Re: Tipping Point author in town

Date: Tue Feb 05 2002 - 04:45:54 GMT

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    In a message dated 2/4/2002 10:02:47 PM Central Standard Time, Joe Dees
    <> writes:

    > >OK, for the moment, let's assume he will have no idea what the Godelian
    > >threshold is- could you send me a nicely phrased, quickly asserted,
    > >question I could rehearse and learn?
    > >
    > >All the while realizing that I will be among a group of remarkable
    > >miscellany, as I'm sure you're aware.
    > >
    > Godel's Incompleteness Theorems I and II are the most important in 20th
    > century mathematics. It is asserted that beyond a certain level of
    > complexity, that any axiomatic system contains undecideable statements; the
    > reason for this is the emergence of self-reference in complex systems.
    > postulate axiomatic system A, and state that all true statements, and only
    > true statements, are inside A. Now let us construct statement B. B is
    > recursive and self-referential; that is, it refers to its own relation with
    > axiomatic system A, and what it contends is that "B is not an axiom of A".
    > What has happened here? If we include B in A, then B contains the false
    > statement that B is not an axiom of A, and thus does not contain only true
    > statements, but if we exclude B from A, then A does not contain all true
    > statements, for it does not include the true statement that B is not an
    > of A. To put it plainly, B either belongs BOTH inside and outside A, or
    > NEITHER inside nor outsi!
    > de A, and the dilemma is unresolveable within system A. B is undecideable
    > with reference to A. The bottom drops out; mathematics is revealed as a
    > koan.
    > But in reference to the universe A, WE are B, for we are within a universe
    > that we nevertheless entertain a perspectival (point of) view upon; in
    > words, Krishnamurti notwithstanding, as far as self-conscious awareness
    > within our environs goes, we are at once NOT and NOT-NOT the world ("Neti,
    > neti." (Not this, not that). Mind and world are not one, not two, not
    > but are components od a dynamic and recursive interrelational system.
    > hope this helps.

    Hi Joe.

    It would help a lot more if Douglas Hofstadter were giving the talk!


    --Aaron Lynch

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