"To the Pythagoreans, numbers were both living entities and universal principles, permeating everything from the heavens to human ethics. In other words, numbers had two distinct, complementary aspects. On the one hand, they had a tangible physical existence; on the other, they were abstract prescriptions on which everything was founded. For instance, the monad (the number 1) was understood both as a generator of all other numbers, an entity as real as water, air, and fire that participated in the structure of the physical world, and as an idea—the metaphysical unity at the source of all creation."