the ham sandwich theorem

Distinctions! Distinctions! ,she said.
Or was it: distinctions, distinctions? I forget.

After serious and profound meditation I have come to the conclusion that there are only two types of people in the world: those who like Cinnamon rolls and those who don't. That is fundamental. Okay, there's also the supremely important: those who like hats and those who don't. And, oh yes, those who are Muslims and those who are infidels. Well, also: the red and the blue. How many does that make? (Yikes! Help me here, Nabs).

Okay, the ham sandwich theorem....later, got to watch the Double Life of Veronique first.

So, here goes. It's like this.

A friend is talking on the phone about "existential questions"

I ask: "what are they?"

He laughs: "It's nothing like Camus or Sartre, it's more like..."

Drum roll, please....

The Ham Sandwich Theorem.

Take a piece of plane paper readers. On it draw six red dots. Done? Okay, now draw six blue crosses (making sure that no three things -dots or crosses- are on a straight line) Now, the idea is that there exists a line that divides the paper so that there are three dots and three crosses on either side of it. [Have you found it?]

Why is that? I've only got some of the intuition and no idea of the implications. But it was cool and it extends to areas and more than two things/objects (I think).

So, if you're cutting a ham sandwich and there's lettuce, ham, and tomatoes then if you have a sharp knife you can cut it so that there's equal amounts of the things for both of us..even if you put the tomato in the corner. Anyway, it wouldn't work because I'd have to swap you my ham for some tomatoes or mustard.