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Pythagoras and the Music of the Spheres

Pythagoras of Samos, c569 - c475BC: music of the spheres

Pythagoras of Samos (569-475 BC), artist unknown

 

 

 

Our particular perspective of the universe—our western cosmology—can be traced back at least to Pythagoras of Samos (c.569 – c.475 BC). Although early authors attributed divine powers to him and treated him like a god, none of Pythagoras’ writings remain. His relevance to this book is that his model of the universe and his teachings have infused our culture for over 2000 years.

In about 535 BC Pythagoras went to Egypt to study. But unlike many of his contemporaries who also studied in what was then the greatest center of learning in the world, he sought and was admitted to the Egyptian priesthood. Ten years later Persia invaded Egypt and Pythagoras was taken to Babylon as a prisoner. (The theorem now known as the Pythagorean theorem was known to the Babylonians 1000 years before Pythagoras, but he may have been the first one to prove it.) From there he mysteriously gained his freedom and returned to Samos around 520 BC. His own city didn’t care for the symbolic method of teaching Pythagoras had learned in Egypt, and after a few years he left to found a popular philosophical and religious school in southern Italy. The inner circle of his followers there was called the mathematikoi. Living permanently within the society, the mathematikoi were taught by Pythagoras himself, were vegetarians, and had no personal possessions. Pythagoras believed in and taught metempsychosis, or reincarnation, and it was said that he remembered four of his previous lives in detail.

The Pythagoreans adored numbers. They thought that the essential qualities of man and nature—reason, masculinity, femininity, justice and marriage—had objective representations in whole numbers or in relationships between whole numbers (the latter of which we call fractions or rational numbers today). The Pythagoreans literally had a "rational" view of the universe: all things were understandable through the properties of whole numbers and their fractions. Not only was everything for them composed of numbers; but they also believed that the explanation of an object’s existence could only be found in numbers.

Initially 0, negative numbers, and numbers like √2 and π that cannot be expressed as fractions didn’t exist for them. They discovered, however, that the diagonal of a square with sides 1 unit long can never be represented by a fraction of whole numbers. Therefore its length, which we now call √2, is "irrational." This discovery was fundamentally unsettling to the Pythagoreans. The √2 was a number that could not be formed from the building blocks or essences of the world. Thus the world itself must be made of things that make no sense and are irrational. So threatening was the discovery of this first irrational number to the Pythagoreans that they kept its existence a secret. When one of their members told some outsiders about it, they drowned him in a lake. To continue with Pythagoras and the five regular solids, click here.

This Pythagoras-Music of the Spheres page and much of this 550-page website are excerpted from the personalized Fine Art Book You and the Universe.

 

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© Carl Woebcke: Pythagoras and the Music of the Spheres, 1991-2014. All rights reserved.