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@iiii It is mathematically impossible for a Turing machine to determine whether another Turing machine will halt, which is why such an ability would prove that I have a higher computational class than a Turing machine.

@homolorens that just means there's a machine that accepts programs that a Turing machine can't. We could then just build something along that superTuring machine and then you're back to square one.

@rememberMe for completion if the superTuring machine cannot be built on a large scale, therefore stagnating the state of computers to Turing machines, the ability could be achieved! (Recap: assuming the human brain can elevate to this superTuringmachine state and that said state cannot be commercially replicated)

iiii91932y@homolorens as I remember, the proof is not really constrained by the actor being only a Turing machine. It is true for any machine

@iiii The proof relies on feeding the machine its own blueprint. It proves that no machine can solve the halting problem for its own computational class, which is why in order to be able to solve the halting problem for Turing machines, I have to be in a computational class that cannot be represented as a Turing machine.

iiii91932y@homolorens but the fact that you need a higher class means that halting problem is unsolvable in principle, because the next class will require the class superior to it and so for

@iiii That's shifting the goal because the task is to prove the halting for the machine at hand, not (in general) for the machine that does the proof.

superboot142yThat ability would solve a lot more than the two cases you pose. It would be a major landscape changing ability. Other than the fact that you are human, and can't scale like a computer system.

@superboot I did not ask for a reproducible blueprint of such machine, just the ability, so it isn't as useful as you might think.
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I want to be able to look at a program and immediately know whether it halts. Partly because that would be proof that I cannot be a very elaborate computer program, and partly because it could be used to answer any yes/no question that I understand well enough to write a program for.
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