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.
Hypercomputation is a domain of decidable but only approximately computable problems. For instance, most of geometry is decidable but not computable with finite resources. The three body problem is another well-known example.
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But computation, and the problems you compute on, are two different categories.
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For example, what if I implement a Turing machine by using aperiodic tilings (or some other Penrose ideas) such that running this machine for any significant program is decidable but not computable?
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