Computationalism (the idea that everything in existence is fully characterized by states and transition functions) is
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Replying to @Plinz
Not sure that states+transitions is a sufficient definition. It covers Turing completeness, but various oracle functions can extend it in qualitatively different ways, while still being of the flavor of computation. But computation as a concept being universal, yes.
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Replying to @ngutten
Could you please point me to a noncomputational oracle function?
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Replying to @Plinz
So for example, a universe that has halting oracles can't be emulated in finite time/space on a Turing machine. It's still computation, just a superclass of what we can actually implement in our universe as far as we know.
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Replying to @ngutten
How would you know that it actually is a perfect halting oracle?
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Replying to @Plinz
I'm not sure you'd need to know that, but you'd find that to make accurate predictions of consistent events in the universe requires divergent computational effort on a Turing machine. You could probably probe it experimentally with asymmetric problems that are easy to confirm.
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For a concrete example, a halting oracle could search an unstructured space of size N in log(N) operations. So e.g. crack an encryption key in time linear in it's length.
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Replying to @ngutten
Yes, in the worst case you can put the physical universe on hold, compute whatever you want, and then continue the regular program. In this way, you can even do acausal computation on a bounded Turing machine.
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Replying to @Plinz
Computationally, systems with different kinds of infinite computing power behave in qualitatively different ways than finite ones. So presenting computation from the point of view of Turing machines alone misses those things or handles them awkwardly.
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It is unfortunate that the Turing machine gained such prominence. We can only ever use finite state machines, because we cannot wait for infinite numbers of steps to pass. This changes almost everything.
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