The Mathematics of Beauty > Point

Pythagorean Number Symbolism

Aristotle is perhaps the main source of information about the Pythagoreans. In his Metaphysica, he sums up the Pythagoreans' attitude toward numbers. "The [Pythagoreans were] . . . the first to take up mathematics . . . [and] thought its principles were the principles of all things. Since, of these principles, numbers . . . are the first, . . . in numbers they seemed to see many resemblances to the things that exist . . . more than [just] air, fire and earth and water. [but things such as] justice, soul, reason, opportunity . . ."

The Pythagoreans did not recognize all the numbers we use today; they recognized only the positive whole numbers. Zero, negative numbers, and irrational numbers didn't exist in their system. Moreover, the Pythagoreans' idea of a number was different from the quantitative one we have today. Now we use a number to indicate a quantity, amount, or magnitude of something, but for the Pythagoreans, each number had its own particular attribute. For example, the number one, or unity, which they called the monad, was seen as the source of all numbers. "Unity is the principle of all things and the most dominant of all that is: All things emanate from it and it emanates from nothing. It is indivisible and . . . it is immutable and never departs from its own nature through multiplication (1 x 1 = 1). Everything that is intelligible and not yet created exists in it . . ."

The number two, the dyad, represented by duality, subject and object. The Pythagoreans believed the world to be composed of pars of opposites, as given by Aristotle in this famous table:

With three, the triad, that dualism was resolved. The two extremes were united, giving Harmonia. This idea of reconciliation of opposites will appear again in the discussions of the golden mean.