In Western cultures, our architectural instinct surfaced in the Pythagoreans and became central, revealing that the soul, which took on various material shapes, was ultimately form.  Studying form was thus the true purification.

Sanctuary is a primary human requirement.  The shape, form and geometry of a building carry a unique signal; a force field of electromagnetic energy, which invokes an unconscious response.  Certain shapes signal us to approach, while others suppress their signals so that we do not enter their realms.  Circles and domes protect within their circumference, while crosses, squares, four-multiples, and spiral shapes extend and suppress over wide distances, creating the most favorable conditions for protection.

“There are no unsacred places; there are only sacred places and desecrated places.”   Wendell Berry

Since intense study in general, and in particular of structures rather than things, lessens the sense of self and so seems to free soul from body, those that thought about number and shape extracted the mind from the material world.

“Geometry, my noble friend, will draw the soul toward the truth, and create the spirit of philosophy…the knowledge at which geometry aims is knowledge of the eternal.

“After plane geometry we proceeded at once to astronomy, instead of taking the third dimension, which is concerned with cubes and dimensions of depth.

“That is true, Socrates, but so little seems to be known as yet about these subjects…”  Plato, The Republic

“Even those who have never studied geometry, mathematics, music, or architectural proportion can begin to see the outline of the prehistoric God, and through the practice of these arts direct contact can be made with the minds of former adepts.  Kepler said that while compiling his system of the universe he felt that he was following God in the sequence of his thoughts.”  John Michell   The View over Atlantis

“I set out with a more or less religious belief in a Platonic eternal world, in which mathematics shone with a beauty like that of the last Cantos of the Paradiso.  I came to the conclusion that the eternal world is trivial, and that mathematics is only the art of saying the same thing in different ways.” Bertrand Russell

“That which fills the naive mind with amazement is seen, by mathematical analysis, as tautology, and therefore self-evident.”    Walter Burkert

Early monumental building plans seem to have been largely based on geometry and proportion, derived from basic right triangles whose sides measured in whole units of 3-4-5, or one of the other five combinations of small whole numbers, which demonstrate the Pythagorean theorem. Dimensions were numeric ratios corresponding to defined proportions, some based on musical harmonies. Designs were incised at full scale on floors and walls.

Medieval master masons carried measuring rods divided into proportional ratios of ½,1/3,and ¼.  Their developed drawings can still be seen on the tracing floors of cathedrals such as York Minster.

Palladio gave dimensions in his local unit of measure, the Vincentine foot, .347m.  Leonardo da Vinci, citing Vitruvius, tells us that “…four fingers make one palm and four palms make one foot; six palms make a cubit.”

Classical architecture used the Attic or Greek foot, .328m, or the Roman foot, .295m.  After the 4^th century AD, the Byzantine foot, .312m became standard.  By the 18^th century, France used the Paris foot, .32485m, divided into twelve pouces, which were further divided into twelve lignes.  While the British and American standard foot was .3048m, divided into twelve inches, divided into half, quarter, eighth, sixteenth, thirty-second…

The nineteenth century witnessed the flowering of the Enlightenment (cogito, ergo sum) and the eventual adoption of the metric system, where everything is conveniently divided into tenths, ad nauseum.