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Thursday, 13 May 2010


In 6th century BC, Island of Samos was a commercial rival to Miletus. Polycrates became the tyrant of Samos in around 535 BC. Polycrates was not a man with moral scruples. Since the rival Miletus was destroyed by Persia, Polycrates used his navy primarily for Piracy. To stop the westward expansion of Cambyses, the Persian King, Polycrates aligned himself with Amasis, the king of Egypt. When Cambyses devoted all his energy against Amasis, Polycrates realized that he was part of losing side. Such an unscrupulous man he was, he sent his navy against Egypt. The Navy mutinied and returned to attack Polycrates but mutiny was suppressed. Eventually his avarice got rid of him. He was captured at the Persian Satrap at Sardes and was executed. Despite all his covetousness he was a patron of art and learning. He modernized Samos with public works.

Pythagoras was a citizen of Samos during the time of Polycrates. Pythagoras did not like Polycrates and might have left to Egypt where it is supposed that he learned Egyptian wisdom. But what is certain that Pythagoras established himself at Croton, an important city in southern Italy. At Croton Pythagoras founded a society of disciples, which was influential in the city but eventually the citizen turned against him and he had to move to another southern Italian city of Metapontion, where he died.

Pythagoras is the one of the most interesting and puzzling men in history. He founded a religion whose main tenet was transmigration of soul. He advocated the control of state by religion and rules of saints. Some taboo from Pythagorean religion are listed below:

1) Not to eat from beans
2) Not to pick up what has fallen
3) Not to touch a white cock
4) Not to break bread
5) Not to step over a crossbar
6) Not to stir the fine with iron
7) Not to eat with whole loaf
8) Not to pluck a garland
9) Not to sit on a quart measure
10) Not to eat the heart
11) Not to walk on highway
12) Not to let swallows share one’s roof
13) When the pot is taken of the fire, not to leave the mark of it in the ashes, but to stir them together
14) Do not look in the mirror beside a light
15) When you rise from the bedclothes, roll them together and smooth out the impression of body

Cornford in his book “From Religion to Philosophy” says that
The school of Pythagoras represents the main current of that mystical tradition which we have set in contrast with the scientific tendency”

Conford regards Parmenides, whom he calls “the discoverer of Logic” as “an off shoot of Pythagoreanism”. Pyathgoreanism was a movement to reform Orphism as Orphism was a movement to reform the worship of Dionysus.

Pythagoras believed that the soul is immortal and is transmigrated from one being to another . In a Pythagorean society men and women were admitted on equal terms, property was held in common and there was a common way of life, even the scientific and mathematical discoveries were deemed collective.

When Pythagoras said “all things are numbers”, what he might have intended is that the numbers are there in all aspects of life. He discovered numbers in music, shape, size, everywhere. He presumably thought world as atomic and of bodies as built up of molecules composed of atoms in various shapes. The greatest discovery of Pythagoras was that the sum of square sides of a right angled triangle is equal to the square of hypotenuse (3^2 + 4^2 = 5^2). But unfortunately this led to the discovery of incommensurable. For e.g. in an isosceles right angled triangle of sides 1 inch each let the length of hypotenuse be m/n where there is no common factor between m & n. That means one of them is odd and one even. But m^2/n^2 = 2 or m^2 = 2 n^2. This shows that neither m can be odd or n can be odd. So no fraction m/n will measure hypotenuse. This is a contra hypothesis. But with the help of geometry Euclid explained this proposition of incommensurable. This convinced the Greek mathematicians that geometry must be established independent of Mathematics and geometry remained superior to mathematics till the time of Rene Descartes. 

The influence of geometry upon philosophy and scientific method has been profound. Geometry starts with axioms which are self evident, and proceeds by deductive reasoning, to arrive at theorems that are very far from self evident. It thus appeared to be possible to discover things about the actual world by first noticing what is self evident, and then using deductive reasoning to prove complex phenomena. Theology, in its exact scholastic forms, takes it style from this source. The combination of mathematics and theology which began with Pythagoras characterized religious philosophy in Greece, in middle ages, and in modern time to Kant.

1 comment:

Anonymous said...

I did not understand the m/n funda. First of all, let one side by 3 and other be 5. so both are odd arent they? If isoscales, m = n and th expression is meaningless.

Kindly let me know what am I missing here.

- Bhaiyyu