IÃ¢â‚¬â„¢m not a mathematician and as far as I am aware none of my work has no real mathematical basis. My geometric Ã¢â‚¬ËœstudiesÃ¢â‚¬â„¢ are instead based in an intuitive and philosophical affinity with the geometric relationships I have derived my art from over the last decade and a bit.
I have an nerdy obsession with symmetry and this obsession leads me into very abstract areas of thought. I also have a preoccupation with trying to understand the nature of reality. Geometry for me, as it was for the Greeks, is a philosophical language. It is a language that allows me to explore these abstract areas of thought and also give expression to what I find and feel is significant in it. Also, thrown into the mix is the influence of my Buddhist practice and the Buddhist teachings I have read.
The Buddhist concept of void and form, for me within geometry, has a parallel in the concept of infinity and zero. The Buddhist notion of self and relativity also has some expression within geometry as the notion of Ã¢â‚¬ËœoneÃ¢â‚¬â„¢ and symmetry.
The figure above shows how 1 sits at the centre of infinity, and that the progression to infinity and zero from 1 are actually the same thing.. Conventional mathematics gives us a picture of infinity that looks like this:
-infinityÃ¢â‚¬Â¦.. -5,-4,-3,-2,-1,0,1,2,3,4,5Ã¢â‚¬Â¦Ã¢â‚¬Â¦ infinity
The picture has zero in the middle and +/- infinity at either end. Infinity in this picture is far away in the distance and can never be shown however far we zoom out.
The Zen view and experience of reality is that the whole universe is here right now in this moment. Taking this concept into the realm of numbers, this universe is infinite as it is simultaneously void of inherent, permanent existence. A Zen axiom is that all things are born and return to emptiness. Now, all magnitudes relative to zero are infinite. Or we could say any number divided by zero equals infinity.
My diagram represents numbers as arcs except number 1 which is a straight line, or rather a portion of an arc of infinite radius.
The inverted figure contains a theoretical progression of all numbers from zero through to infinity with the number 1 shown in the middle. The values shown to the left of 1 are the reciprocal of the values shown to the right.
We thus get a Ã¢â‚¬ËœpictureÃ¢â‚¬â„¢ of reality like this:-
However, the progression to zero is the mirror image of the progression to infinity. This could be seen as a delineation of the Zen notion of Ã¢â‚¬Ëœall form is void: all void is formÃ¢â‚¬â„¢.
Thus we picture the geometry of this as representing:-
0, infinity, 0 or 0, 1, 0
This is all a bit heady and is not intended to be a proof or some absolute representation of the nature of reality. The geometric sketch above is simply my attempt to give an alternative expression to concepts that are very difficult to communicate with the spoken word. When I first started messing around with this geometry many years ago, my own view of relativity and reality shifted in response to what was revealed in the language of the geometry. It may not have shifted any closer to gaining a closer experience of reality, but my revelations seemed profound enough at the time and I figure there could be great potential in geometry to communicate this abstract area of thought and experience.
The work above is a sketch originally intended as personal notes on key geometric relationships. I hope to develop it into a more resolved work of art, but unlike my previous work, i will not be looking to hide the underlying philosophical component, but instead making it central to the work. Much of my work over the last ten years or so contains geometric/philosophical intrigue for me at least, however the language I have used by enlarge was designed to cover up much of what could be potentially elaborated on from a conceptual point of view. This was probably in response to what I used to see as the over conceptualisation of art.
Above: Study from around 2000 based on the same geometric relationships shown at the top of the page, but where the potential conceptualÃ‚Â component in not explored.