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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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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Replying to @Plinz
"human understanding … cannot be computationally simulated" Then he shows a few such uncomputable things.https://youtu.be/eJjydSLEVlU?t=7m40s …
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Yes, and he is wrong here. Understanding means proving, i.e. creating a mapping to something that you know how to compute. All things a human can prove are computable.
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Replying to @Plinz
He is talking about understanding itself, not what is understood. But I agree, he is wrong, it's about feature extraction, abstractions, and re-application. All that has to do with learning.
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Did you have a chance to read my paper "Consciousness From a Learning Perspective"? I mailed it to you about a week ago.
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