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Pythagoras Him.Self Discovered the Pythagorean Theorem

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Pythagoras Him.Self Discovered the Pythagorean Theorem the Pythagorean theorem. I may as well break the news right away: there's no good literary character-a vessel for the ideas and imaginings of other people. And while evidence that Pythagoras him.self discovered the Pythagorean theorem. It was, we like to think we have some reasonably vivid idea of the real Socrates, thanks to however, known to his followers, the Pythagoreans. That rather sets the tone for Plato and other authors like the historian Xenophon, in the case of Pythagoras we the rest of our discussion of Pythagoras. We know a great deal about the tradition of are really just sifting through legends and myths. Not only is Pythagoras quite a Pythagoreans which takes its name fromhim, but we know hardly anything about bit earlier than Socrates, but his way of doing philosophy-if he did philosophy at the man himself. Among the Pre-Socratics, all of whom are surrounded by a good all-was a lot less public than Socrates'. Whereas Socrates would walk up to people deal of misinformation and legend, he stands out as the one figure who is more in the marketplace and harass them by askingthem to define virtue, Pythagoras and myth than man. But what a myth! He's credited with being the first to fuse his young students in Croton supposedly observeda code of silence, to prevent their philosophy and mathematics, with being a worker of miracles, being divine or secret teachings from being divulged to the uninitiated. Of course, maybe that code semi-divine, the son of either Apollo or Hermes. The beliefs ascribed to him range of silence is just another legend, but the fact remains that we have very little idea from arcane metaphysical and religious ideas... to homely ethical teachings... what Pythagoras him.self said or thought, not only because of a lack of reliable But before we get carried away with the myth-and don't worry, we'll be getting evidence, but because the stray bits of reliable evidence oftens eem to be deliberately carried away shortly, since the myth is too good to pass over in silence-let's start obscure. with what we do know about the man. We've seen that the first Pre-Socratics hailed To make things worse, these bits of reliable evidence are buried under an from Miletus, on the coast of Asia Minor in modem-day Turkey. Xenophanes too avalanche of more dubious evidence from people who thought of themselves as was from there, but traveled west. The same is true of Pythagoras: we have good "Pythagoreans." This tradition of Pythagoreanism is one of the most durable in evidence that he was from Samos, an island off the same coast (§264). But he too ancient Greek philosophy. It begins, obviously enough, with Pythagoras him.self and traveled across the Mediterranean, possibly having left his birthplace because he his immediate followers. There was then a reasonably well-defined Pythagorean didn't see eye to eye with the local tyrant, Polycrates (§266). The place he's most movement in the fifth century; and Plato and Aristotle in the fourth century had associated with is therefore not Samos but Croton, a city in southern Italy associates and students who styled themselves as Pythagoreans. Aristotle found this (§§269-70). In fact ancient authors liked to give him credit for founding a phenomenon interesting enough that he wrote a book about Pythagoras and his distinctive philosophical tradition, the so-called "Italian school" of philosophy. Here followers, but unfortunately this is lost. It's really the fifth-century Pythagoreans, it might be worth mentioning again that Sicily, Italy, and other parts of the western afterPyth agoras himself was dead but beforePlat o comes along, who should get the Mediterranean had been settled by Greek colonists in the centuries previous to the credit for fusing philosophy with mathematics. Ideas like the harmony of the emergence of the Pre-Socratics. The Greeks held on in southern Italy for quite a spheres-the notion that the proportions of the celestial bodies are arranged long time, until the Romans finally pushed them out of this region, which they according to some kind of musical ordering-probably emerged in this period. called Magna Graecia. Pythagoras him.self would have lived there in the sixth Still, all ancient authors assume that Pythagoras himself had an intense interest in century BC, about two centuries after the settlement of Croton in the late eighth mathematics, and we may as well go along with this, while remembering that his century. 3 But getting really clear about his dates is not an easy matter. We know interest may have been more religious or symbolic than technical. that both Xenophanes and Heraclitus refer to him by name, meaning that he's a The ancient authors who talk about early Pythagoreanism build up a probably rough contemporary of these thinkers, which is good enough for our purposes. fictitious contrast between two types of followers of the divine Pythagoras (§280). So there's Pythagoras, in southern Italy, not discovering the Pythagorean the­ There are the ones who are interested in the religious and ethical precepts that he orem. Another thing he was not doing is writing books. In fact, it's striking that laid down, the so-called acusmata (§§275-6); and then there are the math geeks. It's in Pythagoras and Socrates are, arguably, the most famous philosophers prior to Plato the ethical precepts that we get the instruction, for instance, not to eat ... meat. ... As and Aristotle, and yet neither of them wrote anything. Maybe they are so famous for the math geeks, precisely because they never wrote anything. Socrates, like Pythagoras, became a 24 25 these are the Pythagoreans ·who really interest Plato and Aristotle. They get men­ Pythagoras has blossomed so that he is seen as the definitive sage, able to work tioned in Aristotle's existing works as well as his lost work on the Pythagoreans, miracles and apparently inexhaustible in his wisdom. At one point Iamblichus says which we only know in fragments. These were thinkers who went so far as to say that there are three kinds of two-footedbeings: birds, humans, and Pythagoras. And that things in the physical universe are somehow made of numbers (§§430-2). ... well he might, in light of the miraculous events he ascribes to this ancient sage and The mathematically inclined Pythagoreans had a deeply symbolic, maybe even wonder-worker. (Some were already reported much earlier, for instance by Aris­ mystical, understanding of number. These were people like Philolaus, from totle.) ... He's able to see the future, for instance, by predicting an earthquake. He Pythagoras' adopted home Croton. ... A particularly important number for them can talk to animals, and even give them instructions: Iamblichus has him was 10, which among other things is the sum of the first four numbers, which confronting a bear who had been attacking people in the local area, and persuading they called the tetrakiys; in other words, 1 + 2 + 3 + 4 = 10. Aristotle, in fact, tells us the bear to mind its manners. If that's not enough to impress you, he can also talk that the Pythagoreans thought there must be a heavenly body which is always to geographical features: both Aristotle and Iamblichus tell us that he was once hidden from us, the so-called "counter-earth," because the visible heavenly bodies greeted by a river (§273). including the sun and moon counted 9, but there must be 10 of them because 10 is ... Iamblichus most definitely sees Pythagoras as a philosopher. He sees him, in the most important number (§§446-7). fact, as the philosopher: the founder of Iamblichus' own intellectual tradition and AfterAristotle and Plato's immediate followersthe Pythagoreansfade away a bit, even the first man to call himself a philosophos, which means "lover of wisdom," sophia being the Greek word for wisdom. On this account, Pythagoras was the first but they make a big comeback in the first centuryBC. At this point we begin to see a powerful tendency to combine Plato's ideas with Pythagorean ideas like number to make the love of wisdom 'into a way of life. symbolism. This tendency lives on until the end of pagan Greek philosophy, with As we might expect, Iamblichus also emphasizes Pythagoras' connections with the tradition we nowadays refer to as "Neoplatonism": we call the late ancient mathematics, especially music. From very early on in the Pythagorean tradition philosophers of the third to sixth centuries BC Neoplatonists because they were music and mathematics were intimately related. And no wonder, because the followersof Plato, but also had a lot of "new'' ideas which modem scholars do not relationships between notes are just examples of mathematical ratios. In fact, you findin Plato. For them one of the biggest influenceswas the tradition of Pythagoras, would make a Greek lyre by stretching numerous strings at the same tension: the whom they saw as an ultimate source of Plato's own ideas. Thus Pythagoras,one of different lengths of the strings give you the different notes. ... the veryearliest Greek thinkers, became one of the most important authoritiesand intellectual heroes of the Greek thinkers in late antiquity, a full millenium later. One of the Neoplatonists who most admired Pythagoras was Iamblichus, who lived in the third to fourth century AD. We'll get to him as a philosopher in his own right in a future volume of this series. I mention him now because he wrote a work called On the PythagoreanW try of Life, which shows the way Pythagoras was perceived by that much later period of Greek philosophy.4 By Iamblichus' day the legend of 26 27 The Pythagoreans believed that the musical harmonies had some kind of affinity with, and effect on, the human soul.
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