I don't even see a way to conceive of the existence of non-computational things; everything that exists must be implemented, and computation (which can be characterized by sets of discernible differences and transition functions) is precisely the realm of implementation.
I suspect that the edge lengths don't matter because when you zoom in at particle dynamics, you are looking at the local topology only, and when you zoom out to GR, you look at statistical aggregates of the local topologies 30 magnitudes above the Planck length.
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Yes, Rovelli's perspective on LQG is close. But I think that the loonies: Zuse, Fredkin, Wolfram, t'Hooft are more likely correct, and the Church Turing Thesis is going to turn out to be a physical law. :)
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