stop being humanmaintained and replaced by efficient programmatic methods. No analysis, just sourcing. These methods, as the title of the paper suggests, rely on the hypertextual links that Berners-Lee developed to connect documents. The web can be thought of as a web because there are all these nodes arbitrarily linked together, no fixed distances, center or end. The web creates new challenges for information retrieval. The amount of information on the web is growing rapidly, as well as the number of new users inexperienced in the art of web research. People are likely to surf the web using its link graph, often starting with high 8 Figure: Still from Yahoo TV commercial from the 90s, Youtube (accessed ). 9 Sergey Brin and Larry Page are American computer scientists who developed Google Search, Google's first online service, as a research project at Stanford University. Today, they are the President and CEO, respectively, of Alphabet, Inc., Google's parent company. Alphabet s portfolio encompasses several industries and research areas. Alphabet works on smart homes, urban innovation, geopolitics, heath care and prevention, artificial intelligence, self-driving cars, energy and internet access, among others. See (accessed ). 211

213 quality human maintained indices such as Yahoo! or with search engines. Human maintained lists cover popular topics effectively but are subjective, expensive to build and maintain, slow to improve, and cannot cover all esoteric topics. (Ibid.) Crawling is colloquially known as downloading. It is the action of sourcing, of taking information from the infinite source. A web search engine constantly sources and indexes the web. New documents are constantly added and modified. For example, the homepage of changes a few times per day. A web search provider must keep up, and a good service may be as good as its index of the web. Creating a search engine which scales even to today s web presents many challenges. Fast crawling technology is needed to gather the web documents and keep them up to date. Storage space must be used efficiently to store indices and, optionally, the documents themselves. (Ibid.) New stabilities on the web, out of the understanding of its contents, are built by the search engine. As Brin and Page present, one is by creating a new meter that will measure every web document, PageRank, and the other by characterizing every web document following the web's characterization of itself. The Google search engine has two important features that help it produce high precision results. First, it makes use of the link structure of the Web to calculate a quality ranking for each web page. This ranking is called PageRank and is described in detail Second, Google utilizes link to improve search results. (Ibid.) Brin and Page model the web as a graph, just like Christopher Alexander does, but one of the main differences is that the connections of the web's graph does not follow any logic. For Alexander, it is necessary to rationalize the relation between two components. For Brin and Page, not; for them, the mere existence of a link is enough. Brin and Page think of their meter as a very good way to measure the people's subjective idea of importance. For them, if many documents are pointing to one document, this document must be important, for whatever reason. The citation (link) graph of the web is an important resource that has largely gone unused in existing web search engines. We have created maps containing as many as 518 million of these hyperlinks, a significant sample of the total. These maps allow rapid calculation of a web page s PageRank, an objective measure of its citation importance that corresponds well with people s subjective idea of importance. Because of this correspondence, PageRank is an excellent way to prioritize the results of web keyword searches. For most popular subjects, a simple text matching search that is restricted to web page titles performs admirably when PageRank prioritizes the results (demo available at google.stanford.edu). For the type of full text searches in the main Google system, PageRank also helps a great deal. (Ibid.) PageRank is defined as follows: We assume page A has pages T1...Tn which point to it (i.e., are citations). The parameter 212

214 d is a damping factor which can be set between 0 and 1. We usually set d to There are more details about d in the next section. Also C(A) is defined as the number of links going out of page A. The PageRank of a page A is given as follows: PR(A) = (1-d) + d (PR(T1)/C(T1) PR(Tn)/C(Tn)) Note that the PageRanks form a probability distribution over web pages, so the sum of all web pages PageRanks will be one. (Ibid.) We see now that this novel meter is, for the most part, a probability distribution, whose origins can be indexed by Markov Chains, 100 years ago. We will discuss this next. PageRank or PR(A) can be calculated using a simple iterative algorithm, and corresponds to the principal eigenvector or the normalized link matrix of the web. (Ibid.) Figure 3.5: PageRank algorithms are implemented in many programming languages and libraries. This figure shows an implementation on Python and networkx library. All open-source. One line (1) to import the library; one line (2) to create a graph; and one line (4) to calculate the node's PageRank. Brin's and Page's intuition is based on chance. A very general one, because the web covers the world and a web search engine accommodates the world any user and any question. What we suggest in our interplays is that local measures should be explored as well, and by us architects, because a 'labyrinth' does not mean the same to the world as it does to us, for example. PageRank can be thought of as a model of user behavior. We assume there is a random surfer who is given a web page at random and keeps clicking on links, never hitting back but eventually gets bored and starts on another random page. The probability that the random surfer visits a page is its PageRank. And, the d damping factor is the probability at each page the random surfer will get bored and request another random page. One important variation is to only add the damping factor d to a single page, or a group of pages. This allows for personalization and can make it nearly impossible to deliberately mislead the system in order to get a higher ranking. (Ibid.) And one more. Another intuitive justification is that a page can have a high PageRank if there are many pages that point to it, or if there are some pages that point to it and have a high PageRank. Intuitively, pages that are well cited from many places around the web are worth looking at. Also, pages that have perhaps only one citation from something like the Yahoo! homepage are also generally worth looking at. If a page was not high quality, or was a broken link, it is quite likely that Yahoo s homepage would not link to it. PageRank 213

215 handles both these cases and everything in between by recursively propagating weights through the link structure of the web. (Ibid.) Just like in our interplays, an object is characterized by itself and by what its community says about it. When we look at the example of a newspaper's homepage, the title of an article is the hyperlink to the article itself, and most of the time it is accompanied by a short text that already talks about the article. A search engine will characterize the article by its contents and by the contents of the homepage that links to the article. The text of links is treated in a special way in our search engine. Most search engines associate the text of a link with the page that the link is on. In addition, we associate it with the page the link points to. This has several advantages. First, anchors often provide more accurate descriptions of web pages than the pages themselves. Second, anchors may exist for documents which cannot be indexed by a text-based search engine, such as images, programs, and databases. This makes it possible to return web pages which have not actually been crawled. (Ibid.) A web page is also characterized by the visual representation of its contents. These 'fine' features are an example of the free characterizations that an object can have, and they all depend on what kind of questions we are trying to ask. Aside from PageRank and the use of anchor text, Google has several other features. First, it has location information for all hits and so it makes extensive use of proximity in search. Second, Google keeps track of some visual presentation details such as font size of words. Words in a larger or bolder font are weighted higher than other words. Third, full raw HTML of pages is available in a repository. (Ibid.) A web crawler is also known as a web spider, web bot, or simply a bot. As seen here and in our pre-specific talks, a web search engine, or any other application that sources information in order to operate, sources the web by making requests to a web server and storing the documents for future use, non-stop. Running a web crawler is a challenging task. There are tricky performance and reliability issues and even more importantly, there are social issues. Crawling is the most fragile application since it involves interacting with hundreds of thousands of web servers and various name servers which are all beyond the control of the system. (Ibid.) A web bot typically starts with what is called a seed address. The bot requests the document at that address, stores the response locally and looks for the hyperlinks in it. For example, if the seed document has ten hyperlinks pointing to other documents, at this point, the bot has stored one document and has ten more to go. It continues; the bot requests one of the ten documents, stores it, and looks for the hyperlinks in it. It finds seven and, at this point, the bot has stored two documents and has sixteen more to go. This goes ad infinitum. In order to scale to hundreds of millions of web pages, Google has a fast distributed crawling system. A single URLserver serves lists of URLs to a number of crawlers (we typically ran about 3). Both the URLserver and the crawlers are implemented in Python. 214

216 (Ibid.) Brin and Page stress three movements of a web bot, parsing, indexing, and sorting. As we mentioned with Berners-Lee, a web document follows a protocol based on a Markup Language. Markup Languages have the ability of remain 'structurally' open, which in turn means more work when building a universal parser, because the structural options are vast. Parsing Any parser which is designed to run on the entire Web must handle a huge array of possible errors. These range from typos in HTML tags to kilobytes of zeros in the middle of a tag, non-ascii characters, HTML tags nested hundreds deep, and a great variety of other errors that challenge anyone s imagination to come up with equally creative ones. (Ibid.) Large indexes are built. A parsed document points to all the words that it contains. Indexing Documents into Barrels After each document is parsed, it is encoded into a number of barrels. Every word is converted into a wordid by using an in-memory hash table the lexicon. New additions to the lexicon hash table are logged to a file. Once the words are converted into wordid s, their occurrences in the current document are translated into hit lists and are written into the forward barrels. (Ibid.) And in turn each word points to the document in which it is contained. The vocabulary on the web goes beyond any dictionary or encyclopedia. Meaning is being created every day and placed in motion, and a web search engine is able to keep up with this phenomenon by its ability to source it and index it. For example, 'ice bucket challenge : The fixed proximity of these three words have a meaning that goes beyond any definition, and when we web search that term we will most probably find out what it means. Sorting In order to generate the inverted index, the sorter takes each of the forward barrels and sorts it by wordid to produce an inverted barrel for title and anchor hits and a full text inverted barrel. This process happens one barrel at a time, thus requiring little temporary storage. (Ibid.) When presenting a query to a web search engine, it returns a list of links in which we most probably will find what we are looking for. The goal of searching is to provide quality search results efficiently. we have focused more on quality of search in our research, although we believe our solutions are scalable to commercial volumes with a bit more effort. The google query evaluation process is show in Figure 4 [3.6]. (Ibid.) 215

217 Figure 3.6: Google Query Evaluation. 10 It is arranged in descending order; at the top is the document in which the search engine is more confident we will find what we are looking for. The list follows a ranking function, where all the previously discussed measures and characterizations by Brin and Page take place. Google maintains much more information about web documents than typical search engines. Every hitlist includes position, font, and capitalization information. Additionally, we factor in hits from anchor text and the PageRank of the document. Combining all of this information into a rank is difficult. We designed our ranking function so that no particular factor can have too much influence. (Ibid.) The user follows the links presented to him, and the web search engine records the user s behavior. This feedback is used in the ranking function. If, for example, a number of users click the second query more times than the first one, this will have an impact in the results of future users. The ranking function has many parameters like the type-weights and the type-proxweights. Figuring out the right values for these parameters is something of a black art. In order to do this, we have a user feedback mechanism in the search engine. A trusted user may optionally evaluate all of the results that are returned. This feedback is saved. Then when we modify the ranking function, we can see the impact of this change on all previous searches which were ranked. Although far from perfect, this gives us some idea of how a change in the ranking function affects the search results. (Ibid.) For Brin and Page, the quality of a web search is indexed by its meter, PageRank. They evaluate their results based on a universal notion of quality, which in principle does not belong to the philosophy of the web, because as we see it, the web is about locally differentiated notions, including quality. The three prominent online applications presented in this chapter and in turn, 10 Figure: (Brin-Page 1998). 216

218 our pre-specific talks encounter the same phenomenon: They cannot be significantly evaluated by the well-established evaluation processes. The concept of evaluation must be also rearticulated. We see that these applications are, and must be evaluated in terms of what and how they are doing it over the truths that they produce. This question will be further addressed towards the end of this final chapter. The most important measure of a search engine is the quality of its search results. While a complete user evaluation is beyond the scope of this paper, our own experience with Google has shown it to produce better results than the major commercial search engines for most searches. As an example which illustrates the use of PageRank, anchor text, and proximity, Figure 4 [3.7] shows Google s results for a search on bill clinton. (Ibid.) Figure 3.7: Sample Results from Google. 11 We will present now the contribution that we see at the core of the online application at hand. It is an over one hundred-year-old mathematical model of probability, Markov Chains. 11 Figure: from (Brin-Page 1998). 217

219 [3/5] Markov Chains probability, predictions, change, sequences, immanences Figure 3.8: Diagram of a Markov chain of three states. 12 Andrey Andreyevich Markov s 13 most prominent contribution is the Markov Chains, whose origin can be indexed by the work of his mentor, P. L. Chebyshev, and a public quarrel between Markov and his contemporary, P. A. Nekrasov. The extension of Chevyshev s work motivated by the will to expose his colleague s errors led to the creation of a new field of research, the Markov Chains. A Markov Chain is a process of making predictions of future steps based only in the present state. The concept of chains first appeared in Markov s 1906 paper where he defined the simple chain as: an infinite sequence x1, x2,, xk, xk+1,, of variables connected in such a way that xk+1 for any k is independent of x1, x2,, xk 1, in case xk is known. 14 Markov called the chain homogeneous if the conditional distributions of xk+1 given xk were independent of k (Basharin 2004:15). A Markov Chain diagram, like figure 3.8, can be read as follows. There are three states in the process, s1, s2, s3. The probability of change from state s1 to s2 is 1; the probability of change from s2 to s3 is 1/3, and to stay in s2 2/3; the probability of change from s3 to s1 is 1/2, and to stay in s3 1/2. One of the most prominent applications is done by Markov himself. In 1913, for the 200th anniversary of Jakob Bernoulli s publication, 15 Markov had the third edition of his textbook Figure: from (Norris 1997). 13 Andrey Andreyevich Markov ( ) was a Russian mathematician. He was professor at St. Petersburg University and member of St. Petersburg Academy of Sciences. He extensively worked on number theory, continuous fraction theory, differential equations, probability theory, and statistics. His most prominent work has now his name and their applications can be seen in the solution of many fundamental problems of modern science and technology. See (accessed ). 14 A.A. Markov, Rasprostranenie zakona bol shih chisel na velichiny, zavisyaschie drug ot druga, Izvestiya Fizikomatematicheskogo obschestva pri Kazanskom universitete, 2-ya seriya 15 (94) (1906) Jakob Bernoulli. Ars Conjectandi, Opus Posthumum, Accedit Tractatus de Seriebus infinitis, et Epistola Gallice scripta de ludo Pilae recticularis, Basileae, 1713 (Ch. 1-4 translated into English by B. Sung, Ars Conjectandi, Technical Report No. 2, Dept. of Statistics, Harvard University, 1966). 16 Andrei A. Markov. Ischislenie veroyatnostej, SPb, 1900; 2-e izd., SPb, 1908, Translated into German, ahrscheinlichkeitsrechnung, Teubner, Leipzig-Berlin, 1912; 3-e izd., SPb, 1913; 4-e izd., Moskva,

220 published. This edition included his 1907 paper 17 enriched by the materials from his 1913 paper. 18 In that edition, he writes: Let us finish the article and the whole book with a good example of dependent trials, which approximately can be regarded as a simple chain. Here, Markov studied the sequence of 20,000 letters in A. S. Pushkin s poem, Eugeny Onegin, discovering that the stationary vowel probability is p = 0.432, that the probability of a vowel following a vowel is p1 = 0.128, and that the probability of a vowel following a consonant is p2 = In the same article, Markov also gave the results of his other tests; he studied the sequence of 100,000 letters in S. T. Aksakov s novel, The Childhood of Bagrov, the Grandson. For that novel, the probabilities were p = 0.449, p1 = 0.552, and p2 = (Basharin 2004). Until that time, the theory of probability ignored temporal aspects related to random events. Mathematically speaking, no difference was made between the following two events: a dice thrown a thousand times versus a thousand dice thrown once each. Even dependent random events do not necessarily imply a temporal aspect. In contrast, a temporal aspect is fundamental in Markov s Chains (Von Hilgers 2006:157). Figure 3.9: Left background: The first 800 letters of 20,000 total letters compiled by Markov and taken from the first one and a half chapters of Pushkin s poem, Eugeny Onegin. Markov omitted spaces and punctuation characters as he 17 Andrei A. Markov. Issledovanie zamechatel nogo sluchaya zavisimyh ispytanij, Izvestiya Akademii Nauk, SPb, VI seriya, tom 1, 9 3, 1907, (Translated into French, Recherches sur un cas remarquable d epreuves dependantes, Acta mathematica, Stockholm, 33, 1910, ). 219

221 compiled the Cyrillic letters from the poem. Right foreground: Markov s count of vowels in the first matrix of 40 total matrices of letters. The last row of the 6 6 matrix of numbers can be used to show the fraction of vowels appearing in a sequence of 500 letters. Each column of the matrix gives more information. Specifically, it shows how the sums of counted vowels are composed by smaller units of counted vowels. Markov argued that if the vowels are counted in this way, then their number proved to be stochastically independent. 19 Beyond the contribution to mathematics, what is interesting for us is Markov s symbolization of a poem, decoupled from purport or meaning, into a relational matrix, just numbers, from which he models a probabilistic structure with which to navigate through the whole poem, finding the proper text passage, without analyzing it all and prior to any semantic interpretation of it. According to Markov, the spirit of the text is not within the letters. The spirit is not within the references. It resides in the immanences. And with his schematic indexing system, he demonstrates for the first time that it is possible to operate with immanences (Hovestadt 2014:90). This is Markov s contribution. We will see now another example of such a meter, in this case from quantum electrodynamics. [4/5] The Strange Theory of Light and Matter probability, prediction, quantum electro dynamics, light, photons, refractions, gnomon "But what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light by a choice of only one of the two languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do." Albert Einstein and Leopold Infeld. The Evolution of Physics, 1938: Richard P. Feynman s 20 book, QED: The Strange Theory of Light and Matter, is the documentation of the lectures on quantum electrodynamics that he gave at UCLA, where he describes the interaction of light and electrons. QED as a field of study was developed by a number of physicists in At its origins, he argues, was a troubled theory, as rough calculations would result in reasonable answers, but beyond certain accuracy the calculations 18 Andrei A. Markov. Primer statisticheskogo issledovaniya nad tekstom Evgeniya Onegina, illyustriruyuschij svyaz ispytanij v cep, Izvestiya Akademii Nauk, SPb, VI seriya, tom 7, 9 3, 1913, Figure and comment: from (Von Hilgers 2006:156). 220

222 would result in nonsense. And this is where Feynman s contribution takes place; his theory has been around for almost 70 years and there is no significant difference between experiment and theory, yet. But what is it about? It describes all the phenomena of the physical world, except the gravitational effect and radioactive phenomena, by measuring the probability of an event happening. The first experiment: In this experiment some photons of the same color let's say, red light are emitted from a light source down toward a block of glass. A photomultiplier is placed at A, above the glass, to catch any photons that are reflected by the front surface. To measure how many photons get past the front surface, another photomultiplier is placed at B, inside the glass. (Feynman 1985:17) The count of this first experiment is as follows: from 100 photons shot, 4 arrived at A and 96 arrived at B, i.e., 4% of the photons are reflected and 96% are transmitted. Already we are in great difficulty: how can light be partly reflected? Each photon ends up at A or B how does the photon make up its mind whether it should go to A or B? (Ibid.) Figure 3.10: An experiment to measure the partial reflection of light by a single surface of glass. 21 It is impossible to precisely know which photon would go where, a limit of Feynman s theory. Nevertheless, he tries another experiment. We'll do a second experiment, in which we will measure the partial reflection of light by two surfaces. We replace the block of glass with a very thin sheet of glass its two surfaces are exactly parallel to each other and we place the photomultiplier below the sheet of glass, in line with the light source. This time, photons can reflect from either the front surface or the back surface to end up at A; all the others will end up at B. (Ibid.:20) From this experiment, we would expect the first surface to reflect 4%, and the back, the 4% of the remaining 96%, making a total of 8%. But that just doesn t happen why? Would the thickness influence the phenomenon? He tests that idea. Starting out with the thinnest possible layer of glass, we'll count how many photons hit the photomultiplier at A each time 100 photons leave the light source. Then we'll replace 20 Richard P. Feynman was an American theoretical physicist. He got the Nobel Prize in Physics in 1965 for his contributions to the development of quantum electrodynamics. 21 Figure: from (Feynman 1985). 221

223 the layer of glass with a slightly thicker one and make new counts. After repeating this process a few dozen times, what are the results? (Ibid.:21) With the thinnest possible layer of glass, the reflected photons are zero. By increasing the thickness of the glass, the number of photons reflected also increases, but up to a point though, 16%, and then decreases to zero again, and then up again. So it turns out that our prediction of 8% is right as an overall average (since the actual amount varies in a regular pattern from zero to 16%), but it's exactly right only twice each cycle like a stopped clock (which is right twice a day). (Ibid.) Figure 3.11: The results of an experiment carefully measuring the relationship between the thickness of a sheet of glass and partial reflection demonstrate a phenomenon called interference. As the thickness of the glass increases, partial reflection goes through a repeating cycle of zero to 16%, with no signs of dying out. 22 These are the observations with which Feynman puts together his theory. Counting light particles whose probability to reflect goes up and down, like a wave. I will only show you how to calculate the correct probability that light will be reflected from glass of a given thickness, because that's the only thing physicists know how to do! What we do to get the answer to this problem is analogous to the things we have to do to get the answer to every other problem explained by quantum electrodynamics. All we do is draw little arrows on a piece of paper that s all! (Ibid.:24) His first rule says: According to the rules of how we count the beans, the probability of an event is equal to the square of the length of the arrow. (Ibid.) Looking back to the first example, the probability that a photon would be reflected was 4%; to that corresponds an arrow with length 0.2, because 0.2 squared is But which direction? To determine the direction of each arrow, let's imagine that we have a stopwatch that can time a photon as it moves. This imaginary stopwatch has a single hand that turns around very, very rapidly. When a photon leaves the source, we start the stopwatch. As long as the photon moves, the stopwatch hand turns (about 36,000 times per inch for red light); when the photon ends up at the photomultiplier, we stop the watch. The hand ends up pointing in a certain direction. That is the direction we will draw the arrow. (Ibid.:27) The last rule, when the photon is bouncing off the first surface of the glass, the arrow is reversed; when the photon is bouncing off the back surface, the arrow stays the same. 222

224 Now, let's draw the arrows for the case of light reflecting from an extremely thin layer of glass. To draw the front reflection arrow, we imagine a photon leaving the light source (the stopwatch hand starts turning), bouncing off the front surface, and arriving at A (the stopwatch hand stops). We draw a little arrow of length 0.2 in the direction opposite that of the stopwatch hand [Figure 3.12]. (Ibid.) Figure 3.12: In an experiment measuring reflection by two surfaces, we can say that a single photon can arrive at A in two ways via the front or the back surface. 23 To draw the back reflection arrow, we imagine a photon leaving the light source (the stopwatch hand starts turning), going through the front surface and bouncing off the back surface, and arriving at A (the stopwatch hand stops). This time, the stopwatch hand is pointing in almost the same direction, because a photon bouncing off the back surface of the glass takes only slightly longer to get to A it goes through the extremely thin layer of glass twice. We now draw a little arrow of length 0.2 in the same direction that the stopwatch hand is pointing [Figure 3.13]. (Ibid.) Figure 3.13: A photon bouncing off the back surface of a thin layer of glass takes slightly longer to get to A. 24 Now let's combine the two arrows. Since they are both the same length but pointing in nearly opposite directions, the final arrow has a length of nearly zero, and its square is even closer to zero. Thus, the probability of light reflecting from an infinitesimally thin layer of glass is essentially zero [Figure 3.14]. (Ibid.:28) Figure: from (Feynman 1985). Figure: from (Feynman 1985). Figure: from (Feynman 1985). 223

225 Fig 3.14: The final arrow, whose square represents the probability of reflection by an extremely thin layer of glass. 25 Feynman s theory explains how partial reflections can be exactly measured, within probability space, and with a stopwatch, a circle with infinite relations to the center. But this circle is beyond rational reasoning and geometrical measuring. This circle is a gnomon, in the sense that it is witnessing the passing of time in relation to a symbolization of an event; in this case, the bouncing of a photon. 26 Feynman s code and this witness can measure all the phenomena of the physical world, within the probability space. 27 I feel more dignified when I say we are computing the probability amplitude for an event. I prefer, though, to be more honest, and say that we are trying to find the arrow whose square represents the probability of something happening. (Ibid.:33) Next, we will talk about operating immanences within the probability space in relation to interpretation. [5/5] Of Reasoning in General sign, interpretation, reason, signification, fact, determination, observation, perception, knowledge, ideas, causality, icon-index-symbol "Logic is the art of reasoning." Charles Sanders Peirce 1895:11 The concept of the index finds a very prominent place in Charles Sanders Peirce s 28 general theory of signs a theory that presents signs inseparable from mind and logic. In our work, numerous times we have placed next to each other the architect s understanding of its tradition and the online application s understanding of the world, and talked about them in terms of logic and reason. We have said that architects try to see inner structures based on logic or the symbolized interiors of an architectural artifact. If, according to Peirce, we cannot escape from 25 Figure: from (Feynman 1985). 26 Vera Bühlmann (2017) proposes a circularity in terms of a gnomonic space as a language of coding. 27 The idea of the gnomon is not alien to the tradition of architecture, for Vitruvius, the subject matter of architecture included buildings, machinery, and clocks (gnomons). Vitruvius: De Architectura Libri Decem, book one. 28 Charles Sanders Peirce was an American theorist of logic, language, communication, and the general theory of signs (which he called semeiotic ). He wrote extensively on a wide range of topics, from mathematics, mathematical logic, physics, geodesy, spectroscopy, and astronomy, to psychology, anthropology, history, and economics. His published works run to about 12,000 printed pages and his known unpublished manuscripts run to about 80,000 handwritten pages. See (accessed ). 224

226 a process of signification, what do we mean when we say that we need to give up logic and understanding in order to think about architecture today? And how is the global network challenging these notions and motivating our ideas? In short, we say that the novelty lies in the ability to operate signs before reasoning. We start by talking about Peirce s nature of signs. A sign is an object which stands for another to some mind. I propose to describe the characters of a sign. In the first place like any other thing it must have qualities which belong to it whether it be regarded as a sign or not. Thus a printed word is black, has a certain number of letters and those letters have certain shapes. Such characters of a sign I call its material quality. In the next place a sign must have some real connection with the thing it signifies so that when the object is present or is so as the sign signifies it to be, the sign shall so signify it and otherwise not. (Peirce 1873:141) He presents an early example of a sign in which he stresses the necessity of a material quality and real connections to that which is signified. A weathercock is a sign of the direction of the wind. It would not be so unless the wind made it turn round. There is to be such a physical connection between every sign and its object. (Ibid.) For Peirce, the observation and perception of an event are acts around signs. Take any statement which is made concerning a matter of fact. It is caused or determined by the fact. The fact has been observed & the perception of the fact which was caused by it in its turn causes the statement to be made. (Ibid.:142) A sign can point to a future event; if the event happens, it can be traced back to a knowledge of its cause, which in turn can be traced back to a cognition of the mind, and back to the signs. The statement may be a prediction. In that case it cannot be said that that which follows after has caused that which precedes it, the prediction, but if the event has been predicted it has been through some knowledge of its cause and this same cause which precedes the event also precedes some cognition of the mind which gave rise to the prediction so that there is a real causal connection between the sign and the thing signified although it does not consist in one's being the effect of the other but in both being the effect of the same cause. (Ibid.) A sign is only a sign if the mind sees it as so, if it sees a connection to that which it is signifying. The connection is not there to be seen, though. The connection needs to be constructed by the mind, for which, first, an idea of a connection needs to exist, and this idea may come from previous knowledge that was acquired by another sign. it is necessary for a sign to be a sign that it should be regarded as a sign for it is only a sign to that mind which so considers and if it is not a sign to any mind it is not a sign at all. It must be known to the mind first in its material qualities but also in its pure demonstrative application. That mind must conceive it to be connected with its object so that it is possible to reason from the sign to the thing. Let us now see what the appeal of 225

227 a sign to the mind amounts to. It produces a certain idea in the mind which is the idea that it is a sign of the thing it signifies and an idea is itself a sign, for an idea is an object and it represents an object. The idea itself has its material quality which is the feeling which there is in thinking. (Ibid.) Peirce s nature of a sign seems to point us to infinity, as signs circulate in our mind ad infinitum. They condense into knowledge, and evaporate back again into signs. Our ideas have also a causal connection with the things that they represent without which there would be no real knowledge. (Ibid.:143) ON THE SIGN We can find throughout Peirce s writings a number of definitions of a sign. Sign [Lat. signum, a mark, a token]: Ger. Zeichen; Fr. signe; ItaL. segno. (I) Anything which determines something else (its interpretant) to refer to an object to which itself refers (its object) in the same way, the interpretant becoming in turn a sign, and so on ad infinitum. (1901-5:239) We see in this definition that signs consist of three inter-related parts: a sign, an object, and an interpretant. We can think of the sign as the signifier, as a written word, for example; of the object as whatever is signified, the object to which the written word is attached; of the interpretant, as the understanding that we have of the sign-object relation. The importance of the interpretant for Peirce is that signification is not a simple dyadic relationship between sign and object: a sign signifies only in being interpreted. This makes the interpretant central to the content of the sign, in that, the meaning of a sign is manifest in the interpretation that it generates in sign users. 29 Explicitly motivated by Kant s recognition of the frequency in logical analytics of trichotomies or three-fold distinctions (Peirce 1991[1885]:180), Peirce sees a triad in the kinds of signs, the index being one of them. One very important triad is this: it has been found that there are three kinds of signs which are all indispensible in all reasoning; the first is the diagrammatic sign or icon, which exhibits a similarity or analogy to the subject of discourse; the second is the index, which like a pronoun demonstrative or relative, forces the attention to the particular object intended without describing it; the third is the general name or description which signifies its object by means of an association of ideas or habitual connection between the name and the character signified. (Peirce 1885:181) Here again. There are three kinds of signs. Firstly, there are likenesses, or icons; which serve to convey ideas of the things they represent simply by imitating them. Secondly, there are indications, or indices; which show something about things, on account of their being 226

228 physically connected with them. Thirdly, there are symbols, or general signs, which have become associated with their meanings by usage. Such are most words, and phrases, and speeches, and books, and libraries. (Peirce 1894:5) And again. A sign is either an icon, an index, or a symbol. An icon is a sign which would possess the character which renders it significant, even though its object had no existence; such as a lead-pencil streak as representing a geometrical line. An index is a sign which would, at once, lose the character which makes it a sign if its object were removed, but would not lose that character if there were no interpretant. Such, for instance, is a piece of mould with a bullet-hole in it as sign of a shot; for without the shot there would have been no hole; but there is a hole there, whether anybody has the sense to attribute it to a shot or not. A symbol is a sign which would lose the character which renders it a sign if there were no interpretant. Such is any utterance of speech which signifies what it does only by virtue of its being understood to have that signification. (Peirce :239) We have a special interest in the index since the index forces the attention, points and connects to an object without describing it, and has an existence detached from what it is pointing to. An index s direction is not fixed, nor limited. The same index can point to multiple objects, and this in turn can receive multiple indexes. This constant intermittence of indexes contributes to the interpretation of the sign, hence cognition, hence knowledge. Such an understanding of the index presented here by Peirce is over a hundred years old, but still present when we place it next to the novel instruments that operate the web. As we have seen in our pre-specific talks and with the web search engines, one object can be freely characterized by thousands of indexes in constant circulation. These instruments operate mainly the indexical not iconic, or symbolic characterizations towards our interpretation. They present a way to operate indexes prior to any interpretation, because as Peirce shows here, interpretation is with us, and not with the computer. On logic and semiotics, Peirce recognizes three kinds of conscious experiences: feeling, reaction, and thinking. It is necessary to recognize three different states of mind. First, imagine a person in a dreamy state. Let us suppose he is thinking of nothing but a red color. Not thinking about it, either, that is, not asking nor answering any questions about it, not even saying to himself that it pleases him, but just contemplating it, as his fancy brings it up. This is about as near as may be to a state of ind in which something is present, without compulsion and without reason; it is called Feeling. (Peirce 1894:4) Feeling is presence with no compulsion, or reason. The dream is violently interrupted, questions appear, what is going on? 29 Atkin, Albert, "Peirce's Theory of Signs", The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.) at (accessed ). 227

229 Second, imagine our dreamer suddenly to hear a loud and prolonged steam whistle. At the instant it begins, he is startled. He instinctively tries to get away; his hands go to his ears. It is not so much that it is unpleasing, but it forces itself so upon him. The instinctive resistance is a necessary part of it: the man would not be sensible his will was borne down, if he had no self-assertion to be borne down. This sense of acting and of being acted upon, which is our sense of the reality of things, both of outward things and of ourselves, may be called the sense of Reaction. It essentially involves two things acting upon one another. (Ibid.) Two different things are recognized, they are facing each other, they are connected, but the dreamer does not know how. Third, let us imagine that our now-awakened dreamer, unable to shut out the piercing sound, jumps up and seeks to make his escape by the door, which we will suppose had been blown to with a bang just as the whistle commenced. But the instant our man opens the door let us say the whistle ceases. Much relieved, he thinks he will return to his seat, and so shuts the door, again. No sooner, however, has he done so than the whistle recommences. He asks himself whether the shutting of the door had anything to do with it; and once more opens the mysterious portal. As he opens it, the sound ceases. He is now in a third state of mind: he is Thinking. That is, he is aware of learning, or of going through a process by which a phenomenon is found to be governed by a rule, or has a general knowable way of behaving. (Ibid.:5) By observation and a constant interplay between that which is observed and a mental process, the dreamer learns how to behave, and the dreamer thinks and constructs reason. There are three kinds of interest we may take in a thing. First, we may have a primary interest in it for itself. Second, we may have a secondary interest in it, on account of its reactions with other things. Third, we may have a mediatory interest in it, in so far as it conveys to a mind an idea about a thing. In so far as it does this, it is a sign, or representation. (Ibid.) Reasoning necessarily involves a process of signification. For Peirce, it is a path from resemblance to connection to interpretation. A regular progression of one, two, three may be remarked in the three orders of signs, Likeness, Index, Symbol. The likeness has no dynamical connection with the object it represents; it simply happens that its qualities resemble those of that object, and excite analogous sensations in the mind for which it is a likeness. But it really stands unconnected with them. The index is physically connected with its object; they make an organic pair. But the interpreting mind has nothing to do with this connection, except remarking it, after it is established. The symbol is connected with its object by virtue of the idea of the symbol-using mind, without which no such connection would exist. (Ibid.:9) All intellectual operations involve the three kinds of symbols. A symbol, as we have seen, cannot indicate any particular thing; it denotes a kind of 228

230 thing. Not only that, but it is itself a kind and not a single thing. You can write down the word star ; but that does not make you the creator of the word, nor if you erase it have you destroyed the word. (Ibid.) From symbols to symbols, they merge, and a handful of them become one. What was signified by a few, now it is by one. This one merges with others, and splits again to become another. This process goes on ad infinitum. How much is enough, and where to stop? This question we have asked before; for Peirce, the answer is in the act of reasoning. Symbols grow. They come into being by development out of other signs, particularly from likenesses or from mixed signs partaking of the nature of likenesses and symbols. We think only in signs. These mental signs are of mixed nature; the symbol-parts of them are called concepts. If a man makes a new symbol, it is by thoughts involving concepts. So it is only out of symbols that a new symbol can grow. (Ibid.:10) When reasoning, we cannot escape from signs, because reasoning is about their constant arrangement. In all reasoning, we have to use a mixture of likenesses, indices, and symbols. We cannot dispense with any of them. Suppose a man to reason as follows: The Bible says that Enoch and Elijah were caught up into heaven; then, either the Bible errs, or else it is not strictly true that all men are mortal. What the Bible is, and what the historic world of men is, to which this reasoning relates, must be shown by indices. The reasoner makes some sort of mental diagram by which he sees that his alternative conclusion must be true, if the premise is so; and this diagram is an icon or likeness. The rest is symbols; and the whole may be considered as a modified symbol. It is not a dead thing, but carries the mind from one point to another. The art of reasoning is the art of marshalling such signs, and of finding out the truth. (Ibid.) Peirce goes further in depth to the relationship between logic and semiotics. Logic is the art of reasoning is the first line that can be read in Of Reasoning in General. He starts by defining the concepts to build up his argument. Reasoning is the process by which we attain a belief which we regard as the result of previous knowledge. (Peirce 1895:11) And inference is not the same as reasoning, even though a belief is the effect of other beliefs. a given belief may be regarded as the effect of another given belief, without our seeming to see clearly why or how. Such a process is usually called an inference; but it ought not to be called a rational inference, or reasoning. (Ibid.:12) On argument, conclusion, premise, and consequence. The word illation signifies a process of inference. Reasoning, in general, is sometimes called ratiocination. Argumentation is the expression of a reasoning. Argument may be mental or expressed. The belief to which an inference leads is called the conclusion, the beliefs from which it sets out are called the premises. (Sometimes written premisses.) The 229

231 fact that the premises necessitate the truth of the conclusion is called the consequence, or following of the conclusion from the premises. (Ibid.) On belief and logical proposition. A Belief is a state of mind of the nature of a habit, of which the person is aware, and which, if he acts deliberately on a suitable occasion, would induce him to act in a way different from what he might act in the absence of such habit. An act of consciousness in which a person thinks he recognizes a belief is called a judgment. The expression of a judgment is called in logic a proposition. (Ibid.) The unit of thought is the judgment. The unit of speech is the sentence, says one of the most illustrious of living linguists, the Rev. A. H. Sayce, in the article Grammar in the Encyclopaedia Britannica. Modern logicians have come to a conclusion analogous to that of modern linguists in holding that the unit of thought is the judgment. (Ibid.) Peirce has a setup that seems to be ready to accommodate signs. A sign is a thing which serves to convey knowledge of some other thing, which it is said to stand for or represent. This thing is called the object of the sign; the idea in the mind that the sign excites, which is a mental sign of the same object, is called an interpretant of the sign. Signs are of three classes, namely, Icons (or images), Indices, and Symbols. (Ibid.:13) He presents yet another characterization of signs, starting with the icon, a static likeness of an object. An icon is a sign which stands for its object because as a thing perceived it excites an idea naturally allied to the idea that object would excite. Most icons, if not all, are likenesses of their objects. A photograph is an icon, usually conveying a flood of information. A piece of mimicry may be an auditory icon. A diagram is a kind of icon particularly useful, because it suppresses a quantity of details, and so allows the mind more easily to think of the important features. (Ibid.) The index, or the dynamic link to the object. An index stands for its object by virtue of a real connection with it, or because it forces the mind to attend to that object. Thus, we say a low barometer with a moist air is an indication of rain; that is, we suppose that the forces of nature establish a probable connection between the low barometer with moist air and coming rain. A weathercock is an indication, or index, of the direction of the wind; because, in the first place, it really takes the selfsame direction as the wind, so that there is a real connection between them, and in the second place, we are so constituted that when we see a weathercock pointing in a certain direction it draws our attention to that direction, and when we see the weathercock veering with the wind, we are forced by the law of mind to think that direction is connected with the wind. (Ibid.:14) 230

232 Icons and indexes tell nothing by themselves. Icons and indices assert nothing. If an icon could be interpreted by a sentence, that sentence must be in a potential mood, that is, it would merely say, Suppose a figure has three sides, etc. Were an index so interpreted, the mood must be imperative, or exclamatory, as See there! or Look out! (Ibid.:16) On the other hand, the symbol does tell about the object, and at this point the indexes and icons do not matter any longer because the connection has been made. A symbol is a sign naturally fit to declare that the set of objects, which is denoted by whatever set of indices may be in certain ways attached to it, is represented by an icon associated with it. (Ibid.:17) For Peirce, language is an example of how differently one and the same object can be perceived. This suggests that there is no single unique way to reason about the same thing. The astonishing variety which exists in the syntax of different languages shows that different men think the same fact: in very different ways. There is no respect in which the constructions of languages differ more than in regard to the noun. (Ibid.) And these different reasonings must converge towards a logical construction. Thinking a fact in a different way will not alter its value as a premise or as a conclusion. Whether from the judgment, A, it is proper to infer the judgment, C, depends upon whether or not the fact which A expresses could possibly take place without the fact which C expresses going along with it. On this connection of facts mere thinking can have no effect. (Ibid.:18) For Peirce, this is what logic is about. Logic can be thought of as a plane of comparison for different reasonings. Different reasonings on the same fact are equivalent. The principal business of logic is to ascertain whether given reasonings are good or bad, strong or weak. In this regard, whether we think our propositions in one form or in another is of no more consequence than whether we express them in English or in German, whether we write them or enunciate them, whether we drawl or gabble. In the eye of logic, two propositions expressing the same fact are equivalent, or virtually (at least) identical. (Ibid.) To find out if a reasoning is right, it is necessary to look at the fact it is expressing, at the object, and not at the reasoning itself. To say whether a given way of thinking is correct or not, it is requisite to consider what facts the thought expresses. To this, then, those who occupy themselves with the art of reasoning must attend. The logician cannot be asked to teach the tongues: it is the business of the philologist to do that. (Ibid.) And every form of thinking must speculate, must betray itself in order to construct new reasons, new ways to construct signs. 231

233 So, cultivators of the art of reasoning found themselves long ago obliged to institute a speculative grammar which should study modes of signifying, in general. It is best regarded as separate from logic proper; for one of these days philologists may take it in hand, for which logicians will thank them. (Ibid.:19) Betrayal is celebrated in favor of reason. An art of thinking ought also to recommend such forms of thinking as will most economically serve the purpose of Reason. The doing of this in a well-reasoned way involves a great theory. (Ibid.) On the nature of a proposition, a proposition is the expression of a judgment, and a judgment is the recognition of a belief, and a belief is a state of mind where a person is aware of something. We can think of a proposition as a logical awareness. For Peirce, the nature of a proposition is deeply linked to the sign. we virtually resolve upon a certain occasion to act as if certain imagined circumstances were perceived. This act which amounts to such a resolve, is a peculiar act of the will whereby we cause an image, or icon, to be associated, in a peculiarly strenuous way, with an object represented to us by an index. This act itself is represented in the proposition by a symbol, and the consciousness of it fulfills the function of a symbol in the judgment. (Ibid.) On the nature of inference, an inference is a process whereby a given belief is regarded as the effect of another given belief, without a clear why or how. Peirce s analysis starts by defining a colligation. The first step of inference usually consists in bringing together certain propositions which we believe to be true, but which, supposing the inference to be a new one, we have hitherto not considered together, or not as united in the same way. This step is called colligation. The compound assertion resulting from colligation is a proposition with a composite icon, as well as usually with a composite index. (Ibid.:22) What follows is the observation of the icon towards the production of new icons. The next step of inference to be considered consists in the contemplation of that complex icon, the fixation of the attention upon a certain feature of it, and the obliteration of the rest of it, so as to produce a new icon. (Ibid.) Thus, then, it is that the complex icon suggests another that is a feature of it. Whenever one thing suggests another, both are together in the mind for an instant. (Ibid.:24) One icon calls another one, and for a moment both are together; the question is if they must stay together, or if they should merge, or if one should substitute the other. In other words, a conclusion is needed. the mind is not only led from believing the premises to judge the conclusion true, but it further attaches to this judgment another that every proposition like the premise, that is having an icon like it, would involve, and compel acceptance, of a proposition related to it 232

234 as the conclusion then drawn is related to that premise. (Ibid.) This process shows to Peirce the nature of knowledge. It thus appears that all knowledge comes to us by observation. A part is forced upon us from without and seems to result from Nature's mind; a part comes from the depths of the mind as seen from within, which by an egotistical anacoluthon we call our mind. The three essential elements of inference are, then, colligation, observation, and the judgment that [what] we observe in the colligated data follows a rule. (Ibid.) Knowledge is an interplay between what can be observed and the mind. Peirce calls it an inner and outer world. There is a great distinction between reasoning which depends upon the laws of the inner world and reasoning which depends upon the laws of the outer world. (Ibid.) The outer world is of conventions and shared beliefs, like the mathematical models with which we can fly or instantly communicate with each other regardless of location or language. We observe the outer world and seem to catch the idea of a given line of phenomena. In this way, we have so well detected the nature of the regularity in the motions of the stars that we can make very accurate predictions about them. (Ibid.) The inner world is important as well, but the outer rules do not apply. Peirce suggests celebrating this distinction, and not submitting ourselves to one set of laws. To practice a constant talk between these two, to observe signs that will construct other signs, this is what reasoning is about. But reasoning based upon the laws of the inner world is not thus uncertain. It is called demonstrative reasoning, or demonstration. For instance, if you add up a column of five hundred figures, you get the sum total by mathematical reasoning. It is said to be absolutely certain that your result will be correct. This is an exaggeration. We have seen that it depends upon observation; and observation is always subject to error. But experimentation is so handy upon creations of our own imagination. (Ibid.:25) In truth, positive certainty is unattainable by man. Are you sure twice two are four? Not at all. A certain percentage of the human race are insane and subject to illusions. It may be you are one of them, and that your idea that twice two is four is a lunatic notion, and your seeming recollection that other people think so, the baseless fabric of a vision. Or twice two may ordinarily be five, but when anybody counts it up, that may have the effect of temporarily reducing it to four. (Ibid.:26) For Peirce, the two worlds are equally important. The remark that reasoning consists in the observation of an icon will be found equally important in the theory and the practice of reasoning. (Ibid.) 233

235

236 3.3 Content Sharing Platforms Content sharing platforms and social networks are a re-articulation of the concept of community. Individuals gather to desire, construct, celebrate, circulate, and care about objects. By experience, we can see that communities emerge on the global network with little or no restrictions. Any common interest can gather a community around it in days. Online communities influence societies to a never-before-seen degree, Facebook, Instagram, Tumblr, and Twitter are a prominent part of the digital culture today. Philosophically, we can see how this re-articulation challenges the notion of individuation, or the becoming of an I within a we. For Bernard Stiegler, the re-articulation we are experiencing now is fatal. The substitution of old programs by the global network and by computers in general without the explicit introduction of new ones, places the I in a precarious situation, where there is no chance for projection but only for submission, where becoming is an ill-becoming. For Stiegler, a community is the sum of the individuals, therefore, and an ill I is an ill we. Another view of this phenomena affirms that communities are formed around a common object in infinite circulation. Michel Serres metaphorically tells us that a community is like a ball game, and that the we is formed by the circulation of the ball, and that the ball he calls it the quasi-object while being held by a team member designates the I. For Serres, the construction of the collective is done with jokers wild cards as anything is built with anything. What we see that circulates in the content sharing platforms is information. Messages are being transmitted at the speed of light. Mathematically, a theory of communication explains how messages circulate from source to destination. For Claude Shannon, the fundamental problem is the exact reproduction of a message in two points, decoupled from meaning. Shannon s model is symmetrical; there is a source, a transmitter, and noise in the middle, then a receiver and a 235

237 destination. We see that his idea of successful communication includes a specific notion of a message and code that team together against the noise entropy. If entropy disappears, information emerges, regardless of its meaning and interpretation. If we place this mathematical theory next to a philosophy of natural economy a gesture that aims to cast a shadow over the circulation of information on content sharing platforms we see that interpretation cannot be left aside in the community s communication, but at the same time, that an I cannot interpret it all. Serres finds in the Pentecost a metaphor to characterize a model of communication in which noise is not killed but celebrated because interpretation or meaning-making happens due to the noise and at the same time without mediation. Content sharing platforms and social networks also see that they do not need to understand it all in order to effectively operate the information that circulates in their networks. A prominent instrument that reflects such an understanding is the Self-Organizing Map (SOM). Teuvu Kohonen presents a process for the automatic mapping of any abstract or conceptual objects into a one- or two-dimensional space, or better, a process that creates a computable symbolic space pulled out from any observable event. A SOM observes coherent inputs coherent in their own terms and creates a new space of immanences, outside interpretation and meaningmaking. To link it back, a content sharing platform could, for example, observe all of its community members, create such a new space, and start recognizing similarities and differences from their immanences, and not from an understanding of the members which is actually what happens and what we experienced in our applications. [1/6] Cinematic Time and the Question of Malaise internet, information, telecommunication, applications, individuation, capitalism, market, diachrony, synchrony, globalization, confusion, programs Figure 3.15: Pan American Unity mural, Diego Rivera Figure: City College of San Francisco at (accessed ). 236

238 In the third volume of Technics and Time: Cinematic Time and the Question of Malaise, dedicated to Jacques Derrida, Bernard Stiegler 2 addresses the question of individuation in our digital condition. We are interested in Stiegler s account of the process of becoming a community in the shadow of the global network, which we want to link back to the content sharing platforms and social networks at hand. Stiegler recognizes the global network and its impacts on society today. He stresses the convergence of the distributed ways in which we used to communicate. The internet has become the implementer of standard interoperability among digital infrastructures, called TCP-IP, that has made innumerable new services, tools, and uses possible and that, combined with new standards for text, image, and sound compression, has allowed for the colossal phenomenon we now know as the convergence of informational, telecommunications, and audiovisual technologies (Stiegler 2011:2) It is not only that many media now converge to one by the computers ability to symbolize and operate, but also that computers are everywhere and that societies celebrate them without knowing the catastrophic consequences of such actions, he argues. He further sees our digital condition as a fertile ground for capitalistic systems to freely mutate from the industrial to the 'hyper-industrial' condition without society having the time to reason about it, a kind of state of vulnerability with no way out. In addition to the concretizing of the processes now in and about to take place, there will doubtless be an increase in the amount of time spent in front of screens of all kinds, which will be then re-conceptualized and redefined in their functions (becoming terminals of tele-action), their various applications expanding into the thousands, most notably at the professional level; these processes will pursue, at an increasingly complex level and with increasing ease and sensitivity, the industrial temporalization of consciousness. This convergence, in bringing together industrial logistics (informatics), transmission (telecommunications), and the symbolic (audiovisuals), also integrates the functions of technological, industrial, and capitalistic mnemotechnical systems into the technical systems producing material goods, in turn facilitating the transmutation of the industrial world into the hyperindustrial and subordinating the entire worlds of culture, knowledge, and the mind, along with artistic creation and advanced research and instruction, to the imperatives of development and the market. (Ibid.) New markets are fast enough to be ahead of our consciences; they are in control, he says, mostly because of the integration of the symbolic (the alphabet, the analog) and the logistic (the digital) in industries. Making the industries' reaction time to the consumers perception and desire as fast as the speed of light. Markets are above all consciences acting as places for exchange by consumers whose 2 Bernard Stiegler is a French philosopher, head of the Institut de recherche et d innovation (IRI), which he founded in 2006 at the Centre Georges-Pompidou. Since 2010, he has established a philosophy school in Épineuil-le-Fleuriel, France, called pharmakon.fr, where he runs a course for lycée students, a doctoral program conducted by videoconference, and a summer academy. 237

239 consciousnesses are themselves consumer 'goods,' and for market financiers whose 'consciousnesses' are investors and speculators. Yet at the moment at which management has orders to react in real time, thus producing reactivity in the double sense of the word (in terms of management, as rapidity and ease of adaptation, and in Nietzschean terms, as ressentiment and group behavior against exceptions), the functional integration of the symbolic and logistic industries produces total control of markets as collectivities of a temporal stream of consciousness always in need of being synchronized. (Ibid.) But this has not always been the case, Stiegler says. Before we had free consciousness; now, not. The synchronic changes that we are experiencing not giving 'time' for changes to happen will bring tragic consequences. A consciousness, in the eighteenth- and nineteenth-century sense of the word, is essentially free, that is, diachronic, or perhaps exceptionally, singularly, irreducibly mine this could also be called ipseity. Diachrony and synchrony are tendencies that form and re-form ceaselessly, and we will see that they cannot be in opposition over a significant amount of time without tragic consequences. Yet their composition is precisely what from the hyperindustrialization of temporal objects constitutes the possibility of de-composition. (Ibid.:3) But there is no need to experience such consequences in order to liberate our consciousness again, Stiegler suggests. The fact that consciousness is always in struggle assures us that new conditions can be built. He calls for a new commerce. Yet as evident and ineluctable as the integration of the logistic (digital) and the symbolic (alphabetic and analogic) industries may be, nothing indicates that such an integration will always be effective in its (or any) current form contemporarily, as the systematic and unlimited exploitation of consciousnesses for 'market access.' Consciousness as a temporal object is always in struggle, today as a core issue of the current industrial revolution, as it builds the conditions necessary for what I call a new commerce in the broadest sense of the word. (Ibid.) Stiegler sees that the conscious synthesis is disappearing in our society and is being replaced by the systematic industrialization of the retentional devices that prevent consciousness. A prosthetization of consciousness is happening. Prostheticity is a decisive element in such transformations when, as we will see, it creates conditions for what Kant calls schematism, the implementing of new forms of what I call tertiary retentions, the material inscription of the memory retentions in mnemotechnical mechanisms I have defined in relation to the Husserlian concepts of primary and secondary retention (a connection to which I will return in the first chapter below). Prosthetization of the synthesis that always includes the flux of consciousness (i.e., Kant's sense of synthesis), with the industrial production of temporal objects, can reach a stage at which the transformation of this consciousness is simply destroyed. This means that 238

240 the current prosthetization of consciousness, the systematic industrialization of the entirety of retentional devices, is an obstacle to the very individuation process of which consciousness consists. (Ibid.:4) This is part of Stiegler's diagnosis of our digital condition. We see now how individuals are identified in our society Stiegler s principle of individuation, or better, the lack of it. The development and integration of logistic and symbolic technologies mean a loss of individuation in the sense in which Gilbert Simondon analyzes it with regard to the manual laborer and the nineteenth-century machine-tool, the 'technical individual' replacing the worker who, having had his skills exteriorized, could therefore no longer be individuated but was instead condemned to be proletarized. The confusing of the logistic with the symbolic their non-critical integration has led to a straightforward proletarization of the mind and to the pauperization of the culture. (Ibid.) The industries of the global condition, by replacing the technical individual with a computer program, for example, kill the individual s capacity for projection, giving him no option but to submit to their industrialized processes and illusions of individuation. The individual becomes nobody. The result has been a slow destruction of the unifying capacities of the temporal flux in which individual consciousness exists and the destruction of its capacity for projection for desire which can only be singular (objective): if an individual consciousness is cut off from 'world,' it aims either at embedding itself in the archi-flux of the programming industries or being trapped in the webs of 'user profiling whose goal is to subdivide and tribalize them into subcommunities through devices that can observe the behavior of the programmed consumers within the wide variety of informational internet content that then, on the basis of those observations, can create models for the hypersegmentation of the target audiences of advertising, while still giving them the impression that the system is responding to them personally; this is obviously pure illusion, since this system is always one of industrializing what had never been industrializable individual behaviors thereby reinforcing them until the consumer, being locked in, can no longer escape; she can be perfectly anticipated and controlled, no longer an individuated and individuating 'person' but in a real sense Nobody [personne; outis], a perspectiveless cyclops. (Ibid.) And the risks of putting the individual in this position is the transformation of the community into a globalized, impersonal One. An ill-society participant and an ill-society all-together. This loss of individuation, in which I persists as a yawning void, no longer moving toward a We who, being everything, the confusion of all possible I's in an undifferentiated flux (the totalitarian model of 'community'), is condemned to dissolve into a globalized, impersonal One. This loss of individuation leads to immense existential suffering: in the most tragic cases, this quasi-inexistence produces multiple personalities, and the danger of taking deadly drugs, of violence, tribal or individual, and suicide, which in France has become the second most common cause of death in adolescents and the most common in young 239

241 adults. (Ibid.:5) For Stiegler, the inability to become in a non-totalitarian model of community only leads to an illbecoming, hence, an ill-society. This is the inescapable malaise at work today. It would be possible to say that in certain respects this malaise is precisely, itself, 'the age of the contemporary being were one to think that 'the question of being' as Heidegger sees it is still a salient question, and if the contemporary version of the concept has not been completely transformed by a radical parallel shift in the meaning of becoming that is, if 'the question of being' is not now dominated by an ontological indifference; if this malaise is not the border, the limit, the very question of being within the ever-returning question of suffering: mis-becoming as the agent of becoming-ill. (Ibid.) Stigler s solution is to construct new programs that will substitute the old ones in which diachrony is possible and a new collective can be engendered. an epoch is only clearly constituted as such when 'the suspension of programs' engendered by the technical system leads to the constituting of new programs and to a second suspension a re-doubling of doubling through which a new unity of space and time is constructed, a new psychic and collective individuation. (Ibid.:7) Because our current condition has no future. Today, the conditions of the second re-doubling are not integrated. The re-doubled double has no place. Becoming, which has been disrupted, does not produce a future. (Ibid.) For Stiegler, a community is the sum of its individuals, where a process of individuation is marked by a flux of consciousness that will position the individual within a community. The individual with his desires influences the community. For him, because the community is the sum of individuals, an ill-individual can risk the health of the whole community. We will distance and place Stiegler in perspective, and look at a much more optimistic and promising scenario that characterizes a community not by the sums of the individuals, but by that which we all care about, celebrate, and circulate. 240

242 [2/6] Theory of the Quasi-Object community, individual, collective, i, we, circulation, object-subject, relation, building, joker Figure 3.16: Self-Portraits (Harlequin and Pierrot), Alexandre Jacovleff with Vasiliy Shukhaev In the book, The Parasite, Michel Serres 4 develops a philosophy of natural economy based on communication. He characterizes the parasite as a one-way, irreversible relation that is at the foundations of any communication and community, including science, religion, and history. And as mentioned before, we are interested in linking the questions of the individual and the collective back to the communities online engendered by the global network. We want to cast a shadow over the online communities that we see are changing the way we create and circulate objects. The problem with the preceding meditations is that they do not say distinctly enough whether they are a philosophy of being or of relation. Being or relating, that is the whole question. It is undoubtedly not an exclusive one. I still shall not decide whether the parasite is relational or real, whether it is an operator or a monad. (Serres 1982:224) Serres tells us about a game in which one person is distinguished from the rest the expelled. The community circulates an object, trying to hide it from the expelled, and whoever is caught with it becomes the expelled. We have all played the game of hunt-the-slipper or button, button, who's got the button. The one who is caught with the furet [the slipper or button] has to pay a forfeit. The furet points him out. One person is marked with the sign of the furet. Condemned, he goes to the center; he's it ; he sees, he looks. (Ibid.:225) For Serres, the object that circulates is central in the game; the whole community exists because of it, and he calls it a quasi-object. 3 Figure: from Wikiart at (accessed ). 4 Michel Serres is a renowned French philosopher, author, and leading intellectual. He is a professor in the history of science at Sorbonne, Paris, and at Stanford University. He was elected to the Academie Francaise in

243 This quasi-object is not an object, but it is one nevertheless, since it is not a subject, since it is in the world; it is also a quasi-subject, since it marks or designates a subject who, without it, would not be a subject. He who is not discovered with the furet in his hand is anonymous, part of a monotonous chain where he remains undistinguished. He is not an individual; he is not recognized, discovered, cut; he is of the chain and in the chain. He runs, like the furet, in the collective. The thread in his hands is our simple relation, the absence of the furet; its path makes our indivision. Who are we? Those who pass the furet; those who don't have it. This quasi-object, when being passed, makes the collective, if it stops, it makes the individual. If he is discovered, he is it [mort]. Who is the subject, who is an I, or who am I? The moving furet weaves the we, the collective; if it stops, it marks the I. (Ibid.) Another example is with a ball game. We tend to think of the players as masters of the ball, but this cannot be more wrong for Serres. Players, or the community, move around the ball; the ball is the sun and players move around it. And similarly, whoever holds the sun, whoever tries to hold it, to own it, is expelled from the community. A ball is not an ordinary object, for it is what it is only if a subject holds it. Over there, on the ground, it is nothing; it is stupid; it has no meaning, no function, and no value. Ball isn't played alone. Those who do, those who hog the ball, are bad players and are soon excluded from the game. They are said to be selfish [personnels]. The collective game doesn't need persons, people out for themselves. Let us consider the one who holds it. If he makes it move around him, he is awkward, a bad player. The ball isn't there for the body; the exact contrary is true: the body is the object of the ball; the subject moves around this sun. Skill with the ball is recognized in the player who follows the ball and serves it instead of making it follow him and using it. It is the subject of the body, subject of bodies, and like a subject of subjects. Playing is nothing else but making oneself the attribute of the ball as a substance. The laws are written for it, defined relative to it, and we bend to these laws. (Ibid.) The ball circulates just like the furet. The better the team, the quicker the ball is passed. Sometimes the ball is said to be a hot coal that burns one's fingers so badly that one must get rid of the ball as quickly as possible. (Ibid.:226) The ball and the furet, the center of the community, that which the community celebrates and circulates is what designates who is who. The ball is the quasi-object and quasi-subject by which I am a subject, that is to say, submitted. Fallen, put beneath, trampled, tackled, thrown about, subjugated, exposed, then substituted, suddenly, by that vicariance. The list is that of the meanings of subjicere, subjectus. (Ibid.:227) In any community, there is the 'we, the 'I', and the quasi-object that assigns by circulation when the 'I' becomes a 'we' and the 'we' becomes an 'I'. 242

244 This quasi-object that is a marker of the subject is an astonishing constructer of intersubjectivity. We know, through it, how and when we are subjects and when and how we are no longer subjects; We : what does that mean? We are precisely the fluctuating moving back and forth of 'I.' The 'I' in the game is a token exchanged. And this passing, this network of passes, these vicariances of subjects weave the collection. (Ibid.) The 'we' is not the sum of the 'I'. So, if everybody carries his stone, the wall is built? No, Serres says. A community is about the circulating. Everything happens as if, in a given group, the I, like the we, were not divisible. He has the ball, and we don't have it any more. What must be thought about, in order to calculate the we, is, in fact, the passing of the ball. But it is the abandon of the I. Can one's own I be given? There are objects to do so, quasi-objects, quasi-subjects; we don't know whether they are beings or relations, tatters of beings or end of relations. (Ibid.) In this constant circulation, Serres recognizes a loss of authority or supremacy of power or rank. There is something there, some movement, that resembles the abandon of sovereignty. The we is not a sum of I s, but a novelty produced by legacies, concessions, withdrawals, resignations, of the I. The we is less a set of I s than the set of the sets of its transmissions. (Ibid.:228) And he suggests that the constant circulation, a full participation of the community, could reach a point of ecstasy. Participation is just that and has nothing to do with sharing, at least when it is thought of as a division of parts. Participation is the passing of the I by passing. It is the abandon of my individuality or my being in a quasi-object that is there only to be circulated. (Ibid.) This moment is delicate, because a community is always on the edge of the self, of individuation, and this is the moment when the ball can be kept by one I. Collective ecstasy is the abandon of the I s on the tissue of relations. This moment is an extremely dangerous one. Everyone is on the edge of his or her inexistence. But the I as such is not suppressed. It still circulates, in and by the quasi-object. This thing can be forgotten. It is on the ground, and the one who picks it up and keeps it becomes the only subject, the master, the despot, the god. (Ibid.) Serres argues that the nature of a quasi-object is indexed by the jokers, like wild cards that can take any value. This shows to Serres that anything is built with anything, as long as there is a community that cares about it, that circulates it. The furet, the ball, are tokens in a game, passed from one to another; they are probably jokers. The construction of the collective is done with jokers and an amazing act of building. Anything is built with anything. This logic is highly undetermined and is the most difficult to note. (Ibid.:229) We see that, in Serres terms, information is what circulates in the online communities, text, 243

245 images, videos, traditional objects, and computational objects; they all inform. We look now at the concept of information. [3/6] Information and Thinking emit, receive, store, process, information, entropy, negentropy, rare, networks, circulation Information is like the photons from the solar stream: an elementary abounding and discrete packages of powerful indefiniteness. Vera Bühlmann 2013:98 In an address to the Society for European Philosophy, Serres talks about the object's and subject's universal activities that suggest a constant role-change between them, i.e., an object becomes a subject, a subject becomes an object, through the circulation of a quasi-object. What is at the center of these activities, what circulates, is information. Bacteria, fungus, whale, sequoia, we do not know any life of which we cannot say that it emits information, receives it, stores it and processes it. Four universal rules, so unanimous that, by them, we are tempted to define life but are unable to do so, because of the following counterexamples. Crystal, indeed, rock, sea, planet, star, galaxy: we know no inert thing of which we cannot say that it emits, receives, stores and processes information. Four universal rules, so uniform that we are tempted to define anything in the world by them, but are unable to do so because of the following counterexamples. Individuals, but also families, farms, villages, cities, nations, we do not know any human, alone or in groups, of which we cannot say that it emits, receives, stores and processes information. (Serres 2014:1) For Serres, information is a common ground of any existing thing, where there is no fixed or final categorization between the objects. The circulation of information suggests then that we reconsider fixed roles of objects and subjects, for example an exchange of information turns an object into a subject, and a subject into an object. These four rules of information, which is itself defined, in turn, by its rarity, change the idea we have had of thinking and, likewise, the subject-object relationship. Because information circulates universally within and between the totality of all existing things, we really cannot say that we are as exceptional as we think we are. (Ibid.) This characterization does not feel too far from Claude Shannon s entropy, which we will discuss next, where the states of the totality seem to be not differentiated, entropy. But, if operating information means inventing, then inventing seems to be what breaks the entropic state. We can 244

246 think of inventing then as the information that is not in balance. If thinking means inventing, what is there left to say? Emitting information that becomes increasingly rare, increasingly controlled during the emission, increasingly independent from the reception, storage and process, increasingly removed from its balance. (Ibid.:2) If we play this characterization of information and thinking, then information cannot be what we see in content sharing platforms and social media at hand, i.e., photos, comments, thoughts, events, images, messages, live streams, 24/7. Information needs to be thought of differently. Common to everything that has had the chance to exist, information has nothing in common with what we call by that name; media channels overwhelm us every day with it; it is often reduced to dreary repetitions, ad nauseam, to announcements of corpses, disasters of power and death, while war and violence are ranked at the bottom of global causes of human deaths. (Ibid.) Information then is the negative of Facebook s News Feed, for instance a stream of information that tends to entropy. What would be then the negative of a hundred thousand posts that talk about your closer network? According to Serres, those are rare. The information that I am speaking of, instead, is closer to a rarity. Léon Brillouin defines it as the opposite of entropy, that is the characteristic of high energies. He even says: negentropy. As entropy, in fact, reigns the hard, so information is equivalent to what I call the soft. 5 (Ibid.) The idea that media gives no information seems counterintuitive. Repetition provides stability but not rarity. Serres wants rarity. Thinking is getting a hold of the rare. Information, in its everyday sense, contradicts that sense several times: the repetitions are opposed to its rarity, as the identical is opposed to the new and death to life. In the sense of information theory, the information of the media thus provides mostly no information. Inversely, thinking means inventing: getting hold of rarity (Ibid.) The web is another network where information circulates. Circulation is ancient, and networks are ancient. Where does this information circulate? Basically, in networks. we have continued to cover our landscapes and the portolans of the Silk Roads, of the Incas or of spices... of land, maritime, rail or air roads... we still decorate the planet with a web of hertz, an electronic web... with a thousand and one names, repeating, thereby, a hominid practice that is at least a thousand years, at most a million years old. (Ibid.:3) If information is at the center of our four universal activities, it is expected that networks are at the foundations of any relations. Even better, every life constructs itself from admirable networks whose number of paths 245

247 and connections defies the combinatorial explosion and whose delicacy surprises us. (Ibid.) Serres argues that the distinction between object-subject, when talking about information and thinking, is not very helpful, and that neither is the distinction between matter and information. If interactions happen crisscross between all things in the world, interactions then are not only material (hard), they are also informational (soft). Information circulates through the inert, living and human world, where everything and everyone emits it, receives it, exchanges it, conserves it and processes it. Interactions are thus not only material, or hard, they are also informational, or soft; interactions, for sure, of causes, of forces, of energies, but also of interferences, interpretations, intersections of signs, of codes and of images, co-possibilities, filters. (Ibid.:4) This characterization reconsiders the idea that the things in the world are necessarily different from each other, or better, that different things of the world cannot talk to each other, that there are natural distinctions or fixed relations. All of them are talking about the whole world, in their own way. Something powerfully new has emerged in our vision of the world: the universe is made up of matter and information, paired and without doubt inseparable. This means that all things express, in some way, other things and the world; that all things conspire and consent to it; that all things, in some way, perceive; see, write, read... Just like us. (Ibid.) In order to make an image and characterize these interactions, Serres presents Julio Verne s cave in The Star of the South as a metaphor. In this novel, the two heroes are at the center of an immense grotto ground of sand and gold, walls of crystals. From total darkness to splendid brilliancy, flashing and flowing from every side. The most astonishing combination of light and color that had ever dazzled the eyes of a man (Verne 1883). Jules Verne's cave reverses the Platonic one. The latter sings the glory of one sun, discovered in the daylight, as one emerges from the shadow, while the former is an invitation to penetrate under a vault that is so deep that one's gaze is as lost as if it stared at a starry sky: here, in this cave, a thousand lights dazzle the thinker. (Ibid.:6) The act of thinking is closer to the night than to the day, Serres argues. Full light lit a truth, while the night engenders intuition, by only presenting constellations to think about. Thus the day makes us believe in the unicity of truth. In fact, thinking is much less like the day than like the night where every star shines like a diamond, where every galaxy flows like of river of pearls, where every planet, like a mirror, reflects the light it receives. Thus authentic knowledge overflows with results and intuitions; it sets up multiple reference points grouped into constellations with forms that are as disparate as those of scholarly disciplines. (Ibid.) 5 By soft age, Serres understands a time in which we finally understand that the four rules that I have set forth govern, and they always have been the case, and they without doubt will forever be, in relation to all that, being contingent, has 246

248 A last remark on day and night in relation to information and thinking, and truth. The gap between day and night spells the difference between cruel ideology and just knowledge that is right, evident, multiple, precise and ever evolving. Shimmering with the brightness of billions of glorious, colorful, and modest suns, the night with its countless truths resembles the high cave and its shining gems. (Ibid.:7) We see in Serres characterization of information an affirmation of infinity, circulation and relations and a negation of fixed differentiations between the things in the world. In this setup, information is to be celebrated, and distinctions that are rare are to be found and held on to. To place Serres information in perspective, we will look at the most prominent scientific contribution on information of the 20c, Claude Shannon s. [4/6] A Mathematical Theory of Communication communication, message, noise, entropy, probability, channel, bit, measure, binary logarithm, computing Figure 3.17: Schematic diagram of a general communication system. 6 In 1948, The Bell System Technical Journal published A Mathematical Theory of Communication, by Claude Shannon. 7 In it, the unit bit joined the inch, the pound, the quart, and the minute as a fundamental unit of measure (Gleick 2011), a unit for measuring information. What we today call information has always been there, but it was not until it became countable and operable that we would see it everywhere. Shannon introduced a mathematical model to distinguish information from uncertainty, entropy, chaos, from which the origins of computing can be indexed. Information theory is the glue between mathematics, electrical engineering, and computing. We index what remains at stake in a mathematical model of information when placed next to philosophical and operational accounts on information. The problem is formulated the rare chance to exist. (Serres 2014:2). 6 Figure: from (Shannon 1948). 7 Claude Elwood Shannon was an American mathematician, electrical engineer, and cryptographer. He is widely known for his digital circuit design theory and for the paper at hand. He contributed to the field of cryptoanalysis for national defense during the war. 247

249 by Shannon as follows: The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. (Shannon 1948) The meaning of a message is left aside. Sentences and words mean nothing, but the concept of sentence and word exists; they are actually defined by a probability model. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages. (Ibid.) Messages in the system are discrete, and their measure relies on this discretization. If the number of messages in the set is finite then this number or any monotonic function of this number can be regarded as a measure of the information produced when one message is chosen from the set, all choices being equally likely. (Ibid.) The unit for measuring information has a base two, which only means that one unit can be either one or zero, true or false, yes or no, black or white. The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly bits, a word suggested by J. W. Tukey. A device with two stable positions, such as a relay or a flip-flop circuit, can store one bit of information. (Ibid.) There are five parts that compose a system, as shown in figure In a non-mathematical based system, or better, in a non-systematic view on communication, this linearity seems to just not be there. We could say, for instance, that in social networks, sources, destinations, and noise seem to be all connected, crisscrossed. Shannon characterizes the components of his system. 1. An information source which produces a message or sequence of messages to be communicated to the receiving terminal. 2. A transmitter which operates on the message in some way to produce a signal suitable for transmission over the channel. 3. The channel is merely the medium used to transmit the signal from transmitter to receiver. 4. The receiver ordinarily performs the inverse operation of that done by the transmitter, reconstructing the message from the signal. 5. The destination is the person (or thing) for whom the message is intended. (Ibid.) Shannon classifies systems in three categories: discrete, like the ones briefly mentioned; continuous functions, like radio; and a mix of them. The discrete system stands above them all, since it is the basis for a continuous system, and for a mix system. And very importantly for us, it is the one at the foundations of computers. 248

250 We may roughly classify communication systems into three main categories: discrete, continuous and mixed. By a discrete system we will mean one in which both the message and the signal are a sequence of discrete symbols. A continuous system is one in which the message and signal are both treated as continuous functions A mixed system is one in which both discrete and continuous variables appear (Ibid.) Telegraphy is an example of a discrete system. Telegraphy discretizes a message to its most basic units, letters and numbers. These are then encoded and transmitted from A to B. The code is arbitrary, but most commonly Morse. The transmission of each letter, hence of the message, has a certain duration in time. The first big question for Shannon then is, how can we measure the capacity of a channel? Generally, a discrete channel will mean a system whereby a sequence of choices from a finite set of elementary symbols S1,, Sn can be transmitted from one point to another. Each of the symbols Si is assumed to have a certain duration in time ti seconds. (Ibid.) The capacity equals the logarithm of the largest real root of the determinant equation. See figure Theorem 1: Let bij(s) be the duration of the sth symbol which is allowable in state i and leads to state j. Then the channel capacity C is equal to logw where W is the largest real root of the determinant equation: (Ibid.) Looking at the discrete source of information, Shannon notices that the sequence of letters in a message are not random, and that a statistical model of a language can be done. That is to say that some letters appear more often than others. How is an information source to be described mathematically, and how much information in bits per second is produced in a given source? The main point at issue is the effect of statistical knowledge about the source in reducing the required capacity of the channel, by the use of proper encoding of the information. (Ibid.) Shannon thinks of the source of information as a system that produces a sequence of symbols in a stochastic process. Any discretized phenomena can be thought of like this, as we have seen with the Markov Chains. We can think of a discrete source as generating the message, symbol by symbol. It will choose successive symbols according to certain probabilities depending, in general, on preceding choices as well as the particular symbols in question. A physical system, or a mathematical model of a system which produces such a sequence of symbols governed by a set of probabilities, is known as a stochastic process. (Ibid.) Shannon presents a number of handy examples of such stochastic processes. He stresses the value of such processes in sending and receiving a message in his communication model. 249

251 There exist a finite number of possible states of a system; S1, S2,, Sn. In addition there is a set of transition probabilities; pi(j) the probability that if the system is in state Si it will next go to state Sj. To make this Markoff process into an information source we need only assume that a letter is produced for each transition from one state to another. The states will correspond to the residue of influence from preceding letters. (Ibid.) Fig. 3.19: A graph of the probability distribution of the letters A, B, C, D, E. 8 There is a Markov process in which the probability of every next state is equal, as there is actually no probabilistic distinction at all. We could say that in this case, to have a Markov model or not makes no difference. This special class consists of the ergodic processes and we shall call the corresponding sources ergodic sources. In an ergodic process every sequence produced by the process is the same in statistical properties. Thus the letter frequencies, digram frequencies, etc., obtained from particular sequences, will, as the lengths of the sequences increase, approach definite limits independent of the particular sequence. Roughly the ergodic property means statistical homogeneity. (Ibid.) This ergodic process is what Shannon calls entropy. The moment when a probabilistic model makes no difference in the communication process. The following graph shows the entropic value of an event with two possible outcomes: p and 1-p. Flipping a coin, for example, has.5 probability on each side; hence, entropy maximum, 1. Fig 3.20: Entropy in the case of two possibilities with probabilities p and (1-p). 9 8 Figure: from (Shannon 1948). 250

252 Suppose we have a set of possible events whose probabilities of occurrence are p1,p2,,pn. These probabilities are known but that is all we know concerning which event will occur. Can we find a measure of how much choice is involved in the selection of the event or of how uncertain we are of the outcome? (Ibid.) For Shannon, the communication entropy of a system is at its max when all the messages have equal probability of happening; hence, there s no distinction noise. He presents the equation for the communication entropy of an information source. Consider a discrete source of the finite state type considered above. For each possible state i there will be a set of probabilities pi(j) of producing the various possible symbols j. Thus there is an entropy Hi for each state. The entropy of the source will be defined as the average of these Hi weighted in accordance with the probability of occurrence of the states in question. (Ibid.) Shannon characterizes information in terms of probability, and he does not consider the actual content in terms of interpretation. For him the messages, The earth is flat, and Truth is in the bottom of a water well, may have the same amount of information, while the meaning is totally different. When placed next to Serres' account on information, we can see a different interest in noise. On the one hand, noise is to be celebrated, because the more noise, the more chances for rare things to appear. And on the other, noise is to be pushed down, canceled, so we can listen clearly to the message, to the information that is being transmitted. We recognize Shannon s great contribution, we celebrate computers, but also we are interested in constructing our personal and soft gnomons as discussed in the previous talk to celebrate noise and be attentive for the rare, just before interpretation but not decoupled from interpretation. This is what we presented in our pre-specific talks. There, we celebrate and operate infinity, to the moment just before interpretation, just before decision. We turn now to a philosophical account of models of communication, which further index our pre-specific talks. 9 Figure: from (Shannon 1948). 251

253 [5/6] Pentecost communication, exchange, network, mediation, language, collective, give, take Figure 3.21: Pentecost by El Greco, c Serres finds in the Paraclete a handy metaphor to talk about exchange. He presents three systems of communication: the one introduced by Leibniz, the one of Hermes, and that in the Pentecost. Their differences are around how communication happens and the relations between the sender, the receiver, and the noise referred here as the parasite. Serres has a special interest in the one introduced by the Paraclete because it presents an impossibility towards the whole while at the same time an immediacy, as there is no third mediator. The first known system of communication is that of Leibniz. It is both radical and simple. No one relates to anyone or anything; doors and windows are not only closed but absent; everything and everyone relates to everything else by the intermediate of God. (Serres 1982:43) God is the unique mediator with all the knowledge and all the power. In this setup, noise is reduced to almost nothing; it is almost not there. This system is perfect, can be mathematically determined in its parts, de jure and de facto. Inversely, this mathematics is optimal communication. The problem of evil is brought back to harmony by the calculation of the optimum. (Ibid.) Next is Hermes. There are no boundaries between words, all languages are spoken, he is everywhere. Many-one-many relations can be seen here. The message that Hermes delivers is 10 Figure: from Wikiart at (accessed ). 252

254 always the sender s plus or minus the noise. The second system is that of Hermes. He is a polytheist, is multi-centered, a chain of hourglasses, a network of such chains. The angels that pass, be they gods or demons, occupy the crossroads: knots of exchange, changes, cuts, bifurcations of decision, spindles, bundles, where the many come in one single hand. (Ibid.:44) In the Paraclete, any speaker speaks in his own language, and every hearer understands in his own, whatever the language and whatever the location, crisscross. Hermes is displaced. The third system connects many to many without an intermediate. It is the invention of the Paraclete, on the Pentecost. The many regulate themselves. This is something quite new, so new that it is believed to be the result of a miracle. (Ibid.) We have a network with many nodes, all of them well-known; one circulates throughout the network, and another with an almighty in the middle. In the second network, the demons and gods are many and well-known: local kinglets and chieftains, little leaders and procurers of money or ideology, blackmail or information, single despots of regional rackets. In the first, everything reaches its limit; the local moves toward the global and the plural to the singular. In the center, the King is seated, that is to say, the Sun King, the Sun. God is the name Leibniz gives him. (Ibid.) The Paraclete invites us to think of a de-centralized network of many-many relations. A graph that cannot be fully plotted. We think of it as the graph that Alexander refers to when talking about a city not as a tree. It is a question of knowing whether a network without constraints of crossroads, interchanges, intersections with parasites can be constructed. Where a given element can have a relation to another element without the constraints of mediation. This is the model of Pentecost. (Ibid.) It is not difficult for Serres to imagine the limits of a Hermes-like communication and neither to characterize the miraculous one, Pentecost, which he believes we should explore. I can have a relation directly to some object without an intercepter coming in between either to intercede or to forbid [interdire]. Is the absence of a parasite so rare? Is immediacy so miraculous? Must the word [parole] always be a parable, that is to say, always aside, para-? No. If it is not a miracle, can we build it? (Ibid.:43) To think of a communication without interchanges, Serres looks at the act of exchange. The ancient, venerable theology of the Paraclete matches in part the anthropology of exchange. When the Holy Ghost comes, so do gifts. The gift has a source but is not a point of reception. There is no exchange. What come from it are Wisdom, Knowledge, Intelligence, Advice, Force, Piety, the Fear of God. (Ibid.:45) An exchange connects. When a gift is in circulation, for instance, the receiver points to the outside not to the circulating gift, nor to the gift-giver, but to God by saying, Thank you. 253

255 Then the gift-giver confirms the outside by saying, You are welcome. No exchange could take place, no gift could be given in any of the languages I have heard spoken, if the final receiver did not say thank you at the end of the line. The terminal offers thanks. What purpose would giving serve, I ask you, if this minimal recognition did not recognize the superb and the generous? Moreover, the thanker moves away from the last position, one, by the way, that is rather difficult to maintain. To have the last word is to leave the last position to the other and to jump to the penultimate. Thus the host or the gift-giver quickly answers: Don't mention it; you're welcome; at your service, and thereby brings back the receiver to his place. (Ibid.) But this is not that obvious when we say it in English, Serres affirms. He refers to the Greek words, eucharist and parakalo. In saying thank you, the Hellene says eucharist. Good graces. Eucharist: God is in our relation; our relation is God himself, incarnate. (Ibid.) Parakalo is, as we know, the closing response. Don't mention it and, yes, you're welcome. Parakletos, the Paraclete, the common name of the Holy Ghost, the third person. He intervenes, interrupts, comes in through the walls, during meals or meetings He is the gift, the being of the gift, the universal donor. You say you're welcome because he has received, because it is he who gives. (Ibid.:46) Serres affirms the impossibility of knowing all about the interchanges in the network, and it should not be a problem, he says. By doing so, he makes the real not rational, renders it improbable and miraculous. We will perhaps never know what passes and what happens in our collective. What passes is the object or the word that is exchanged. What happens after giving? (Ibid.:46) We link back to Serres position, on the one hand, to Alexander and the contemporaries discussed in the first chapter, to those who tried to understand infinity and felt overwhelmed by complexity. And on the other hand, to the pre-specific talks presented in the previous chapter hence to the online application at hand. The online communities are engendered by circulation of quasi-objects that all members care about and celebrate. Serres suggests that we not try to understand what happens in the collective. We can think of our pre-specific talks as an attempt to be part of a community, in which we are able to grasp it all, without the will to understand it all. And this gesture is enough for us to find stability and to put value on the community and the circulations Remarks In this sub-chapter we have so far discussed the question of community and communication in 254

256 philosophical and mathematical terms. We have linked these positions back to the online application at hand. Content sharing platforms and social networks are a novel re-articulation of community. We see there, by experience, how these applications celebrate the network and provide the infrastructure for quasi-objects to circulate, more or less freely. We see in these applications, as well as in our pre-specific talks, how they present to us renderings of the community, highly curated and designed by them, where the user has little or no say in what or how she wants to experience it. 11 This control and design from their side is motivated by economy, we argue. A user, nevertheless, can have a sneak peek of their actions by joining the community with a business profile, for example. 12 This opens a small window into their abilities to model the community without a rigorous nor fixed understanding of the members or the quasiobjects in circulation. With a few dollars per day, a business can identify and target a small network within the community at an intimate level. 13 We have already argued in our pre-specific talks that to do what these communities do is necessary, for the main part, a certain understanding of information linked to our concept of indexicality and the proper instruments, which in principle happen to be open-source. They are there for us to use them, as we have shown. What follows is one of these instruments of many in which we see a synchronous abstraction in with the philosophical and mathematical interest of our research in general. We see it as a complement of Markov s contribution. [6/6] Self-Organized Formation of Topologically Correct Featured Maps symbolic space, automatic symbolic representation, topologically correct map, n-dimensional space, machine learning Figure 3.22: Computable symbolic space using SOM For an investigation into Facebook data and machine learning techniques see (Foletti 2017). 12 See Facebook Business at (accessed ) or Google Ads at (accessed ). 13 Ibid. 14 Figure: Moosavi 2014 at (accessed ). 255

257 Teuvo Kohonen s 15 most famous contribution is now known as the Self-Organizing Map, first published in This work contains a theoretical study and computer simulations of a new self-organizing process. The principal discovery is that in a simple network of adaptive physical elements which receives signals from a primary event space, the signal representations are automatically mapped onto a set of output responses in such a way that the responses acquire the same topological order as that of the primary events. (Kohonen 1982:59) Kohonen s work is motivated by the work 16 of a group of neuroscientists on explaining the selforganization of patterned neural connections during the origination and development of an organism. This principle is a generalization of the formation of direct topographic projections between two laminar structures known as retinotectal mapping. (Ibid.) As a generalization of such a process, it can be implemented to the automatic mapping of any abstract or conceptual items. It is here where we place value on Kohonen s contribution, in the ability to operate before semantic definitions or linguistic interpretations. Like Markov, Kohonen is operating immanences. There are no restrictions on the automatic formation of maps of completely abstract or conceptual items provided their signal representations or feature values are expressible in a metric or topological space which allows their ordering. (Ibid.) Kohonen s process can topologically map any event into a one- or two-dimensional space. They are both the observations and the map characterized in the same terms. The main objective of this work has been to demonstrate that external signal activity alone, assuming a proper structural and functional description of system behavior, is sufficient for enforcing mappings of the above kind into the system. (Ibid.) Kohonen s map constructs a new space from a known space. It is an automatically made model that, as such, informs and communicates about an object. Kohonen s process has been a key contribution to challenging traditional modeling paradigms; for example, those based on the idealization, full understanding, and representation of their objects. Vahid Moosavi s PhD thesis (Moosavi 2015) directly addresses these and other modeling questions in the shadow of Kohonen s maps. The possibility of constructing spatial maps for attributes and features in fact revives the old question of how symbolic representations for concepts could be formed automatically; most of the models of automatic problem solving and representation of knowledge have simply skipped this question. (Ibid.:60) 15 Teuvo Kohonen is professor emeritus of the Academy of Finland. He has made many contributions to the field of artificial neural networks. Kohonen has published several books and over 300 peer-reviewed papers. Kohonen has received for his scientific achievements a number of prizes including the IEEE Neural Networks Council Pioneer Award in 1991, Technical Achievement Award of the IEEE Signal Processing Society in 1995, and the Frank Rosenblatt Technical Field Award in

258 A Kohonen process has four main elements. A one- or two-dimensional array of processing units between the observations and the final map, the array and the map are both of the same shape. An element of selection of the unit that is more alike to the observation at hand. An element of interaction between the observation, the unit, and the unit s neighbourhood. And a moment of uniform adaptation of the interaction. In order to elucidate the self-organizing processes discussed in this paper, their operation is first demonstrated by means of ultimately simplified system models. The essential constituents of these systems are: 1. An array of processing units which receive coherent inputs from an event space and form simple discriminant functions of their input signals. 2. A mechanism which compares the discriminant functions and selects the unit with the greatest function value. 3. Some kind of local interaction which simultaneously activates the selected unit and its nearest neighbours. 4. An adaptive process which makes the parameters of the activated units increase their discriminant function values relating to the present input. (Ibid.) In a diagram of a process that produces an ordered one-dimensional map, we distinguish an input layer which are the observations of the world; a moment of automatic interaction between the observation and the map; and an output layer that will be projected to an array of test vectors, which at the end of the process is thought of as the topologically correct map or array. Consider Fig. [3.23] which delineates a simple one-level self-organizing system. Information about the events A1, A2, A3,... taking place in the exterior world is mediated in the form of sensory signals to a set of processing units (shown here as a onedimensional array for simplicity) via a relaying network. (Ibid.) Figure 3.23: Diagram of a Kohonen process of a one-dimensional array of processing units. 17 In a simple one-dimensional map as the one suggested in figure 3.23, its correct order can be easily identified, without any further process. the topology of the array is simply defined by the definition of neighbours to each unit. If the unit with the maximum response to a particular event is regarded as the image of the latter, then the mapping is said to be ordered if the topological relations of the images and 16 See in the paper s introduction cited here, some indexes to Kohonen s work from neuroscience. 257

259 the events are similar. (Ibid.) The process of a two-dimensional map is slightly different. Here, the input events are not connected to all the processing units; there is a selection process, one at a time. Today it is referred to as finding the Best Matching Unit (BMU). Consider Fig. [3.24] which delineates a rectangular array of processing units. In the first experiment, the relaying network was neglected, and the same set of input signals {E1, E2,, En} was connected to all units. (Ibid.) Figure 3.24: Diagram of a two-dimensional array of processing units. The input events are at the top and the output responses at the bottom. 18 The input events are thought of as a vector, or as an array, and in each iteration, one event is randomly selected, then this event is compared with the units of the map following a similar function. In accordance with notations used in mathematical system theory, this set of signals is expressed as a column vector x=[e1, E2,, En]T e Rn where T denotes the transpose. Unit i shall have input weights or parameters ui1, ui2,, uin which are expressible as another vector mi=[ui1, ui2,, uin ]T e Rn. The unit shall form the discriminanant function. (Ibid.:61) The BMU is the unit with the biggest value; that is to say, more similar to the observation at hand. A discrimination mechanism shall further operate by which the maximum of the ni is singled out: (Ibid.:61) Once the observation s BMU is identified, the interaction between the observation, the BMU, and its neighbourhood takes place. The influence is concentric and gradually diminishes, i.e., in the center is strong and in the periphery is weak. 17 Figure: from (Kohonen 1982). 258

260 For unit k and all the eight of its nearest neighbours (except at the edges of the array where the number of neighbours was different) the following adaptive process is then assumed to be active: (Ibid.) In each iteration, the influence that the observation will have with the map decreases gradually; at the beginning it is strong and at the end it is weak. where the variables have been labelled by a discrete time index t (an integer), alpha is a gain parameter in adaptation, and the denominator is the Euclidean norm of the numerator. (Ibid.) Kohonen presents a few experiments of this process, first with identical inputs to all units. This process is iterative. The initial state of the map is entropic; hence, nothing is distinguishable, see figure 3.25b. As the process goes on, the processing units map their output to the map and as the process goes on, information emerges 3.25c. A sequence of training vectors {x(t)} was derived from the structured distribution shown in Fig. [3.25a]. Without much loss of generality, the lengths of the x(t) were normalized to unity whereby their distribution lies on the surface of the unit sphere in R3. The training vectors were picked up noncyclically, in a completely random fashion from this distribution. The initial values for the parameters Uij were also defined as random numbers. The gain parameter alpha was made a function of the iteration step, e.g., proportional to 1/t. (A decreasing sequence was necessary for stabilization, and this choice complies with that frequently used in mathematical models of learning systems). (Ibid.) Figure 3.25: a Distribution of training vectors, i.e., observations. b The initial map, i.e., test vectors, which will receive the outputs of the processing unit array. c The test vectors at the output. 19 As with the one-dimensional array, observation is enough to test the correctness of the map. In Figure: from (Kohonen 1982). Figure: from (Kohonen 1982). 259

261 figure 3.25c, an ordered map can be seen after the iterations are over. Consecutive numbers go from 11 to 18, 21 to 28, and so on. To test the final state of the system after many iterations, a set of test vectors from the distribution of Fig. [3.25a], as shown in Fig. [3.25b], was defined. The images of these vectors (i.e. those units which gave the largest responses to particular input vectors) are shown in Fig. [3.25c]. It may be clearly discernible that an ordered mapping has been formed in the process. The map has also formatted itself along the sides of the array. (Ibid.) Kohonen s self-organization is in great part due to the corrective process, the Eq. (3), which is iteratively looking at an entropic state and gradually modifying it towards an abstraction of the observations. What actually caused the self-ordering? Some fundamental properties of this process can be determined by means of the following argumentation. The corrective process of Eq. (3) increases the parallelism of the activated (neighboring) vectors. Thus the differential order all over the array will be increased on the average. However, differential ordering steps of the above kind cannot take place independently of each other. As all units in the array have neighbours which they affect during adaptation, changes in individual units cannot be compatible unless they result in a global order. The boundary effects in the array delimit the format of the map in a manner somewhat similar to the way boundary conditions determine the solution of a differential equation. (Ibid.) Figure 3.26: Distribution of the weight vectors mi(i) at different times. The number of training steps is shown above the distribution. Interaction of nearest neighbours only. 20 In the same experiment but using computer graphics, the correctness of the map is visually clearer. In a first state, the test vectors are in disarray but maintain their topology, and as the 20 Figure: from (Kohonen 1982). 260

262 process goes on, after various iterations, an ordered grid is formed. A clear conception of the ordering process is obtainable if the sequence of the weight vectors is illustrated using computer graphics. For this purpose, the vectors were assumed to be three-dimensional. Obviously the distribution of the weight vectors tends to imitate that of the training vectors x(t). Since the vectors are normalized, they lie on the surface of a unit sphere in R3. The order of the weight vectors in this distribution can be indicated simply by a lattice of lines which conforms with the topology of the processing unit array. A line connecting two weight vectors mi and mj is used only to indicate that the two corresponding units i and j are adjacent in the array. Figure [3.26] now shows a typical development of the vectors mi(t) in time; the illustration may be self-explanatory. (Ibid.:62) In another experiment, Kohonen shows that for his self-organizing process, non-identical but coherent inputs are sufficient. Going back to the interplays discussed in the previous chapter, coherence here can be thought of as the consistency of a blog. All posts in a blog are characterized in the same terms but are different from each other; they are observations that alltogether make the consistency of the blog. Consider Fig. [3.27], which depicts a one-dimensional array of processing units governed by system equations (1) through (3). In this case each unit except the outermost ones has two nearest neighbours. (Ibid.) Figure 3.27: Diagram of a Kohonen process of a one-dimensional array of processing units for the formation of a frequency map. 21 Since Kohonen s simulation is observing sine waves, the output is an increasing or decreasing one-dimensional map, i.e., from 0 to 1 or from 1 to 0. This system will receive sinusoidal signals and become ordered according to their frequency. Assume a set of resonators or bandpass filters tuned at random to different frequencies. Five inputs to each array unit are now picked up at random from the resonator outputs, so that there is no initial correlation or order in any structure or parameters. Next we shall carry out a series of adaptation operations, each time generating a new sinusoidal signal with a randomly chosen frequency. After a number of 21 Figure: from (Kohonen 1982). 261

263 iteration steps the array units start to become sensitized to different frequencies in an ascending or descending order. (Ibid.:63) From its first publication until today, Kohonen s map has been modified and extended, and is mostly known by Self-Organizing Map (SOM). SOM has been used in many applications across different scientific and practical areas and for different tasks, most of them related to modeling. 22 Moosavi (2015:6.3.1) puts together a number of indexes around the concept of SOM that help to characterize it, see table The functionalities indexed here are not exclusively addressed by SOM. There are a number of open-source and proprietary libraries, across different programming languages, e.g., Mathematica, Matlab, Python, Java, that implement the same, similar, and complementary functions. A simple web search of machine learning plus the name of a programming language will present relevant links to extensive documentation for its installation, functionalities, and examples. Specifically for this thesis, the pre-specific talks presented in the previous chapter implemented a number of these instruments for unsupervised learning functions using an opensource library called scikit-learn 23 for Python, for dimensionality reduction and clustering of data. The reader can find in the appendix an inventory of the open-source libraries used in this thesis. Table Such as the visualization of a high dimensional space (Vesanto 1999); clustering and classification (Ultsch 1993, Vesanto and Alhoniemi 2000); and prediction and function approximation (Barreto and Araujo 2004; Barreto and Souza 2006), among others. 23 See (accessed ). 24 Figure: from (Moosavi 2015). 262

264 3.4 Online Translations Prominent online applications like Google Translate, Yandex Translate, and Microsoft Translator instantly translate text between over a hundred natural languages. It is a re-articulation of language operations. Their models, methods, and instruments engendered on the global network differ significantly from those used before. From a scientific perspective, Ferdinand de Saussure defines language as the definite object of study over speech and meaning, for example. He presents a modern and extensive characterization of language from which other studies depart. He, for instance, addresses the difficulty of defining an atomic unit of a language is it a sentence, a word, or a bigram? Saussure also differentiates word relations in those inside discourse and outside discourse, respectively characterizing them as linear and rhizomatic. Those relations that are not in the mind but in praesentia follow observable syntagmatic relations. Linguists see in the study of these relations a potential for language operation. Noam Chomsky s interest, for example, is in the analysis of a language towards the synthesis of its underlying syntactic structures. The promise of these structures is the ability to differentiate sentences that are grammatically correct from those that are not, and the further automatic generation of grammatically correct sentences. He thinks of the sentence as the unit of a language. His analyses followed state decompositions, hierarchical decompositions, and sentence transformations, from which not relevant synthesis followed. In retrospective, we index 263

265 the lack of success in operating a language by a non adequate characterization of language and language usage. He wants to analyze and synthesize idealities, 1 objects that are just not possible to directly grasp. The impossibility of this phenomena does not necessarily limit the abilities to construct and operate such objects, though. A prominent example of this is Dedekind Cut. In number theory, rational numbers are directly graspable q = m/n, where q is a rational number and m and n are integers and are constructed arithmetically in a continuous line, one after the other. Irrational numbers do not have this ability, e.g., square root of two; they are impossible to grasp directly because they have no common measure. What Richard Dedekind did was to introduce an irrational number in the infinite line of rational numbers with a cut, making the irrational graspable and operable by all the rest of the numbers that it is not. Linking this back to Chomsky s interest, we see an opposition between analysis towards synthesis and ratios towards own-terms definitions. Machine Translation characterizes a language in the language s own terms. We see in Statistical Machine Translation how it learns to translate a sentence from one language to another by looking at previously translated texts a lot of them and not by a pre-defined set of rules of a language. There is no ideal speaker or hearer, but a large number of texts in parallel that were written and translated by humans. A document is translated according to the probability distribution that a string in the target language is the translation of a string in the source language. For these applications to translate is to distinguish one string from many, to select the one with the highest probability to be the correct translation. They see the difficulties of fixing meanings, values, or truths, and find stability within the probabilities. [1/5] Course in General Linguistics language, speech, audition, phonation, concept, sound-image, sign, ideogram, phonem, discourse Figure 3.29: Diagram of a speaking circuit. 2 1 Non-adequate for our current understanding in science and philosophy of science. See the paradoxes of quantum physics, for example. 2 Figure: from (Saussure 1959). 264

266 In the Course in General Linguistics, Ferdinand de Saussure 3 re-articulates the object of study of language, which is considered now the starting point of the so-called structural linguistics. Here, he places his work in line with three previous stages of linguistic studies. First, grammar, initiated by the Greeks, which was based on logic. It lacked a scientific approach and was detached from language itself. Next, philological, which corrects, interprets, and comments upon written text, and applies methods of criticism for their own purposes. And, comparative philology, which, as its name suggests, discovered that languages can be compared with one another (Saussure 1959:1-5). For Saussure, they all failed to define the nature of the linguistic object of study, which is at the basis of any science. The difficulty resides in the fact that the linguistic phenomenon always has two related sides, each deriving its values from the other (Ibid.:8). He presents examples. 1) Articulated syllables are acousitcal impressions perceived by the ear, but the sound would not exist without the vocal organs We simply cannot reduce language to sound or detach sound from oral articulation; reciprocally, we cannot define the movements of the vocal organs without taking into account the acoustical impression. 2) a sound, a complex acoustical-vocal unit, combines in turn with an idea to form a complex physiological-psychological unit. 3) Speech has both an individual and a social side, and we cannot conceive of one without the other. 4) Speech always implies both an established system and an evolution; at every moment it is an existing institution and a product of the past. (Ibid.) This Janus-like characterization of a language makes it difficult to pin down its object of study. Saussure cannot decouple the sound from the vocal organs, the sound with an idea, the individual with the social usage, nor the present with the historical usage. From whatever direction we approach the question, nowhere do we find the integral object of linguistics. Everywhere we are confronted with a dilemma: if we fix our attention on only one side of each problem, we run the risk of failing to perceive the dualities pointed out above; on the other hand, if we study speech from several viewpoints simultaneously, the object of linguistics appears to us as a confused mass of heterogeneous and unrelated things. (Ibid.:9) His solution is to create a natural order where language comes first and all other manifestations after. What follows in his book unfolds from this classification and is the major contribution to linguistic studies that we want to stress. As I see it there is only one solution to all the foregoing difficulties: from the very outset we 3 Ferdinand de Saussure was a Swiss linguist and semiotician. He is considered one of the founders of modern linguistics. Saussure is said to lament the dearth of principles and methods that marked linguistics during his developmental period, and throughout his lifetime, he searched out the laws that would give direction to his thought amid the chaos (Bally and Sechehaye 1915). In 1906, he started lecturing at the University of Geneva, where he made known the ideas developed during those years. From the notes on his lectures from 1906 until 1911, Course of General Linguistics was put together by people around him, and published after his death in

267 must put both feet on the ground of language and use language as the norm of all other manifestations of speech. Language, on the contrary, is a self-contained whole and a principle of classification. As soon as we give language first place among the facts of speech, we introduce a natural order into a mass that lends itself to no other classification. (Ibid.) In this understanding, language contains different and complementary aspects, the physiological and psychological, the individual and the collective, the present and the past. It provides unity. To give language first place in the study of speech, we can advance a final argument: the faculty of articulating words whether it is natural or not is exercised only with the help of the instrument created by a collectivity and provided for its use; therefore, to say that language gives unity to speech is not fanciful. (Ibid.:11) Figure 3.30: Saussure s diagram of a communication circuit using speech. 4 Now that Saussure has defined the object of study, he starts to characterize it and justifies its relevancy over speech. In figure 3.30, language covers all elements of the circuit, including the ones inside the individuals, marked with a circle. It can be localized in the limited segment of the speaking-circuit where an auditory image becomes associated with a concept. It is the social side of speech, outside the individual who can never create nor modify it by himself; it exists only by virtue of a sort of contract signed by the members of a community. Moreover, the individual must always serve an apprenticeship in order to learn the functioning of language; a child assimilates it only gradually. (Ibid.:14) He justifies his decision to place language first, and speech second. Some of the abilities that he s interested in are that dead languages can be studied, that the union of meaning and sounds-images can be delimited and studied, and that language encapsulates a whole society in our heads. Language, unlike speaking, is something that we can study separately. Although dead languages are no longer spoken, we can easily assimilate their linguistic organisms. We can dispense with the other elements of speech; indeed, the science of language is possible only if the other elements are excluded. 4 Figure: from (Saussure 1959). 266

268 Whereas speech is heterogeneous, language, as defined, is homogeneous. It is a system of signs in which the only essential thing is the union of meanings and sound-images, and in which both parts of the sign are psychological. Language is concrete, no less so than speaking; and this is a help in our study of it. Linguistic signs, though basically psychological, are not abstractions; associations which bear the stamp of collective approval and which added together constitute language are realities that have their seat in the brain. (Ibid.:15) He further defines the science that will study these associations between sound-images and meaning; he calls it semiology. Linguistics is part of this new science. A science that studies the life of signs within society is conceivable; it would be a part of social psychology and consequently of general psychology; I shall call it semiology (from Greek sēmeîon 'sign'). Semiology would show what constitutes signs, what laws govern them. Since the science does not yet exist, no one can say what it would be; but it has a right to existence, a place staked out in advance. Linguistics is only a part of the general science of semiology; the laws discovered by semiology will be applicable to linguistics, and the latter will circumscribe a well-defined area within the mass of anthropological facts. (Ibid.:16) Writing text is a crucial object of language. It is because of it that the change of language over time can be studied, and it is a fundamental instrument for learning a new language. The concrete object of linguistic science is the social product deposited in the brain of each individual, i.e. language. But we generally learn about languages only through writing. Even in studying our native language, we constantly make use of written texts. (Ibid.:23) For Saussure, written text, as second in the natural order, exists only to serve a language. And in turn, the spoken form of a text exists only to serve the text. Language and writing are two distinct systems of signs; the second exists for the sole purpose of representing the first. The linguistic object is not both the written and the spoken forms of words; the spoken forms alone constitute the object. But the spoken word is so intimately bound to its written image that the latter manages to usurp the main role. (Ibid.) Saussure identifies two systems of writing, the ideographic and the phonetic. His studies are solely purposed to the latter which is not the case in our applications at hand. We will see how they are able to translate from ideographic language to a phonetic language. In an ideographic system each word is represented by a single sign that is unrelated to the sounds of the word itself. Each written sign stands for a whole word and, consequently, for the idea expressed by the word. The classic example of an ideographic system of writing is Chinese. The system commonly known as phonetic tries to reproduce the succession of sounds 267

269 that make up a word. Phonetic systems are sometimes syllabic, sometimes alphabetic, i.e., based on the irreducible elements used in speaking. (Ibid.:25) In order to study and operate the linguistic s object of study, units need to be identified. It is a very difficult task, Saussure says, even raising the question of its mere existence. He does not celebrate this impossibility, though, as we see that our applications at hand do. He rather sees it as a problem. delimiting them is such a delicate problem that we may wonder at first whether they really exist. Language then has the strange, striking characteristic of not having entities that are perceptible at the outset and yet of not permitting us to doubt that they exist and that their functioning constitutes it. Doubtless we have here a trait that distinguishes language from all other semiological institutions. (Ibid.:107) In language, everything is based on relations. There are two categories, each one engendering their own values. The categories: relations inside discourse and relations outside discourse. The former is linear and the latter rhizomatic. In discourse, on the one hand, words acquire relations based on the linear nature of language because they are chained together. This rules out the possibility of pronouncing two elements simultaneously. The elements are arranged in sequence on the chain of speaking. Combinations supported by linearity are syntagms. Outside discourse, on the other hand, words acquire relations of a different kind. Those that have something in common are associated in the memory, resulting in groups marked by diverse relations. (Ibid.:123) Figure 3.31: Associative relations of the french word enseignement. 5 The relations formed outside discourse are inside the mind. In our mind, one word can be linked to an undetermined number of other words without cause. These relations are called associative. In figure 3.31, Saussure diagrams the relations of enseignement. We see that the co-ordinations formed outside discourse differ strikingly from those formed inside discourse. Those formed outside discourse are not supported by linearity. Their seat is in the brain; they are a part of the inner storehouse that makes up the 268

270 language of each speaker. They are associative relations. (Ibid.) The relations that happen inside the discourse are called syntagmatic, and they happen in a series; one follows the next. The syntagmatic relation is in praesentia. It is based on two or more terms that occur in an effective series. Against this, the associative relation unites terms in absentia in a potential mnemonic series. (Ibid.) We can think of our pre-specific talk Mind Palace (chapter 2.3) as a celebration of these relations. There, we construct a space that can accommodate elements and relations without defining a cause. The space is operable; we can move things around and navigate. Furthermore, one of its movements allows us to arrange elements in space following our interests, and we could say that such arrangement points towards communication. Saussure identifies the system of associations linked to the system of grammar. The latter fixes word-families, inflectional paradigms, and formative elements in our minds. All these things exist in language, but as abstract entities; their study is difficult because we never know exactly whether or not the awareness of speakers goes as far as the analyses of the grammarian. But the important thing is that abstract entities are always based, in the last analysis, on concrete entities. (Ibid.:138) The grammarian makes a conscious and methodical classification of the state of the language at one point outside history and grammars in turn are to be mapped into the spoken language. Word order is unquestionably an abstract entity, but it owes its existence solely to the concrete units that contain it and that flow in a single dimension. To think that there is an incorporeal syntax outside material units distributed in space would be a mistake. (Ibid.:139) We look now at a number of contributions that fixed their object of study in one of Saussure s systems, grammar, with the goal of constructing methods for language operation. 5 Figure: from (Saussure 1959). 269

271 [2/5] Syntactic Structures syntax, natural language, structure, linguistic theory, grammar, parsing, transformation, analysis, synthesis Figure 3.32: Decomposition of a sentence by Chomsky. 6 In one of his firsts major publications, Noam Chomsky defines syntax as his main object of study. He is concerned with the synthesis of the fundamental underlying grammar of all natural languages a theory of linguistic structure. For him, such a structure should be abstract enough to accommodate any given language so it can help identify grammatically correct sentences from those that are not. Syntax is the study of the principles and processes by which sentences are constructed in particular languages. Syntactic investigation of a given language has as its goal the construction of a grammar that can be viewed as a device of some sort for producing the sentences of the language under analysis. More generally, linguists must be concerned with the problem of determining the fundamental underlying properties of successful grammars. The ultimate outcome of these investigations should be a theory of linguistic structure in which the descriptive devices utilized in particular grammars are presented and studied abstractly, with no specific reference to particular languages. One function of this theory is to provide a general method for selecting a grammar for each language, given a corpus of sentences of this language. (Chomsky 1957:11) Chomsky identifies and categorizes the elements in a language that determine a grammatical structure, a kind of units of grammar. These units are to be strictly analyzed so rules are synthesized towards the construction of new, grammatically correct sentences. The central notion in linguistic theory is that of linguistic level. A linguistic level, such as phonemics, morphology, phrase structure, is essentially a set of descriptive devices that are made available for the construction of grammars; it constitutes a certain method for 6 Figure: from (Chomsky 1957). 270

272 representing utterances. We can determine the adequacy of a linguistic theory by developing rigorously and precisely the form of grammar corresponding to the set of levels contained within this theory, and then investigating the possibility of constructing simple and revealing grammars of this form for natural languages. (Ibid.) Chomsky defines a sentence as the unit of a language. This unit is constructed by a finite set of elements words which in turn are constructed by a finite set of letters the alphabet. From now on I will consider a language to be a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements. (Ibid.:13) Chomsky s goal is two-folded, first, he aims to identify the underlying structure of a sentence, that is, to identify the rules that a grammatically correct sentence follow, for then to generate all sequences of this sentence. Analysis, synthesis and generation. The fundamental aim in the linguistic analysis of a language L is to separate the grammatical sequences which are the sentences of L from the ungrammatical sequences which are not sentences of L and to study the structure of the grammatical sequences. The grammar of L will thus be a device that generates all of the grammatical sequences of L and none of the ungrammatical ones. (Ibid.) He decouples grammar from meaning in a sentence. A sentence with no sense is considered a successful sentence, because of the simple fact that it follows the synthesized rule, even when the purpose of language, i.e., communication, is defeated. the notion grammatical cannot be identified with meaningful or significant in any semantic sense. Sentences (1) and (2) are equally nonsensical, but any speaker of English will recognize th at only the former is grammatical. (1) Colorless green ideas sleep furiously. (2) Furiously sleep ideas green colorless. (Ibid.:15) Chomsky looks at his contemporaries work on the statistical study of language and grammar, for example. Their premise was that a grammatically correct sentence has a larger probability of being observed than the grammatically incorrect (Hockett 1955). The notion grammatical in English cannot be identified in any way with the notion high order of statistical approximation to English. (Ibid.) He dismisses this work and justifies the study of grammar decoupled from meaning. We will see how statistical studies of languages, today, have achieved what Chomsky was not able to, i.e., to operate any natural language. Despite the undeniable interest and importance of semantic and statistical studies of language, they appear to have no direct relevance to the problem of determining or characterizing the set of grammatical utterances. I think that we are forced to conclude that grammar is autonomous and independent of meaning, and that probabilistic models give no particular insight into some of the basic problems of syntactic structure. (Ibid.:17) 271

273 The first elementary linguistic theory was not very successful. Chomsky looked here for a model to generate simple grammatically correct sentences in English, given a sentence of the same kind. Assuming the set of grammatical sentences of English to be given, we now ask what sort of device can produce this set (equivalently, what sort of theory gives an adequate account of the structure of this set of utterances). We can think of each sentence of this set as a sequence of phonemes of finite length. (Ibid.:18) This first theory considers the smallest grammatical unit as also the smallest unit of analysis. Chomsky s assumption is that the phonemic structure of a sentence is contained in its morpheme structure. Instead of stating the phonemic structure of sentences directly, the linguist sets up such 'higher level' elements as morphemes, and states separately the morphemic structure of sentences and the phonemic structure of morphemes. It can easily be seen that the joint description of these two levels will be much simpler than a direct description of the phonemic structure of sentences. (Ibid.) Figure 3.33: A state diagram to generate grammatically correct sentences. 7 The simple unit is the word, and a sentence is required to have a finite number of words. He identifies and fixes initial states and final states, and identifies sequences in-between. He implements a Markov model. See figure Given a state diagram, we produce a sentence by tracing a path from the initial point on the left to the final point on the right, always proceeding in the direction of the arrows. Having reached a certain point in the diagram, we can proceed along any path leading from this point, whether or not this path has been traversed before in constructing the sentence in question. Each node in such a diagram thus corresponds to a state of the machine. We can allow transition from one state to another in several ways, and we can have any number of closed loops of any length. The machines that produce languages in this manner are known mathematically as finite state Markov processes. (Ibid.:20) To construct a finite state grammar for English sounds difficult because English is not a finite state language. Such a process presented by Chomsky here is unable to create and incorporate not-before-observed sentences; novelty cannot be considered grammatically correct, even if it is. Despite Chomsky s lack of success, sequences of morphemes called n-grams 8 are used 7 8 Figure: from (Chomsky 1957). See n-gram entry on Wikipedia at (accessed ). 272

274 today to predict future sequences, and these also implement probabilistic models. As opposed to Chomsky, these models are not used to synthesize the grammatical rules of a language, but rather, they are used for general operations, like machine translations, which we will discuss shortly. In short, the approach to the analysis of grammaticalness suggested here in terms of a finite state Markov process that produces sentences from left to right, appears to lead to a dead end (Ibid.:24) The second attempt presented in this book also takes a sentence as the unit of a language. It identifies its components and classifies them in a tree. He finds this approach at firsthand more powerful. Customarily, linguistic description on the syntactic level is formulated in terms of constituent analysis (parsing). We now ask what form of grammar is presupposed by description of this sort. We find that the new form of grammar is essentially more powerful than the finite state model rejected above, and that the associated concept of linguistic level is different in fundamental respects. (Ibid.:26) A simple example of the new form for grammars synthesized from a rigorous analysis. See figure This approach does not fail in the same way as the previous, but it certainly does. As soon as Chomsky attempts to analyze a more complicated sentence, he runs into great difficulties and complications due to the complexity of the language itself. The strongest possible proof of the inadequacy of a linguistic theory is to show that it literally cannot apply to some natural language. A weaker, but perfectly sufficient demonstration of inadequacy would be to show that the theory can apply only clumsily; that is, to show that any grammar that can be constructed in terms of this theory will be extremely complex, ad hoc, and 'unrevealing', that certain very simple ways of describing grammatical sentences cannot be accommodated within the associated forms of grammar, and that certain fundamental formal properties of natural language cannot be utilized to simplify grammars. (Ibid.:34) After two unsuccessful, in his own terms, attempts to come up with a general theory of syntax, Chomsky reassesses his goals. He adopts a transformational approach in the description of English syntax. Our goal is to limit the kernel 9 in such a way that the terminal strings underlying the kernel sentences are derived by a simple system of phrase structure and can provide the basis from which all sentences can be derived by simple transformations: obligatory transformations in the case of the kernel, obligatory and optional transformations in the case of non-kernel sentences. (Ibid.:61) These transformations aim to simplify the language s syntax, by treating negatives and 9 Chomsky defines the kernel of the language as the set of sentences that are produced when he applies obligatory transformations to the terminal strings of the grammar (Chomsky 1957:45). 273

275 interrogatives equally, for example. transformational analysis brings out the fact that negatives and interrogatives have fundamentally the same structure, and it can make use of this fact to simplify the description of English syntax. (Ibid.:64) With his transformative approach, a step towards a general theory is accomplished, he argues, but is not fully there, nor does he develop how he could actually get there. Making use of phrase structure and transformations, we are trying to construct a grammar of English that will be simpler than any proposed alternative; and we are giving no thought to the question of how one might actually arrive at this grammar in some mechanical way from an English corpus, no matter how extensive. Our weaker goal of evaluation instead of discovery eliminates any fear of vicious circularity in the cases discussed above. (Ibid.:84) Chomsky s main goal remained unaccomplished. The diagnosis of his work is not a total failure, though; it is said to be useful for grammarians, just not the way he initially wanted it to be. In this discussion we have stressed the following points: The most that can reasonably be expected of linguistic theory is that it shall provide an evaluation procedure for grammars. (Ibid.:106) [3/5] Aspects of the Theory of Syntax grammar, transformations, rules, ideal speaker-hearer, explicit, perfection, generative Figure 3.34: Generation of a sentence based on the synthesis of English s deep structure. 10 In a follow-up book from 1965, Chomsky presents his continuous interest in constructing explicit generative grammars. Even when he does not reach a conclusion here either, he sees the interest and support of the community, especially in his grammatical transformations. 274

276 the central role of grammatical transformations in any empirically adequate generative grammar seems to me to be established quite firmly, though there remain many questions as to the proper form of the theory of transformational grammar. (Chomsky 1965:vi) This publication is an update, since such a theory is not formulated here. Chomsky deals with some defects in his early work and re-applies his grammatical transformations without any definite conclusion. This study deals, then, with questions that are at the border of research in transformational grammar. For some, definite answers will be proposed; but more often the discussion will merely raise issues and consider possible approaches to them without reaching any definite conclusion. (Ibid.) We see that Chomsky s work is concerned with the grammar. with the syntactic component of a generative grammar, that is, with the rules that specify the well-formed strings of minimal syntactically functioning units (formatives) and assing structural information of various kinds both to these strings and to strings that deviate from well-formedness in certain respects. (Ibid.:3) And grammar for Chomsky is: A grammar of a language purports to be a description of the ideal speaker-hearer s intrinsic competence. If grammar is, furthermore, perfectly explicit in other words, if it does not rely on the intelligence of the understanding reader but rather provides an explicit analysis of his contribution we may (somewhat redundantly) call it a generative grammar. (Ibid.:4). Chomsky s work aims to synthesize the rules of an ideal speech, perfectly explicit. The online applications operate symbolizations with no distinction of ideality or perfection. The online application at hand is not the exception; it abstracts from idealizing a natural language. It does not look for the ideal speech or text so as to learn from it, for example. It looks at all the text possible, right or wrong. As a compliment to this idea of abstraction from ideals, we present a mathematical theory that defines any real number, including the ungraspable irrational numbers, decoupled from questions of ideality and perfection. 10 Figure: from (Chomsky 1965). 275

277 [4/5] Continuity and Irrational Numbers continuity, cut, real numbers, measurability, icommesurability, compliment, negation, operation Figure 3.35: An irrational number in continuum with rational numbers by Dedekind Cut. 11 While teaching differential calculus at now ETH Zurich, Richard Dedekind 12 saw the need to define any real number in a purely arithmetic manner. When talking about the notion of the approach of a variable magnitude to a fixed limiting value, the fastest and most intuitive way to explain this to students is to consider geometric evidence. The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explanation of this continuity is nowhere given; even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but, with more or less consciousness of the fact, they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never established in a purely arithmetic manner. (Dedekind 1901:1) For Dedekind, arithmetic is about counting. Counting the successive creation of the infinite series of integers, in which each number is defined by the one immediately preceding. From a formed number to the consecutive new one. This system, which I shall denote by R, possesses first of all a completeness and selfcontainedness which I have designated in another place 13 as characteristic of a body of numbers [Zahlkörper] and which consists in this that the four fundamental operations are always performable with any two individuals in R, i. e., the result is always an individual of R, the single case of division by the number zero being excepted. (Ibid.:2) But for the problem at hand, Dedekind says, there is another property that is even more important, that of the infinite length of R. it may be expressed by saying that the system R forms a well-arranged domain of one dimension extending to infinity on two opposite sides. (Ibid.) From the difference between two rational numbers, Dedekind presents three laws: 11 Figure: Hyacinth 2015 at _square_root_of_two.png (accessed ). 12 Richard Dedekind was a mathematician who made important contributions to abstract algebra, algebraic number theory, and the definition of real numbers. He taught at the Polytechnic school in Zürich, now ETH Zürich. 13 See Vorlesungen über Zahlentheorie, by P. G. Lejeune Dirichlet. 2d ed

278 I. If a > b, and b > c, then a > c. b lies between the two numbers a, c. II. If a, c are two different numbers, there are infinitely many different numbers lying between a, c. III. If a is any definite number, then all numbers of the system R fall into two classes, A1 and A2, each of which contains infinitely many individuals. (Ibid.:3) Dedekind compares these laws with the points in a straight line, and deduces the initial propositions that will take him to prove the continuity of real numbers. The above-mentioned properties of rational numbers recall the corresponding relations of position on the points of a straight line L. If the two opposite directions existing upon it are distinguished by 'right' and 'left,' and p, q are two different points, then either p lies to the right of q, and at the same time q to the left of p, or conversely q lies to the right of p and at the same time p to the left of q. A third case is impossible, if p, q are actually different points. (Ibid.) In a continuous straight line, there are infinitely many points that correspond to irrational numbers. The existence of irrational numbers was already observed by the Greeks; the diagonal of the square, whose sides are rational, is irrational. If the point p corresponds to the rational number a, then, as is well known, the length o p is commensurable with the invariable unit of measure used in the construction, i. e., there exists a third length, a so-called common measure, of which these two lengths are integral multiples. But the ancient Greeks already knew and had demonstrated that there are lengths incommensurable with a given unit of length, e.g., the diagonal of the square whose side is the unit of length. If we lay off such a length from the point o upon the line we obtain an end-point which corresponds to no rational number. (Ibid.:4) Figure 3.36: The hypotenuse s length is incommensurable with the unit of length. 14 This is Dedekind s goal: the arithmetical construction of irrational numbers within the continuity of the rational numbers. If now, as is our desire, we try to follow up arithmetically all phenomena in the straight line, the domain of rational numbers is insufficient and it becomes absolutely necessary that the instrument R constructed by the creation of the rational numbers be essentially improved by the creation of new numbers such that the domain of numbers shall gain the 14 Figure: Fredrik 2008, simplified by Rubber Duck at (accessed ). 277

279 same completeness, or as we may say at once, the same continuity, as the straight line. (Ibid.) Dedekind's problem of constructing irrational numbers has been previously solved, not in the same way, though. Previous constructions are based on magnitudes of the same kind, i.e., irrational magnitudes. the way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes which itself is nowhere carefully defined and explains number as the result of measuring such a magnitude by another of the same kind. 15 Instead of this I demand that arithmetic shall be developed out of itself. (Ibid.) But by looking at the rational numbers that contain different number domains, and that all follow the same laws of construction and operation, Dedekind argues that irrational numbers should be no different and that continuity must be constructed. Just as negative and fractional rational numbers are formed by a new creation, and as the laws of operating with these numbers must and can be reduced to the laws of operating with positive integers, so we must endeavor completely to define irrational numbers by means of the rational numbers alone. The question only remains how to do this. (Ibid.:5) Dedekind defines continuity so as to establish the scientific basis for further valid deductions. He finds the essence of continuity in the following principle: If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions. (Ibid.) The creation of a real number is done by a cut, Dedekind's Cut. He has shown how any cut of the rational system of numbers produces a separation into two, such that every number of the first class is less than every number in the second class. If now any separation of the system R into two classes A1, A2 is given which possesses only this characteristic property that every number a1 in A1 is less than every number a2 in A2, then for brevity we shall call such a separation a cut [Schnitt] and designate it by (A1, A2). (Ibid.:6) Dedekind argues that such cuts can be done similarly by irrational numbers, and presents an example, where the following cut D is produced by no rational number. Let D be a positive integer but not the square of an integer, then there exists a positive integer lambda such that: lambda^2 < D < (lambda + 1)^2 (Ibid.) Similarity, for any cut produced by an irrational number, like D, one set of infinite numbers is on each side of it. All elements of A1 are smaller than all elements of A2, and all elements of A1 are 278

280 smaller than D, and all elements of A2 are greater to D. Whenever, then, we have to do with a cut (A1, A2) produced by no rational number, we create a new, an irrational number alpha, which we regard as completely defined by this cut (A1, A2); we shall say that the number alpha corresponds to this cut, or that it produces this cut. From now on, therefore, to every definite cut there corresponds a definite rational or irrational number, and we regard two numbers as different or unequal always and only when they correspond to essentially different cuts. (Ibid.:7) For Dedekind, the operation of all the real can be done by two cuts produced by two numbers, alpha and beta, for example. In order to obtain a basis for the orderly arrangement of all real, i. e., of all rational and irrational numbers we must investigate the relation between any two cuts (A1, A2) and (B1, B2) produced by any two numbers alpha and beta. (Ibid.) Continuity can be established by having two rational numbers, alpha and beta, and an irrational between them: c. Dedekind will always find a rational number bigger than c, no matter how close it is. Continuity is then established. From this we obtain finally the following: If alpha > beta, i. e., if there are infinitely many numbers in A1 not contained in B1 then there are infinitely many such numbers that at the same time are different from alpha and from beta; every such rational number c is < alpha, because it is contained in A1 and at the same time it is > beta because contained in B2. (Ibid.:9) In number theory, any rational number q can be constructed by infinite pairs of integer values (m, n) such as m/n = q. This is not the case with the transcendental numbers, like pi, e, phi, or the golden ratio. This makes a fundamental distinction between them; q is directly graspable, while 2 is not. What we want to stress from Dedekind's contribution in relation to Chomsky's characterization and operation of a natural language is that, even when an irrational number cannot be directly graspable, it can be operable, as it is placed in a continuum along with other graspable numbers. Dedekind does not need to 'hold' this object because that is simply impossible in order to construct with it or even construct it. With a cut, Dedekind characterizes an irrational number as the negation of all the elements that are not the object, that is, the negation of its complement. We turn now to the online application at hand. 15 "The apparent advantage of the generality of this definition of number disappears as soon as we consider complex numbers. According to my view, on the other hand, the notion of the ratio between two numbers of the same kind can be clearly developed only after the introduction of irrational numbers. (Dedekind 1901:4). 279

281 [5/5] Statistical Machine Translation translation, parallel corpora, natural language, word mapping, phrase reorder, word alignment, decoding, n-gram, probability, Markov 3.37: Automatic translation on a smart phone using Google Translate app. 16 Philipp Koehn 17 developed and patented together with Kevin Knight the Statistical Machine Translation (SMT) for automatic translation of natural languages. This model was the first used by Google Translate from 2006 until As a data-driven model, vast pairs of texts are needed for an automatic machine translation. A pair of corpus can be, for example, the same title of a book in two different languages. These books are translated by humans who are usually specialists in the topic of the book, and this is important to recognize because the use of words differs between communities. In our experiments, we use pairs of corpora as well, when we model a character from a TV series and the Swiss architectural bureaux. Text collections are called corpora, and for statistical machine translation we are especially interested in parallel corpora, which are texts, paired with a translation into another language. Texts differ in style and topic, for instance transcripts of parliamentary speeches versus news wire reports. Preparing parallel texts for the purpose of statistical machine translation may require crawling the web, extracting the text from formats such as HTML, as well as document and sentence alignment. (Koehn 2010:6) Statistical machine translation uses two translation models. One is the word-based model, which, as its name suggests, uses a word as an atomic element to translate. This model decouples the definitions and the grammar of a sentence, which then needs to be addressed by other methods. The initial statistical models for machine translation are based on words as atomic units that may be translated, inserted, dropped, and reordered. Viewing the translation between a sentence pair as a mapping of the words on either side motivates the notion of word alignment (see Figure [3.38] for an illustration), which may be modeled with an alignment function. (Ibid.) 16 Figure: Google c Philipp Koehn is a lecturer in the School of Informatics at the University of Edinburgh. He is the scientific coordinator of the European EuroMatrix project and is also involved in research funded by DARPA in the USA. 18 See 280

282 Figure 3.38: Aligning the words in a sentence pair is the first step of many SMT methods. 19 The second translation model is the phrase-based model, which takes the sentence as the basic unit for translation. This model does not call for an alignment function but reordering may be necessary. The currently most successful approach to machine translation uses the translation of phrases as atomic units. See Figure [3.39] for an illustration. These phrases are any contiguous sequences of words, not necessarily linguistic entities. In this approach, the input sentence is broken up into a sequence of phrases; these phrases are mapped oneto-one to output phrases, which may be reordered. (Ibid.:8) Figure 3.39: Phrases are identified from the input text. 20 This model is more effective because it directly looks at the pair of corpus. Because in principle, chapters in a book have the same number of sentences, and their order remains the same. Translation between these sentences is learned so future translations can be measured against these previous translations. Commonly, phrase models are estimated from parallel corpora that were annotated with word alignments All phrase pairs that are consistent with the word alignment are extracted. Probabilistic scores are assigned based on relative counts or by backing off to lexical translation probabilities. (Ibid.) When translating with an SMT model, there is no single correct translation. Various translations are done for a single text, word-based, phrase-based, and their corresponding methods. What happens in a decoding process is that the translation of the text is constructed. Probabilistic models in statistical machine translation assign a score to every possible translation of a foreign input sentence. The goal of decoding is to find the translation with the best score. In the decoding process, we construct the translation word by word, from Figure: from (Koehn 2010). Figure: from (Koehn 2010). 281

283 start to finish. The word-based and phrase-based models are well suited for this, since they allow the computation of scores for partial translations. (Ibid.:9) Decoding creates a table of hypotheses, a kind of partial translation from which the most probable correct translation is constructed. This model operates language in the probability space. Before translating a foreign input sentence, we first consult the translation table and look up the applicable translation options. During decoding, we store partial translations in a data structure called a hypothesis. Decoding takes the form of expanding these hypotheses by deciding on the next phrase translation, as illustratd in Figure [3.40]. (Ibid.) Figure 3.40: The decoding process, choosing a path from left to right. 21 This translation model is then followed by a language model, which can be thought of as a tuning process where the finest details towards a translation are done. The construction of a language model shows an understanding of the infinity of a language, because even when the digitized corpora of English language is vast, not all the possible translations can be contained. A language model is then constructed by the digitized text plus those generated by the machine following a new human text. Language models measure the fluency of the output and are an essential part of statistical machine translation. They influence word choice, reordering and other decisions. Mathematically, they assign each sentence a probability that indicates how likely that sentence is to occur in a text. N-gram language models use the Markov assumption to break the probability of a sentence into the product of the probability of each word, given the (limited) history of preceding words. Language models are optimized on perplexity, a measure related to how much probability is given to a set of actual English text. (Ibid.) Koehn recognizes the difficulty of discussing the validation of his method. The statistical methods implemented to such processes offer intervals, and spectrums, not more. A hotly debated topic in machine translation is evaluation, since there are many valid translations for each input sentence (see Figure [3.41] for an illustration). At some point, we need some quantitative way to assess the quality of machine translation systems, or at least a way to be able to tell if one system is better than another or if a change in the system led to an improvement. One way is to ask human judges to assess the adequacy (preservation of meaning) and fluency of machine translation output, or to rank different translations of an individual sentence. (Ibid.:10) 21 Figure: from (Koehn 2010). 282

284 Figure 3.41: Ten different translations of the same Chinese sentence. 22 To translate is measured in confidence values, and confidence is a good adjective, because confidence oscillates. The more observations the application has, the better the models, and the confidence changes. 22 Figure: from (Koehn 2010). 283