homestudio - revue audiolab

The Circle and the Square
and the Square Root of Two

THE SQUARED CIRCLE

Anyone who while standing in a city street has looked up at the dome of the sky will recognise this figure as being the distillation of a fundamental condition of human life. On the one hand order, sometimes man-made, sometimes natural, and on the other hand boundless encircling space. On the one hand things as they appear to be, and on the other a space of unlimited possibility.

Circle
Sky
Heaven
Infinite
Non-manifest Essence
Interior Cause
All-Encompasing
Centre
Square
Earth
Earth
Finite
Manifest Things
Exterior Effect
Things Encompased
Four Directions

Those who drew the squared circle and who investigated its geometrical relationships found that the diagonal of the square seemed to have some importance as is shown in the following figure:

When early geometers came to try to understand mathematically the proportional relationship between the side of a square and its diagonal, they found that there was no straightforward way. Cut and divide as many times as you like, there can be no numerical relationship between the two. Today our system of numbers is able to describe the relationship as 1:1.414...(etc., a decimal without end...), but the two sides of the relationship remain incommensurable. We refer to the relationship as "irrational", not meaning "without reason", but "without numerical ratio".

Because the irrational relationship between the square and its diagonal seems to give a glimpse of a kind of order which is not resultant from (or dependent on) manifest number, but appears to indicate a"meta-physical" cause, it has in the past been held by architects and artists to have special significance.
Its appearance in the underlying geometry of the Squared Circle echoes or symbolises the "dialogue" between the Heavens and the Earth, the Infinite and the Finite.

Summary

Musica Mundana , the Music of the Spheres, the exquisite and rarified interior sound of the Cosmos, is reflected in the harmonious relationships of certain sounds and geometrical forms within the space of our universe....
The relationship between the side and diagonal of a square is not of this same order, but nevertheless fulfills the same function as a symbol (analogous to the squared circle) of the harmonious relationship between Form and Essence, Finite and Infinite.

Selected Reading:
Leon Battista ALBERTI, The Ten Books of Architecture, 1775 Leoni Edt. (Dover)
Andrea PALLADIO, The Four Books of Architecture (Dover)
Keith CRITCHLOW, Order in Space, 1979
PLAT0, The Timaeus
Rudolf WITTKOVER, Architectural Principals in the Age of Humanism 1949/1988

Anyone who while standing in a city street has looked up at the dome of the sky will recognise this figure as being the distillation of a fundamental condition of human life. On the one hand order, sometimes man-made, sometimes natural, and on the other hand boundless encircling space. On the one hand things as they appear to be, and on the other a space of unlimited possibility.
Circle Sky Heaven Infinite Non-manifest Essence Interior Cause All-Encompasing Centre	Square Earth Earth Finite Manifest Things Exterior Effect Things Encompased Four Directions