Re: Panu Raatikainen's review of two of Chaitin's books.

From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 05/15/04

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    Date: Sat, 15 May 2004 01:15:09 GMT

    "Eray Ozkural exa" <erayo@bilkent.edu.tr> wrote in message
    news:fa69ae35.0405130556.28994da@posting.google.com...
    > Torkel Franzen <torkel@sm.luth.se> wrote in message
    news:<vcbsme5pup8.fsf@beta19.sm.ltu.se>...
    > > erayo@bilkent.edu.tr (Eray Ozkural exa) writes:
    > >
    > >
    > > > Wow! I am truly impressed! I didn't read any of Chaitin's more
    > > > philosophical books, just the proofs in AIT, so this comes as a shock
    > > > to me. I could find no errors in the proofs, and they did show that
    > > > there *is* a direct dependence between the complexity of a FAS and its
    > > > power to prove theorems (say in determining digits of Omega) as
    > > > defined in AIT!!!
    > >

    I did notice an interersting philosophical article by Chaitin.

    http://arxiv.org/abs/math.HO/0210035

    Gregory Chaitin, IBM Research Division

    Abstract: We discuss views about whether the universe can
    be rationally comprehended, starting with Plato, then
    Leibniz, and then the views of some distinguished
    scientists of the previous century. Based on this, we
    defend the thesis that comprehension is compression, i.e.,
    explaining many facts using few theoretical assumptions,
    and that a theory may be viewed as a computer program for
    calculating observations. This provides motivation for
    defining the complexity of something to be the size of the
    simplest theory for it, in other words, the size of the
    smallest program for calculating it. This is the central
    idea of algorithmic information theory (AIT), a field of
    theoretical computer science. Using the mathematical
    concept of program-size complexity, we exhibit irreducible
    mathematical facts, mathematical facts that cannot be
    demonstrated using any mathematical theory simpler than
    they are. It follows that the world of mathematical ideas
    has infinite complexity and is therefore not fully
    comprehensible, at least not in a static fashion. Whether
    the physical world has finite or infinite complexity
    remains to be seen. Current science believes that the world
    contains randomness, and is therefore also infinitely
    complex, but a deterministic universe that simulates
    randomness via pseudo-randomness is also a possibility, at
    least according to recent highly speculative work of S.
    Wolfram. [Written for a meeting of the German Philosophical
    Society, Bonn, September 2002.]

    SH: Psuedo-randomness represents a pattern, though it may be
    too difficult to discern so that it may not be possible for humans
    to distinguish between the very complex pattern of psuedo-
    randomness from 'true' randomness.

    Regards,
    Stephen

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