Darwin and the Mathematicians
ENV: In the past, you've remarked about mathematicians and their opinions of Darwin's theory of evolution. They were skeptical, you said; very skeptical. John Von Neumann was an example. How do you know that about him and about other mathematicians?
DB: 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), RenÃ© 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.
Among the mathematicians that I knew from very roughly 1970 to 1995, the general attitude toward Darwin's theory was one of skepticism. These days, I do not get around all that much, and whatever the mathematician's pulse, I do not have my finger on it. But the reactions of which I speak were hardly surprising. Until recently, mathematicians have been skeptical of any discipline beyond mathematics, and I say until recently because attitudes as well as times have changed.
In talking of the mathematician's skepticism, I mentioned Von Neumann because his name was widely known. I might have mentioned Gian-Carlo Rota. He despised the enveloping air of worship associated with Darwin; he thought biology primitive and dishonest.
How do I know this? I know it because we were close friends, and because he said so. He said so to me.
Gian-Carlo had, in fact, read closely one of my unpublished papers on Darwinian evolution. Written in late 1970, during my stay at IIASA (the International Institute for Applied Systems Analysis), my essay later made its way into Black Mischief: Language, Life, Logic & Luck, stripped by then of almost all of its technical details.
A few mathematicians at IIASA had already read what I had written; they had, after all, encouraged me to write it. When we met later in the year, Gian-Carlo offered me his delighted agreement, which he extended in the spirit of it's about time; he urged me to keep at it; he considered publishing my essay in his journal; but after some back and forth between us, he decided that it would be best were I never to publish another word on the subject.
Gian-Carlo was a man of very refined political sensibilities.
It is a mistake to read back into the recent past the political and emotional structure of discussions now current.
Reading things backwards is vulgar as intellectual history and false to the facts -- vulgar because it assigns an aspect of permanence to our own obsessions; and false because it distorts the play of forces playing just a few decades ago.
In the first part of the 20th century, Darwin v. Dissent had not yet acquired its riveting incarnation as a melodrama of intolerance. No heresy, no heretics is a useful proverb, and using, say, 1950 as a reference point, there were no heretics among the mathematicians because there was yet no heresy. Darwin's theory was not then considered totemic; and his touch was not widely understood to cure erysipelas. Darwin v. Dissent is of our time and place.
Now Von Neumann turned from pure mathematics in the 1940s and the early 1950s. Like so many other mathematicians and physicists, he regarded the theory of evolution as a place holder, the full and so the real theory waiting somewhere in the wings of time.
When Erwin SchrÃ¶dinger published What is Life? in 1944, he electrified the mathematicians and the physicists; and he influenced profoundly biologists such as Francis Crick, the latter a form of Rural Electrification, I suppose. SchrÃ¶dinger's impact is easy to understand: He gave biologists a set of ideas that they had been unable to give themselves.
"How can the events in space and time," SchrÃ¶dinger asked, "which take place within the spatial boundary of living organism be accounted for by physics and chemistry."
These words were written in 1944, just sixty-six years ago.
"The preliminary answer which this little book will endeavor to expound," SchrÃ¶dinger went on to say, ... "can be summarized as follows: the obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that they can be accounted for by those scientists.''
I have placed in italics words that establish SchrÃ¶dinger attitude. I do not know which word to stress more: The obviousness of an inability, or the inability of an obviousness.
So I have stressed them together. They reflect the attitude of mathematicians and physicists toward biology during the 1940s, 1950s, and at least a part of the 1960s.
Having asked for a clue, SchrÃ¶dinger found one on his own. He predicted the existence of a code script, one governing heredity. Just eight years later, Watson and Crick published the first of their two great papers on the structure of DNA.
Everyone took notice, the biologists because SchrÃ¶dinger had been prophetic, and the mathematicians and physicists because SchrÃ¶dinger had been one of their own.
These remarks belong to the considerable category of things that must be kept in mind.
So keep them in mind.
What was it that comprised Von Neumann's skepticism about evolution?
It was an attitude in three aspects. Von Neumann, in the first place, saw what mathematicians had seen since Darwin first published his theory. The theory required life to clamber over some very sobering improbabilities; indeed, it seemed to require miracles. Other mathematicians were making the same point. "[T]he formation within geological time of a human body," Kurt GÃ¶del remarked in conversation with Hao Wang, "by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field, is as unlikely as the separation by chance of the atmosphere into its components."
Note the word geological. GÃ¶del, like everyone else, quite understood that Darwin's theory played out over long stretches of time. He might even have grasped the concept of natural selection, commonly said to be too difficult for all but a handful of initiates. He was skeptical nonetheless. It was precisely to do battle against this kind of skepticism that Richard Dawkins wrote The Blind Watchmaker. His proximate target may have been the physicist, Fred Hoyle, but his general target was a whole climate of opinion current among mathematicians and physicists.
Von Neumann, in the second place, thought Darwin's theory inadequate. He thought the theory inadequate because the theory did not yet exist. This is as inadequate as it gets. What did exist lacked the fundamentals. It answered no questions. It had no depth. And it was largely anecdotal. This sense of anecdotal has nothing to do with the idea of just-so stories made popular by Lewontin and Gould. Darwin's theory was anecdotal, Von Neumann suggested, because it lacked the rich and productive concepts that only mathematicians could provide the sciences.
Writing in the 1967 Wistar Symposium, Murray Eden offered a fine sense of the way in which mathematicians and physicists thought Darwin's theory inadequate. "...[T]he continuity of evolution does not demonstrate that natural laws are operative, for the laws are not known."
Murray then added a most useful analogy. "It is," he wrote referring to Darwin's theory, "as if some pre-Newtonian cosmologist had proposed a theory of planetary motion which supposed that natural force of unknown origin held the planets to their courses."
Just so. This is what Darwin's theory is like; and it was how it appeared to a great many mathematicians and physicists.
And then Murray added a demurral. "The supposition is right enough and the idea of a force between two celestial bodies is a very useful one, but it is hardly a theory."
Far from being controversial among mathematicians in the 1940s and 1950s, a sense of the inadequacy of Darwin's theory was widespread.
And there is a third and final component to Von Neumann's skepticism, this one no more than a hint. To say that Von Neumann was skeptical of Darwin's theory is not to say that he was a supporter of intelligent design. I have no reason to think so. I know nothing about his religious views. Yet there is a curious remark he made to Stan Ulam. I suspect that he made the remark at the end of his life. Von Neumann pointed to a house in the distance and remarked to Ulam how absurd it would be to think that the house just assembled itself. The men were discussing Darwin's theory. It was not simply a doubt about improbability to which Von Neumann gave voice: It was a more general susurrus of discontent. The remark suggests that just possibly Von Neumann's sensibility had undergone a change. Ulam never said anything more to Marco and Marco never said anything more to me.
There remains nonetheless that air of intellectual poignancy. Perhaps Von Neumann was aware of his impending death.
So much for what mathematicians thought and think; so much for what Von Neumann thought and thank.
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.
Stanislaw Ulam was close to von Neuman -- very close; and Ulam was also close to Marco and Gian-Carlo Rota -- very close again. They were close enough to share their views. I knew Marco and Gian-Co very well; and they were close friends of mine.
Since Marco and I were writing a book together about evolution, our interest in Von Neuman's views was natural. Natural, but not consuming. It was a part of the chatter, and it would be wrong to suppose that our curiosity was anything more than curiosity. The subject came up. What had Von Neumann thought? We discussed it. Von Neumann stories were told, as they always were.
Let me fix the time and place:
The winter of 1979 - 1980.
And again a year later in Los Angeles at the University of Southern California, where I gave a lecture and Gian-Carlo acted as my host and the source for further stories.
When this issue first emerged, I was asked for references. I am not a Von Neumann scholar, and I have not consulted any of the sources. What I know of Von Neumann's views, I know from his friends. But what I know is entirely consistent with the development of his own ideas. Von Neumann's work on self-reproducing automata is an interesting attempt to make good the deficiencies of a theory that he understood had deficiencies and needed remedying, a demonstration of the thesis, left unremarked, unanalyzed and unstated in Darwin's theory, that a self-reproducing automata is logically possible. It fills one hole.
Ulam's paper 'On some mathematical problems suggested by problems in biology,' fills another hole. In it he introduced what he called a "biological metric space" into theoretical biology. The date is 1970. The place is the Rockefeller Institute. And the idea, by the way, is pure Marco. Ulam's paper marks his indifference to the dominant paradigm of Sewell Wright's population genetics. Gone are both Euclidean metrics and Wright's very elaborate apparatus of differential equations.
Whether a theory with quite so many holes in its plush is worth mending is another question entirely.
When the issue of Von Neumann's views appeared in the Bogosphere, Douglas Theobold, a contributor to the Panda's Thumb, much occupied in discharging his indignation, wrote a little post. Von Neumann had apparently said something: "I shudder," Von Neumann wrote in a letter to George Gamow, "at the thought that highly purposive organizational elements, like the protein, should originate in a random process."
Having shuddered, Von Neumann apparently got hold of himself. "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."
"This," Theobold writes, "may be the ultimate source of many of the claims that von Neumann was anti-evo."
It may well be, but it is not my source as I have explained in detail.
Still, what lends to this exchange its lurid aspect is that having shuddered, Von Neumann might have kept right on shuddering, for if Von Neumann was criticizing Gamow's theories about protein formation, he was right to do so because Gamow's theories were wrong.
And there is the final, the inimitable, touch. I have never claimed that Von Neumann was "anti-evo."
What an idea. No one is. What I did claim is that like so many others, Von Neumann was profoundly skeptical about Darwin's theory of evolution.
And I have just said why.
Check out David Berlinski's newest book, The Deniable Darwin and Other Essays, here.