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Monday, March 19, 2012


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.


Bjorn said...

Reading of your struggles with complex mathematics makes me think of my own quasi-regret: that I didn't go into science. I always had a knack for mathematics, although I never really enjoyed it much.

Instead I went into philosophy (of the severe, analytic, Anglo-Saxon kind) and then into the history of eighteenth century philosophy. I do enjoy it a great deal. Still, it is a source of some resentment to me that the extensive and painstaking education in logic, philosophy of language, metaphysics, epistemology, ethics, social science and history earned over the span of a decade brings me but a fraction of the respect I would immediately get if I were, say, a geneticist, or a geologist, or a doctor.

In a practically minded, materialistc and technocratic world, it becomes ever more difficult to persuade people of the worth of the human branches of knowledge. Family gatherings are dreadful for me. I usually steal a line out from Bruce Lee. When they say "Philosophy? What do you do with that?", I quickly respond "I think very deep thoughts about the nature of unemployment."

Bjorn said...
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Unknown said...

I response to Bjorn, may I suggest that your answer to the occupational question should be the most abstruse one rather than the one most immediately obvious to laymen. I am a retired biophysicist who worked in biomagnetism, and that answer, rather than biologist, MD, chemist or physicist tended to stop further questions in their tracks with no need to justify myself. Most people won't inquire further.

Bjorn said...

You mean something like "I work in qualitative textual hermeneutics, with a focus on the ontology of normative statements"?

Yeah, that might work :)

JP said...

Concerning your reflections about the different ways in which minds can work: I recommend Gleick's 'Genius: The life and science of Richard Feynman'. It has a lot of intelligent speculation about the different kinds of genius (given that Feynman was an extreme example of one kind). For what it's worth, Poundstone's 'Prisoner's Dilemma' is a fun book about von Neumann, though I suspect that some of what it says about game theory may annoy you.

mesnenor said...

I recall once reading a study performed by some psychologists who were interested in how chess masters saw chess boards. They briefly showed random chess positions to chess masters, and to some control group of non-chess masters, and then asked the subjects to reproduce the positions from memory. In terms of absolute accuracy in reproducing the positions, the chess masters were actually no better than the control group. But the chess masters were very good at reproducing the relationships between the pieces. Their memory of the glimpses of the chessboards was no better than anyone else's with regards to the absolute positions of the pieces relative to the board itself, but their expertise in chess meant that they saw the positions of the pieces relative to one another much more clearly than people without expertise in chess.

Robert Paul Wolff said...

Since my son, Patrick, is a very famous chess grandmaster, this is something I have thought about. It turns out that if you show a grandmaster a random distribution of pieces on a chess board he or she is no better at remembering it than anyone else. But show that same grandmaster an actual position from a real game, and he or she can recall it precisely. Indeed, my son can recall the positions of pieces from games he played as a young boy 30 years ago!

Don Schneier said...

Between difference of kind and difference of speed--I'm not convinced one way or the other. However, if it is not already clear, the stronger argument for the latter is that it is a difference of speed of synthesis, not of aggregation. In other words, it is not that von Neumann's powers of aggregation approach infinity, it is that our gestalting powers are slower, and perhaps more obstructed, than his are.

Superfluous Man said...

I am reminded of the parable of the blind men and the elephant. I hope everyone has heard of it.

I know someone who has a son who always asks a person for their birth date when he first meets them. He then proceeds to tell that person what day of the week that day occurred on, and you can name any date within the last century or so, and he can tell you what day of the week the date occurred. Years later when you meet him again he can name your birthday and the day of the week you were born on. He has many other talents as well, too numerous to post here. Yet society has no place for him as he is autistic and his ability has not yet found a home. Only occasionally do we get persons who have such unique gifts as my friend's son, but who can also serve society in some unique fashion, those who are well educated as well as those who are lucky to have been endowed with such unique talents. We are all part of the whole of humanity, however, there are some who society currently deems as individuals as not usable, but who should cause us to marvel at the complexity of the human mind.

I have heard it said that Google's attempts to scan all of the books ever published was not necessarily meant for individuals only, but also to be used by machines that "think".

As the trancendentalist Henry David Thoreau once said, "If you have built castles [and cathedrals too I suppose] in the air, your work need not be lost; that is where they should be. Now put the foundations under them."

wow gold said...
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