Supertasks: Doing Infinite Things

What happens when you complete infinitely many steps? Joel David Hamkins walks through a series of supertasks that challenge ordinary intuition about infinity. He begins with Thompson's Lamp, a puzzle about toggling a light switch infinitely many times, then connects it to Zeno's paradox to show that supertasks may not be as exotic as they seem. The lecture builds toward deeper puzzles: a deal with the devil, balls placed into and removed from a sack where the final count defies expectation, and a stochastic version where probability-zero events become surprisingly relevant. Hamkins carefully distinguishes between what holds for every individual ball and what holds for all balls collectively, exposing a subtle logical gap. The lecture culminates in the chocolatier's game, where questions about finite versus infinite servings, memory, and the axiom of choice determine whether a glutton can guarantee tasting every flavor. Throughout, Hamkins shows how rigorous thinking about infinity upends common sense.