Bust of Pythagoras

Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a very inspirational source for Plato and Platonism.

Later resurgence of ideas similar to those held by the early Pythagoreans are collected under the term Neopythagoreanism.

Two schools

According to tradition, Pythagoreanism developed at some point into two separate schools of thought, the akousmatikoi ("listeners") and the math?matikoi ("learners"). The math?matikoi were supposed to have extended and developed the more mathematical and scientific work begun by Pythagoras, while the akousmatikoi focused on the more religious and ritualistic aspects of his teachings. The akousmatikoi claimed that the math?matikoi were not genuinely Pythagorean, but followers of the "renegade" Pythagorean Hippasus. The math?matikoi, on the other hand, allowed that the akousmatikoi were Pythagorean but felt that they were more representative of Pythagoras.^[1]

Pythagorean natural philosophy

Pythagorean thought was dominated by mathematics, but it was also profoundly mystical. In the area of cosmology there is less agreement about what Pythagoras himself actually taught, but most scholars believe that the Pythagorean idea of the transmigration of the soul is too central to have been added by a later follower of Pythagoras. The Pythagorean conception of substance, on the other hand, is of unknown origin, partly because various accounts of his teachings are conflicting. The Pythagorean account actually begins with Anaximander's teaching that the ultimate substance of things is "the boundless," or what Anaximander called the "apeiron." The Pythagorean account holds that it is only through the notion of the "limit" that the "boundless" takes form.

Pythagoras wrote nothing down, and relying on the writings of Parmenides, Empedocles, Philolaus and Plato (people either considered Pythagoreans, or whose works are thought deeply indebted to Pythagoreanism) results in a very diverse picture in which it is difficult to ascertain what the common unifying Pythagorean themes were. Relying on Philolaus, whom most scholars agree is highly representative of the Pythagorean school, one has a very intricate picture. Aristotle explains how the Pythagoreans (by which he meant the circle around Philolaus) developed Anaximander's ideas about the apeiron and the peiron, the unlimited and limited, by writing that:

Continuing with the Pythagoreans:

Pythagoreans celebrate sunrise by Fyodor Bronnikov

A musical scale presupposes an unlimited continuum of pitches, which must be limited in some way in order for a scale to arise. The crucial point is that not just any set of limiters will do. One may not simply choose pitches at random along the continuum and produce a scale that will be musically pleasing. The diatonic scale, also known as "Pythagorean," is such that the ratio of the highest to the lowest pitch is 2:1, which produces the interval of an octave. That octave is in turn divided into a fifth and a fourth, which have the ratios of 3:2 and 4:3 respectively and which, when added, make an octave. If we go up a fifth from the lowest note in the octave and then up a fourth from there, we will reach the upper note of the octave. Finally the fifth can be divided into three whole tones, each corresponding to the ratio of 9:8 and a remainder with a ratio of 256:243 and the fourth into two whole tones with the same remainder. This is a good example of a concrete applied use of Philolaus? reasoning. In Philolaus' terms the fitting together of limiters and unlimiteds involves their combination in accordance with ratios of numbers (harmony). Similarly the cosmos and the individual things in the cosmos do not arise by a chance combination of limiters and unlimiteds; the limiters and unlimiteds must be fitted together in a "pleasing" (harmonic) way in accordance with number for an order to arise.

This teaching was recorded by Philolaus' pupil Archytas in a lost work entitled On Harmonics or On Mathematics, and this is the influence that can be traced in Plato. Plato's pupil Aristotle made a distinction in his Metaphysics between Pythagoreans and "so-called" Pythagoreans. He also recorded the Table of Opposites, and commented that it might be due to Alcmaeon of the medical school at Croton, who defined health as a harmony of the elements in the body.

After attacks on the Pythagorean meeting-places at Croton, the movement dispersed, but regrouped in Tarentum, also in Southern Italy. A collection of Pythagorean writings on ethics collected by Taylor show a creative response to the troubles.

The legacy of Pythagoras, Socrates and Plato was claimed by the wisdom tradition of the Hellenized Jews of Alexandria, on the ground that their teachings derived from those of Moses. Through Philo of Alexandria this tradition passed into the Medieval culture, with the idea that groups of things of the same number are related or in sympathy. This idea evidently influenced Hegel in his concept of internal relations.

The ancient Pythagorean pentagram was drawn with two points up and represented the doctrine of Pentemychos. Pentemychos means "five recesses" or "five chambers," also known as the pentagonas ? the five-angle, and was the title of a work written by Pythagoras' teacher and friend Pherecydes of Syros.^[2]

The Pythagorean symbols are central to the mystery in the novel The Oxford Murders (Crímenes imperceptibles, 2003) by Guillermo Martinez.

Pythagorean cosmology

The Monad was a symbol referred by the Greek philosophers as "The First," "The Seed," "The Essence," "The Builder," and "The Foundation"

Pythagorean vegetarianism

The Pythagoreans were well-known in antiquity for their vegetarianism, which they practised for religious, ethical and ascetic reasons, in particular the idea of metempsychosis - the transmigration of souls into the bodies of other animals.^[3] "Pythagorean diet" was a common name for the abstention from eating meat and fish, until the coining of "vegetarian" in the nineteenth century.^[4]

The Pythagorean code further restricted the diet of its followers, prohibiting the consumption or even touching any sort of bean. The reason is unclear: perhaps the flatulence they cause, perhaps as protection from potential favism, but most likely for magico-religious reasons,^[5] such as the belief that beans and human beings were created from the same material.^[6]

Pythagorean view of women

Women were given equal opportunity to study as Pythagoreans; however, they learned practical domestic skills in addition to philosophy.^[7] Women were held to be different from men, but sometimes in good ways.^[7]

Neo-Pythagoreanism

Neopythagoreanism was a revival in the 2nd century BC?2nd century AD period, of various ideas traditionally associated with the followers of Pythagoras, the Pythagoreans.

Notable Neopythagoreans include first century Apollonius of Tyana and Moderatus of Gades. Middle and Neo-Platonists such as Numenius and Plotinus also exhibited some Neo-Pythagorean influence.

In 1915 a subterranean basilica was discovered near Porta Maggiore on Via Praenestina, Rome where Neo-Pythagoreans held their meetings in the 1st century. The groundplan shows a basilica with three naves and an apse similarly to early Christian basilicas that appeared only much later, in the 4th century. The vaults are decorated with white stuccoes symbolizing Neopythagorean beliefs but its exact meaning remains a subject of debate.^[8]

Sentiments similar to Neopythagoreanism can be found in modern philosophy, such as Hilary Putnam's Realist thesis, "Internal Realism," whereby one could be a Pythagorean in this way.

Influences

• The Pythagorean idea that whole numbers and harmonic (pleasing) sounds are intimately connected in music, must have been well known to lute-player and maker Vincenzo Galilei, father of Galileo Galilei. While possibly following Pythagorean modes of thinking, Vincenzo is known to have discovered a new mathematical relationship between string tension and pitch, thus suggesting a generalization of the idea that music and musical instruments can be mathematically quantitated and described. This may have paved the way to his son's crucial insight that all physical phenomena may be described quantitatively in mathematical language (as physical "laws"), thus beginning and defining the era of modern physics.
• Pythagoreanism has had a clear and obvious influence on the texts found in the hermetica corpus and thus flows over into hermeticism, gnosticism and alchemy.
• The Pythagorean cosmology also inspired the Arabic gnostic Monoimus to combine this system with monism and other things to form his own cosmology.
• The pentagram (five-pointed star) was an important religious symbol used by the Pythagoreans, which is often seen as being related to the elements theorized by Empedocles to comprise all matter.
• The Pythagoreans were advised to "speak the truth in all situations," which Pythagoras said he learned from the Magi of Babylon.

References

1. ↑ On the two schools and these differences, see Charles Kahn, p. 15, Pythagoras and the Pythagoreans, Hackett 2001.
2. ↑ This is actually a lost book whose contents are preserved in Damascius, de principiis, quoted in Kirk and Raven, The Pre-Socratic Philosophers, Cambridge Univ. Press, 1956, page 55.
3. ↑
4. ↑ See for instance the popular treatise by Antonio Cocchi, Del vitto pitagorico per uso della medicina, Firenze 1743, which initiated a debate on the "Pythagorean diet".
5. ↑ Gabrielle Hatfield, review of Frederick J. Simoons, Plants of Life, Plants of Death, University of Wisconsin Press, 1999. ISBN 0-299-15904-3. In Folklore 111:317-318 (2000).
6. ↑ Riedweg, Christoph, Pythagoras: his life, teaching, and influence. Ithaca : Cornell University Press, pp. 39, 70. (2005), ISBN 0-8014-4240-0
7. ↑ ^{a b} Glenn, Cheryl, Rhetoric Retold: Regendering the Tradition from Antiquity Through the Renaissance. Southern Illinois University, 1997. 30-31.
8. ↑

Further reading

• O'Meara, Dominic J. Pythagoras Revived: Mathematics and Philosophy in Late Antiquity , Clarendon Press, Oxford, 1989. ISBN 0-19-823913-0
• Riedweg, Christoph Pythagoras : his life, teaching, and influence ; translated by Steven Rendall in collaboration with Christoph Riedweg and Andreas Schatzmann, Ithaca : Cornell University Press, (2005), ISBN 0-8014-4240-0

See also

• Pythagoras
• Pythagorean tuning
• Esoteric cosmology
• Sacred geometry
• Numerology
• Incommensurable magnitudes
• Unit-point atomism

Pythagorean symbols

• Monad
• Dyad
• Triad
• Tetrad
• Pentad
• Decad
• Tetractys
• Vesica piscis

External links

• Pythagoreanism Web Article
• Pythagoreanism Discussion Group
• Pythagoreanism Web Site
• Pythagoreanism Web Site

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