Teana is a town and comune in the province of Potenza , in the southern Italian region of Basilicata .
126-462: The name Teana is a derivative of the Greek word "Theano", the wife of Pythagoras , the philosopher and mathematician . Local legend states the town was formed from members of Pythagorean school. The village of 600 is home to a distinctive pasta shape — rasccatieddi di miscchieddu — that was the subject of an episode of the program Shape of Pasta . Some of the local landmarks and points of interest are
252-553: A Sonchis of Sais ). According to the Christian theologian Clement of Alexandria ( c. 150 – c. 215 AD), "Pythagoras was a disciple of Sonchis, an Egyptian archprophet, as well as a Plato of Sechnuphis ." Some ancient writers claimed that Pythagoras learned geometry and the doctrine of metempsychosis from the Egyptians. Other ancient writers, however, claimed that Pythagoras had learned these teachings from
378-556: A pseudepigraphal poem. Empedocles , who lived in Magna Graecia shortly after Pythagoras and Parmenides, knew that the earth was spherical. By the end of the fifth century BC, this fact was universally accepted among Greek intellectuals. The identity of the morning star and evening star was known to the Babylonians over a thousand years earlier. Sizeable Pythagorean communities existed in Magna Graecia, Phlius , and Thebes during
504-473: A single unique world (31b). Additionally, because the demiurge wanted his creation to be a perfect imitation of the Eternal "One" (the source of all other emanations), there was no need to create more than one world. The creator decided also to make the perceptible body of the universe by four elements, in order to render it proportioned . Indeed, in addition to fire and earth, which make bodies visible and solid,
630-505: A Scythian priest of Apollo by the name of Abaris the Hyperborean : Abaris stayed with Pythagoras, and was compendiously taught physiology and theology; and instead of divining by the entrails of beasts, he revealed to him the art of prognosticating by numbers, conceiving this to be a method purer, more divine, and more kindred to the celestial numbers of the Gods. This shouldn't be confused with
756-537: A close friend of Plato and he is quoted in Plato's Republic . Aristotle states that the philosophy of Plato was heavily dependent on the teachings of the Pythagoreans. Cicero repeats this statement, remarking that Platonem ferunt didicisse Pythagorea omnia ("They say Plato learned all things Pythagorean"). According to Charles H. Kahn , Plato's middle dialogues, including Meno , Phaedo , and The Republic , have
882-472: A cube, of air an octahedron, of water an icosahedron, and of fire a tetrahedron. Each of these perfect polyhedra would be in turn composed of triangular faces the 30-60-90 and the 45-45-90 triangles. The faces of each element could be broken down into its component right-angled triangles, either isosceles or scalene, which could then be put together to form all of physical matter. Particular characteristics of matter, such as water's capacity to extinguish fire,
1008-422: A deadly snake bit Pythagoras, he bit it back and killed it. Both Porphyry and Iamblichus report that Pythagoras once persuaded a bull not to eat fava beans and that he once convinced a notoriously destructive bear to swear that it would never harm a living thing again, and that the bear kept its word. Riedweg suggests that Pythagoras may have personally encouraged these legends, but Gregory states that there
1134-457: A divine figure, sent by the gods to benefit humankind. Iamblichus, in particular, presents the "Pythagorean Way of Life" as a pagan alternative to the Christian monastic communities of his own time. For Pythagoreans, the highest reward a human could attain was for their soul to join in the life of the gods and thus escape the cycle of reincarnation. Two groups existed within early Pythagoreanism:
1260-433: A five-year initiation period, during which they were required to remain silent. Sources indicate that Pythagoras himself was unusually progressive in his attitudes towards women and female members of Pythagoras's school appear to have played an active role in its operations. Iamblichus provides a list of 235 famous Pythagoreans, seventeen of whom are women. In later times, many prominent female philosophers contributed to
1386-472: A fragment, Aristotle writes that Pythagoras had a golden thigh, which he publicly exhibited at the Olympic Games and showed to Abaris the Hyperborean as proof of his identity as the "Hyperborean Apollo". Supposedly, the priest of Apollo gave Pythagoras a magic arrow, which he used to fly over long distances and perform ritual purifications. He was supposedly once seen at both Metapontum and Croton at
SECTION 10
#17328580839091512-484: A golden wreath atop his head and to have worn trousers after the fashion of the Thracians . Diogenes Laërtius presents Pythagoras as having exercised remarkable self-control ; he was always cheerful, but "abstained wholly from laughter, and from all such indulgences as jests and idle stories". Pythagoras was said to have had extraordinary success in dealing with animals. A fragment from Aristotle records that, when
1638-455: A lady of Crete and the daughter of Pythenax and had several children with her. Porphyry writes that Pythagoras had two sons named Telauges and Arignote , and a daughter named Myia, who "took precedence among the maidens in Croton and, when a wife, among married women." Iamblichus mentions none of these children and instead only mentions a son named Mnesarchus after his grandfather. This son
1764-436: A lawgiver. The so-called Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it they came to believe that its principles are the principles of everything. According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application. They believed that all things were made of numbers. The number one (the monad ) represented
1890-427: A likely story" (29d). Timaeus suggests that since nothing "becomes or changes" without cause, then the cause of the universe must be a demiurge or a god, a figure Timaeus refers to as the father and maker of the universe. And since the universe is fair, the demiurge must have looked to the eternal model to make it, and not to the perishable one (29a). Hence, using the eternal and perfect world of " forms " or ideals as
2016-591: A major revival in the first century BC among Middle Platonists , coinciding with the rise of Neopythagoreanism . Pythagoras continued to be regarded as a great philosopher throughout the Middle Ages and his philosophy had a major impact on scientists such as Nicolaus Copernicus , Johannes Kepler , and Isaac Newton . Pythagorean symbolism was also used throughout early modern European esotericism , and his teachings as portrayed in Ovid 's Metamorphoses would later influence
2142-537: A new body. This teaching is referenced by Xenophanes, Ion of Chios, and Herodotus. Nothing whatsoever, however, is known about the nature or mechanism by which Pythagoras believed metempsychosis to occur. Empedocles alludes in one of his poems that Pythagoras may have claimed to possess the ability to recall his former incarnations. Diogenes Laërtius reports an account from Heraclides Ponticus that Pythagoras told people that he had lived four previous lives that he could remember in detail. The first of these lives
2268-489: A person should always put the right sandal on before the left. The exact meanings of these sayings, however, are frequently obscure. Iamblichus preserves Aristotle's descriptions of the original, ritualistic intentions behind a few of these sayings, but these apparently later fell out of fashion, because Porphyry provides markedly different ethical-philosophical interpretations of them: New initiates were allegedly not permitted to meet Pythagoras until after they had completed
2394-405: A popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole hecatomb , to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough . The Pythagorean theorem was known and used by
2520-579: A proclivity towards tyranny. Other accounts claim that Pythagoras left Samos because he was so overburdened with public duties in Samos, because of the high estimation in which he was held by his fellow-citizens. He arrived in the Greek colony of Croton (today's Crotone , in Calabria ) in what was then Magna Graecia . All sources agree that Pythagoras was charismatic and quickly acquired great political influence in his new environment. He served as an advisor to
2646-503: A result of Pherecydes's influence. Another story, which may be traced to the Neopythagorean philosopher Nicomachus , tells that, when Pherecydes was old and dying on the island of Delos , Pythagoras returned to care for him and pay his respects. Duris , the historian and tyrant of Samos, is reported to have patriotically boasted of an epitaph supposedly penned by Pherecydes which declared that Pythagoras's wisdom exceeded his own. On
SECTION 20
#17328580839092772-558: A school in which initiates were sworn to secrecy and lived a communal, ascetic lifestyle. In antiquity, Pythagoras was credited with many mathematical and scientific discoveries, including the Pythagorean theorem , Pythagorean tuning , the five regular solids , the Theory of Proportions , the sphericity of the Earth , and the identity of the morning and evening stars as the planet Venus . It
2898-428: A secure basis for philosophy, science, and morality. Plato and Pythagoras shared a "mystical approach to the soul and its place in the material world" and both were probably influenced by Orphism . The historian of philosophy Frederick Copleston states that Plato probably borrowed his tripartite theory of the soul from the Pythagoreans. Bertrand Russell , in his A History of Western Philosophy , contends that
3024-562: A simplified version known today as " Pythagorean numerology ", involving a variant of an isopsephic technique known – among other names – as pythmenes ' roots ' or ' base numbers ' , by means of which the base values of letters in a word were mathematically reduced by addition or division, in order to obtain a single value from one to nine for the whole name or word; these 'roots' or 'base numbers' could then be interpreted with other techniques, such as traditional Pythagorean attributions. This latter form of numerology flourished during
3150-440: A soul, the demiurge "put intelligence in soul, and soul in body" in order to make a living and intelligent whole. "Wherefore, using the language of probability, we may say that the world became a living creature truly endowed with soul and intelligence by the providence of God" (30a–b). Then, since the part is imperfect compared to the whole, the world had to be one and only. Therefore, the demiurge did not create several worlds, but
3276-479: A specific building that was still in use during his own time, appears to be motivated by Samian patriotic interest. Around 530 BC, when Pythagoras was about forty years old, he left Samos. His later admirers claimed that he left because he disagreed with the tyranny of Polycrates in Samos, Riedweg notes that this explanation closely aligns with Nicomachus's emphasis on Pythagoras's purported love of freedom, but that Pythagoras's enemies portrayed him as having
3402-423: A strong "Pythagorean coloring", and his last few dialogues (particularly Philebus and Timaeus ) are extremely Pythagorean in character. According to R. M. Hare , Plato's Republic may be partially based on the "tightly organised community of like-minded thinkers" established by Pythagoras at Croton. Additionally, Plato may have borrowed from Pythagoras the idea that mathematics and abstract thought are
3528-520: A synthesis of everything Pythagoras had learned from Orpheus, from the Egyptian priests, from the Eleusinian Mysteries , and from other religious and philosophical traditions. Riedweg states that, although these stories are fanciful, Pythagoras's teachings were definitely influenced by Orphism to a noteworthy extent. Of the various Greek sages claimed to have taught Pythagoras, Pherecydes of Syros
3654-458: A template, he set about creating our world, which formerly only existed in a state of disorder. Timaeus continues with an explanation of the creation of the universe, which he ascribes to the handiwork of a divine craftsman. The demiurge, being good, wanted there to be as much good as was the world. The demiurge is said to bring order out of substance by imitating an unchanging and eternal model (paradigm). Ananke , often translated as 'Necessity',
3780-401: A third element was required as a mean: "two things cannot be rightly put together without a third; there must be some bond of union between them". Moreover, since the world is not a surface but a solid, a fourth mean was needed to reach harmony: therefore, the creator placed water and air between fire and earth. "And for these reasons, and out of such elements which are in number four, the body of
3906-466: A vow of silence that they would not reveal these symbols to non-members. Those who did not obey the laws of the community were expelled and the remaining members would erect tombstones for them as though they had died. A number of "oral sayings" ( akoúsmata ) attributed to Pythagoras have survived, dealing with how members of the Pythagorean community should perform sacrifices, how they should honor
Teana - Misplaced Pages Continue
4032-526: Is a sensible object, the inner circle of the Diverse transmits its movement to the soul, whereby opinions arise, but when it is an intellectual object, the circle of the Same turns perfectly round and true knowledge arises (37a–c). The world as a whole, the planets, and the stars are living, visible gods (39e) that have an important role in creating human beings and regulating their moral life (41d). Timaeus claims that
4158-413: Is mentioned most often. Similar miracle stories were told about both Pythagoras and Pherecydes, including one in which the hero predicts a shipwreck, one in which he predicts the conquest of Messina , and one in which he drinks from a well and predicts an earthquake. Apollonius Paradoxographus , a paradoxographer who may have lived in the second century BC, identified Pythagoras's thaumaturgic ideas as
4284-478: Is no direct evidence of this. Anti-Pythagorean legends were also circulated. Diogenes Laërtes retells a story told by Hermippus of Samos, which states that Pythagoras had once gone into an underground room, telling everyone that he was descending to the underworld. He stayed in this room for months, while his mother secretly recorded everything that happened during his absence. After he returned from this room, Pythagoras recounted everything that had happened while he
4410-456: Is one of Plato's dialogues , mostly in the form of long monologues given by Critias and Timaeus , written c. 360 BC. The work puts forward reasoning on the possible nature of the physical world and human beings and is followed by the dialogue Critias . Participants in the dialogue include Socrates , Timaeus, Hermocrates , and Critias. Some scholars believe that it is not the Critias of
4536-404: Is postponed to Critias . The main content of the dialogue, the exposition by Timaeus, follows. Timaeus begins with a distinction between the physical world, and the eternal world. The physical one is the world which changes and perishes: therefore it is the object of opinion and unreasoned sensation. The eternal one never changes: therefore it is apprehended by reason (28a). The speeches about
4662-504: Is the one from Diogenes Laërtius 's Lives and Opinions of Eminent Philosophers . The two later biographies were written by the Neoplatonist philosophers Porphyry and Iamblichus and were partially intended as polemics against the rise of Christianity . The later sources are much lengthier than the earlier ones, and even more fantastic in their descriptions of Pythagoras's achievements. Porphyry and Iamblichus used material from
4788-763: The Protrepticus . Aristotle's disciples Dicaearchus , Aristoxenus , and Heraclides Ponticus (who all lived in the 3rd century BC) also wrote on the same subject. Most of the major sources on Pythagoras's life are from the Roman period , by which point, according to the German classicist Walter Burkert , "the history of Pythagoreanism was already ... the laborious reconstruction of something lost and gone." Three ancient biographies of Pythagoras have survived from late antiquity, all of which are filled primarily with myths and legends. The earliest and most respectable of these
4914-463: The Babylonians and Indians centuries before Pythagoras, but he may have been the first to introduce it to the Greeks. Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof . Burkert rejects this suggestion as implausible, noting that Pythagoras was never credited with having proved any theorem in antiquity. Furthermore, the manner in which
5040-629: The Byzantine era , and was first attested among the Gnostics of the second century AD. By that time, isopsephy had developed into several different techniques that were used for a variety of purposes; including divination, doctrinal allegory, and medical prognosis and treatment. In the visits to various places in Greece— Delos , Sparta , Phlius , Crete , etc.—which are ascribed to him, he usually appears either in his religious or priestly guise, or else as
5166-488: The Celts and Iberians . Ancient sources also record Pythagoras having studied under a variety of native Greek thinkers. Some identify Hermodamas of Samos as a possible tutor. Hermodamas represented the indigenous Samian rhapsodic tradition and his father Creophylos was said to have been the host of his rival poet Homer . Others credit Bias of Priene , Thales, or Anaximander (a pupil of Thales). Other traditions claim
Teana - Misplaced Pages Continue
5292-517: The Egyptian priest in Sais about long-term factors on the fate of mankind: There have been, and will be again, many destructions of mankind arising out of many causes; the greatest have been brought about by the agencies of fire and water, and other lesser ones by innumerable other causes. There is a story that even you [Greeks] have preserved, that once upon a time, Phaethon , the son of Helios , having yoked
5418-668: The Magi in Persia or even from Zoroaster himself. Diogenes Laërtius asserts that Pythagoras later visited Crete , where he went to the Cave of Ida with Epimenides . The Phoenicians are reputed to have taught Pythagoras arithmetic and the Chaldeans to have taught him astronomy. By the third century BC, Pythagoras was already reported to have studied under the Jews as well. Contradicting all these reports,
5544-460: The Thirty Tyrants who appears in this dialogue, but his grandfather, also named Critias. At the beginning of the dialogue, the absence of another, unknown dialogue participant, present on the day before, is bemoaned. It has been suggested from some traditions— Diogenes Laertius (VIII 85) from Hermippus of Smyrna (3rd century BC) and Timon of Phlius ( c. 320 – c. 235 BC)—that Timaeus
5670-574: The Timaeus had a strong influence on medieval Neoplatonic cosmology and was commented on particularly by 12th-century Christian philosophers of the Chartres School , such as Thierry of Chartres and William of Conches , who, interpreting it in the light of the Christian faith, understood the dialogue to refer to a creatio ex nihilo . Calcidius himself never explicitly linked the Platonic creation myth in
5796-702: The Timaeus with the Old Testament creation story in Genesis in his commentary on the dialogue. The dialogue was also highly influential in Arabic-speaking regions beginning in the 10th century AD. The Catalogue (fihrist) of Ibn al-Nadīm provides some evidence for an early translation by Ibn al-Bitriq ( Al-Kindī 's circle). It is believed that the Syrian Nestorian Christian Hunayn ibn Ishaq (809 – 873 AD) corrected this translation or translated
5922-466: The mathematikoi ("learners") and the akousmatikoi ("listeners"). The akousmatikoi are traditionally identified by scholars as "old believers" in mysticism, numerology, and religious teachings; whereas the mathematikoi are traditionally identified as a more intellectual, modernist faction who were more rationalist and scientific. Gregory cautions that there was probably not a sharp distinction between them and that many Pythagoreans probably believed
6048-834: The planets move according to mathematical equations and thus resonate to produce an inaudible symphony of music. Scholars debate whether Pythagoras developed the numerological and musical teachings attributed to him, or if those teachings were developed by his later followers, particularly Philolaus of Croton . Following Croton's decisive victory over Sybaris in around 510 BC, Pythagoras's followers came into conflict with supporters of democracy , and Pythagorean meeting houses were burned. Pythagoras may have been killed during this persecution, or he may have escaped to Metapontum and died there. Pythagoras influenced Plato, whose dialogues , especially his Timaeus , exhibit Pythagorean teachings. Pythagorean ideas on mathematical perfection also impacted ancient Greek art . His teachings underwent
6174-399: The world-soul . He then divided following precise mathematical proportions, cutting the compound lengthways, fixed the resulting two bands in their middle, like in the letter chi (Χ) and connected them at their ends, to have two crossing circles. The demiurge imparted on them a circular movement on their axis: the outer circle was assigned Sameness and turned horizontally to the right, while
6300-611: The Babylonians employed Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources. Pythagoras's biographers state that he also was the first to identify the five regular solids and that he was the first to discover the Theory of Proportions . According to legend, Pythagoras discovered that musical notes could be translated into mathematical equations when he passed blacksmiths at work one day and heard
6426-444: The Egyptian priests at Diospolis (Thebes), and that he was the only foreigner ever to be granted the privilege of taking part in their worship. The Middle Platonist biographer Plutarch ( c. 46 – c. 120 AD) writes in his treatise On Isis and Osiris that, during his visit to Egypt, Pythagoras received instruction from the Egyptian priest Oenuphis of Heliopolis (meanwhile Solon received lectures from
SECTION 50
#17328580839096552-521: The Pythagoreans during one of their meetings, either in the house of Milo or in some other meeting-place. Accounts of the attack are often contradictory and many probably confused it with the later anti-Pythagorean rebellions, such as the one in Metapontum in 454 BC. The building was apparently set on fire, and many of the assembled members perished; only the younger and more active members managed to escape. Sources disagree regarding whether Pythagoras
6678-399: The account (20b) to do so. Critias proceeds to tell the story of Solon 's journey to Egypt where he hears the story of Atlantis , and how Athens used to be an ideal state that subsequently waged war against Atlantis (25a). Critias believes that he is getting ahead of himself, and mentions that Timaeus will tell part of the account from the origin of the universe to man. Critias also cites
6804-522: The age of 40, which would give a date of birth around 570 BC. Pythagoras's name led him to be associated with Pythian Apollo ( Pūthíā ); Aristippus of Cyrene in the 4th century BC explained his name by saying, "He spoke [ ἀγορεύω , agoreúō ] the truth no less than did the Pythian [ πυθικός puthikós ]". During Pythagoras's formative years, Samos was a thriving cultural hub known for its feats of advanced architectural engineering, including
6930-431: The boys' "raging willfulness" was quelled. The Pythagoreans also placed particular emphasis on the importance of physical exercise ; therapeutic dancing , daily morning walks along scenic routes , and athletics were major components of the Pythagorean lifestyle. Moments of contemplation at the beginning and end of each day were also advised. Pythagorean teachings were known as "symbols" ( symbola ) and members took
7056-553: The building of the Tunnel of Eupalinos , and for its riotous festival culture. It was a major center of trade in the Aegean where traders brought goods from the Near East . According to Christiane L. Joost-Gaugier, these traders almost certainly brought with them Near Eastern ideas and traditions. Pythagoras's early life also coincided with the flowering of early Ionian natural philosophy . He
7182-459: The city of Metapontum , where they took shelter in the temple of the Muses and died there of starvation after forty days without food. Another tale recorded by Porphyry claims that, as Pythagoras's enemies were burning the house, his devoted students laid down on the ground to make a path for him to escape by walking over their bodies across the flames like a bridge. Pythagoras managed to escape, but
7308-422: The creator was to bring order and clarity to this substance. Therefore, all the properties of the world are to be explained by the demiurge's choice of what is fair and good; or, the idea of a dichotomy between good and evil . First of all, the world is a living creature . Since the unintelligent creatures are in their appearance less fair than intelligent creatures, and since intelligence needs to be settled in
7434-413: The development of Neopythagoreanism . Pythagoreanism also entailed a number of dietary prohibitions. It is more or less agreed that Pythagoras issued a prohibition against the consumption of fava beans and the meat of non-sacrificial animals such as fish and poultry. Both of these assumptions, however, have been contradicted. Pythagorean dietary restrictions may have been motivated by belief in
7560-439: The dialogue addresses the creation of humans, including the soul , anatomy , perception , and transmigration of the soul . Plato also discusses the creation of the body, as well as the causes of bodily and psychic diseases. The Timaeus was translated into Latin first by Marcus Tullius Cicero around 45 BC (sections 27d–47b), and later by Calcidius in the 4th century AD (up to section 53c). Cicero's fragmentary translation
7686-449: The doctrine of metempsychosis . Some ancient writers present Pythagoras as enforcing a strictly vegetarian diet. Eudoxus of Cnidus , a student of Archytas, writes, "Pythagoras was distinguished by such purity and so avoided killing and killers that he not only abstained from animal foods, but even kept his distance from cooks and hunters." Other authorities contradict this statement. According to Aristoxenus , Pythagoras allowed
SECTION 60
#17328580839097812-420: The earliest texts to describe the numerological and musical theories that were later ascribed to Pythagoras. The Athenian rhetorician Isocrates ( c. 436 – c. 338 BC) was the first to describe Pythagoras as having visited Egypt. Aristotle ( c. 384 – c. 322 BC) wrote a treatise On the Pythagoreans , which no longer exists. Some of it may be preserved in
7938-399: The early fourth century BC. Around the same time, the Pythagorean philosopher Archytas was highly influential on the politics of the city of Tarentum in Magna Graecia. According to later tradition, Archytas was elected as strategos ("general") seven times, even though others were prohibited from serving more than a year. Archytas was also a renowned mathematician and musician. He was
8064-531: The elites in Croton and gave them frequent advice. Later biographers tell fantastical stories of the effects of his eloquent speeches in leading the people of Croton to abandon their luxurious and corrupt way of life and devote themselves to the purer system which he came to introduce. Diogenes Laërtius states that Pythagoras "did not indulge in the pleasures of love" and that he cautioned others to only have sex "whenever you are willing to be weaker than yourself". According to Porphyry, Pythagoras married Theano ,
8190-515: The entire work himself. However, only the circulation of many exegeses of Timaeus is confirmed. There is also evidence of Galen 's commentary on the dialogue being highly influential in the Arabic-speaking world, with Galen's Synopsis being preserved in a medieval Arabic translation. During much of the Middle Ages in the Latin-speaking West the Timaeus was the sole work of Plato which
8316-418: The exact details of Pythagoras's teachings are uncertain, it is possible to reconstruct a general outline of his main ideas. Aristotle writes at length about the teachings of the Pythagoreans, but without mentioning Pythagoras directly. One of Pythagoras's main doctrines appears to have been metempsychosis , the belief that all souls are immortal and that, after death, a soul is transferred into
8442-471: The exclusion of outsiders. Ancient sources record that the Pythagoreans ate meals in common after the manner of the Spartans . One Pythagorean maxim was " koinà tà phílōn " ("All things in common among friends"). Both Iamblichus and Porphyry provide detailed accounts of the organization of the school, although the primary interest of both writers is not historical accuracy, but rather to present Pythagoras as
8568-478: The fields of music , astronomy , and medicine . Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides" —that is, a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} . According to
8694-461: The first to teach that the Earth was spherical , the first to divide the globe into five climatic zones , and the first to identify the morning star and the evening star as the same celestial object (now known as Venus ). Of the two philosophers, Parmenides has a much stronger claim to having been the first and the attribution of these discoveries to Pythagoras seems to have possibly originated from
8820-461: The gods, how they should "move from here", and how they should be buried. Many of these sayings emphasize the importance of ritual purity and avoiding defilement. For instance, a saying which Leonid Zhmud concludes can probably be genuinely traced back to Pythagoras himself forbids his followers from wearing woolen garments. Other extant oral sayings forbid Pythagoreans from breaking bread, poking fires with swords, or picking up crumbs and teach that
8946-490: The grounds of all these references connecting Pythagoras with Pherecydes, Riedweg concludes that there may well be some historical foundation to the tradition that Pherecydes was Pythagoras's teacher. Pythagoras and Pherecydes also appear to have shared similar views on the soul and the teaching of metempsychosis. Before 520 BC, on one of his visits to Egypt or Greece, Pythagoras might have met Thales of Miletus , who would have been around fifty-four years older than him. Thales
9072-420: The historian Herodotus of Halicarnassus ( c. 484 – c. 420 BC), who describes him as one of the greatest Greek teachers and states that Pythagoras taught his followers how to attain immortality . The accuracy of the works of Herodotus is controversial. The writings attributed to the Pythagorean philosopher Philolaus of Croton ( c. 470 – c. 385 BC) are
9198-411: The influence of Pythagoras on Plato and others was so great that he should be considered the most influential philosopher of all time. He concludes that "I do not know of any other man who has been as influential as he was in the school of thought." A revival of Pythagorean teachings occurred in the first century BC when Middle Platonist philosophers such as Eudorus and Philo of Alexandria hailed
9324-427: The inner circle was assigned to Difference and turned diagonally and to the left (34c–36c). The demiurge gave the primacy to the motion of Sameness and left it undivided; but he divided the motion of Difference in six parts, to have seven unequal circles. He prescribed these circles to move in opposite directions, three of them with equal speeds, the others with unequal speeds, but always in proportion. These circles are
9450-439: The lost writings of Aristotle's disciples (Dicaearchus, Aristoxenus, and Heraclides) and material taken from these sources is generally considered to be the most reliable. There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account. Herodotus , Isocrates , and other early writers agree that Pythagoras
9576-469: The minute particle of each element had a special geometric shape : tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth). Timaeus makes conjectures on the composition of the four elements which some ancient Greeks thought constituted the physical universe: earth, water, air, and fire. Timaeus links each of these elements to a certain Platonic solid : the element of earth would be
9702-480: The modern vegetarian movement. No authentic writings of Pythagoras have survived, and almost nothing is known for certain about his life. The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical . The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon ( c. 570 – c. 478 BC), who had been one of his contemporaries. In
9828-693: The mythic bard Orpheus as Pythagoras's teacher, thus representing the Orphic Mysteries . The Neoplatonists wrote of a "sacred discourse" Pythagoras had written on the gods in the Doric Greek dialect, which they believed had been dictated to Pythagoras by the Orphic priest Aglaophamus upon his initiation to the orphic Mysteries at Leibethra . Iamblichus credited Orpheus with having been the model for Pythagoras's manner of speech, his spiritual attitude, and his manner of worship. Iamblichus describes Pythagoreanism as
9954-401: The neighboring colony of Sybaris in 510 BC. After the victory, some prominent citizens of Croton proposed a democratic constitution , which the Pythagoreans rejected. The supporters of democracy, headed by Cylon and Ninon, the former of whom is said to have been irritated by his exclusion from Pythagoras's brotherhood, roused the populace against them. Followers of Cylon and Ninon attacked
10080-447: The novelist Antonius Diogenes , writing in the second century BC, reports that Pythagoras discovered all his doctrines himself by interpreting dreams . The third-century AD Sophist Philostratus claims that, in addition to the Egyptians, Pythagoras also studied under sages or gymnosophists in India . Iamblichus expands this list even further by claiming that Pythagoras also studied with
10206-499: The number philosophy attributed to him was really an innovation by Philolaus. According to Burkert, Pythagoras never dealt with numbers at all, let alone made any noteworthy contribution to mathematics. Burkert argues that the only mathematics the Pythagoreans ever actually engaged in was simple, proofless arithmetic , but that these arithmetic discoveries did contribute significantly to the beginnings of mathematics. Both Plato and Isocrates state that, above all else, Pythagoras
10332-499: The orbits of the heavenly bodies : the three moving at equal speeds are the Sun, Venus and Mercury, while the four moving at unequal speeds are the Moon, Mars, Jupiter and Saturn (36c–d). The complicated pattern of these movements is bound to be repeated again after a period called a 'complete' or 'perfect' year (39d). Then, the demiurge connected the body and the soul of the universe: he diffused
10458-415: The origin of all things and the number two (the dyad ) represented matter. The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo . The number four signified the four seasons and the four elements . The number seven was also sacred because it
10584-481: The permanent reality behind superficial appearances. Early Archaic sculpture represents life in simple forms, and may have been influenced by the earliest Greek natural philosophies. The Greeks generally believed that nature expressed itself in ideal forms and was represented by a type ( εἶδος ), which was mathematically calculated. When dimensions changed, architects sought to relay permanence through mathematics. Maurice Bowra believes that these ideas influenced
10710-507: The poem, Xenophanes describes Pythagoras interceding on behalf of a dog that is being beaten, professing to recognize in its cries the voice of a departed friend. Alcmaeon of Croton ( fl. c. 450 BC), a doctor who lived in Croton at around the same time Pythagoras lived there, incorporates many Pythagorean teachings into his writings and alludes to having possibly known Pythagoras personally. The poet Heraclitus of Ephesus (fl. c. 500 BC), who
10836-540: The priestess Aristoclea ( Aristokleia ). Ancient authorities furthermore note the similarities between the religious and ascetic peculiarities of Pythagoras with the Orphic or Cretan mysteries , or the Delphic oracle . Porphyry repeats an account from Antiphon , who reported that, while he was still on Samos, Pythagoras founded a school known as the "semicircle". Here, Samians debated matters of public concern. Supposedly,
10962-687: The proportion, not of the elements (materials), but of the interrelation of parts with one another and with the whole. In the Greek architectural orders, every element was calculated and constructed by mathematical relations. Rhys Carpenter states that the ratio 2:1 was "the generative ratio of the Doric order , and in Hellenistic times an ordinary Doric colonnade, beats out a rhythm of notes." Timaeus (dialogue) Timaeus ( / t aɪ ˈ m iː ə s / ; Ancient Greek : Τίμαιος , romanized : Timaios , pronounced [tǐːmai̯os] )
11088-666: The result of confusion with a different man named Pythagoras, who was an athletics trainer. Diogenes Laërtius records Milo's wife's name as Myia. Iamblichus mentions Theano as the wife of Brontinus of Croton. Diogenes Laërtius states that the same Theano was Pythagoras's pupil and that Pythagoras's wife Theano was her daughter. Diogenes Laërtius also records that works supposedly written by Theano were still extant during his own lifetime and quotes several opinions attributed to her. These writings are now known to be pseudepigraphical . Pythagoras's emphasis on dedication and asceticism are credited with aiding in Croton's decisive victory over
11214-725: The rise of a "new" Pythagoreanism in Alexandria . At around the same time, Neopythagoreanism became prominent. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. The later first-century Neopythagorean philosopher Moderatus of Gades expanded on Pythagorean number philosophy and probably understood the soul as a "kind of mathematical harmony". The Neopythagorean mathematician and musicologist Nicomachus likewise expanded on Pythagorean numerology and music theory. Numenius of Apamea interpreted Plato's teachings in light of Pythagorean doctrines. Greek sculpture sought to represent
11340-548: The ruins of a Lombard Castle, the Church of our Lady of Mount Carmel, the Chapel of San Christofaro, and the Chapel of Santa Maria delle Grazie. In the past, the region was known for the production of silk from silkworms. This Basilicata location article is a stub . You can help Misplaced Pages by expanding it . Pythagoras Pythagoras of Samos ( Ancient Greek : Πυθαγόρας ; c. 570 – c. 495 BC)
11466-425: The same time . When Pythagoras crossed the river Kosas (the modern-day Basento ), "several witnesses" reported that they heard it greet him by name. In Roman times, a legend claimed that Pythagoras was the son of Apollo. According to Muslim tradition , Pythagoras was said to have been initiated by Hermes (Egyptian Thoth ). Pythagoras was said to have dressed all in white. He is also said to have borne
11592-451: The school became so renowned that the brightest minds in all of Greece came to Samos to hear Pythagoras teach. Pythagoras himself dwelled in a secret cave, where he studied in private and occasionally held discourses with a few of his close friends. Christoph Riedweg, a German scholar of early Pythagoreanism, states that it is entirely possible Pythagoras may have taught on Samos, but cautions that Antiphon's account, which makes reference to
11718-422: The soul from the center of the body to its extremities in every direction, allowing the invisible soul to envelop the visible body. The soul began to rotate and this was the beginning of its eternal and rational life (36e). Therefore, having been composed by Sameness, Difference and Existence (their mean), and formed in right proportions, the soul declares the sameness or difference of every object it meets: when it
11844-688: The soul of the world was created (Plato's following discussion is obscure, and almost certainly intended to be read in light of the Sophist ). The demiurge combined three elements: two varieties of Sameness (one indivisible and another divisible), two varieties of Difference (again, one indivisible and another divisible), and two types of Being (or Existence, once more, one indivisible and another divisible). From this emerged three compound substances: intermediate (or mixed) Being, intermediate Sameness, and intermediate Difference. Compounding these three intermediate substances together, one final substance resulted:
11970-493: The sound of their hammers clanging against the anvils. Thinking that the sounds of the hammers were beautiful and harmonious, except for one, he rushed into the blacksmith shop and began testing the hammers. He then realized that the tune played when the hammer struck was directly proportional to the size of the hammer and therefore concluded that music was mathematical. In ancient times, Pythagoras and his contemporary Parmenides of Elea were both credited with having been
12096-421: The steeds in his father's chariot , because he was not able to drive them in the path of his father, burnt up all that was upon the earth, and was himself destroyed by a thunderbolt. Now this has the form of a myth, but really signifies a declination of the bodies moving in the heavens around the earth, and a great conflagration of things upon the earth, which recurs after long intervals. The history of Atlantis
12222-439: The theory of Pythagoras and his students, who believed that "all things are numbers". During the sixth century BC, the number philosophy of the Pythagoreans triggered a revolution in Greek sculpture. Greek sculptors and architects attempted to find the mathematical relation ( canon ) behind aesthetic perfection. Possibly drawing on the ideas of Pythagoras, the sculptor Polykleitos wrote in his Canon that beauty consists in
12348-467: The tradition linking Pythagoras to the tetractys is probably genuine. Modern scholars debate whether these numerological teachings were developed by Pythagoras himself or by the later Pythagorean philosopher Philolaus of Croton . In his landmark study Lore and Science in Ancient Pythagoreanism , Walter Burkert argues that Pythagoras was a charismatic political and religious teacher, but that
12474-421: The two approaches were compatible. The study of mathematics and music may have been connected to the worship of Apollo. The Pythagoreans believed that music was a purification for the soul, just as medicine was a purification for the body. One anecdote of Pythagoras reports that when he encountered some drunken youths trying to break into the home of a virtuous woman, he sang a solemn tune with long spondees and
12600-426: The two worlds are conditioned by the different nature of their objects. Indeed, "a description of what is changeless, fixed and clearly intelligible will be changeless and fixed," (29b), while a description of what changes and is likely, will also change and be just likely. "As being is to becoming, so is truth to belief" (29c). Therefore, in a description of the physical world, one "should not look for anything more than
12726-426: The use of all kinds of animal food except the flesh of oxen used for ploughing , and rams . According to Heraclides Ponticus, Pythagoras ate the meat from sacrifices and established a diet for athletes dependent on meat. Within his own lifetime, Pythagoras was already the subject of elaborate hagiographic legends. Aristotle described Pythagoras as a wonder-worker and somewhat of a supernatural figure. In
12852-417: The world a rotatory or circular movement , which is the "most appropriate to mind and intelligence" on account of its being the most uniform (34a). Finally, he created the soul of the world , placed that soul in the center of the world's body and diffused it in every direction. Having thus been created as a perfect, self-sufficient and intelligent being, the world is a god (34b). Timaeus then explains how
12978-430: The world was created, and it was harmonised by proportion" (31–33). As for the figure, the demiurge created the world in the geometric form of a globe . Indeed, the round figure is the most perfect one, because it comprehends or averages all the other figures and it is the most omnimorphic of all figures: "he [the demiurge] considered that the like is infinitely fairer than the unlike" (33b). The creator assigned then to
13104-552: Was a contemporary of the philosophers Anaximander , Anaximenes , and the historian Hecataeus , all of whom lived in Miletus , across the sea from Samos. Pythagoras is traditionally thought to have received most of his education in the Near East. Modern scholarship has shown that the culture of Archaic Greece was heavily influenced by those of Levantine and Mesopotamian cultures. Like many other important Greek thinkers, Pythagoras
13230-462: Was a native of Samos , descending from a geomoroi family. Apollonius of Tyana , gives her name as Pythaïs. Iamblichus tells the story that the Pythia prophesied to her while she was pregnant with him that she would give birth to a man supremely beautiful, wise, and beneficial to humankind. As to the date of his birth, Aristoxenus stated that Pythagoras left Samos in the reign of Polycrates , at
13356-535: Was a philosopher, scientist, mathematician, and engineer, also known for a special case of the inscribed angle theorem . Pythagoras's birthplace, the island of Samos , is situated in the Northeast Aegean Sea not far from Miletus . Diogenes Laërtius cites a statement from Aristoxenus (fourth century BC) stating that Pythagoras learned most of his moral doctrines from the Delphic priestess Themistoclea . Porphyry agrees with this assertion but calls
13482-594: Was an ancient Ionian Greek philosopher , polymath , and the eponymous founder of Pythagoreanism . His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato , Aristotle , and, through them, the West in general. Knowledge of his life is clouded by legend; modern scholars disagree regarding Pythagoras's education and influences, but they do agree that, around 530 BC, he travelled to Croton in southern Italy, where he founded
13608-547: Was as Aethalides the son of Hermes , who granted him the ability to remember all his past incarnations. Next, he was incarnated as Euphorbus , a minor hero from the Trojan War briefly mentioned in the Iliad . He then became the philosopher Hermotimus , who recognized the shield of Euphorbus in the temple of Apollo. His final incarnation was as Pyrrhus, a fisherman from Delos . One of his past lives, as reported by Dicaearchus ,
13734-505: Was as a beautiful courtesan. Another belief attributed to Pythagoras was that of the " harmony of the spheres ", which maintained that the planets and stars move according to mathematical equations, which correspond to musical notes and thus produce an inaudible symphony. According to Porphyry, Pythagoras taught that the seven Muses were actually the seven planets singing together. In his philosophical dialogue Protrepticus , Aristotle has his literary double say: When Pythagoras
13860-492: Was asked [why humans exist], he said, "to observe the heavens", and he used to claim that he himself was an observer of nature, and it was for the sake of this that he had passed over into life. Pythagoras was said to have practiced divination and prophecy . The earliest mentions of divination by isopsephy in Greek literature associate it with Pythagoras; he was viewed as the founder of this practice. According to his biographer, Iamblichus, he taught his method of divination to
13986-661: Was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, mocked Pythagoras as a clever charlatan, remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured a wisdom for himself—much learning, artful knavery." The Greek poets Ion of Chios ( c. 480 – c. 421 BC) and Empedocles of Acragas ( c. 493 – c. 432 BC) both express admiration for Pythagoras in their poems. The first concise description of Pythagoras comes from
14112-427: Was credited with devising the tetractys , the triangular figure of four rows which add up to the perfect number, ten. The Pythagoreans regarded the tetractys as a symbol of utmost mystical importance. Iamblichus, in his Life of Pythagoras , states that the tetractys was "so admirable, and so divinised by those who understood [it]," that Pythagoras's students would swear oaths by it. Andrew Gregory concludes that
14238-457: Was gone, convincing everyone that he had really been in the underworld and leading them to trust him with their wives. Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem , as well as discoveries in
14364-579: Was highly influential in late antiquity, especially on Latin-speaking Church Fathers such as Saint Augustine who did not appear to have access to the original Greek dialogue. The manuscript production and preservation of Cicero's Timaeus (among many other Latin philosophical works) is largely due to the works of monastic scholars, especially at Corbie in North-East France during the Carolingian Period. Calcidius' more extensive translation of
14490-603: Was influenced by a book about Pythagoras , written by Philolaus , although this assertion is generally considered false. The dialogue takes place the day after Socrates described his ideal state. In Plato's works, such a discussion occurs in the Republic . Socrates feels that his description of the ideal state was not sufficient for the purposes of entertainment and that "I would be glad to hear some account of it engaging in transactions with other states" (19b). Hermocrates wishes to oblige Socrates and mentions that Critias knows just
14616-463: Was known as the founder of a new way of life. The organization Pythagoras founded at Croton was called a "school", but, in many ways, resembled a monastery . The adherents were bound by a vow to Pythagoras and each other, for the purpose of pursuing the religious and ascetic observances, and of studying his religious and philosophical theories. The members of the sect shared all their possessions in common and were devoted to each other to
14742-470: Was present when the attack occurred and, if he was, whether or not he managed to escape. In some accounts, Pythagoras was not at the meeting when the Pythagoreans were attacked because he was on Delos tending to the dying Pherecydes. According to another account from Dicaearchus, Pythagoras was at the meeting and managed to escape, leading a small group of followers to the nearby city of Locris , where they pleaded for sanctuary, but were denied. They reached
14868-445: Was raised by Pythagoras's appointed successor Aristaeus and eventually took over the school when Aristaeus was too old to continue running it. Suda writes that Pythagoras had 4 children (Telauges, Mnesarchus, Myia and Arignote). The wrestler Milo of Croton was said to have been a close associate of Pythagoras and was credited with having saved the philosopher's life when a roof was about to collapse. This association may have been
14994-449: Was related to mathematics and that numbers were important, but it is debated to what extent, if at all, he actually contributed to mathematics or natural philosophy . The teaching most securely identified with Pythagoras is the "transmigration of souls" or metempsychosis , which holds that every soul is immortal and, upon death, enters into a new body . He may have also devised the doctrine of musica universalis , which holds that
15120-419: Was said that he was the first man to call himself a philosopher ("lover of wisdom") and that he was the first to divide the globe into five climatic zones . Classical historians debate whether Pythagoras made these discoveries, and many of the accomplishments credited to him likely originated earlier or were made by his colleagues or successors. Some accounts mention that the philosophy associated with Pythagoras
15246-631: Was said to have studied in Egypt . By the time of Isocrates in the fourth century BC, Pythagoras's reputed studies in Egypt were already taken as fact. The writer Antiphon , who may have lived during the Hellenistic Era, claimed in his lost work On Men of Outstanding Merit , used as a source by Porphyry, that Pythagoras learned to speak Egyptian from the Pharaoh Amasis II himself, that he studied with
15372-496: Was so despondent at the deaths of his beloved students that he committed suicide. A different legend reported by both Diogenes Laërtius and Iamblichus states that Pythagoras almost managed to escape, but that he came to a fava bean field and refused to run through it, since doing so would violate his teachings, so he stopped instead and was killed. This story seems to have originated from the writer Neanthes, who told it about later Pythagoreans, not about Pythagoras himself. Although
15498-455: Was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine , that even numbers were feminine , and that the number five represented marriage, because it was the sum of two and three. Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Pythagoras
15624-418: Was the only other co-existent element or presence in Plato's cosmogony . Later Platonists clarified that the eternal model existed in the mind of the demiurge. Timaeus describes the substance as a lack of homogeneity or balance, in which the four elements ( earth , air , fire and water ) were shapeless, mixed and in constant motion. Considering that order is favourable over disorder, the essential act of
15750-405: Was the son of Mnesarchus, and that he was born on the Greek island of Samos in the eastern Aegean . According to these biographers, Pythagoras's father was not born on the island, although he got naturalized there, but according to Iamblichus he was a native of the island. He is said to have been a gem-engraver or a wealthy merchant but his ancestry is disputed and unclear. His mother
15876-467: Was then related to shape and size of the constituent triangles. The fifth element (i.e. Platonic solid) was the dodecahedron , whose faces are not triangular, and which was taken to represent the shape of the Universe as a whole, possibly because of all the elements it most approximates a sphere, which Timaeus has already noted was the shape into which God had formed the Universe. The extensive final part of
#908091