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Pythagoras

Pythagoras ()
Pre-Socratic philosopher
Antiquity
Bust of Pythagoras - Capitoline Museums - Rome
Bust of Pythagoras - Capitoline Museums - Rome
Birth about 580 BC. AD ( Samos )
Deaths to 495 BC. AD ((Metapontum)) (85)
School / tradition Pythagorean
Main interests Ethics , logic , mathematics , music , philosophy , politics
Notable ideas Pythagorean scale , Harmony of the Spheres , Golden Number , Pythagorean Theorem
Influenced by Milesian school
Influenced Plato , Archytas of Tarentum , Cicero , Porphyry
Adjectives derived Pythagorean, Pythagorean, Pythagorean, Pythagorean
change Consult the documentation of the model

Pythagoras (in ancient Greek / is a philosopher , mathematician and scientist Presocratic who was born around 580 BC. BC at Samos , an island in the Aegean Sea to the southeast of the city of Athens is established to his death 495 BC. AD at the age of 85.

The name of Pythagoras or Pyth-agora, etymologically "that which was announced by the Pythia , "follows the announcement of his birth his father made a trip to Delphi.

The enigmatic life of Pythagoras makes it difficult to clarify the history of the religious reformer, mathematician, philosopher and miracle worker.

The nopythagorisme is nevertheless imbued with a mysticism of numbers, already present in the mind of Pythagoras. Herodotus mentions it as "one of the greatest minds of Greece, the wise Pythagoras' .

According to a prominent echo of Heraclides of Pontus , Pythagoras was the first Greek thinker to have described himself as a "philosopher" . Cicero recalls the famous anecdote about creating the word "love wisdom ", by Pythagoras:

"For the same reason, no doubt, all those who have been attached to science contemplative, were held to Wise, and were appointed as, up to the time of Pythagoras, who started the first popular name of philosophers. Heraclides of Pontus, a pupil of Plato, and very clever man himself, tells the story well. One day, he said, Leo, King of Phliasians, Pythagoras heard discoursing on some points with so much learning and eloquence, that the prince, struck with admiration, asked him what was then the art which he professed ? What Pythagoras replied that he knew none, but he was a philosopher. And thereupon the king, surprised at the novelty of the name, asked him to tell him who then were the philosophers, and how they differed from other men. "

- Cicero, Tusculans, V, 3, 8

Summary

Biography of Pythagoras

Many documents, late, have been published on the life of Pythagoras , , , . Researchers, including Eduard Zeller and Andr-Jean Festugiere , challenging in particular traveling in Egypt and Chaldea.

Birth

Pythagoras was born in Samos in -569 and -606 according to Eratosthenes and Diogenes Laertius , in -590 by Iamblichus in -580 by Porphyry , and he died in -494 or -497 to Metaponto in Italy.

His father, Mnesarchos , engraver of rings, and his mother, Parthenis, the most beautiful of Samian, both descended from Ancaeus hero, son of Zeus, who had founded the town of Samos. This Mnesarchos Samos queries the Pythia of Delphi on a trip and gets a reply that:

"His wife was pregnant and would give birth to a child who would win in beauty and wisdom. From that moment, he changed the name of his wife "Parthenis" to "Pythas .

Later, Pythagoras says he is the reincarnation of thalids (son of Hermes ), of spurge (hero of the Trojan War), of Hermotimus of Clazomenae (Apollonian shaman), and Pyrrhus (a fisherman Delos ), and he remembered those earlier incarnations , .

Adolescence and Maturity

Pythagoras is an athlete . According to tradition, Pythagoras participates in Olympic Games at the age of 17. That would be the 57 th Olympiad (-552) (not the 48 E, -588, according to Eratosthenes). He won every competition of boxing (ancient sport similar to boxing ).

Sources differ on the number of children he would have had to Theano : two or four. The names are: Tlaugs (who succeeded his father who, according to some, taught Empedocles ) Mnesarchos Myia (who married Milo of Croton), Arignot .

Education

Pythagoras, detail from School of Athens by Raphael , 1509

First initiation. At 18 years, -551, he left Samos. He will learn to Lesbos with Pherecydes of Syros (c. -585/-499) , , a sage, the first to say that "the souls of men are eternal" the first to teach that man has two souls, one from land, the other of divine origin, a magician, too, which makes predictions, receives dreams . What philosophies are similar, it is safe for men to be met is uncertain, but the theory of the immortal soul, individual Pherecydes authorizes the Pythagorean theory of transmigration () souls.

Then, biographers like to provide it with all possible initiatives to insiders of the time and in the Mysteries. He would meet "the descendants of the prophet and naturalist Mkhos" and hierophants Phoenicia, the hirogrammates Egypt, the Magi of Chaldea, insiders of Mount Ida, the Thracian Orphic, the priestesses of Delphi.

Second initiation, "Syria" or "Phoenicia." He met the descendants of the prophet and naturalist Mkhos Sidon. He attended hierophants. He is initiated into Tyre and Byblos and elsewhere . He returned to Samos, the first time, follow the teachings of Hermodamas of Samos, a Homeric scholar in , .

Third initiation. From Hecataeus of Abdera, historians argue that Pythagoras went to Egypt to -547, to Memphis and Diospolis ( Thebes in Egypt ), for several years , . In this city is the sanctuary of Zeus Ammon. He was received by the priests under Amasis , pharaoh of -568 to -526 and known Polycrates of Samos . He learned the language center in Memphis, founded by interpreting Psammetichus I (Pharaoh -663). He studied geometry, astronomy of the Egyptians. He was initiated into the Mysteries of Diospolis and doctrine of the resurrection of Osiris , according to Plutarch, the priests would have applied to the thigh the winged disc of Atum - Ra , gold leaf, which earned him the nickname Pythagoras 'chrysomre', thigh Golden .

Fourth initiation. Some traditions add that it is expelled as a slave or prisoner to Babylon from Egypt by Cambyses II, king of Persia came to conquer Egypt -525 . It would then go "among the Chaldeans and the Magi." This episode is much less evidence that the trip to Egypt, and dates are problematic, especially when Antiphon says that Pythagoras stayed 22 years in Egypt (from -547 to -525?) And 12 years in Babylon (from -525 to - 513?) . It is impossible that he met Zoroaster (as would Porphyry), because the Iranian prophet taught them about -594.

Fifth initiation: Pythagoras traveled to Crete , in the cave of Ida, esoteric mecca, led, they say, of Epimenides of Crete , and insiders of Cocksfoot (magician), Morges , . Fifth initiation: it goes in Thrace, to meet the Orphic.

Sixth initiation: he meets " Themistocles , the priestess of Delphi " , .

Routes and death

He returned to Samos again. He began teaching in an outdoor amphitheater, the Chamber , with little success.

Magna Grecia in 280 BC. AD

Banned by Polycrates , "tyrant" of Samos of -535 to -522, or fleeing, according Aristoxenus , "the tyranny of Polycrates" , he left Samos to -535, he left with his old master Hermodamas. It goes in Magna Graecia and landed at Sybaris , a city rich and voluptuous on the Gulf of Taranto.

He prefers to settle in Crotone , always on the Gulf of Taranto, in Calabria, as the city has a cult of Apollo and a medical school clbre.Le famous athlete Milo of Croton , six time champion at the Olympic Games , and priest of Hera Lacinia, married his daughter, Myia. His influence on Croton extends from the meeting for children through teens and women who all came to listen. It does probably not laws to Croton, but it supports a political regime of oligarchic type, that is to say "aristocratic, reserved for an elite. Undemocratic, he thinks "it's a senseless thing to take into account the views of many people" . The 300 disciples administer the city . His public lectures attracted 600 people. The Croton identify the Apollo Hyperborean . This influence in Crotone is the opportunity for Porphyry of Tyre to give an enthusiastic presentation of Pythagoras:

"Citizens of Croton realized they were dealing with a man who had traveled extensively, an exceptional man, who held the fortune of many physical benefits: it was, indeed, noble-looking and slender, her voice , his character and all the rest of him came from an infinite grace and beauty. "

He founded his school in Crotone in -532 . It is a community, almost a sect, at once philosophical, scientific, political, religious, initiatory. He founded other communities in the cities of Italy and Greece: Taranto, Metaponto, Sybaris, Caulonia, Locri, and in Sicily, Rhegium Tauromenium, Catania, Syracuse. It does not seem to want to start a political federation of the cities of the Gulf of Taranto (Taranto, Metaponto, Sybaris, Croton, in the heel of Italy). At Crotona, he would meet with the Scythian Abaris , great magician and "shaman."

In -510 , a popular revolution to Sybaris, led by a Democratic speaker, Telys, massacre of the Pythagoreans, and 500 aristocrats took refuge in Crotone. A war ensues between Sybaris and Croton, recommended - according to Diodorus of Sicily - by Pythagoras. The aristocracy of Crotona, under the leadership of Milo of Croton, won with 100,000 men against 300,000; it in turn massacre the population and shaves Sybaris .

He worries about progress of the democratic party. "He told his followers that an uprising would break out" , and from - according Aristoxenus - for Metapontum port of Lucania, always on the Gulf of Taranto. Without doubt there is a Pythagorean community already installed. He has followers who become famous, including the doctor Alcmaeon Crotone , mathematician Hippasus of Metapontum , . The inhabitants of his house Metapontum called "the temple of Demeter," and his alley "temple of the Muses."

Perhaps, in -499, it will bury Delos, a great religious center, his old master Pherecydes Syros .

Pythagoras dies in Metapontum -497. Cicero says: "I went with you to Metapontum. I have not agreed to go with our host before seeing the place where Pythagoras died and where he had his seat. " .

Between -440 and -454, -450 to, a riot occurs anti-Pythagorean amalgamated by some historians to war pro-Pythagorean -510. A noble of Croton, Cylon of Croton, Sybaris governor, fomenting a conspiracy. He wants to avenge that Pythagoras would have found unfit to follow the teachings of the school. It raises the public against the Pythagoreans, followers of an aristocratic regime and conservative. The fire is put to the house of Milo of Croton , where 40 Pythagoreans met. Only two managed to escape: Lysis of Tarentum Taranto Archippus or Lysis and Philolaus , , . This persecution led to the dispersal of members of the Pythagorean school , which bases centers elsewhere, especially in Rhegium, Phlius of Lucania and Thebes . The decline of the Pythagorean influence in Italy begins. The last bastion was Tarentum , with Archytas of Tarentum , strategist, philosopher, mathematician, inventor, but also a friend and savior of -388 and -361 Plato. Other versions of the death of Pythagoras seem questionable: Diogenes Laertius and Porphyry argued that Pythagoras died in the fire at the house of Milo, Hermippus of Smyrna declares that Pythagoras would have been killed by Syracusiens, during flight, before a he refused field beans, beans by taboo, crossing .

Legend (especially Porphyry and Iamblichus) attributes to Pythagoras wonderful powers: it tames a bear, in Olympia he sent down an eagle from heaven, he knows his former lives, he predicted the revolution in Crotone, he guesses the amount of fish that will bring fishermen, charm and he heals through his music, he hears the harmony of the spheres, he commanded the winds and hail, etc.. Of course, it is given as an expert in arithmology (occult art of numbers), arithmosophy (esoteric knowledge of numbers), arithmomancie (divination by numbers): "With the numbers in question, he practiced an admirable method of prediction, and the gods worshiped by the numbers, because the nature of their number is completely related " , . During the Hellenistic period, the word "Pythagorean" () became to mean "occult, esoteric, magician" . Even the sober Aristotle admits: "Pythagoras first and foremost work hard in mathematics and numbers around, but later he arrived not knowing renounce the practice of miraculous Pherecydes .

The Pythagorean community

The Pythagorean school of Crotone later became a Hetairia ( = brotherhood) aristocratic political power .

It is a fraternity philosophical, religious and scientific, near the Orphism. It seems now a college in the sense that Freemasonry and the Rosicrucians are orders.

The community is spread over four degrees of initiation and hierarchical , as in many organizations initiation. Women and foreigners are allowed. Laymen (bbloi) are "outsiders" (oi exo ), the common people, to whom nothing is revealed.

First level: applicants

Pythagoras observed in those who present themselves as candidates, the facial features (physiognomy) and gestures (kinetic) , but also relationships with parents, laughter, desire, dating. It is admitted or not .

Second level: beginners

Their probation period lasts three years, during which examines Pythagoras perseverance, the desire to learn. After they are rejected or accepted. Accepted, they swear the oath of silence :

"No, he Third step: acousmaticiens

The acousmaticiens - or acousmatic - ( "listeners"). They are taught five years, given as oral teachings (), without proof, to be kept in memory, for example: "Not having opinions about the gods or hasty words. "These five are five years of silence. Listeners are before the curtain behind which lurks Pythagoras. They put their goods in common .

Postulants, novices and listeners are the degree of "exoteric" () or novices.

Fourth and last step: Mathematicians

Mathematicians ( "scholars") or "esoteric" or sindonites (dressed flax). "They became esoteric ()" , insofar as they access the knowledge inside, hidden. They are allowed to see Pythagoras behind the curtain. Taught himself as "symbols" () within the meaning of coded forms, which are demonstrated, for example: "Do not touch a white cock. "According to Photius we see a division of "esoteric" to "venerable" (sebastikoi ), "political" (politikoi), "contemplative." The venerable and pious care for religion. Policies concerned with laws, human affairs, both in the Pythagorean community in the city. The "contemplative" study arithmetic, music, geometry, astronomy: the four science by Archytas, which form the quadrivium the Middle Ages. It should be added physicists and naturalists (), which explore the concrete sciences: geography, meteorology, medicine, mechanical ... but also grammar, poetry ... It is more likely that "acousmaticiens" are "political, administrative or legislative" and "mathematicians" of the "pious" or "contemplative" .

Many rules, if not taboo, the one who needed to adopt "the Pythagorean Life ( ) .

  • dietary laws (pure vegetarianism to "vegetarianism" selective) : no eating of red mullet, heart, brain, marrow, beans, eggs ... anything that symbolizes life. Consumption of the flesh of sacrificed animals seem allowed by some Pythagoreans, perhaps as a concession to the official religion.
  • religious rites: bloodless sacrifices and without fire, "to honor the gods, avoid hunters and butchers, worship" gods flour, honey, fruits, flowers and other products of the earth " , "cleansing, washing and spraying" unctions and lustral ...
  • Spiritual Exercises: respect for self, examination of conscience each evening , sexual continence, "exercising his memory," "sing to the accompaniment of the lyre, read inspirational books together ...
  • physical exercise , : gymnastics, athletics, walk two or three, dance ...
  • sacred objects, "wearing white" linen (but no wool, animal), recognition of signs (the pentagram), symbols ( tetraktys ) ...

Rivalry acousmaticiens / mathematicians

From Hippasus (about -450?), It seems that there was rivalry between two ideological (rather than initiation degrees) in the Pythagoreans: the "Acousmaticiens" and "mathematicians . "It is no longer the hierarchy novice / insider, but the polarity moralist / scientist. On the one hand, Acousmaticiens emphasize the lyrics ("Acousmate) bequeathed by Pythagoras and emphasize the moral, ritual prescriptions, the" Pythagorean way of life "between -420 and -350, the authors of comedies (Cratinus, Mnsimaque, etc..) describe "Pythagoras", as Diodorus Aspendos (around -380) and Lycon of lasus, vegetarian and drinking water, long-haired and bearded, barefoot, wearing a simple cloak (Tribon) , stick in hand, making a vow of silence and not washing. On the other hand, "Mathematicians" (Hippasus, Philolaus Archytas, Eurytus, Eudoxus of Cnidus) within the meaning of scholars insist on demonstrations and science focus.

Doctrine

Just as the historical figure of Pythagoras is uncertain, his thinking is akin to the Pythagorean school. The thought of Pythagoras himself is thus covered by the successive contributions of his followers. That of the Pythagorean school covers all areas: "Science on the intelligible and the gods, then physics, philosophy, ethics and logic, all kinds of knowledge in mathematics and science" . Archytas , the first designs that will quadrivium: arithmetic, music (arithmetic sensitive), geometry, astronomy finally (geometry sensitive) . Pythagoras saw their relationship: he brought the figures of geometry to the number of arithmetic, the sounds of musicians proportions of arithmeticians ... Correspondence () are established, for example, "1 is the point, 2 line, 3 triangle

Arithmetic (and arithmology)

"Everything is numbers. "The great contribution of Pythagoras is the importance of the concept of number and mathematical development of a demonstrative (as well as religious) . For ancient Greek, the number always designates an integer and stands for "system arranged numerically" (??), "plurality orderly," "structured thing" other, "a" is not considered as a number before Archytas . For Pythagoreans, things are numbers, or things consist of numbers, or things imitate the numbers (which are principles), or things have numbers: some uncertainty remains.

According to Aristotle , for the Pythagoreans, things are numbers, for example, and spirit are, in the intervals of the musical tones are reports of numbers ; according Philolaos of Croton : things have numbers, are made numbers, for example, the pyramid contains the number 10, the sky consists of 10 celestial bodies (stars, 8 planets, Anti-Earth) ; according Hippasus, things to models numbers .

The famous statement "Things are numbers" means both: a) is the number which is the intelligible structure of things (because this principle based mathematical physics), b) the fundamentals of mathematics are the elements of things (this principle affirms the possibility of defining a structure of the mind which is a structure of things and are the notions of finite and infinite, and a multiple, etc.). .

Aristotle : "The Pythagoreans first applied themselves to mathematics ... Finding things

img alt = "" src = "http://upload.wikimedia.org/wikipedia/commons/thumb/6/66/Tetractys.svg/200px-Tetractys.svg.png" width = "200" height = "167" class = "thumbimage" />
The Tetraktys

Pythagorean numbers gives a geometrical representation .

Photius : "They proclaimed that all is number and the full number is ten. The number ten, the 1 + 2 + 3 + 4 = 10: number of triangular side 4, where the tetrad is the decade and cache reports fourth harmonic intervals (3:4), fifth (2:3) and octave ( 1:2) . From Archytas or perhaps after Plato, the Pythagoreans associate a point on 2 line, 3 on the surface (the two-dimensional geometric figure: circle, triangle, square, etc..) 4 to the solid (the geometrical figure of three dimensions: cube, sphere, pyramid, ect.).

"He discovered the mdits "proportions, formulas averages Pythagoras discovered 3 of the 11 possible ratio between 3 terms (a, b, c): the proportions arithmetic , geometric and harmonic , the others will be discovered by d other Pythagoreans, whose Hippasus of Metaponto , Archytas.

  • The arithmetical fact that the first term exceeds the second by the same amount that it exceeds the third: a - b = b - c.
  • Geometrical proportion (very important in philosophy and art) that the first term is the second that the second is the third: a / b = b / c.
  • The harmonic proportion (essential in music) that, "whatever the part of himself which the first term exceeds the second, the second exceeds the third in the same share of the third" a = b + a / n. In the harmonic proportion 12:8:6, we see that 8:6 is the fourth, the fifth 12:8, 12:6 octave. The Pythagoreans were able to theorize the range of music.

The science of numbers is both arithmetic and therefore scientific, and arithmology, so symbolic. Each number is a symbol. The court's four, life (and marriage) is five , perfection is ten, etc.. . Philolaus is the number 1 symbolizes the point, line 2, 3 triangles, 4 the volume .

Music

Everything begins with the discovery that there is a relationship between the length of a vibrating string and the height of the sound. Four strings, the first is 1, the second has a length representing 3 / 4 of the first, third and 2 / 3 and the last 1 / 2. When these strings are plucked successively means the C, then the fourth of the C = F, then the fit of the C = G, then the C an octave. The sound is mathematical.

"The Pythagoreans say that music is a harmonious combination of opposites, a unification of the multiple and agreement of opposites. ( Theon of Smyrna )

Pythagoras discovered the laws of the harmonic . Aristotle : "These philosophers noticed that all modes of musical harmony and relationships that make up the resolve in proportional numbers. " The proportion governs harmonic musical intervals. In the harmonic proportion 12, 8 and 6, the ratio 12 / 6 = 2 corresponds to the octave, the ratio 8 / 6 = 4 / 3 corresponds to the fourth, the report 12 / 8 = 3 / 2 corresponds to the fifth. The Pythagorean scale is a range built on musical intervals of fifths, whose frequency ratio is 3 / 2. Pythagorean frequencies of the note C are as follows: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 ...

Diogenes Laertius also Pythagoras the inventor of the gun monotone , monotone a musical instrument called "canon". It illustrates the law that "the pitch is inversely proportional to the length of the rope."

The music has an ethical and medical. "It was starting education through music, through certain melodies and rhythms, through which he produced cures in the character traits and the passions of men, brought harmony between the faculties of the soul" .

The music has a cosmic dimension, such as astronomy has a musical dimension: Plato says that music and astronomy are "sister science" . cf. harmony of the spheres, music worldwide . Pythagoras would have asked that the distances between the orbits of the sun, moon and fixed stars correspond to the proportions set the intervals of the octave, the fifth and fourth . Later, "the voice of the seven planets, that of the sphere of The order is (for the first Pythagoras or the Pythagoreans) : sphere of fixed stars, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, Earth, Anti-Earth, Fire Central, or 10 units. Pythagoras found that the harmonic proportion for 12: 8: 6 shows that 12:6 is the octave, the fifth 12:8, 8:6 the fourth. If the radius of the fire is central 1, the radius of the orbit of the Anti-Earth 3, Earth 9, Moon 27, Mercury 81, Venus 243, Sun 729. Between the sphere of fixed stars and Saturn, among Saturn and Jupiter, Jupiter and Mars there is a semitone, a tone between Mars and Sun, and we get a fourth, between Sun and Earth we get a fifth between fixed stars and Earth one octave . "Pythagoras held out his hearing and fixed his mind upon the agreements of the celestial universe. He alone, as it seemed, heard and understood the universal harmony and unison of the spheres

Geometry

Main article: Geometric Algebra.
Basic demonstration of a particular case of the theorem of Pythagoras.

The school of Pythagoras inherits a double mathematics. This Ionian , initiated by Thales of Millet , he brings a geometric orientation and a willingness to demonstrate . The Mesopotamian heritage provides calculation procedures for solving the issue of the second degree , or even to approximate square roots by fractions .

This dual heritage associates on a misconception, one that any length can be expressed as a fraction, "the Pythagoreans left of the idea, natural to every human being uneducated, that any length is necessarily commensurate with the unit. . This error is nevertheless successful. If any length is a fraction and as long as you choose the unity of the figure, it becomes possible to work only on figures whose lengths are integers. This approach provides the first evidence partial, of the Pythagorean theorem , already known by the Egyptian and Mesopotamian but probably never demonstrated in the Mediterranean. The type of proof is explained on the left figure . A right triangle whose sides other than the hypotenuse are lengths of 3 and 4, has a hypotenuse of a square (in blue on the figure) equal to 25.

Mesopotamian allows the calculation of further progress. Construct a pentagon regular means building on the proportion of extreme and mean right, now called the golden number. It is the ratio between a diagonal and one side. The calculation Mesopotamian allows to overcome and this is probably the Pythagorean Hippasus of Metapontum that we owe this discovery . However, this procedure has Mesopotamian more objective calculation, but a geometrical construction.

This use of the calculation, to address issues of secondary education, shows that the proportions are not fractions. You can build and lengths, as the diagonal and the side of a regular pentagon, there is no such unit for expressing these two lengths as integers. Such lengths are called incommensurable. The discovery of these proportions is probably the work of the early Pythagoreans . It is sometimes attributed to Hippasus with reasoning on the pentagon . This discovery, which historians describe as Michael and Itard rape fruitful initially creates a serious crisis, and nourishes and enriches for two centuries Greek mathematics.

Astronomy: the cosmos

Pythagoras brought knowledge that amazes even the logician Frege : the evening star (the one you see first at dusk) and the Morning Star are one and the same is Venus . This identity was known from -685 to Babylon.

Pythagoras "was the first to call the sky cosmos (order) and say that the Earth is round" , but more often attributed the theory of curvature of the Earth Parmenides. The disciples develop the Pythagorean astronomy .

Philolaos of Croton (fifth century -470/-fin-) state, the first, long before Copernicus , the translation of the Earth around the Sun and therefore heliocentrism. Philolaus said: "It is the fire which occupies the middle. " , yet this is not the central Fire Sun, it remains invisible, one perceives that its light reflected from the Sun is a physical force in the middle of the world. So Pythagoreanism has not discovered the heliocentric theory. However, the discovery of the Earth's rotation on itself amounts to another Pythagorean Hictas of Syracuse (400-335), for whom "the earth rotates on its axis and rotates at very high speed" . Ecphantos of Syracuse, a disciple of Hictas (according Boekh August), also said that "the Earth center of the world The soul, the transmigration of souls

For Pythagoras, the body (soma) is a tomb (sema), both prison and "sign" or "protection" of the soul : this is a thesis Pythagorean, Orphic not . Philolaus: "The ancient theologians and soothsayers also show that it is a punishment for certain sins that the soul has been attached to the body and buried him in a tomb. "

The soul is a number, in that it is harmony, good proportion, combination of properties making up the body (the Pythagorean theory Simmias in the Phaedo, 86d, Plato). It is life as movement.

Pythagoras believed that "the soul is immortal, then it happens in other animal species in addition to specific periods which has been reborn, that nothing is absolutely new, it takes recognize the same species in all beings who receive life. The interval between incarnations would be 216 years (6 to cube). And the explanation lies in the nature of the soul: there is transmigration of the soul because, by nature, she is immortal and moving, Pythagoras does not involve divine justice, a retribution of the soul , since n 'matter what soul can enter any body . Where did Pythagoras to his theory of transmigration () of Souls? Orpheus? Pherecydes of Syros? from India? We do not know. Pythagoras said his former existences, in a list fixed by Heraclides of Pontus : Aethalide (son of Hermes living partly on land and partly in the Hereafter), spurge (priest of Apollo), Hermotimus (shaman), Pyrrhus (simple fisherman). It is possible that Pythagoras had believed in reincarnation for himself.

"He (Pythagoras) was telling about himself following things: he had once been Aithalids and passed to the son of Hermes, Hermes had told him to choose what he wanted, except immortality. He had asked to keep living as if dead, the memory of what happened to him. Thus in his life, he remembered everything, and once dead he retained memories intact. Later, he entered the body of spurge and was wounded by Menelaus. Spurge and said he had been Aithalids . "

This vegetarianism is linked to reincarnation as Pythagoras proposes in his philosophy, thinking and the fate of living in the full sense of interdependence, the philosopher has a special sensitivity that typically found in civilization Hindu (with Ahimsa and Jainism, especially):

"Heaven and all we see below it, the earth and all it contains, change shapes. We are also part of this world, we change, and as we have souls that can wander, our body, pass into the bodies of animals, leave them in peace and respect the asylum inhabited by souls of our parents, our brothers, those we loved, souls of men, at last, taking care not to make feasts of Thyestes. As it is horrible tastes, as he prepares to one day make human blood, one who kills in cold blood a lamb, which lend an ear insensible to her plaintive bleating, one who can mercilessly kill the young kid and heard wailing like a child who can eat the bird he has fed his hand! There away from the crime to the last of the crimes, homicide? Opener does not there the way? Let the plow ox, and not die of old age, let us bring the sheep against the icy blast of Boreas, and goats have their breasts filled with hand-pressed. Ests and more lakes, more treacherous inventions; attract more flies on the glue, do not push more frightened deer in your paintings, no more hiding under a misleading bait, the tip of the hook. "

- Ovid , Metamorphoses .

Medicine

The general biological principle of harmony is not like the similar or the fight to the contrary otherwise, but - as in music - the harmony of opposites, the balance of power in the body. Just as the soul (confused with life) is defined as a good proportion of the properties of the body, health is the restoration of good proportions between the opposite properties of the body, namely the wet and dry, medium and the viscous, bitter and sweet, even and odd, ect .

In medicine , the Pythagoreans were their techniques: diet, poultices , drugs , refusal of incisions and cauterization , "incantations for certain diseases," Music, "chosen to Homer and Hesiod." You can find the tripartite Indo-European: 1) herbal medicine producers falling, 2) medicine incisions and cauterization falling warriors, 3) medicine incantations falling king-priests or philosophers . As soul music purge, purge the body of medicine . The concept of purification or catharsis is central .

Alcmaeon Crotone , which seems Pythagorean practice dissection , it puts the thought in the brain, not in the heart, like other thinkers: "The hegemony has its headquarters in the brain. "

Political science (and action)

Pythagoras was the founder of political science. He defended the aristocratic regime, that is to say that the government entrusts to an elite of scholars that for him. It provides a model reduction in the functioning of the community . It divides society into three social functions - like all Indo-European producers, warriors, priest-kings. He wants to organize the city so mathematical and rational. It develops laws, conservative, family-friendly, recommending compliance with laws and magistrates. The Pythagorean is militaristic, to defend this idea: "We must fight, not in words but in deeds, because it is just and righteous to war when one man against man. "The big idea is that you replace the democratic equality, arithmetic type (x = y), plebeian, for proportionality, geometric type (A / B = C / D), aristocratic, as the merit, and that incorporation will spread to the world organization. In justice, therefore, recommend the Pythagorean law of retaliation , which shocked Aristotle: "It is the reciprocity that is simply justice. Such was the doctrine of the Pythagoreans, who defined simply as the fair reciprocity. But reciprocity does not coincide with distributive justice or even with corrective justice. "

Archytas of Tarentum , Tarentum strategist for 7 years but Pythagorean scholar and philosopher, is the type of the philosopher-king. Plato the physical meeting of -388 and he imagines the philosopher-king in his ideal Republic -370: "Until philosophers are not kings in cities or those now called kings and rulers will not really serious and philosophers ... there will stop the evils of cities "(Republic, V, 473 c).

Some Democrats, however, were Pythagorean, which Theages .

Esoteric Teachings

Pythagoras provides exoteric principles, known to all, for instance: "It is forbidden to pray for oneself," "Between friends all is common" . But others are esoteric teachings, that is to say, reserved for insiders and symbolic expression, and they are the secrets of nature and gods. These secret teachings were called Memoirs (hypomnmata ) because it must be remembered without writing. These are, firstly, the "Acousmate () of the said (pronounced in Greek Doric, the language of the Pythagoreans), oral precepts, are, on the other hand, the" symbols "() coded forms, summaries (kephalaia ) , . Because "everything can not be said to everyone. " "There was among them .

Iamblichus Acousmate classifies into three types, as they reveal the essence ("what?"), The absolute ("What is best?") Or duty (as should be done or not? ").

  • "What the Islands of the blessed? - The Sun and the Moon. "
  • "What is the oracle of Delphi? - The tetraktys. "
  • "What is most accurate? - Offer a sacrifice (of self, in other words "know to give up something to move forward").
  • "What more is learned? - The number. "
  • "Not helping to unload a burden. - Do not encourage the lack of effort. "
  • "Am God ( )" . Is the motto of Pythagoreanism.

In addition acousmatic abstract precepts, there is another category of precepts, symbols, which are imaged practical precepts. Laymen see it as superstition or nonsense, but insiders () know to decipher an idea or an act.

  • "Do not pass over a scale. In other words: "Practicing all righteous acts," or "does not seek more than its share," not avoid so superstitious "pass over a scale."
  • "Do not eat the heart." Avoid raw meat, or "not biting sorrow."

In addition, there are the "secret symbols" (aporrta sumbola) or "signs of recognition" (sunthmata, ), which allowed the Pythagoreans insiders to recognize them. The most famous symbols are the famous secret pentagram with 5 branches and 5 sides and tetraktys.

The divine Pythagoras (...) never put in mind of his letters, or 'joy' or 'prosperity', he always began by Hugiaine! ( Health). (...) That is why the triple triangle intertwined, consisting of five lines

History of Pythagoreanism

Coin bearing the image of Apollonius of Tyana

Successors (the Diadochi) from Pythagoras to the head of the Pythagorean community were: Aristeas of Crotone (at -494), his son or his son Mnesarchos Telauges, Boulagoras (-380) Gartydas Crotone, Ares Lucania, Diodorus of Aspendos (-380). The Pythagorean is divided into various schools:

  • School palopythagoricienne (Pythagoreanism ancient period who knew Pythagoras): Theano (wife of Pythagoras), Alcmaeon Crotone (-500), Epicharmus Cos (active ca -480), Hippasus of Metaponto (active ca -460 ). The Pythagoreans seem to have a politically controlled territory from Locri Metapontum up to -450.
  • School mdiopythagoricienne of Greece (Pythagoreanism Middle and Late): Hippo (-480), Damon the musician (-460), Ion of Chios (-450), Polyclitus (-420) Philolaus Crotone (-400) , even in his oral teaching, which he said the numbers for previous ideas. Then come Heraclides of Pontus (replacing the Academy of Plato in -360), Speusippus (scolarque, that is to say, rector of the Academy of Plato in -348), Xenocrates (scolarque in -339). Already the distinction Pythagorean / Platonic blurs. Speusippus replaces the Ideas of Plato by Numbers mathematics, derived from two principles, the One and the Many. Xenocrates assimilates ideas from Plato to the numbers (according to Aristotle, Metaphysics, N, 3) and it takes the soul to "a number that moves by itself." Between numbers and sensible things (known by the senses), a Pythagorean does not cut, whereas Plato does, it separates things and Numbers .
  • School mdiopythagoricienne Rome: Appius Claudius Caecus (from -312), Scipio Africanus (c. -210) , Cato the Elder (-209), Ennius (-180). "Most philosophers - Academic, Stoic, Peripatetic - pythagorisrent any way to Rome"
Main article: Nopythagorisme.

Legacy

Statue of Pythagoras to the Cathedral of Chartres

Influences received

Clearly, Pythagoreanism was influenced by the Orphism , but also by the shamanism of Apollonian Hyperborean ( Proconnesus of Aristeas , etc..) probably by Egyptian thought, perhaps by mathematics and astronomy from Babylon.

Influences Data

The richness of the work undertaken by the Pythagorean school was such that his ideas and discoveries have inspired a number of schools of thought. Pythagoras influenced all eras and cultures of East and West, all disciplines: mathematics, music, philosophy, astronomy, etc.. His encyclopaedic actually complete a thought, with interpenetration and ramifications.

In art, Pythagoras inspires the Roman architect Vitruvius in the first century theorists and golden as Luca Pacioli illustrated by Leonardo da Vinci in 1509.

Schoolchildren studying the Pythagorean theorem or learn multiplication tables are part of his lineage.

Pythagoras founded a religion, and many legends. In the esoteric and initiatory, his work continues. From 1410 , the Cooke Manuscript (line 216), a basic document of Freemasonry operative, says Hermes and "pictagore" . Lodges Masonic claim of Pythagorean thought, as the Grand Lodge Swiss Alpine (GLSA) , the French Freemasonry and the Lodge of Italy.

Bibliography

Pour une synthse et une introduction sur Pythagore : Jean-Franois Matti , (1993), PUF, coll. Que-sais-je ?

Works

Selon la majorit des auteurs, Pythagore n'aurait rien crit. Le philosophe Porphyre de Tyr est, ce sujet, formel : Car de Pythagore lui-mme il n'y avait aucun crit.

Mais ce point est contredit par plusieurs autres notamment Hraclite qui attribue Pythagore les trois traits suivants : , et . Ou encore pour Alexandre Polyhistor , Pythagore aurait laiss uniquement cet ouvrage : . Ces attributions sont fort incertaines, et, ds l'Antiquit, on pensait que ces livres avaient t crits par des disciples de Pythagore. Et puis, on peut aussi considrer qu'en raison de la coutume persistante de l'sotrisme chez Pythagore, il n'aurait jamais engag le moindre crit de ses penses.

crits pythagoriciens


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