michael perelman wrote:
Mirowski says that Godel's proof rattled both Turing & Van Neuman, making them turn from formalizing to matters such as game theory & computers.
i grabbed a copy of Goldstein's book this morning in the bookstore and gave it a fast read (good on history and philosophical context for the work, weak on appreciation of what Godel produced, IMHO: too much loose philosophical interpretation). turns out von Neumann was at the conference where Godel presented his results, and caught its significance immediately, particularly in after-lecture discussions with Godel. He returned to Princeton and really pushed the ideas in lectures and discussions. he wrote Godel shortly thereafter with an extension to Godel's theorem which the latter hadnt presented in the conference but in fact had already worked out. Godel was evidently pleased that a "giant" like von neumann got the message, a result that Goldstein says was absent in the case of Wittgenstein's misunderstandings of Godels proofs.
Likewise Turing picked up the ball in the mid-30's and ran rather far with it in computational matters, as ravi points out in a later post. This thread continues to the present day, to the point where a commited amateur can now browse the web for work of Gregory Chaitin and actually download programs which concretely illustrate the results (Chaitin as i recall provides a slightly modified LISP suitable for running his code).
in relation to a question raised on marxmail regarding any relationship between Godel's and Heisenberg's work: next to Goldstein's book at the Border's Bookstore math section stood an interesting work by Palle Yourgrau (philosopher at Brandeis) entitled "A World Without Time: The Forgotten Legacy Of Godel And Einstein". midway into the book Yourgrau relates an incident involving John Wheeler, a Princeton physicist, and the two co-authors of his (ahem) massive treatise on general relativity (Gravitation). Wheeler et al one afternoon decided to pay Godel a visit across campus, and they asked him directly if there was any relationship between the incompleteness theorems and the uncertainty principle. Godel's answer was apparently fairly brief with a "NO" for the upshot. Yourgrau goes on to speculate on why Godel would have felt this way, and discusses how Godel abhorred the positivist-like approach of the Copenhagen school whereas Godel would have seen himself -- an unabashed Platonist and believer in the reality of mathematical ideas -- and his theorems as in part exposing the barrenness of a formalism which would also deny physical reality to electrons et al.
Both Goldstein and Yourgrau discuss extensively the Vienna school, and i am hoping Jim Farmelant kicks in here with some further insights. [Jim: i'll get to Dumain's questions hopefully tmw]
les schaffer
