Is God a Mathematician? Read Online Free Page B

820–91). The main problem with attempting to assess Pythagoras’s personal contributions lies in the fact that his followers and disciples—the Pythagoreans—invariably attribute all their ideas to him. Consequently, even Aristotle (384–322 BC) finds it difficult to identifywhich portions of the Pythagorean philosophy can safely be ascribed to Pythagoras himself, and he generally refers to “the Pythagoreans” or “the so-called Pythagoreans.” Nevertheless, given Pythagoras’s fame in later tradition, it is generally assumed that he was the originator of at least some of the Pythagorean theories to which Plato and even Copernicus felt indebted.
    There is little doubt that Pythagoras was born in the early sixth century BC on the island of Samos, just off the coast of modern-day Turkey. He may have traveled extensively early in life, especially to Egypt and perhaps Babylon, where he would have received at least part of his mathematical education. Eventually he emigrated to a small Greek colony in Croton, near the southern tip of Italy, where an enthusiastic group of students and followers quickly gathered around him.
    The Greek historian Herodotus (ca. 485–425 BC) referred to Pythagoras as “the most able philosopher among the Greeks,” and the pre-Socratic philosopher and poet Empedocles (ca. 492–432 BC) added in admiration: “But there was among them a man of prodigious knowledge, who acquired the profoundest wealth of understanding and was the greatest master of skilled arts of every kind; for whenever he willed with all his heart, he could with ease discern each and every truth in his ten—nay, twenty men’s lives.” Still, not all were equally impressed. In comments that appear to stem from some personal rivalry, the philosopher Heraclitus of Ephesus (ca. 535–475 BC) acknowledges Pythagoras’s broad knowledge, but he is also quick to add disparagingly: “Much learning does not teach wisdom; otherwise it would have taught Hesiod [a Greek poet who lived around 700 BC] and Pythagoras.”
    Pythagoras and the early Pythagoreans were neither mathematicians nor scientists in the strict sense of these terms. Rather, a metaphysical philosophy of the meaning of numbers lay at the heart of their doctrines. 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 one hand, they had a tangible physical existence; on the other, they were abstract prescriptions on which everythingwas founded. For instance, the monad (the number 1) was understood both as the 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. The English historian of philosophy Thomas Stanley (1625–78) described beautifully (if in seventeenth century English) the two meanings that the Pythagoreans associated with numbers:
    Number is of two kinds the Intellectual (or immaterial) and the Sciential. The Intellectual is that eternal substance of Number, which Pythagoras in his Discourse concerning the Gods asserted to be the principle most providential of all Heaven and Earth, and the nature that is betwixt them …This is that which is termed the principle, fountain, and root of all things …Sciential Number is that which Pythagoras defines as the extension and production into act of the seminal reasons which are in the Monad, or a heap of Monads .
    So numbers were not simply tools to denote quantities or amounts. Rather, numbers had to be discovered, and they were the formative agents that are active in nature. Everything in the universe, from material objects such as the Earth to abstract concepts such as justice, was number through and through.
    The fact that someone would find numbers fascinating is perhaps not surprising in itself. After all, even