The story of Sessa and chess is a classic for explaining exponential growth: a grain of rice on the first square, doubling up to the 64th. The final result, about 18 quintillion grains, exceeds global production for a century. However, there are mathematical processes that generate even more colossal numbers, reducing that mountain of rice to a simple anecdote.
Hyperaccelerated sequences and their logical limits 🚀
While simple doubling follows a geometric progression, functions like the power tower or Knuth's up-arrow notation grow at a dizzying pace. In mathematical logic, these sequences challenge axiomatic systems, where proofs based on initial axioms must be sound. The author of Huge Numbers points out that exploring these numbers is not a game, but a way to understand the foundations of computation and set theory.
The king should have asked for a calculator ♟️
If the king had known Knuth's notation, he might have opted for a more modest reward, like a latte. But no, he asked for rice. And although Sessa ended up executed for his cunning, the real punishment was for the monarch, who was left without his chess game and with an empty silo. The moral: before asking for a favor, make sure the mathematician doesn't have access to a blackboard.