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At last, a Darwinist mathematician tells the truth about evolution

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.

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82 Responses to At last, a Darwinist mathematician tells the truth about evolution

  1. VJ,

    I’m currently writing a new software tool for others to use at work. While developing this program I’ve given some thought to the relevance of software design to biological systems. I’ll write an essay for UD entitled Software Design Methodology and Fault Tolerance, as it Relates to Biological Systems.

    Fault tolerance (error trapping and error handling) in software design is something that has not be adequately addressed as it relates to biological systems engineering, in my opinion. Living systems exhibit exquisite error-detection and repair/compensation algorithms (errors not just internally induced, but those resulting from sources outside the system, the analogy being that a software user might choose a pathway through the user interface that was not anticipated by the software engineer, which results in a catastrophic bug).

    In addition to the fault-tolerance issue I’ll address another aspect of software design as it relates to biological systems, which is that in order to give a program a new functional and useful feature (that is, to improve the program’s “viability”), advanced planning is always required. This involves designing subroutines which by themselves provide no useful function, but which must be programmed and debugged before they are finally integrated with multiple interactive calls that provide the final functionality.

  2. VJ, excellent post. Very enlightening. If this shows that evolution could not work on it’s own without an Intelligent Designer, then I wonder why we have to bother trying to uphold the goo to you evolutionary hypothesis at all.

    So I was sorry to see this at the end of your post:

    “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.”

    I disagree with this. I would rephrase it like this: “There is excellent evidence that evolution has occurred, if one simply defines “evolution” as the process as change within original created kinds as genes get shuffled and separated out.” I still don’t see the validity of or necessity of extrapolating from micro-evolution to macro-evolution. There are other ways to explain common homology, etc. The fossils are still missing. Information increasing mutations are still missing. This idea is still does not agree with the Creator’s testimony in His Word.

    “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.”

    True, but it is still nothing more than a proposed model. It is nothing more than one possibility put forth by humans living in the present day.

    If you are going to allow for the role of an Intelligent Designer, then why not also allow for the possibility that the Designer created the universe and life just as He said in His Word – allowing for small changes among the original created kinds, but not for information increasing mutations that change organisms from one kind to another totally different kind. A common Designer explains some of this “evidence” for evolution very well.

  3. 3

    OUTSTANDING!

  4. Chaitin is a truly marvelous character, and I have emailed him on a few occasions. His toy evolutionary model is quite intriguing, though I do not know enough of the deeper parts of algorithmic information theory to comment or criticize. One issue, however, is that Chaitin’s evolutionary model, as I understand it, does not model death adequately. Obviously, it is a toy system, so it cannot model everything. But death/extinction is such a key and powerful part of evolution that it seems difficult to imagine a theory without it.

    As I recall, Chaitin’s model the organism can continue indefinitely, no matter how many times it fails. However, in life, eventually an organism, or a line of organisms, fails, if it does not reach a stable point.

    The other points of his evolutionary system seem rather sound. His system has the following points in its benefit:

    1) The solution space is open-ended, i.e. he is using a Turing-complete language
    2) The problem space is not directly related to the solution space. I.e. it requires complexity to produce a solution to the problem. (the problem is the busy-beaver problem in computer science)
    3) His evolutionary model does capture the idea of random mutations.

    Against his model are the following issues:

    1) the replication loop is not embedded in his organisms. This is one thing I thought Avida did particularly well.
    2) his evolutionary model, because it lacks death, actually doesn’t model natural selection very well. Instead, it does have a slight ring of artificial selection to it. I am not sure how much this affects his conclusions, but it is interesting to note.

    Anyway, Chaitin is first-class in his thinking on this subject.

  5. Dr Torley:

    Excellent job, as usual.

    I make a quick observation from the Chaitin (great mathematician!) paper, p. 1:

    . . . in this paper we present a technical discussion of the mathematics of this new way of thinking about biology. More precisely, we present an information theoretic analysis of Darwin’s theory of evolution, modeled as a hill-climbing algorithm on a fi tness landscape. Our space of possible organisms consists of computer programs, which are subjected to random mutations. We study the random walk of increasing fitness made by a single mutating organism.

    1 –> As a preliminary footnote, those who so stridently objected to my suggestions about hill-climbing in recent days should note that I am clearly in rather good company to view the suggested evolutionary mechanisms in terms of hill-climbing, generally and broadly understood.

    2 –> However, notice the built-in assumption:

    Darwin’s theory of evolution, modeled as a hill-climbing algorithm on a fi tness landscape.

    3 –> In short, all of this is within a frame in which we have existing functionally specific and complex function, and in effect the combination of metabolic, informational macromolecule-driven metabolism and informational macromolecule-driven genetic reproduction.

    4 –> So, this is fundamentally a model of adaptation of an existing body plan, i.e of microevolution, which is not controversial, not even among Young Earth Creationists. (On this, note Behe’s recent rule of thumb about specialisation by throwing away adverse information in a particular present environment; which of course then becomes a bear to recover if one has a new environment. The recent Tomcod studies seem to fit this model. Notice the ones adapted to the toxic environment of was it the Hudson, are not spreading out and dominating the zone around Long Island.)

    5 –> At a deeper level, the underlying issue is origin of main body plans, in a context where functional complexity and specificity, multiplied by the prevalence of irreducible complexity in ever so many functions, makes the islands of function view the most plausible one.

    6 –> That would mean that, first, though the concept presented is that of unlimited variation and “descent” with modification, the context implies that a much more likely outcome is adaptations and variety within islands of function, leading to adaptive radiation of a body plan, but not to the ability to leap from one plan to the next.

    7 –> The first such challenge of course is the first body plan, OOL. In that context, I have argued that the very von Neumann self-replicator mechanism that must be joined to the metabolic system, is functionally specific, code [thus, language . . . ] and algorithm based, and irreducibly complex.

    8 –> In the OOL context as well, the rise of a viable network of metabolic reactions is itself a major chemical engineering challenge, as anyone who has had to analyse the piping and instrument diagram of a fairly complex plant can tell. (Cf. Fig. I.2 here, and note the linked chart of integrated cellular biochemical pathways in the caption to panel b.)

    9 –> When we move up to novel, multicellular, integrated body plans, we have to pass the zygote to embryo to mature body barrier, i.e. the organism must be able to unfold the body plan per regulatory networks, in a context that is again functionally specific, complex, integrated and in many respects irreducibly complex, forming a tightly meshed integrated, interlocking whole.

    10 –> All of which puts the Darwinian tree of life model in the centre of the issues. Unless the OOL challenge can be soundly answered, the DTOL has no viable root, and unless the branching pattern demonstrates a vast continent of life forms traverse-able by a random walk filtered by incremental uphill progress in varied directions, the whole framework becomes deeply questionable.

    11 –> This brings us to the fossil life issue, and the fact that the observed pattern that dominates the record is sudden diversity, stasis and disappearance and/or continuation into the modern world. This, notoriously, Gould acknowledged as a challenge in his last book (2002); building on remarks he had made in the 1970′s:

    . . . long term stasis following geologically abrupt origin of most fossil morphospecies, has always been recognized by professional paleontologists. [[The Structure of Evolutionary Theory (2002), p. 752.]

    . . . . The great majority of species do not show any appreciable evolutionary change at all. These species appear in the section [[first occurrence] without obvious ancestors in the underlying beds, are stable once established and disappear higher up without leaving any descendants.” [[p. 753.]

    . . . . proclamations for the supposed ‘truth’ of gradualism – asserted against every working paleontologist’s knowledge of its rarity – emerged largely from such a restriction of attention to exceedingly rare cases under the false belief that they alone provided a record of evolution at all! The falsification of most ‘textbook classics’ upon restudy only accentuates the fallacy of the ‘case study’ method and its root in prior expectation rather than objective reading of the fossil record. [[p. 773.]

    “The absence of fossil evidence for intermediary stages between major transitions in organic design, indeed our inability, even in our imagination, to construct functional intermediates in many cases, has been a persistent and nagging problem for gradualistic accounts of evolution.” [[Stephen Jay Gould (Professor of Geology and Paleontology, Harvard University), 'Is a new and general theory of evolution emerging?' Paleobiology, vol.6(1), January 1980,p. 127.]

    “All paleontologists know that the fossil record contains precious little in the way of intermediate forms; transitions between the major groups are characteristically abrupt.” [[Stephen Jay Gould 'The return of hopeful monsters'. Natural History, vol. LXXXVI(6), June-July 1977, p. 24.]

    “The extreme rarity of transitional forms in the fossil record persists as the trade secret of paleontology. The evolutionary trees that adorn our textbooks have data only at the tips and nodes of their branches; the rest is inference, however reasonable, not the evidence of fossils. Yet Darwin was so wedded to gradualism that he wagered his entire theory on a denial of this literal record:

    The geological record is extremely imperfect and this fact will to a large extent explain why we do not find intermediate varieties, connecting together all the extinct and existing forms of life by the finest graduated steps [[ . . . . ] He who rejects these views on the nature of the geological record will rightly reject my whole theory.[[Cf. Origin, Ch 10, "Summary of the preceding and present Chapters," also see similar remarks in Chs 6 and 9.]

    Darwin’s argument still persists as the favored escape of most paleontologists from the embarrassment of a record that seems to show so little of evolution. In exposing its cultural and methodological roots, I wish in no way to impugn the potential validity of gradualism (for all general views have similar roots). I wish only to point out that it was never “seen” in the rocks.

    Paleontologists have paid an exorbitant price for Darwin’s argument. We fancy ourselves as the only true students of life’s history, yet to preserve our favored account of evolution by natural selection we view our data as so bad that we never see the very process we profess to study.” [[Stephen Jay Gould 'Evolution's erratic pace'. Natural History, vol. LXXXVI95), May 1977, p.14.] [[HT: Answers.com]

    ____________

    So, there are a few fairly serious challenges that are highlighted by Chaitin’s work, and it looks ever moreso to this interested onlooker that the most viable view of life forms is that fundamental body plans were designed, and made to adapt to niches in environments, through a robustness maximising philosophy. Optimisation, despite how we tend to praise it, is often quite brittle, once circumstances are not static. It may well be that a viable mechanism is to use something like special viri to “infect” target populations [duly isolated for the purpose], and create a planned transformation.

    What I would love to see is a genome decompiler, and a genome compiler — including the regulatory networks. I suspect that would be a project for the next 50 – 100 years.

    But then, if I were the science policy guy, my top priorities would be energy related [especially pebble bed, thorium and fusion technologies, with a significant renewables side focus], and on water and recovery of major croplands in currently marginal environments, with restoration of rail as a major means of long-haul land transport. Creation of viable sustainable communities would be next — I like what Jakubowsky and others are trying to do — and any number of other things, so the genome project, through important would be a second tier item.

    We have to survive across this century to benefit from any such things. (Of course, if there is a way to genetically engineer algae to create oil and/or feedstocks for key alcohols [I favour butanol as a 1:1 gasoline replacement], that would tie a tier 2 project to a tier 1 issue. . . )

    Recall: to progress, first, you have to survive.

    GEM of TKI

  6. vjtorley:

    “1. DNA really is a kind of programming language. In fact, Professor Chaitin believes it’s a universal programming language.”
    ====

    Wow, this is going to chap and fry the “Please Define Information”(‘What Is Truth?) gang!
    —-

    vjtorley:

    “Chaitin candidly admits that “there is no fundamental mathematical theory inspired by Darwin’s theory of evolution.”
    ====

    You mean like those NASA (Intelligently Designed) “Evolution Algoithms” which are actually nothing of the sort after all ??? LOL
    —-

    vjtorley:

    “Instead, a simplified “toy model” is required in order to rigorously demonstrate that evolution can go on forever, without grinding to a halt.”
    ====

    LOL – And don’t these online Sci-Fi gamer freaks love their toys ??? The computer age has been wonderfully kind to Darwinism. In those intelligently designed computer animations, anything is capable of evolving.
    —-

    vjtorley:

    “For example, in Chaitin’s toy model, life itself isn’t even embodied (it’s purely software), there’s no population, . . ”
    ====

    You mean like George Gilder’s reference to John 1:1 – “In the beginning was the Word . ” = bytes/bits , plans , ideas , blueprints , schematics , algorithms , codes , etc, etc, etc ???
    —-

    vjtorley:

    “8. Of the three kinds of evolution examined by Turing, Intelligent Design is the only one guaranteed to get the job done on time.”
    ====

    Oh this is easy. Just use intelligent design to accomplish your purposed evolutionary outcomes in an experiment, then lable all the various intelligent componants with loads of evolutionary signage which are clearly nothing more than the lying and cheating which are nothing more than the under the table insertions of the intelligent fingerprints of a Lab Coated Nerd with resentful accountability issues.

    Then when called on the carpet for the lying and cheating on the part of the Lab Coat, employ intelligently designed debate strategies loaded with all sorts of purpose and intent from the vivid imagination of a Darwinist by use of ‘classic burden shift’, deflection’ definition shell games, name calling, foul language, insults, character assasinations, etc, etc, etc!!!

    LOL!

  7. vjtorley, those links to the paper do not work (at least for me). In case others are having trouble this one seems ok.
    http://www.umcs.maine.edu/~chaitin/darwin.pdf

    The issue of the origin of life is an important one especially in the political context of the United States where there are some people who would like to show Darwin’s theory doesn’t work because of their religious convictions. The evidence is rather convincing that it does work (the empirical evidence).

    One of the things I’ve noticed with these people (good people and good scientists) they’ve sort of retreated to say “Well the problem that shows there was a designer is the origin of life“. The intelligent people of this community have given up on evolution because the evidence is overwhelming.

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

    Challenge accepted.

    “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?”

    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.”

    “Isn’t that a Designer smuggled in via the back door?”
    Hardly, natural selection is unintelligent.

    “2. Where’s your evidence that Darwinian evolution can generate the diversity of life-forms we find on Earth today, in the time available?”

    Where is your evidence that it can’t? Certainly not Professor Chaitin’s simulation of something completely different from biological evolution using non-Darwinian processes.

    “Current modeling suggests that it cannot.”

    Whose? Professor Chaitin’s model? He’s modeling some sort of obscure mathematical function that apparently requires intelligent judging to see if it’s any better than what went before. He also has a population of 1 which would lead to just about guaranteed extinction of any biological organism.

    JohnnyB: “Chaitin is a truly marvelous character, and I have emailed him on a few occasions.”

    Why don’t you email him once more, with a link to this discussion, and see what he has to say?

  9. vjtorley:

    Wonderful! Now I just need the time to read everything with the due attention…

  10. I find it interesting that he refers to DNA as a “programming language.” It really is, as it directs the formation, growth, maintenance, and reproduction of of the trillions of cells in a human body.

    If the entire “library” of information stored in DNA (the genome) were transcribed, it would consist of 1,000-page-long telephone-book sized books, which would fill 200 volumes.

    To attribute this library of informationn to blind, unguided processes conflicts with both reason and human experience. This belief stretches faith to the breaking point.

  11. dmullenix,

    Thank you for rising to my challenge.

    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? First of all, they’re not obscure. They’re very simple. Here’s how Professor Chaitin describes them in his talk:

    …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….

    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 …. 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. (Emphases mine – VJT.)

    If you’re going to mathematically define the simplest kind of thing for which Darwinian evolution can be proven to work, then you need to show that your model can evolve without having recourse to intelligent guidance. This is not the case for Professor Chaitin’s simplest possible life-form, as it requires a Turing oracle. And how does Chaitin describe the oracle? In his 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.” There you have it: intelligent guidance. And in the very next sentence, Chaitin admits: “So I need an oracle to enable me to carry out this random walk.” Even his stupidest kind of evolution (exhaustive search) requires a Turing oracle.

    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?

    Next, you unfairly disparage Professor Chaitin’s model in the following comment:

    He’s modeling some sort of obscure mathematical function that apparently requires intelligent judging to see if it’s any better than what went before. He also has a population of 1 which would lead to just about guaranteed extinction of any biological organism.

    No, Professor Chaitin is modeling the simplest kind of mathematical program – something far, far simpler than an organism – that is capable of evolving according to Darwin’s theory. And he can afford to have a population of 1, because his organism doesn’t have to fight for its life; it just has to improve – i.e keep calculating bigger and bigger numbers. As I said, it’s a very simple model. And as Professor Chaitin points out, if you try to make it much more realistic, then you won’t be able to prove anything with it mathematically, so there’s a trade-off.

    You also propose that in the biological world, an organism’s reproductive success serves as 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.”

    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. (I wonder if that’s what happened to horseshoe crabs, which haven’t changed for hundreds of millions of years?)

    Now, if there were a mathematical model of an organism that was capable of evolving over an indefinite period of time, by a Darwinian process, without the need for an oracle, then I would acknowledge that there was a strong case for saying that evolution in the real world did not require intelligent guidance of any sort. But since there is no such mathematical model, the very possibility of Darwinian evolution working in the real world without the need for intelligent guidance remains in doubt. After all, if we can’t even get Darwinian evolution to work without intelligent guidance in a simplified, idealized case, then why on Earth should we believe that it is capable of working without intelligent guidance in the real world, which is much more complex?

    In answer to my second question, “Where’s your evidence that Darwinian evolution can generate the diversity of life-forms we find on Earth today, in the time available?”, you reply:

    Where is your evidence that it can’t? Certainly not Professor Chaitin’s simulation of something completely different from biological evolution using non-Darwinian processes.

    Excuse me, but the whole point of Professor Chaitin’s mathematical life-forms was to develop something, as he put it, “that I can prove actually does evolve according to Darwin’s theory.” He even ran them on his own model of Darwinian evolution. And the times he came up with, when modeling Darwinian evolution, were too long to account for the four-billion-year history of life on Earth.

    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. As far as we know, the time required for Darwinian evolution to work is orders of magnitude greater than the time taken for life to evolve on Earth (four billion years). So once again I ask: shouldn’t we be highly skeptical of the efficacy of Darwinian evolution, given what we know so far?

  12. 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. (I wonder if that’s what happened to horseshoe crabs, which haven’t changed for hundreds of millions of years?)

    Hence the observed fact of extinction. And the fact that diversification is mainly confined to periods following mass extinctions.

    Exactly why does the designer allow extinction?

  13. What I would love to see is a genome decompiler, and a genome compiler — including the regulatory networks. I suspect that would be a project for the next 50 – 100 years.

    All you have to do is find a storage medium capable of containing all the possible protein folds.

    And capable of storing all the possible coding strings and their effects. And all the environmental variables that impinge on viability.

  14. Exactly why does the designer allow extinction?

    It is part of the design- ever hear of an “etch-a-sketch”- part of its design is the ability to wipe itself clean.

  15. 15

    Petrushka,

    Why would such extensive storage be necessary? I use decompilers all the time. They are relatively small programs, even though the software they decompile has astronomically unlimited possibilities.

    That being said, I don’t think a decompiler is the best analogy. What we need is most likely an emulator which could take a given genome and emulate its growth and development.

    But, as you said, we could never account for the environment in such a scenario. Such an emulation might be limited to phenotypic expression of the genome, and even then the environmental inaccuracies would probably throw it way off track.

  16. Eocene,

    Thank you for your post. May I humbly and courteously suggest that you appear to have some “issues” with Intelligent Design proponents, whom you sweepingly accuse of “use of ‘classic burden shift’, deflection definition shell games, name calling, foul language, insults, character assasinations, etc, etc, etc!!!” (I loved those three exclamation marks.)

    I try to keep my comments polite and free of invective, crudity and insults, and I’m not interested in deflecting anyone’s attention from what I’m doing. I’m a philosopher, not a conjurer, and I’m an up-front kind of person. What you see is what you get.

    As for burden shift: I really do think it is appropriate here. We currently have no mathematical theory of Darwinian evolution that can explain how it works without invoking intelligent guidance in some form, and we currently have no mathematical theory of Darwinian evolution that guarantees that it can generate life on Earth in the time required. I’d say those are two pretty big problems for Darwinism. Wouldn’t you?

    You cast doubt on Professor Chaitin’s assertion (scroll down to the beginning of section 2) that “there is no fundamental mathematical theory inspired by Darwin’s theory of evolution.” But as I said, Chaitin cites nine references to back up his statement. Here they are:

    [1] D. Berlinski, The Devil’s Delusion, Crown Forum, 2008.
    [2] S. J. Gould, Wonderful Life, Norton, 1990.
    [3] N. Shubin, Your Inner Fish, Pantheon, 2008.
    [4] M. Mitchell, Complexity, Oxford University Press, 2009.
    [5] J. Fodor, M. Piattelli-Palmarini, What Darwin Got Wrong, Farrar, Straus and Giroux, 2010.
    [6] S. C. Meyer, Signature in the Cell, HarperOne, 2009.
    [7] J. Maynard Smith, Shaping Life, Yale University Press, 1999.
    [8] J. Maynard Smith, E. Szathmary, The Origins of Life, Oxford University Press, 1999; The Major Transitions in Evolution, Oxford University Press, 1997.
    [9] J. P. Crutcheld, O. Gornerup, “Objects that make objects: The population dynamics of structural complexity,” Journal of the Royal Society Interface 3 (2006), pp. 345-349.

    There are some pretty big names here.

    You mention NASA evolution algorithms. An algorithm is not a mathematical theory. Darwinian evolution is a biological theory, so if we want to prove it’s mathematically valid, an algorithm alone won’t do. We need a mathematical theory. And that’s just what we currently lack.

    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.

    Finally, if you’re wondering what Professor Chaitin meant when he referred to DNA as a universal programming language, then you might like to have a look at his paper, where he writes: “Programming languages are commonly universal, that is to say, capable of expressing essentially any algorithm.”

    Cheers.

  17. OK, Vincent, I can’t resist a challenge!

    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?

    No, it isn’t “a Designer smuggled in via the back door”. Chaitin’s “oracle” is just a criterion by which his system “decides” whether an “organism” breeds or not. His model doesn’t seem even to be a model of populations btw, and it’s a “hill-climber” not a Darwinian model. But that’s by the by. The crucial point is that the “oracle” in nature is, simply, the environment. Populations adapt to their environment because the environment is the thing they have to breed in! It only has to be an “oracle” in a computer simulation, because you need to model the role the environment plays in nature.

    And, check out Tierra.

    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.

    What current modeling suggests that it cannot? My response to your question is that we cannot demonstrate definitively “that Darwinian evolution can generate the diversity of life-forms we find on Earth today, in the time available”, but we 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. Hence my counter question :)

  18. Thanks for the links, Vincent. I’ve posted a parallel thread here, in case you are interested:

    http://theskepticalzone.com/wp/?p=234

  19. I take it you wrote this firmly tongue in cheek.

  20. BTW, I would agree that “Life as evolving software” is a good model of evolution, though I don’t think Chaitin’s actual model is a terribly good one.

    But if he’s right in principle (and I’d say he is) then he’s demonstrating, formally, “how the information gets into the genome”.

    Without a programmer :)

    Or, if you prefer, he’s taking my approach, which is to see evolutionary processes as a form of intelligence.

  21. Hi kairosfocus,

    Thank you very much for your thoughtful comments. With regard to the origin of body plans, it is interesting to see that Professor Chaitin himself recognizes that the very low probabilities of highly complex body plans emerging as a result of a Darwinian process, when he writes in section 10 of his 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?

    and later: “We have by no means presented in this paper a mathematical theory of evolution and biological creativity comme il faut.” (Bold emphases mine.)

    I don’t think Professor Chaitin is anywhere close to accounting for the origins of fundamental body plans, as occurred during the Cambrian explosion.

    On the subject of challenges facing humanity in the next 50-100 years: I agree with you that thorium and fusion technologies are the way to go (and I notice that India and China are both proceeding with thorium reactors). Interestingly enough, Professor Chaitin himself is a fan of fusion, judging from this link on his Web page: Cold Fusion Poised to Become an Industrial Reality! by Mahadeva Srinivasan. Hope it works…

    Regarding fuels for urban transport, here’s an article that may interest you: Nuclear Ammonia – A Sustainable Nuclear Renaissance’s ‘Killer App’ by Darryl Siemer (Idaho National Lab – retired), with Kirk Sorensen (FLiBe Energy) and Bob Hargraves (Institute for Lifelong Education at Dartmouth College). The paper argues that ammonia is an attractive synfuel fuel for vehicles which require more range/power than can be provided by reasonable-size batteries. Moreover, if that ammonia is produced with energy generated by a “renewable” nuclear fuel cycle it will become extremely cheap, absolutely “green”, and available forever.

    As for water, my attitude is this: if we have an unlimited energy source by 2050, then we never need to run about water running out. Here’s the reason: desalination (already used in Perth, Western Australia).

    ScottAndrews2: I share your doubts about the possibility of an emulator which could take a given genome and emulate its growth and development.

  22. “Without a programmer”

    Except for the one who set it up

  23. They are self-programming algorithms.

    But sure, you need a minimal self-replicator to start with.

  24. At 17:53 : “the simplest thing that PROVABLY evolves according to Darwin’s theory” in contradistinction to actual lifeforms.

    Hehe

  25. 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.

  26. Well, that’s mathematicians for you.

  27. More than that. You need a self-replicator that is stable, and that can self-program itself with greater complex function.

  28. It’s good sense for you.

  29. 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 be tter, 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.

  30. 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 fi tness 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)

  31. 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.

  32. 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.

  33. 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.

  34. “1 We are now able to show that random evolution will become cumulative and will reach fi tness 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 6×10^9 bits. About that he says, “he has a point, he has a point.”

  35. 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 be tter, 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?

  36. 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.

  37. Hi Barry,

    Glad you liked it.

  38. 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.

  39. 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).

  40. 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?

  41. 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.

  42. 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.

  43. 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?

  44. “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.

  45. 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.

  46. 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)

  47. 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,,, :)

  48. 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!

  49. Pav: I truly believe you nailed Chaitin’s hidden assumption! i.e. For ‘unlimited evolution’ to be possible the oracle must be God!

  50. 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

  51. “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.

  52. Further food for thought

  53. 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/publication.....ation-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/publication.....gic-avida/

  54. 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.

  55. 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.

  56. 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! :)

  57. 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.

  58. 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.

  59. 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.

  60. 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.

  61. 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?

    TJ

  62. 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/darwi.....ee_of_life

    tj

  63. 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.

  64. 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.

  65. 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.

  66. 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/periodical.....27241.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/proceed.....l_3_22.pdf

  67. 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! ;)

  68. Or like Legos, Tinkertoys and Lincoln Logs with their ability to take themselves apart.

  69. So extinction events are part of the design as well?

  70. 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?

  71. 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?

  72. 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.

  73. Right- the design isn’t going the way the designer(s) thought so they changed it up a bit.

  74. 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?

  75. 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?

  76. 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).

  77. 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.

  78. Of which algorithms do you speak?

  79. 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.

  80. 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.

  81. Yet there aren’t any free-living things without DNA in it. So those “investigators” you are alleging need something to support their position.

  82. 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.

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