Ant on a rubber rope is a mathematical puzzle with a solution that appears counterintuitive or paradoxical. It is sometimes given as a worm, or inchworm, on a rubber or elastic band, but the principles of the puzzle remain the same.
The details of the puzzle can vary, but a typical form is as follows:
- An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch by 1 km per second (so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc). Will the ant ever reach the end of the rope?
At first consideration it seems that the ant will never reach the end of the rope, but in fact it does (although in the form stated above the time taken is colossal). In fact, whatever the length of the rope and the relative speeds of the ant and the stretching, providing the ant's speed and the stretching remain steady the ant will always be able to reach the end given sufficient time.
Read more about Ant On A Rubber Rope: A Formal Statement of The Problem, Applications of The Problem
Famous quotes containing the words ant on, ant, rubber and/or rope:
“An ant on the tablecloth
Ran into a dormant moth
Of many times his size.
He showed not the least surprise.
His business wasn’t with such.
He gave it scarcely a touch,”
—Robert Frost (1874–1963)
“Go to the ant, thou sluggard; consider her ways, and be wise.”
—Bible: Hebrew Proverbs, 6:6.
The words were rendered by Samuel Johnson in the opening lines of The Ant: “Turn on the prudent ant thy heedful eyes, Observe her labours, sluggard, and be wise.”
“Time for the flat-headed man. I recognize that listener,
Him with the platitudes and rubber doughnuts,
Melting at the knees, a varicose horror.
Hello, hello. My nerves knew you, dear boy.
Have you come to unhinge my shadow?”
—Theodore Roethke (1908–1963)
“Mankind is a rope tied between beast and superman—a rope over an abyss.”
—Friedrich Nietzsche (1844–1900)