Pythagoras and Pythagoreanism
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Pythagoras believed: All things are numbers. Mathematics is the basis for everything, and geometry is the highest form of mathematical studies. The physical world can understood through mathematics. The soul resides in the brain, and is immortal. It moves from one being to another, sometimes from a human into an animal, through a series of reincarnations called transmigration until it becomes pure. Pythagoras believed that both mathematics and music could purify. Numbers have personalities, characteristics, strengths and weaknesses. The world depends upon the interaction of opposites, such as male and female, lightness and darkness, warm and cold, dry and moist, light and heavy, fast and slow. Certain symbols have a mystical significance. All members of the society should observe strict loyalty and secrecy. He never wrote anything down And he divides the life of man thus. A boy for twenty years ; a young man (neaniskos) for twenty years; a middle-aged man (neanias) for twenty years; an old man for twenty years. And these different ages correspond proportionably to the seasons: boyhood answers to spring; youth to summer; middle age to autumn; and old age to winter.
Sources:
Laertius, Diogeners. "Life of Pythagoras." The Lives and Opinions of Eminent Philosophers. N.p., n.d. Web. 18 Nov. 2012. <http://www.mlahanas.de/Greeks/LaertiosPythagoras.htm>.
Math Open Reference. "Biography of Pythagoras - Math Word Definition - Math Open Reference." Math Open Reference. N.p., 2009. Web. 18 Nov. 2012. <http://www.mathopenref.com/pythagoras.html>.
Pythagoreanism
4 Doctrines that became well known: 1. The soul is immortal
2. The soul transmigrates into other kinds of animals
3. That after certain intervals certain things that have already happened happen again, so that nothing is completely new
4. All Animate beings belong to the same family
Source: Huffman, Carl. "Pythagoras." (Stanford Encyclopedia of Philosophy). Stanford University, 23 Feb. 2005. Web. 18 Nov. 2012. <http://plato.stanford.edu/entries/pythagoras/>.
Daily Life of a Pythagorean Pythagoreans took morning walks alone and in such places where there was suitable calmness and stillness, and where there were temples and sacred groves and anything else that gladdened the heart. For they thought it necessary not to meet anyone until they set their own soul in order and were composed in their intellect; and such quietness is agreeable to the composure of the intellect. For to be shoved together in crowds immediately on arising hey considered disturbing. thus all Pythagoreans always selected places most becoming the sacred. And after the morning walk, they associated with one another, especially in temples; but if not, at least in similar places. They used this time for instruction and lessons, and for the improvement of their characters. After such study, they turned to the care of their bodies. Most used oil-rubs and took part in foot races; a less number wrestled in gardens and groves: some engaged in long jumping or in shadow boxing, taking care to choose exercises well adapted to their bodily strength.
For breakfast, Pythagoras prescribed, as part of his dietetics, honey and bread, and for supper bread made from millet or barley, cooked or raw vegetables, and on rare occasions meat from sacrificed animals, and even then not from every part of the animal. This is a reference to old Pythagorean rules that do not absolutely prohibit eating meat, but only the consumption of certain parts of the animal, such as the heart.
Pythagorean daily life also included moments of self reflection in the morning and in the evening. Most of all, he [Pythagoras] recommended two moments for thoughtful reflection: when one goes to sleep and when one wakes up. For in each
of these two moments it is fitting to think about what has already been done and what is yet to happen, each person accounting to him or herself for what has happened, but taking precautions for the future. Thus before sleeping everyone should sing himself these verses:
Also, do not receive sleep on you tender eyes, before you have thrice gone through each of the dayâ&#x20AC;&#x2122;s deeds: Where have I failed myself? What have I done? What duty have I not fulfilled?
Before getting up, sing these verses:
When you awaken from sleep, the honey to the hear, first watch you very carefully, what deeds you want to perform this day.
Above are excerpts from: Riedweg, Christoph. Pythagoras: His Life, Teaching, and Influence. Ithaca: Cornell UP, 2005. Print.
Number Philosophy According to Aristotle, Pythagoreans considered the whole of reality as numerical in its nature. Of numbers not only all bodily things consist, but also the musical fitting together and the whole heaven along with the stars that move in harmony. Also, concepts which we would consider as abstract, such as “insight”, the “whole” or “justice,” and even the gods they equated with numbers.
How did they arrive at this view? According to Aristotle, they discovered “resemblances” - between all things on one hand, and numbers, as well as what “happens in them” (in simple mathematical operation), on the other:
In numbers they seemed to see many resemblances to the things that exist and come into being - since, again, they saw that the modifications and the ratios of the musical scales were expressible in numbers, and they saw that all other things in the whole nature seemed to be modeled on numbers, so they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. And all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangement of the heavens, they collected and fitted in their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory make sense.
-They called the number five wedding, since a wedding is a coming together of a male and female, but in the Pythagoreans’ view, male is odd, while female is even; but this is the first number that originates from two, as the first even number, and three, the first odd number
-They called the number one “insight” and “essence”. Because of its constancy, its equality in every respect, and its ruling quality, they called insight unity and the number one essentiality which means basic importance. -They called the number two “opinion”, since it can change in both directions; but they also called it “movement” and “attack”
Drawing on writings from Aristotle, we can add two more things the Pythagoreans thought about certain numbers:
-They called three the number of the whole
-They thought ten was the perfect number, since it seems to comprise the whole nature of numbers
Above are excerpts from: Riedweg, Christoph. Pythagoras: His Life, Teaching, and Influence. Ithaca: Cornell UP, 2005. Print.
Equal Treatment of Women The Greeks considered Pythagoras the “father of philosophy.” He taught a system of natural science, mathematics, and ethics that profoundly influenced the Western canon. Ah, but who taught Pythagoras? A woman: Themistoclea. It is a curious fact that while the Greeks were hailing Pythagoras as the “father of philosophy,” they also recorded that he’d learned most of what he knew from Themistoclea, a priestess at Delphi.
"Pythagoras spoke captivatingly, and it is for this reason not to be wondered at that his orations brought about a change in the morals of Kroton's inhabitants; crowds of listeners streamed to him. Besides the youth who listened all day long to his teaching some 600 of the worthiest men of the city, matrons and maidens, came together at his evening entertainments; among them was the young, gifted and beautiful Theana, who thought it happiness to become the wife of the 60 year old teacher."
She and Pythagoras married although she was 36 years his junior. They had 5 children: three daughters (Damo, Myia and Arignote) and two sons (Mnesarchus and Telauges).
She taught mathematics in Samos and Croton and is said to be the author of the treatise on the Golden Mean, an important concept in mathematics. The 'Golden Mean' is found in nature and used in both art and architecture.
After Pythagoras' death she became the head of Pythagoras' school and, with the help of her daughters,(Damo, Myria and Arignote) all of whom were philosophers
and one of her sons, she continued the Pythagorean school of wisdom. She and her children not only kept the school and its doctrines alive, they were central to the spread of Pythagorean thought. Some would say that without the work of Theano after his death, Pythagoras's ideas and the Pythagorean Brotherhood would probably not have had as much influence in the ancient world around the Mediterranean.
It appears that Theano corresponded with Callisto on child psychology and the best way to bring up a family.
Some would say that it was the work of these Early Pythagorean women that perpetuated Pythagoreanism in the ancient world. So these women who were Early Pythagoreans were very important to our knowledge of the community and its doctrines.
What is of enormous interest for the history of philosophy is that we have many more extant texts by Early Pythagorean Women that we do men.
Source: Women-Philosophers.com. "Early Pythagoreans: Women Philosophers: Arignote, Damo, Myia, Theano I." Women Philosophers. Women-Philosophers.com, n.d. Web. 18 Nov. 2012. <http://www.women-philosophers.com/Early-Pythagoreans.html>.
Music and the Harmony of Spheres Pythagoras is famous for another discovery that still ensures him a place in every manual or dictionary of music history: the discovery that music has mathematical foundations, most notably that the perfect intervals of an octave, a fifth, and a fourth can be reduced to simple numerical relations. â&#x20AC;&#x153;Pythagoras discovered that the intervals in music also do not originate without numbers. Often, Pythagoras is considered at the same time also as the discoverer of the monochord, which is a straight rod or straight edge, on which a string was provided with a moveable bridge, and on which the mathematical relationships of musical intervals could be clearly demonstrated.
Once when Pythagoras was deep in thought about whether he could invent an aid for hearing similar to the circle, the straight edge, and the scale, he walked by a forge, where he heard by a divine chace hammers beating iron on an anvil, and making mixed sounds in full harmony with one another, except for one combination. He recognized in these the octave and the fifth and the fourth. Delighted that his project had the backing of the Gods, he rushed into the forge, and with varied tests he found that the difference of sounds was produced by the weights [sizes[ of the hammers, not by the force of the blows or by the shapes of the hammers or by the position of the iron being struck.
Above are excerpts from: Riedweg, Christoph. Pythagoras: His Life, Teaching, and Influence. Ithaca: Cornell UP, 2005. Print.
Transmigration
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Pythagoras believed in metempsychosis [transmigration of the soul] and thought that eating meat was an abominable thing, saying that the souls of all animals enter different animals after death. He himself used to say that he remembered being, in Trojan times, Euphorbus, Panthus' son, who was killed by Menelaus. They say that once when he was staying at Argos he saw a shield from the spoils of Troy nailed up, and bust into tears. When the Argives asked him the reason for his emotion, he said that he himself had borne that shield at Troy when he was Euphorbus. They did not believe him and judged him to be mad, but he said he would provide a true sign that it was indeed the case; on the inside of the shield there had been inscribed in archaic lettering EUPHORBUS. Because of the extraordinary nature of his claim they all urged that the shield be taken down - and it turned out that on the inside the inscription was found.
It is crucial to recognize that most Greeks followed Homer in believing that the soul was an insubstantial shade, which lived a shadowy existence in the underworld after death, an existence so bleak that Achilles famously asserts that he
would rather be the lowest mortal on earth than king of the dead (Homer, Odyssey XI. 489). Pythagoras' teachings that the soul was immortal, would have other physical incarnations and might have a good existence after death were striking innovations that must have had considerable appeal in comparison to the Homeric view. According to Dicaearchus, in addition to the immortality of the soul and reincarnation, Pythagoras believed that “after certain periods of time the things that have happened once happen again and nothing is absolutely new” (Porphyry, VP 19). This doctrine of “eternal recurrence” is also attested by Aristotle's pupil Eudemus (Fr. 88 Wehrli). The doctrine of transmigration thus seems to have been extended to include the idea that we and indeed the whole world will be reborn into lives that are exactly the same as those we are living and have already lived.
Sources: Source: "Pythagoras on the Transmigration of the Soul" is from Jonathan Barnes, Early Greek Philosophy (Baltimore, MD: Penguin Books 1969), p. 87, accessed from: http://web.jjay.cuny.edu/~mbstwck/pythagoras.htm
Huffman, Carl. "Pythagoras." (Stanford Encyclopedia of Philosophy). Stanford University, 23 Feb. 2005. Web. 18 Nov. 2012. <http://plato.stanford.edu/entries/pythagoras/>.
The Golden Ratio – Φ
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