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    Hypercomputation models (Malament-Hogarth spacetimes, Tur... — Carmelics
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    Challenges→The notion of a computable set generalizes effective decidability: a relation R is computable just in case there is an algorithm for deciding whether R holds of any tuple of natural numbers that always returns an answer after a finite (though potentially unbounded) number of steps

    Hypercomputation models (Malament-Hogarth spacetimes, Turing's o-machines) permit decision procedures that transcend finite-step termination constraints.

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    Reasons For

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    • 1.Malament-Hogarth spacetimes permit observers to access infinite computation via causal structure without violating local physical laws.
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    • 2.Turing o-machines formalize oracle access as mathematically coherent, showing transcendence of Turing-computability is logically possible.
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    • 3.If physical spacetime permits closed timelike curves or naked singularities, finite agents could exploit these to simulate hypercomputational processes.
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    Reasons Against

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    • 1.No empirical evidence confirms Malament-Hogarth spacetimes exist; general relativity permits them mathematically but not necessarily physically.
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    • 2.Turing o-machines assume oracles as primitive; this merely relocates computation rather than transcending Church-Turing limits fundamentally.
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    • 3.Extracting results from hypercomputational processes requires finite observation windows; infinite convergence guarantees collapse under realistic constraints.
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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Extracting results from hypercomputational processes requires finite observation...If physical spacetime permits closed timelike curves or naked singularities, fin...Malament-Hogarth spacetimes permit observers to access infinite computation via ...No empirical evidence confirms Malament-Hogarth spacetimes exist; general relati...
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    The notion of a computable set generalizes effective decidability: a relation R ...Turing o-machines assume oracles as primitive; this merely relocates computation...Turing o-machines formalize oracle access as mathematically coherent, showing tr...

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