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Sigma Series in Stochastics, Volume 1, 95--116
Heldermann Verlag 2004

Who Is Afraid of Randomness?

Cristian S. Calude
Dept. of Computer Science, University of Auckland, Auckland, New Zealand

Randomness - the mark of anxiety, the cause of disarray or misfortune, the cure for boring repetitiveness, is, like it or not, one of the most powerful driving forces of life. Is it bad? Is it good? The struggle with uncertainty and risk caused by natural disasters, market downturns or terrorism is balanced by the role played by randomness in generating diversity and innovation, in allowing complicated structures to emerge through the exploitation of serendipitous accidents. To many minds any discussion about randomness is purely academic, just another mathematical or philosophical pedantry. False! Randomness could be a matter of life or death, as in the case of Sudden Infant Death Syndrome (SIDS), a merciless child-killer. The present paper describes some difficulties regarding the mathematical modelling of randomness, contrasts silicon-computer generated pseudorandom bits with quantum-computer "random" bits, succinctly presents the algorithmic definition of randomness proposed by algorithmic information theory and the relations between randomness and (logical) incompleteness, briefly presents some applications of algorithmic randomness in physics and finishes by advocating "experimental mathematics", a quasi-empirical, more pragmatic view of mathematics.