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

From: Luis A. Rodriguez (luiroto_at_yahoo.com)
Date: 05/22/04

  • Next message: Torkel Franzen: "Re: Panu Raatikainen's review of two of Chaitin's books." 
    Date: 22 May 2004 04:20:52 -0700

    > "But appearances notwithstanding, this is simply wrong. In fact, there
    > is no direct dependence between the complexity of an axiom system and
    > its power to prove theorems..."
    >
      I fully endorse this criticism of Raatikainen on Chaitin's work.
      An axiom system can be assimilate to a computer program and
    Raataikinen sentence can be paraphrased :
     " ...there is no direct dependence between the complexity (length) of
    a program and its power to produce complex sequences of numbers."
      Contrary to Chaitin's assertion :
    "The complexity of a finite sequence of numbers can be mesured by the
    length of the minimum program that reproduce it." (Randomness and
    Mathematical Proof)
    That is utterly false.

    Take for example the program that iterates X = k*X^2 - 1 ; Xo = .567
    If k = 1.2 the product is simply a repeating sequence of two numbers.
    If k = 2 the product is a chaotic non-repeting sequence.
    But the Chaitin's complexity (length) of the two programs is the same.

    Take the parametric equations:
    X = T + sin(5*Y)
    Y = T - cos(2*X)
    T being the parameter ; Yo = 0 ; To = -3.14
    This a mild curve symetric to the origin.
    Change the Y by X in the first equation and the X by Y in the second.
    Now you have the Ludovicus Curve . A chaotic curve, never repeating
    and estructurless. The length of the two programs, naturaly, are the
    same.

  • Next message: Torkel Franzen: "Re: Panu Raatikainen's review of two of Chaitin's books."

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