Omega

This article describes the work of Marcus Chown, who has followed in the footsteps of Godel and Turing, extending the reach of mathematical undecidability. Yet again, new vistas of chaos in mathematics, the most rigorous science, have opened yawning before us. We have glimpsed the Leviathan.

Marcus Chown has demonstrated that there is a real number between 0 and 1, that is unique, exists, and is fundamental to mathematics, but each of its digits bears no relation to any of the others - there is absolutely no means of calculating it. This number, named Omega, is simply the probability that an arbitrary computer program will halt if left to run indefinitely. More damningly, he has witnessed this beast swimming through the waters of number theory (the math you learned in grade school, that uses only +, -, x, and /).

Philosophically, this tells us that not only are there truths that cannot be proven (as Godel discovered), but that truth is predominantly random and unknowable. Those truths which reveal other truths are exceptional, for by an infinite margin, unconnected, arbitrary truths outnumber structured truths. The deepest structure of mathematics is noise.

Chown has brought mathematics low. Exploring mathematics is as arbitrary as any other pursuit. Here then is proof that no life is more exalted than any other.