Daily Linz 16 - Fundamental Stuff 4
by Lindsay Perigo
Last week we left Heraclitus and Parmenides slugging it out over whether you could step into the same river twice. Heraclitus was in the “It’s the changing, Stoopid—everything changes, nothing abides” corner, Parmenides in the “It’s the One, Stoopid—nothing changes, everything is One” corner. This week, we must back up a bit and take note of another contestant, contemporary with Heraclitus, whose significance was to lie in his influence on a participant who wouldn’t step into the ring for another hundred years or so. Herclitus and Parmenides, as previously noted, were part of a new tradition, the abandonment of revelation and the independent exercise of one’s mind. But the old tradition was still very much alive. Pythagoras (flourished in southern Italy, 525-500 B.C.) was a part of that tradition, a fact that profoundly influenced his own contribution to the “fundamental stuff” debate that was to have a decisive influence on Plato. Pythagoras took the view that everything is reducible to numbers, and pointed to empirical phenomena to make his case. Given his straddling of the new tradition and the old, he is described, hilariously, by Bertrand Russell as “a combination of Einstein and Mrs. Eddy” (meaning Mary Baker Eddy, the founder of Christian Science). He is credited, incidentally, with the coining of the terms philosophy and cosmos.
Pythagoras founded a religion of his own, an offshoot of an offshoot of Dionysus-worship, which had had a strong influence on his early life. Worshippers were organised into small secret societies devoted to cleansing the soul and earning immortality in the most interesting of ways. There would be frenzied singing and dancing, and at the height of their frenzy worshippers would tear apart animals in whom they believed Dionysus resided and drink their blood, thus partaking of the spirit of their god. Attendees at SOLO Conferences will recognise the excellent Dionysian influence on the goings-on there. With Pythagoras, however, things took a turn for the worse. While he displayed commendably prescient concern about greenhouse gasses in forbidding the eating of beans, he also banned meat.
Pythagoras believed the type of purification his predecessors gained from frenzy could best be attained by the study of mathematics. Why? Well, for Pythagoras, as for Marty Lewinter, mathematical thought was quite simply the most pure activity possible.
How did he make that out? Well, Pythagoras reckoned there were distinct qualities of lives (and souls) embodied in the three different categories of people who attended the Olympic Games. The lowest souls belonged to those who went to sell their wares—the hot dog vendors if you like, out to make a buck. On the next rung up were those who competed. They were after the honour and glory of victory, which was not ideal, but better than worship of the mighty drachma. The highest type of attendee was the spectator. He looked on and analysed disinterestedly, uncorrupted by the fray (how or whether he was supposed to do so without purchasing the lowly nourishment offered by the dregs is not clear).
Now, a mathematician, according to Pythagoras, is like the spectator—his thought is liberated from mundane particulars and focused on the permanent world of numbers. His ultimate triumph in this liberation is being set free from the wheel of birth, where his soul is released from the process of endless transmigration and returns home to God. (There is a story that Pythagoras stopped a man beating his dog because he recognised in the dog's whelps the voice of a deceased friend.)
Numbers were the basic stuff, and to contemplate them was the way of salvation.
Numbers were everywhere. In music, for instance. The intervals between notes were expressed numerically. A string making a sound an octave—eight intervals—lower than another was twice as long. Harmony was a matter of numerical ratio.
Numbers were in medicine. Medcine required having striking the right numerical balance of elements and functions in the human body. The body was like a musical instrument, needing to be properly tuned—disease was the result of failure to do so.
Pythagoras and his followers used pebbles to count. Number one was a single pebble—all other numbers were created by the addition of pebbles.
They established the relationship between arithmetic and geometry. This relationship was a function of the connection between number and magnitude—numbers were manifest in figures, such as a triangle, rectangle, square, etc.. Shape and size, it’s all a matter of numbers and their relationships. “Squaring” and “cubing” of numbers? That’s Pythagoras. As every schoolboy learns, Pythagoras is credited with the famous theorem that the square of the hypotenuse is equal to the squares on the other two sides of a right-angled triangle.
They distinguished between odd and even numbers, and explained the differences among phenomena by reference to their odd-even combination. One and many, square and oblong, straight and curved, rest and motion, light and dark, male and female, good and evil—all could be explained by their odd/even permutation.
Numbers were the means by which form was imposed on matter. It was all very well for the Milesians to talk about fundamental stuff, said the Pythagoreans, but look at the strife they got into trying to explain how things could be differentiated from the stuff! Form, said the Pythagoreans, required limits, and limits could only be imposed and expressed numerically.
Bertrand Russell rates Pythagoras as “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, and in him is intimately connected with a peculiar form of mysticism. The influence of mathematics on philosophy, partly owing to him, has, ever since his time, been both profound and unfortunate.”
As Objectivists, we should hold the thought that Pythagoras’ doctrines were to resurface in Plato—to devastating effect. While there is no denying his groundbreaking, fruitful brilliance, the fact that his discoveries were steeped in mysticism set the scene for Plato’s full-on rationalism and intrinsicism, with everything that implied for the future of Western thought and civilisation.
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