Pythagoras — Out of darkness light
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Out of darkness light
Who was Pythagoras?

Summary

Pythagoras was a celebrated philosopher who lived in the sixth century before Christ. In the course of his extensive travels through Ionia, Syria, and Egypt, he had been initiated into all the famed mysteries of these kingdoms. It was a desire likely to arise in the mind of such a benevolent and reflective man, to form a perfect system of philosophy, by selecting from the systems into which he had been initiated, whatever seemed peculiarly excellent, and perhaps even improving on them. He settled in Crotona, in Italy, and there, about 550 B.C., founded a fraternity of disciples, called, after him, Pythagoreans. Before any one was received into the number of his disciples, a most rigid inquiry was made into his moral character. If the result was favorable, he was then bound by a solemn engagement to conceal from the uninitiated the mysteries and knowledge in which he might be instructed. The doctrines of charity, of universal benevolence, and of peculiar regard for the brethren of the order, were inculcated on the new disciple. The members were distinguished by wearing white garments as emblems of purity and innocence, and they had also particular words and signs by which they could recognise each other and correspond at a distance. They were advanced from one degree of knowledge to another, and they were instructed in arts and sciences, united with ethics and a system of theology; and this instruction was communicated to the initiated by cyphers and symbols. They were also strictly forbidden to commit their secrets to writing, and relied on oral tradition only to preserve the knowledge of their mysteries. This philosophy, remembered now only by the familiar tenets of the transmigration of souls and avoidance of beans, exercised at one time much influence on the nations where it flourished, and was confessedly the means of greatly exalting the mind and moral character of the initiated. The noblest, wisest, and best of the nation were members, and, though suffering much persecution, they were eminently distinguished by the greatest fidelity in all their engagements, and their strict performance of all moral duties.

Details

Pythagoras of Samos (Greek: Πυθαγόρας; circa 582 BC – circa 507 BC) was an Ionian (Greek) mathematician, astronomer, scientist and philosopher,[1] founder of the mathematical, mystic, religious, and scientific society called Pythagoreans. His name led him to be associated with Pythian Apollo; Aristippus explained his name by saying, "He spoke (agor-) the truth no less than did the Pythian (Pyth-)," and Iamblichus tells the story that the Pythia prophesied that his pregnant mother would give birth to a man supremely beautiful, wise, and of benefit to humankind.[2]

He is best known for the Pythagorean theorem which bears his name. Known as "the father of numbers," Pythagoras made influential contributions to philosophy and religious teaching in the late 6th century BC. Because legend and obfuscation cloud his work even more than with the other pre-Socratics, one can say little with confidence about his life and teachings. We do know that Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be predicted and measured in rhythmic patterns or cycles. According to Iamblichus, Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons."

He was the first man to call himself a philosopher, or lover of wisdom. Many of the accomplishments of Plato, Aristotle and Copernicus were based on the ideas of Pythagoras. His ideas mirror other great philosophies such as the Yin-Yang, Buddhism and String Theory. Unfortunately, very little is known about Pythagoras because none of his writings have survived. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors.

Life

Pythagoras was born on the island of Samos (a Greek island in the Eastern Aegean), off the coast of Asia Minor. He was born to Pythais (his mother, a native of Samos) and Mnesarchus (his father, a merchant from Tyre). As a young man, he left his native city for Croton, Calabria, in Southern Italy, to escape the tyrannical government of Polycrates. According to Iamblichus, Thales, impressed with his abilities, advised Pythagoras to head to Memphis in Egypt and study with the priests there who were renowned for their wisdom. He also was discipled in the temples of Tyre and Byblos in Phoenicia. It may have been in Egypt where he learned some geometric principles which eventually inspired his discovery of the theorem that is now called by his name. This possible inspiration is presented as an example problem in the Berlin Papyrus.

Upon his migration from Samos to Croton, Calabria, Italy, Pythagoras established a secret religious society very similar to (and possibly influenced by) the earlier Orphic cult.

Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of followers around himself called Pythagoreans. Very strict rules of conduct governed this cultural center. He opened his school to male and female students alike. Those who joined the inner circle of Pythagoras's society called themselves the Mathematikoi. They lived at the school, owned no personal possessions and were required to assume a vegetarian diet. Other students who lived in neighboring areas were also permitted to attend Pythagoras's school. Known as Akousmatikoi, these students were permitted to eat meat and own personal belongings.

According to Iamblichus, the Pythagoreans followed a structured life of religious teaching, common meals, exercise, reading and philosophical study. Music featured as an essential organizing factor of this life: the disciples would sing hymns to Apollo together regularly; they used the lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to aid the memory.

Bust of Pythagoras, VaticanFlavius Josephus relates that, according to Hermippus of Smyrna, Pythagoras was familiar with and an admirer of Jewish customs and wisdom (De Pythagora, Contra Apionem I, 162/165). Hermippus is quoted as saying about Pythagoras: "In practicing and repeating these precepts he was imitating and appropriating the doctrines of Jews and Thracians. In fact, it is actually said that that great man introduced many points of Jewish law into his philosophy." (trans. H. St. J. Thackeray, The Loeb Classical Library, Cambridge (Mass.)-London)

Pythagoras is commonly given credit for discovering the Pythagorean theorem, a theorem in trigonometry that states that in a right-angled triangle the area of the square whose side is the hypotenuse (the side opposite the right angle), c, is equal to the sum of the areas of the squares of the other two sides, b and a, that is, a2+b2=c2.

The history of the Pythagorean theorem that bears his name is complex. Whether Pythagoras himself proved this theorem is not known, as it was common in the ancient world to credit a famous teacher with the discoveries of his students. The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch. There are many ancient references to the facts stated in the Pythagorean Theorem; it is the proof of the theorem which is attributed to Pythagoras.

Today, Pythagoras is revered as a prophet by the Ahlu l-Tawhīd or Druze faith along with his fellow Greek, Plato.

Pythagoreans

The organization was in some ways a school, in some ways a brotherhood, and in some ways a monastery. It was based upon Pythagoras’ religious teachings and was very secretive. At first, the school was highly concerned with the morality of society. Members were required to live ethically, love one another, share political beliefs, practice pacifism and vegetarianism, and devote themselves to the mathematics of nature.

Pythagoras's followers were commonly called "Pythagoreans." For the most part we remember them as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.

The Pythagoreans observed a rule of silence called echemythia, the breaking of which was punishable by death. This was because the Pythagoreans believed that a man's words were usually careless and misrepresented him and that when someone was "in doubt as to what he should say, he should always remain silent". Another rule that they had was to help a man "in raising a burden, but do not assist him in laying it down, for it is a great sin to encourage indolence", and they said "departing from your house, turn not back, for the furies will be your attendants"; this axiom reminded them that it was better to learn none of the truth about mathematics, God, and the universe at all than to learn a little without learning all. (The Secret Teachings of All Ages Hall, Manly P.).

In his biography of Pythagoras (written seven centuries after Pythagoras's time), Porphyry stated that this silence was "of no ordinary kind." The Pythagoreans were divided into an inner circle called the mathematikoi ("mathematicians") and an outer circle called the akousmatikoi ("listeners"). Porphyry wrote "the mathematikoi learned the more detailed and exactly elaborate version of this knowledge, the akousmatikoi (were) those which had heard only the summary headings of his (Pythagoras's) writings, without the more exact exposition." According to Iamblichus, the akosmatikoi were the exoteric disciples who listened to lectures that Pythagoras gave out loud from behind a veil.

The akousmatikoi were not allowed to see Pythagoras and they were not taught the inner secrets of the cult. Instead they were taught laws of behavior and morality in the form of cryptic, brief sayings that had hidden meanings. The akousmatikoi recognized the mathematikoi as real Pythagoreans, but not vice versa. After the murder of Pythagoras and a number of the mathematikoi by the cohorts of Cylon, a resentful disciple, the two groups split from each other entirely, with Pythagoras's wife Theano and their two daughters leading the mathematikoi.

Theano, daughter of the Orphic initiate Brontinus, was a mathematician in her own right. She is credited with having written treatises on mathematics, physics, medicine, and child psychology, although nothing of her writing survives. Her most important work is said to have been a treatise on the principle of the golden mean. In a time when women were usually considered property and relegated to the role of housekeeper or spouse, Pythagoras allowed women to function on equal terms in his society.

The Pythagorean society is associated with prohibitions such as not to step over a crossbar, and not to eat beans. These rules seem like primitive superstition, similar to "walking under a ladder brings bad luck". The abusive epithet mystikos logos ("mystical speech") was hurled at Pythagoras even in ancient times to discredit him.

The key here is that akousmata means "rules", so that the superstitious taboos primarily applied to the akousmatikoi, and many of the rules were probably invented after Pythagoras's death and independent from the mathematikoi (arguably the real preservers of the Pythagorean tradition). The mathematikoi placed greater emphasis on inner understanding than did the akousmatikoi, even to the extent of dispensing with certain rules and ritual practices. For the mathematikoi, being a Pythagorean was a question of innate quality and inner understanding.

There was also another way of dealing with the akousmata — by allegorizing them. We have a few examples of this, one being Aristotle's explanations of them: "'step not over a balance', i.e. be not covetous; 'poke not the fire with a sword', i.e. do not vex with sharp words a man swollen with anger, 'eat not heart', i.e. do not vex yourself with grief," etc. We have evidence for Pythagoreans allegorizing in this way at least as far back as the early fifth century BC. This suggests that the strange sayings were riddles for the initiated.

The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed and developed various rules of living which they believed would enable their soul to achieve a higher rank among the gods.

Much of their mysticism concerning the soul seem inseparable from the Orphic tradition. The Orphics advocated various purificatory rites and practices as well as incubatory rites of descent into the underworld. Pythagoras is also closely linked with Pherecydes of Syros, the man ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that Pherekydes was Pythagoras's most intimate teacher. Pherekydes expounded his teaching on the soul in terms of a pentemychos ("five-nooks", or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a symbol of recognition among members and as a symbol of inner health (ugieia).

Pythagoras, the man in the center with the book, teaching music, in The School of Athens by RaphaelPythagoras was interested in music and the Pythagoreans were musicians as well as mathematicians. He wanted to improve the music of his day, which he believed was not harmonious enough and was too chaotic.

According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was one day as he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools. He discovered that it was because the anvils were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on." The Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Pythagoras believed in something called the harmony of the spheres. He believed that since planets and the stars all moved in the universe according to mathematical equations that these mathematical equations could be translated into musical notes and thus produce a symphony.[3]

Religion and Science

Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. However, they are looked at separately in the 21st century. Religiously, Pythagoras was a believer of metempsychosis. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became moral. His ideas of reincarnation were probably borrowed from Hinduism. According to him, the soul was a string-like independent number, like a string from String Theory. He was one of the first to propose that the thought processes and the soul where quartered in the brain and not the heart. He himself claimed to have lived four lives that he could remember in detail, and heard the cry of his dead friend in the bark of a dog.

Other accomplishments

One of his major accomplishments was the discovery that music was based on proportional intervals of four. He believed that the number system, and therefore the universe system, was based on the sum of these numbers: ten. Pythagoreans swore by the Tetrachtys of the Decad, or ten, rather than by the gods. He assigned roles for the numbers as follows: one was reason, two was opinion, four was justice, five was marriage because it was the sum of the first odd and the first even numbers (one was disregarded), seven was virgin because it neither factors or produces among the numbers one through ten. Odd numbers were masculine and even were feminine. He discovered the theory of mathematical proportions, constructed from three to five geometrical solids, and discovered irrational numbers, like the square root of two. He was one of the first to think that the earth was round, that all planets have an axis, and that all the planets travel around one central point. He originally identified that point as Earth, but later renounced it for the idea that the planets revolve around a central “fire” that he never identified as the sun. He also believed that the moon was another planet that he called a “counter-Earth” – furthering his belief in the Limited-Unlimited and bringing the number of planets to ten. He theorized that the year and the day were both equal to twenty-four hours.

Literary works

No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. Ancient Pythagoreans usually quoted their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the essentially oral nature of his teaching. Pythagoras appears as a character in the last book of Ovid's Metamorphoses , where Ovid has him expound upon his philosophical viewpoints. Pythagoras has been quoted as saying, "No man is free who cannot command himself."

Influence on Plato

Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According to R. M. Hare, his influence consists of three points: a) the platonic Republic might be related to the idea of "a tightly organized community of like-minded thinkers", like the one established by Pythagoras in Croton. b) there is evidence that Plato possibly took from Pythagoras the idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for substantial theses in science and morals". c) Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both have been influenced by Orphism.[4]

Plato's harmonics were clearly influenced by the work of Archytas, a genuine Pythagorean of the third generation, who made important contributions to geometry, reflected in Book VIII of Euclid's Elements.

Roman influence

In the legends of ancient Rome, Numa Pompilius, the second King of Rome, is said to have studied under Pythagoras. This is unlikely, since the commonly accepted dates for the two lives do not overlap.

Influence on esoteric groups

Pythagoras started a secret society called the Pythagorean brotherhood devoted to the study of mathematics. This had a great effect on future esoteric traditions, such as Rosicrucianism and Freemasonry, both of which were occult groups dedicated to the study of mathematics and both of which claimed to have evolved out of the Pythagorean brotherhood. The mystical and occult qualities of Pythagorean mathematics are discussed in a chapter of Manly P. Hall's The Secret Teachings of All Ages entitled "Pythagorean Mathematics".

Pythagorean theory was tremendously influential on later numerology, which was extremely popular throughout the Middle East in the ancient world. The 8th-century Islamic alchemist Jabir ibn Hayyan, inventor of numerous important chemical processes still in use today, grounded his work in an elaborate numerology greatly influenced by Pythagorean theory

References

Source: Wikipedia.org

Primary sources

Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations. Other texts usually build solely on information from these four books.

Diogenes Laertius, Vitae philosophorum VIII (Lives of Eminent Philosophers). circa 200, which in turn reference the lost work Successions of Philosophers by Alexander Polyhistor) — Pythagoras, Translation by C.D. Yonge

Porphyry, Vita Pythagorae (Life of Pythagoras), circa 270

Iamblichus, De Vita Pythagorica (On the Pythagorean Life), circa 300.

Apuleius also writes about Pythagoras in Apologia, including a story of him being taught by Babylonian disciples of Zoroaster, circa 150.

Hierocles, 1983. Golden Verses of Pythagoras, Concord Grove Pr.

Secondary sources

Burkert, Walter. Lore and Science in Ancient Pythagoreanism, Harvard University Press, June 1, 1972. ISBN 0-674-53918-4

Guthrie W. K. 1979. A History of Geek Philosophy - Earlier Presocratics and the Pythagoreans, Cambridge University Press ISBN 0-521-29420-7

Kingsley, P. 1995. Ancient Philosophy, Mystery, and Magic - Empedocles and the Pythagorean Tradition, Oxford University Press

Hermann, Arnold (2005). To Think Like God: Pythagoras and Parmenides-The Origins of Philosophy. Parmenides Publishing. ISBN 978-1-930972-00-1

O'Meara, Dominic J. Pythagoras Revived, Clarendon Press, Oxford, 1989. ISBN 0-19-823913-0 (paperback), ISBN 0-19-824485-1 (hardcover)

M.F. Burnyeat. The Truth about Pythagoras, London Review of Books, 22 February 2007.

Notes