Dear Jim . . . (#21) Re: Space

More from Jon:

The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.” – G. H. Hardy
Dear Jim,
So at the end of your letter on time you asked for a letter about space. Conveniently, space – in its broadest sense – is what Measurement by Paul Lockhart is about. I will come back to that. First allow me a series of digressions.
(The Greeks treated all of mathematics spatially. Three was a line three times longer than a line of length one. To add you put the lines end to end, to subtract you cut away a stick of the relevant length. They did all their maths in this way, shapes were vital.)