"Randomness Everywhere," by C. S. Calude and G. J. Chaitin. Nature, 22July 1999, pages 319-320.
This article discusses recent results concerning what are known as Omeganumbers. Omega numbers are real numbers, like the number pi, but they have thestrange property that there is no way of computing more than a finite number oftheir digits. This property is called "algorithmic randomness". Furthermore,Omegas are "computably enumerable", meaning that, given an Omega, there is aninfinite process for computing the Omega, but at any step in the process onecannot tell how close one is to the final value. According to the article, therecent work on Omegas "reinforces the message of algorithmic information theorythat randomness is as fundamental and as pervasive in pure mathematics as it isin theoretical physics."
--- Allyn Jackson