Pythagoras and the Pythagoreans
Historically, Pythagoras means much more that the familiar theorem about right triangles. The philosophy of Pythagoras and his school has impacted the very fiber of mathematics and physics, even the western tradition of liberal education no matter what the discipline.
Pythagorean philosophy was the prime source of inspiration for Plato and Aristotle; the influence of these philosophers is without question and is immeasurable.
Pythagoras and the Pythagoreans
Little is known of his life. Pythagoras (fl 580-500, BC) was born in Samos on the western coast of what is now Turkey. He was reportedly the son of a substantial citizen, Mnesarchos. There he lived for many years under the rule of the tyrant Polycrates, who had a tendency to switch alliances in times of conflict -- which were frequent.
He met Thales, likely as a young man, who recommended he travel to Egypt. It seems certain that he gained much of his knowledge from the Egyptians, as had Thales before him.
Probably because of continual conflicts and strife in Samos, Pythagoras settled in Croton, on the eastern coast of Italy, a place of relative peace and safety.
Even so, just as he arrived, Croton lost a war to neighboring city Locri, but soon thereafter defeated utterly the luxurious city of Sybaris.
This is where Pythagoras began his society.
The Pythagorean School
The school of Pythagoras was every bit as much a religion as a school of mathematics. For example, here are some of the rules:
Vegetarianism was strictly practiced probably because Pythagoras preached the transmigration of souls.
The school of Pythagoras represents the mystic tradition in contrast with the scientific!!
Indeed, Pythagoras regarded himself as a mystic and even semi-divine. Said Pythagoras
"There are men, gods, and men like Pythagoras."
It is likely that Pythagoras was a charasmatic.
Life in the Pythagorean society was more-or-less egalitarian.
The Pythagorean Philosophy
The basis of the Pythagorean philosophy is simply stated:
"There are three kinds of men and three sorts of people that attend the Olympic Games. The lowest class is made up of those who come to buy and sell, the next above them are those who compete. Best of all, however, are those who come simply to look on. The greatest purification of all is, therefore, disinterested science, and it is the man who devotes himself to that, the true philosopher, who has most effectually released himself from the 'wheel of birth.'"
The message of this passage is radically in conflict with modern values. We need only consider sports and politics.
Is not reverence these days is bestowed only on the ``super-stars"?
Are not there ubiquitous demands for accountability!!
The Pythagorean Philosophy
The gentleman, of this passage, has had a long run with this philosophy, because he was associated with the Greek genius, because the ``virtue of comtemplation" acquired theological endorsement, and because the ideal of disinterested truth dignified the academic life.
The Pythagorean Philosophy ála Bertrand Russell
From Bertrand Russell, we have
"It is to this gentleman that we owe pure mathematics. The comtemplative ideal -- since it led to pure mathematics -- was the source of a useful activity. This increased it's prestige and gave it a success in theology, in ethics, and in philosophy."
Mathematics, so honored, became the model for other sciences. Thought became superior to the senses; intuition became superior to observation.
The combination of mathematics and theology began with Pythagoras. It characterized the religious philosophy in Greece, in the Middle ages, and down through Kant. In Plato, Aquinas, Descartes, Spinoza and Kant there is a blending of religion and reason, of moral aspiration with logical admiration of what is timeless.
Platonism was essentially Pythagorean ism. The whole concept of an eternal world revealed to intellect but not to the senses can be attributed from the teachings of Pythagoras.
The Pythagorean School gained considerable influence in Croton and became politically active -- on the sid