Experiment!: Planning, Implementing and Interpreting

3.3 Divine Mathematics

When later philosophers describe the early Greek attempts at a scientific explanation of the world, they distinguish between two schools of thought. On the one hand there is the Ionian school that we have discussed. They sometimes call it atheistic, as it relied only on material causes. The other school is a religious one, arising in greater Greece in the west. In Plato's account, the Ionian school does not recognize any form of intentional creation in Nature. It claims that only the human mind creates intentionally and it, too, arises from material causes. The religious school, by contrast, claims that purpose and thought precede the properties of matter. Nature is ruled by reason [2].

This religious tradition begins with Pythagoras, who is known to most school children through his famous theorem. Figure 3.1 gives a simple geometric proof of it. He was originally from the island Samos, just a stone's throw off the coast from Miletus, but he moved to Croton in southern Italy where he founded a religious community. They practiced asceticism and taught that it was, for some reason, sinful to eat beans. They also spent time contemplating mathematics, where they saw the key to understanding the world.

Figure 3.1 A simple, geometric proof of Pythagoras’ theorem. Calculating the area of the large square by adding the areas of the four right-angled triangles and the small square, it directly follows that c2 = a2 + b2. It is not known if Pythagoras himself could ...