Re: More Godel

[Les Schaffer <schaffer@xxxxxxxxxxxxx>]

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