Koan 59

How do you square a circle?


You don’t.

With only a compass and a straightedge (the tools of classical geometry), it’s impossible to square a circle (to construct a square with the same area as a given circle) due to the transcendental mathematical constant π (pi). That is, the space inside a circle is the the product of multiplying the diameter of the circle times pi. As pi is a transcendental number (an infinite, non-repeating decimal expansion), the space inside a circle is imprecise. The space inside a square is precise. Thus, as an imprecise space cannot precisely fill a precise space, one can never square a circle.

Transcendental numbers arise naturally in exponential growth and decay processes and are used extensively in calculus, probability, and mathematical analysis. Transcendental is also the nature of the universe; infinite (eternal) and everchanging.

Like trying to square a circle, the mind cannot precisely grasp or contain the entire universe. The mind, like a square, views things with words and thoughts that describe a universe as linear, logical and finite. Yet, the universe, like the space in a circle, is transcendental; infinite and everchanging.

While our eyes tell us that the space inside a circle must be a precise measure; in reality, the precise space will never be known precisely.