When Einstein Walked with Gödel: Excursions to the Edge of Thought

by Jim Holt

First, the depth, power, and sheer beauty of the ideas they convey. Einstein’s theory of relativity (both special and general), quantum mechanics, group theory, infinity and the infinitesimal, Turing’s theory of computability and the “decision problem,” Gödel’s incompleteness theorems, prime numbers and the Riemann zeta conjecture, category theory, topology, higher dimensions, fractals, statistical regression and the “bell curve,” the theory of truth—these are among the most thrilling (and humbling) intellectual achievements I’ve encountered in my life.

My ideal is the cocktail-party chat: getting across a profound idea in a brisk and amusing way to an interested friend by stripping it down to its essence (perhaps with a few swift pencil strokes on a napkin). The goal is to enlighten the newcomer while providing a novel twist that will please the expert. And never to bore.

What Einstein had shown was that there is no universal “now.”

This energy, the optimists say, could be harnessed by our deep-future descendants to power an infinite amount of computation, giving rise to an infinite number of thoughts. Because these thoughts would unfold at a faster and faster pace, subjective time would seem to go on forever, even though objective time was about to come to an end. The split second before the big crunch would thus be like a child’s endless summer: a virtual eternity.

“Time is a great teacher, but unfortunately it kills all its pupils.”

In general, things that have been around for a long time will likely be around for a lot longer. Conversely, things of recent origin likely won’t be. Both of these conclusions flow from the “Copernican principle,” which says, in essence, you’re not special.

Mathematics, after all, is supposed to be the most universal part of human civilization.