Pythagoras: A Universe Made of Numbers

Pythagoras:

A Universe made of Numbers

PART 1 Ð'- Pythagoras & His Philosophy

Pythagoras of Samos is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet there is relatively little known about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, there is nothing of Pythagoras's writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today Pythagoras is a mysterious figure. This does not mean that we cannot gain some incite on who he was or what he taught or believed, because there are details of Pythagoras's life from early biographies which use important original sources. Yet these biographies are written by authors who attribute divine powers to him, and whose aim was to present him as a god-like figure. What will be presented in the rest of this paper is an attempt to collect together the most reliable sources to reconstruct an account of Pythagoras's meta-physic, epistemology, and ethics, but first, in order to understand Pythagoras more fully, a brief journey into his life will be dealt with first.

Pythagoras was born in 580 B.C. to a more than wealthy family. He received the finest formal education in gymnastics, music, mathematics, and natural sciences and was taught to think and see the world as a scientist. He traveled widely, from Egypt, to the Mediterranean, and most of Asia, where he learned culture customs, geometry, and astronomy. His traveling experiences, observation, and questions and ideas are probably the ferment of Pythagoras's philosophy.

At the age of fifty, Pythagoras moved to Italy and set up a school of antiquity. Over the gate of the Academy, a sign read: "Only mathematicians enter here" Members of this school took up strict rules in learning mathematics, science, music, the arts, and vocations in the care of the home and family. Pythagoras stressed solidarity, education of the mind, health and worship of Apollo, as well as the practice of divination. The main belief was that all can identify with the One and attune themselves to the cosmic rhythm.

Pythagoras was over all the community as chief philosopher and his followers were convinced that he performed miracles and magic. This school was eventually destroyed and the students, Pythagoras included, had to flee due to the fact that the city's people thought them to be a cultic group and a threat. The community lasted about a century and then vanished from history, with all its writings and doctrines.

The Basic meta-physic for Pythagoras was that everything has its own vibration and the entire universe is a matter-in-motion, a mathematic structure. Aristotle says that Pythagoreanism, as known in his day, is characterized by the view that the principles of mathematics are the principles of all things. Aristotle writes,

Contemporaneously with these philosophers and before them, the so-called Pythagoreans, who were the first to take up mathematics, not only advanced this study, but also having been brought up in it they thought its principles were the principles of all things. Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into beingÐ'--more than in fire and earth and water (such and such a modification of numbers being justice, another being soul and reason, another being opportunityÐ'--and similarly almost all other things being numerically expressible); since, again, they saw that the modifications and the ratios of the musical scales were expressible in numbers;Ð'--since, then, all other things seemed in their whole nature to be modeled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.

The Pythagoreans hold that the principles of mathematics are the principles of all things; in other words, the basic structure of Being is mathematical. Everything somehow can be explained in mathematical terms. It is the archas, or principle, of mathematics that make things what they are, that give to everything its distinctiveness. To use later terminology, it seems that the Pythagoreans view the principles of mathematics as providing structure or form to Being. Even though they are immaterial, the principles of mathematics, nevertheless, are more "real," as it were, than that to which they give structure or form: that which is an archÐ"Є is more real in the sense that without it other things would not be what they are; their greater reality consists in their logical priority.

In the above quotation, Aristotle adds that the Pythagoreans hold that in fact it is the elements of numbers that are the elements of all things; this makes their teaching more difficult to understand. It seems they reasoned that, since numbers were by nature "first" with respect to mathematicsÐ'--in other words, since mathematics is impossible without numbersÐ'--everything must somehow be numbers. Aristotle explains how impressed the Pythagoreans were to discover that musical scales could be expressed as ratios (using numbers); from this discovery they may have sought to ascribe numbers to all things. Indeed, they conclude that the whole heaven to be a musical scale and a number. This part of Pythagoreanism has perplexed scholars, however, since it is not obvious how numbers resemble things that come into being, including abstract ideas.

When it comes to Pythagoras's epistemology, Pythagoras suggested that matter and mind are mystically connected. Logic, numbers, spirit, and soul were expressions of the same reality. He thought the soul to be immortal and wandering on a path of transmigration from one body to another. This Pythagorean thought had a geometrical conception of the world. They believed that the mind is attuned to the processes of nature, in particular to the laws of mathematics. Mathematics is seen as the true essence of mind. Pythagorean thinking was of the very essence of applied mathematics that is found in the history of science. It was because number theory and its application to arithmetic and geometry were clear and exciting that empirical observation took shape that is now called science.

Pythagoras's ethics and virtues are that he believed that human beings are composed of a body and a soul, that the soul is immortal and that souls transmigrate upon the death of the body. At its deepest level, reality is

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