I am ordinarily a pretty fast reader, but the book I am now reading, Turing's Cathedral, is astonishingly slow going. After plugging away at it conscientiously for a while, I am only on page 137! Still and all, it has some rather interesting things in it, aside from endless detail about the backgrounds, ancestors, and personal characteristics of each one of the scores, if not hundreds, of characters who make their appearance in the story. The book is about the early stages of the development of the modern computer, a development in which John von Neumann played a central role.
The core of the theory of the computer can be found in the writings of Leibniz, and in the modern era, Alan Turing, John von Neumann, and -- surprisingly, Kurt Gödel -- pretty well had that nailed early on. But the actual construction of a working model turned out to be an engineering nightmare. The enterprise was launched at the Institute for Advanced Study in Princeton, with von Neumann and several others overseeing the effort. Many of the ethereal residents of the Institute looked with great disfavor on the entire project, which involved engineers who actually did things with their hands other than erasing symbols from a blackboard. The most eminent of the humanists, the great art historian Erwin Panofsky, was apparently particularly put out by the presence of engineers.
This entire story is something that I knew nothing about [hence my decision to read the book], and aside from the endless detail, which George Dyson cannot stop himself from retailing, there are some real surprises for me. Perhaps the thing I most totally failed to realize is that the engineers [and the theorists] had to deal with the fact that the electronic components they were able to get their hands on -- vacuum tubes, relays, and the like -- were very unreliable.
Now, this unreliability posed a major threat to the very possibility of a working computer. The problem is this [I have the feeling I am telling you something you all know, but since I have just learned it, let me continue]: As Leibniz foresaw, a computer essentially does certain very elementary things over and over again with blinding speed, remembering [so to speak] the result of each step, and entering that as input into the next step. To illustrate with a trivial example, a computer adds 5 and 7 by adding 5 and 1, then taking the result, which is 6, and adding 1 to that, then taking the result, which is 7, and adding 1 to that, and so on, until it arrives at the answer, which is 12. [I choose the example, of course, in honor of the memory of Immanuel Kant.] Now, when thousands of steps are being concatenated, if somewhere along the line a vacuum tube misfires or misbehaves, the entire process will yield a wrong answer.
Some way must be found to get satisfactory results from imperfect, fallible components. And this problem, much to my surprise, was one that Norbert Wiener and others had already been struggling with in their effort to devise ways of making anti-aircraft guns more accurate when fired at enemy bombers!
I am of course typing this on a desk-top computer, in preparation for posting it on my blog. The interaction between my brain, my fingers, and the computer is seamless [save for the fact that I am the world's worst typist, and must repeatedly backtrack and correct my typing errors -- but even that is made easier by the fact that my word processing program very politely underlines in red each word that has been garbled by my errant forefingers.] We all know that the amount of memory required, and the speed required, for this seamless process is staggering. But it is good, nevertheless, I find, to read about the struggles of the men and women who actually invented and physically assembled the first primitive computers. It may have been obvious to Leibniz or Turing or von Neumann or Wiener or Gödel how the first and simplest steps would lead necessarily to the most sophisticated advanced computer operations, but the actual physical steps were not obvious to them or to anyone else, and required a very great deal of effort by a large number of superbly talented people.
This might be a good place to respond to a comment posted by Don Schneier several days ago, on the occasion of my first remarks about the Dyson book. I have been mulling them over in my mind, and there are a few things I want to say by way of elaboration and response. Reacting to my fantasies about having a mind like that of von Neumann, Dr. Schneier writes [Don is an old student, which is how I know to write "Dr."]: "On the one hand, there is Spinoza's distinction between 'Intuition' and 'Reason'. But, on the other, "blinding speed" may indicate a difference in rate, not in kind, of intellectual process."
This is actually directly apposite to what I have been saying. A computer does function by performing elementary operations over and over and blinding speed. But though it is of course the case that von Neumann's mind worked a lot faster than mine [to put it mildly] -- indeed, if Dyson is to be believed, a lot faster than just about everybody's mind, except maybe Gödel's -- that is not, I think, the real difference between his mind and mine.
Let me try to explain to illustrate what I take to be the difference by means of a story that I think I actually told in some chapter of my Autobiography. My favorite uncle was Dr. Anoch Lewart, the husband of my father's sister, Rosabelle. In addition to being a fine surgeon and a wonderful man, Anoch was an intellectual. He loved to read, and for many years was part of a reading group that also included my father. Late in life, Anoch began to lose his peripheral vision [I forget what this condition is called], and eventually it reached the point at which he could only see what was in the very center of his visual field, under bright light. He quite literally could not see a line of text, or even an entire word. He had made for himself a reading box, I might call it -- a box that backlit a very much enlarged text under very intense light. Anoch could only see a part of a word at a time, but he would laboriously scan a text, word by word, remembering what he had just seen and assembling it into a sentence. In this way, very, very slowly, he could read entire paragraphs or even pages of text. You can perhaps see that in a sense, he was reduced to doing what a computer does, but very, very slowly.
I thought about him once when I was in the Louvre in Paris. I was walking through one of those seemingly interminable series of galleries, and as I passed through an arch, I glanced to my right. There, hanging on a wall, quite unpretentiously, was one of my favorite paintings: La Bohémienne by Frans Hals. Now, here is the point. Had my uncle been with me, he would have had to look at the canvas one tiny piece at a time, and struggle to integrate into a complete image what I could see immediately and grasp as a whole. I do not think that I was doing the same thing he would have been doing, only faster. To use a term that came into fashion with a certain school of Psychology, I grasped the entire image in a gestalt [from the German for "shape" or "form."]
Something like this, I believe, is the way von Neumann grasped formal mathematical structures. Whereas I am compelled, when I am attempting to master a mathematical theorem, to go through the proof step by step [like my uncle], carrying along what I have learned from the previous steps until I can assemble the entire idea of the proof in my mind, von Neumann and other great mathematicians grasp the central idea of the theorem in a gestalt, immediately. It may then take them a long time to spell out their intuition in a series of correct steps leading from premises to conclusion, but they can see the theorem in the same way I can see a painting.
Well, back to page 138.
