6.5 Our Intuitions About Large Numbers Are Completely Unreliable

Gödel's incompleteness proof[godel][hofstadter] involved constructing an enormous number, arrived at through entirely routine recursive operations, which encoded a statement about itself. The number was just a number. The operations were just operations.

But their accumulation produced something that transcended what the system could say about itself. This is the pattern of 3: when events accumulate and nest across enough iterations, something qualitatively new appears that was not visible in the parts. The threshold where arithmetic becomes self-referential is one example. The threshold where chemistry becomes life is another.