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Herme of Pythagoras (around 120 AD); Capitoline Museums , Rome

As Pythagoreans (also Pythagoreans , ancient Greek Πυθαγόρειοι Pythagóreioi or Πυθαγορικοί Pythagorikoí ) are the members of a religious-philosophical, also politically active school, the Pythagoras of Samos in the twenties of the sixties. In southern Italy and which continued for a few decades after his death. In a broader sense, it means everyone who has since taken up ideas of Pythagoras or ideas ascribed to him and made them an essential part of their worldview.

Because of the confused sources, many details of the philosophical beliefs and political goals of the Pythagoreans are unclear, and numerous questions are highly controversial in research. What is certain is that in a number of Greek cities in southern Italy there were communities of Pythagoreans who viewed themselves as a social and political reform movement and, with reference to the teachings of the school founder, intervened massively in politics. This led to serious, violent clashes that began in the 5th century BC. Were carried out with varying success and finally ended with defeats of the Pythagoreans. In most cities, the Pythagoreans were killed or driven out.

A characteristic of the Pythagoreans is the conviction that the cosmos forms a harmonious unit built up according to certain numerical relationships, the individual components of which are also structured harmoniously or, as far as human living conditions are concerned, should be designed harmoniously. They assumed that in all areas - in nature, in the state, in the family and in individual people - the same numerically expressible laws apply, that balance and harmony are to be striven for everywhere and that knowing the relevant numerical relationships is a wise, natural way of life enables. They did not limit the pursuit of harmony to human society, but extended it to all living beings, which was reflected in the demand for consideration for the animal world.

Research problems

No authentic writings have come down to us from Pythagoras; only some of the verses ascribed to him are possibly authentic. Even in antiquity, there were different opinions about which of the teachings considered Pythagorean actually go back to him. The distinction between early Pythagorean and later ideas is still one of the most difficult and controversial questions in the history of ancient philosophy. In research it is even disputed whether the teaching of Pythagoras was actually about philosophy and scientific endeavors or about a purely mythical-religious cosmology . The early onset of exuberant legend formation contributes to these difficulties.

The school of Pythagoras

The political history of the school up to its demise in the 5th century BC Is known in outline. Historians, however, have diverged views as to their purpose, mode of operation and organization.

Political history of the school

Pythagoras came from the Greek island of Samos . He emigrated between 532 and 529 BC. In an area of ​​southern Italy then settled by Greeks, where he first settled in Croton (today Crotone in Calabria ). There he founded the school, which from the outset also pursued political goals in addition to studies. The Pythagoreans took an active part in the war between Croton and the likewise Greek city of Sybaris , which started from Sybaris and was fought with great brutality. The commander of the Crotonia Army, the famous athlete Milon , was a Pythagorean.

Ancient Greek cities in southern Italy

After the victory over Sybaris, which was conquered and sacked (510), the Pythagoreans became embroiled in violent clashes within the citizens of Croton. It was about the distribution of the conquered land and a constitutional amendment. Because of this unrest, Pythagoras moved his residence to Metapontion (today Metaponto in Basilicata ). There he continued his teaching activity, while in Croton his hard-pressed followers were defeated and had to leave the city temporarily. A distinguished citizen named Kylon emerged as the leader of the opposing party (hence “Cylon riots”), and a popular speaker named Ninon also incited against the Pythagoreans. Reports from individual sources that there was already bloody persecution at the time are apparently based on confusion with later events.

Since the school had considerable charisma, Pythagorean communities formed in other Greek cities in southern Italy, and they probably intervened in politics there as well. However, there was no institutionalized rule of the Pythagoreans in Croton, Metapontion or anywhere else, only a more or less successful influence on the respective city council and on the citizens' assembly. Several sources report that Pythagoreanism also spread among the non-Greek population. The tribes of the Lucanians and Messapians are named .

Pythagoras died in the last few years of the 6th century or the early 5th century. After his death, his students continued their activities in the cities. There was no longer any central control of the school, because Pythagoras apparently had no successor as the generally recognized head of the school. The Pythagoreans were - in accordance with their worldview, which was generally oriented towards harmony and stability - politically conservative. This made them allies of the sexes traditionally dominating city councils. However, as the example of Kylon shows, they also encountered opposition from influential families. Their natural enemies were everywhere the agitators, who advocated overthrow and the introduction of democracy and only in this way could gain power.

By the middle of the 5th century or a little later, democratically-minded popular orators came to power in a number of cities. Following the custom of the time, they proceeded with great severity against the supporters of the defeated party. This led to bloody persecutions of the Pythagoreans, who were either killed or had to flee the cities. The political turmoil apparently lasted for a long time. The Pythagoreans were able to prevail again at times; eventually they were defeated everywhere except in Taranto , where they had a strong position until the middle of the fourth century. Many of them emigrated to Greece. The school ceased to exist as an organization.

The lesson and its purpose

According to some sources, the Pythagoreans fell into two groups or directions, the "mathematicians" and the "acousmatists". “Mathematicians” were those who dealt with “mathemata”, that is, with written learning objects and empiricism (also, but not only, mathematics in the current sense of the word). This can be seen as an early form of mathematical and scientific research. Acusmatists were called Pythagoreans, who referred to " Akusmata " (heard), that is, to the only orally communicated teachings of Pythagoras; it was mainly about rules of conduct and the religious worldview.

It is unclear whether Pythagoras divided his students into two groups with different tasks according to their inclinations and abilities, or whether the demarcation between the two directions only became clear after his death. In any case, according to a report that some researchers trace back to Aristotle , at an unknown point in time after the death of the school founder, a split between the two directions occurred . Each of them claimed to continue the authentic tradition of Pythagoras.

The completely different character of these two directions remains a mystery to this day. It is unclear which of the two groups was older, which was larger, and which was more important for Pythagoreanism, which made up the core of the school and was therefore considered more advanced and of higher rank. Research views differ widely on this.

Some scholars (especially Walter Burkert ) believe that all Pythagoreans were acousmatists during Pythagoras lifetime and that Greek science arose outside of Pythagoreanism. According to this, the "mathematicians" were individual Pythagoreans who only began to deal with scientific issues after the school founder had died; Most of her work took place after the school fell. These “mathematicians” were the representatives of Pythagoreanism with whom Plato grappled in the 4th century. They shaped the later (and to this day) prevailing public image of early Pythagoreanism, which in Burkert's view was false, by making it appear as a nursery of scientific research. In addition, the students of Plato and Aristotle already considered Platonic ideas to be Pythagorean. In reality, according to Burkert's interpretation, the school was a union with religious and political goals, which kept its esoteric teachings secret and had no interest in science. Burkert compares the Pythagorean community with the mystery cults .

The main proponent of the opposite view is currently Leonid Zhmud . It says that there was neither a secret doctrine of the early Pythagoreans nor a religious doctrine that was binding for everyone. The school was a "hetairie", a loose association of autonomously researching people. They would have devoted themselves to their scientific and philosophical studies collectively - but without fixation on predetermined dogmas. They were also linked by certain political goals. The reports about the acousmatists are late inventions. The Akusmata - originally called "Symbola" - were only sayings and not concrete, binding rules for everyday life. They are indeed very old, as Burkert also thinks, but for the most part not of Pythagorean origin. Rather, they are partly sayings of wisdom of indefinite origin, partly it is about ancient popular superstition, which has been reinterpreted in a symbolic sense in Pythagorean circles.

Burkert notes: "The modern controversies about Pythagoras and Pythagoreanism are basically just the continuation of the old dispute between 'acousmatists' and 'mathematicians'."

Other scholars like BL van der Waerden take a middle position. They do not assign priority or sole authenticity to one or the other group, but rather believe that the distinction between mathematicians and acousmatists goes back to different endeavors that already existed in school during Pythagoras' lifetime. After the death of the school founder, a contradiction developed that led to the school split.

Late sources describe the Pythagoreans - obviously meaning acousmatists - as a sworn community of disciples who revered their master as a divine or at least superhuman being and blindly believed in his infallibility. This belief is said to have led her to decide every question by appealing to an (alleged) oral utterance of Pythagoras. Only the “proof of authority” through the assurance “He [Pythagoras] said it” applied to them. In this context, reports also belong, according to which Pythagoras first examined applicants who wanted to enter his school physiognomically and then imposed a long (according to some statements five-year) silence on them, after which they were accepted into the community after successful completion.

Early Pythagoreans

The most prominent among the researching Pythagoreans of the early period was the mathematician and music theorist Hippasus von Metapont . He is said to have carried out sound experiments to determine the relationship between consonances and measurable physical quantities. He is best known for the prevailing view in the past that he triggered a “fundamental crisis” of Pythagoreanism by discovering incommensurability and thus refuting the claim that all phenomena can be explained as manifestations of integer ratios. Allegedly, the Pythagoreans then excluded Hippasus and viewed his death by drowning in the sea as a divine punishment for “betraying secrets”. The discovery of incommensurability may be a historical fact, but the suggestion that this led to a fundamental crisis has been rejected in recent research.

The early Pythagoreans also included:

  • Milon von Kroton, one of the most famous ancient athletes. He was the only one to win the Olympics six times . He was the victorious general of Croton in the war against Sybaris (510). Milon is said to have married a daughter of Pythagoras named Myia .
  • Demokedes of Croton, who, according to Herodotus, was the best doctor of his time. He was the son-in-law of Milon von Kroton and took part on the Pythagorean side in the political struggles in his hometown. His father, the doctor Kalliphon, is said to have been influenced by Pythagoras.
  • possibly also the famous natural philosopher Alkmaion von Kroton , who understood health as a harmonious balance of opposing forces in the body. Whether he also practiced as a doctor is controversial.

In the early days women are also said to have been active in the movement. In particular, the name of Pythagoras' wife Theano is often mentioned in the sources . Numerous sayings and writings were later ascribed to her, dealing primarily with virtue and piety, as well as seven letters that have survived.

The philosopher Parmenides is said to have been a pupil of a Pythagorean named Ameinias; Pythagorean influence on him is assumed by current research, but the extent is unclear. The philosopher Empedocles , who admired Pythagoras, was not a Pythagorean in the strict sense, but was very close to the Pythagorean world of thought.

Lessons and Legends

In spite of the enormous personal authority of Pythagoras, the early as well as the later Pythagoreanism was not a binding, self-contained and detailed doctrinal structure. Rather, it was a particular way of looking at the world, which left scope for different approaches. All Pythagoreans shared the basic conviction that the entire recognizable world is a unit built up on the basis of certain numbers and numerical relationships, in principle harmoniously designed. This law determines all areas of reality equally. They therefore regarded the knowledge of the relevant numerical relationships as the key to understanding everything and as a prerequisite for a good, natural lifestyle. Her goal was to bring the different and opposing forces through balance to a harmonious harmony, both in the human body and in the family and in the state. They wanted to find what they thought they recognized as measure, order and harmony everywhere in nature and preserve it in their own lives. So they started from a holistic interpretation of the cosmos. What they wanted to bring back into natural order was what had gotten out of order in him. In the sense of this worldview, they considered all animated beings to be related to one another and derived a command of consideration from this. On the details, however, their opinions often differed widely.

Soul teaching

The doctrine of the immortality of the soul belongs to the oldest inventory of early Pythagorean philosophy. It is one of the most important similarities between Pythagoreanism and Platonism , which influenced each other in the course of their development and, for some philosophers, fused with one another. The Pythagoreans, like the Platonists, were convinced of the transmigration of souls . In doing so, they assumed no essential difference between human and animal souls. This idea presupposed the immortality of the soul. However, since the Pythagoreans saw the foundation of the world order in the harmonic numerical relationships, they also had the idea that the soul is a harmony, namely the harmonious balance of the forces that determine the body. That is difficult to reconcile with the immortality idea. This contradiction shows the incompleteness of the developing Pythagorean philosophizing. In his dialogue Phaedo, Plato dealt with the interpretation of the soul as harmony and tried to refute it.

Another area in which disparate ideas were apparently represented within the Pythagorean movement and not combined into a coherent whole was the question of the destiny and future of the soul. An essential component of Pythagoreanism, although not clearly attested to in the early period, which was very poor in sources, was the religious conviction that the human soul was of divine origin and nature. From this it followed (as with the Orphics and the Platonics) that it is the task and determination of the soul to return from this world to its homeland on the other side. She should prepare for this through training and right living. She was trusted to regain her divine abilities and possibilities. The fact that Pythagoras was regarded by many of his followers as a god-like being shows that such a goal seemed in principle achievable. Difficult to reconcile with this striving for salvation, however, was another concept, which was based on an eternal, unalterable cycle of world events. The assumption that a unified cosmos is always and everywhere determined by the same mathematical conditions, and the cyclical nature of the steady movements of the heavenly bodies led to the fate of mankind being understood as predetermined and cyclical. Therefore, at least some of the Pythagoreans had an astrological fatalism , that is, the idea of ​​the inevitable eternal return of all earthly conditions according to the movements of the stars. According to this idea, world history begins again as an exact repetition as soon as all planets have returned to their original position after a long cosmic period, the “Great Year”.

As a religious doctrine of salvation, Pythagoreanism presented itself in particular in a very popular ancient poem by an unknown author, the " Golden Verses ". There the person who adheres to the philosophical rules of life and has advanced to the knowledge of the laws of the world is given the prospect that his soul can escape suffering and mortality and change into the mode of existence of immortal gods. Empedocles had formulated this as a goal as early as the 5th century.

Diet and clothing

Like many other philosophical directions, the Pythagoreans advocated the mastery of desires and thus also for a simple way of life and frugal nutrition. The fact that they rejected all luxury - especially the luxury of clothes - resulted from their general demand to maintain the right measure and thus to achieve harmony.

A core component of the original Pythagoreanism was vegetarianism . He was described as "abstaining from the ensouled". This designation points to the ethical and religious roots of Pythagorean vegetarianism. It was connected with the conviction that the souls of humans and those of animals are not essentially different and that one owes the animals consideration. Various legends, according to which Pythagoras was able to understand animals, bear witness to the Pythagoreans' special proximity to the animal world. Therefore, in addition to the meat food, the animal sacrifices were also discarded. However, this was associated with social problems, because participation in the traditional sacrifices and the subsequent sacrificial meals was one of the most important community-building customs, and the politically active Pythagoreans had to value their reputation among the citizens. Therefore, there was apparently no mandatory requirement for everyone, and only some of the Pythagoreans were vegetarian.

A strict taboo was directed against the consumption of beans. The original reason for the bean ban was already unknown in antiquity, it has been puzzled over. Occasionally a health reason was suggested, but most of the time it was assumed that it was a religious taboo. It was even assumed that the ban was so comprehensive that it absolutely forbade even touching a bean plant. This is why legends arose according to which Pythagoreans (or Pythagoras himself) fleeing from persecutors would rather accept death than cross a bean field. The actual reason for the bean taboo has not yet been clarified. The possibility of a connection with favism , a hereditary enzyme disease in which the consumption of field beans (Vicia faba) is dangerous to health, has been considered several times as an explanation. This hypothesis finds no concrete support in the sources and is therefore speculative.

Ideal of friendship

The concept of friendship (philía) played an important role in Pythagoreanism . This term has been greatly expanded from its normal meaning. Since the Pythagoreans understood the cosmos as a unity of related and harmoniously interacting components, they assumed a natural friendship between all living beings (including the gods). This ideal of universal friendship and harmony in the world is reminiscent of the myth of the paradisiacal golden age . The aim was to recognize the connectedness of all and to implement it in one's own life. But this - as the participation in the war against Sybaris shows during the lifetime of Pythagoras - was not connected with an absolute renunciation of force in the sense of pacifism .

In particular, the Pythagoreans practiced friendship among themselves. Some of them understood it as an unconditional loyalty not only to their personal friends, but to every Pythagorean. Some anecdotes have come down to us about loyalty to friends. The most famous is the story of Damon and Phintias , which Friedrich Schiller used for his ballad Die Bürgschaft . It is said that the Pythagorean Phintias was sentenced to death for a plot against the tyrant Dionysius , but was given permission to regulate his personal affairs before execution, as his friend Damon vouched for his return as a hostage. Phintias returned in time; otherwise Damon would have been executed in his place. This impressed the tyrant strongly, whereupon he pardoned Phintias and asked in vain for admission to the friendship covenant. According to one version, Dionysius had arranged the whole incident only in pretense to test the legendary loyalty of the Pythagoreans, according to another version it was a real conspiracy.

In ancient times, the Pythagorean principle was known that the property of friends was common (koiná ta tōn phílōn) . But this is not to be understood in the sense of a “communist” community of property; this was practiced by only a few, if at all. What was meant was that the Pythagoreans supported each other spontaneously and generously in material emergencies.

Mathematics and number symbolism

Numbers and numerical relationships have played a central role in Pythagorean teaching from the beginning. This is a feature that sets Pythagoreanism apart from other approaches. But whether this means that Pythagoras was already doing math is debatable. Some researchers (especially Walter Burkert) have taken the view that he was only concerned with number symbolism, scientific thinking was alien to him, and it was not until the middle of the 5th century that Hippasus was the first Pythagorean to turn to mathematical studies. Leonid Zhmud's opposing position is that the early Pythagoreans were mathematicians and that the speculation of numbers came late and was only practiced by a few Pythagoreans.

The basic idea behind number speculation is often summed up in the core phrase “Everything is number”. In the parlance of the time, this means that the number for the Pythagoreans was the archē , the constituent primal principle of the world. The role that Thales had assigned to water and Anaximenes to air would then fall to the number . However, this view is not proven in early Pythagoreanism. Aristotle attributes them to "the Pythagoreans" without naming them. He criticizes them, assuming that the Pythagoreans understood numbers to be something material.

In the second half of the 5th century, the Pythagorean Philolaos wrote that everything we know is necessarily linked to a number, because that is a prerequisite for mental comprehension. His statement only relates to the human process of knowledge. In the sense of an ontology of number, it does not mean that all things consist or arise from numbers. The notion that numbers themselves are things is often referred to as typically Pythagorean. However, this is just Aristotle's possibly erroneous understanding of Pythagorean teaching. What was essential for Philolaos was the difference between the limited in number, size and shape and the unlimited, which he considered in principle inexplicable, and the interplay of these two factors.

The starting point of the concrete number speculation was the contrast between even and odd numbers, whereby the odd numbers were designated as limited (and thus higher ranking) and - as in Chinese yin and yang - as male and the even numbers as unlimited and female. One, understood as the principle of unity, was considered to be the origin from which all numbers emerge (and consequently all of nature); Seen in this way, it was actually not a number itself, but stood beyond the world of numbers, although mathematically it appears as a number like all others. Thus, paradoxically, the one could be described as even and odd at the same time, which is mathematically incorrect. The numbers were represented with counting stones, and the properties assigned to the numbers were demonstrated with the flat geometric figures that can be placed with such stones (for example an equilateral triangle). Great importance was attached to the tetraktys ("quartet"), the totality of the numbers 1, 2, 3 and 4, the sum of which is 10, which was used by Greeks and "barbarians" (non-Greeks) as the basic number of the decimal system . The tetraktys and the "perfect" ten were seen as fundamental to the world order.

In ancient times, individual mathematical findings were - rightly or wrongly - attributed to the Pythagoreans or a certain Pythagorean. Pythagoras evidence of the eponymous theorem of Pythagoras found on the right triangle. The construction of the dodecahedron inscribed into a sphere and the discovery of incommensurability were ascribed to Hippasus of Metapontium . Pythagoreans played an unknown role in the development of the doctrine of the three means ( arithmetic , geometric and harmonic mean ). Furthermore, among other things, they should have proven the theorem about the sum of angles in the triangle. It is possible that large parts of Euclid's elements - both the arithmetic and the geometrical books - come from lost Pythagorean literature; this included the theory of land application.

Cosmology and astronomy

In astronomy, the Pythagoreans did not hold a uniform position. The oldest model we know is that of Philolaus from the second half of the 5th century. It assumes a central fire, which forms the center of the universe and around which the celestial bodies, including the earth, revolve. For us it is invisible, because the inhabited areas of the earth are on the side that is always turned away from it. Around the central fire circles on the innermost track, the Counter-Earth , which is also invisible to us because it is covered by the central fire. This is followed (from inside to outside) by the earth's orbit and the orbits of the moon, sun and five planets (Mercury, Venus, Mars, Jupiter and Saturn). The whole thing is enclosed by a spherical shell on which the fixed stars are located. Aristotle criticized this system because it was not based on appearances but on preconceived notions; The counter-earth was only introduced to bring the number of bodies in motion in the sky to ten, since this number was considered perfect.

Aristotle mentions that "some" Pythagoreans included a comet among the planets. This contradicts the ten number in Philolaos. The Pythagoreans also had no unanimous opinion about the Milky Way. From this it can be seen that the early Pythagoreans did not have a common cosmos model that was binding for all. Some researchers assume that before Philolaos there was a completely different, geocentric Pythagorean model. It provided that the spherical earth is in the center of the cosmos and is orbited by the moon, the sun and the five planets known at the time.

One of the most important assumptions of the Pythagoreans was the idea of ​​the harmony of the spheres or - as the name is in the oldest sources - "heavenly harmony". It was assumed that the celestial bodies and the movements of earthly objects produce noises. Because of the uniformity of movement, this could only ever be one constant tone for each celestial body. The totality of these tones, the height of which depended on the different speeds and the distances between the heavenly bodies, should result in a cosmic sound. This was viewed as inaudible to us, as it sounds continuously and we would only become conscious through its opposite, through a contrast between sound and silence. However, according to a legend, Pythagoras was the only person able to hear the heavenly harmony.

Since the tones of the heavenly bodies could only be thought of as sounding simultaneously, not one after the other, a sound that was also always unchanged had to be assumed as the result of their coincidence. Therefore the popular term “music of the spheres” is certainly inappropriate. The fact that the harmony is harmonious results in this model from the assumption that the distances of the celestial bodies from the center and their correspondingly higher speeds with greater distance have a certain arithmetic proportion that makes this possible.


Music was the area in which the basic idea of ​​a harmony based on numerical relationships was most easily demonstrated. The Pythagoreans paid special attention to musical regularities. They seem to have experimented in this area as well. Pythagoras was widely regarded as the founder of the mathematical analysis of music in ancient times. Plato described the Pythagoreans as the originators of the musical theory of numbers, his pupil Xenocrates attributed the decisive discovery to Pythagoras himself. It was about the representation of the harmonic intervals through simple numerical relationships. This could be illustrated by measuring the distance, since the pitch depends on the length of a vibrating string. The monochord with an adjustable bridge was suitable for such experiments . Another, equally suitable way of quantification was found by Hippasus, who examined the tones of bronze disks of different thicknesses with the same diameter.

However, the legend of Pythagoras in the forge is certainly unhistorical , according to which Pythagoras happened to walk past a forge and, when he heard the different sounds of the differently heavy hammers, was inspired by this observation to experiment with metal weights suspended from strings.

Plato, who called for a purely speculative music theory derived from general principles and who considered the sensory experience through the ear to be insufficient, criticized the Pythagoreans for their empirical approach.

The music was suitable to support the thesis of a universal harmony and the interweaving of all parts of the cosmos. Through the idea of ​​the sounding heavenly harmony it was connected with astronomy, through the measurability of the pitches with mathematics, through its effect on the mind with the science of the soul, ethical education and the art of healing. The Pythagoreans studied the different effects of different instruments and keys on the human mind. According to the legends, Pythagoras used selected music specifically to influence unwanted affects and for healing purposes, thus practicing a kind of music therapy.

Development after the Antipythagorean Riots

Of the Pythagoreans of the second half of the 5th century, the natural philosopher Philolaos seems to have been one of the most prominent. Apparently he was one of those who went to Greece because of the political persecution in Italy. In any case, he taught in Thebes, at least temporarily . His cosmology with the assumption of a central fire in the middle of the universe was very different from the previously dominant one. He considered the moon to be inhabited, the sun to be glass-like (that is, it did not emit its own light, but rather it collected foreign light like a lens). His views are only known from fragments of his book, the authenticity of which is in part disputed.

In the 4th century BC The most important Pythagorean was Archytas of Taranto, a friend of Plato . He was a successful statesman and military leader in his hometown as well as a philosopher, mathematician, physicist, music theorist and an outstanding engineer. He applied the Pythagorean concept of a mathematically comprehensible harmony to politics by advocating a calculated balance between the social classes. He attributed the unity of the citizens to an appropriate distribution of property that everyone felt was fair.

Plato dealt intensively with Pythagorean philosophy. The question of the extent to which the views of Philolaus and Archytas shaped his image of her is controversial. After his death the interest in Pythagoreanism continued in the Platonic Academy , and there was a tendency among the Platonists to take up suggestions from this tradition and to interpret Plato in a corresponding sense.

Aristotle wrote a work on the Pythagoreans, of which only fragments have survived, and also dealt critically with Pythagoreanism in other ways. Among other things, he argued against the heavenly harmony (spherical harmony).

In the 4th century there were numerous followers of Pythagoras who had fled from Italy. A distinction was now made between “Pythagoreans” and “Pythagorists” (from Πυθαγοριστής Pythagoristḗs “those who follow the Pythagorean way of life”). The latter were a popular target of ridicule by comedy poets as they begged and lived ascetically. Her extremely frugal diet in particular has been targeted in comedies. They were portrayed as dirty nerds.

But there were also scholars among the Pythagoreans who emigrated from Italy who knew how to gain respect. Among them was Lysis . In Thebes he became the teacher of the later famous statesman and general Epameinondas ; in this way Pythagoreanism may have influenced politics for the last time.

The Pythagoreans active in the late 5th and 4th centuries also included:

  • Damon and Phintias from Syracuse, whose famous friendship became exemplary for posterity
  • Diodoros of Aspendos , who particularly represented the Pythagorean vegetarianism and caused a sensation through his appearance as a barefoot, long-haired ascetic
  • Echekrates von Phleius, a student of Philolaos, who appears as a conversation partner in Plato's dialogue Phaedo
  • Ekphantos , who represented a geocentric worldview, where he assumed an axis rotation of the earth from west to east. In epistemology he was a subjectivist .
  • Eurytus , a pupil of Philolaus, who applied the Pythagorean theory of numbers to animals and plants
  • Hiketas of Syracuse , who attributed the daily changes in the sky to the rotation of the earth's axis
  • Kleinias of Taranto , famous for his loyalty to friends; he is said to have dissuaded Plato from the plan to burn all accessible books of Democritus
  • Lykon of Iasus , who advocated a measured way of life based on the model of Pythagoras and criticized Aristotle for his lavish lifestyle
  • Xenophilus of Chalcidice , a student of Philolaus and teacher of the philosopher Aristoxenus

New Pythagoreanism

Pythagoras was held in high regard by the Romans. He was referred to as the teacher of the second king of Rome, Numa Pompilius , but this is chronologically impossible. In the 1st century BC The scholar and senator Nigidius Figulus, who was friends with Cicero , apparently tried to renew Pythagoreanism. As a continuous tradition no longer existed, this was a new beginning. Hence, Nigidius is usually called the first New Pythagorean; however, it is not clear whether his actual views and activities justify this name. New Pythagoreanism lasted into late antiquity , but there was no continuous school operation, only individual Pythagorean-minded philosophers and scholars. The New Pythagoreanism was not a self-contained new doctrine that was clearly delimited from older directions in terms of content.

Marcus Terentius Varro , the most famous Roman polymath , showed a strong interest in Pythagorean ideas . According to his testamentary decree, he was buried “according to the Pythagorean custom”.

In that of Quintus Sextius in the 1st century BC In addition to stoic teachings, neo-Pythagorean doctrines, including vegetarianism, were represented. This (though short-lived) school belonged to Sotion , Seneca's teacher . Seneca adopted the Pythagorean exercise of recapitulating the day in the evening from the sexties, with which one took stock for oneself. This included a self-questioning with questions like: “Which of your (character) ailments have you cured today? What vice did you withstand? In what way have you (got) better? "

In the 15th book of his Metamorphoses, the poet Ovid gave a fictional teaching lecture on Pythagoras and thus contributed to the dissemination of Pythagorean ideas, but there is no evidence that he was himself a New Pythagorean.

In 1917, an underground structure in the form of a basilica from the time of Emperor Claudius (41-54) was discovered in Rome near the Porta Maggiore . It was apparently intended to serve as a meeting room for a religious purpose, but it was closed soon after construction was completed. The historian and archaeologist Jérôme Carcopino has collected a number of pieces of evidence that suggest that the builders were New Pythagoreans. This includes, among other things, the decoration of ceilings and walls with depictions of scenes from mythology, which show the viewer the death perceived as salvation and the post-death fate of the soul.

The most famous New Pythagorean of the Roman Empire was Apollonios of Tyana (1st century AD). Little that is reliable has come down to us about his philosophy. Apparently, his philosophical lifestyle was based strongly on the model of Pythagoras (or the Pythagoras dominant at the time) and thus made a lasting impression on his contemporaries and posterity.

The remaining New Pythagoreans were also Platonists and Neo-Platonists. In New Pythagoreanism, early Pythagorean ideas were fused with legends from the later Pythagorean tradition and (new) Platonic teachings. Moderatos von Gades (1st century AD) regarded numerology as a didactic means to illustrate objects of knowledge in the spiritual world. From Nicomachus (2nd century) an introduction originate in arithmetic (d. H. In the Pythagorean theory of numbers), the textbook was and the Middle Ages in the Latin version of Boethius was very common, and a handbook of musical harmony. In his Latin presentation of music theory (De institutione musica), which was authoritative for the Middle Ages, Boethius proceeded from the musical teachings of Nicomachus and also dealt with the harmony of the spheres. In addition, Nicomachus wrote a biography of Pythagoras that is lost. In the 2nd century there was also the Platonist Numenios of Apameia , who equated Pythagoreanism with the authentic doctrine of Plato and also made Socrates a Pythagorean; he accused the later Platonists of having deviated from Plato's Pythagorean philosophy.

The Neo-Platonist Porphyrios wrote a biography of Pythagoras in the 3rd century and was particularly influenced by Pythagoras in his advocacy of vegetarianism. Pythagorean ideas came to the fore with the somewhat younger Neo-Platonist Iamblichus of Chalkis . He wrote a ten-volume work on the Pythagorean doctrine, parts of which have been preserved, including in particular the treatise "On the Pythagorean Life". His picture of Pythagoras was shaped by an abundance of legendary material, which he gathered. His concern was in particular to combine the metaphysical-religious and the ethical side of Pythagoreanism with mathematics (by which he primarily understood arithmetic and geometric symbolism) and to present this whole as divine wisdom given to people by Pythagoras. Like Numenios, he viewed Plato's teaching only as an embodiment of Pythagorean philosophy.

In the 5th century, the Neoplatonist Hierocles of Alexandria wrote a commentary on the "Golden Verses". He saw this poem as a general introduction to philosophy. By philosophy he understood a Platonism, which he equated with Pythagoreanism. The Neo-Platonist Syrianos , a contemporary of Hierocles, was also convinced that Platonism was nothing more than Pythagoreanism.

Modern reception

Since the Renaissance , individual natural philosophers have so strongly received Pythagorean ideas and so emphatically committed themselves to the Pythagorean tradition that they can be called Pythagoreans. For them it was and is about showing the universe as a cosmos that is meaningful and aesthetically structured according to mathematical rules . This harmonic order should be recognizable in the planetary orbits as well as in musical proportions and in the number symbolism. The laws of harmony are considered to be fundamental principles found in all of nature. Important humanists such as Giovanni Pico della Mirandola (1463–1494), who explicitly described himself as a Pythagorean, and Johannes Reuchlin (1455–1522) professed this way of thinking . They had a forerunner in the late medieval scholar Pietro d'Abano . The astronomer and natural philosopher Johannes Kepler (1571–1630) tried particularly hard to show the movements of the planets as an expression of perfect world harmony and to combine astronomical proportions with musical ones.

In the 20th century, the musicologist Hans Kayser took up the Pythagorean tradition with his "harmonic basic research". His student Rudolf Haase continued his work. These efforts are particularly popular in esoteric circles . Since the basic assumption of a cosmic harmony, from which the modern Pythagoreans start, has the character of a religious conviction, their research receives hardly any attention in science.

Werner Heisenberg , in his essay "Thoughts of Ancient Natural Philosophy in Modern Physics", first published in 1937, assigned the Pythagoreans a pioneering role in the development of scientific thinking, which aims to mathematically grasp the order in nature. Heisenberg wrote that the “discovery of the mathematical conditioned nature of harmony” by the Pythagoreans was based on “the thought of the meaningful power of mathematical structures”, a “fundamental idea that the exact natural science of our time has adopted from antiquity”; modern science is "a consistent implementation of the Pythagorean program". For Heisenberg, the discovery of the rational numerical relationships on which musical harmony is based is "one of the strongest impulses of human science at all".

The Spanish philosopher María Zambrano (1904–1991) saw in Pythagoreanism an orientation of thinking that seeks reality in numerical proportions and thus regards the universe as "a web of rhythms, a disembodied harmony" in which things do not consist in themselves but only let phenomena appear through their mathematical and temporal relationships to one another. The opposite pole to this is Aristotelianism , for which the individual things rest in themselves as substances and thus have their own inner reality. Aristotelianism triumphed because it was initially able to offer a superior explanation of nature and life, but the Pythagorean stance continued to exist as an alternative and modern physics of relativity was a return to it.

See also

Source collections

  • Laura Gemelli Marciano (Ed.): The pre-Socratics . Volume 1, Artemis & Winkler, Düsseldorf 2007, ISBN 978-3-7608-1735-4 , pp. 100–220 (Greek source texts with German translation and explanations)
  • Maurizio Giangiulio (Ed.): Pitagora. Le opere e le testimonianze . 2 volumes, Mondadori, Milano 2001–2002, ISBN 88-04-47349-5 (Greek texts with Italian translation)
  • Jaap Mansfeld , Oliver Primavesi (ed.): The pre-Socratics . Reclam, Stuttgart 2011, ISBN 978-3-15-010730-0 , pp. 122–205 (Greek texts with German translation; some of the introduction does not reflect the current state of research)
  • Maria Timpanaro Cardini (Ed.): Pitagorici. Testimonianze e frammenti . 3 volumes, La Nuova Italia, Firenze 1958–1964 (Greek and Latin texts with Italian translation)


Manual illustrations

Overall representations, investigations

  • Walter Burkert : Wisdom and Science. Studies on Pythagoras, Philolaus and Plato . Hans Carl, Nuremberg 1962
  • Walter Burkert: Lore and Science in Ancient Pythagoreanism . Harvard University Press, Cambridge (Mass.) 1972, ISBN 0-674-53918-4 (revised version of Burkert's Wisdom and Science )
  • Gabriele Cornelli: In Search of Pythagoreanism. Pythagoreanism As an Historiographical Category . De Gruyter, Berlin 2013, ISBN 978-3-11-030627-9
  • Cornelia Johanna de Vogel : Pythagoras and Early Pythagoreanism. An Interpretation of Neglected Evidence on the Philosopher Pythagoras . Van Gorcum, Assen 1966
  • Frank Jacob : The Pythagoreans: Scientific School, Religious Sect or Political Secret Society? In: Frank Jacob (Ed.): Secret Societies: Kulturhistorische Sozialstudien (= Globalhistorische Comparative Studies , Vol. 1), Königshausen & Neumann, Würzburg 2013, pp. 17–34
  • Charles H. Kahn: Pythagoras and the Pythagoreans. A brief history . Hackett, Indianapolis 2001, ISBN 0-87220-576-2
  • James A. Philip: Pythagoras and Early Pythagoreanism . University of Toronto Press, Toronto 1968, ISBN 0-8020-5175-8
  • Christoph Riedweg : Pythagoras: life, teaching, aftermath. An introduction . 2nd edition, Beck, Munich 2007, ISBN 978-3-406-48714-9
  • Bartel Leendert van der Waerden : The Pythagoreans . Artemis, Zurich and Munich 1979, ISBN 3-7608-3650-X
  • Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism . Akademie Verlag, Berlin 1997, ISBN 3-05-003090-9
  • Leonid Zhmud: Pythagoras and the Early Pythagoreans . Oxford University Press, Oxford 2012, ISBN 978-0-19-928931-8

Collections of articles


  • Luis E. Navia: Pythagoras. An Annotated Bibliography . Garland, New York 1990, ISBN 0-8240-4380-4

Web links

Wiktionary: Pythagorean  - explanations of meanings, word origins, synonyms, translations


  1. See for the dating Walter Burkert: Weisheit und Wissenschaft , Nürnberg 1962, p. 176; Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 21-23; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 51f.
  2. Diodorus 12: 9, 5-6; Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 203-206.
  3. See on these events Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 207–217 and Kurt von Fritz : Pythagorean Politics in Southern Italy , New York 1940, pp. 88–90.
  4. ^ Kurt von Fritz: Pythagorean Politics in Southern Italy , New York 1940, pp. 94ff., 108; Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 201f., 207; slightly different Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 190f.
  5. Alfonso Mele: Magna Grecia , Napoli 2007, pp. 259-298; Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 149f.
  6. Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 20-24.
  7. ^ Occasional late authors (including Iamblichos, De vita Pythagorica 265f.) Mention names of alleged successors. Walter Burkert names sources: Weisheit und Wissenschaft , Nürnberg 1962, p. 180, notes 35 and 36.
  8. Kurt von Fritz: Pythagorean Politics in Southern Italy , New York 1940, pp. 29–32, 97–99.
  9. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 217–222; Kurt von Fritz: Pythagorean Politics in Southern Italy , New York 1940, pp. 69-92; Christoph Riedweg: Pythagoras , 2nd edition, Munich 2007, pp. 137-139. Domenico Musti advocates a late dating of the persecution (around 440/420): Le rivolte antipitagoriche e la concezione pitagorica del tempo . In: Quaderni Urbinati di cultura classica NS 36, 1990, pp. 35-65.
  10. For the history of the concept see Kurt von Fritz: Mathematicians and Akusmatiker bei den alten Pythagoreern , Munich 1960, pp. 20f.
  11. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, pp. 190f .; Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 69–73; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreism , Berlin 1997, pp. 100-104, is different .
  12. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 64–70.
  13. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, p. 191.
  14. Ancient documents are compiled by Arthur S. Pease (ed.): M Tulli Ciceronis de natura deorum liber primus , Cambridge (Mass.) 1955, pp. 149f.
  15. Seneca, Epistulae 52.10; Diogenes Laertios 8.10; Gellius , Noctes Atticae 1.9; Apuleius , Florida 15; Porphyrios, Vita Pythagorae 13 and 54; Iamblichos, De vita Pythagorica 71–72 and 74.
  16. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, pp. 431–440; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, pp. 170–175.
  17. Christian Mann: Athlete and Polis in Archaic and Early Classical Greece , Göttingen 2001, pp. 175–177.
  18. ^ Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, pp. 70, 229, 231.
  19. Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreism , Berlin 1997, pp. 42f., 70f., 235f., 239f.
  20. Alfons Städele: The letters of Pythagoras and the Pythagoreans , Meisenheim 1980, p. 288ff.
  21. ^ Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreism , Berlin 1997, pp. 153, 212; Christoph Riedweg: Pythagoras , 2nd edition, Munich 2007, p. 151f.
  22. See on this idea Walter Burkert: Weisheit und Wissenschaft , Nürnberg 1962, pp. 251f .; Carl A. Huffman: Philolaus of Croton, Pythagorean and Presocratic , Cambridge 1993, pp. 330-332.
  23. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, p. 110f.
  24. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, p. 116ff.
  25. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 252–268.
  26. ^ Johan C. Thom: The Pythagorean Golden Verses , Leiden 1995, pp. 94-99 (Greek text and English translation).
  27. Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 232-234; Clara Talamo: Pitagora e la ΤΡΥΦΗ . In: Rivista di filologia e di istruzione classica 115, 1987, pp. 385-404.
  28. Greek ἀποχὴ ἐμψύχων. Iamblichos, De vita Pythagorica 107; 168; 225; Porphyrios, Vita Pythagorae 7 (with reference to Eudoxus of Knidos ).
  29. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, p. 52f.
  30. Johannes Haußleiter : Der Vegetarismus in der Antike , Berlin 1935, pp. 97–157; Carmelo Fucarino: Pitagora e il vegetarianismo , Palermo 1982, pp. 21-31.
  31. On the state of research see Giovanni Sole: Il tabù delle fave , Soveria Mannelli 2004. Cf. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 169–171; Walter Burkert: Wisdom and Science , Nuremberg 1962, pp. 164–166; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 127f.
  32. ^ Iamblichos, De vita Pythagorica 229-230. See also Johan C. Thom: "Harmonious Equality": The Topos of Friendship in Neopythagorean Writings . In: John T. Fitzgerald (Ed.): Greco-Roman Perspectives on Friendship , Atlanta 1997, pp. 77-103.
  33. For the legend and its reception, see Ernst Gegenschatz: The 'Pythagorean Guarantee' - for the history of a motif from Aristoxenus to Schiller . In: Peter Neukam (Ed.): Encounters with new and old , Munich 1981, pp. 90–154.
  34. ^ Edwin L. Minar: Pythagorean Communism . In: Transactions and Proceedings of the American Philological Association 75, 1944, pp. 34-46; Manfred Wacht: Community of property . In: Reallexikon für Antike und Christianentum , Vol. 13, Stuttgart 1986, Sp. 1–59, here: 2–4.
  35. ^ Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreism , Berlin 1997, pp. 261–279.
  36. ^ Carl A. Huffman: Philolaus of Croton, Pythagorean and Presocratic , Cambridge 1993, pp. 37ff., 56ff .; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 263f. However, Hermann S. Schibli pleads for an ontological understanding of the theory of numbers: On 'The One' in Philolaus, fragment 7 . In: The Classical Quarterly 46, 1996, pp. 114-130. See also Charles H. Kahn: Pythagoras and the Pythagoreans. A Brief History , Indianapolis 2001, p. 28.
  37. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 337–363, 392ff .; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, p. 153ff.
  38. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, pp. 293–295.
  39. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, p. 300f.
  40. ^ Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, pp. 213–224; Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 427–438.
  41. Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 100-103, 110f., 434f.
  42. ^ Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreism , Berlin 1997, pp. 219–225.
  43. Barbara Münxelhaus: Pythagoras Musicus , Bonn 1976, pp 25-29, 36-39, 50-55, 57ff .; Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 366–372.
  44. ^ Walter Burkert: Wisdom and Science , Nuremberg 1962, pp. 350–352.
  45. Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 162–166; Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, p. 364f .; Walter Burkert: Wisdom and Science , Nuremberg 1962, p. 355; Leonid Zhmud: Science, Philosophy and Religion in Early Pythagoreanism , Berlin 1997, pp. 181-183, 233.
  46. ^ Carl A. Huffman: Philolaus of Croton, Pythagorean and Presocratic , Cambridge 1993 offers an edition of the Philolaos fragments with commentary; on philosophy p. 37ff.
  47. Christoph Riedweg: Pythagoras , 2nd edition, Munich 2007, pp. 152–157; Charles H. Kahn: Pythagoras and the Pythagoreans. A Brief History , Indianapolis 2001, pp. 63-71. On Plato's relationship to Archytas, see also Carl A. Huffman: Archytas of Tarentum , Cambridge 2005, pp. 32–42.
  48. passages and comment on Maurizio Giangiulio (ed.): Pitagora. Le opere e le testimonianze , Volume 2, Milano 2000, pp. 183-199; see also Bartel Leendert van der Waerden: Die Pythagoreer , Zurich 1979, pp. 182–185.
  49. Bruno Centrone: Introduzione ai pitagorici , Roma 1996, p. 52.
  50. The break with tradition is attested by Cicero ( Timaeus 1); this includes individual Pythagorean activities in Italy in the 3rd and 2nd centuries BC. Not off. See Cornelia J. de Vogel: Pythagoras and Early Pythagoreanism , Assen 1966, pp. 28ff.
  51. On Varro's neo-Pythagorean ideas see Yves Lehmann: Varron théorien et philosophe romain , Bruxelles 1997, pp. 299–314; Leonardo Ferrero: Storia del pitagorismo nel mondo romano , 2nd edition, Forlì 2008, pp. 291-304; Burkhart Cardauns : Marcus Terentius Varro. Introduction to his work , Heidelberg 2001, pp. 70f.
  52. Seneca, De ira 3,36,1-3.
  53. Jérôme Carcopino: La basilique pythagoricienne de la Porte Majeure , Paris 1927.
  54. Ubaldo Pizzani: Studi sulle fonti del "De Institutione Musica" di Boezio . In: Sacris erudiri 16, 1965, pp. 5–164, here: 27ff.
  55. Dominic J. O'Meara: Pythagoras Revived. Mathematics and Philosophy in Late Antiquity , Oxford 1989, pp. 10-14.
  56. See the thorough investigation by Gregor Staab: Pythagoras in der Spätantike. Studies on De Vita Pythagorica des Iamblichos von Chalkis , Munich 2002 (with a complete overview of the rest of the neo-Pythagorean times of the empire, pp. 75-143).
  57. Dominic J. O'Meara: Pythagoras Revived. Mathematics and Philosophy in Late Antiquity , Oxford 1989, pp. 114-118.
  58. Dominic J. O'Meara: Pythagoras Revived. Mathematics and Philosophy in Late Antiquity , Oxford 1989, pp. 119ff.
  59. ^ Paolo Casini: L'antica sapienza italica. Cronistoria di un mito , Bologna 1998, pp. 56-61.
  60. Christiane Joost-Gaugler: Measuring Heaven. Pythagoras and His Influence on Thought and Art in Antiquity and the Middle Ages , Ithaca 2006, p. 130.
  61. Ekkehart Schaffer: The Pythagorean tradition. Studies on Platon, Kepler and Hegel , Cologne 2004, pp. 65–98; Charles H. Kahn: Pythagoras and the Pythagoreans. A Brief History , Indianapolis 2001, pp. 162-171.
  62. Werner Heisenberg: Thoughts of ancient natural philosophy in modern physics . In: Werner Heisenberg: Changes in the fundamentals of natural science , 8th, extended edition, Stuttgart 1949, pp. 47–53, here: 50f.
  63. María Zambrano: Man and the Divine , Vienna 2005, pp. 64–99.
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