Who Can Name the Bigger Number?

Aaronson's classic essay (a UT Austin lecture-turned-paper) on the human pursuit of really big numbers. He opens with a fifteen-second contest — name the biggest whole number you can in standard notation — and walks the reader through place value, exponentials, stacked exponentials, the Ackermann function, and Tibor Radó's Busy Beaver function (uncomputable, growing faster than any computable function). Threaded throughout is the parallel to Petr Beckmann's A History of π: curiosity and reason produce these notational leaps; ignorance and fatalism stall them. The story of big numbers is a story of human progress.