On Feynman and "Genius"
I admire both Feynman and Gardner, and have read their books with admiration and pleasure, and indeed owe most of their books.
And while I would not say that Gleick's book is "splendidly written" it seems a good biography, that must have taken a lot of work, and got a lot of cooperation of Feynman's family, colleagues and friends, and also seems fairly objective and very informed about the man, his background and his work, for indeed - to limit myself to the last - Gleick "seems to have read every paper", and does a lot of explaining.
But here "seems" is the operative word, at least for me, as I now will explain, starting with two problems or puzzles I'll invite you to consider for a brief while.
Here are two puzzles, that both involve no more mathematics than I had learned in high school at age 12 and which I ask you to try to solve mentally - I will explain them later, and you shouldn't worry if you can't, as I also will try to explain:
A. What is the square of the number 48?
As I said: Don't worry if you can't do them. I can, but I like mathematics, and either takes me 3 seconds or less, so somebody like John von Neumann probably did them in the wink of an eye.
Here are two bits quoted from Gleick's biography - and to start with you should know that Hans Bethe, like Feynman, was a great theoretical physicist, and also like Feynman the winner of a Nobel Prize for physics.
First problem. The scene is Los Alamos, during WW II, where both were involved in developing the first atom bomb, together with some 30 other top physicists:
When Bethe and Feynman went up against each other in games of calculating, they competed with special pleasure. Onlookers were often surprised, and not because the upstart Feynman bested his famous elder. On the contrary, more often the slow-speaking Bethe tended to outcompute Feynman. Early in the project they were working together on a formula that required the square of 48. Feynman reach across his desk for the Marchant mechanical calculator.
Feynman started to punch the keys anyway. "You want to know exactly?" Bethe said. "It's twenty-three hundred and four. Don't you know how to take the square of numbers near fifty?" He explained the trick. (op. cit. p. 176-7)
Gleick proceeds explaining the trick, per obscurum, if you ask me. What I did mentally was this: 48 squared = (50-2) squared = (50*50) - (2*2*50) + (-2)*(-2) = 2500 - 200 + 4 = 2304, simply by using (a-b) squared = (a squared) - (2*a*b) + (b squared), as I learned at age 12, and as is very easily verified.
Now my problem is this: I am not a great theoretical physicist, and what I did seems to me the most elementary and obvious thing to do. How could Bethe and Feynman possibly miss this, and Bethe give an explanation, according to Gleick, that is considerably more complicated?
Second problem. This is from a little further on in the book, and starts next to fairly abstruse looking so called Feynman diagrams, with paths sub-atomic particles would take. Gleick gives what is presented as explanations and then writes, in the context of "Shrinking infinities" in path integrals (and such - don't worry if it's beyond you):
It meant that quantum mechanics produced good first approximations followed by a Sisyphean nightmare. The harder a physicist pushed, the less accurate his calculations became. Such quantities as the mass of the electron became - of the theory were taken to its limit - infinite. The horror of this was hard to comprehend, and no glimmer of it appeared in popular accounts of science at the time. Yet it was not merely a theoretical knot. A pragmatic physicist eventually had to face it. "Thinking I understand geometry," Feynman said later, "and wanting to fit the diagonal of a five foot square, I try to figure out how long it must be. Not being an expert I get infinity - unless...
It is not philosophy we are after, but the behavior of real things. So in despair, I measure it directly - lo, it is near to seven feet - neither infinity nor zero. So, we have measured these things for which our theory gives such abnormal answers....
Richard Feynman - "Genius", theoretical physicist, mathematician extra-ordinaire, claimed once by Time Magazine 'the smartest man on earth' - measured the diagonal of a five foot square to an integer approximation?!
Again, what I did mentally was this: It's given it is a square, so Pythagoras Theorem applies, that I learned age 12 in high school, that says that in a straight angled triangle with a and b the sides with the straight angle between them, the diagonal is the c in the formula (a squared plus b squared equals c squared). Since it is given it is a five foot square, both a and b are 5 feet so (a squared) plus (b squared) = 25 + 25 = 50 and the square root of that is a little over 7, since 7 squared is 49.
Now my problem is this: How could a man like Feynman possibly miss that?!
As I said, I solved each problem within 3 seconds at most - and I am no theoretical physicist who won the Nobel Prize, but a - logical - philosopher and a psychologist, who is not well, and who likes mathematics and logic, but usually is too tired to do as I know I could before I fell ill. Even so: 3 seconds at most, and I am not bragging, since I believe anybody with basic mathematics - as I said: I learned what I used when I was 12, at school - who is not stupid and has a little experience with it could easily solve the problems as I did, mentally, and as quick or quicker.
So... I'm sorry for Mr. Gleick, but it is my guess that Feynman would have said he must have been bullshitting:
Bullshit is commonly used to describe statements made by people more concerned with the response of the audience than in truth and accuracy, such as goal-oriented statements made in the field of politics or advertising.
I also can't believe that Mr Gleick - with a degree from Harvard in English and linguistics, Wikipedia says - would have written as I have quoted faithfully if only he had understood the trivial maths involved, so I am afraid he must have written a Cargo Cult biography of a truly great man - but yes...now I also do understand why I didn't understand most of his quantum mechanical explanations, in spite of my having read Feynman and others on the subject.
Finally, I would not have written this piece if it had been about a lesser or another scientist than Feynman, but one of the great things about Feynman is that he detested bullshit.
And I find it odd that this must have been missed by many, including Mr Gleick's editors and his many enthusiastic reviewers.
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