May 15, 2011

On Feynman and "Genius"

   So we really ought to look into theories that don't work, and science that isn't science. I think the educational and psychological studies I mentioned are examples of what I would like to call cargo cult science. In the South Seas there is a cargo cult of people. During the war they saw airplanes land with lots of good materials, and they want the same thing to happen now. So they've arranged to imitate things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head like headphones and bars of bamboo sticking out like antennas--he's the controller--and they wait for the airplanes to land. They're doing everything right. The form is perfect. It looks exactly the way it looked before. But it doesn't work. No airplanes land. So I call these things cargo cult science, because they follow all the apparent precepts and forms of scientific investigation, but they're missing something essential, because the planes don't land.
    From Richard Feynman: Cargo Cult Science

Today something else than ME - a puzzle, or a small set of them, having to do with my title, about which I know a fair amount.

Just in case you might worry about that: I do not want to suggest Richard Feynman was not a genius - on the contrary: I want to discuss two fairly strange items in his biography by James Gleick called "Genius" (*) that struck me as I leaved through it yesterday, having originally read most of it some 11 years ago. But yes... it has to do with genius and also with Mr. Gleick's "Genius", and also with mathematics, though I won't make it difficult - or so I would say, but that's precisely a principal part of my own problems - and you get twice two puzzles or problems, the first two from Gleick's book, and the last two, which are mine, given the first two, as I will explain.


1. On Feynman and "Genius"
2. Two mathematical puzzles
Two mathematical problems from Gleick
4. A solution

1. On Feynman and "Genius"

James Gleick wrote "Genius - The life and science of Richard Feynman". I've got a paperback version, published by Vintage Books in 1991, 532 pages in all, thoroughly researched, it would seem, and glowingly reviewed. Here is, for example, a blurb by Martin Gardner, quoted on its  opening page, with four others.

"Not until now have we been given a full account of Feynman's extraordinary career and no less extraordinary personality...[It is] splendidly written, scrupulously documented... Gleick... seems to have read every paper and personal letter and to have talked to everyone who ever knew Feynman.... A readable, accurate account of Feynman's great contribution to quantum mechanics.     -- Martin Gardner, Raleigh News and Observer.

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.

2. Two mathematical puzzles

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?
B. What is the
approximate length of the diagonal of a square with sides 5 ?

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.

3. Two mathematical problems from Gleick

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.

Bethe said. "It's twenty-three hundred."

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....
(op. cit. p.231-2)

Really now?!

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?!

4. A solution

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.
"Bullshit" does not necessarily have to be a complete fabrication; with only basic knowledge about a topic, bullshit is often used to make the audience believe that one knows far more about the topic by feigning total certainty or making probable predictions. It may also merely be "filler" or nonsense that, by virtue of its style or wording, gives the impression that it actually means something.
From: Bullshit - Wikipedia

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 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.

(*) James Gleick: The Life and Science of Richard Feynman, Pantheon. (ISBN 0-679-74704-4).

P.S. Corrections, if any are necessary, have to be made later.
-- May 15, 2011: Improved a few sentences (word order) and added a link and the following remarks:

(1) I simply can't believe the quotations I gave from Mr Gleick's biography of Feynman are factually true, and my reason is as given: Any genius in theoretical physics, indeed any theoretical physicist should see my reasoning as a matter of course, for it does not require genius at all, but merely an understanding of some very elementary mathematics, far more elementary than the stuff they do professionally, as a matter of course.

(2) I find it odd nobody seems to have seen this, though, and I can only explain it by mentioning a difference between me and others I noted as a toddler, age 4, when I had to go to school: The other children seemed not imagine what the words and sentences they used meant. I still think this is a difference between me and others: I try to make a mental representation of what words and sentence mean (and conclude I don't understand or the text is nonsense if I can't do so). Then again, there is another explanation, rather more cynical:

(3) Most physicists and mathematicians who read the book did notice it, but did not say so, in public, because that's not the way to keep friends and make careers.

(4) I do think it is .... peculiar, and that is my problem: It is like saying in a biography of Dr. Johnson that he and Edmund Burke could spell "fish" or "English" - as spelled in his time: with long s as in the integral sign - without the help of a dictionary and relay that as a true story showing their great intellectual capacities.

(5) It also does shed an interesting light on "fact checking" and accuracy of semi-popular scientific works, for it's true Mr Gleick's book embodies a lot of work and research on Feynman, and that it is interesting and probably mostly correct in the story of Feynman's life, and useful for anyone wanting to know about that. Then again, as I just said, it reads to me like biography of Dr. Johnson, in which it is told, as if it is a true story, that he and Edmund Burke were most remarkable intellects for not needing a dictionary to spell ordinary English words correctly.

It's a strange world I live in.

As an aside a remark on my html-editor: Given yesterday's note and the text of the day before that, I am very pleased to say this text was written in KompoZer 08.b3 and not in MS Frontpage.

As to ME/CFS (that I prefer to call ME):

1. Anthony Komaroff

Ten discoveries about the biology of CFS (pdf)

3. Hillary Johnson

The Why

4. Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf)
5. Eleanor Stein

Clinical Guidelines for Psychiatrists (pdf)

6. William Clifford The Ethics of Belief
7. Paul Lutus

Is Psychology a Science?

8. Malcolm Hooper Magical Medicine (pdf)

Short descriptions:

1. Ten reasons why ME/CFS is a real disease by a professor of medicine of Harvard.
2. Long essay by a professor emeritus of medical chemistry about maltreatment of ME.
3. Explanation of what's happening around ME by an investigative journalist.
4. Report to Canadian Government on ME, by many medical experts.
5. Advice to psychiatrist by a psychiatrist who understands ME is an organic disease
6. English mathematical genius on one's responsibilities in the matter of one's beliefs:
   "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence".
7. A space- and computer-scientist takes a look at psychology.
8. Malcolm Hooper puts things together status 2010.

    "Ah me! alas, pain, pain ever, forever!

No change, no pause, no hope! Yet I endure.
I ask the Earth, have not the mountains felt?
I ask yon Heaven, the all-beholding Sun,
Has it not seen? The Sea, in storm or calm,
Heaven's ever-changing Shadow, spread below,
Have its deaf waves not heard my agony?
Ah me! alas, pain, pain ever, forever!
     - (Shelley, "Prometheus Unbound") 

    "It was from this time that I developed my way of judging the Chinese by dividing them into two kinds: one humane and one not. "
     - (Jung Chang)


See also: ME -Documentation and ME - Resources

Maarten Maartensz (M.A. psy, B.A. phi)

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