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Pythagoras: Numbers
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Pythagoras believed the mystery of the universe revealed itself in numbers, to which he ascribed qualities like maleness (odd numbers) and femaleness (even numbers). He discovered that strings in a 2:1 radio vibrate an octave apart, while those in a 3:2 ratio produce a musical fifth, etc. In Pythagoras's cosmology, the solar system revolved around a "central fire." In the third century B.C., the Phythagorean astronomer Aristarchus put the earth and planets revolving around the sun, 1800 years earlier than Copernicus. But while Plato embraced Phythagorian concepts, Aristotle rejected mathematics as the means of explaining the true nature of the world and modern physicists have charged him with holding back physics for 2000 years.
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Pythagoras is known as one of the world's first pure mathematicians. He is ... considered one of the founding fathers of Geometry and was the inventor of the Pythagorean Theroem. Pythagoras believed that all relations could be reduced to number relations.
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It is believed that Pythagoras (or at least the Pythagoreans since they had a habit of attributing all their discoveries to Pythagoras) ... developed several of the figurate numbers: numbers derived from arranging dots is regular patterns. For example, the square numbers n2, are the numbers of dots that can be arrange in a square. are the number that can be arrange in a triangle where each row of the triangle has one more dot than the previous row. The nth triangular number is n(n+1)/2.
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Pythagoras did a great deal work in astronomy. His most important belief was the belief that the earth was in motion. Sadly, he failed to prove that all parts of the universe could be expressed in terms of whole numbers. But this attempt helped the development of math and science.
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Pythagoras held that reality, including music and astronomy, was at its deepest level, mathematical in nature, numbers were the ultimate reality. He was the first to point out the Evening Star and the Morning Star, which we now know to be the planet Venus, were the same, and he was the first one to articulate that the earth was a globe that moved around a central fire. (2)
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Music was not the only field that Pythagoras considered worthy of study, in fact he saw numbers in everything. He was convinced that the divine principles of the universe, though imperceptible to the senses, can be expressed in terms of relationships 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.
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