Pythagoras
Pre-Socratic philosophy |
|
|
Name
|
|
|
Birth
|
c. 580 B.C.-572 B.C.
|
|
Death
|
c. 500 B.C.-490 B.C.
|
|
School/tradition
|
Pythagoreanism
|
|
Main interests
|
Metaphysics, Music, Mathematics, Ethics, Politics
|
|
Notable ideas
|
Musica universalis, Golden ratio,
Pythagorean tuning, Pythagorean
theorem
|
|
Influences
|
Thales, Anaximander, Pherecydes
|
|
Influenced
|
Philolaus, Alcmaeon, Parmenides, Plato, Euclid, Empedocles, Hippasus, Kepler
|
Pythagoras of Samos (Greek: Πυθαγόρας; between
580 and 572 BC–between 500 and
490 BC) was an Ionian (Greek) philosopher[1] and founder of the religious movement called Pythagoreanism.
He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions
to mathematics or natural philosophy. [2] His name led him
to be associated with Pythian Apollo; Aristippus explained his name by saying, "He spoke (agor-) the truth no less than did the Pythian
(Pyth-)," and Iamblichus tells the story that the Pythia prophesied that
his pregnant mother would give birth to a man supremely beautiful, wise, and of benefit to humankind. [3]
He is best known for the Pythagorean theorem which bears his name. Known as "the
father of numbers", Pythagoras made influential contributions to philosophy and religious
teaching in the late 6th century BC. Because legend and obfuscation cloud his work even
more than with the other pre-Socratics, one can say little with confidence about
his life and teachings. We do know that Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality and, through mathematics, everything could be
predicted and measured in rhythmic patterns or cycles. According to Iamblichus,
Pythagoras once said that "number is the ruler of forms and ideas and the cause of gods and demons."
He was the first man to call himself a philosopher, or lover of wisdom,[4] and Pythagorean ideas exercised a marked influence on Plato.
Unfortunately, very little is known about Pythagoras because none of his writings have survived. Many of the accomplishments
credited to Pythagoras may actually have been accomplishments of his colleagues and successors.
Life
Pythagoras was born on Samos, a Greek island in the eastern Aegean, off the coast of
Asia Minor. He was born to Pythais (his mother, a native of Samos) and Mnesarchus (his father,
a Phoenician merchant from Tyre). As a young man, he
left his native city for Croton, Calabria, in Southern
Italy, to escape the tyrannical government of Polycrates. According to Iamblichus, Thales, impressed with his abilities, advised Pythagoras to head to Memphis in Egypt and study with the priests there who were renowned for their wisdom. He also was
discipled in the temples of Tyre and Byblos in Phoenicia. It may have been in Egypt where he learned some geometric principles
which eventually inspired his formulation of the theorem that is now called by his name. This
possible inspiration is presented as an example problem in the Berlin Papyrus.
Upon his migration from Samos to Croton, Calabria,
Italy, Pythagoras established a secret religious society very similar to (and possibly influenced
by) the earlier Orphic cult.
Pythagoras undertook a reform of the cultural life of Croton, urging the citizens to follow virtue and form an elite circle of
followers around himself called Pythagoreans. Very strict rules of conduct governed this cultural center. He opened his school to
male and female students alike. Those who joined the inner circle of Pythagoras's society called themselves the
Mathematikoi. They lived at the school, owned no personal possessions and were required to assume a mainly
vegetarian diet (meat that could be sacrificed was allowed to be eaten). Other students
who lived in neighboring areas were also permitted to attend Pythagoras's school. Known as Akousmatikoi, these students
were permitted to eat meat and own personal belongings.
According to Iamblichus, the Pythagoreans followed a structured life of
religious teaching, common meals, exercise, reading and philosophical study. Music featured as an essential organizing factor of
this life: the disciples would sing hymns to Apollo together regularly; they used the
lyre to cure illness of the soul or body; poetry recitations occurred before and after sleep to aid
the memory.
Towards the end of his life he fled to Metapontum because of a plot against him and his
followers by a noble of Croton named Cylon. He died in Metapontum around 90 years old from
unknown causes.
Influence
Flavius Josephus relates that, according to Hermippus of
Smyrna, Pythagoras was familiar with and an admirer of Jewish customs and wisdom (De
Pythagora, Contra Apionem I, 162/165). Hermippus is quoted as saying about Pythagoras: "In practicing and repeating these
precepts he was imitating and appropriating the doctrines of Jews and Thracians. In fact, it
is actually said that that great man introduced many points of Jewish law into his philosophy."
(trans. H. St. J. Thackeray, The Loeb Classical Library, Cambridge (Mass.)-London)
Pythagoras is commonly given credit for discovering the Pythagorean theorem, a theorem in trigonometry that states that in a
right-angled triangle the square of the hypotenuse (the side opposite the right angle), c, is equal to the sum of the
squares of the other two sides, b and a—that is, a² + b² = c².
While the theorem that now bears his name was well known and previously utilized by the Babylonians, Egyptians and Indians,
he, or his students, are thought to have constructed the first proof. Because of the secretive nature of his school and the
custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved
this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems. Some
attribute it as a carefully constructed myth by followers of Plato over two centuries after the
death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to
Pythagoras. This attribution has stuck, down the centuries up to modern times. [5] The earliest known mention of Pythagoras's name in connection with the theorem occurred five
centuries after his death, in the writings of Cicero and Plutarch. There are many ancient references to the facts stated in the Pythagorean theorem; Egyptian and
Chinese tablets and writings show that they knew the theorem.
Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze faith along with his fellow Greek, Plato.
Pythagoreans
-
The organization was in some ways a school, in some ways a brotherhood, and in some ways a monastery. It was based upon
Pythagoras’ religious teachings and was very secretive. At first, the school was highly concerned with the morality of society.
Members were required to live ethically, love one another, share political beliefs, practice pacifism, and devote themselves to
the mathematics of nature.
Pythagoras's followers were commonly called "Pythagoreans." For the most part we remember them as philosophical mathematicians
who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by
Euclid in The Elements.
The Pythagoreans observed a rule of silence called echemythia, the breaking of which was punishable by death. This was because
the Pythagoreans believed that a man's words were usually careless and misrepresented him and that when someone was "in doubt as
to what he should say, he should always remain silent". Another rule that they had was to help a man "in raising a burden, but do
not assist him in laying it down, for it is a great sin to encourage indolence", and they said "departing from your house, turn
not back, for the furies will be your attendants"; this axiom reminded them that it was better to learn none of the truth about
mathematics, God, and the universe at all than to learn a little without learning all. (The Secret Teachings of All Ages
by Manly P. Hall).
In his biography of Pythagoras (written seven centuries after Pythagoras's time), Porphyry stated that this silence was "of no ordinary kind." The Pythagoreans were divided into
an inner circle called the mathematikoi ("mathematicians") and an outer circle called the akousmatikoi
("listeners"). Porphyry wrote "the mathematikoi learned the more detailed and exactly elaborate version of this knowledge,
the akousmatikoi (were) those which had heard only the summary headings of his (Pythagoras's) writings, without the more
exact exposition." According to Iamblichus, the akosmatikoi were the
exoteric disciples who listened to lectures that Pythagoras gave out loud from behind a
veil.
The akousmatikoi were not allowed to see Pythagoras and they were not taught the inner secrets of the cult. Instead
they were taught laws of behavior and morality in the form of cryptic, brief sayings that had hidden meanings. The
akousmatikoi recognized the mathematikoi as real Pythagoreans, but not vice versa. After the murder of a number of
the mathematikoi by the cohorts of Cylon, a resentful disciple, the two groups split from
each other entirely, with Pythagoras's wife Theano and their two daughters leading the mathematikoi.
Theano, daughter of the Orphic initiate Brontinus, was a mathematician in her own right. She is credited with having written
treatises on mathematics, physics, medicine, and child psychology, although nothing of her writing survives. Her most important
work is said to have been a treatise on the principle of the golden mean. In a time
when women were usually considered property and relegated to the role of housekeeper or spouse, Pythagoras allowed women to
function on equal terms in his society.
The Pythagorean society is associated with prohibitions such as not to step over a crossbar, and not to eat beans. These rules
seem like primitive superstition, similar to "walking under a ladder brings bad luck". The
abusive epithet mystikos logos ("mystical speech") was hurled at Pythagoras even in
ancient times to discredit him. The prohibition on beans could be linked to favism, which is relatively widespread around the Mediterranean.
The key here is that akousmata means "rules", so that the superstitious taboos primarily applied to the
akousmatikoi, and many of the rules were probably invented after Pythagoras's death and independent from the
mathematikoi (arguably the real preservers of the Pythagorean tradition). The mathematikoi placed greater emphasis
on inner understanding than did the akousmatikoi, even to the extent of dispensing with certain rules and ritual
practices. For the mathematikoi, being a Pythagorean was a question of innate quality and inner understanding.
There was also another way of dealing with the akousmata — by allegorizing them. We have a few examples of this, one
being Aristotle's explanations of them: "'step not over a balance', i.e. be not covetous;
'poke not the fire with a sword', i.e. do not vex with sharp words a man swollen with anger, 'eat not heart', i.e. do not vex
yourself with grief," etc. We have evidence for Pythagoreans allegorizing in this way at least as far back as the early fifth
century BC. This suggests that the strange sayings were riddles for the initiated.
The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute
the true nature of things. They performed purification rites and followed and developed various rules of living which they
believed would enable their soul to achieve a higher rank among the gods.
Much of their mysticism concerning the soul seem inseparable from the Orphic
tradition. The Orphics advocated various purificatory rites and practices as well as incubatory rites of descent into the
underworld. Pythagoras is also closely linked with Pherecydes of Syros, the man
ancient commentators tend to credit as the first Greek to teach a transmigration of souls. Ancient commentators agree that
Pherekydes was Pythagoras's most intimate teacher. Pherekydes expounded his teaching on the soul in terms of a pentemychos
("five-nooks", or "five hidden cavities") — the most likely origin of the Pythagorean use of the pentagram, used by them as a
symbol of recognition among members and as a symbol of inner health (ugieia).
Musical theories and investigations
Pythagoras was very interested in music, and so were his followers. The Pythagoreans were musicians as well as mathematicians.
Pythagoras wanted to improve the music of his day, which he believed was not harmonious enough and was too hectic.
According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when
one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and
harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He
went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the anvils
were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on." (See
Pythagorean tuning.)
The Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Pythagoras
believed in something called the harmony of the spheres. He believed that since planets and the stars all moved in the universe
according to mathematical equations that these mathematical equations could be translated into musical notes and thus produce a
symphony.[6]
Religion and science
Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. However, they are looked at
separately in the 21st century. Religiously, Pythagoras was a believer of metempsychosis.
He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables
until it became moral. His ideas of reincarnation were influenced by Greek Mythology. He was one of the first to propose that the
thought processes and the soul were located in the brain and not the heart. He himself claimed to have lived four lives that he
could remember in detail, and heard the cry of his dead friend in the bark of a dog.
One of Pythagoras' beliefs was that the essence of being is number. Thus, being relies on stability of all things that create
the universe. Things like health relied on a stable proportion of elements; too much or too little of one thing causes an
imbalance that makes a being unhealthy. Pythagoras viewed thinking as the calculating with the idea numbers. When combined with
the Folk theories, the philosophy evolves into a belief that Knowledge of the essence of being can be found in the form of
numbers. If this is taken a step further, one can say that because mathematics is an unseen essence, the essence of being is an
unseen characteristic that can be encountered by the study of mathematics.
Literary works
No texts by Pythagoras survive, although forgeries under his name — a few of which remain extant — did circulate in
antiquity. Critical ancient sources like Aristotle and Aristoxenus cast doubt on these writings. Ancient
Pythagoreans usually quoted their master's doctrines with the phrase autos ephe ("he himself said") — emphasizing the
essentially oral nature of his teaching. Pythagoras appears as a character in the last book of Ovid's Metamorphoses, where Ovid has him expound upon his
philosophical viewpoints. Pythagoras has been quoted as saying, "No man is free who cannot command himself."
Lore
There is another Pythagoras, who is the subject of elaborate legends surrounding his persona. Aristotle described Pythagoras
as wonder-worker and somewhat of a supernatural figure, attributing to him such aspects as a golden thigh, which was a sign of
divinity. According to Aristotle and others' accounts, some ancients believed that he had the ability to travel through space and
time, and to communicate with animals and plants.[7] An
extract from Brewer's Dictionary of Phrase and Fable's entry
entitled "Golden Thigh":
Pythagoras is said to have had a golden thigh, which he showed to Abaris, the Hyperborean priest, and exhibited in the
Olympic games.[8]
Another legend, also taken from Brewer's Dictionary, describes his writing on the moon:
Pythagoras asserted he could write on the moon. His plan of operation was to write on a looking-glass in blood, and place
it opposite the moon, when the inscription would appear photographed or reflected on the moon's disc.[9]
Other accomplishments
One of his major accomplishments was the discovery that music was based on proportional intervals of the numbers one through
four. He believed that the number system, and therefore the universe system, was based on the sum of these numbers: ten.
Pythagoreans swore by the Tetrachtys of the Decad, or ten, rather than by the gods. He assigned roles for the numbers as follows:
one was reason, two was opinion, four was justice, five was marriage because it was the sum of the first odd and the first even
numbers (one was disregarded), seven was virgin because it neither factors or produces among the numbers one through ten. Odd
numbers were masculine and even were feminine. He discovered the theory of mathematical proportions, constructed from three to
five geometrical solids. One of his order, Hippasos, also discovered irrational numbers, but the idea was unthinkable to Pythagoras, and according to one version this
member was executed. Pythagoras (or the Pythagoreans) also discovered square numbers. They found that if one took, for example,
four small stones and arranged them into a square, each side of the square was not only equivalent to the other, but that when
the two sides were multiplied together, they equaled the sum total of stones in the square arrangement, hence the name "Square
Root". He was one of the first to think that the earth was round, that all planets have an axis, and that all the planets travel
around one central point. He originally identified that point as Earth, but later renounced it for the idea that the planets
revolve around a central “fire” that he never identified as the sun. He also believed that the moon was another planet that he
called a “counter-Earth” – furthering his belief in the Limited-Unlimited.
Groups influenced by Pythagoras
Influence on Plato
Pythagoras or in a broader sense, the Pythagoreans, allegedly exercised an important influence on the work of Plato. According
to R. M. Hare, his influence consists of three points: a) the platonic Republic might be related to the idea of "a tightly organized community of like-minded
thinkers", like the one established by Pythagoras in Croton. b) there is evidence that Plato possibly took from Pythagoras the
idea that mathematics and, generally speaking, abstract thinking is a secure basis for philosophical thinking as well as "for
substantial theses in science and morals". c) Plato and
Pythagoras shared a "mystical approach to the soul and its place in the material world". It is probable that both have been influenced by Orphism.[10]
Plato's harmonics were clearly influenced by the work of Archytas, a genuine Pythagorean of the third generation, who made
important contributions to geometry, reflected in Book VIII of Euclid's Elements.
Roman influence
In the legends of ancient Rome, Numa Pompilius,
the second King of Rome, is said to have studied under Pythagoras. This is unlikely, since the commonly accepted dates for the
two lives do not overlap.
Influence on esoteric groups
Pythagoras started a secret society called the Pythagorean brotherhood devoted to the study of mathematics. This had a great
effect on future esoteric traditions, such as Rosicrucianism and Freemasonry, both of which were occult groups dedicated to the
study of mathematics and both of which claimed to have evolved out of the Pythagorean brotherhood. The mystical and occult
qualities of Pythagorean mathematics are discussed in a chapter of Manly P. Hall's The Secret Teachings of All Ages
entitled "Pythagorean Mathematics".
Pythagorean theory was tremendously influential on later numerology, which was extremely
popular throughout the Middle East in the ancient world. The 8th-century Islamic alchemist
Jabir ibn Hayyan grounded his work in an elaborate numerology greatly influenced by Pythagorean
theory.
See also
References
Primary sources
Only a few relevant source texts deal with Pythagoras and the Pythagoreans, most are available in different translations.
Other texts usually build solely on information from these four books.
- Diogenes Laertius, Vitae philosophorum VIII (Lives of Eminent Philosophers), c. 200
AD, which in turn reference the lost work Successions of Philosophers by Alexander
Polyhistor) — Pythagoras, Translation by C.D. Yonge
- Porphyry, Vita Pythagorae (Life of Pythagoras), c. 270 AD
- Iamblichus, De Vita Pythagorica (On the Pythagorean Life), c.
300 AD
- Apuleius also writes about Pythagoras in Apologia, including a story of him being
taught by Babylonian disciples of Zoroaster, c. 150 AD
- Hierocles of Alexandria, Golden Verses of Pythagoras, Concord Grove
Pr., 1983
Secondary sources
- Burkert, Walter. Lore and Science in Ancient Pythagoreanism. Harvard University Press, June
1, 1972. ISBN 0-674-53918-4
- Burnyeat, M. F. "The Truth about
Pythagoras". London Review of Books, 22 February 2007.
- Guthrie, W. K. A History of Greek Philosophy: Earlier Presocratics and the Pythagoreans, Cambridge University Press,
1979. ISBN 0-521-29420-7
- Kingsley, Peter. Ancient Philosophy, Mystery, and Magic: Empedocles and
the Pythagorean Tradition. Oxford University Press, 1995.
- Hermann, Arnold. To Think Like God: Pythagoras and Parmenides—the Origins of
Philosophy. Parmenides Publishing, 2005. ISBN 978-1-930972-00-1
- O'Meara, Dominic J. Pythagoras Revived. Oxford University Press, 1989. ISBN 0-19-823913-0 (paperback), ISBN
0-19-824485-1 (hardcover)
Notes
- ^ According to Diogenes Laertius,
”Pythagoras was the first person who invented the term philosophy, and called himself
a philosopher” (Φιλοσοφίαν δὲ πρῶτος ὠνόμασε Πυθαγόρας καὶ ἑαυτὸν φιλόσοφον: Lives of Philosophers
1.12 (Greek).
- ^ Walter Burkert's seminal work Lore and Science in Ancient
Pythagoreanism (see sources) sheds considerable doubt on the widely held traditions of late Classical Greece, accepted
without scrutiny until the beginning of the 20th century, that Pythagoras made substantial contributions to mathematics and
science.
- ^ Christoph Riedweg, Pythagoras: His Life, Teaching and Influence,
trans. Steven Rendall (Cornell UP, 2005), pp. 5-6, 59, 73.
- ^ Cicero, Tusculan Disputations, 5.3.8-9 = Heraclides
Ponticus fr. 88 Wehrli, Diogenes Laertius 1.12, 8.8, Iamblichus VP 58. Burkert attempted to discredit this ancient tradition, but it has been
defended by C.J. De Vogel, Pythagoras and Early Pythagoreanism (1966), pp. 97-102, and C. Riedweg, Pythagoras: His
Life, Teaching, And Influence (2005), p. 92.
- ^ From Christoph Riedweg , Pythagoras, His Life, Teaching and
Influence, Cornell: Cornell University Press, 2005: "Had Pythagoras and his teachings not been since the early Academy
overwritten with Plato’s philosophy, and had this ‘palimpsest’ not in the course of the Roman Empire achieved unchallenged
authority among Platonists, it would be scarcely conceivable that scholars from the Middle Ages and modernity down to the present
would have found the Presocratic charismatic from Samos so fascinating. In fact, as a rule it was the image of Pythagoras
elaborated by Neopythagoreans and Neoplatonists that determined the idea of what was Pythagorean over the centuries."
- ^ Christoph Riedweg , Pythagoras, His Life, Teaching and Influence, Cornell:
Cornell University Press, 2005 .
- ^ Huffman, Carl. Pythagoras (Stanford Encyclopedia of Philosophy) [1]
- ^ Brewer, E. Cobham, Brewer's Dictionary of Phrase and Fable [2]
- ^ Brewer, E. Cobham, Brewer's Dictionary of Phrase and Fable [3]
- ^ R.M. Hare, Plato in C.C.W. Taylor, R.M. Hare and Jonathan Barnes, Greek
Philosophers, Socrates, Plato, and Aristotle, Oxford: Oxford University Press, 1999 (1982), 103-189, here 117-9.
External links
Wikiquote has a collection of quotations related to:
Wikimedia Commons has media related to:
- “Other Lives” by M.F. Burnyeat,
an article about current Pythagoras scholarship
- Pythagoreanism Web Site
- References
for Pythagoras
- Pythagoras, Internet
Encyclopedia of Philosophy
- Pythagoras of Samos, The MacTutor History of Mathematics archive, School of Mathematics and Statistics, University
of St Andrews, Scotland
- Pythagoras and the
Pythagoreans, Fragments and Commentary, Arthur Fairbanks Hanover Historical Texts Project, Hanover College Department of
History
- The Complete Pythagoras, an on-line
book containing all survived biographies and Pythagorean fragments.
- Pythagoras
and the Pythagoreans, Department of Mathematics, Texas A&M University
- Pythagoras and
Pythagoreanism, The Catholic Encyclopedia
- Pythagoreanism Web Article
- Occult
conception of Pythagoreanism
- Pythagoras of Samos
- Stanford Encyclopedia of
Philosophy entry
- Tetraktys
- Golden Verses of
Pythagoras
- Pythagoras
on Vegetarianism Quotes from primary source historical literature on Pythagoras' view on Vegetarianism, Justice and
Kindness