28 April 2009

Noneuclidean space and Margaret Wertheim

What is truly interesting about the existence of Noneuclidean space is that it shows that math (or at least one axiom of math) is not a priori knowledge. That is, you have to check experience to see what kind of math is 'true' about the world. Since Socrates and before (but especially in "The Mino" by Plato where Socrates shows a young boy that he knows the truth of the Pythagorean theorem despite never being taught it) the axioms of math were said to be a special example of universal, necessary, and certain knowledge about the world which we (humans) had without reference to experience. Now we know that isn't totally the case.