Universal computation is the set of rulesets that allow to implement all rulesets that allow universal computation. I suspect that hypercomputation lies outside of universal computation, but a-causal computation does not, i.e. hypercomputation cannot be implemented.
Yes, you can use computable models to explore uncomputable domains, such as the real numbers. You can also use such uncomputable constructs to define Turing machines, but you cannot implement them. The set of hypercomputatable functions is a true superset of the computable ones.
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So to your original tweet. Were you implying there could be another kind of compute? Or was it a statement on complexity classes?pic.twitter.com/2EVsZ5yQyB
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The classically computable universe is the set of mappings between the integers. Traditional physics assumes geometric hypercomputation, i.e. allows the universe to implement continuous functions between the reals. Quantum mechanics allows functions from reals to complex and back
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I don't know enough about Penrose's tilings to know why they would be uncomputable though. Do they depend on infinities?
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"human understanding … cannot be computationally simulated" Then he shows a few such uncomputable things.https://youtu.be/eJjydSLEVlU?t=7m40s …
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