A CLOSING STATEMENT ON PYTHAGORAS

So, what about Pythagoras’ legacy to the world and to our Western Civilization in particular, in a nutshell? Our already much quoted friend W. T. Jones deserves to be quoted again on this subject.

They said that justice is four, marriage is seven, and so on. This is, of course, nonsense, but even when the Greeks talked nonsense, it was on so grand a scale as to contain ideas which future generations could work with profit. So it is with this Pythagorean notion of there being number at the heart of the universe.

Pythagoreanism and Atomism complement each other in a remarkable way.-- Pythagoreanism conceived of a world which, when measured, shows simple mathematical relationships, but it never thought through its way to a world which is capable of being measured. The Atomists conceived of a world reduced to spatial and temporal relations of particles, which is in essence measurable, but they never conceived the utility of measuring those relations, and so discovering the mathematical relationships which obtain. If we combine Pythagorean mathematics and measurement with the Atomists’ (physics), we have the conception, whence modern physical theory began its great career.

Another great, perhaps, even greater idea, and one whose conclusions the Pythagoreans did work out, was the idea of cosmos, the notion of the universe as being not a chaotic hodgepodge, but a thoroughly ordered system, where every element is harmoniously related to every other. How could science with its techniques of experimentation and measurement ever have made a beginning without the Pythagorean conviction that the universe constitutes a cosmos pervaded by a single intelligible order?

In addition to this, I can remind the reader to revisit the opinion of Bertrand Russell, who said, as I repeat, that “Pythagoras was intellectually one of the most important men who ever lived, both when he was wise, and when he was unwise. Mathematics, in the sense of demonstrative deductive argument begins with him, and in him is intimately connected with a peculiar form of mysticism.” And also this: “I don’t know of any other man who has been as influential as he was in the sphere of thought. I say this because what appears as Platonism, is, when analyzed, found to be in essence Pythagoreanism.”

And then, of course, we can remember the astronomers--- Copernicus, whose greatest discovery was influenced by Pythagorean ideas, and Galileo Galilei, who was also a mathematician and a physicist of genius, whose discoveries in several fields of scientific endeavor are astonishing. He was a Pythagorean in his philosophy, and to him belongs the dictum about the “Book of Nature being written in mathematical characters.”

So, once again, and to wind this up, Vivat Pythagoras!