I began rejecting some delusionally influenced lines of thinking which had been characteristic of my orientation. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos. For example, a non-Zoroastrian could think of Zarathustra as simply a madman who led millions of naive followers to adopt a cult of ritual fire worship. But without his "madness" Zarathustra would necessarily have been only another of the millions or billions of human individuals who have lived and then been forgotten. It seemed desirable more for personal and social reasons than academic ones to accept the higher-paying instructorship at M.I.T. The first break led to a curious result about the embeddability being realizable in surprisingly low-dimensional ambient spaces provided that one would accept that the embedding would have only limited smoothness. And later, the problem was solved in terms of embeddings with a more proper degree of smoothness.
2006-12-05
03:53:29
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7 answers
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asked by
Anonymous
in
Society & Culture
➔ Religion & Spirituality
Statistically, it would seem improbable that any mathematician or scientist, would be able through continued research efforts, to add much to his or her previous achievements.
However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future. Of course I can't consciously remember anything from the first two or three years of my life after birth. (And, also, one suspects, psychologically, that the earliest memories have become "memories of memories" and are comparable to traditional folk tales passed on by tellers and listeners from generation to generation.) But facts are available when direct memory fails for many circumstances. I never saw my grandfather because he had died before I was born but I have good memories.
2006-12-05
03:59:40 ·
update #1
as a result of that exposure to economic ideas and problems, arrived at the idea that led to the paper "The Bargaining Problem" which was later published in Econometrical. And it was this idea which in turn, when I was a graduate student at Princeton, led to my interest in the game theory studies there which had been stimulated by the work of von Neumann and Morgenstern. As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "Non-Cooperative Games", also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph.D. thesis with the other results. But in the event the game theory ideas, which deviated somewhat from the "line" (as if of "political party lines") of von Neumann and Morgenstern's book
2006-12-05
04:02:21 ·
update #2