In my architectural practice, in the 1960s, in Berkeley California I had seen the affects of drug use, so much a part of the social scene of that time. I had employees come and go, not always surviving their experimenting with drugs. I knew, from a one time use of marijuana that my sense perceptions, which affected and distorted my space perceptions
and momentarily affected my work, such that I wanted nothing more to do with it.
One day, while alone in my office, I went to a large drawing surface on a wall and, without knowing why I was doing it, I drew a large circle. This was my unconscious coming to the fore and with this event I knew this was significant – It would become my Mandala. About this time I was reading Carl B. Boyer’s History of Mathematics. He tells of the
inverse geometry of Professor Jakob Steiner, an Eighteenth Century geometer who taught at the University of Berlin. He was born in the countryside, a Canton near Bern,
Switzerland, the same as was Carl Jung and later the Gnostic Valentinians of my family. I went to Bern, to the Municipal Library where I found numerous unbound folders of
Steiner’s unpublished work, among them his ‘inverse geometry’ drawing and accompanying notes.
He is quoted as saying that he could not tolerate analytical geometry, as he was working solely in synthetic geometry. This, of course, needs elaboration, which can best be done
philosophically. In Immanuel Kant’s Critique of Pure Reason he defines these as two subjects: one being the geometric synthetic, the other being the arithmetic synthetic. The
arithmetic synthesis noted by Kant is that which has evolved into modern mathematics. It was, and continues to be analytical, and through Descartes, Fermat and others the subject
of geometry also became analytical and in large part became numbers. This, all too briefly, explains Jakob Steiner’s dislike of the analytical in favor of synthetic (synthesis) of geometry.
Today, we have a dramatically different connotation of the word synthetic. It means to us something false, cheap or a substitute of the original. This was caused, in my
understanding, by the substitution of numbers and modern mathematics for the classic geometry of Euclid. Jakob Steiner and his inverse geometry makes possible, the
geometric expression of that which is ‘inner’ in relation to that which is ‘outer’ – in our selves. This is the subject of my book; Geometric Wholeness of the Self.