22 Apr 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 circumference of a circle (the space inside) 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 ever square a circle.

Transcendental numbers arise naturally in exponential growth and decay processes and are used extensively in calculus, probability, and mathematical analysis. Transcendental (meaning, spiritual) numbers also reveal the nature of the nonphysical/non-now nature of he universe; it is infinite (eternal) and everchanging, however unnoticeably.

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 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.