Monday, March 27, 2006

Potpourri .. Math etc.

Gathering for Gardner

Seventh Gathering for Gardner (G4G7) was held recently in Atlanta, where a potent jumble of mathematicians, computer scientists, artists, writers, engineers, magicians, inventors, puzzlists gathered to honor Martin Gardner, whose writings in recreational mathematics and magic over many years had exerted such a profound influence over their lives. Catch up with the details in Science News Online here ..


The Limits of Reason

More than a century ago, David Hilbert declared that there was a theory of everything for mathematics following the rules of logic. Later, Kurt Godel refuted this statement and proposed that mathematics contains many true statements / axioms, which cannot be proved. In the March 2006 issue of Scientific American, mathematician Gregory J. Chaitin of the IBM Thomas J. Watson Research Center, has put forth a delightful exposition of his theory on this subject. Chaitin relates this subject with Turing's Halting Problem, for which no general solution exists. If we consider the ensemble of all possible computer programs, then will a program chosen at random halt? This probability, which he calls, omega, is the probability that the machine will eventually come to a halt when supplied with a stream of random bits. He goes on to show that omega cannot be computed since knowing omega will let us solve the Halting Problem, known to be unsolvable. Ivars Peterson's MathTrek also covers this article by Chaitin in detail.

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