media kit Contact : Valérie Abrial valerie.abrial@lelaboratoire.org +33 (0)1 78 09 49 55 +33 (0)6 84 37 96 23 V L Ryoji Ikeda & Benedict Gross 11 october 2008 to 12 january 2009 data.tron 2007 Ryoji Ikeda photo by Kazuo Fukunaga (courtesy of Yamaguchi Center for Arts and Media) 1 Le Laboratoire Media kit
Contents V L Ryoji Ikeda & Benedict Gross... p 3 Biographies... p 4 Conversation between Benedict Gross and David Edwards... p 6 Conversation between Ryoji Ideka and Caroline Naphegyi... p 10 V L according to Andrei Rodin, mathematicien... p 13 Synapses... p 15 Available images... p 16 Also happening... p 18 Pratical info... p 19 2 Le Laboratoire Media kit
V L Ryoji Ikeda & Benedict Gross press release Le Laboratoire is pleased to present, for the first time in Europe, a personal exhibition of the Japanese artist Ryoji Ikeda, a major figure of the sound and visual electronic scene. From his correspondence with the American mathematician Benedict Gross, he has conceived a work where the definition of the sublime blends with the immateriality of infinity. Welcome to a world of millimeter precision. An avant-garde composer of ultra-sonic frequencies; an explorer of minimal sounds; an artist of visible waves, Ryoji Ikeda explores the interference between reality and unexplored dimensions. His musical structures strive to develop perception by bodies; his sound and visual installations fill up a design space, between darkness and light. Decibels take life and run up against each other; sounds are oppressive yet liberating; is it resonance or silence that we re hearing? Waves make light of the light, gently mocking; from shadow to light the atmosphere vibrates inside an sonic and audiovisual temporality, whose only hidden meaning is in the suggested truth. From Infinity to the sublime, Ryoji Ikeda instills a new dimension whose theoretical definition embraces the science of mathematics. The sublime exists Benedict Gross, a number theorist at Harvard University contributed to this mathematical and philosophical sphere. His encounter with Ryoji Ikeda suggests the possibility of a common aesthetic language for art and science. According to Benedict Gross, when you discover a mathematical truth, everything immediately becomes clear. It s so easy to understand. You don t want to touch it. The beauty of mathematics is just a pleasure to behold. V L V denotes the von Neumann universe and L denotes Godel s constructible universe. Their equality or inequality is a disputed point, and the position one chooses to take on whether V=L or V L reveals a great deal about one s philosophy of mathematics. If V L then not every set of numbers is constructible. The removal of this restriction allows for the inclusion of numbers that are almost beyond the limits of human comprehension. More than just a mathematical equation, this expression inspires contemplation of that which we cannot perceive, which can lead to a transcendent experience of the sublime. What is this immensity hidden behind number? And what if the multitude of figures making up a number was made palpable... Would this make infinity accessible? Would the immaterial be then rendered material? This is the driving issue behind the latest experiment of Le Laboratoire. As an artist/composer, my intention is always polarized by concepts of the beautiful and the sublime. To me, beauty is crystal; rationality, precision, simplicity, elegance, delicacy. The sublime is infinity; infinitesimal, immensity, indescribable, ineffable. The purest beauty is the world of mathematics. Its perfect assemblage amongst numbers, magnitudes and forms persist despite us. The aesthetic experience of the sublime in mathematics is awe-inspiring. It is similar to the experience we have when we confront the vast magnitude of the universe, which always leaves us openmouthed. The aim of this project is to engage in dialogue with the mathematician Benedict Gross and other number theorists to find a common language on aesthetics. Ryoji Ikeda 3 Le Laboratoire Media kit
Biographies Ryoji Ikeda Japan s leading electronic composer/artist, Ryoji Ikeda, focuses on the minutiae of ultrasonics, frequencies and the essential characteristics of sound itself. Ryoji Ikeda featured in Forma s launch season with his audiovisual concert formula [ver.1.0] and in concerts with Carsten Nicolai and Mika Vainio. For the past six years, Forma has produced and toured all of Ikeda s exhibition and performance projects worldwide. Since 1995, Ikeda has been intensely active through concerts, installations, and recordings, integrating sound, acoustics and sublime imagery. In the artist s works, music, time and space are shaped by mathematical methods as Ikeda explores sound as sensation, pulling apart its physical properties to reveal its relationship with human perception. Ikeda has gained a reputation as one of the few international artists working convincingly across both visual and sonic media. Using computer and digital technologies to the utmost limit, his audiovisual concerts datamatics (2006 present), C4I (2004 2007) and formula (2000 2006) suggest a unique orientation for our future multimedia environment and culture. His acclaimed installations data.tron [prototype] (2007), data.film nº1-a (2007), data. spectra (2005), spectra [for terminal 5, jfk] (2004), spectra II (2002), db (2002) and his first large-scale, public arena work spectra [amsterdam], (a commission for Dream Amsterdam 2008), continue to diffuse Ikeda s aesthetic of ultra minimalism to the art world. Ikeda s latest body of work, datamatics, is a long-term programme of moving image, sculptural, sound and new media works that use data as their theme and material to explore the ways in which abstracted views of reality data are used to encode, understand and control the world. He has been hailed by critics as one of the most radical and innovative contemporary composers for his live performances, sound installations and album releases. His albums +/- (Touch, 1996), 0 C (Touch, 1998) and matrix (Touch, 2000) pioneered a new minimal world of electronic music, employing sine waves, electronic glitch sounds, and white noise. Ikeda released his critically acclaimed, seventh solo album entitled dataplex (raster-noton), as part of the datamatics series, in 2005. His latest release test pattern (raster-noton) was released in April 2008. The versatile range of Ikeda s research is demonstrated by his collaborations with Carsten Nicolai on the project cyclo and with choreographer William Forsythe/Frankfurt Ballett, artist Hiroshi Sugimoto, architect Toyo Ito and artist collective Dumb Type, among others. The first complete catalogue of Ikeda s seminal work, formula [book + dvd] (Forma) was published in 2005. Ikeda has exhibited and performed at many of the world s leading festivals and venues including: the Australian Centre for the Moving Image, 2005 (Melbourne); MIT, 2006 (Massachusetts); Centre Pompidou 2004, 2007 and La Villette 2002 (all Paris); Sónar 2006 (Barcelona); Architectural Association 2002, Barbican 2006, Tate Modern Turbine Hall 2006 (all London); Irish Museum of Modern Art 2007 (Dublin); Auditorium Parco della Musica 2003 (Rome); ICC 2005, Tokyo International Forum 2006 (Tokyo); Art Beijing 2007 (Beijing); Göteborg Biennial 2003 (Göteborg); Mutek Festival 2007 (Mexico City); Le Fresnoy 2007 (Tourcoing) and Paradiso (opening event, Dream Amsterdam 2008). A solo exhibition of new and existing works by Ikeda, was recently presented at Yamaguchi Center for Arts and Media in Japan (Mar - May 2008). In 2001, Ikeda was awarded the Ars Electronica Golden Nica prize in the digital music category and he was short-listed for a World Technology Award in 2003. Ryoji Ikeda is represented worldwide by Forma Arts and Media Limited www.forma.org.uk 4 Le Laboratoire Media kit
Benedict Gross When you discover a mathematical truth, everything immediately becomes clear. It s so easy to understand. You don t want to touch it. The beauty of mathematics is just a pleasure to behold. Benedict Gross has always been interested in mathematics, from his youth in New Jersey to his current position as George Vasmer Leverett Professor of Mathematics at Harvard University. Attending college during the height of the political turmoil of the 60 s, Gross struggled with how mathematics fit into the bigger picture. He spent three years traveling in Africa, Asia, and Europe, playing music, and reading mathematics, before returning to the United States to study number theory. During his graduate career he was taught by such great mathematicians as John Tate, Jean-Pierre Serre, Raoul Bott, and Barry Mazur. One of Gross major contributions was his collaboration with Don Zagier to prove the Gross-Zagier formula, an identity for the first derivative of the L-functions of elliptic curves. Gross has taught at Princeton, Brown, and Harvard and has had over 30 PhD students. In addition to numerous scientific publications, Gross has been the recipient of several awards and honors, including a MacArthur Fellowship and the Cole Prize in Number Theory. He is a member of the American Academy of Arts and Sciences and the National Academy of Science. Along with mathematician Joe Harris, he co-authored The Magic of Numbers (2007, Prentice Hall), an example-driven book elucidating the joy and wonder of mathematics to a non-mathematical audience. Gross served as Dean of Harvard College from 2003-2007 but has since happily returned to full-time mathematical research, in the fields of number theory and representation theory. About the collaboration with Ryoji Ikeda I first heard from David Edwards that Ryoji wanted to meet with me last December; we first met when he visited Boson in January. I was intrigued by his work, and by the depth of his questions about mathematics. We spent several hours discussing orders of infinity, fractional dimension, and the work of Georg Cantor. It was surprising to me how two people could come at the same material from such different viewpoints. I ve never worked with an artist like Ryoji before. Our collaboration has made the subject even more interesting for me. 5 Le Laboratoire Media kit
Conversation Benedict gross and David Edwards (scientist, writer and founder of le Laboratoire) august 2008 / Cambridge, Massachusetts, USA David Edwards: I d love to hear you describe what interests you in working with/dialoguing with an artist like Ryoji. Benedict Gross: Ryoji s a great musician, he s a great artist, and he knows huge amounts of mathematics for an amateur, unbelievable amounts of mathematics! in particular what I like is that in some sense he s exploring as an artist exactly the questions that we are desperately trying to understand as mathematicians, and where he s at the border of his art and we re at the border of our mathematics, there s a lot of intersection. And we both like to grapple with things that are difficult to contemplate, let alone describe, and he s very comfortable in that milieu. Mathematicians are a little less comfortable because we like to be standing on firm ground. We don t want to take another step until we re pretty sure that what we re standing on is established, whereas artists are more willing to take a big, big leap. And I find that really stimulating, and [Ryoji] sort of forced me to think about these questions in a way that I never went about before. I think that we both found our vocation through music, which is very strange I studied violin, and carnatic violin in India for several months, and I thought that would be a way that I could really create something I came to the conclusion that if I was going to do something creative, I had more talent in mathematics I ve been able to continue with music, and I think there is a huge connection between music and mathematics that everyone knows but no one really understands. They re both concerned with pure form and I think Ryoji as an artist is very concerned with pure form and that s one of the reasons he loves mathematics so much. David Edwards: The synergy between music and math goes back a really long way and in the last decades there has been this reemergence of attention on the subtle and not so subtle interactions between art and science. This is sort of an abstract question, but in your interactions, how much of this collaboration belongs in today, and how much of this is just an eternal dialogue that has been going on since Pythagoras? Benedict Gross: That s a really good question. I think it ebbs and flows. Science has had periods in its history, mathematics has had periods in its history where it tries to present itself as ultimately a rigorous subject which has strict rules, has nothing to do with art. I think we re in a period of science and mathematics that is an exploratory period; so much has been discovered in the last 30, 40 years, we are still trying to process it I think we are in a period where there s going to be more interactions between scientists and artists as we both realize that we re occupying the same endeavor. I found that at universities, there s a funny tension between the people who are doing science and the people who are doing creative art but the people who are on the edge of their fields, and trying to push it to the next place, have an awful lot in common. You know, the frustrations are the same, the victories are the same 6 Le Laboratoire Media kit
David Edwards: That s a fascinating bit of conversation, partly because you were the Dean of Harvard College. So the opportunity to work with Ryoji, and to kind of play together how does it relate to being a Dean? Benedict Gross: Well, first of all, it s great now that I have the time! I think it would be terrific for institutions like Harvard to try to attract more creative artists like Ryoji our students would love to have more people like Ryoji around. I think Harvard has to make a move in the direction of creative art because the people doing really creative work at Harvard are the scientists! David Edwards: So coming back to Ryoji many of the themes that interest Ryoji like beauty, the sublime, and infinite are big themes, and as a mathematician, presumably you see those themes early Benedict Gross: but you don t focus on them on a day to day basis. David Edwards: Right! So how relevant are they? Benedict Gross: That s a good question. I mean, everyone has big questions in mathematics in the back of his or her minds: the different orders of infinity, the size of the integers, and size of real numbers and that s a famous question and anyone who can say anything about that. Boy if I could do that, I would love to do that. It s like climbing a wall. If you re faced with a big incline, you are trying to get the first foothold. And you look up at the wall every once in a while and think, boy it would be nice to get to the top of that, but you gotta figure out what the next handhold is and where you gotta put your right foot. And so on a day to day basis you re trying to cut out little pieces of mathematics that you can understand, based on what you know or based on the theoretical picture in your head, and every once in a while you glance up you know, just to see where the whole structure is. But the great piece of mathematics: it s somehow usually after you do it you re working on some little thing, and you do it, and you realize how it fits into the larger constellation and that s the real beauty of it. So you can t possibly lose track of the big questions. But I won t address them on a day to day basis. David Edwards: That, as you describe it metaphorically, kind of brings up the other thread of your dialogue with Ryoji related to the platonic view and non-platonic mathematicians he was so moved when he heard you say that 7 Le Laboratoire Media kit
Benedict Gross: I do feel that mathematicians are somehow discovering this perfect world, and it would be nice if artists were discovering a perfect world, but if you look at the history of art it really just goes here and it goes there. It seems to depend on a great vision of someone. We might not have had Cubism, we might not have had the paintings of Caravaggio, we might not have had these things. But with mathematics you somehow feel like you re uncovering these beautiful things that have been laid out beforehand, and so there s really only one way to go, at least I believe that. I believe that if we were to encounter another civilization, that it might be based on a different biology, it might be based on a different physics, but they would have the same mathematics, and we would be able to eventually compare what we ve understood to what they ve understood and that would be a wonderful moment. But it s hard to believe that they would have the same art. So it seems to me that there are different pathways for great creative art, but there s one pathway for great creative mathematics that s not to say there isn t more than one way to understand something, there s always more than one way to understand something. There is never a dogma in mathematics that says you have to do it this way, but there is somehow one truth. And the main evidence I give is that when people make major discoveries in mathematics everyone kind of stands back and goes WHOA! It s much more beautiful than you thought it was! Even the person who discovered it can t possibly realize how beautiful it will be to the world. And because it s much more beautiful than any of us could have imagined beforehand, that gives me some confidence that it was there before us and is there for us to discover. That doesn t make it any less enjoyable or any less creative or any less this or that you just feel like you are a part of a grand enterprise that s going back...to the time of Pythagoras, to the time of Archimedes, to the time of the Babylonians, we re all a part of it. Whereas you can imagine that art in India is going this way and art in Japan is going this way and art in Greece is going this way. David Edwards: I ll come back to the beginning of the conversation and at one point you talked about those who are pushing the boundaries of their disciplines kind of have similar characteristics and of course you have talked a lot here about the joy and fascination about working with an artist so here s math, and we think of math as this way of discovering, and art is being about something else and yet there s a place where there s a lot of richness at the intersection, and very clearly, with Ryoji, who is completely OB- Benedict Gross and David Edwards: -SESSED! Benedict Gross: That s a good word! David Edwards: So what s going on there? 8 Le Laboratoire Media kit
Benedict Gross: I just think that there are these problems that we don t understand, fundamental problems on sets, on size, on numbers that are equally stimulating to artists and mathematicians. And listening to Ryoji rap about them (because that s really what I do!) I just think, boy that s a really cool way of thinking about it! And looking at Ryoji illustrating a gigantic number, and saying that this is really just one number of many that s a different way than mathematicians would approach it. No mathematician would write this number in any way but 2 to a power minus one. There it is. It s like that much space. And to print out! Why are you printing it out?! The digits don t mean anything, it s just a prime number. But seeing his vision of it gives you another way of thinking about it. So I would say that we come together around a fundamental group of misunderstood or partially understood problems that are equally stimulating. And we come together with the same kind of obsession to know it. So I was reading the paper today and there s this movie out now of who walk across the wire between the two world trade centers. it s called wire to wire Which was done in the 1970 s He s a riot of a guy, I heard him speak once. And he s a very good juggler And he describes him as an obsessive kid you know, didn t want to do anything besides walking on wires between things. And I read this, and I said to myself, this guy sounds like a mathematician. Ryoji thinks like a mathematician. When he s on to something, everything else goes blank. It s just fun to me to meet another one of our tribe. It s the only way I can describe it. David Edwards: It s a process really you re talking about? Benedict Gross: Exactly! It s this incredible focus, I want to eat this stuff, I want to sleep this stuff. I don t want to do anything else. It s just fun to see it expressed in this way. I don t think anything he s going to do in this exhibition is going to lead to an advance in mathematics. Likewise, I don t think there s anything I could prove in mathematics that would lead Ryoji to any new creation. But it s just very stimulating to be around. And I m sure you re gonna see hundreds of French mathematicians come to this exhibit. Not just because they like to see mathematics in museums, but just because this is cool. 9 Le Laboratoire Media kit
Conversation Ryoji Ikeda and Caroline Naphegyi (exhibition curator ) september 2008 - Paris Caroline Naphegy: Many examples of dialogs between music and mathematic are known (but no one really understands it according to Benedict). Benedict considers that you have a mathematical way of thinking, a common interest in purity of form. How do you explain your interest in mathematics, how as it started? Ryoji Ikeda: I don t think at all that I am good at mathematics. But since my childhood, I ve been having a sense that music might be a variation of mathematics, especially while listening to Bach. I have never formally studied mathematics but at least I thought I would be able to know what s been going on in mathematics itself. I am more interested in knowing the development of mathematics than using mathematics. Through chasing the development and the history, I ve been able to grasp vaguely the direction where mathematics is headed for. The more I knew it, the more I m convinced that I have no talent in mathematics. Benedict is the first-rate player of mathematics (like Zidane for football), and he also plays the viola. In that sense, I am just a listener or an audience of mathematics, never a player. Even for music, I ve never been a player too. I am a listener and a composer. Caroline Naphegyi: What does the collaboration with Benedict brings to your art work on a conceptual level? Ryoji Ikeda: There exists the truth in mathematics. Mathematicians are like explorers who search a vast jungle of mathematics to find unknown treasures. Mathematicians invent extremely creative tools and methods to discover them. My interest is a certain field of mathematics that tries to update the whole map of the jungle. V L is touching this kind of subject. There may be no conclusion, but I want to develop my understanding towards it. However, it has no direct connection to my art works. For this exhibition, V L is an engine to drive me further, which also triggers a contemplation about the beautiful and the sublime. Caroline Naphegyi: One of your installations focuses on a prime number and a random number. How did you finally choose those numbers? Ryoji Ikeda: In spite of the conceptual dialog, I cannot ask anything concrete to Benedict for my art works at very practical levels, because the materialization, which is the primal job of artists, is much more like a carpenter s job - even if it requires precision. To fill the gap between conceptual thought (conceptualization) and carpenter job (materialization) is my mission. I agree with the point as Benedict stated I don t think great art will necessarily lead to advances in mathematics, or that advances in our mathematical knowledge will necessarily inspire artistic creation. But they illuminate and excite each other. For me, in art, the process and the result must be thought separately. For example, when you have a fantastic dinner, you would never want to ask how and why the chef cooked the dishes that way. We simply appreciate the taste of food and enjoy the atmosphere. Exhibition is the result for an artist. Exhibition is the end point for artists and the start point for visitors at the same time. 10 Le Laboratoire Media kit
On the other hand, the process is always an adventure for the artists. Every journey has different story, encounter and destination. The process can be described but the best is always to see it through the result at the same time. Sushi is never cooked just as a live performance in front of the customers, but with very careful preparation from early morning. We immediately can judge the excellence of the result and recognize the efforts of the process when we taste. So, if the work is excellent enough, people can enjoy without being explained the process by words. In this sense, I m not afraid to say that the prime number and the random number are important but not really essential for the works as the result. For example, apples and oranges were not essential for Cezanne s paintings (whose compositions were surely essential as everyone knows). The core of the exhibition must stand on experience. Personally, if visitors appreciate the works as if they were listening to music, that would be ideal (people would never ask the meaning of a melody of Mozart before they listen). Then if something comes up in visitors minds, their journeys have already started. For this, I will prepare some explanations to fill their satisfaction if they have questions. But again, ideally, it s better to explain with the least words possible. Because there is no answer in art. Art is not the things to be understood. You can t teach or study art in essence. You just feel and judge everything by yourself. There are many practical and physical reasons for the final decision-making of materialization, but it is always done by intuition and inspiration in terms of the aesthetic point of view, beauty is always next to me, which can t be logical. Caroline Naphegyi: In the context of Le Laboratoire you will present two works as symmetric dialogs; one is material in its appearance, the other one, immaterial. Sounds and videos, which stand for your usual language, are absent. What is the issue of such a medium based on mathematics, as a way to structure your thoughts? In the process of a music composer? Ryoji Ikeda: It is a challenge to compose the exhibition itself without using any actual musical elements. But the works are highly musical to me. Because it s live (for visitors). The exhibition is a show. You directly can see and hear the works. It s a real-time process of your experience like listening music. I show the result of my process. The process is mostly based on composition. Composition is always the key, even though without sound. In my opinion, all genres of art have their own notions of composition, but their common denominator is surely mathematics (or structure), which is less essential than science though. For mathematicians, lecturing the Mersenne prime by words and writing is live. The purpose is one. To let people understand. There is the answer. 11 Le Laboratoire Media kit
For me (not all artists), showing the Mersenne prime as a large photo print is live (actually only for visitors). The purpose is kaleidoscopic. To let people feel free. There is no answer. Doing mathematics or doing art means all about the process and all about life for mathematicians and artists. The result is always theorem or work, which absolutely speaks for itself. Caroline Naphegyi: Are they at the edge of knowledge, something that has to be rediscovered by mathematicians? What is the issue as your aesthetic experience in the context of mathematics? Benedict said that most mathematicians believe that the truth in mathematics is something that we are honored to discover. We don t create it, we simply uncover pieces of it. You seem to share that thought in your side when you say how skeptical you are with the words art and creation, and willing to share an aesthetic experience more than a creation. Are you questioning something beyond, undefined and absolute as truth and the sublime? Ryoji Ikeda: Take a notion of line. A line is one of the most fundamental elements for artists (even for children to make drawings). After knowing art, I see the horizon a straight line. My point of view was upgraded. After knowing physics, there is no straight line in nature. The world was different from yesterday. After knowing mathematics, a line is not merely a line anymore. A straight line is the infinite. There are infinitely more real numbers than all numbers of integer on the line - even between 0 and 1. Truly mind-blowing. I myself was different from yesterday. I stop using the word creation which sounds rather pretentious in front of mathematicians and for mathematical truths. 12 Le Laboratoire Media kit
Andrei Rodin post-doctoral researcher at department of history and philosophy of science of university paris-diderot / researcher in institute of logic and cognitive science, moscow about v l Is there anything bigger than any big number? Yes, infinity is by far bigger. Philosophers and theologians speculated about infinity for centuries but it was only in the end of 19th century when thanks to Georg Cantor (1845-1918) the infinite became a subject-matter of pure mathematics. Consider the first three positive integers: 1, 2, 3. Number 3 is the biggest one in this string, which contains exactly 3 items. Similarly the string 1, 2, 3,..., N contains exactly N items. Now think of the series of all positive integers: 1, 2, 3,.... What about the number of items in this infinite string? Since it has no biggest element the method of counting just used for finite strings doesn t work in this case. However since we somehow manage to talk and think about all positive integers (even without being able to identify them all) and moreover consider 1, 2, 3,... to be an appropriate symbolic expression of this idea it is not unreasonable to associate a notion of infinite number with it like we do it in the finite case. Another classical example of infinity, which was around since Antiquity, is the number of points on a given line. Cantor provided a strong mathematical argument showing that the number of points is strictly bigger than the number of positive integers in the following precise sense: however you enumerate points on a given line by positive integers some of these points escape the enumeration. Having this basic example in hands Cantor showed how one may conceive of yet higher infinities. The wide recognition of Cantor s work in 20th century apparently changed the common conception of the infinite quite a lot; in eyes of people habituated to higher cardinals the infinity of 1, 2, 3,... (technically called countable infinity) hardly looks any longer impressive. Remarkably really big (albeit finite) numbers remain as impressive as ever. Cantor s mathematical advances didn t resolve all the controversies about the infinite noticed by philosophers long before. The controversies soon struck back in the new more sophisticated setting. Cantor s Mengenlehre, i.e. Set theory, turned to be full of contradictions, which are better known to public under the respectful names of antinomies and paradoxes. To save the theory some people tried to develop it on an explicit axiomatic basis. An axiomatic theory of sets first proposed by Ernst Zermelo in 1908 and later improved by Abraham Fraenkel (1891-1965) remains standard until today. This theory is called ZF after the names of its authors; ZFC refers to ZF with the axiom of choice. NBG is another axiomatic set theory called after the names of Neumann, Bernays and Goedel, which is essentially equivalent to ZFC but has more expressive power. In particular, ZFC forbids the notion of set of all sets and offers no replacement. NBG offers a replacement conventionally called V: this name refers to the universe of sets, which itself is not a set but a proper class, i.e. an entity which like a set has some elements but unlike a set cannot be itself an element. These and other axiomatic theories of sets presently found on the market help avoiding all the known paradoxes of Cantor s Set theory (often described as naive by the builders of axiomatic theories) but promise no protection from new paradoxes, which may eventually show up in the future. I am a Moscow-born philosopher currently living and working in Paris. I am academically affiliated with the University Paris-Diderot in the Department of History and Philosophy of Science. At present, my principle research deals with a topic I describe as foundations of mathematics, which is closely related to the foundations of natural science, and especially to mathematical physics. I have in mind a notion of foundations, which is both classical and very dynamic. Foundations, in my understanding, comprise basic theoretical concepts that subsist only through continuing revision. I began my research career with an historico-philosophical study of Euclid s Elements but later focused on more recent developments in fields related to set theory and category theory. This career reflects my understanding of foundations, which is essentially historical: I think of foundations in terms of a passage from the past to the future rather than in terms of the eternal present. Foundations is an area where science and philosophy have traditionally worked together. Foundations is also, in my view, a natural point of contact between science and arts. Andrei Rodin 13 Le Laboratoire Media kit
Cantor conjectured that the infinity of points on a given line is exactly the second least infinity after the countable infinity, but didn t manage to prove this claim. This conjecture became known as Continuum Hypothesis or CH for short. The first significant advance concerning CH has been made in the new axiomatic setting by Kurt Goedel only in 1940. Goedel constructed a special model of ZF, which he called L (also known under the name of constructible universe) where CH provably holds. This showed that CH is compatible with ZF i.e. doesn t contradict its axioms. Historically L was the first example of inner model; to get an inner model of ZF one first takes for granted some model M of ZF and then construct out of it the desired new model through an appropriate restriction of M. Importantly if one relativizes this whole construction to L, i.e. takes L instead of M to begin with, one gets L back. So L remains stable in this sense. A related fact about L is that in L (V=L) holds. It turns out that L is the only model of ZF having this property. Thus we have V L in any other model of this theory. Unlike V Goedel s constructible universe L has been hardly ever seriously considered as a refined version of the naive Cantor s universe. Perhaps this is because L appeared to be both too restrictive for classically-minded ones and not sufficiently restricted for constructivelyminded ones (this is the reason why Goedel s universe is conventionally called constructible but not constructive). Anyway Goedel s own motivation behind L was different and more specific: he conjectured the independence of CH from ZF and built L trying to prove this conjecture. The part of the desired argument, which Goedel missed, was supplied in 1963 by Paul Cohen, who used his new method of forcing for building models of ZF where CH fails. Cohen s result showed that ZF indeed doesn t imply anything definite about CH: in some models (namely in L) CH holds and in some other models it fails. Whether or not this independence result resolves the whole issue (by showing that it is in fact empty) or only shows that ZF is not appropriate for the purpose remains a controversy among set-theorists. But in any event Cohen s invention of forcing significantly changed the research landscape in the field. In particular, it made V L, which earlier might sound like an article of faith, into an obvious truth about well-controllable mathematical constructions. 14 Le Laboratoire Media kit
synapses Starting this autumn, each of Le Laboratoire s experiments will be accompanied by public meetings between artists and scientists. These evening events, known as Synapses (a biological word for the vital junctions between neurons), will offer debates, discussions and sometimes experiments with the public, on themes specifically connected with Le Laboratoire s current activities. In October, Ryoji Ikeda and Benedict Gross will discuss the V L experiment. In November, the debate will focus on the way artists portray data, and its influence on contemporary genetic science. In December, to coincide with the launching of Andrea, a commercial version of the Bel-Air design that resulted from Le Laboratoire s first experiment, a Synapse will be devoted to the question of Nature and Ethics. sunday october 12 at 19h synapses about V L With Ryoji Ikeda, Benedict Gross, Andrei Rodin and moderated by David Edwards Free entrance Priority to the LaboClub members 15 Le Laboratoire Media kit
available images data.tron (2007) Photo : Ryuichi Maruo (courtesy of Yamaguchi Center of Arts and Media) data.film [nº1-a] (2007) Photo : Ryuichi Maruo (courtesy of Yamaguchi Center of Arts and Media) spectra II (2002) Photo : Robin Reynders, 2004 (courtesy of Forma Arts and Media) data.tron (2007) Photo : Ryuichi Maruo (courtesy of Yamaguchi Center of Arts and Media) 16 Le Laboratoire Media kit
available images datamatics [ver.2.0] (2007) Photo : Ryuichi Maruo (courtesy of Yamaguchi Center of Arts and Media) test pattern [nº1] (2008) Photo : Kazuo Fukunaga (courtesy of Yamaguchi Center of Arts and Media) datamatics [ver.2.0] (2007) Photo : Ryuichi Maruo (courtesy of Yamaguchi Center of Arts and Media) 17 Le Laboratoire Media kit
also happening... Concert datamatics [ver.2.0] Composed & directed by Ryoji Ikeda Centre Pompidou 21 & 22 november 2008 at 20h30 Dans la nuit, les Images Grand Palais from 18 to 31 décembre 2008 Festival d Automne à Paris is partner of Ryoji Ikeda & Benedict Gross Exhibition Press department Festival d Automne à Paris Remi Fort, Margherita Mantero, assistant : Magda Kachouche r.fort@festival-automne.com m.mantero@festival-automne.com Tel. + 33 1 53 45 17 13 18 Le Laboratoire Media kit
pratical info admission Regular: 6 euros Reduced : 4,50 euros Opening days Friday, Saturday, Sunday, Monday from noon to 7 p.m. Le Laboratoire 4, rue du Bouloi +33 (0)1 78 09 49 50 www.lelaboratoire.org F-75001 Paris info@lelaboratoire.org Métro Vélib Contact press Louvre Rivoli, ligne 1 (350 m) Palais- Royal / Musée du Louvre, lignes 1 & 7 (300 m) 12, rue du Colonel Driant 29, rue J.-J. Rousseau 192, rue Saint- Honoré Parking Valérie Abrial valerie.abrial@le laboratoire.org +33 (0) 1 78 09 49 55 +33 (0) 6 84 37 96 23 Bus 48, 74, 85, 21, 81, 67 devant Le Laboratoire : Parking Vinci, rue Croix des Petits Champs 19 Le Laboratoire Media kit