Think of all the sub-atomic particles listed by scientists. Do any of these particles have any properties that cannot be characterised mathematically? There isn’t a single thing about them that isn’t defined by numbers, shapes, quantities, dimensions and mathematical formulae i.e. all the stuff of mathematics. So in what way are these objects of science rather than objects of mathematics? It’s only because we (humanity) have chosen to think of mathematics as fundamentally unreal and abstract that we perversely regard objects that are in every way defined mathematically, and which have no non-mathematical features, as objects of science rather than of mathematics.
Quantum mechanics, relativity theory and M-theory (the theory that is trying to harmonise quantum mechanics and relativity) are all astoundingly mathematical. Are these scientific theories or ontological mathematical theories? If we rebrand science as ontological mathematics then it becomes much clearer why abstract mathematics reflects science so well: “science” is just mathematics as reality rather than as abstraction.
There’s a gulf between conventional science and ontological mathematics in terms of three critical numbers: zero, infinity and the imaginary number, i. Conventional science, an expression of extreme philosophical materialism, asserts that zero, infinity and the imaginary number have no ontological reality within any region of space and time. Conventional science involves a hypothesis that only real numbers are ontological or have any bearing on reality. There is not a single rational reason why this should be the case: it is pure empiricist materialist dogmatism. Science refuses to address the issue of why it accepts only real numbers greater than zero and less than infinity. It gives no rational reason for rejecting zero, infinity, negative numbers and imaginary numbers beyond the simplistic one that they are not empirically detectable. Science thus enshrines empiricist materialism in how it regards mathematics. This is not a scientific but a philosophical stance, and indeed a faith-based position since the ontology of mathematics is not something that can be determined via fallible human senses.
Abstract mathematics – which has no ideological hostility to zero, infinity and the imaginary number (or negative numbers for that matter) – is considered irrelevant to science in respect of these key numbers. Any scientist will tell you that nothing infinite can exist within any localised region of reality because it would literally destroy the fabric of existence in that region, and no such catastrophic tears are observed except, arguably, in the specific cases of the mysterious singularities associated with black holes and the Big Bang. Scientists maintain that there is something wrong with the existing scientific theories regarding singularities and their dreaded infinities and that these problems will be resolved by some new theory such as M-theory.
Scientists will also tell you that they associate zero with non-existence i.e. it is devoid of ontological significance. Descartes defined res cogitans (thinking substance) as having no extension i.e. it had no presence in the extended world of matter. Scientists, as strict materialists, have dismissed the Cartesian concept of independent thinking substance (mind). Mind, for scientists, is a mysterious aspect of matter. It cannot exist separately from matter, hence is some kind of material phenomenon or epiphenomenon. According to science, the Cartesian mind, the domain of zero, is pure nonsense. It simply isn’t there. Of all the catastrophic errors of science, this is the greatest because it turns out that zero is the quintessence of existence and completely defines it.
As for the imaginary number, i, this appears in a vast number of scientific equations, yet scientists regard it as purely instrumental i.e. it helps to produce the right answers but has no ontological reality. Mathematician Marcus du Sautoy declared, “Calculating with imaginary numbers is the mathematical equivalent of believing in fairies.” It seems extraordinary that extremely highly qualified individuals should accept “fairies” in the midst of some of the most successful theories and equations of all time and not conclude that either these theories and equations are the purest moonshine, or else imaginary numbers are anything but imaginary. It is poverty of both reason and imagination that makes mainstream scientists and mathematicians so blind to the ontological reality of imaginary numbers. There are no “fairies” in mathematics. Neither zero, infinity nor imaginary numbers are fairies. On the contrary, they are essential to existence. They are the most solid, substantial entities of them all, every bit as solid and ontological as real numbers.
So, Illuminism defines two types of mathematics: abstract (conducted purely in the mind or on paper) and ontological (that unfolds as reality itself) – the two are of course extremely closely related, with energy being what separates them. Ontological mathematics can be further divided into ontological mathematical materialism (science) and ontological mathematical idealism (the mathematics of zero and infinity).
The imaginary number belongs to mathematical materialism (though scientists haven’t grasped this yet). What this means is that the imaginary number has real existence in the physical world – which is why it appears in so many key equations of science. It is not an instrument for getting the right answer: it is part of the fabric of reality. In fact, it is the basis of time.
The two branches of ontological mathematics constitute a complete account of reality – a grand unified theory if you will. What the two branches achieve is the resolution of Cartesian dualism.
Excerpt from The God Game
Published by Hyperreality Books
Copyright © Mike Hockney 2012
Artwork by Pretty Psychedelic