(cross-posted at the Book of Face):

Wittgenstein's Ribbon: Ludwig Wittgenstein used to pose a form of this problem to his students at Cambridge University in order to demonstrate that they could not always rely on their intuition: the circumference of the earth at the equator is 24,900 miles. Assume for the sake of the problem that the earth’s surface is absolutely uniform: no mountains, no valleys. Given a uniform sphere of 24,900 miles, imagine a ribbon tied around the equator so that it touches the surface at every point.

Now, we want to increase the length of this ribbon so that its still circles the equator, but that it is now one inch above the surface at every point.

How much longer does the ribbon have to be to increase the gap between ribbon and surface by one inch over the course of 24,900 miles?

Them as remember high school geometry will arrive at the solution without undue difficulty, but the answer will surprise many. For extra credit, run the problem again using as the sphere a basketball of arbitrary but approximately real-world circumference. Smack your forehead. Register your admiration in the comments.

cordially,