Pythagoras’ Table of Opposites

On March 14 (aka Pi Day, aka International Day of Mathematics, aka Save a Spider Day), the New York Times reposted a 2012 piece about infinity by Natalie Angier (originally published on New Years’ Eve, aka Leap Second Time Adjustment Day, aka Make Up Your Mind Day). For obvious reasons, I thought the essay might be of interest to readers of this blog. It doesn’t delve particularly deeply into any one facet of infinity, but offers a nice overview of some views of the infinite through history.

One thing to which I was introduced by Angier’s piece is Pythagoras’ Table of Opposites, which collects ten pairs of contrasting qualities, placing those viewed positively by the Pythagoreans on the left and those viewed negatively on the right (which is sort of ironic given the fourth pair of opposites in the table below). Here is a (translation of) a version of the Pythagorean Table of Opposites found in work of Aristotle:

Finite	Infinite
Odd	Even
One	Many
Right	Left
Male	Female
Rest	Motion
Straight	Curved
Light	Darkness
Good	Evil
Square	Oblong

I’m not going to write too much about this, as I’m certainly not an expert in ancient Greek philosophy, but let me just make a few observations:

• It’s no surprise that “infinite” was placed on the negative side of the table, given the Pythagoreans’ antipathy to irrational numbers and the accompanying infinities. We have written previously about mathematicians’ growing acceptance of infinity, especially in the last 150 years, though there are still a few mathematicians who would rather do away with the concept of infinity in mathematics.
• The pairs “One/Many” and “Rest/Motion” play central roles in the paradoxes of Zeno of Elea, covered in this previous post.
• The association of “right” with “good” and “left” with “bad” is certainly not unique to the ancient Greeks, showing up in a number of other societies throughout the world. It even persists in slightly hidden form in modern etymology: the Latin word for “right” is “dexter”, from which the English words “dextrous” and “dexterity” derive, while the Latin word for “left” is “sinister”, from which, naturally, the English word “sinister” derives. For a deeper and more rigorous account of “left” and “right” and other pairs of opposites in ancient Greek philosophy, see G.E.R. Lloyd’s paper, “Right and Left in Greek Philosophy”.

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Cover Image: “PH-929” by Clyfford Still

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