Chaos theory is not as interesting as it sounds. How could it be? After all, the name “chaos theory” makes it seem as if science has discovered some new and definitive knowledge about some utterly random and incomprehensible phenomena….By calling certain physical systems “chaotic,” scientists lead us to think that they are totally unintelligible - just a muddle of things happening with no connections or structures. So when they find interesting mathematical patterns in these unpredictable systems, they can exclaim that they have discovered the secrets of “order within chaos,” even though only by christening these systems chaotic in the first place can they make such an impressive result possible.
— Stephen Kellert , In The Wake of Chaos

Archive for the 'Hilbert Formalism' Category

Effective Processes, Computation, and Complexity

Sunday, May 6th, 2007

 

In 1936, two important papers in the field of mathematics and logic were published. One was “An Unsolvable Problem of Elementary Number Theory” by Alonzo Church. [1] The other was “On computable numbers, with an application to the Entscheidungsproblem” by Alan Turing. [2] These papers were aimed at providing formal and rigorous definitions of the […]

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