Jonathan Dickau,
I enjoyed your essay because it is open to the idea that math itself contains the seeds of consciousness. I am an agnostic when it comes to the existence of consciousness or volition before it emerges in physical form but do agree with you that these must be based on a mathematical structure.
Fractal structures are ubiquitous in nature; causal lattices find a home in various mappings from the most fundamental particle interactions through the most complex structures in the universe, neural nets.
Also, I think that to dismiss imaginary and complex numbers as nonphysical is shortsighted as the equations that contain them fit with physical observation in a way that classical equations (those with just real numbers) do not. You put it well when you say: "... Nor does it make sense to assert that the real world is content to function within the space of real numbers."
Hawking's question: "what puts the fire in the equations?" becomes relevant here. It has long been the contention of philosophers that abstract objects are causally inert; and here again I am an agnostic. There is the old saw in physics, which may well be operant, that whatever is not forbidden is mandatory; so given a start, any start, to physical existence, even a probabilistic one, it opens the door for a physical emergence of consciousness.
Another of your observations, beautifully put: "... non-zero ordinary or simple numbers are the end of the process chain."
I am being speculative here, but it seems the complex interference patterns of the eigenstates of physical being held in superposition takes place in a complex space. And, as George Ellis puts it, collapse of the wavefunction is contextual. The inner product of that interference pattern is discarded by observation (probabilistically, by decoherence or by a conscious intervention) and what remains is the real number part.
The rules of non-commutative and non-associative math make it a tougher slog to an understanding. In none of my science classes was this presented as a path forward. At the point where the math becomes that much more challenging, for those of us who possess more scientific curiosity than mathematical ability, it becomes very discouraging indeed to be confronted with this much homework; it becomes a barrier to entry. When the phenomenon we see in nature do not yield to the simple formulations about the mathematics we know well, and then again to the intermediate formulations and then again to the more difficult formulations, it then finally occurs to us that, yes indeed, it can be this difficult. It goes against the grain of the human tendency to look for the keys under the lamp post, where the looking is easier.
Also, I really like the idea that, on its smallest levels, the structure (quantized discrete structures?!) of space goes (go) back to being 2-D and you go on to suggest that dimensionalities should be viewed as a spectrum, and further they are not limited to integer values and change over time, which opens the idea even more. Well done, sir! That opens the problem up nicely. I don't believe we will ever be able to go back to conceiving of physical reality limited to a simple Euclidean form.
I don't think of nature or math as an orchestrator of relationships; nature does not have to resort to trying these combinations out in sequence. Mathematics holds all of the eigenstates of physical being in superposition and can solve them by the interference patterns they produce; they shimmer into existence by virtue of their holographic fruitfulness.
Some of the underlying structures are more fruitful than others, so one would intuit that evolution would occur over a spacio-temporal spectrum of emergence. As you say: "we will see that math requires it."
Best regards,
Jim Stanfield
