Summary

The enigmatic life of Pythagoras makes it difficult to clarify the story of this religious reformer, mathematician, philosopher and wonder worker. He never wrote anything, and the seventy-one lines of the Golden Verses attributed to him are apocryphal and are a sign of the immense development of the legend formed around his name.

Neopythagoreanism is nevertheless marked by a mysticism of numbers, already present in the thought of Pythagoras. Herodotus mentions him as "one of the greatest minds of Greece, the wise Pythagoras". He retains great prestige; Hegel said that he was "the first universal master".

According to a striking echo of Heraclides of Pontus evoked by Cicero, Pythagoras would be the first Greek thinker to have qualified himself as φιλόσοφος (philosophos), the meaning of which is "friend of knowledge or wisdom":

"By the same reason, undoubtedly, all those who have since attached themselves to the contemplative sciences have been held to be Sages, and have been called such, until the time of Pythagoras, who first put the name of philosophers into vogue. Heraclides of Pontus, a disciple of Plato, and a very clever man himself, tells the story thus. One day, he says, Leo, king of the Phliasians, heard Pythagoras speak on certain points with such knowledge and eloquence, that this prince, seized with admiration, asked him what was the art of which he made a profession. To which Pythagoras answered, that he knew none; but that he was a philosopher. And on this, the king, surprised at the novelty of this name, asked him to tell him who the philosophers were, and in what way they differed from other men.

- Cicero, Tusculanes, V, 3, § 8

No authentic writings of Pythagoras have survived and almost nothing is known for certain about his life. The earliest sources are brief, ambiguous and often satirical. The earliest on Pythagoras' teachings is a satirical poem probably written after his death by Xenophanes, who was one of his contemporaries. In the poem, Pythagoras helps a dog that is being beaten by professing to recognize in its cries the voice of a missing friend. Alcmaeon of Crotone, a physician who lived in Crotone around the same time as Pythagoras, incorporates many Pythagorean teachings into his writings and alludes to the fact that he may have known Pythagoras personally. The philosopher Heraclitus of Ephesus, who was born a few miles from Samos and may have been alive at the same time as Pythagoras, calls him a clever charlatan, remarking that "Pythagoras, the son of Mnesiarchus, practiced research more than any other man, and by choosing from these writings he made for himself a wisdom - a lot of learning, a skillful trickery."

In the fifth century B.C., the Greek poets Ion of Chios and Empedocles both express their admiration for Pythagoras in their poems. The first concise description of Pythagoras comes from the historian Herodotus, who describes him as "not the most insignificant" of the Greek sages and states that Pythagoras taught his followers how to achieve immortality. The accuracy of Herodotus' work is controversial. Writings attributed to the Pythagorean philosopher Philolaos of Crotone, who lived in the late fifth century B.C., are the first texts to describe the numerological and musical theories that were later attributed to Pythagoras. The Athenian rhetorician Isocrates is the first to describe Pythagoras as having visited Egypt. Aristotle wrote a treatise on the Pythagoreans, which no longer exists, part of which is perhaps preserved in the Protrepticus. Aristotle's disciples, Dicearchus, Aristoxenus and Heraclides of Pontus, also wrote on the same subject.

Most of the major sources on the life of Pythagoras date from the Roman period. At that time, according to the German classicist Walter Burkert, "the history of Pythagoreanism was already ... the laborious reconstruction of something lost and vanished." Three biographies of Pythagoras have survived from late antiquity, all filled mostly with myth and legend. The oldest and most respectable of these is Diogenes Laërce's Lives, Doctrines and Sentences of the Illustrious Philosophers. The last two lives are written by the Neoplatonic philosophers Porphyry of Tyre and Jamblicus and are partly conceived as polemics against the rise of Christianity. The later sources are much longer than the earlier ones and even more fantastic in their descriptions of Pythagoras' achievements. Porphyry and Jamblicus used material from the lost writings of Aristotle's disciples, and the material from these sources is generally considered the most reliable.

Birth

His father, Mnesarch, a ring cutter, and his mother, Parthenis, who according to the myth was the most beautiful of the Samian women, were both descendants of the hero Anceus, son of Poseidon, who had founded the city of Samos. This Mnesarch of Samos questions the Pythia of Delphi about a journey and obtains an answer that :

"his wife was pregnant and would give birth to a child who would prevail in beauty and wisdom. From that moment he changed his wife's name from 'Parthenis' to 'Pythais'; he called his son 'Pythagoras' [Πυθαγόρας, 'foretold by the Pythia', or 'announced by the Pythian god', for the reason that he had been announced by the Pythian god]."

- Jamblique, Life of Pythagoras, § 7.

Adolescence and maturity

Pythagoras is an athlete. According to a tradition, Pythagoras participated in the Olympic Games at the age of 17. It would be the 57th Olympiad (-552) or the 48th (-588) according to Eratosthenes. He won all the competitions of pugilism (sport of the Antiquity comparable to boxing).

The sources diverge on the number of children that he would have had of Théanô: two or four. The names quoted are : Télaugès (who succeeded his father and who, according to some, taught Empedocles), Mnésarque, Myïa (who married Milon of Crotone), Arignote.

Instruction

First initiation: at 18 years, in 551 BC, he leaves Samos. He goes to learn in Lesbos with Phérécyde of Syros (about 585

Then, the biographers like to give him all the possible initiations near the initiates of the time and in the Mysteries. He would meet "the descendants of the prophet and naturalist Mochus" and the hierophants of Phoenicia, the hierogrammatists of Egypt, the Magi of Chaldea, the initiates of the mount Ida, the orphics of Thrace, the priestesses of Delphi.

Third initiation. As early as Hecataeus of Abdera, historians maintain that Pythagoras went to Egypt around 547 BC, to Memphis and Diospolis, for several years. In this city is the sanctuary of Zeus Ammon. He is received by the priests, under Amasis, pharaoh from 568 to 526 BC and known by Polycrates of Samos. He learns the language in Memphis in an interpreting center founded by Psammetius I (pharaoh in 663 BC). He studied geometry and the astronomy of the Egyptians. He was initiated into the Mysteries of Diospolis and the doctrine of the resurrection of Osiris; according to Plutarch, the priests applied to his thigh the winged disc of Atum-Ra, made of gold leaf, which earned him the nickname of Pythagoras "Chrysomer, with a golden thigh".

Fourth initiation. Some traditions add that he was expelled as a slave or prisoner from Egypt to Babylon by Cambyses II, king of Persia who came to conquer Egypt in 525 BC. He would then have gone "to the Chaldeans and the Magi". This episode is much less attested than the trip to Egypt, and the dates are problematic, especially when Antiphon claims that Pythagoras stayed 22 years in Egypt (from 547 to 525 B.C.?) and 12 years in Babylon (from 525 to 513 B.C.?). It is impossible that he met Zoroaster - as Porphyry of Tyre would have it - because the Iranian prophet was teaching around 594 BC. Plutarch, in his explanation of the creation of the world according to Plato's Timaeus, also gives him as his teacher Zaratas of Assyria, in whom some authors see in fact a deformation of Zoroaster's first name.

Fifth initiation: Pythagoras goes to Crete, in the lair of Ida, esoteric high place, under the guidance, it is said, of Epimenides of Crete, and the initiates of the Dactyl (magician), Morges. Fifth initiation: it goes in Thrace, to meet the orphics.

Sixth initiation: he meets " Thémistocléa, the priestess of Delphes ".

Journey and death

He returned to Samos a second time. He starts teaching in an open-air amphitheater, the Hemicycle, without much success.

Banished by Polycrates, tyrant of Samos from -535 to -522, or fleeing, according to Aristoxenes, "the tyranny of Polycrates", he leaves Samos around -535, he leaves with his old master Hermodamas. He went to Magna Graecia and disembarked in Sybaris, a rich and voluptuous city on the gulf of Taranto.

He prefers to settle in Crotone, still on the gulf of Taranto, in Calabria, because the city has a cult for Apollo and a famous school of medicine. The famous athlete Milon of Crotone, six times champion at the Olympic games, and priest of Hera Lacinia, married his daughter, Myia. His influence on Crotone extends from the assembly to the children, passing by the teenagers and the women who all came to listen to him. He probably does not give laws to the Crotoniates, but he supports a political regime of oligarchic type, i.e. aristocratic, reserved to an elite. Antidemocrat, he thinks that "it is a foolish thing to take into account the opinion of the great number". The 300 disciples administered the city. His public conferences attracted 600 people. The Crotoniates identify him with Apollo Hyperborean. This influence in Crotone is the occasion for Porphyry of Tyre to give an enthusiastic presentation of Pythagoras:

"The citizens of Crotone understood that they were dealing with a man who had traveled a lot, an exceptional man, who had many physical advantages from Fortune: he was, in fact, noble and slender in appearance, and from his voice, his character and everything else about him emanated infinite grace and beauty."

He founded his school in Crotone in -532. It is a community, almost a sect, at the same time philosophical, scientific, political, religious, initiatory. He founded other communities in the cities of Italy and Greece: Taranto, Metapontum, Sybaris, Caulonia, Locres, and, in Sicily, Rhegium, Tauromenium, Catania, Syracuse. It does not seem that he wanted to found a political federation of the cities of the Gulf of Taranto (Taranto, Metapontum, Sybaris, Crotone, in the heel of the boot of Italy). In Crotone, he would meet Abaris the Scythian, a great magician and "shaman".

In 510 BC, a popular revolution in Sybaris, under the leadership of a democrat orator, Télys, massacred the Pythagoreans, and 500 aristocrats took refuge in Crotone. A war ensued between Sybaris and Crotone, recommended - according to Diodorus of Sicily - by Pythagoras. The aristocracy of Crotone, under the control of Milon of Crotone, won with 100 000 men against 300 000 : it massacred in its turn the population and razed Sybaris.

He is worried about the progress of the democratic party. "He announced to his disciples that an uprising was about to break out", and invited them to leave - according to Aristoxenus - for Metapontum, port of Lucania, still on the gulf of Taranto. No doubt he found a Pythagorean community already established there. He had disciples who became famous, among them the physician Alcmaeon of Crotone, the mathematician Hippasius of Metapontum. The inhabitants of Metapontum called his house "the temple of Demeter", and his alley "the temple of the Muses".

Perhaps, in -499, he goes to bury in Delos, great religious center, his old master Pherecyde of Syros.

Pythagoras died in Metapontum in 497 BC. Cicero testifies: "I went with you to Metapontum. I did not agree to go to our host's house until I had seen the place where Pythagoras died and where he had his seat."

Between -440 or -454, towards -450, occurs an anti-pythagorean riot, amalgamated by certain historians with the pro-pythagorean war of -510. A noble of Crotone, Cylon of Crotone, governor of Sybaris, foments a plot. He wants to be avenged of Pythagoras who would have judged him unfit to follow the teachings of the school. He raises the population against the Pythagoreans, partisans of an aristocratic and conservative regime. The fire is put at the house of Milon of Crotone where 40 Pythagoreans are gathered. Three only succeed in saving themselves: Philolaos of Crotone, Lysis of Taranto and Archippe of Taranto, or Lysis and Philolaos. These persecutions lead to the dispersion of the members of the Pythagorean school, who found centers elsewhere, especially in Rhegium, Phlionte and Thebes of Lucania. The decline of the Pythagorean influence in Italy begins. The last bastion was Taranto, with Archytas of Taranto, strategist, philosopher, mathematician, inventor, but also friend and savior of Plato in -388 and -361. The other versions of Pythagoras' death seem doubtful: Diogenes Laërce and Porphyry maintain that Pythagoras would have died in the fire of Milon's house, Hermippus of Smyrna declares that Pythagoras would have been killed by the Syracusians, during his flight, in front of a field of beans that he refused, by taboo of the beans, to cross.

The legend (especially in Porphyry and Jamblicus) attributes to Pythagoras marvelous powers: he tamed a bear, in Olympia he made an eagle come down from the sky, he knew his previous existences, he predicted the revolution in Crotone, he guessed the quantity of fish that the fishermen would bring back, he charmed and healed by his music, he heard the harmony of the celestial spheres, he commanded the hail and the winds, etc. Of course, he is given as an expert in arithmology (occult art of numbers), arithmosophy (esoteric knowledge of numbers), arithmomancy (divination by numbers): "Thanks to the numbers in question, he practiced an admirable method of prediction, and he worshipped the gods according to numbers, because the nature of the number is completely related to them. In Hellenistic times, the adjective "Pythagorean" (πυθαγόρειος) came to mean "occultist, esotericist, magician". Even the sober Aristotle admits this: "Pythagoras before all worked hard in the mathematical sciences and around numbers, but later it happened that he did not know how to renounce the miraculous practice of Phecydes of Syros".

The Pythagorean school of Crotone later became a political hetairia (in ancient Greek, ἑταιρεία = brotherhood) of aristocratic current. It was a philosophical, religious and scientific fraternity, close to Orphism.

First Degree: Applicants

Pythagoras observes, in those who present themselves as candidates, the features of the face (physiognomy) and the gestures (kinesics), but also the relations with the parents, the laughter, the desires, the company. One is admitted or not.

Second degree: the neophytes

Their probation period lasts three years, during which Pythagoras examines their perseverance and desire to learn. At the end they are refused or accepted. If accepted, they take the oath of silence:

"No, by him who found the tetraktys of our wisdom, Source which contains in it the roots of eternal nature."

Third degree: acousticians

Acousmaticians - or acousmatics - (άκουσματικοί: "listeners"). They are taught for five years, given in the form of oral precepts (e.g., "Do not hold hasty opinions or words about the gods." These five years are five years of silence. The listeners stand before the curtain behind which Pythagoras hides. They pool their goods.

Postulants, neophytes, and auditors form the rank of "exoterics" (έξωτερικοί) or novices.

Fourth and final degree: mathematicians

Mathematicians (μαθηματικοί, "scholars") or "esoterics" or sindonites (dressed in linen). "They became esoteric (έσωτερικοί)," insofar as they gained access to inner, hidden knowledge. They are allowed to see Pythagoras behind his curtain. He himself teaches in the form of "symbols" (e.g., "Do not touch a white rooster." According to Photius we see a division of the "esoteric" into "venerable" (σεβαστικοί, sebastikoi), "political" (πολιτικοί, politikoi), "contemplative". The venerable or pious are concerned with religion. The politikoi are concerned with laws, with human affairs, both in the Pythagorean community and in the city. The "contemplatives" study arithmetic, music, geometry, astronomy: the four sciences according to Archytas, which will form the quadrivium of the Middle Ages. We should add the physicists or naturalists (φυσικοί), who study the concrete sciences: geography, meteorology, medicine, mechanics... but also grammar, poetry... It is more likely that the "acousmaticians" are "politicians, administrators or legislators" and the "mathematicians" are "pious" or "contemplatives".

Many rules, not to say taboos, are imposed on whoever adopts "the Pythagorean life" (βίος πυθαγορικός).

The acoustician rivalry

As early as Hippasius (around 450?), there seems to have been rivalry between two ideological tendencies (and no longer initiatory degrees) among the Pythagoreans: the "acousmaticians" and the "mathematicians". It is no longer a question of the novice hierarchy

Just as the historical figure of Pythagoras is not well known, his thought is assimilated to the Pythagorean school. The thought of Pythagoras himself is thus covered by the successive contributions of his disciples. That of the Pythagorean school covers all the fields: "the science relating to the intelligibles and the gods; then physics; ethical philosophy and logic; all kinds of knowledge in mathematics and sciences". Archytas, the first, conceived what will be the quadrivium: arithmetic, music (sensible arithmetic), geometry, finally astronomy (sensible geometry). Pythagoras saw their links: he brought the figures of geometry to the numbers of arithmetic, the sounds of musicians to the proportions of arithmeticians... Correspondences (ὁμοιὠματα) are established, for example "the 1 is the point, the 2 the line, the 3 the triangle".

Arithmetic (and arithmology)

"Everything is number." The great contribution of Pythagoras is the importance of the notion of number and the development of a demonstrative (but also religious) mathematics. For an ancient Greek, number always meant a whole number and signified "numerically arranged system", "ordered plurality", "structured thing"; on the other hand, "one" was not considered a number before Archytas. For the Pythagoreans, things are numbers, or things consist of numbers, or things imitate numbers (which would be principles), or things have numbers: a certain vagueness remains.

According to Aristotle, for the Pythagoreans, things are numbers; for example, one and spirit are identical, in music the intervals of the tones are ratios of numbers; according to Philolaos of Crotone: things are numbers, are made of numbers; for example, the pyramid contains the number 10, the sky consists of 10 celestial bodies (according to Hippasius, things have for models the numbers.

The famous statement "Things are number" means both: a) it is number that constitutes the intelligible structure of things (b) the fundamental elements 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 which is constituted by the notions of finite and infinite, of one and multiple, etc.).

Aristotle: "The Pythagoreans first applied themselves to mathematics... Finding that things essentially model their nature on all numbers and that numbers are the first principles of the whole of nature, the Pythagoreans concluded that the elements of numbers are also the elements of everything that exists, and they made the world a harmony and a number... The elements of number are the even and the odd; and the one is finite [limited, structuring, like a geometric figure], while the other is infinite .  " There is "similarity of the even and the feminine, of the odd and the male".

Pythagoras gives a geometrical representation of numbers. Arithmetic and geometry are sisters. Arithmetic demonstrations are based on figures and this method is called geometric arithmetic. Each unit is represented by a point, so we have plane numbers (1, 3, 6, 10, etc. are triangular), rectangular, solid (cubic, pyramidal, etc.), linear, polygonal. The first pyramidal number is 4 (according to Philolaos). This method allows the calculation of the sum of the first integers, the first odd integers or the calculation of Pythagorean triplets.

Photius: "They proclaimed that everything is a number and that the complete number is ten. The number ten, the , is a compound of the first four numbers that we count in their order. That is why they called Tetraktys the whole constituted by this number." 1 + 2 + 3 + 4 = 10: triangular number of side 4, where the tetrad is worth the decade and hides the harmonic ratios of the intervals of fourth (3:4), fifth (2:3) and octave (1:2). As early as Archytas perhaps or after Plato, the Pythagoreans associate the 1 with the point, the 2 with the line, the 3 with the surface (the two-dimensional geometrical figure: circle, triangle, square, etc.), the 4 with the solid (the three-dimensional geometrical figure: cube, sphere, pyramid, etc.).

"He discovered the medietes": the proportions, the formulas of averages. Pythagoras discovered 3 of the 11 possible proportions between 3 terms (the others were discovered by other Pythagoreans, including Hippas of Metapontum, Archytas.

The science of numbers is both arithmetic, therefore scientific, and arithmology, therefore symbolic. Each number is a symbol. Justice is four, life (and marriage) is five. Philolaos holds that the number 1 symbolizes the point, the 2 the line, the 3 the triangle, the 4 the volume, the 5 the qualities and the colors, the 6 the soul, the 7 the spirit, the health and the light, the 8 the love, the friendship, the cunning and the intellection, the 9 the gestation.

Music

It all began with the discovery that there is a relationship between the length of a vibrating string and the pitch of the sound emitted. Let's say four strings are stretched, the first one is worth 1, the second one has a length representing the 3

"The Pythagoreans assert that music is a harmonic combination of opposites, a unification of multiples, and an agreement of opposites." (Theon of Smyrna)

Pythagoras discovered the laws of harmonics. Aristotle: "These philosophers noticed that all the modes of musical harmony and the relations that compose it are resolved in proportional numbers." The harmonic proportion governs the musical intervals. In the harmonic proportion 12, 8 and 6, the ratio 12

Diogenes Laërce also makes Pythagoras the inventor of the monochord canon, a single-stringed musical instrument called a "canon". It illustrates the law that "the height of the sound is inversely proportional to the length of the string".

Music has an ethical and medical value. "He started education with music, by means of certain melodies and rhythms, thanks to which he produced cures in the traits of character and passions of men, brought back harmony between the faculties of the soul".

Music has a cosmic dimension, just as astronomy has a musical dimension: Plato would say that music and astronomy are "sister sciences" (cf. The harmony of the spheres, planetary music). Pythagoras would have posited that the distances between the orbits of the Sun, the Moon and the fixed stars correspond to the proportions regulating the intervals of the octave, the fifth and the fourth. Later, "from the voice of the seven planets, from that of the sphere of the fixed stars" and, in addition, from that of the sphere above us that is called "Anti-Earth", he made the nine Muses. The order is (for Pythagoras or the first Pythagoreans): sphere of the fixed stars, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, Earth, Anti-Earth, central Fire, that is 10 units. Pythagoras finds the harmonic proportion where, for 12:8:6, we see that 12:6 is the octave, 12:8 the fifth, 8:6 the fourth. If the radius of the central fire is 1, the radius of the orbit of the Anti-Earth is 3, of the Earth 9, of the Moon 27, of Mercury 81, of Venus 243, of the Sun 729. Between the sphere of the fixed stars and Saturn, between Saturn and Jupiter, Jupiter and Mars there is a semitone, a tone between Mars and the Sun, and one obtains a fourth; between the Sun and Earth one obtains a fifth, between the fixed stars and Earth an octave. "Pythagoras stretched his hearing and fixed his intellect on the celestial chords of the universe. He alone, it seemed, heard and understood the universal harmony and unison of the spheres.

Geometry

The school of Pythagoras inherits a double mathematical culture. The Ionian mathematics, initiated by Thales of Miletus, brings him a geometrical orientation, as well as a will of demonstration. The Mesopotamian heritage offers calculation procedures allowing the resolution of the second degree equation, or the approximate evaluation of square roots by fractions.

This double heritage is associated with a false idea, the one according to which any length can be expressed as a fraction: "the Pythagoreans started from the idea, natural to any uneducated man, that any length is necessarily commensurable to the unit." This error is nevertheless fruitful. If any length is a fraction, and provided that the unit of the figure is well chosen, it becomes possible to work only on figures whose lengths are whole. This approach allows the first partial proofs of the Pythagorean theorem, already known by the Egyptians and the Mesopotamians but probably never demonstrated, in the Mediterranean basin. The type of demonstration is explained on the figure on the left. A right-angled triangle whose sides other than the hypotenuse are of lengths 3 and 4, has a hypotenuse of square (in blue on the figure) equal to 25.

This use of calculus to deal with questions of the second degree highlights proportions that are not fractions. One can construct lengths, such as the diagonal and the side of a regular pentagon, such that there is no unit to express these two lengths as integers. Such lengths are called incommensurable. The discovery of these proportions was probably made by the early Pythagoreans. It is sometimes attributed to Hippasius using a reasoning on the pentagon. This discovery, which the historians Michel (it) and Itard describe as a fertile rape, initially caused a serious crisis, but then nourished and enriched Greek mathematics for two centuries.

Astronomy: the cosmos

Pythagoras brings a knowledge that still amazes the logician Frege: the evening star (the one we see first at nightfall) and the morning star are one and the same: Venus. This identity was known in Babylon since -685.

Pythagoras" was the first to call the sky cosmos (but the theory of the sphericity of the Earth is more often attributed to Parmenides. The disciples developed the Pythagorean astronomy.

Philolaos of Crotone (-470

"Others think that the Earth moves. Thus, Philolaos the Pythagorean says that the Earth moves around the Fire in an oblique circle, as do the Sun and the Moon. Heraclides of Pontus and Ecphantos the Pythagorean do not, it is true, give the Earth a translational motion [motion around the Sun, heliocentrism]... Starting from there, I too began to think about the mobility of the Earth."

(Copernicus: Letter to Pope Paul III, preface to Of the Revolutions of the Celestial Orbs. De revolutionibus orbium caelestium, 1543).

Aristarchus of Samos, an Aristotelian astronomer, was the first to assert, around -280, the rotation of the Earth on its own axis and the translation of the Earth around the Sun.

The soul, the transmigration of souls

For Pythagoras, the body (sôma) is a tomb (sêma), both a prison and a "sign" or "protection" of the soul: this is a Pythagorean thesis, not an Orphic one. Philolaos: "The ancient theologians and diviners also testify that it is as a punishment for certain faults that the soul was attached to the body and buried in it like a tomb."

The soul is a number, in the sense that it is harmony, good proportion, combination of the properties composing the body (this is the theory of the Pythagorean Simmias in Plato's Phaedo, 86d). It is life, because movement.

Pythagoras thought "that the soul is immortal; then, that it passes into other animal species; furthermore, that at certain periods what has been is reborn, that nothing is absolutely new, that it is necessary to recognize the same species to all beings that receive life. To many of those who approached him he reminded them of the previous life that their soul had once lived before being chained to their present body. And he himself, by irrefutable proofs, demonstrated that he reincarnated Euphorbius, son of Panthoos". The interval between incarnations would be 216 years (6 cubic). And the explanation comes from the nature of the soul: there is transmigration of the soul because, by nature, it is immortal and moving, Pythagoras does not make intervene the divine justice, a retribution of the soul, since any soul can enter any body.

Where did Pythagoras get his theory of the transmigration ("παλιγγενεσία") of souls? from Orpheus? from Phecydes of Syros? from India? It is not known. Pythagoras indicated his previous existences, in a list set by Heraclides of Pontus, Euphorbius (priest of Apollo), Hermotime (shaman), Pyrrhus (simple fisherman). It is possible that Pythagoras believed in reincarnation only for himself.

"He (Pythagoras) told the following about himself: he had once been Aithalides and passed for the son of Hermes; Hermes had told him to choose whatever he wanted, except immortality. He had therefore asked to keep, both alive and dead, the memory of what happened to him. Thus in his life he remembered everything, and once dead he kept his memories intact. Later, he entered the body of Euphorbia and was wounded by Menelaus. And Euphorbius said that he had been Aithalides, and that he had received from Hermes this present and this way that the soul had to pass from one place to another, and he told how it had accomplished its journeys, in which plants and which animals it had been present, and all that his soul had experienced in Hades, and what the others endured there. Euphorbius died, his soul passed in Hermotime who, wanting himself to give a proof, returned near the Branchidae and penetrating in the sanctuary of Apollo, showed the shield which Menelaus had dedicated there (it said indeed that this last, when he had left Troy, had dedicated this shield to Apollo), a shield which was from that time decomposed, and of which there remained only the ivory face. When Hermotime died, he became Pyrrhos, the delirious sinner; again, he remembered everything, how he had been before Aithalides, then Euphorbus, then Hermotime, then Pyrrhos. When Pyrrhos died, he became Pythagoras and remembered all that has just been said.

- Diogenes Laërce, VIII, 5.

In his theory of the transmigration of souls, Pythagoras admits a type of reincarnation comparable to that conceived in Hinduism or Jainism, because his belief in metempsychosis corresponds to a soul that can come from and enter a non-human, vegetable or animal body:

"One day, passing by someone who was mistreating his dog, it is said that he was moved with compassion and addressed the individual with these words: "Stop and do not strike again, because it is the soul of a man who was my friend, and I recognized him by the sound of his voice"

- Diogenes Laërce, VIII, 36.

Vegetarianism

Pythagoras is considered in the western tradition as the first adept of vegetarianism of the humanity which does not live any more in the golden age, golden age where one was indeed vegetarian (whether it is in the Greco-Roman philosophical mythology, or the Hebrew mythology (Bible), with Adam and Eve until the Flood).

The Presocratics are zoophiles. It is Ovid who defends vegetarianism by means of this passage concerning Pythagoras, in his famous work the Metamorphoses:

"He was the first to make it a crime for man to load his table with the flesh of animals; he was the first to give those sublime lessons which were not heeded: "Stop, mortals, from defiling yourselves with abominable food! You have the harvests; you have the fruits whose weight inclines the branches to the earth, the grapes hanging on the vine, the tasty plants and those whose fire can soften the juices and soften the fabric; you have the milk of the herds, and the honey scented with thyme; the earth lavishes its treasures on you, innocent and pure foods, which are not bought by murder and blood. What a horrible thing! entrails swallowing entrails, a body fattening on another body, an animated being living on the death of an animated being like him! What! in the midst of the riches that the earth, this beneficent mother, produces for our needs, you only like to tear with a cruel tooth palpitating flesh; you renew the barbaric tastes of the Cyclops, and, without the destruction of a being, you cannot satisfy the unregulated appetites of a ravenous stomach! But in that ancient age of which we have made the golden age, man was rich and happy with the fruits of the trees and the plants of the earth; blood did not stain his mouth. Then the bird could, without danger, play in the air; the hare ran boldly in the countryside; the credulous fish did not come to hang on the hook. There were no enemies, no traps to fear, but a profound peace. Cursed be the one who first disdained the frugality of this age, and whose greedy belly swallowed up living food! he opened the way to crime."

This vegetarianism being linked to the reincarnation proposed by Pythagoras in his philosophy, thus thinking the destiny of the living in the sense of a total interdependence, the philosopher proposes a particular sensibility which is usually found in the Hindu civilization (with Ahimsâ and Jainism in particular):

"The sky and all that is seen beneath it, the earth and all that it contains, change form. We too, a portion of this world, change; and, as we have a wandering soul which can, from our body, pass into the body of animals, let us leave in peace and respect the asylum where live the souls of our parents, of our brothers, of those whom we loved, of the souls of men, finally: let us beware of making feasts of Thyestes. How horrible are his tastes, how he prepares himself to shed human blood one day, the one who slaughters a lamb in cold blood, and lends an insensitive ear to its plaintive bleating; the one who can without pity kill the young kid and hear it wagging like a child; the one who can eat the bird that he has fed with his hand! How far is it from this crime to the last of crimes, homicide? Does it not open the way? Let the ox plough, and only die of old age; let the sheep provide us against the icy breath of Boreas, and the goats present their full udders to the hand that presses them. No more rêts and lakes, no more perfidious inventions; no more lure the bird on the glue, no more push the frightened deer into your webs, no more hide, under a deceitful bait, the point of the hook."

- Ovid, The Metamorphoses.

Medicine

The great biological principle is neither the harmony of like with like nor the struggle of the opposite with the opposite, but - as in music - the harmony of opposites, the balance of powers 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 wet and dry, fluid and viscous, bitter and sweet, even and odd, etc.

In medicine, the Pythagoreans had their own techniques: diet, cataplasms, medicines, refusal of incisions and cauterizations, "incantations for certain diseases", music, "selected verses of Homer and Hesiod". We find the Indo-European tripartition:

Alcméon of Crotone, who seems to be a Pythagorean, practices dissection; he places thought in the brain, and not in the heart, like all the other thinkers: "The hegemonic has its seat in the brain."

Although the use of his incantations may seem more mythical than scientific, we can also see in them the beginning of theories concerning Psychosomatics. Indeed, Pythagoras healed the mind in order to heal the body; and although this may have seemed unusual for his time, we now know that some pains and illnesses are psychosomatic.

Political Science

According to Jamblicus, Pythagoras was known to the Neoplatonists as the founder of political science. An almost unanimous tradition describes his political vision as conservative and aristocratic. Indeed, he was in favor of entrusting power to educated people who were accountable to the people and who passed it on to their children. Politics, like music, must lead to harmony and to expose his ideas on justice, he uses mathematical parallels. He is in favor of the proportionality of the political right (to each according to his value) rather than the equality advocated by the democrats.

The functioning of the city must be based on laws of divine origin to which all are subjected, senators included. The good citizen must not only respect them but protect them if necessary by denunciation and repression. For him, the law, assimilated, leads to freedom. Justice must be applied in an egalitarian way according to the principle of reciprocity (law of retaliation). This point is moreover disapproved by Aristotle: "It is reciprocity which constitutes purely and simply justice. This was the doctrine of the Pythagoreans, who defined justice simply as reciprocity. But reciprocity does not coincide with distributive justice or even with corrective justice".

If it is now accepted that the Pythagoreans, organized in a hetairie, did play a political role already at the time of Pythagoras, the role of the latter is subject to debate: political leader? legislator? simple inspirer? For Delatte, the conclusion is clear: Pythagoras' initial plan was not political but moral, but gradually his ideas, through his school, invaded the political field.

Archytas of Taranto, strategist of Taranto for 7 years but also scholar and Pythagorean philosopher, is the type of the philosopher-king. Plato met him physically as early as -388 and he imagines the ideal philosopher-king in -370 in his Republic : " As long as philosophers are not kings in the cities, or as long as those who are now called kings and rulers are not really and seriously philosophers... there will be no end to the evils of the cities " (The Republic, V, 473 c).

Esoteric teachings

Pythagoras dispenses exoteric principles, known to all, for example: "It is forbidden to pray for oneself", "Between friends, everything is common". But other teachings are esoteric, i.e. reserved for the initiated and of symbolic expression; and they concern the secrets of nature and the gods. These secret teachings are called Memories (hypomnêmata, Ύπομνήματα), because they must be remembered, without writing them down. These are, on the one hand, the "acousmates" (they are, on the other hand, the "symbols" (σύμβολα), coded formulas, summaries (kephalaia, κεφάλαια). For "not everything can be told to everyone." "There was among them the absolute rule of silence".

Jamblique classifies acousmates into three types, according to whether they reveal the essence ("what is it?"), the absolute ("what is the most?") or the duty ("what should be done or not done?").

In addition to acousmates, abstract precepts, there is another category of precepts, symbols, which are pictorial practical precepts. The profane see in them superstition or nonsense, but the initiated (μύσται) know how to decipher in them an idea or an act.

In addition, there are the "secret symbols" (απόρρητα σύμβολα, aporrêta sumbola) or "signs of recognition" (sunthémata, συνθήματα), which allowed initiated Pythagoreans to recognize each other. The most famous secret symbols are the famous pentagram with 5 branches and 5 sides and the tetraktys. "The divine Pythagoras never put at the head of his letters either "Joy" or "Prosperity"; he always began with "hygiainé!", (ὑγίαινε, Health!). That is why the triple entwined triangle, formed of five lines , which served as a symbol for all those of this sect, was called by them "the sign of health."

The successors (diadochos) of Pythagoras at the head of the Pythagorean community were: Aristaeus of Crotone (Boulagoras (-380), Gartydas of Crotone, Aresas of Lucania, Diodorus of Aspendos (-380).The Pythagorean current is divided into various schools:

Influences received

Obviously, Pythagoreanism was influenced by Orphism, but also by the Apollonian shamanism of the Hyperboreans (Aristaeus of Proconnesus, etc.), certainly by Egyptian thought, perhaps by the mathematics and astronomy of Babylon.

Influences given

The richness of the work undertaken by the Pythagorean school was such that its ideas and discoveries inspired many currents of thought. Pythagoras influenced all eras and all cultures of the West and the East, all disciplines: mathematics, music, philosophy, astronomy, etc. His encyclopedism makes him a total thought, with interpenetrations and ramifications.

In art, Pythagoras inspired the Roman architect Vitruvius in the first century and then the theorists of the golden ratio like Luca Pacioli illustrated by Leonardo da Vinci in 1509.

Schoolchildren who study the Pythagorean theorem or learn the multiplication table - known as the Pythagorean table - are part of his lineage.

Pythagoras founded a true religion, and many legends. In the esoteric and initiatory field, his work continues. As early as 1410, the Cooke manuscript (line 216), a basic document of operative freemasonry, mentions Hermes and "Pictagoras". Freemasonic lodges claim to be based on Pythagorean thought, such as the Swiss Alpine Grand Lodge (GLSA), French Freemasonry and the Italian Lodge.

Works

According to most authors, Pythagoras did not write anything. The philosopher Porphyry of Tyre is, on this subject, formal: "Because of Pythagoras himself there was no writing. This point is contradicted by several authors, notably Heraclitus who attributes the following three treatises to Pythagoras: On education, On politics and On nature. According to Alexander Polyhistor, Pythagoras would have left only this work: Pythagorean Memoirs. These attributions are very uncertain, and, since antiquity, it was thought that these books had been written by disciples of Pythagoras. It is also possible that, because of Pythagoras' persistent custom of esotericism, he would never have committed any of his thoughts to paper.

Pythagorean writings

: document used as a source for the writing of this article.

Sources

1. Pythagoras
2. Pythagore