What did Hans Bethe think of von Neumann's quantum logic?

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Nobel laureate Hans Bethe was a friend of mathematician-physicist John von Neumann, and he once said:

"I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man"

and

"[von Neumann's] brain indicated a new species, an evolution beyond man"

This indicates that Bethe admired von Neumann's work very much.

My question is: Did he think the same about von Neumann's quantum logic? Did he like it?
 

Answers and Replies

  • #2
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I don't think anyone can answer that question definitively unless Prof Bethe had put it in writing somewhere.

Many people were impressed with John Von Neumann so I imagine that includes the things he worked on. From Wikipedia we have:

https://en.wikipedia.org/wiki/John_von_Neumann

Cognitive abilities[edit]
Nobel Laureate Hans Bethe said "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man",[19] and later Bethe wrote that "[von Neumann's] brain indicated a new species, an evolution beyond man".[185] Seeing von Neumann's mind at work, Eugene Wigner wrote, "one had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch."[186] Paul Halmos states that "von Neumann's speed was awe-inspiring."[18] Israel Halperin said: "Keeping up with him was ... impossible. The feeling was you were on a tricycle chasing a racing car."[187] Edward Teller admitted that he "never could keep up with him".[188] Teller also said "von Neumann would carry on a conversation with my 3-year-old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us."[189] Peter Lax wrote "Von Neumann was addicted to thinking, and in particular to thinking about mathematics".[190]

When George Dantzig brought von Neumann an unsolved problem in linear programming "as I would to an ordinary mortal", on which there had been no published literature, he was astonished when von Neumann said "Oh, that!", before offhandedly giving a lecture of over an hour, explaining how to solve the problem using the hitherto unconceived theory of duality.[191]

Lothar Wolfgang Nordheim described von Neumann as the "fastest mind I ever met",[192] and Jacob Bronowski wrote "He was the cleverest man I ever knew, without exception. He was a genius."[193] George Pólya, whose lectures at ETH Zürich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."[194] Eugene Wigner writes: "'Jancsi,' I might say, 'Is angular momentum always an integer of h? ' He would return a day later with a decisive answer: 'Yes, if all particles are at rest.'... We were all in awe of Jancsi von Neumann".[195] Enrico Fermi told physicist Herbert L. Anderson: "You know, Herb, Johnny can do calculations in his head ten times as fast as I can! And I can do them ten times as fast as you can, Herb, so you can see how impressive Johnny is!"[196]

Halmos recounts a story told by Nicholas Metropolis, concerning the speed of von Neumann's calculations, when somebody asked von Neumann to solve the famous fly puzzle:[197]

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover? The slow way to find the answer is to calculate what distance the fly covers on the first, southbound, leg of the trip, then on the second, northbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained.
The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles.
When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann, "All I did was sum the geometric series."[18]
Eugene Wigner told a similar story, only with a swallow instead of a fly, and says it was Max Born who posed the question to von Neumann in the 1920s.[198]

Von Neumann was also noted for his eidetic memory (sometimes called photographic memory). Herman Goldstine wrote:

One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes.[199]
Von Neumann was reportedly able to memorize the pages of telephone directories. He entertained friends by asking them to randomly call out page numbers; he then recited the names, addresses and numbers therein.[19][200]
 
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