I’ve always had a fascination with math, including most of its subdisciplines. I’m not very good at it; my undergrad career suggested CS was a much wiser choice than physics, even if we didn’t get to play with lasers.
I guess I am much better than the typical non-STEM person; I can make change without help and calculate a tip in my head. Evidence suggests these are vanishing skills. And I can’t think of anyone (else) who would buy a couple of used calculus books to self-study DEs so I could decode the equations in a physics book.
One really cool area that most people can appreciate, even if the details might give them a headache, is topology. Cut a 1″ wide strip off a piece of paper, flip ONE end over, and tape it together. You’ve created a Möbius strip: a bounded, one-sided, nonorientable surface.
If you trace along its length with a pencil, you will come back to the starting point without lifting the pencil. It seems like it has two sides, but it does not. Non-orientable means there’s no way to distinguish between clockwise and counterclockwise. The recycling symbol is an example. Bounded means it has an edge. In this case, exactly one. A sphere is an example of an unbounded object.
As cool as a Möbius strip is, you can make something even cooler if you connect two Möbius strips edge to edge. Now you have a one-sided object with no boundary. Well, actually, you have a 3D representation of a Klien bottle, a proper one does not self-intersect, but you need four dimensions to make that work…
I told you it was deeply nerdy. Look, I am sparing you any equations or discussion of manifolds…
Anyway, there’s a Stanford mathematics professor (Cliff Stoll) who figured out how to produce these out of glass. He got a company to make an order of them, and he sells them as the ultimate math geek gift. I saw it and had to have one. So, I ordered one.
Even though it technically has zero volume, you can fill it with water. But it’s not easy. Nor is drying it out…
