Did Von Neumann Not Believe in Evolution?

over at the Panda’s Thumb

Jeffrey Shallit pointed me to a youtube video, in which David Berlinski makes the following remarkable claim: “… von Neumann, one of the great mathematicians of the 20th century, just laughed at Darwinian theory. He hooted at it.”

Thankfully, Douglas L. Theobald goes to some length to clear Von Neumann’s good name, and shows how such nonsense turns out to be … well, nonsense.  Von Neumann, one of the greats of Game Theory (and plenty of other maths) clearly believed in evolution and did substantial work in areas of mathematics that have directly affected the field of biological evolution in remarkably positive ways.

Von Neumann (from the horses mouth):

Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.

Furthermore, it’s equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today’s organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it’s inconceivable how any kind of description of the later, complex organisms could have existed in the earlier one. It’s not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produces something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.

If this man didn’t believe in evolution, I don’t know who does.

Evolutionary Dynamics

A review of a new book, “Evolutionary Dynamics” by Martin A. Nowak

Martin Nowak is certainly not alone when he argues, in Evolutionary Dynamics, that evolution is the single most significant idea in biology. But almost all major mathematical syntheses of evolution have been confined to population genetics–the study of gene frequency changes in populations. By contrast, Nowak (a professor of biology and mathematics at Harvard) follows up on Hardy’s last qualification for a great idea by showing the many ways in which the mathematics of evolution lead to advances in diverse subjects, including cancer, game theory, and language.

Busy-ness! And a love for Maple…

The quarter is off to a running start! I wish I could post more here, but… Whew!  Hopefully this post will make up for my absence!

So here’s a little potpourri for you:

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Free Will, God, and Newcomb’s Problem: Part 2

In the last post on Newcomb’s problem and Free Will, we went over a 2 person game to be played with God. The key problem we were facing was whether or not Free will can coexist with an all knowing being that has powerful predictive capabilities. That is, if God always knows what you are going to do, and is in fact able to change the future based on what he knows about your actions now, are you really free?

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Quantum Game Theory: Lansburg’s Paper

for those that may not know anything about Quantum Game Theory but are interested, here’s the major paper by Steve Landsburg on the subject. It’s a good primer. Though, we’re still going through the proofs to determine if it all holds true, it opens the doors of possibility.

EDIT:  The above link is the simplified friendly version.  The full paper by Landsburg (all 57 pages of it) can be found here.

The Existence of Free Will: Newcomb’s Problem

William Newcomb, a physicist at the Livermore Radiation Lab in California, in 1960 posed a problem, about which the great Philosopher Robert Nozick said, “it is a beautiful problem. I wish it were mine.”It’s a problem that highlights the trouble with the idea of Free Will. To illustrate it, I am using the Game Theoretic interpretation of this problem used by Philip D. Straffin, in his book “Game Theory and Strategy.”

To quote Straffin:

Suppose there are two black boxes which you cannot see into. Box #1 contains $1000. Box #2 contains either $1,000,000 or nothing, depending on something we’ll mention in a moment. You have two choices.

1. you may take both boxes, or

2. you may take only box #2

Now, let us assume there is a God, or someone with equally powerful predictive powers. Sometime in the past, God made a prediction about which box you, today, are going to choose.

If God predicted that you were a greedy bastard with no sense of adventure, and would choose option number 1, taking both boxes, then he would smite you and leave box number 2 empty.

On the other hand, if God thought you the gambling type, and predicted that you’d choose option 2, taking only the mystery box, then he would have rewarded your future gutsy-ness by putting in the full 1 million.

The next key is that you, of course, as a good Religious person, believe that God is one heck of a good predictor of outcomes. He may not be perfect, but you assume he’s right at least a good 90% percent of the time. You trust him.

But, then again, as a learned child of the enlightenment, you also strongly believe that God gave us all free will. That we have a choice in life. Life, and our actions are not all predetermined.

What would you do?

Next time we’ll go over the arguments to be made for both choices and what Robert Nozick had to say about them.

The Acceleration of Human Evolution

John Hawks has recently come out with a powerful paper about the Acceleration of Human Evolution. In a recent Blog Post he goes into it.

It is quite simple; the rate of mutations in a population is a linear product of the rate per genome and the population size.

Not all mutations are advantageous, and not all advantageous mutations will be fixed. The vast majority are lost. If a mutation has a selective advantage, then the chance that it will proceed toward fixation (and attain high frequency) is 2s — “s” here is the fitness advantage. That means that 90 percent of new mutations with a 5 percent fitness advantage are simply lost.

The most beneficial mutations are very rare; it is much more likely that a new mutation will be weakly selected. This is another aspect of selection that has been well-known since Fisher. So the chance of fixation increases with s, but the likelihood of the mutation decreases with s — in fact, the number decreases exponentially as selection is stronger and stronger.

If you put all these together, you can predict how many selected changes you should see in a population that has been growing in size. This tells us the number of new adaptive mutations that should come into the population each generation. It is still linear with population size — a larger population should have more mutations in precise proportion to its size.

He goes on:

From that standpoint, the ecological changes documented in human history and the archaeological record create an exceptional situation. Humans faced new selective pressures during the last 40,000 years, related to disease, agricultural diets, sedentism, city life, greater lifespan, and many other ecological changes. This created a need for selection.

Larger population sizes allowed the rapid response to selection — more new adaptive mutations. Together, the the two patterns of historical change have placed humans far from an equilibrium. In that case, we expect that the pace of genetic change due to positive selection should recently have been radically higher than at other times in human evolution.