At last, a Darwinist mathematician tells the truth about evolution

_{Vincent Torley

November 6, 2011

Intelligent Design}

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For some time, I’ve been looking for a way of communicating to Darwinists, in their own language, just how problematic the whole idea of neo-Darwinian evolution is. A couple of months ago, I had the good fortune to listen to a talk posted on Youtube, entitled, Life as Evolving Software. The talk was given by Professor Gregory Chaitin, a world-famous mathematician and computer scientist, at PPGC UFRGS (Portal do Programa de Pos-Graduacao em Computacao da Universidade Federal do Rio Grande do Sul.Mestrado), in Brazil, on 2 May 2011. I was profoundly impressed by Professor Chaitin’s talk, because he was very honest and up-front about the mathematical shortcomings of the theory of evolution in its current form. As a mathematician who is committed to Darwinism, Chaitin is trying to create a new mathematical version of Darwin’s theory which proves that evolution can really work. Next year, Professor Chaitin will be publishing a book entitled, Proving Darwin: Making Biology Mathematical (Pantheon, forthcoming May 2012, ISBN: 978-0-375-42314-7), which I would strongly urge Uncommon Descent readers to go out and buy, as I’m sure it will contain plenty of food for thought.

In September 2011, Professor Chaitin wrote an online paper with the same title as the talk he gave in May, but written for people with a strong mathematical background. In today’s post, I won’t be discussing Chaitin’s mathematical paper. I’d prefer to focus on the non-technical presentation which Chaitin gave in his talk in May. However, I was struck by the fact that in his paper, Chaitin candidly admits that “there is no fundamental mathematical theory inspired by Darwin’s theory of evolution.” He then cites no less than nine references to back up this assertion, the first of which is The Devil’s Delusion by Dr. David Berlinski, a man who surely needs no introduction to regular readers of this blog. Clearly, Gregory Chaitin is a man who reads widely and is not afraid to confront the problems raised by the critics of neo-Darwinian evolution.

For people who don’t like reading long posts, here is a short nine-point summary of what Professor Chaitin said in his talk, concerning Darwinism and Intelligent Design.

1. DNA really is a kind of programming language. In fact, Professor Chaitin believes it’s a universal programming language.
2. Building on the work on John Maynard Smith, Chaitin claims that life itself is evolving software, and that biology can be defined as the study of ancient software – software archaeology, if you like.
3. At the present time, there is no adequate mathematical theory of Darwinian evolution. In fact, even the possibility of evolution being able to continue indefinitely without grinding to a halt (which is absolutely fundamental to Darwin’s theory) had not been mathematically demonstrated before Chaitin did his research.
4. Unfortunately, the genes of modern organisms are too complicated and too messy to use, if you want to create a mathematical model which rigorously demonstrates the possibility of evolution. Instead, a simplified “toy model” is required in order to rigorously demonstrate that evolution can go on forever, without grinding to a halt.
5. Of necessity, this “toy model” of evolution is extremely unrealistic. For example, in Chaitin’s toy model, life itself isn’t even embodied (it’s purely software), there’s no population, there’s only one organism and there’s no sex. As a mathematician, Chaitin believes that if you try to make his toy model much more realistic and true to life, you won’t be able to prove anything with it, mathematically, so there’s a trade-off.
6. Even Chaitin’s toy model requires something called a Turing oracle to make evolution work. A Turing oracle means that the model is being directed by an outside intelligent source answering Yes-No questions which enable the model to proceed. So Chaitin’s work fails to show that an Intelligent Being is not required for evolution to work.
7. Chaitin looks at three kinds of evolution in his toy model: exhaustive search (which stupidly performs a search of all possibilities in its search for a mutation that would make the organism fitter, without even looking at what the organism has already accomplished), Darwinian evolution (which is random but also cumulative, building on what has been accomplished to date) and Intelligent Design (where an Intelligent Being selects the best possible mutation at each step in the evolution of life). All of these – even exhaustive search – require a Turing oracle for them to work – in other words, outside direction by an Intelligent Being. In Chaitin’s own words, “You’re allowed to ask God or someone to give you the answer to some question where you can’t compute the answer, and the oracle will immediately give you the answer, and you go on ahead.”
8. Of the three kinds of evolution examined by Turing, Intelligent Design is the only one guaranteed to get the job done on time. Darwinian evolution is much better than performing an exhaustive search of all possibilities, but it still seems to take too long to come up with an improved mutation.
9. Even if Chaitin could prove that Darwinian evolution can work in the time available, his model still says nothing about the evolution of life. It simply takes life for granted.

In what follows, I’ve transcribed brief excerpts from Professor Chaitin’s talk, given in May 2011, under several headings, so that readers can follow the logic of his argument. (Note: The excerpts below broadly follow the sequence of Chaitin’s talk, but not always.)

A. The mathematical inadequacy of Darwin’s theory

[W]hat I want to do is make a theory about randomly evolving, mutating and evolving software – a little toy model of evolution where I can prove theorems, because I love Darwin’s theory, I have nothing against it, but, you know, it’s just an empirical theory. As a pure mathematician, that’s not good enough.

B. What Chaitin is trying to do

I’m trying to create a new field, and I’d like to invite you all to leap in, join [me] if you feel like it. I think we have a remarkable opportunity to create a kind of a theoretical mathematical biology…

So let me tell you a little bit about this viewpoint … of biology which I think may enable us to create a new … mathematical version of Darwin’s theory, maybe even prove that evolution works for the skeptics who don’t believe it …

I don’t want evolution to stagnate, because as a pure mathematician, if the system evolves and it stops evolving, that’s like it never evolved at all…I want to prove that evolution can go on forever.

C. Living things really do contain software

[P]eople often talk about DNA as a kind of programming language, and they mean it sort of loosely, as some kind of metaphor, and we all know about that metaphor. It’s especially used a lot, I think, in evo-devo. But it’s a very natural metaphor, because there are lots of analogies. For example, people talk about computer viruses. And another analogy is: there is this sort of principle in biology as well as in the software world that you don’t start over. If you have a very large software project, and it’s years old, then the software tends to get complicated. You start having the whole history of the software project in the software, because you can’t start over… You … can try adding new stuff on top…

So the point is that now there is a well-known analogy between the software in the natural world and the software that we create in technology. But what I’m saying is, it’s not just an analogy. You can actually take advantage of that, to develop a mathematical theory of biology, at some fundamental level.

D. DNA really is a kind of programming language

Here’s basically the idea. We all know about computer programming languages, and they’re relatively recent, right? Fifty or sixty years, maybe, I don’t know. So … this is artificial digital software – artificial because it’s man-made: we came up with it. Now there is natural digital software, meanwhile, … by which I mean DNA, and this is much, much older – three or four billion years. And the interesting thing about this software is that it’s been there all along, in every cell, in every living being on this planet, except that we didn’t realize that … there was software there until we invented software on our own, and after that, we could see that we were surrounded by software.

E. DNA is a universal programming language

So this is the main idea, I think: I’m sort of postulating that DNA is a universal programming language. I see no reason to suppose that it’s less powerful than that. So it’s sort of a shocking thing that we have this very very old software around…

F. Life is evolving software

So here’s the way I’m looking at biology now, in this viewpoint. Life is evolving software. Bodies are unimportant, right? The hardware is unimportant. The software is important….

So let me mention by the way that in case some of you like bodies and metabolism, to justify throwing the body away, metabolism away – as a theoretician, of course, it’s easy to justify, you know, “Consider a spherical elephant” is a typical beginning of a math paper that doesn’t exist, but that’s the spirit of pure mathematics sometimes. Anyway, the idea is, there is a discussion by John Maynard Smith, a wonderful population geneticist, in 1986, in a book called “The Problems of Biology”, of a whole chapter. He’s saying, “What is life? How can we define life?” And he says, well the obvious definition is: a living being has a metabolism. Chemicals go in, chemicals go out, the organism maintains its structure – and that’s the metabolism.Plus, it reproduces itself. And he says, “Well, that’s the obvious definition, right?” and he says, “But it’s not a good definition.”… And he gives the example of a flame. A flame will reproduce itself – it has oxygen and stuff going in … but it’s not alive and it won’t evolve, because it has no heredity. A flame doesn’t remember if it was started with a match, with a cigarette lighter, from a forest fire – it has no heredity and therefore it will not evolve. So he says, Maynard Smith, a deeper definition of life is a system which has heredity and mutations and can evolve. In other words it may sound a little bit circular, but basically, John Maynard Smith is saying that we define life as something that evolves according to Darwin’s theory of evolution. Now this may seem that it’s totally circular reasoning, but it’s not. It’s not that kind of reasoning, because the whole point, as a pure mathematician, is to prove that there is something in the world of pure math that satisfies this definition – you know, to invent a mathematical life-form in the Pythagorean world that I can prove actually does evolve according to Darwin’s theory, and to prove that there is something which satisfies this definition of being alive. And that will be at least a proof that in some toy model, Darwin’s theory of evolution works – which I regard as the first step in developing this as a theory, this viewpoint of life as evolving software.

G. Biology is software archaeology

And biology would then be a kind of a field of looking at very very old software and trying to figure out what’s there. So it’s software archaeology, in my opinion. You’re looking at this very old software, this very complicated messed up software… And there’s a field that does this, called evo-devo – evolutionary developmental biology – which is the question of how the embryo develops, and the software, the DNA that is for this. And let me recommend a very nice book by Neil Shubin about this. There’s an article in “Scientific American” [about it]. It’s a book [called] “Your Inner Fish”…

There’s a lot of things in a human being which are basically left-over from when we were fish, as Neil Shubin points out in his book, and you sort of make the minimum changes to turn a fish into a mammal, and if you could start over the design would be a lot better. There are a lot of strange things in designs, things that make people sick… They can have problems that come from the fact that you couldn’t throw all the software away and start over from scratch. You can’t do that in the world of software technology either…

We have things that come from sponges, some of the first multicellular organisms, and we have stuff that comes from amphibia, and we’ve got a lot of stuff that comes from fish… And this is why I’m saying that biology is software archaeology.

H. The relevance of computational theory to understanding how life works: a brief history

I’ll just mention briefly a little bit of history… So I’m referring to events that we all know. So basically Turing in 1936, … he’s a logician who sort of creates a trillion-dollar industry as a mathematical idea. He’s been working on the foundations of mathematics, on the Hilbert program, and for a philosophical reason he has a paper where the Turing Machine is invented, and the Universal Turing Machine appears in it.

The Universal Turing Machine is a general purpose computer. It’s a flexible machine. It’s a notion of hardware and software. It’s a machine that can simulate being any other digital machine, if you insert the right software. So this is a very powerful idea, and I learned by reading von Neumann as a student. Von Neumann credits Turing with founding the computer industry as a concept. Now it’s true that actually building these things … requires engineering techniques and stuff like that, and Turing wasn’t really involved with that. But as a mathematical idea, … it’s all there in Turing’s 1936 paper, very clearly….

If you look at it from the point of view of biology, … I’ll give you a revisionist version of this. Turing fumbles the ball. He’s surrounded by software everywhere, in the natural world, in the biosphere. There’s software everywhere, he’s just finally realized what it is that makes biology work, but he doesn’t get it… He’s too trapped in the pre-Turing viewpoint….

So it’s von Neumann, … who did not come up with the original idea that Turing did, but who appreciated infinitely better than Turing the full scope and implications of this new viewpoint. And this is sort of typical of von Neumann. He’s a wonderful mathematician, he’s my hero….

So von Neumann looked at this work of Turing and said, “This applies not just to artificial automata, Turing machines, which are computers, it applies in the biological world. And von Neumann has a paper published in 1951, … called … “The General and Logical Theory of Automata”, and he’s talking about natural automata and artificial automata. Artificial automata are computers; natural automata are biological organisms. And von Neumann makes a self-reproducing automaton, and this is before Watson and Crick discovered the molecular basis for DNA, for heredity. And in this paper by von Neumann, he has something that looks like DNA, and it has this software on it. These are the instructions for … building an organism. And he sees the pattern, which is that you follow the instructions first, to build a copy of the organism, then you copy the instructions. You have that, and then you have … self-reproduction.

This… wonderful paper inspired Sydney Brenner, a Nobel Prize winner, … and he took the idea to Francis Crick. So this idea – actually, I’ve uncovered evidence that it was very influential. Most molecular biologists were inspired by a little book by Schrodinger, “What is Life?” But Sydney Brenner says in his case it was von Neumann’s work. And Sydney Brenner was the invisible half of Francis Crick. Francis Crick couldn’t work on his own. First he worked with Watson – they shared an office – and then he worked for many years with Sydney Brenner, who didn’t get much of the credit perhaps, but he was half of Crick. And Brenner took this idea to Crick. And Brenner says about von Neumann that it’s an amazing piece of mathematical … prognostication, seeing the future, that von Neumann sees this idea, which it took ten years to fully verify was the way that DNA works. But inspired by this, you see, Brenner talked to Crick all the time, … and Crick was sort of the leader of the beginning of molecular biology. He was the theorist. He was the person who sort of told the troops in which direction to go. And so this was very … influential, but it’s a forgotten piece of history that I found out by reading Sydney Brenner’s autobiography.

OK, so this is this revisionist history of the discovery of software in computer technology, in here, where there’s much more of it, which is everywhere in the biological world – a fact that is not appreciated. OK, so software is everywhere there, and what I want to do is make a theory about randomly evolving, mutating and evolving software – a little toy model of evolution where I can prove theorems, because I love Darwin’s theory, I have nothing against it, but, you know, it’s just an empirical theory. As a pure mathematician, that’s not good enough,

I. Modern organisms are too messy to use if you want a mathematical model which rigorously demonstrates the possibility of evolution

Biology is too much of a mess. DNA is a programming language which is billions of years old and which has grown by accretion, and … we know a little bit about it, but it’s just a catastrophe. So instead of working with randomly mutating DNA, let’s work with randomly mutating computer programs, where we invented the language, and we can keep it a theoretical computer program, one that a theoretician would make, so you know, you specify the semantics, you know the rules of the game.

And … I’m proposing that as a more tractable question to work on… So I propose to call this new field metabiology, and you’re all welcome to get involved in it. So far there’s just me and my wife Virginia working on this. It’s wide open. And the idea is to exploit this analogy between artificial software – computer programs – and natural programs, DNA.

[I]nstead of trying to prove theorems about what happens with random mutations on DNA, we’re going to try to prove theorems about random mutations on computer programs. OK. This is the proposal – to make a field like that.

J. A toy model is required to rigorously demonstrate the possibility of evolution

So, my organisms are software organisms. They are only software. My organisms are programs. You pick some language, and the space of all possible organisms is the space of all possible programs in that language. And this is a very rich space. So that’s the idea… So let me mention by the way that in case some of you like bodies and metabolism, to justify throwing the body away, metabolism away – as a theoretician, of course, it’s easy to justify, you know, “Consider a spherical elephant” is a typical beginning of a math paper that doesn’t exist, but that’s the spirit of pure mathematics sometimes. Anyway, the idea is, there is a discussion by John Maynard Smith, a wonderful population geneticist, in 1986, in a book called “The Problems of Biology”, of a whole chapter. He’s saying, “What is life? How can we define life?” And he says, well the obvious definition is: a living being has a metabolism. Chemicals go in, chemicals go out, the organism maintains its structure – and that’s the metabolism. Plus, it reproduces itself. And he says, “Well, that’s the obvious definition, right?” and he says, “But it’s not a good definition.”… And he gives the example of a flame. A flame will reproduce itself – it has oxygen and stuff going in … but it’s not alive and it won’t evolve, because it has no heredity. A flame doesn’t remember if it was started with a match, with a cigarette lighter, from a forest fire – it has no heredity and therefore it will not evolve. So he says, Maynard Smith, a deeper definition of life is a system which has heredity and mutations and can evolve. In other words it may sound a little bit circular, but basically, John Maynard Smith is saying that we define life as something that evolves according to Darwin’s theory of evolution. Now this may seem that it’s totally circular reasoning, but it’s not. It’s not that kind of reasoning, because the whole point, as a pure mathematician, is to prove that there is something in the world of pure math that satisfies this definition – you know, to invent a mathematical life-form in the Pythagorean world that I can prove actually does evolve according to Darwin’s theory, and to prove that there is something which satisfies this definition of being alive. And that will be at least a proof that in some toy model, Darwin’s theory of evolution works – which I regard as the first step in developing this as a theory, this viewpoint of life as evolving software….

…I want to know what is the simplest thing I need mathematically to show that evolution by natural selection works on it? You see, so this will be the simplest possible life form that I can come up with.

K. Toy models are extremely unrealistic

So, my organisms are software organisms. They are only software. My organisms are programs. You pick some language, and the space of all possible organisms is the space of all possible programs in that language. And this is a very rich space. So that’s the idea…

So how do we make a toy model of evolution? What is this artificial life that I’m going to create? Well, it’s very very simple… In fact, it’s so simple that you’ll say, “It’s not very realistic biologically.” And really it’s not, but in fact physicists would call this a toy model, which in Portuguese sounds bad, but they say is great. The idea is, first of all you want to forget about the things which are not so important, to concentrate on the important things so you can get some mathematical understanding. And the other thing is, I want to know what is the simplest thing I need mathematically to show that evolution by natural selection works on it? You see, so this will be the simplest possible life form that I can come up with. It’s true we are very complicated life, but I would like to look at the sort of pure case, at the simplest thing that provably evolves according to Darwin’s theory.

OK, here comes the toy model…. So the model is very simple. There’s only one organism. Not only there’s no bodies, it’s a program… There is no population, there is no environment, there is no competition… [but] it’ll evolve anyway. Let me tell you what there is. So it’s a single software organism, it’s a program, and it will be mutated and evolving … What does this program do? Well, I’m interested in programs that calculate a single positive whole number, and then they halt… So my organism is really a pure mathematician or a computer scientist. And the reason that I’m going to get them to evolve is that I’m going to give them something challenging to do, something which can use an unlimited amount of creativity. So what is the goal of this organism? … How do I decide if an organism has become more fit? What is the notion of fitness … for this organism? What is its goal in life? Well its goal is … the Busy Beaver problem. It’s a very simple problem … and it’s just the idea of: name a very big positive integer. And this might sound like a trivial, stupid thing, but it’s not. It’s sort of the simplest problem which requires an unlimited amount of creativity, which means that in a way, Godel’s incompleteness theorem applies to it. There is no general method… No closed system will give you the best possible answer. There are always better and better ways to do it. So the reason is basically that this problem is equivalent to Turing’s halting problem. So that’s the theoretical basis of why this problem is so fundamental and can utilize an unlimited amount of mathematical creativity. OK, so the fitness of this organism, which comes from the program, is the number it calculates. The bigger the number, the better the organism. So that’s their goal in life. ..These are mathematicians and their aim is to calculate enormously big numbers. The bigger, the better.

Now the other thing I should tell you is: how do I do mutations? And that’s a very crucial thing. At first I tried to do what … biologists think is a natural kind of mutation, and the most natural one for biologists is I think what’s called a point mutation, which means you change one base in the DNA, or maybe you change a few continuous bases, or you remove them, or insert them. It’s a local change in a strand of DNA. And I worked for two years with that kind of a notion of mutation, and I didn’t get very far. I stumbled around… and I got a feeling for what was going on, but it was a mess, and I couldn’t really prove what I wanted to prove, which was that evolution works.

So there was a breakthrough. The breakthrough was using mathematics from the 1970s. The breakthrough is to allow algorithmic mutations – very powerful mutational mechanisms which, as far as I know, are not the case in biology, but nobody really knows all the mutational mechanisms in biology. So this is a very high-level kind of mutation. An algorithmic mutation means: I will take a program – my mutation will be a program – that I give the current organism as input and it produces a mutated organism as output. So that’s a function. It’s a computable function. That’s a very powerful notion of mutation. And the crucial thing is: what is the probability going to be? How do you distribute probability on the space of all possible mutations? That’s a very important decision, and from algorithmic information theory, we know how to do that. The notion is that if the program M that maps you from the original organism to the mutated organism is a K-bit program, you give this a probability of 2 to the minus K…

OK, so this is the idea. If the algorithmic mutation M which is a function basically, a computable function which takes the organism and maps it into the mutated organism. If that’s a K-bit program then this will have a probability of 1 over 2 to the K. That’s a very natural measure, and for those of you who have heard of the halting probability, which was mentioned in the very nice introduction, which is the probability that a Turing machine halts, which is my version of Turing’s halting problem. You see this field knows how to associate probabilities with algorithms in a natural way. … Those of us who work in this field are convinced that this is a natural way – we can give various reasons – for associating probabilities on computer programs. OK?

So from a mathematical view this is now a very natural way to assign a probability to a mutation. And so this is how I did my mutations. Now let me point out how different this is from point mutations, even ones which can affect an arbitrarily large number of bits, which is presumably a probability which decreases exponentially with the number of bits. There is a very simple mutation which flips every bit. Right? That’s a very small program. You take the organism and you just change 0 to 1, and 1 to 0. So that’s a very probable mutation…. This mutation will be tried a fixed percentage of the time. It’ll be a very common mutation to try, because it’s a very simple transformation of the program, algorithmically. But you see, from the point of view of point mutations, this is an extremely violent and infinitesimally… extremely unlikely mutation. Because in point mutations the probability of affecting the number of bits you change … as that grows bigger, the probability of the point mutation drops exponentially. You’re most likely to change just one bit in the program. You know, changing two bits is going to be a lot less likely, and changing all the bits in the program is possible but it’s extremely unlikely. But with this approach, this is a very probable mutation.

L. Even toy models of evolution require a Turing oracle in order to work properly

So … we have, only a single organism at a time, which is trying to be a better mathematician, to improve him or her or itself, and this gives us a random walk in software space, which is calculating bigger and bigger numbers…

Now one important thing to say is that there’s a little problem with this: we need something which Turing invented, not in his famous paper of 1936, but in a less well-known but pretty wonderful paper of 1938, which are called oracles. And [for] those of you who have done theoretical computer science or at least computability theory, which … I’d say is theoretical theoretical computer science, which is even more theoretical than normal computer science, because there are no time bounds on computations … this notion of an oracle is a wonderful idea.

And basically what an oracle is, it’s something you add to a normal computer, to a normal Turing machine, that enables the machine to do things that are uncomputable. You’re allowed to ask God or someone to give you the answer to some question where you can’t compute the answer, and the oracle will immediately give you the answer, and you go on ahead. So I need an oracle to enable me to carry out this random walk. Why? The reason is as follows. If you pick at random a mutation, an algorithm, a mapping from the organism to the mutated organism with these probabilities, some of the time, the algorithm you pick never produces any output. You don’t get a mutated organism. Another possibility is that you get a mutated organism, but it’s something that never finishes calculating. It never … calculates an integer, and maybe it never halts. So you can get stuck waiting for the mutation to finish and give you a new organism, or you can get stuck running the new organism to see what it calculates, you see, and you’ll go on forever, and it’ll never calculate anything, so you’re just stuck there and the random walk dies. So we’ve got to keep that from happening. And if you actually want to do that, as a thought experiment, you would need an oracle.….

The first thing I … want to see is: how fast will this system evolve? How big will the fitness be? How big will the number be that these organisms name? How quickly will they name the really big numbers? So how can we measure the rate of evolutionary progress, or mathematical creativity of my little mathematicians, these programs? Well, the way to measure the rate of progress, or creativity, in this model, is to define a thing called the Busy Beaver function. One way to define it is the largest fitness of any program of N bits in size. It’s the biggest whole number without a sign that can be calculated if you could name it, with a program of N bits in size. This is a slightly different version from the original Busy Beaver function, [where] you know, people chalk up the number of states in a Turing machine. Anyway, this is a better measurement than the original one. OK, so this is the highest possible fitness of any program up to N bits on size. This will be among all the programs up to N bits in size. It’s like, the fittest one. It succeeds in naming the biggest integer … You name an integer by calculating it and evolving it. OK, so that’s the best mathematician among the N-bit programs in my competition.

Now, this number is highly uncomputable … and the reason is, one way to put it, is that it grows faster than any computable function of N. And another way to put it is: it’s sort of the N bits of inspiration to be able to calculate the Busy Beaver function of N. This is sort of the number of Yes-No questions you’d have to ask an oracle in order to be able to calculate, if you’re only allowed to ask “Yes-No” questions. So this is the meaning of creativity when it talks about inspiration. You see, my model … has an algorithmic part, but it’s going to do better than any mechanical procedure. Where is the inspiration, where is the non-algorithmic stuff coming from? It’s coming from the use of an oracle to see if one organism is fitter or not than another. You see I need an oracle. It’s part of the process of seeing if my mutated organism is fitter than the original one, because of the problem that the mutated organism may not ever stop running.

So this is where the inspiration comes from. This is where we’re getting non-algorithmic information.

[He then talks about his worst possible case scenario for evolution: exhaustive search, which is much, much slower than Darwinian evolution.]

OK, so this is the worst possible [model of evolution] and this already has fitness increasing faster than a computable function. So there’s something non-mechanical, non-algorithmic happening here…

And this is the worst case of an evolution model. So what I need to point out is: … already … there is a kind of creativity going on, even with this stupid regime, because, you see, if you take organisms and you improve them mechanically, algorithmically, there is no oracle, no inspiration, then you have a … you’ve got a sequence of organisms that are computable, and you don’t need any oracles any more. There’s no inspiration, there’s no creativity. Then the fitness can only grow as a computable function of the time. If you mechanically improve, if you have an algorithm and given one organism that gives you the next one, and you keep always using that sort of mechanical way of improving organisms, then the fitness will only grow as a computable function of the time. So even this scheme is doing better, it’s growing faster than any computable function of the time. But the reason it’s doing this is that, remember, we have an oracle that we’re allowed to use in a very constrained way. I mean if you’re allowed an oracle in general, you can use it any way you like. You can just calculate the Busy Beaver function of N from N. But I’m only allowed to use the oracle to see if a mutated organism is better than the original organism…. This is where the creativity … in this model is coming from – the biological and mathematical creativity. In this model they’re sort of the same.

M. There are three kinds of evolution: Intelligent Design is the smartest possible kind, followed by Darwinian evolution; exhaustive search is much slower than both

So anyway, let me tell you about three different evolutionary regimes you can have with this model. This is the one I’m really interested in. This is cumulative random evolution. OK? But first I want to tell you about two extremes, two sort of evolutionary regimes, because we want to get a feeling for how well this model does, when you’re picking the mutations at random, in the way I’ve just described. So to get that sort of bracket, the sort of best and worst possibilities, to see how this kind of model behaves, you need to look at two extremes which are not normal cumulative evolution in the way I’ve described. So one extreme is total stupidity. You don’t look at the current organism. For the next organism, you pick an organism at random. In other words, the mutation isn’t told of the current organism. It just gives you a new organism at random without being able to use any information from the current organism. It’s stupid. So what this does, this basically amounts to exhaustive search, in the space of all possible programs with a probability measure that comes from algorithmic information theory. And if you do that, this is the stupidest possible way to evolve… your organism will reach fitness – the Busy Beaver function of N – in time exponential of N. Why? Because basically that’s the amount of time it takes to try every possible N-bit program, and it’ll find the one that is the most fit, and that one has this fitness. You see, so this is, sort of, the worst case. But notice that time 2 to the N is what? You’ve tried 2 to the N mutations. That’s the timing in here. Every time you try, you generate a mutation at random and try it, to see if that gives you a bigger integer, and that counts as one clock.

Now, what is the smartest possible way, the best possible way to get evolution to take place? This is not Darwinian. This is if I pick the sequence of mutations. It has to be a computable sequence of mutations, but I get to pick the best mutations, the best order, you know, do the best possible mutations, one after the other, that will drive the evolution – the mutations you try – … as fast as possible. But it has to be done in a computable manner with the mutations. So that you could sort of call Intelligent Design. I’m the one that’s designing that, right? In my model, …in this space, I get to pick the sequence, I get to indicate the sequence of mutations that you try, that will really drive the fitness up very fast. So that’s sort of the best you can do, and what that does, it reaches Busy Beaver function of N in time N, because basically in time N it got to go to the oracle N times, and each time, you’re getting one bit of creativity, so this is clearly the best you can do, and you can do it in this model. So this is the fastest possible regime.

So this [here he points to exhaustive search] of course is very stupid, and this [here he points to Intelligent Design] requires Divine Inspiration or something. You know, [in Darwinian evolution] you’re not allowed to pick your mutations in the best possible order. And mutations are picked at random. That’s how Darwinian evolution works.

So what happens if we do that, which is sort of cumulative random evolution, the real thing? Well, here’s the result. You’re going to reach Busy Beaver function N in a time that is – you can estimate it to be between order of N squared and order of N cubed. Actually this is an upper bound. I don’t have a lower bound on this. This is a piece of research which I would like to see somebody do – or myself for that matter – but for now it’s just an upper bound.

N. Only Intelligent Design is guaranteed to evolve living things in the four billion years available. It seems that Darwinian evolution would take too much time

So what happens if we do that, which is sort of cumulative random evolution, the real thing? Well, here’s the result. You’re going to reach Busy Beaver function N in a time that is – you can estimate it to be between order of N squared and order of N cubed. Actually this is an upper bound. I don’t have a lower bound on this. This is a piece of research which I would like to see somebody do – or myself for that matter – but for now it’s just an upper bound. OK, so what does this mean? This means, I will put it this way. I was very pleased initially with this.

Table:
Exhaustive search reaches fitness BB(N) in time 2^N.
Intelligent Design reaches fitness BB(N) in time N. (That’s the fastest possible regime.)
Random evolution reaches fitness BB(N) in time between N^2 and N^3.

This means that picking the mutations at random is almost as good as picking them the best possible way. It’s doing a hell of a lot better than exhaustive search. This is BB(N) at time N and this is between N squared and N cubed. So I was delighted with this result, and I would only be more delighted if I could prove that in fact this [here he points to Darwinian evolution] will be slower than this [here he points to Intelligent Design]. I’d like to separate these three possibilities. But I don’t have that yet.

But I told a friend of mine … about this result. He doesn’t like Darwinian evolution, and he told me, “Well, you can look at this the other way if you want. This is actually much too slow to justify Darwinian evolution on planet Earth. And if you think about it, he’s right… If you make an estimate, the human genome is something on the order of a gigabyte of bits. So it’s … let’s say a billion bits – actually 6 x 10^9 bits, I think it is, roughly – … so we’re looking at programs up to about that size [here he points to N^2 on the slide] in bits, and N is about of the order of a billion, 10^9, and the time, he said … that’s a very big number, and you would need this to be linear, for this to have happened on planet Earth, because if you take something of the order of 10^9 and you square it or you cube it, well … forget it. There isn’t enough time in the history of the Earth … Even though it’s fast theoretically, it’s too slow to work. He said, “You really need something more or less linear.” And he has a point….

O. More realistic models of evolution won’t allow you to rigorously prove anything about evolution

But what happens if you try to make things a little more realistic? You know, no oracles, a limited run time, you know, all kinds of things. Well, my general feeling is that it would sort of be a trade-off. The more realistic your model is – this is a very abstract fantasy world. That’s why I’m able to prove these results. So if it’s … more realistic, my general guess will be that it’ll be harder to carry out proofs. And it may be that you can’t really prove what’s going on, with more realistic situations….

Let’s say for example that we limit the run time, or we limit the kind of programming language to a language which is not universal, a more restricted programming language. Now let’s say we do a computer experiment, you know, … so then, if you limit the run time, and you have, say, a more restricted programming language, not a universal programming language – if you have programs in some sub-recursive language – so… you could actually carry out simulations of this random walk, on a computer, and then you could get experimental evidence of how this kind of evolution behaves, which I think would be fun. But I think you might need to run a computer experiment, because I suspect it’ll be a trade-off. Either you’re going to prove beautiful theorems because your model is very much in the fantasy world of pure math, of if you make it more realistic, I suspect it would be very difficult or impossible to prove theorems, but you may be able to do massive computer experiments and accumulate suggestive empirical data, so to speak, from big computer runs, looking at typically how these random walks behave.. So there are a number of possibilities for going forward with this kind of research.

P. Chaitin’s model is the first mathematical model that actually demonstrates evolution can continue indefinitely

Now, I did ask some physicists at the Santa Fe Institute, in January, I gave a talk on this there. And that’s a place which is very well known for their work on complexity, complex systems. So I asked some of the people there: “Is there a model of evolution, a toy model, that is run on a computer in which evolution seems to go on forever?” And they said, “No. All the models up to now … maybe they go for a while and then they stagnate. So we don’t have empirical evidence that some model of evolution is going on. That’s the problem of the stagnation. And I asked them, “Is there a theoretical model? And they told me that their feeling was that this was probably the first case where somebody can prove that you get evolution to continue.

Q. Chaitin’s model does not address the origin of life

Now let me mention, by the way, that this model has life in it from the beginning. This model does not talk about the origin of life, because I already have a universal programming language here at the beginning. The origin of life is how you pick your programming language, where that comes from. So that’s an interesting question, but this is not discussed here. I have some thoughts about that, but that’s not in this model. In this model, you start off with life there – DNA there – and then you just see what happens afterward.

(END OF MY SUMMARY OF PROFESSOR CHAITIN’S TALK)

Concluding thoughts

Well, that’s all, folks! May I suggest that readers now go and listen to Professor Chaitin’s talk for themselves, and form their own judgment. At any rate, I for one will be looking forward to the upcoming release of Gregory Chaitin’s book, Proving Darwin: Making Biology Mathematical (Pantheon, forthcoming, ISBN: 978-0-375-42314-7), in May 2012.

Let me close with a final thought. There is excellent evidence that evolution has occurred, if one simply defines “evolution” as the process by which the first living cell developed into the various existing life-forms we find on Earth today. However, the assertion that evolution is a Darwinian process is very poorly supported, from a mathematical standpoint. Darwinian evolution is by definition an unguided process, but Professor Chaitin had to make use of a Turing oracle to make his Darwinian model of evolution work – and even then, it seems it would still take far too long to generate the diversity of life-forms currently found on Earth. At the present time, Intelligent Design is the only version of evolution which is known to be capable of generating the diversity of life-forms on Earth today, within a four-billion-year time span.

May I suggest that in future, when engaging with Darwinists, we force them to confront these two questions:

1. Why do you scoff at the notion of an Intelligent Designer, when even your own brand of evolution relies on a Turing Oracle to make it work, in current mathematical models? Isn’t that a Designer smuggled in via the back door?
2. Where’s your evidence that Darwinian evolution can generate the diversity of life-forms we find on Earth today, in the time available? Current modeling suggests that it cannot.

Thoughts, anyone? And now, over to you.

Comments

Further food for thoughtkairosfocus_{November 7, 2011
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"This suggests that his N^2 reduction of exp^N random search time, stands, or falls, on the presence of an Oracle." For the love of Pete... Biological evolution is *always and everywhere* an NP complete problem. This is true by its very construction. Either Chaitin was not modelling evolution or he's claiming that the upper bound on *all* NP complete problems is N^3. Thus NP is in P, the question is solved, and everyone that has been working on NP problems with Darwinian processes and heuristics is completely off their rockers for failing to show that result in the last few decades of practice on the subject. So rather than assume he made one of several common errors I went ahead and skimmed the paper on the basis of your quote. Chaitin modeled a system in which there is no hysteresis and absolute fixation over a single perfectly monotonic, linear, and infinite fitness landscape. And then threw in a sorely vindictive culling agent that disallowed drift through maniacally applied eugenics. So yes, his results are perfectly valid and the upper bound for his system is indeed N^3. This result can be verified by perusing any common literature on the construction of software to parse languages. His usages of Oracles in this constraint are not out of line or even remarkable. All of which is fine as long as we're not talking about modelling genetics. Or even pretending to.Maus_{November 7, 2011
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This finding reminds me of this scripture:
John 15:5 "I am the vine; you are the branches. If a man remains in me and I in him, he will bear much fruit; apart from me you can do nothing.
Music:
Third Day - Creed - Acoustic http://www.youtube.com/watch?v=mxEFqjH9G9Y
bornagain77_{November 7, 2011
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Pav: I truly believe you nailed Chaitin's hidden assumption! i.e. For 'unlimited evolution' to be possible the oracle must be God!bornagain77_{November 7, 2011
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What strikes me, in particular, is Chaitin's statement:
It follows that the bits of the dyadic expansion of OMEGA are irreducible mathematical information; they cannot be compressed into a theory smaller than they are.
Where have I heard that word "irreducible" before? More to the substance however, I believe that what Chaitin is saying here is that to be able to have a "program" that can "solve the halting problem for all programs p which compute a positive integer that are up to n bits in size," we have to know the "halting probability" = OMEGA, an irrational (non-repeating) number, up to n bits in size. This requires, per Chaitin, "concentrated mathematical creativity". Further, OMEGA contains "infinite irreducible complexity" for it must perform the task of "provid[ing] a perfect simulation in pure mathematics . . . of contingent, accidental truths . . . ," such as "historical facts or biological frozen accidents." Doesn't this amount to the very description of God? Isn't this a mathematical definition of God's omniscience? Isn't this the Intelligent Designer we speak of? _________________________ More particularly,if I understand Chaitin correctly, the "proofs" and "theorems" that are part of AIT won't go anywhere unless OMEGA exists and is available as a knowable bit string. This suggests that his N^2 reduction of exp^N random search time, stands, or falls, on the presence of an Oracle. But this strikes me as saying that if it were not for the presence of vast amounts of information (bordering on the infinite) present in an organism's genome, NS couldn't possibly work. Thus, the information that NS is meant to explain, simply is assumed. And circular reasoning ensues: where did the information in the mammalian genome come from? Answer: from RV + NS. What makes NS possible? Answer: the information in the mammalian genome. IOW, with an "intelligent designer", the time for climbing the fitness landscape is linear with N, the number of "bits of information" needed for the climb, presuming the presence of an Oracle. Finally, in one of his footnotes we find that in this new, enhanced version of "metabiology", instead of limiting mutations to considerations only of various forms of SNP's, he's included---guess what?---"gene duplication" and mutation within the duplicated genes. He was forced to do this because, any time he considered only SNP's, he couldn't get any increase in fitness. The program went nowhere. Ah, yes, the powers of Darwinian selection!PaV_{November 7, 2011
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Dr. Torley; you being a philosopher, I think you might be interested in a couple of examples of where the 'unlimited evolution' philosophical precept leads a person into absurdity: In this following video, at the 6:48 minute mark,,,
Anthropic Principle - God Created The Universe - Michael Strauss PhD. - video http://www.metacafe.com/watch/4323661
Dr. Strauss states:
'So what are the theological implications of all this? Well Barrow and Tippler wrote this book, 'The Anthropic Cosmological Principle', and they saw the design of the universe. But they are atheists basically, there's no god. And they go through some long arguments to describe why humans are the only intelligence life in the universe. That's what they believe. And, so they got a problem. If the universe is clearly the product of design, but humans are the only intelligent life in the universe, who creates the universe? So you know what Barrow and Tippler's solution is? Heh, It makes perfect sense. Humans evolve to a point, someday, where they reach back in time and they create the universe for themselves. (audience laughs) Hey, these guys are respected scientists. So what brings them to that conclusion. It is because the evidence for design is so overwhelming that if you don't have God, you have humans creating the universe, back in time, for themselves.' - Michael Strauss PhD. Particle Physics
Although a bit more abstract, Here is another absurdity that the 'unlimited evolution' philosophical precept leads people to:
ARE YOU LIVING IN A COMPUTER SIMULATION? BY NICK BOSTROM Department of Philosophy, Oxford University VII. CONCLUSION A technologically mature “posthuman” civilization would have enormous computing power. Based on this empirical fact, the simulation argument shows that at least one of the following propositions is true: (1) The fraction of human-level civilizations that reach a posthuman stage is very close to zero; (2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero; (3) The fraction of all people with our kind of experiences that are living in a simulation is very close to one. If (1) is true, then we will almost certainly go extinct before reaching posthumanity. If (2) is true, then there must be a strong convergence among the courses of advanced civilizations so that virtually none contains any relatively wealthy individuals who desire to run ancestor-simulations and are free to do so. If (3) is true, then we almost certainly live in a simulation. In the dark forest of our current ignorance, it seems sensible to apportion one’s credence roughly evenly between (1), (2), and (3). Unless we are now living in a simulation, our descendants will almost certainly never run an ancestor-simulation. http://www.simulation-argument.com/simulation.html
Thus, according to the neo-Darwinian philosophical precept of virtually unlimited computational power in the future for Evolutionary Algorithms, either we are currently living in a computer simulation, or future humanity becomes extinct so as to not run the simulation!!!,,, or, an option that was not mentioned in the above philosophical argument, Evolutionary Algorithms are, in reality, extremely limited in their ability to optimize computer programs above what intelligence can do by itself; My intuition is firmly on the latter,,, :)bornagain77_{November 7, 2011
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My suggestion is that even before any attempt to understand Chaitin's paper (and proofs contained therein), we should examine first his Appendix, where the background of AIT (Algorithmic Information Theory) is given. I don't know if I'm understanding things perfectly here, but I think Chaitin is attempting to pack away a lot of "explaining to do" down in this Appendix. (There are also some footnotes that tend to relegate to the bottom of the page certain distasteful considerations). Frankly, I don't see this putative Turing Oracle the same way Chaitin does. The assumptions/conclusions/interpretations Chaitin has, should be examine before all else. There are some smart, informed, people here at UD. I hope some of them can draw out some of the hidden assumptions that may be lurking here and there. My own sense is that things look far worse for Darwinism than Chaitin is letting on. Here's the final portion of Chaitin's paper (pp. 20-21) wherein he deals with what amounts to his Turing Oracle: (I've had to change some things so that the sense of Chaitin's mathematical symbols can be maintained. It's sloppy; but, hopefully, the meaning comes through----you can always access the paper. One such example is "> or = to" standing for the mathematical symbol for "greater than, or equal, to".)
What are these properties? OMEGA is a form of concentrated mathematical creativity, or, alternatively, a particularly economical Turing oracle for the halting problem, because knowing n bits of the dyadic expansion of OMEGA enables one to solve the halting problem for all programs pwhich compute a positive integer that are up to n bits in size. It follows that the bits of the dyadic expansion of OMEGA are irreducible mathematical information; they cannot be compressed into a theory smaller than they are. (footnote 18: More precisely, it takes a formal axiomatic theory of complexity > or= to (n -c) (i.e., one requiring a >or = to n-c) bit program to enumerate all its theorems) to enable us to determine n bits of OMEGA). From a philosophical point of view, however, the most striking thing about OMEGA is that it provides a perfect simulation in pure mathematics (where all truths are necessary truths) of contingent, accidental truths---i.e., of truths such as historical facts or biological frozen accidents. Furthermore, OMEGA opens a door for us from mathematics to biology. The halting probability OMEGA contains infinite irreducible complexity and in a sense shows that pure mathematics is even more biological then biology itself, which merely contains extremely large finite complexity. For each bit of the dyadic expansion of OMEGA is one bit of independent, irreducible mathematical information, while the human genome is merely 3 x 10^9 bases = 6 x 10^9 bits of information.
(My emphasis)PaV_{November 7, 2011
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A note on Turing Oracles: Traditionally a Turing Oracle has the correct answer to every question that can be put to it. Such that, if we do not posit an infinitely large Oracle, it must necessarily answer a finite set of questions. It is likewise consider, in some fashion, external to the questioner. This may simply be as a look-up table within the software rather than an external device. You already (I may be slandering you here) know that there is no such external Oracle per se, and that this is a central flaw of nearly all GA's. But it is a mistake to state that there is no Oracular concept involved. Namely that the current individual genome *and* it's complete time-based environment generate the Oracle for the given agent over its lifespan. If we drop the time requirement, and there are valid arguments for just such, then it is indeed an Oracle in the truest sense. Chaitin doesn't seem touch on this; and not without reason. If the Oracle is determined to be completely external then the problem is analytical. If the Oracle is partially self-determined then you've a state machine with -- conceptually -- non-linear feedbacks. Which is most definitely *not* analytical unless there are some significant oddities involved. You can, for certain individual limits, talk about saddle points and the rest of that rot at this point. But that all goes back to the notions of limits in a stochastic process. No matter how small the odds? If it happened then it happened. Even in Chaitin's horrible model the lower limit is N = 1. The odds are terrible, but that doesn't mean that it hasn't occurred. At best Chaitin is only lending his panache to the arguments already made by numerous ID folks even if he's still spooling up on the math from the opposite viewpoint.Maus_{November 7, 2011
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"Well, I meant that mathematicians prove things. Scientists don’t." Mathematicians prove things about equations. However, you are fond of stating -- paraphrase -- that science is all about creating models that have predictive value. That is, scientists go about the business of generating systems of equations that match replicable tests within some bounded error. Or they do not. And if they do not then science is defined as a field that generates pure philosophical models -- qualitative models -- that are accepted so long as they are not laughably false on the basis of experiment. (Which is to some degree correct, but only half the story.) In which case ID would be considered a proper and robust science. Now before you twist your knickers I'll point you to the notion that Chaitin is merely duplicating work done by Behe and others of the ID cloth. Sift back through his discussion of mapping functions and the like if you're unaware of why that is so. That said, Chaitin is off tilting at windmills as both the Darwinian and Teleological processes are stochastic once we're beyond the OOL. It's mere gambling in either case. No matter which *may* be correct to historical reality the present creatures that infest this planet are then the required result of that process. That the probability is terribly small for any or all of them has no bearing on the matter whatsoever. That's just the basic math lurking underneath.Maus_{November 7, 2011
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Thanks vjtorley, sleep well :)
Re your comment: “ID doesn’t do that job because (and I expect to be howled down by this) it could explain anything”, may I direct you to my remarks on terra-forming in 10.2 above. May I also point out that according to Professor Chaitin’s definition of Intelligent Design, the Designer selects the best mutation that could occur at each step.
Which is yet another reason it's a terrible model! It seems to have only one fitness dimension, and it's exclusively a "hill climber". Darwinian evolution doesn't work that way, nor do human designers!
So here’s my proposal. Take any species you like – Homo sapiens will be fine. Take the first living cell, whose genome we may one day be able to reconstruct with a reasonable degree of accuracy. Now try to find the shortest viable pathway from the latter to the former. Compare that with what the evidence in our genes actually suggests, and look for any evidence of time-wasting roundabout routes from the Ur-cell to where we are now. Intelligent Design would predict that there shouldn’t be any. It would predict that the path taken, over billions of years (and I explained in 10.2 why the Designer would need billions of years) was an efficient one and not a circuitous one.
How on earth would you calculate that? By what criteria would you decide something was "circuitous"? And have you forgotten that our own lineage (assuming you are assuming common descent) is a continuous series of populations that have inhabited very different environments? And aren't you presupposing that there is only one form that the Designers desired end product could possibly take? Why not evolve intelligent beings from molluscs? Why do women have such inadequate pelvises for our large-brained offspring? And why don't we have wings? Do you see my problem?Elizabeth Liddle_{November 7, 2011
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Simply fascinating talk,,, stripping everything out, making the simplest, most abstract, model possible to demonstrate 'unlimited' evolution, He still required a 'oracle' to make the model work, and He showed that evolution would take far too long for the information we find in life, and, in typical Darwinian fashion, he didn't even listen to what his own results were telling him.bornagain77_{November 7, 2011
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Hi Elizabeth, I must retire shortly (it's very late where I am), but I'll just make a couple of quick remarks before I do. I'm not a biologist, and I know very little about Tierra, but I'll check out the link you provided. Re your comment: "ID doesn’t do that job because (and I expect to be howled down by this) it could explain anything", may I direct you to my remarks on terra-forming in 10.2 above. May I also point out that according to Professor Chaitin's definition of Intelligent Design, the Designer selects the best mutation that could occur at each step. So here's my proposal. Take any species you like - Homo sapiens will be fine. Take the first living cell, whose genome we may one day be able to reconstruct with a reasonable degree of accuracy. Now try to find the shortest viable pathway from the latter to the former. Compare that with what the evidence in our genes actually suggests, and look for any evidence of time-wasting roundabout routes from the Ur-cell to where we are now. Intelligent Design would predict that there shouldn't be any. It would predict that the path taken, over billions of years (and I explained in 10.2 why the Designer would need billions of years) was an efficient one and not a circuitous one. That's my suggestion, anyway. When I referred to the "current models" that suggest there isn't enough time for Darwinian evolution, I had in mind Professor Chaitin's Busy Beaver function. To repeat a point I made above in reply to dmullenix:
Now to be fair, Professor Chaitin does point out that as yet, we only have an upper bound for the time taken for random evolution to reach the Busy Beaver function N - somewhere between N^2 and N^3, which is too slow to account for the evolution that has occurred on planet Earth. No-one has computed a lower bound yet. If somebody could show that the lower bound for random evolution was N*(log N) instead of N^2, then that would be much closer to the time required for Intelligent Design, which is just N. In that case, Darwinian evolution might still be fast enough to generate the diversity of life-forms we see around us today. That would be an interesting result. But we don't have that result yet.
And now I really must retire. Back in a while.vjtorley_{November 7, 2011
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Looking at your other comments, I see that whale evolution is an example of something that you think happened too rapidly to be attributable to current evolutionary theories. Can you elaborate?Elizabeth Liddle_{November 7, 2011
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Hi Jello, Thanks for pointing out that broken link. I've now fixed it. Re Darwinian evolution: I have no problem in saying that it works up to a point. I obviously don't believe that the hundreds of species of cichlid fish were all created separately. On the other hand, when I am confronted with the impressive anatomical, fossil and embryological evidence that whales are descended from land-dwelling mammals, I don't believe in rushing to the conclusion that the process whereby whales evolved from land-dwelling ancestors was a Darwinian one. Given the time constraints and the massive anatomical changes involved, I think the ball is in the Darwinists' court: it is incumbent on them to establish the adequacy of the mechanism they postulate, to bring about such a great transformation in such a short time (10 million years at the very most, and probably less than that).vjtorley_{November 7, 2011
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He goes on to say "if these collapse", i.e, if the ID and the random regimes "collapse" then "it's a big embarrassment for this theorem." At any rate, his attempt goes to show the sorry lack of mathematical rigorous proof for the Modern Synthesis. This is the sort of thing I would like to see developed, for better or worse.mike1962_{November 7, 2011
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Hi Barry, Glad you liked it.vjtorley_{November 7, 2011
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Hi tjguy, Thank you for your post. I take your point that evolution has not been demonstrated to occur on a large scale - say, at the level of the family. As for alternative explanations: the piece of evidence in favor of evolution which I find most compelling is the existence of nested hierarchies. Design by a Creator does not necessitate the existence of such hierarchies, and it seems that common descent is the only thing that does necessitate them, so I tend to take these hierarchies as powerful provisional evidence for the fact that living things sprang from a common stock. I should add that the massive input of information by a Designer from time to time could be regarded as an act of creation, using the term broadly: it's certainly an intelligent act.vjtorley_{November 7, 2011
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I seldom have time to post on other blogs, I’m afraid, but thanks for the offer, anyway.
No problem, I just thought you should have the link. There might be some interesting comments.
Except that Professor Chaitin himself doesn’t see it that way. In his paper, Life as Evolving Software, he candidly remarks:
In this connection, note that there are two uses of oracles in this theory, one to decide which of two organisms is better, and another to eliminate non-terminating mutations. It is perfectly ne for a proof to be based on taking advantage of the oracle for organisms, but taking advantage of the oracle for mutations is questionable. (Bold emphasis mine.)

Yes, it is most definitely questionable. That's another reason it's not a very good model. Although I don't think his terminology is very good - in both cases, he's using the oracle on the phenotype (the organism) but in the first case he's comparing how good they are at doing something, and in the second he's dumping them if they don't halt. He's not actually using the oracle (as I see it) to reject mutations, but certain phenotypes. So essentially, he's got two criteria in his fitness function: does it perform at all? Does it perform better than its parent? But it's difficult to map his model on to biology because it's not a population model. Tierra, in contrast (and AVIDA for that matter) is much better.
So my answer to your Darwinian “oracle” is that it is insufficient. An organism’s reproductive success doesn’t guarantee that it is capable of continuing to evolve. It might get stuck in a “same ol’ same ol’” groove, where it is no longer capable of evolving into anything different.
And here we hit the same problem: organisms don't evolve, populations do. That's my main problem with Chaitin's paper, although it's certainly interesting. But when he appears to "prove Darwinism", and you all start trying to pick holes in it, remember that it was us Darwinists that picked the holes first :D Yes, populations sometimes get "stuck in a “same ol’ same ol’” groove", because they have "found" a niche in which they fit. But subpopulations frequently move off that groove, and there's nothing to stop them doing so, if they turn out to be capable of increasing in fitness along another dimension. It's the high-dimensionedness of fitness space that provides the density of networks along which populations and sub-populations can evolve. Interestingly, in Tierra, there is no externally provided fitness function at all - the environment is, simply, the virtual environment, including whatever it happens to find on the computer it happens to inhabit. Ray talks about his virtual organisms evolving to take advantage of night-time reproduction, as people are less likely to be using their computers for other operations then. He deliberately set out not to try to "guide" his organisms, but to set them loose in the fairly rich environment of interlinked computers.
Uh, no. The data strongly support the hypothesis that life evolved in the time available, by some method. However, the data do not tell us that this evolution was entirely or even predominantly Darwinian.
Well, not definitively - they can't. But they strongly support the hypothesis I would say.
I might add that your willingness to continue believing Darwinian evolution, “[i]n the absence of compelling evidence that it could not have done” the job of producing the life-forms we see on Earth today (emphasis mine) is setting the epistemic bar rather too high, in my opinion. Why the overwhelming presumption in favor of Darwinism? Wouldn’t the balance of probabilities be a better way to decide the issue?
Well, only if we had a competing hypothesis with which to compare datafit. ID doesn't do that job because (and I expect to be howled down by this) it could explain anything. What I find compelling about Darwinian evolutionary theory is that it not only explains what we do see but what we don't. We can also of course see it happening in real time (as in "microevolution", as well as a substantial amount of data linking genetics to selectable phenotypic traits, and congruence between genetic and phenotypic phylogenies. On the other hand, I have to repeat: we have no good reason (that I have been persuaded of) to think that what we observe happening in real time won't also happen over extended time. You mentioned that "current models" suggest there isn't enough time - what models were you referring to?Elizabeth Liddle_{November 7, 2011
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"1 We are now able to show that random evolution will become cumulative and will reach fitness BB(N) in time that grows roughly as N2, so that random evolution behaves much more like intelligent design than it does like exhaustive search."
Right. That *is* interesting. He also says at 42:38 that he doesn't have a lower bound and that he would like to prove the random search is indeed slower than the ID search. (43:20) Then he goes on to quote his friend who "doesn't like Darwinian evolution" saying "it's much too slow to justify Darwinian evolution on earth" given the time frame unless it's basically "linear" since the human genome is roughly 6x10^9 bits. About that he says, "he has a point, he has a point."mike1962_{November 7, 2011
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Before I address your comments, let’s step back and ask ourselves: why does Professor Chaitin employ the “obscure mathematical objects” you mention in your post?
Probably because that's his "thing". Chaitin has been constructing obscure mathematical objects throughout his professional life. Some of it is controversial. For example, Torkel Franzen (an expert in Godel's incompleteness work until Franzen's untimely death) has been very critical of Chaitan writings about incompleteness.
There is no population, there is no environment, there is no competition… [but] it’ll evolve anyway.
(That's from your quote of Chaitan). Darwinism is all about adaptation of a population to the environment under the pressure of competition. Chaitin has removed everything Darwinian from that. He is, instead, constructing a combinatorial system to investigate what can result from the combinatorics alone without the Darwinian processes. It might turn out to be interesting and useful. But it has nothing to do with biological evolution, and it is unlikely to be relevant to the debates over ID.Neil Rickert_{November 7, 2011
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Hi johnnyb, Thank you for your very helpful comments. I can see that you are thoroughly familiar with the strengths and weaknesses of the various models of evolution, which I am not. I'm afraid I know little about Avida. I just wish someone would explain it to me as clearly as Professor Chaitin explained his model. I do think you made a very persuasive point about the need for a toy model of evolution to incorporate death. That certainly is a pretty fundamental feature of biological life. I wonder if there's any possibility in the future of constructing a hybrid model which combines the best features of Professor Chaitin's model with those of other models, such as Avida. That would be interesting.vjtorley_{November 7, 2011
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Petrushka, Good question. I think it has to do with terra-forming: extinction events are bloody, but they also help prepare the earth for the next phase in the evolution of complex life. In a nutshell, the early Earth was extremely inhospitable to complex life, and it had to go through a number of environmental transformations before it could develop stable feedback systems and cycles that could support complex life-forms. A process like that necessarily takes billions of years, I believe: even a Deity couldn't possibly do it faster, if He wanted an Earth capable of supporting complex life without the need for massive continual intervention. Intelligent Design does not require that kind of intervention. It requires the production of proteins at the dawn of life, and of the first living cell, as well as production of fundamental body plans, as well as each of the various families that have existed during the history of life on Earth (I'm assuming here that the family represents the approximate "edge of evolution"). If you're a front-loader, you're free to believe that all this was accomplished by fine-tuning the Big Bang to produce these results billions of years later. If that scenario strikes you as implausible, consider this: there are probably no more than 100,000 families of organisms that have existed during the four-billion-year history of life. That's one new family of organisms produced by the Designer every 40,000 years. That's hardly massive intervention, although at various times (e.g. after the Permian extinction) the frequency of intervention would of course have been somewhat greater.vjtorley_{November 7, 2011
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Well, I meant that mathematicians prove things. Scientists don't. But a mathematical proof of Darwinian processes would be quite cool. Interesting that in his paper he says:
This paper advances beyond the previous work on metabiology [10, 11, 12] by proposing a better concept of mutation. Instead of changing, deleting or inserting one or more adjacent bits in a binary program, we now have high-level mutations: we can use an arbitrary algorithm M to map the organism A into the mutated organism A0 = M(A). Furthermore, the probability of the mutation M is now furnished by algorithmic information theory: it depends on the size in bits of the self-delimiting program for M. It is very important that we now have a natural, universal probability distribution on the space of all possible mutations, and that this is such a rich space. Using this new notion of mutation, these much more powerful mutations,enables us to accomplish the following: 1 We are now able to show that random evolution will become cumulative and will reach fitness BB(N) in time that grows roughly as N2, so that random evolution behaves much more like intelligent design than it does like exhaustive search. 2 We also have a version of our model in which we can show that hierarchical structure will evolve, a conspicuous feature of biological organisms that previously [10] was beyond our reach.
(my bold)Elizabeth Liddle_{November 7, 2011
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Hi Elizabeth, I seldom have time to post on other blogs, I'm afraid, but thanks for the offer, anyway. Thank you for accepting my challenge. Regarding question 1 (does Darwinism smuggle in a Designer via the back door?), you argue that the "oracle" in nature is, simply, the environment, and you add: "It only has to be an 'oracle' in a computer simulation, because you need to model the role the environment plays in nature." No problem for Darwinism, it seems. Except that Professor Chaitin himself doesn't see it that way. In his paper, Life as Evolving Software, he candidly remarks:
In this connection, note that there are two uses of oracles in this theory, one to decide which of two organisms is better, and another to eliminate non-terminating mutations. It is perfectly ne for a proof to be based on taking advantage of the oracle for organisms, but taking advantage of the oracle for mutations is questionable. (Bold emphasis mine.)
In this connection, I'd like to reiterate a point I made earlier, in reply to dmullenix above:
But survival and reproduction are not the problems that Professor Chaitin is worried about. What worries him most is stagnation. As he puts it:
I don't want evolution to stagnate, because as a pure mathematician, if the system evolves and it stops evolving, that's like it never evolved at all... I want to prove that evolution can go on forever.
So my answer to your Darwinian "oracle" is that it is insufficient. An organism's reproductive success doesn't guarantee that it is capable of continuing to evolve. It might get stuck in a "same ol' same ol'" groove, where it is no longer capable of evolving into anything different.
So I have to say I am skeptical of claims that Darwinian evolution doesn't require a Designer. Regarding question 2 (can Darwinian evolution work in the time available?) you write:
...[W]e can demonstrate that the system works, and that the data support the hypothesis that it did so in the time available. In the absence of compelling evidence that it could not have done, I don't see the problem.
Uh, no. The data strongly support the hypothesis that life evolved in the time available, by some method. However, the data do not tell us that this evolution was entirely or even predominantly Darwinian. I might add that your willingness to continue believing Darwinian evolution, "[i]n the absence of compelling evidence that it could not have done" the job of producing the life-forms we see on Earth today (emphasis mine) is setting the epistemic bar rather too high, in my opinion. Why the overwhelming presumption in favor of Darwinism? Wouldn't the balance of probabilities be a better way to decide the issue? Over to you.vjtorley_{November 7, 2011
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It's good sense for you.mike1962_{November 7, 2011
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More than that. You need a self-replicator that is stable, and that can self-program itself with greater complex function.mike1962_{November 7, 2011
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Well, that's mathematicians for you.Elizabeth Liddle_{November 7, 2011
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Hi Barb, Thank you for your post. I too was immensely heartened to see Professor Chaitin referring to DNA as a universal programming language. And I notice that Chaitin says this about his model: "This model does not talk about the origin of life, because I already have a universal programming language here at the beginning." It was very honest of him to point that out, I thought.vjtorley_{November 7, 2011
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At 17:53 : "the simplest thing that PROVABLY evolves according to Darwin's theory" in contradistinction to actual lifeforms. Hehemike1962_{November 7, 2011
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They are self-programming algorithms. But sure, you need a minimal self-replicator to start with.Elizabeth Liddle_{November 7, 2011
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