“Was not their mistake once more bred of the life of slavery that they had been living?—a life which was always looking upon everything, except mankind, animate and inanimate—‘nature,’ as people used to call it—as one thing, and mankind as another, it was natural to people thinking in this way, that they should try to make ‘nature’ their slave, since they thought ‘nature’ was something outside them” — William Morris

Sunday, October 23, 2011

Geometry as Object Orientation

Over the entrance to the Academy Plato had inscribed something like “Don't even THINK of coming in here unless you know geometry.” What did he mean?

I was thinking this afternoon about the Delian problem: the oracle at Delphi reputedly told the people of Delos to double the size of the Altar to Apollo. Plato took this to mean that they should chill by contemplating higher things, rather than be plagued with plague.

Later, Plato got pretty mad at Eudoxus and Archytas for solving the problem using mechanical means, rather than using pure geometry. But what is that?

Pure geometry just means “with a compass and a straight edge only.” The Delian problem is about how to use tools to make objects. So Plato had this in mind when he put that inscription over the entrance to the Academy.

Which brings me to a sublime discovery Ian Bogost shared with me: instructional videos can be very beautiful. (More to follow if I remember to.) What if we thought of Graham Harman's “philosophical installations” along these lines? (See my previous.)

(By the way, you can't double a cube using a compass and a straight edge...)

ἀγεωμέτρητος μηδεὶς εἰσίτω

1 comment:

Bill Benzon said...

Well, Tim, one of my pet ideas is that Plato got the idea of the Ideal Forms from geometry. One of the things that gets pounded into you in middle school geometry class is that the triangles we actully draw (yes, with compass and straight edge) aren't 'true' triangles. They've always got defects. But the abstract triangles in geometrical constructions and proofs, they're 'true', they're 'pure'. So, take that insight from geometry, where it becomes very 'real' through practice, and extend it to everything. Hence The Forms.