At last, a Darwinist mathematician tells the truth about evolution

_{Vincent Torley

November 6, 2011

Intelligent Design}

Share: Facebook; Twitter; LinkedIn; Flipboard; Print; Email

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

I agree. It is great to see honest scientists like him out there. On the one hand, all it takes as far as scientific ethics is concerned, is openness and willingness to seek scientific truth. And yet there are many scientists who don't have these qualities.Eugene S_{November 14, 2011
November
11
Nov
14
14
2011
05:53 AM
5
05
53
AM
PST}

Yet there aren't any free-living things without DNA in it. So those "investigators" you are alleging need something to support their position.Joseph_{November 14, 2011
November
11
Nov
14
14
2011
04:48 AM
4
04
48
AM
PST}

I think he proved there that he's not involved in OOL studies. I don't know of a single investigator that believes the first living thing had DNA in it.dmullenix_{November 14, 2011
November
11
Nov
14
14
2011
04:42 AM
4
04
42
AM
PST}

One more VJ. Dr. Walter Remine wrote a book entitled The Biotic MEssage. In that book he has a section where he takes on the idea of nested hierarchies as evidence for common descent. He shows how it can also be viewed as evidence for creation. If you have a chance to look at that book, you might enjoy that section.tjguy_{November 10, 2011
November
11
Nov
10
10
2011
09:07 PM
9
09
07
PM
PST}

Of which algorithms do you speak?ciphertext_{November 10, 2011
November
11
Nov
10
10
2011
10:27 AM
10
10
27
AM
PST}

Again, you seem to be confused as to the oracle function of the oracle. As already discussed, the second oracle's function is to determine which is faster, A or A'. In the real world Time makes this determines, but for very practical reasons, Chaitin doesn't want to run the simulation on a 1:1 time scale. And that's one of the benefits of running a simulation is that you can compress some of the variables down to a smaller, more managable scale. Likewise for the first oracle's function, the halting-complete determination. Without this "cheat", the simulation would calculate the mutated algorithm (A') with the very real possibility of getting caught in a loop. THIS IS NOT EQUIVALENT TO STAGNATION. Stagnation in Chaitin's model would be a state in which every forthcoming generation, A' would be functionally equivalent to its parent, A. Please note; the oracles do not prevent this from happening in the simulation. A real-world analogy of the non-halting problem (the kind that would appear in Chaitin's model) would be a cell that lived forever and never reproduced - a true failure in a multiple generation study because 1) the simulation would hang, and 2) there is no real-world counterpart to these "immortal virgins". Again, the simulation does not care if it encounters evolutionary progression, regression, or stagnation, only that the simulation comes to a pre-programmed end.rhampton7_{November 9, 2011
November
11
Nov
9
09
2011
10:36 PM
10
10
36
PM
PST}

Hi vjtorley, First, I apologize for my previous comment because I think you were actually talking about Chaitin's model rather than what occurs in nature (that's what I get for skimming). However, now that you've actually addressed what happens in nature, namely your comment:
Some readers have proposed that they stopped evolving because their environments stopped changing, but in view of what has happened to our Earth in the past 250 million years (think Permian and Cretaceous extinctions), I find this wildly implausible.
This doesn't make sense to me. If a species is adapted to it's environment and that environment changes, then the species must change, or go extinct. Thus, if we see a species that has shown a long period of stasis (i.e. fossil forms are exactly like extant forms) then we can conclude that their environment, for the most part, has remained stable over their history. Also, consider that a preferred environment might be quite localized. For a given environment/habitat to last hundreds of millions of years doesn't seem such a stretch to me. Especially ocean environments, which can be stable over very long periods (e.g. deep sea hydrothermal vent habitats, which may have been around for billions of years).NormO_{November 9, 2011
November
11
Nov
9
09
2011
02:57 PM
2
02
57
PM
PST}

rhampton7 and NormO Thank you for your comments, and for the explanation of the function of the Turing oracle in Chaitin's program. Before I reply in detail, I'd just like to cite a brief excerpt from Professor Chaitin's talk:
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.
The general philosophical point I want to make here is that if you're trying to show that unguided Darwinian evolution can work, then it's illicit to do so by creating a program which requires guidance in the form of a Turing oracle in order for it to continue. The second point I want to make is that there is no guarantee that evolution in the real world does not halt. I mentioned the horseshoe crab and coelacanth above. Some readers have proposed that they stopped evolving because their environments stopped changing, but in view of what has happened to our Earth in the past 250 million years (think Permian and Cretaceous extinctions), I find this wildly implausible. These creatures cannot evolve any further, it seems, without falling off their fitness peak. They just happen to be flexible enough to have survived the massive environmental transformations that they have experienced in the past millions of years. Finally, rhampton7, I noticed that you wrote:
... in Chaitin’s toy model, the program does not bother to evaluate the fitness of a uniquely evolved algorithm unless it first knows said algorithm will halt once run. In other words, reproduction doesn’t occur unless a particular living descendent is proven to be mortal, so an immortal being never gets to reproduce.
but also
The oracle does not determine nor care what fate may befall future generations.
Well, which is it? Does the program care about the future or not?vjtorley_{November 9, 2011
November
11
Nov
9
09
2011
02:03 PM
2
02
03
PM
PST}

The question isn't did the impact cause the extinction. The questions are: 1. Did the Designer cause the impact to happen? 2. What was the impact's effect on the Design? If front-loading, how did the Designer front-load which species would survive and re-radiate to fill the empty ecological niches? 65MYA is a very long time before anything even remotely resembling a modern human is seen. If not, when/how did the Designer intervene after the impact?GinoB_{November 9, 2011
November
11
Nov
9
09
2011
12:26 PM
12
12
26
PM
PST}

Right- the design isn't going the way the designer(s) thought so they changed it up a bit.Joseph_{November 9, 2011
November
11
Nov
9
09
2011
10:47 AM
10
10
47
AM
PST}

But, but if that impactor caused the extinction then there would be dinosaur fossils littering the KT boundary and layer right above it. Yet we only have dino fossils BELOW the KT- and that should tell anyone with any thinking ability that the alleged impactor was not the cause of the extinction.Joseph_{November 9, 2011
November
11
Nov
9
09
2011
10:46 AM
10
10
46
AM
PST}

The problem, as I see it, is that an organism’s evolution might get stuck at a point where the organism might be incapable of evolving any further.
You have mistaken what the experiment demonstrates. The oracle determines if a given mutated algorithm is halting complete - that is, determines if one particular living descendent is effectively immortal. This is necessary because in Chaitin's toy model, the program does not bother to evaluate the fitness of a uniquely evolved algorithm unless it first knows said algorithm will halt once run. In other words, reproduction doesn't occur unless a particular living descendent is proven to be mortal, so an immortal being never gets to reproduce. [That's why I believe the algorithm is representative of the reproductive cycle] The oracle does not determine nor care what fate may befall future generations. That an algorithm may become "stuck" is exactly why the experiment exists, what Chaitin hopes to discover, not something to be avoided: can life evolve?rhampton7_{November 8, 2011
November
11
Nov
8
08
2011
05:34 PM
5
05
34
PM
PST}

What is ID's position on the 10km wide asteroid that struck the Earth 65 MYA and is thought to have caused the KT extinction? Was the Deity responsible? Did the Deity intervene after that impact? How can you tell?GinoB_{November 8, 2011
November
11
Nov
8
08
2011
04:28 PM
4
04
28
PM
PST}

So extinction events are part of the design as well?paragwinn_{November 8, 2011
November
11
Nov
8
08
2011
04:21 PM
4
04
21
PM
PST}

Or like Legos, Tinkertoys and Lincoln Logs with their ability to take themselves apart.paragwinn_{November 8, 2011
November
11
Nov
8
08
2011
04:19 PM
4
04
19
PM
PST}

vjtorley: I wasn't actually implying that God is irreducible mathematical complexity. Rather, I simply was trying to point out that the description Chaitin gives of the Oracle that sorts out the halting problem sounds like what believers would think of as God. Actually, I think Chaitin has put his finger onto something. It seems to me that what Chaitin said, and the way in which he said it, suggests that there must be some Mind that has to figure out all the historical contingencies that could ever actuate themselves. That's why I said the Oracle was "omniscient". When you consider, e.g., protein domains, and how they MUST arise, the only way in which this could happen is by a Mind already having explored the entire space of possible protein configurations, and then slicing out an infinitely small portion of these possible configurations to serve a particular function. This seems to me to approach "figur[ing] out all the historical contingencies that could ever actuate themselves." (quoting myself here) Be assured; I'm not a pan-theist. I don't believe in Gaia! ;)PaV_{November 8, 2011
November
11
Nov
8
08
2011
02:55 PM
2
02
55
PM
PST}

Dr. Torley, I don't know if this is completely relevant, but since it is basically a mathematical exercise of ascertaining the possibility of 'unlimited evolution', that Chaitin is doing with his 'toy model', I think it is of importance to note the following:
THE GOD OF THE MATHEMATICIANS - DAVID P. GOLDMAN - August 2010 Excerpt: It was Gödel and, later, Paul Cohen who demonstrated respectively that Cantor’s continuum hypothesis could be neither proved nor disproved within existing set theory. Indeed, Cantor’s hypothesis remains maddeningly undecidable. Intuition, added Gödel, strongly suggests that Cantor’s hypothesis is wrong: Among the infinite number of transfinite numbers, there are an infinite number of cardinalities between the integers and the points on the continuum line, and mathematical investigation of the infinite will remain infinitely fruitful. God’s infinitude remains safe in heaven. Mathematicians have proven that an infinite number of transfinite numbers exist but cannot tell what they are or in what order they should be arranged. Gödel noted drily that this represents a problem for philosophy and epistemology rather than for mathematics, which can continue its investigations without ever exhausting the subject. Gödel’s result shows that not even in terms of numbers, the simplest objects we can specify, can natura naturans explain the individuality that we observe. The parallel between Gödel’s attack on the continuum hypothesis and Leibniz’ critique of Spinoza is very strong, and it is remarkable that both hinged on foundational insights into number theory. Whether or not we believe, as did Gödel, in Leibniz’ God, we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel’s critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. There is yet a third place where Kurt Gödel’s mathematical work has theological purchase: in Einstein’s failure to reconcile the deterministic world of general relativity with the probabilistic world of quantum mechanics. Einstein famously declared his belief in “Spinoza’s God”: a god, that is, who is indistinguishable from nature and who reveals himself through natural harmonies. Einstein, we might say, was a “strong Platonist” who actually believed that if one discovers the eternal forms to which natural phenomena correspond, all the world’s mystery will yield itself up to science. The often noted problem is that the intuitively intelligible world Einstein created with the deterministic equations of general relativity jars with the probabilistic world of modern quantum mechanics. Einstein and Gödel were close friends, but they disagreed profoundly on religious and philosophical matters. As Gödel told Hao Wang, “Einstein’s religion [was] more abstract, like Spinoza and Indian philosophy. Spinoza’s god is less than a person; mine is more than a person; because God can play the role of a person.” http://www.faqs.org/periodicals/201008/2080027241.html
And indeed Godel has been vindicated in his disagreement with Einstein:
The Cauchy Problem In General Relativity - Igor Rodnianski Excerpt: 2.2 Large Data Problem In General Relativity - While the result of Choquet-Bruhat and its subsequent refinements guarantee the existence and uniqueness of a (maximal) Cauchy development, they provide no information about its geodesic completeness and thus, in the language of partial differential equations, constitutes a local existence. ,,, More generally, there are a number of conditions that will guarantee the space-time will be geodesically incomplete.,,, In the language of partial differential equations this means an impossibility of a large data global existence result for all initial data in General Relativity. http://www.icm2006.org/proceedings/Vol_III/contents/ICM_Vol_3_22.pdf
bornagain77_{November 8, 2011
November
11
Nov
8
08
2011
02:39 PM
2
02
39
PM
PST}

vjtorley:
The problem, as I see it, is that an organism’s evolution might get stuck at a point where the organism might be incapable of evolving any further. I suggested above that the horseshoe crab might be an example of such an organism. The coelacanth would be another.
It's not the organism (or population) that gets "stuck" and can't evolve any further, it's the environment (both biological and physical characteristics) remaining static over long periods of time, which leads to stabilising selection that results in phenotypic stasis over long periods. Rapid phenotypic change (i.e. speciation) occurs in isolated populations experiencing environmental change. For example, the formation of the Great Rift Valley in East Africa is associated with numerous environmental changes and habitat fragmentation that is thought to have "driven" (short-hand!) the speciation of early hominids.NormO_{November 8, 2011
November
11
Nov
8
08
2011
02:16 PM
2
02
16
PM
PST}

rhampton7, Thanks for your very thoughtful reply. I'm inclined to think you're right in saying that Time would solve the first problem you mention, of comparing the fitness of two organisms. You then suggest that entropy solves Chaitin's second problem (non-halting) in the real world, thus dispensing with the need for an oracle. I'm not so sure. The universe takes a very very long time to run down, so that's not a practicable solution in the short-term. The problem, as I see it, is that an organism's evolution might get stuck at a point where the organism might be incapable of evolving any further. I suggested above that the horseshoe crab might be an example of such an organism. The coelacanth would be another. For all we know, there may be many more such organisms, and it is surely a contingent fact that most of the organisms in our biosphere are capable of evolving for billions of years. We could have been a lot less lucky. Finally, with respect to mutations, I was intrigued by what Professor Chaitin had to say about them in his talk, where he describes his modeling:
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.
I'd be intrigued to know if there's any evidence of such mutations occurring in the real world. I'm also intrigued by the remark in Chaitin's paper:
Presumably DNA is a universal programming language, but how sophisticated can mutations be in actual biological organisms? In this connection, note that evo-devo views DNA as software for constructing the embryo, and that the change from single-celled to multicellular organisms is roughly like taking a main program and making it into a subroutine, which is a fairly high-level mutation. Could this be the reason that it took so long – on the order of 10^9 years – for this to happen?
In order to dispense with the need for a Designer in evolution, Chaitin would need to show that these powerful mutations can occur naturally, even in a "blind" system lacking foresight. At the present time, such a demonstration is lacking - which is another reason to doubt Darwinism as an explanation.vjtorley_{November 8, 2011
November
11
Nov
8
08
2011
01:54 PM
1
01
54
PM
PST}

Hi PaV, I was intrigued by your remarks on infinite irreducible complexity. I would certainly agree that the presence of this kind of complexity in Nature could only be explained by postulating an Infinite Intelligence - i.e. what everyone would call God. Incidentally, I remember reading something by either Elsberry or Shallit, to the effect that for all we know the fine structure constant alpha may turn out to possess an infinite Kolmogorov complexity. There's just one thing I'd like to point out, though, and that is that according to traditional classical theism, God Himself cannot be synonymous with infinite irreducible complexity, as God is conceived of as simple in His essence. The argument is that anything composite is contingent and therefore not God. Is this argument a demonstrative one? I don't think so. Personally I'm happy to accept the traditional doctrine that God is simple in His essence, but as a matter of strict logic, I should point out that the argument assumes that anything composed of parts is separable. What if the parts are not just physically but metaphysically inseparable - like right and left - so that you can't have one without the other? Then the whole wouldn't be contingent, after all. One could refer to the kind of irreducible complexity in which the parts are metaphysically inseparable as integrated complexity, and it would be a special case of irreducible complexity. So the question then arises: could there be a Being which possesses the property of infinite integrated complexity? I don't know.vjtorley_{November 8, 2011
November
11
Nov
8
08
2011
01:34 PM
1
01
34
PM
PST}

vj, Here is an interesting article that questions the whole idea of Darwin's Tree of Life. I'll copy the first part and if you are interested in looking at the rest, I'll give the website. Any comments would be appreciated - if you have time. Darwin’s “Tree of Life” is a myth. It’s based on circular reasoning. It is a pattern imposed on the data, not a fact emerging from the evidence. We should give up the search for a single tree of life (TOL) as a record of the history of life on earth, because it is a “quixotic pursuit” unlikely to succeed – and the evidence is against it. Who said this? Not creationists, but a new member of the National Academy of Sciences in his inaugural paper for the academy’s Proceedings.1 W. Ford Doolittle and Eric Bapteste decided to celebrate this inauguration with fireworks. What they wrote is less a scientific paper than a reprimand. They let Darwin-lovers have it between the eyes: "Darwin claimed that a unique inclusively hierarchical pattern of relationships between all organisms based on their similarities and differences [the Tree of Life (TOL)] was a fact of nature, for which evolution, and in particular a branching process of descent with modification, was the explanation. However, there is no independent evidence that the natural order is an inclusive hierarchy, and incorporation of prokaryotes into the TOL is especially problematic. The only data sets from which we might construct a universal hierarchy including prokaryotes, the sequences of genes, often disagree and can seldom be proven to agree...." http://crev.info/content/darwinists_topple_darwin146s_tree_of_life tjtjguy_{November 8, 2011
November
11
Nov
8
08
2011
05:03 AM
5
05
03
AM
PST}

Thanks VJ for your note. So for you the clincher is the existence of nested hierarchies? Isn’t that an ever-changing and very opinionated branch of science? Wasn’t it Linnaeus, a true creationist by the way, who, back in the pre-Darwin era, first classified things according to nested hierarchies? If so, that idea didn’t seem to present a problem for his creationist views. Isn’t it a bit difficult for us to say how the Creator did or should have created life/living things with much accuracy and conviction? Perhaps it would be your opinion that God would not have used nested hierarchies, but rather than guess about that, I guess I prefer to take Him at His Word where He actually tells us how He created. I think it is very possible that the Creator would use the same excellent design over and over. At the least, I think you would grant that as a possibility. Isn’t it true that as more and more morphological details are considered, it usually becomes harder and harder for evolutionists to decide which feature is the result of presumed shared ancestry and which is supposedly independently derived? Aren’t there many such traits that do not fit the pattern of a nested hierarchy? For instance, what about when the same trait appears in living things which are not believed to be closely related by evolution? This is not a rare thing. When we try and reconstruct the past like this, there is so much interpretation going on that it doesn’t seem all that certain or even scientific to me. Isn’t it true that a lot of assumed nested hierarchies have been overturned as more information came to light? One instance of that would be that mesonychians and cetaceans were long believed to be sister groups based on a closely knit series of shared similarities, but this pattern is now no longer believed to indicate a close evolutionary relationship. Given the large amount of personal opinion and interpretation that is behind the idea of Darwin’s Tree and nested hierarchies, it all seems very unstable and unscientific to me. Perhaps a nested hierarchy might do well at characterizing living things when viewed in terms of general similarities and differences, but do these hierarchies really exist or are they accurate when large numbers of detailed morphological similarities and differences are simultaneously considered? I doubt it. Just curious, but what particular examples of nested hierarchy are particularly impressive to you? TJtjguy_{November 8, 2011
November
11
Nov
8
08
2011
04:46 AM
4
04
46
AM
PST}

vjt: “If you’re going to mathematically define the simplest kind of thing for which Darwinian evolution can be proven to work…” 1: Chaitin’s program doesn’t use anything like Darwinian Evolution. He’s using a SINGLE program where evolution REQUIRES a population. (Either that or some sort of KF-style latching, which doesn’t exist in the real world.) 2: The program he uses needs an intelligent agent to see if it halts. One of Turing’s great discoveries was that there is no mechanical way to prove that a program will halt. DE doesn’t have that problem. Every organism eventually halts, what counts is passing on the genes before that happens. 3: Chaitin seems to need an intelligent agent to see if the new program is better than the original. DE doesn’t need that because improved organisms tend to increase their percentage of the population. vjt: “So here’s my point. If even the simplest kind of mathematical life-form designed to show the possibility of Darwinian evolution requires intelligent guidance (i.e. a Turing oracle) to enable it to evolve, and biological life-forms are a lot more complicated than these software life-forms, then shouldn’t it be all the more difficult for biological life-forms to continue evolving, without the need for intelligent guidance? “ Chaitin isn’t using anything remotely like Darwinian evolution, which never uses an oracle, yet you’re drawing conclusions about DE from it. And his divergences from DE are critical. I have no problems with the lack of a body, but a POPULATION of evolving organisms is critical. vjt: “survival and reproduction are not the problems that Professor Chaitin is worried about. What worries him most is stagnation.” …” (I wonder if that’s what happened to horseshoe crabs, which haven’t changed for hundreds of millions of years?)” Everybody understands that the horseshoe crabs that are alive today are different species from the ones that lived 400 million years ago, right? Considering the billions of years that life has been evolving and the fantastic array of living creatures alive today (and the much larger numbers of extinct creatures that used to be alive) I don’t think that stagnation is any problem. You might get your occasional horseshoe crab or coelacanth that lucks onto a good design and stays in an environment that doesn’t change much, but the rest of the life on earth continues to evolve away. For that matter does everybody understand that the only way evolution CAN stagnate is if all mutations cease? And that’s never going to happen? The takeaway here is that Chaitin has ginned up a system that departs radically from Darwinian evolution. He may or may not be able to get some useful knowledge from it about stagnation – but it’s almost impossible for DE to stagnate in the first place so who cares? Meanwhile, the UD readers are mistakenly drawing completely inappropriate conclusions about Darwinian evolution from his example.dmullenix_{November 8, 2011
November
11
Nov
8
08
2011
04:42 AM
4
04
42
AM
PST}

vjtorley: "You sneer at George Gilder for quoting John 1:1 – “In the beginning was the Word” – because the Word is totally unembodied. But comparing that to Professor Chaitin’s “toy life” is beside the point. The Word doesn’t evolve, and nobody ever said it did. Toy life, on the other hand, does evolve." ==== Sneer ??? No I loved George Gilder's take on information and John 1:1. Interestingly I don't find much reference to him anymore. Not sure even just how religious he really is. But his take actually brought together for me personally some other scriptural references that made perfect sense in cross referencing. Colossians 1:15 & Proverbs 8:22-30 The expression, "In the beginning" is referencing a time before anything else was created, heaven or earth. We know of Christ's title as the 'Word' as representing God's spokesman to all other intelligent creation, again to both spirit and human. Yet, "In the beginning", neither intelligent creation had been as yet created in either the spirit realm or physical realm. So what was that information which existed "In the beginning" ??? I also like his references to heirachal structure which is found in nature for which information controls everything that happens, but also the fact that in real life we all understand that information itself is immaterial and is subject to it's creator.Eocene_{November 8, 2011
November
11
Nov
8
08
2011
01:43 AM
1
01
43
AM
PST}

vjtorley, In Chaitin's "toy model" (which is his term for the simplest mathematical representation of a self-evolving mathematical problem solver) the oracle's role has two functions: first, to determine if A or its mutated offspring A' grows faster (a substitution for natural selection); second, to determine if A' will eventually halt (otherwise the simulation would to hang). But remember, the model is only an analogy. Life does not need an intelligent oracle to fulfill Chaitin's two functions. In the first instance, Time evaluates the answers: which is faster A or A'. In the second instance, a non-halting problem is conveniently avoided because entropy prevents all biology (that we know of) from operating eternally. And although Chaitin hasn't said specifically what the problem solving portion of his toy model represents, I suspect it's the ability to reproduce. If the self-evolving algorithm halts, it successfully reproduces (allowing the next step, the fitness of A' to be tested), but if it algorithm doesn't halts, then it fails to reproduce (A' is rejected before its fitness can be tested - equivalent to a cell's failure to split.) But at least you're willing to listen to Chaitin's arguments. As you know, he believes he has demonstrated that:
This paper advances beyond the previous work on metabiology 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 A' = 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: * We are now able to show that random evolution will become cumulative and will reach fitness BB(N) in time that grows roughly as N^2, so that random evolution behaves much more like intelligent design than it does like exhaustive search. * 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 was beyond our reach.
rhampton7_{November 7, 2011
November
11
Nov
7
07
2011
08:40 PM
8
08
40
PM
PST}

Yes, that was surprisingly honest. I've often wondered why Darwin bothered with naming his book "the origin" of species, when it primarily discusses their adaptation over time rather than worry about where they came from in the first place.Barb_{November 7, 2011
November
11
Nov
7
07
2011
06:01 PM
6
06
01
PM
PST}

PaV, as you suggested earlier, I hope 'some smart, informed, people here at UD', step up to solidify what seems so obvious from Chaitin. It would would be a extremely neat little piece of confirmatory evidence, for Dembski's COI, from a antagonistic, yet brilliant, Darwinian mathematician no less! :)bornagain77_{November 7, 2011
November
11
Nov
7
07
2011
05:52 PM
5
05
52
PM
PST}

dullmenix:
Says who? Not professor Chaitin. He’s generating some sort of obscure mathematical object which he apparently can’t easily evaluate, so he uses an “oracle”.Darwinian evolution has a better “oracle”. It tries to build and run the new organism with its new DNA. If it survives to reproduce, the “oracle’s” answer is “Yes.”
Did you miss this part of vjtorley's post? Chaitin speaking: 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. That's, theoretically, what makes Chaitin's model significant. But, of course, it needs not one, but two oracles to keep evolution going. And one of the oracles needs an infinite level of irreducible mathematical complexity. How easy it is to say things such as: Darwinian evolution has a better "oracle". But what does this mean, exactly? It's pure metaphor. English majors need not apply here.PaV_{November 7, 2011
November
11
Nov
7
07
2011
05:07 PM
5
05
07
PM
PST}

bornagain77: I think this is the somewhat hidden assumption. However, I first looked at the paper, and then looked at what vjtorley posted from Chaitin's talk. I think Chaitin is straight-up about talking about this need for an oracle. And I think vjtorley is quite correct in making that same assessment of the need, basically, for an Intelligent Designer. Yet, we know that the obfuscations will begin.PaV_{November 7, 2011
November
11
Nov
7
07
2011
04:52 PM
4
04
52
PM
PST}

of related note: I see nothing in Chaitin's 'toy' that is in conflict with the work that Dr Dembski and Marks have already established, in fact I would say it is fairly strong confirmation:
LIFE’S CONSERVATION LAW - William Dembski - Robert Marks - Pg. 13 Excerpt: Simulations such as Dawkins’s WEASEL, Adami’s AVIDA, Ray’s Tierra, and Schneider’s ev appear to support Darwinian evolution, but only for lack of clear accounting practices that track the information smuggled into them.,,, Information does not magically materialize. It can be created by intelligence or it can be shunted around by natural forces. But natural forces, and Darwinian processes in particular, do not create information. Active information enables us to see why this is the case. http://evoinfo.org/publications/lifes-conservation-law/ Evolutionary Synthesis of Nand Logic: Dissecting a Digital Organism - Dembski - Marks - Dec. 2009 Excerpt: The effectiveness of a given algorithm can be measured by the active information introduced to the search. We illustrate this by identifying sources of active information in Avida, a software program designed to search for logic functions using nand gates. Avida uses stair step active information by rewarding logic functions using a smaller number of nands to construct functions requiring more. Removing stair steps deteriorates Avida’s performance while removing deleterious instructions improves it. http://evoinfo.org/publications/evolutionary-synthesis-of-nand-logic-avida/
bornagain77_{November 7, 2011
November
11
Nov
7
07
2011
03:47 PM
3
03
47
PM
PST}

1 2 3 Next

You must be logged in to post a comment.

Leave a Reply