Michael Levin

Imagine that, um, you're playing tic-tac-toe against an alien.

So you're in a room, you don't see him, uh,

So you draw the tic-tac-toe thing on the floor and you know what you're doing.

You're trying to make straight lines with X's and O's.

And you're having a nice game.

It's obvious that he understands the process.

Like sometimes you win, sometimes you lose.

Like it's obvious.

In that one little segment of activity, you guys are sharing a world.

What's happening in the other room next door?

Well, let's say the alien doesn't know anything about geometry.

He doesn't understand straight lines.

What he's doing is he's got a box.

And it's full of basically billiard balls, each one of which has a number on it.

And all he's looking, he's doing is he's looking through the box to find billiard balls whose numbers add up to 15.

He doesn't understand geometry at all.

All he understands is arithmetic.

You don't think about arithmetic.

You think geometry.

The reason you guys are playing the same game is that there's this magic square, right, that somebody constructed that basically is a three by three square where if you pick the numbers right, they add up to 15.