Is it possible for a system to lack information in the details, but gain it in the action; to have little static knowledge but lots of dynamic; to have no information in the boundary conditions, in the initial state, or stored in special registers, but when the power is switched on, suddenly become Einstein?

This is the thesis of the Sante Fe Institute, of Stuart Kauffman's chosen vocation, for this is essentially what Darwin proposed: living things collect information just by being alive. They get smarter the way football jocks pass Algebra 1, just by being there.  Darwin called it natural selection, which doesn't actually explain anything anymore than Nietzche's "what doesn't kill you makes you stronger" is advice on picking mushrooms. But if you had to find a reason for this miracle of dynamic information emergence, you might be tempted to say that it is due to the system, it's designed for this, it's in the ground rules.

But is it? I mean, other than saying that this is the only explanation for the data, which is a bit of a tautology, how can we test whether or not it is in the rules of the game?

Well, in the past century, biologists have bred fruit flies, nematodes, flatworms and other nasty biological pests in an attempt to see how evolution works. We learned a lot about Mendellian genetics, but we haven't actually learned much about natural selection. Part of the problem is that even fruit flies with their 10 days per generation, in the 100 years of fly research there have been at most only 3650 generations to observe evolution. (Not enough! say the Darwinistas.)

Bacteria are bit faster at 20 minutes per generation, and have smaller genomes with sloppier genetic copying, so Richard Lenski proposed to see if Escherichia coli bacteria (common gut bacteria) could evolve the ability to digest a new material--citrate. After 20 years,  and 400,000+ generations, he claimed success.  Only it sorta needed some help, it wasn't exactly survival of the fittest, it looked more like devolution than evolution. And in fact, Michael Behe used wild malaria parasites as his test case for 100 years of evolution in the face of anti-malarial drugs, and sure enough, it was too slow to account for Darwin's magical dynamical emergence.

Well we could wait another 20 years for more results from Lenski, but if Behe is right, we would need millions of years to get anything interesting out of bacteria, and billions of years for fruit flies, and... you get the drift.  What is a thinking man to do?

Computer simulations!

(Reminds me of an old song, "you can get anything you want, at Alice's Internet cafe...")

Well there's no shortage of 30-somethings who want to make their mark on the world, and proving Darwin with a computer is just the ticket to fame and glory. So we have a dozen evolutionary simulations as sophisticated as the best big ticket shoot-em-up game, all cranking on government supercomputers to see how this emergence thing works. 

Not very well. At least, not as well as say, you and I operate, and supposedly we evolved from far less efficient wetware.

Gregory Chaitin, a famous mathematician and computer scientist employed at the IBM flagship Thomas J Watson Research Center (where I spent an enjoyable summer in 1981), has written extensively on information and complexity. He gets quoted favorably by Intelligent Design's resident mathematician--William Dembski. He's not naive about the problem emergence is supposed to solve. But he's embarrassed that the mathematics of evolution has, well, not evolved. Biologists are more scared of math today than 60 years ago when JBS "Jack" Haldane defined the field. So he decided that the problem with all those computer simulations is that they are trying to do too many things at once. On his web site, he proposes the following solution:

• 200th anniversary of Darwin's birth, 150th anniversary of The Origin of Species.
• The unreasonable effectiveness of mathematics in physics (Wigner) versus the lack of effectiveness of mathematics in biology (Gelfand).
• We wish to extract the fundamental mathematical ideas contained in biology.
• We wish to prove theorems about extremely simple unrealistic models, not run simulations of extremely complicated realistic models.
• Our goal is not to realistically simulate biological evolution, but to represent mathematically the fundamental biological principles of evolution in such a manner that we can prove that evolution must take place.
• This may be regarded as a toy model, but we do not see it as a toy, we see it as a way to eliminate inessential distractions that only serve to confuse the issues!
• Theories are lies that help us to see the truth (Picasso).
• Math is extremely single-minded and can only deal successfully with a single idea at a time (Jack: The Pernicious Influence of Mathematics on Science).
• If Darwin's theory of evolution is as fundamental, basic and general as most biologists think, then it must be possible to extract some basic mathematical ideas from it.
• Nothing makes sense in biology except in the light of evolution (Dobzhansky).
• It is scandalous that we do not have a mathematical proof that evolution works!
• I am a pure mathematician, not a biologist: I am trying to find the Platonic ideal of evolution, the archetypical behavior, not the messy version that takes place in the real world!
• The aim is proofs, not realistic simulations.
• Another way our model differs from previous models: Our goal is to understand biological creativity and the major transitions in evolution, not gradual changes.
• Fisher-Wright population genetics studies changes in gene frequencies. We are trying to model how new genes arise, and major changes such as from single-celled to multi-cellular organisms.

But why is Chaitin feeling embarrassed now, after 60 years of bad biological mathematics? Because another mathematician said it couldn't be done. Here's Chaitin's own words,

Our random walk model was inspired by the stimulating critique of Darwinian evolution in D. Berlinski, The Devil's Delusion, Crown Forum, New York, 2008. See especially pp. 192-195. In a nutshell, model = Jack (digital software) + Berlinski (random walk) + Busy Beaver Problem. Our model is an attempt to answer Berlinski's criticisms.

Wow. An ID book having an impact! Who would have thunk it? (Maybe somebody should contact that judge over in Dover PA who said ID wasn't science.) So what will be Chaitin's modus operandi?

• I think this discussion makes a convincing case that a theory of the evolution of randomly mutating software is possible, and that random walks in software space are worth studying.
• How biologically relevant such a theory may be remains to be seen.
• But that it will be an interesting new field of mathematics is now plausible. However, carrying out this research will require a great deal of work. Maybe you would like to work on these problems?
• I propose calling this new field metabiology: I hope that it will eventually develop into a field parallel to biology, dealing with the random evolution of artificial software (computer programs) rather than natural software (DNA), and simple enough that it is possible to prove rigorous theorems or formulate heuristic arguments at the same high level of precision that is common in theoretical physics.
• Whether or not this happens, as the concepts of computation, information and complexity how, mathematics is moving in a biological direction. This trend will continue.

Let me summarize his modus operandi -- a hope and a prayer.

Chaitin quotes a famous mathematical physicist, Eugene Wigner, who pointed out that math works better than it should ("an unreasonable success") in the field of physics. In fact, physicists often don't wait for the mathematician to prove, say, that there exist solutions to the famous supersonic solar flow equations, they just assume the answer because they can see it. And Chaitin is asking, why can't this apply to biology? He tosses off all the excuses "too complicated", "different methodology" and says "look you guys, we had a good start with Jack, why didn't you finish the race?"

Well maybe the failure of 3 generations of mathematicians is because the problem is insoluble, or as they say in math "it is not a well-posed problem". Maybe there isn't any secret method of adding information dynamically. Maybe emergence is a myth. Maybe natural selection doesn't do anything to DNA and only affects the epigenetic response. Maybe Galapagos finch beaks have absolutely nothing to say about speciation and the origin of the species.

U of British Columbia Applied Mathematician, Richard Johns has submitted a paper quantifying the amount of information that supposedly emerges dynamically. It turns out to be a lot. And there are no short cuts by dividing the problem into stages, as the non-mathematical biologist Richard Dawkins suggests.

The late great irrascible mathematical physicist and confirmed atheist, Sir Fred Hoyle, used to propose the following test of emergence. Take a test tube, add some water, the amino acids and ingredients that supposedly produced life 4 billion years ago, but of course at much higher concentrations. Since chemical reactions go as the product of the concentrations, we can easily achieve chemical rates trillions of times above the dilute concentrations produced by the Miller-Urey method. Wait a few minutes, now examine the test tube for life. If life is as emergent as the Darwinists claim, it ought to be trivial to reproduce it in the lab. The fact that we don't see life, on the other hand, put stringent upper limits on the probability of emergence. What makes Hoyle so lovable, is that long before Dembski was talking about improbabilities, he went ahead and calculated all these numbers and published them in The Mathematics of Evolution (1987).

You would think Chaitin would pick a better-posed problem.