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    Hypercomputation theorists like Copeland and Shagrir argu... — Carmelics
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    Challenges→Whether a problem admits a polynomial time algorithm is independent of which model of computation is used to measure time complexity, across a broad class of reasonable models.

    Hypercomputation theorists like Copeland and Shagrir argue that physically realizable systems may exist that transcend polynomial-time simulation by Turing machines.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Physical systems exploiting continuous dynamics (e.g., analog computers, quantum mechanics) aren't obviously bounded by discrete Turing constraints.
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    • 2.Church-Turing thesis describes abstract computation, not physical law; empirical discovery could reveal systems with greater computational capacity.
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    • 3.Supertasks and infinite-precision real-number operations may be physically realizable in principle, enabling hypercomputational processes.
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    Reasons Against

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    Reason against
    ?
    • 1.No known physical system has demonstrated hypercomputational capability; proposals rely on idealized conditions impossible under real constraints.
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    • 2.Measurement uncertainty, noise, and finite precision in any physical implementation collapse claimed hypercomputation to Turing-equivalent bounds.
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    • 3.Hypercomputation proposals often smuggle infinity into physical systems; finite universe suggests computational resources are fundamentally limited.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Church-Turing thesis describes abstract computation, not physical law; empirical...Hypercomputation proposals often smuggle infinity into physical systems; finite ...Measurement uncertainty, noise, and finite precision in any physical implementat...No known physical system has demonstrated hypercomputational capability; proposa...
    +3 moreShow less
    Physical systems exploiting continuous dynamics (e.g., analog computers, quantum...Supertasks and infinite-precision real-number operations may be physically reali...Whether a problem admits a polynomial time algorithm is independent of which mod...

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    2 (1 for, 1 against)
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