16-17 November 17

November 17 marks the birthday of August Ferdinand Möbius, 1790-1868. He is most famous for his mathematical description of the Möbius strip (or loop), which is a looped surface that has only one side. I hope you have had a chance to play with Möbius loops! My tie is made from wide ribbon, and it has only one side. I mean that if you were painting my tie, you could brush smoothly all around the loop until you reached your starting point -- and you would have painted the entire loop -- it has no "inside" versus "outside." Here's your topological/philosophical puzzle for today: In what sense does my tie tack go "through" the loop? We can't say it pokes through "one side" and comes out of the "other side," because the loop has only one side . . . even when I cross the loop over itself . . .