Gregory Chaitin Compendium
May 14th, 2019
My Notes on Gregory Chaitin - Against Method
About the documentary: Gregory Chaitin (b. 1947) already as a young prodigy contributed greatly to the philosophy of mathematics and computer science. He states that although there are truths in science that cannot be proven, there is reason for optimism. He sketches a theory of the source of beauty and creativity in nature. We'll be meeting the Chaitins at the tiny Brazilian island, their intellectual retreat.
I’m singing to make my little departed friends happier.
Four of my Heroes. Great imaginative minds I view as creators of digital philosophy.
- Godel and Turing
Part I: Age of Solitude
I didn’t pay much attention to my teachers.
I taught myself; I am completely self-taught. My last degree was a high school degree. I didn’t have a college degree. I didn’t have a doctorate. I just have honorary doctorates.
So, that’s because I think you should teach yourself. You shouldn’t pay attention to anybody else. And you should pay attention to what people think is the fashionable questions. You shouldn’t pay attention to the funding agencies or the universities. You go out; you look for the ideas that you think are interesting. The questions that need to be thought about and just start doing it on your own. And this is how I worked.
I wasn’t a university professor — wasn’t lots of pressure on me to work on the fashionable subjects. I had piles of books. And I always had projects.
There are questions in math that are as deep as the questions of quantum mechanics or general relativity.
For ages mathematics was thought to be a system of solid truths. In the 30s Kurt Godel and Alan Turing proved the idea was wrong. Some truths are unprovable, some things are uncomputable. Contrary to popular belief an acclaimed mathematician Gregory Chaitin thinks this is something we should celebrate. Math is an open and endlessly creative process, just like evolving nature is, says Chaitin. To investigate if math and life are powered by the same engine, he invents a theory. It is called metabiology."
Mathematics is absolutely fundamental to theoretical physics but it is not absolutely fundamental to biology. Biology seems to be a very different kind of a subject. And however; I believe that we only understand something when we can mathematize it. So, if biologists always say "that Darwins Theory of Evolution is the fundamental theory of biology" that it is so simple and so basic that it is practically obvious the way that they explain it. So, if this is the case, there has got to be a deep, clear way to express this in mathematics. If it cannot be expressed in mathematics it is muddy thinking, as far as I’m concerned. My goal is to define what life is, and to prove that it is going to evolve by evolution by natural selection.
Biology is too messy, too complicated. There are no general rules. There are always exceptions. So, I’m not going to make a theoretical biology. I’m going to make a toy version or a meta-theory. So, I’m dealing with a highly simplified theory of biology. I’m trying to extract the basic concepts.
The simplest system in the platonic world of mathematical ideas that simulates or emulates Darwinian Evolution. Simplest Pythagorean life-form.
Part II: End of Certainty
Meta-biology uses post-modern mathematics (Godel and Turing) — using mathematical methods to do a psychoanalysis of mathematics.
Godel showed that there can’t be a theory of everything for pre-math — there is no axiomatic theory for all math — which sounded bad but it really means that math is open and creative not static and closed.
Turing showed that most things in mathematics cannot be calculated. That there are no general methods for calculating a lot of things.
So, at the time these were interpreted pessimistically. But meta-biology interprets it optimistically. It means this the world of mathematics is not static and closed and it does not provide absolute certainty. The world of mathematics is open and dynamic, and requires creativity all the time. And this is a step in the direction of pure biology.
I don’t know why people want a theory of everything. It would be that there would be certainty in pure mathematics but it would also mean it was dead. It’s much more fascinating that pure math is eternally open.
Mathematics is quasi-empirical. Logicians like to believe that everything is black and white and clear. And the idea that human beings, even in math, will never have a final truth is deeply upsetting for logicians. But this is what? What else would future generations do? Just study the great works of the past?
Part III Wonder of Creation
The normal interpretation of Darwinian Evolution — at least in some places — is really pretty awful. It says the organisms aught to be well adapted. So this was like I remember in the 1950s: That children have to well-adapted, well-socialized, and shouldn’t rock the boat. To be creative aught to be good citizens.
Once organisms were well adapted they would stagnate and they would stop. And I think this is an erroneous interpretation of Darwinina Evolution.
Wild idea called the Red Queen Principle: That you have to keep evolving all the time even if there is no radical change in the climate, if the geology — what most people like is what triggers speciation — the animals you eat are constantly evolving, the people who eat you are constantly evolving, and you have to keep constantly evolving too. And the Red Queen Principle is one of the theoretical justifications for sexuality which otherwise is a mystery. If sexuality was selfish then you wouldn’t throw away half your genome. Dawkins is frank and admits sexuality remains a mystery. And it’s almost universal.
There has to be something fundamentally wrong with our ideas because sexuality doesn’t make sense but its almost universal. There is something big we’re missing and that seems to be Red Queen Principle. The world of biology, creativity continues all the time even when you don’t have changes in the environment that force the organisms to change.
(Talking about his model) One of the interesting features of this model… is that it involves some uncomputable steps. It involves Turing Oracles. Weird idea from Turing in 1939. Imagine computers that can do things that no real computer can do. You give it an Oracle that ask a question for which there is no algorithmic solution. No computable way to answer. My model does use oracles because the reason is when you make a random change on the program (which is to calculate the biggest number it can) it is possible that it doesn’t calculate anything and it just calculates away forever and this would stop the whole evolutionary game. So, you would have to eliminate programs from consideration if they don’t actually calculate anything. Also there are mutations which don’t give you a new organism. The basic model in meta-biology is incomputable model. It cannot be simulated but you can prove (put?) theorems around it. Really, in a way, the Oracle is really where all the creativity is coming from. Because the meta-biology organisms do everything that they can calculate, so where could new information come from? It can’t be something that you can calculate because organisms can already do that. So, it’s coming from an Oracle which can answer questions that the answers can’t be calculated. It can give you uncomputable things.
Intriguing is what you want to do with this… more important than conveying accurate deadly and dull information. You want to intrigue people to maybe try to find out more.
Axioms of Nature
We cannot forget that meta-biology is not only about Darwinian Evolution full stop. It's about how new genes appear. Sometimes Darwinian Evolution is only seen as something that explains — yes, it does explain the diversity because there are the random mutations — but it mostly explains how and why life is possible or in the sense of "how is it that we survive interacting with a changing environment" and also with our competitors? It is used a lot to explain that, less than why is it that there is ( ) diversity. Where is the focus? The creativity… the major transitions in evolution. Population genetics. How is that life survives? How is is that life goes on maintaining itself? Less than how is it that life goes on creating, and recreating itself. It’s more about maintenance and less about creating. More about adaptation to the environment and less about endless creativity.
Another way looking at meta-biology. Attempt to connect mathematical creativity with biological creativity.
Mathematics is essential (Godel and Turing)
Trying to go from Godels Incompleteness Theorum to Darwins Theory of Evolution. In my toy model, biolgical creativity and innovation is not that different from mathematical creativity and innovation. To speak in more general terms, creativity is something mysterious. It is something by definition we don’t know how to do so how can you analyze. But you cannot analyze it by giving it an algorithm for being creative because at that point it would stop being creative. It would become mechanical. So, the definition of creativity is it is always something we don’t know how to do. It is mysterious but you could have a theory of creativity which involves uncomputable elements, Turing Oracles. It is a theory that doesn’t give you a way to simulate creativity but gives you a way to prove theorems about it. This is the question of how you can make a theory about how you can do things that you’re not able to do — there are no general methods or mechanical procedure for doing.
These are all first steps in direction of mathematical theories of creativity. This is how interdisciplinary research works. When you are really fertile. You really have these different fields speaking to each other and making suggestions to other fields from the perspective from the other field. And then you see whether the suggestion works or not. And this enriches ones understanding for a while and then you have to come up with a new model once you’ve gotten all the new ideas from the given model. I think every model has a limited lifetime, as a fertile theory. It may stay int he textbooks but what stays in the textbooks is awful stuff. It is not at the new frontiers of ideas of research.
People need to first see what motivated meta-biology, how it works, and what were those goals.
It’s very inspiring to see all these inventive lifeforms and you wonder how nature created them all. And they’re all very beautiful by the way. It’s a challenge to understand nature’s creativity, nature’s inventiveness — that maybe Darwin explains a little bit. Why they’re so beautiful is a more subtle question. The notion of beauty and why we find many things in nature beautiful — that’s a deeper question I don’t really well. Some people say nature wants to create beauty but that’s not a position that is very popular at this moment, then you need to find another explanation.
I feel the sensuality of the whole country. The tropical atmosphere. Tress, plants and flowers are very lush and beautiful. And the people are too. And I responded to that.
I felt very stimulated by the eland vital (sp?). The English colonies would send husbands and wives and would slaughter the natives. And that is different from what happened in Brazil where there was s a lot of imbreeding, and that produces this remarkable variety of people you see here.
Beautiful African woman marries a handsome European and the children are unimaginative. This is Biology trying to find new possibilities, new combinations to create something new. This is what Brazil is all about. This is what sex is all about. This is what making love is all about. It’s about creating something new. And the attraction among people from different races in Brazil is very much about creativity. Because inbreeding is bad for human beings and it is good, very healthy, when people make love to somebody who is different. For example, Europeans have some health problems that Indians here don’t have. So you get mixtures and they can turn out to be winning combinations, healthier than their source.
Bliss of Truth
The brain. I don’t think most of the stuff going on in the brain is at the cellular level, which is fashionable view. Most of the computing and the memory has to be at the molecular level (DNA, RNA) where there is a greater computing and memory.
Von Noyman: He never saw a computer where the logic and memory were same technology, so why should neurons do both? I think neurons are just the front end and all the real heavy duty work is done at the unconscious at a much lower level.
The fact that I’m not a neurologist gives me more freedom to criticize the prevailing view and maybe propose an alternative view, which may be wrong. Most fields tend to get stuck in a paradigm and people work it to death.
Exploring an information-based view on how the brain could work.
Remember how angry someone whose specialty is the brain got at me. I hadn’t read hundreds of books like she did. And the stuff I said sounded completely crazy to her. it’s a different framework (to life!).
My attitude is sort of slash and burn. Quickly get an idea of what's in the field, criticize it to death, propose an alternative view. Say, maybe people aren’t seeing their hand in front of their nose.
I don’t consider myself a specialist. I’m not afraid to go into a field where i know very little, and criticize the prevailing dogma and think of maybe alternatives, which means i have to be comfortable with not knowing, with not being a specialist. But that gives me more freedom. Because the people who are specialists are really stuck all the existing current framework. They’ve been drilled in it, they’ve exterminated and deviant thoughts so they can concentrate on the field. And that may be good for developing engineering, or a field where you know the basic questions and you just have to work out the details. But if it is a frontier, where you don’t know what to do — like the human brain, which is still mysterious — there you really need new ideas. So Fashion is evil. Talented people should be against fashion. Against the ideas of the majority. Try to find a way to ignore the system and do your thing and don’t care what other people think. You’re just looking for truth. It’s not political success or professional success. It’s the wonderful feeling you get when can you understand a little bit better of something that fascinates you that you didn’t understand. Those are the beautiful moments. The payoff really is when you get a new idea and all of a sudden you realize that it explained something that you were interested in. It lasts very little.
You have these few weeks of euphoria where you’re developing a new idea and consequences. What do you do for the rest of your life? You have love affairs, you have marriages, you travel to different countries; and you’re looking for new ideas everywhere. But you can’t force yourself to have them. You just read a lot and not feel that you have to force yourself to be creative like Universities and Funding Universities want (sausage factory) — may be good for routine science but not good for creating a new field. For a paradigm shift, will never come from normal science or an industrial lab. You have to be crazy. Now being crazy is a necessary but not sufficient condition. There are a lot of people who are just crazy, who do not create a new field of science. But I think craziness is a prerequisite for being able to produce a paradigm shift. Because to disagree with the way everybody else is thinking about some field is crazy — you’d have to be crazy to do that, it’s risky. And there are some of us who can’t help ourselves for personal reasons — we are this way. If you’re lucky you can create a new field. If you’re unlucky then you’re just a crazy person.
You should write a book: What was it like living with this crazy person.
The education systems, society, tend to bring children’s spontaneity and creativity down. And you’re suppose to specialize in something and spend the rest of your life working on it. And that did not happen to you. Maybe that is why some people think you’re a child. With the year’s I’ve gotten more interdisciplinary. More openly interdisciplinary. Leibniz and philosophy, biology and evolution, artificial intelligence and how the brain works. The artistic element in your thinking and decision making is very present. Beautiful.
Ideas have to be beautiful. Beauty is an aesthetic criteria for truth. It’s very true in true math, it’s very true for everything.
Rules of Affection
Mathematics for me that is something sensual and beautiful. There is something erotic and sensual in a beautiful mathematical idea, like a beautiful woman, beautiful music, beautiful mountain. To me, they’re all connected. They leak into each other. And this is all part of the inspiration. I think one needs to draw on the life-force, on beauty, to create more beauty. To create more beauty.
Godel and Physics and Cosmology
Sensuality of Hindu Art
Goddess and Representations of Goddesses. In the West, we don’t have that. But in polytheistic Hindu religion you have these lush, erotic sculptures and goddesses and female gods.
The relation to the body and to sensuality: how it differs in different conceptual frameworks, religions, societies,
1955 in Rio. People are at ease with their bodies. The body is not the place for sin. The body is the place for enjoyment. Enjoyment for being alive. You are a part of nature.
Sex is all about information, that is what sexuality is all about. It’s about exchanging information. These things are all connected.
The definition of randomness mixes ideas from information theories, statistical physics, computers, logic. Meta-biology mixes a whole bunch of fields.
I would have not meta-biology without you. I would have stayed in West Chester and done nothing.
// Ideas that is also flexible and plastic. That’s what’s left out of the system. And I guess digital philosophy or digital physics is a step in that direction but its not going all the way.
In West Chester, where we have a house, all the houses are required to be roughly the same. Every area has to have a certain size of house with a certain size of land. Here it’s a complete jumble. It’s anarchy. It’s called creative anarchy. I love it.
// People need a pre-established ontological ground to step on. Secure ground.
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Virginia: Concept migration, interdisciplarity, and sociology of science. Provides conceptual support for new theory of metabiology.
Gregory: Best known for work on the "Omega" number, which shows that "God plays dice in pure mathematics."
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