High Hopes - Futility Closet
An industrious ant sets out to travel the length of a rubber rope 1 kilometer long. Just as it begins, the rope starts to stretch uniformly at a constant rate of 1 kilometer per second, so that after 1 second the rope is 2 kilometers long, after 2 seconds it’s 3 kilometers long, and so on. The ant advances heroically at 1 centimeter per second relative to the rubber it’s crawling on. Will it ever reach the end of the rope?
This seems hopeless, but the answer is yes. Because the rope’s stretch carries the ant forward, it never loses ground, and because its proportional speed is inversely proportional to the length of the rope, the distance it can travel is unbounded. But it will take a stupendously long time — 8.9 × 1043421 years — to reach the far end.
