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 side of the aristocrasy. Probably because of this, after a time the citizens turned against him and his followers, burning his house. Forced out, he moved to Metapontum, also in Southern Italy. Here he died at the ages of eighty. His school lived on, alternating between decline and re-emergence, for several hundred years.
Tradition holds that Pythagoras left no written works, but that his ideas were carried on by his eager disciples.
What is known of the Pythagorean school is from a book written by the Pythagorean, Philolaus of Tarentum. From this book Plato learned the philosophy of Pythagoras.
The dictum of the Pythagorean school was All is number.
What this meant was that all things of the universe had a numerical attribute that uniquely described them. For example,
Classification of numbers. The distinction between even and odd numbers certainly dates to Pythagoras. From Philolaus, we learn that
"...number is of two special kinds, odd and even, with a third, even-odd, arising from a mixture of the two; and of each kind there are many forms."And these, even and odd, correspond to the usual definitions. But even-odd means a product of an even and odd number. Note: orginally the number 2 was not considered even.
Prime or incomposite numbers and secondary or composite numbers are defined in Philolaus:
Proposition. There are an infinite number of primes.
Proof. (Euclid) Suppose that there exist only finitely many primes . Let . The integer N-1, being a product of primes, has a prime divisor in common with N; so, divides N- (N-1) =1, which is absurd!
The search for primes goes on. Eratsothenes (276 B.C. - 197 B.C.), who worked in Alexandria, devised a seive for determining primes. This seive is based on a simple concept:
Lay off all the numbers, then mark of all the multiples of 2, then 3, then 5, and so on. A prime is determined when a number is not marked out. So, 3 is uncovered after the multiples of two are marked out; 5 is uncovered after the multiples of two and three are marked out.
The Primal Challenge
The sea