Lev
A very thought provoking essay. This is a novel approach to achieving a generalised, consistent formalism with the potential to describe all phenomena from the fundamental "reductionist" standpoint, to the higher level, effective theoretical (chemistry/biology) standpoint in a more seamless way than what we have now.
I agree that the math representations of QM & GR, with their corollary of complex numbers, irrational real numbers with infinite decimal expansions, ideal forms that are not realised in nature, probabilistic interpretations etc, are telling us something. I think that something is that Mother Nature doesn't give two hoots about man's evolved forms of "numerically" making sense of the world!
Whilst I am still getting my head around your scheme, at first glance it seems like an extension of Feynman diagrams, but with the probabilistic "coupling strength" calculations etc replaced by some sort of "class constrained" transformation process to the next state of the representation (at micro scales)? Decoherence seems to be naturally incorporated also.
I'm not sure what your scheme does for our understanding of the "nature of time" though. For instance, could you clarify your statement in footnote (i) to figure 4... "This is the direction of precedence of temporal encoding over the spacial one in nature"? Does this imply the view that change "happens in time" rather than time "emerging from change"? I would have thought from your later claim that ETS "embodies a more general, structural form of temporality", that the latter view would be required? But I may be completely missing the essence of your scheme at this stage.
I was also wondering how in ETS you would represent a quantum superposition, such as a split photon wave function? Or indeed any coherent quantum state? This would have implications for quantum computing for instance.
Congatulations on an excellent essay & good luck withe the contest!
PS: I think if Max Tegmark reads this essay, he will fall off his chair!!!