Gödel, Escher, Bach By Hofstadter Second semester As humans we have try to understand the different systems, that are not written in the human language because those systems are not part of ours. We have are on the search of finding language that are most simple. If we think on the calculus/reasoning are just symbols and rules. Rules are a product of our mind, in our mind is a product of the universe. But how we know the universe is not a product of our mind? What if we change the rules? Are the arbitrary? Is is something isomorphic? This are some of the questions that Hofstadter tries to answer during its book. He compares humans capacity with the abilities that machines are acquiring. A formal system that finds a contradictions, collapse. On the other hand a humans would not destroy. Hofstadter believes that systems can be complete and as well consistence. But what about the universe? If nothing produces nothing then nothing can produce something? indirect self-reference is when we refer to something, without being aware of I m using the same to explain this something. It is that for example, that I am thinking on a model and that same model is the way I describe it (crab canon) to analyze the content and form. Experience to the knowing When we see something from two different points, depending on the circumstances, we can conclude things are are not necessarily false or absolutely true. Know let s ask, are our minds a formal system? Can our minds auto-refer? We know we act without thinking, we allow contradictions and we re under rules that change all the time. But, what is auto-referring something? La autorreferencia es un fenómeno que ocurre en el lenguaje natural o formal consistente en una oración o formúla referente en forma directa a sí misma, a través de algunas oraciones o fórmulas intermedias, o por medio de algunas codificaciones. En filosofía, también se refiere a la habilidad de un sujeto para hablar o referirse a sí mismo. La autorreferencia es posible cuando existen dos niveles lógicos, un nivel y un meta-nivel. Es más comúnmente usada en matemática, filosofía programación y linguística Las oraciones autorreferentes pueden conducir a paradojas.
What if our minds are a formal system? We will try to discover it. Its curios when we questions the same but to the universe. Maybe that gives an answer to the distinction between formal and informal systems. Universe has formal rules for it to work and it s when we interpret that system that it becomes a formal system: as a human product because we auto-refer. I believe is essential to understand the whole picture. 1. What is a system? A set of parts interacting among all. It can be formal (with rules) or informal (no rules). Todo sistema que sea formal pero suficientemente complejo que se puede autoreferir va a ser completo y consistente. Formal systems 1. Typographic 2. Universe * 3. Human s mind * A typographic system has now meaning until we give some. *The universe and our mind can be a formal system under the human conception. I mean, is the interpretation we have give to how this two work what make us believe they are a formal system. But it is a merely human approximation. We believe these systems do work under certain rules, but is it something implicit? What if the universe is a computer and we re just part of that program? How can we create some meaning and therefore rules that make sense? Aren t we under the same rules then? Is that the reason of why don t understand our lowest level (mind)? How we gain the capability of retrospection? As humans we express things (I m talking about hypothesis and theories) that approximates the possible understanding of the whole, but we can t prove them. Should we approach this as a whole or just the sum of it parts? Hello Gödel, Escher, Bach and computers We will try to understand each string: Gödel: Mathematical chains. Escher: Never ending loops. Bach: Musical fugues.
We can understand all in different levels. Is to understand the promising paths and be adventurous enough to start a journey. But to understand all the levels we must have many languages that allows the jump between each. We have a problem, we try to interpret all the systems we don t describe in just one language. To go deeply lets think in computer systems. 1. Clear instructions or commandments. 2. A program to operate data. 3. Data to operate. 4. A sectioned memory. 5. A stablished space (like sections) where to contain the data. But what language does a computer system has? What is? Are computers super-flexible or not? ALGOL: No direct correspondence. The operatives of the data, translate line per line, without the need of an establish program. LISP: Both assemblers and compilers are machine language translators. But now lets think on the constrictions that a program can have, we must construct non ambiguous syntax. That s why it is important that for the computer to understand what it is need to do, the machine must comprehend what is the human expecting. The requisite is not to ask something that over pass the given program. The program we made for the computer (in this case) are the rules of the game for that machine. And the programmer will know the limits, making it more inflexible. A computer doesn t understand its operative system such as us misunderstand our how our cel system is controlled by our body. Software: Anything that can be transmitted in our telephone line (mind). Hardware: The physical thing or the machines (brain). So in a few words, computers just do what we indicate them to do? The cool thing about computers is that they are in many things as humans. You can expect the computer to do something even if you give that computer a well establish program with limits. The behave of the machine can be surprising and unpredictable just like us. Our mind How it works? How is it possible that we just jump it unexpectedly and we get to a solution? Its like if we can jump from one side to another, just like Escher s drawings. Is that something replicable in a machine?
Our self What makes me who I am? Which is the I that is having all this experiences? How can I say it s me? - Past experiences? - Past knowledge? - Physical structure? - Feelings? - Our subjective experience of reality? But if we go to a more complex level. Lets don t focus on our minds, our self but something that can be as complex as both before mentioned. Where does life comes from? Darwin: Environment, diversity and time. Lets imagine that everything was created by a God, anyway had to created God. Is he human? So then if life came from somewhere a long ago, how does complexity arouse? How it works? Chaos? So humans generates and creates as well information. As well as well as rules, but who created the initial rules? 4 entropic principles the weak, two in the middle and the strong. So if the universe has been there always, are rules just a human interpretation after all? There is a epiphenomenon that surges without us understanding it with our mind. In my opinion, we can have many methods to deduce new disciplines that help us to understand. For example, mathematics. Are mathematics implicit in the universe or is rules that we create to make it a formal and useful system? Mathematician have only studied simple and precise systems, looking for patterns. Non objective beauty = non objective truth 433 by Cage Is that composition beautiful? Listen carefully and think if it is beautiful or not. Can we define what beauty really is? Objective or subjectively speaking? Something can be beautiful to me but not to any other. Do we have a universal meaning for what beauty is? Is this meaning changing? La belleza pertenece al domino exclusivo de la mente consiente: la mente que, a travez de la experiencia vital, ha conquistado una profunidad que trasciende las explicaciones de un mero conjunto de reglas. Is this applicable for truth? Is only a irrational thing?
Or maybe it is only a system in which the aspects of our thinking are only seen as rules or descriptions of a high level of a system on the under level, that is governed by simple and formal rules. We can t find patters (as in mathematics) when we are talking about beauty, we have just merely intuitions of what beauty can be. That is in a few words based on each perception. Lets in on tacit knowledge to understand better what beauty (or truth) can be in our formal system. Inductive: Many variables. Deductive: Mathematics, logic, something more physical. We know tacit knowledge is a inductive reasoning. We as well need experience in many fields, but not deductive understanding but pure knowledge. I m not talking about fields en where you just follow the rules and and you are following the system, but something that depends on your perception (it may vary) and experience to make it possible, that is tacit knowledge. It relates with beauty in the sense that in can be pretty relative. In beauty, truth and tacit knowledge you can t say something is good. How can you prove it? It is not a universal understanding. We understand beauty according to our past experiences and knowledge. And in my opinion it is the same way truth works. What I think beauty can be: -Patterns. -Past experiences. -Effort (trying to find the order of things). -Calmness. -Feelings. -Specific meaning we give to things (colors, objects, seasons, etc). Or, Presentation: A rapid perception of how things are according to the universal understanding. Re-presentation: Experimenting something and engaging with it to define beauty to ourselves. Can it be both complex or not complex? Intelligent machines We talked about Watson. A computer that can plays Jeopardy as well, or even better, than human. How can we make that a machine discovers all what we have talked before in the past sections?
its hard to understand that being not able to comprehend our own minds and formal systems (that we have maybe create) we re looking to create artificial intelligence that would recreate us. One thing is intelligence and another is computation. What are we trying to do? Are we super advanced then? What if we re a super computer? Just someone else experiment?