Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Dashing adream," by Tom Siegfried. Dallas Morning News, 5 April 2004.

This article explores the significance of the number Omega, discovered bymathematician Gregory Chaitin in 1974. Earlier, Chaitin had proposed a newdefinition of randomness, thereby rediscovering an idea of the 19th centurymathematician Gottfried Wilhelm von Leibniz. Chaitin suggested that somethingis random if the information it contains cannot be compressed into somethingsmaller than itself. More precisely, a number is random if the shortestcomputer program that can be used to calculate the number is as long as thenumber itself. (Any program or number can be translated into a string of 0sand 1s, and it is the length of those strings that are being compared.) Omegais a "maximally random" number, in the sense that it can be shown that there isno program that will produce Omega as output and that is shorter than Omegaitself. "And the moral, [Chaitin] says, is that no single system of axiomswill suffice for understanding (or compressing) mathematics," Siegfried writes."So mathematicians need intuition. And mathematics must embody creativethought."

--- Allyn Jackson