Monday, February 04, 2013

Algebra vs. Geometry

I read somewhere that once past elementary arithmetic, all of mathematics can be classified as algebra or geometry.

This is a profound distinction.

Algebra deals in axioms, rules of inference and abstract theorems speaking to a digital, verbal intelligence. Geometry, on the other hand, is the visualisation of shape and space ... and feels kind of analogue.

Algebra inhabits a space near to logic - and you feel it would suit lawyers and computer programmers. Geometry deals in complex, high-dimensional manifolds and would not feel strange to visuo-spatial professionals such as architects, pilots and explorers.

One feels that algebra is a creature of the judgemental left-brain while geometry emerges and grows from the intuitive right-brain.

I have always only understood a mathematical theorem when I can visualise a picture of its underlying shape, a model which makes manifest why the result is, when looked at in the right way, obvious.

But then, I'm an INTP. Let the INTJs and ENTJs wave the flag for algebra!