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.
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Replying to @Plinz
I suspect that is wrong. What specifically is hyper computation?
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Replying to @onnlucky
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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Replying to @Plinz
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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Replying to @onnlucky
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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Replying to @Plinz
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 relationship between complexity classes and computability classes is not 1:1. All decidable problems are effectively Turing computable, but not with the same efficiency. But finite state machines can not effectively compute the same things as an infinite Turing machine.
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