Pythagoras; know about pythagoras

PYTHAGORAS (582 -507 BC)

Understanding the world through mathematics was at the heart of Pythagoras’ mission life. Like Thales, Pythagoras is rather known for mathematics than philosophy. Anyone who recall mathematics classes will remember that the first lesson of plane geometry usually start with Pythagorean Theorem about right angle triangle a²+b²=c². In spite of this name the Pythagorean Theorem was not discovered by Pythagoras. The earliest know formulation theorem was down the Indian mathematician Baudhayana in 800Bc. The principle was also known to the earlier Egyptians and Babylonian master builders. However, Pythagoras may have proved the theorem and popularized it in the Greek world. With it, his name and philosophy have survived the turbulence of history.

His immediate followers were strongly influenced by him, even until today, Pythagoras shined through the midst of ages as one of the brightest figures of early Greek antiquity. The Pythagorean Theorem is often cited as the beginning of mathematics in western culture, and ever since mathematics -the act of demonstration and deductive reasoning- has had a profound influence ion western philosophy, which can be observed down to Russell and Wittgenstein.

Pythagoras’ influence found an expression in visual art and music as well, particularly in the renaissance and baroque epoch. The far reaching imprint of his idea is yet more impressive if we consider that he did not leave any original writings. Instead, all what is known about Pythagoras was handed down by generations of philosophers and historiographers, some of whom, like Heraclitus, opposed his views. In this light it is remarkable that Pythagoras’ teachings have survived relatively undistorted until the present day.

Pythagoras was a native of the island of Samos. During his early life, Samos was governed by the powerful, unscrupulous tyrant Polycrates. Pythagoras did not sympathise with his government and thus emigrated to Croton in Southern Italy. Like the ancient Greek cities in Lonia, Croton was a flourishing commercial city that lived from importing and exporting goods. Obviously, it was in Croton where Pythagoras developed most of his important ideas and theories.

After Pythagoras introduced the idea of eternal reoccurrence into Greek thought, which was apparently motivated by the studies of earlier Egyptians scriptures, the idea soon became popular in Greece. It was Pythagoras’ ambition to reveal in his philosophy the validity and structure of a higher order, the basis of divine, for which soul return in a constant circle.

This is how Pythagoras came to mathematics. It could be said that Pythagoras saw and study mathematics as purifier of the soul, just like he considered music as purifying. Pythagoras and his disciples connected music with mathematics and found that intervals between notes can be expressed in numerical terms. They discovered that length of spring of a musical instrument corresponds to those intervals and they can be expressed in numbers. The ratio of the length of two strings with which two tones of an octave step are produced.

Music was not the only field Pythagoras considered worthy of study; in fact he saw numbers in everything. He was convinced that everything that the divine principles of the universe, though imperceptible to the senses, can be expressed in terms of relationship of numbers. He therefore reasoned that the secrets of the cosmos are revealed by pure thought, through deduction and analytic reflection on the perceptible world.

The Egyptians had known that triangle whose sides are 3, 4 and 5 had a right angle, but apparently the Greeks were the first to observed that 3²+4²=5², and acting on this suggestion, to discover a proof of the general proposition. Unfortunately for Pythagoras this theorem led at once to the discovery of incommensurable, which appeared to disapprove the whole philosophy. In a right angled isosceles triangle, the square on the hypotenuse is double of the square on either side.

From Pythagoras we observe that an answer to a problem in science may give rise to new questions. For each door we open, we find another closed door behind it. Eventually these doors will be also be opened and reveal answers in a new dimension of thought. A sprawling tree of progressively complex knowledge evolves in such manner. This Hegelian recursion, which is in fact a characteristic of scientific thought, may or may not have been obvious to Pythagoras. In either way he stands at the beginning of it.

By Osalumese.

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