 The term “incommensurable” suggests the lack of a common measure. This idea has its historical roots in mathematics. For the ancient Greeks, who had not recognized irrational numbers, the dimensions of certain mathematical objects were found to lack a common unit of measurement. Consider the side and the diagonal of a unit square. These can be compared or ranked ordinally, since the diagonal is longer. However, without the use of irrational numbers, there is no way to specify with cardinal numbers exactly how much longer the diagonal is than the side of a unit square. The significance of this kind of incommensurability, especially for the Pythagoreans, is a matter of some debate (Burkert 1972, 455–465). Hippasus of Metapontum, who was thought by many to have demonstrated this kind of incommensurability, is held by legend to have been drowned by the gods for revealing his discovery (Heath 1921, 154; von Fritz 1970, 407).