Good Math, Bad Math

A typical taste of this is right at the start of the article. It's set up as an interview. Berlinski has been claiming that Jon von Neumann was very skeptical of evolution. Naturally, lots of people have called bullshit on that. So the "interviewer" asks him about how he knows what JvN thought of evolution, when he never wrote anything about it. Berlinski's answer:

How do I know? Here's how:

I have been close to a number of mathematicians, and friends with others: Daniel Gallin (who died before he could begin his career), M.P. Schutzenberger (my great friend), René Thom (a friend as well), Gian-Carlo Rota (another friend), Lipman Bers (who taught me complex analysis and with whom I briefly shared a hospital room, he leaving as I was coming), Paul Halmos (a colleagues in California), and Irving Segal (a friend by correspondence, embattled and distraught). Some of these men I admired very much, and all of them I liked.

I had many other friends in the international mathematical community. We exchanged views; I got around.

See, he very typically starts off with lots of name-dropping. What does this list have to do with the question? Nothing, really. It's just that Berlinski always needs to make it clear just how special he is, how he knows lots of famous people, and how truly smart and wonderfully connected he is.

(Remember that this is the guy who tells the story about how he managed to make a bunch of mathematics professors really understand limits for the first time. He's got a really amazing view of himself.)

Anyway... He goes on to explain how Professor Rota really wanted to publish one of Berlinski's anti-evolution screeds, but ended up deciding not to, for fear of the political damage that would be done to Berlinski. Of course, we're supposed to take Berlinski's word for this: that this famous professor of mathematics is really a huge fan of Berlinski's anti-evolution rubbish, but has never admitted to it, because he has "very refined political sensibilities".

After a ridiculous additional amount of self-aggrandizing bullshit, Berlinski finally gets to the point:

I now pass to the point of this exercise. Where did I get my information? Let me tell you. I got my information about Von Neumann from the horse's mouth, the horse one step removed from the horse himself.

Quite obviously I did not know Von Neumann personally. He was too old and I too young ever to have met. So what I know of views I know at second hand. I know it from my friends.

To paraphrase Douglas Adams, ``Ah, this apparently is some entirely new use of the term "from the horses mouth" of which I was previously unaware''.

Berlinski knows what Jon Von Neumann thought of the theory of evolution, because he heard it from the horses mouth. By which he means that some of his friends who might have spoken to JvN about it at some point in time allegedly passed JvNs opinions on to Berlinski long after vN had died.

Now, vN did have some criticisms of the theory of evolution. If you actually look at the things that he wrote about it, it's pretty clear that he was being a typical mathematician. That is, looked at mathematically, the theory of evolution was under-defined. And he was, of course, right about that. Remember that at the time von Neumann was writing, DNA had just been discovered - but no one knew yet how it worked. No one knew how mutations worked. No one knew much of anything about how genes functioned. No one had a particularly good understanding of how the development of organisms from reproductive cells really worked.

All of those things were holes in the completeness of a theory of evolution: evolution could describe how populations change, how selection works, but without being able to explain the mechanisms of inheritance and mutation, the theory was incomplete. (Just like Newton's theory of gravity is incomplete: it can describe most of how gravity works, but it can't explain why; and it can't explain some of the corner cases. It's a damned good theory, and it's close to the truth, but it needs refinements to be accurate and to explain why it works.) Some of those are still gaps in our knowledge: we still don't know a lot about how genes really work. Some we understand pretty well; others we're still completely clueless about.

But what did von Neumann really say? The primary documented quote from von Neumann comes from a letter to George Gamow, a physicist who had some theories about how the structure of DNA could be interpreted to describe proteins:

I still somewhat shudder at the thought that highly purposive organizational elements, like the protein, should originate in a random process. Yet many efficient and purposive media, e.g., language, or the national economy, also look statistically controlled, when viewed from a suitably limited aspect. On balance, I would therefore say that your argument is quite strong.

Hardly a strong criticism, huh? But it gets worse. Berlinski represents this as von Neumann being skeptical of the supposed randomness of evolution. But this wasn't part of a general argument about evolution. This was von Neumann discussing Gamow's theory of how DNA worked. Gamow had worked out an idea of how proteins were formed from DNA. He started with a null hypothesis of random distributions of amino acids in proteins. Then he compared the results of looking at proteins with the result of what his model predicted. His model was much better that the null hypothesis. The correspondence with von Neumann was in relation to von Neumann working with Gamow to develop a complete mathematical model of the random amino-acid hypothesis!

In other words, Gamow and von Neumann were discussing a hypothesis that they were hoping to reject in favor of something that seemed to make more sense!

So, as usual, when you actually look at things in detail, Berlinski is being his usual pompous self. He's got nothing to support his claims except some out-of-context quotes, and a bunch of supposed "personal contacts" which refuse to publicly back him up because of their fears of political retribution.