What Lies Behind Pythagoras’ Theorem

Pythagoras (570-500 BC) was born on the island of Samos in what is now Greece. On the advice of Thales of Miletus, he travelled to Memphis in Egypt where he came into contact with priests renowned for their wisdom. At the age of 40, he fled the tyranny of Polycrates to Croton in Southern Italy, where he established a philosophical and religious community. Those who entered the community’s inner circle were governed by a strict set of ascetic and ethical rules, forsaking personal possessions, assuming a mainly vegetarian diet, and—since words are so often careless and misrepresentative—observing the strictest silence. Some of the community’s more eccentric rules, such as ‘do not break bread’ or ‘do not poke the fire with a sword’ may have been riddles or allegories that required interpreting. Pythagoras’ brotherly community has been hailed as a prototype for later philosophical institutions such as Plato’s Academy, Aristotle’s Lyceum, and Epicurus’ Garden, and, indeed, for the monastic life and associated early universities.

Music played an important role in Pythagoras’ community. Pythagoreans recited poetry, sang hymns to Apollo, and played on the lyre to cure illnesses of both body and soul. It is said that, one day, Pythagoras passed by some blacksmiths at work, and found that their hammering on anvils produced especially harmonious sounds. He then found that the anvils were simple ratios of one another, one being half the size of the first, another two thirds of the size, and so on. This discovery of a relationship between numerical ratios and musical intervals led Pythagoras to believe that the study of mathematics was the key to understanding the structure and order of the universe. According to his ‘harmony of the spheres’, the heavenly bodies move according to mathematical equations that correspond to musical notes and form part of a grand cosmic symphony.

Pythagoras never separated religion from science and philosophy, which, even in his day, left him open to accusations of mysticism. No doubt under the influence of Orphism, an Ancient Greek mystery religion that arose from pre-Hellenic beliefs and the Thracian cult of Zagreus, he believed in the transmigration of the soul; that is, in the reincarnation of the soul over time into the bodies of human beings, animals, or plants (metempsychosis) until such a time as it became moral. He claimed to have lived four lives and to remember them all in great detail, and once recognized the cry of his dead friend in the yelping of a puppy. After his death, the Pythagoreans deified him, and attributed him with a golden thigh and the gift of bilocation (being in two places at once). But in his own lifetime Pythagoras had always been a paragon of modesty, declining to be called a ‘wise man’ or ‘sophos’, and preferring instead to be called ‘a lover of wisdom’ or ‘philosophos’—thereby coining the term ‘philosopher’.

It is said that Numa Pompilius, the second king of Rome, had been schooled by Pythagoras, whence his great wisdom and piety. This story is referred to and discredited by Plutarch and Livy, not least because the dates do not tally, with Pythagoras having lived from about 570 to 500 BC, and so considerably later than the semi-legendary King Numa. Even though Pythagoras and Numa never met, Pythagoras and the Pythagoreans exerted a strong influence on the Roman mind. In the Tusculan Disputations, Cicero indicates that Pythagoras rose to fame in southern Italy at just the same time that Brutus brought an end to the monarchy, and that many Roman usages derived from the Pythagoreans. Unfortunately, he does not elaborate on the nature of these usages. In his Natural History, Pliny the Elder tells us that, in 343 BC, during the war with the Samnites, the god Apollo ordered the Romans to erect one statue to the wisest and another to the bravest of all Greeks, with their choices falling upon Pythagoras for the former and Alcibiades for the latter. Pliny expresses surprise that they picked Pythagoras over Socrates, whom Apollo himself had called the wisest of all men. But the fact is that the Romans liked to think of the Greek-Italian Pythagoras as their very own philosopher, and spun all sorts of stories, such as the one about Numa, to better appropriate him.

Apart from this, Pythagoras also exerted a strong indirect influence on Roman thinking, and indeed on all philosophy and theology, through the teachings of Plato, the principal architect of the western mind. Aristotle, who was Plato’s pupil of twenty years, claimed that his master’s teachings owed much to those of Pythagoras; so much, in fact, that, in his History of Western Philosophy, Bertrand Russell upheld not Plato but Pythagoras as the most influential of all Western philosophers. Pythagoras’ influence is especially evident in Plato’s mystical approach to the soul and in his emphasis on mathematics and, more generally, abstract thinking, as a secure basis for the practice of philosophy.

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Splitting as an ego defense

Whatever is done for love always occurs beyond good and evil. – Nietzsche

Splitting is a very common ego defense mechanism; it can be defined as the division or polarization of beliefs, actions, objects, or persons into good and bad by focusing selectively on their positive or negative attributes. This is often seen in politics, for example, when members of the Labour Party portray members of the Conservative Party as narrow-minded and self-interested, and conversely when members of the Conservative Party caricature members of the Labour Party as self-righteous hypocrites. Other examples of splitting are the deeply religious person who thinks of others as being either blessed or damned, the child of divorced parents who idolises one parent and shuns the other, and the hospital in-patient who sees the doctors as helpful and dedicated and the nurses as lazy and incompetent. An example of splitting in literature can be found in JD Salinger’s Catcher in the Rye. The main protagonist, Holden Caulfield, is mystified by adulthood. To help cope with his fear of becoming an adult, he thinks of adulthood as a world of entirely bad things such as superficiality and hypocrisy (‘phoniness’) and of childhood as a world of entirely good things such as innocence, curiosity, and honesty. He tells his younger sister Phoebe that he imagines childhood as an idyllic field of rye in which children romp and play, and himself as the ‘catcher in the rye’ who stands on the edge of a cliff, catching the children as they threaten to fall over (and presumably die/become adults).

Anyway, I keep picturing all these little kids playing some game in this big field of rye and all. Thousands of little kids, and nobody’s around – nobody big, I mean – except me. And I’m standing on the edge of some crazy cliff. What I have to do, I have to catch everybody if they start to go over the cliff – I mean if they’re running and they don’t look where they’re going I have to come out from somewhere and catch them. That’s all I’d do all day. I’d just be the catcher in the rye and all. I know it’s crazy, but that’s the only thing I’d really like to be.

In contrast to JD Salinger, Miguel de Cervantes uses splitting to great comical effect as his main protagonist, the self-styled Don Quixote de la Mancha, guides us through a world that he has repopulated with heroes and villains, princesses and harlots, giants and dwarves – with the heroes being the greatest, the villains the most cruel, the ladies the fairest and most virtuous, and so on. ‘Take care, your worship,’ cries Sancho Pancha, Don Quixote’s peasant-turned-squire, ‘those things over there are not giants but windmills.’ Splitting diffuses the anxiety that arises from our inability to grasp the nuances and complexities of a given situation or state of affairs by simplifying and schematising the situation and thereby making it easier to think about; it also reinforces our sense of self as good and virtuous by effectively demonizing all those who do not share in our opinions and values. On the other hand, such a compartmentalization of opposites leaves us with a distinctly distorted picture of reality and a restricted range of thoughts and emotions; it also affects our ability to attract and maintain relationships, not only because it is tedious and unbecoming, but also because it can easily flip, with friends and lovers being thought of as personified virtue at one time and then as personified vice at another (and back and forth). Splitting also arises in groups, when members of the in-group are seen to have mostly positive attributes, whereas members of out-groups are seen to have mostly negative attributes – a phenomenon that contributes to groupthink. Finally, it is worth noting that both fairy tales and the Church feature a number of sharp splits, for example, heroes and villains, good and evil, heaven and hell, angels and demons, and saints and sinners; and that the greatest characters of literature, such as the Achilles or the Odysseus of Homer and the Anthony or the Cleopatra of Shakespeare, contain large measures of both good and bad, with the one being intimately related to the other.

Adapted from Hide and Seek: The Psychology of Self-Deception.

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