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