Puzzles
Flip a lamp's switch infinitely many times in two minutes — on or off at the end?
A lamp starts off. You flip its switch after 1 minute, then after another 1/2 minute, then 1/4 minute, then 1/8, and so on — infinitely many flips, all packed into exactly two minutes. Every flip toggles the lamp between on and off. When the two minutes are up, is the lamp on, off, or something else entirely?
Reveal the answer
There's no logically consistent answer — the sequence of flips has no final term, so nothing in the setup determines a last state. Philosopher James F. Thomson devised the puzzle in 1954 to argue that some 'supertasks' (completing infinitely many steps in finite time) are conceptually incoherent, a challenge still debated in philosophy of mathematics and physics today.