Hacking in the real world

3D computer games use Pythagorean geometry to figure out distances. This makes it important that they have a very fast way to calculate inverse square roots – or, at least, approximate inverse square roots, close enough to keep the dungeon walls flat and connected to the floor.

So there was some excitement when John Carmack came up with just such a super-fast inverse root function, in the original Quake.

You can read more about it here, but the take-home message is that Carmack’s approximation technique had just a teeny bit of history behind it. It was an ingenious addition to ‘Newton’s method’, discovered not by Helmut Newton or on an Apple Newton but by Isaac Newton, in the late seventeenth century.

This isn’t exactly the sort of breaking-into-the-Pentagon hack you might have expected me to start with, but I think it underlines the depth of history we’re talking about here. We’re used to regarding eight-inch floppies as if they roughly coincided with the Mycenaean Empire, but the history of hacking is really the history of human cleverness, and that goes back much, much further.