# CJ Eller

## Universes within Learning

At a conference on Aristotle, my friend Franco Lo Piparo pointed out that Euclid, the father of geometry, doesn't define a right angle as an angle of ninety degrees. If we think about it, that definition is correct, but of course it's useless for anyone who doesn't know what an angle is, or doesn't know what degrees are, and I hope that no parents will ever undermine their children by telling them that angles are right angles if they are at ninety degrees.

This is how Euclid explains it: “When a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.”

Got it? You want to know what a right angle is? I'll tell you how to make one, or rather, I'll tell you the story of what steps you take to arrive at it. Then you'll understand. Besides, you can learn what steps to take later, after you've constructed that marvelous intersection between two straight lines.

To me this seems both instructive and highly poetic. It brings us closer to the universe of imagination, where to create stories we imagine worlds, and to the universe of reality, where to understand the world we create stories.

Wanted to pull this passage in full from “Here's the right angle,” a piece from Umberto Eco's posthumous collection of essays, Chronicles of a Liquid Society.

A great reminder of how the best learning weaves together wonder and instruction, has a foot in both the universe of imagination and the universe of reality.