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Monday, August 02, 2021

Review: Journey to the Edge of Reason

 Journey to the Edge of Reason is Stephen Budiansky's biography of Kurt Godel. If you're a computer scientist or mathematician, you've probably at least heard of Godel's incompleteness theorum, but it's rare to hear much else about him or his life. This book reveals why: his wife, Adele, burnt a bunch of letters between him and his family, as well as between her and him, and the book reveals that Godel suffered from hypochondriasis and possibly paranoia:

Gödel’s tragically self-defeating reaction to the fear of never having enough time for his work (“always take on only very little,” he repeatedly admonished himself) was to insist that he must do nothing, however trivial, without first settling on a clear decision and justification for it, which only sank him further into the abyss of indecision and rigidity. “In general, check every hour what you are doing and whether you are adhering to the program (maybe work using a clock at the desk),” he wrote, and sought refuge in an exacting adherence to formality in his clothes, his correspondence, the neatness of his workspace, as a buttress against the disorder of life. Only Gödel could turn the pursuit of moderation and balance in life into unbalanced obsession. (kindle loc 2816)

After his early success (his incompleteness proof was his first post-doctoral work, and his PhD thesis was also similarly impressive), Godel's productivity dropped and eventually worked on Leibniz's philosophy instead, but his conscientiousness made it so that he was still actively providing help and advise in mathematical circles, and it was apparently quite sought after. Ironically, his placement at the Princeton Institute of Advanced Studies with its freedom from the need to publish or teach might have been responsible. Budiansky quotes Menger:

At no time in his life did Gödel need intellectual stimulation to conceive and develop original and unexpected ideas. But he needed a congenial group suggesting that he report his discoveries, reminding and, if necessary, gently pressing him to write them down. All this he had at the beginning of his stay in Princeton. . . . and he presumably could have found such support later. But apparently he never looked for it, and no one seemed to volunteer. The fact is that I could not observe anything of the sort in the 1950s. Rather, it soon became clear to me that he wrote up many brilliant ideas only for his desk drawer if at all. From the point of view of the outside world, his incomparable talent was lying lamentably fallow. (kindle loc 4109)

A mathematician to the end, however, when he was trying to cheer up John Von Neumann as the latter was dying, he  posed the question of P vs NP:

As the logician Gerald Sacks remarked with only slight exaggeration, “I noticed over the years that Gödel’s way of cheering up a dying person was to send him a logical or mathematical puzzle.” But it was also a manifestation of his own denial and fears of serious illness. In his last letter to von Neumann he expressed blithe confidence in his friend’s imminent and complete recovery, before going on to pose what would be one of the most fundamental questions of computer science. Gödel’s letter to his dying colleague was apparently the very first formulation of the so-called “P vs. NP” problem, which offered a striking analogy of his Incompleteness Theorem to the field of computing. “P” is the set of problems easy to solve, for example multiplication and addition. “NP” is the set of problems for which an efficient algorithm exists for checking a given solution, but finding the solution may or may not be easy, such as factoring a large number, solving a sudoku puzzle, or discovering a proof for a formula. (Kindle Loc 4316)

 Godel's life was also characterized by an intense political naiveness, where despite all the signs of brewing war and Nazi party takeover, he traveled back and forth between Princeton and Vienna until it was almost too late for him to leave (he was not Jewish, but was tainted by his work which had been politicized by the Nazis). When he finally took his US citizenship exam, Einstein had to keep him from disqualifying himself:

“Now, Mr. Gödel, where do you come from?” “Where I come from? Austria.” “What kind of government did you have in Austria?” “It was a republic, but the constitution was such that it finally was changed into a dictatorship,” Gödel replied. “That is very bad,” the judge said. “Of course that could not happen in this country.” “Oh, yes,” Gödel exclaimed. “I can prove it!”54 Forman, Einstein, and Morgenstern immediately joined in shutting Gödel up before he could say anything further about his pet idea, and the rest of the ceremony went off without incident. (kindle loc 3905)

One of the unexpected side stories in this book is Godel's relationship with Einstein, and guest star appearances by luminaries such as John Von Neumann:

“The phenomenal feature of von Neumann,” recalled Dean Eisenhart’s son Churchill, who was studying mathematics at Princeton the year the Institute opened, “was that he could go to these parties and party and drink and whoop it up to the early hours of the morning, and then come in the next morning at 8:30, hold class, and give an absolutely lucid lecture. What happened is that some of the graduate students thought that the way to be like von Neumann was to live like him, and they couldn’t do it. (kindle loc 2633)

The book covers Godel's tragedy and his final death via starvation and malnutrition simply because his paranoia kept him from taking any medical advice from doctors, whom he suspected of trying to poison him. His wife would taste his food before he would eat it because he kept suspecting others of trying to poison him.  All in all, it covers the life of someone whom I'd never heard much about. Recommended!

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