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)
“Before me you are a slug in the sun. You are privy to a great becoming and you recognize nothing. You are an ant in the afterbirth. It is in your nature to do one thing correctly: tremble.”
—Michael Mann, U.S. screenwriter. Frances Dollarhyde, aka “The Tooth Fairy” (Tom Noonan)
“First, are you our sort of a person?
Do you wear
A glass eye, false teeth or a crutch,
A brace or a hook,
Rubber breasts or a rubber crotch,
Stitches to show something’s missing?”
—Sylvia Plath (1932–1963)
“The tender skin does not shrink from bayonets, the timid woman is not scared by fagots; the rack is not frightful, nor the rope ignominious. The poor Puritan, Antony Parsons, at the stake, tied straw on his head when the fire approached him, and said, “This is God’s hat.””
—Ralph Waldo Emerson (1803–1882)