I recall seeing some literature on a concept called “reversible computing” that seemed to be about this too. I guess that’s the synthesis side of power efficiency analysis.
I also wonder how much we should rely on physics for tiling. In principle, we can arrange all tiles in a line and let them learn a routing protocol that tiles into a lattice of arbitrary dimensionality. Physical neighborhoods are inflexible but give us the first dims for free.
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Indefinitely scalable dimensions *must* be aligned with physical dimensions, but one can also have finite dimensions until local memory runs out.
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A multi dimensional space is the result of an operator that folds a number line (which we can get from a distance counter) into a lattice. For number theoretic reasons, we'll probably never need more than 8 local dimensions.
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