Everything and More - David Foster Wallace

A Compact History of Infinity

03 Dec 2021

reading

The ability to halt a line of abstract thinking once you see it has no end is part of what usually distinguishes sane, functional people—people who when the alarm finally goes off can hit the floor without trepidation and plunge into the concrete business of the real workaday world—from the unhinged.

Consider the facts that numbers are called ‘digits’ and that most counting systems—not just our base-10 but also the base-5 and -20 systems of prehistoric Europe—are clearly designed around fingers and toes. Or that we still talk about the ‘leg’ of a triangle or ‘face’ of a polyhedron, or that ‘calculus’ comes from the Greek word for pebble, etc…. It was the Greeks who turned math into an abstract system, a special symbolic language that allows people not just to describe the concrete world but to account for its deepest patterns and laws.

…please keep in mind that a language is both a map of the world and its own world, with its own shadowlands and crevasses—places where statements that seem to obey all the language’s rules are nevertheless impossible to deal with.

Here is a definitive quotation from M. Kline: “As science began to rely more and more upon mathematics to produce its physical conclusions, mathematics began to rely more and more upon scientific results to justify its own procedures.”