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"Randomness Everywhere," by C. S. Calude and G. J. Chaitin. Nature, 22 July 1999, pages 319-320.
This article discusses recent results concerning what are known as Omega numbers. Omega numbers are real numbers, like the number pi, but they have the strange property that there is no way of computing more than a finite number of their digits. This property is called "algorithmic randomness". Furthermore, Omegas are "computably enumerable", meaning that, given an Omega, there is an infinite process for computing the Omega, but at any step in the process one cannot tell how close one is to the final value. According to the article, the recent work on Omegas "reinforces the message of algorithmic information theory that randomness is as fundamental and as pervasive in pure mathematics as it is in theoretical physics."
--- Allyn Jackson
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