Geometry is a part of first order experience, being essentially the abstraction of the notion of extension.
No matter what the physicists might tell us, geometry – the measure of the earth – is a matter of direct experience. At some time in prehistory man consciously fixed his sights on a point on the horizon and walked in a straight line towards it. If the land between is relatively flat, there is no more direct route. Such straight lines allowed the plotting of a course and, magically, were confirmed by the shadow projected by a raised stick in sunlight. Each day the sun at its greatest elevation cast its shadow along the same straight line. Here was a measure, a means of orientation, a foothold in the shifting, apparently chaotic, landscape.
If another straight line is set down, intersecting the first but always equidistant from it, another dimension is established, the antithesis of the first, sharing only one point, the extreme of an opposing extension, the extension of the plane of the body when facing the first direction, a fixed plane from arm to arm, from ear to ear. Standing on this point of intersection the body is most balanced, most comfortable when absolutely upright, with the head equidistant always from points set out the same distance along the intersecting lines in opposite directions. Abstracted these three extensions give us the right angled cross in three dimensions which is the most fundamental measure of space and distance we have, later formalised and abstracted in Euclidian geometry and utilised by Cartesian projections.
The almost magical properties of geometry allowed early man a foothold in a seemingly chaotic universe in the way it related to the cyclic and constant phenomena of the sun and stars and ultimately to the structure of material and time. The practicality of the flat plane emerged and the equilibrium of verticality under gravity.
The power and precision of this orientation in space by means of the sun would have been reinforced by the study of the fixed and moving stars at night. The pole star closely aligns with the same point in the heavens determined by the azimuth of the sun. Apart from the wandering planets, the stars rotate around a fixed centre. It is a common attribute of many prehistoric monuments that they mark in some way this solar and astronomic geometry on the land surface with circles and alignments and increasingly precise reinforcements of the reassuringly fixed and cyclic element in an otherwise inscrutable universe. As technologies developed the practical as well as the magical properties of the three planes emerged, in particular the value of the cleared flat, level plane and the stability of the vertical post or wall, which not only measured space and defined territory allowing growth and sub-division and an ordered way but provided man with a clear symbol of his own power and possession of the landscape.
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