Dark Geo is based on a geometrical system called pentaplexity or Penrose tiling, which unlike, say, the Pythagorean theorem or the decimal number system, is something that appeared in mathematics only recently. It has a number of interesting qualities, of which we now concentrate on one, namely that the two rhombuses forming the tiles never occur in a recurring order. The tiling is aperiodic. The pattern provided by the Penrose tiling does not occur in nature, the quasicrystals it describes were the result of elaborate laboratory experiments.
My work was produced by placing drawings on the rhombuses of the Penrose tiling. As the drawings meet where the sides of the rhombuses do, a labyrinth is created, or at least a network. There are two kinds of drawings on the rhombuses; one can be seen by natural light, the other by ultraviolet light. These are the facts.
What follows is not a fact, but a conjecture, speculation, metaphysics. Many think that mathematics is a collection of methods, which can be used to make bridges, election forecasts or atomic bombs. One of those boring things only idiots have an interest in. Others think mathematics is more than that. They think it describes nature, and at such an advanced level that it almost allows a view into the world of ideals. The same people like to contrast moral corruption and human frailty with the imperishable truths of mathematics. Mathematics is the only science, they claim, in which new theories do not overthrow old ones.
As a matter of fact, contemporary mathematics is no longer interested in nature. As I’ve said, the Penrose tiling does not occur in nature. The consistency of mathematics must derive from the fact that it is built entirely from statements made by humans. Even axioms are statements which are based exclusively on human notions. Take for instance the following statement:
If a equals b, and b equals c, then c equals a. Which is the kind of thing mathematics is based on. But how could they not be equal when the very notion of equality is our own idea? This axiom says nothing about a and b, but merely defines equality. And since it is an axiom, it effects the definition by using itself. It is obvious what simplistic thinking it would be to compare mathematical equality with social equality. It is no less than word magic.
I am interested in mathematics as a visual artist. Consequently what interests me is not what mathematics is, but what it means. I do not like the visual universe associated with mathematics. I do not think that works on mathematics should uncritically employ the visual quality of geometric construction. Lines, planes, shaded bodies. All this is good for is a scenery to science.
What does mathematics mean? Why was it invented, why is it pursued? Hindu scientist are fabled to have had a contest in numbers: two Brahmins tried to outdo each other in saying the largest number possible. World economics seems to operate along the same lines. Mathematics, I think, also has a dark side.
Mathematics is the only science that does not deal with nature. It is built solely from human statements. If human intellect is not considered a part of nature, then mathematics is the most unnatural thing man is capable of. Which might be the very point. Time and again we prove that we have left behind the streamlined and ruthless world of natural being once and for all.