A rubber band is 1 meter long. An ant starts at one end, crawling at 1 millimeter per second. At the end of each second, the rubber band is instantaneously stretched by an additional meter. (So, at the end of the nth second, the rubber band becomes n+1 meters long.)

Does the ant ever reach the far end of the band? If so, when?

(In reply to re: The backward ant by Brad Hack)

[Brad Hack] I suspect it will reach the end, but it will take an infinitely long time to reach it.

In mathematical terms, it's finite. But in practical terms, it will take any conceivable computer longer than the lifetime of the universe to arrive at an answer. (Assume a computer that can perform one cycle in the time it takes light to travel across a proton (10^-24 sec). Assume that we can do it with as many parallel threads as there are protons in the solar system (10^57). It would still take longer than the lifetime of the universe to complete. (10^345 years for an answer, vs. 10^100 years for the universe)).

Posted by Jim Lyon on 2002-10-07 11:16:27