Most of classical physics needs classical (not constructionist) mathematics, because it deals with emergent layers of description (like classical mechanics or GR) that are often not computable. But foundational physics must break with this and be constructionist, I think.
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Replying to @Plinz
would it disagree with the idea in quantum theory that every real valued function of an observable is another observable? Since some of those are uncomputable
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Replying to @EvanOLeary
It may depend on how you define "observable". Do you require the observer to be actualized? If you do, I suspect that an uncomputed observable (wrt to the universe state vector) would turn out to be in a superpositional state, which implies that it is not observed.
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Replying to @Plinz
Can't superposition of attributes of a variable be measuring its complementary variable in a sharp attribute with a relabeled measurement apparatus labeling the corresponding mixed states of substrates with the other variable?
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Replying to @EvanOLeary
The weird thing is that QM treats superpositional states as an information surplus that the universe hides away in a complex valued Hilbert space, when they might actually be an information deficit, e.g. due to a particle being insufficiently constrained to project it into 3space
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Replying to @Plinz
hmm... sure there don't exist "sufficient constraints" to allow measurers of superpositions to deliver inconsistent possible results to comparers of their outputs, but that is true in QM too: consistency of measurement is what allows outcomes to be associated with universes.
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Replying to @EvanOLeary
What happens when you try to measure something that does not exist, like a position in spacetime when your universe is not in space but in a graph, and a particular location is underconstrained to be projected into 3space?
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Replying to @Plinz
Building a measurer with that specification is impossible, but I'm not sure what you mean by "underconstrained": what kind of constraints logically allow a given location to exist in the graph model?
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If information is stored in a lattice and moves only along lattice links, you may project it into a space. But if you remove links from the lattice, you get superposition, if you add links, you get nonlocality.
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