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    If the target system's state space is itself finite and d... — Carmelics
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    Challenges→There will always be many more target system states than model states for any computational model

    If the target system's state space is itself finite and discrete, a sufficiently fine-grained computational model can achieve a bijective mapping with physical states.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Physical systems with finite discrete state spaces are in principle fully describable by finite information; computation can represent any finite structure.
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    • 2.Bijective mappings require no causal efficacy—only structural isomorphism between computational and physical states, which finer granularity can approximate.
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    • 3.Digital physics models successfully map quantum systems (discrete energy levels, spin states) to computational states without loss of predictive power.
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    Reasons Against

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    Reason against
    ?
    • 1.Physical discreteness at one scale may emerge from continuous substrates; bijection requires identifying the 'true' fundamental level—which remains undetermined.
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    • 2.Representing a state and causally instantiating it are distinct; a map doesn't capture whether computation *implements* physics or merely describes it.
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    • 3.Measurement contexts, observer dependence, and relational properties in quantum mechanics may resist bijection to context-independent computational states.
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    Modality & Possibility1 linkedSkepticism1 linked

    Related

    Bijective mappings require no causal efficacy—only structural isomorphism betwee...Digital physics models successfully map quantum systems (discrete energy levels,...Measurement contexts, observer dependence, and relational properties in quantum ...Physical discreteness at one scale may emerge from continuous substrates; biject...
    +3 moreShow less
    Physical systems with finite discrete state spaces are in principle fully descri...Representing a state and causally instantiating it are distinct; a map doesn't c...There will always be many more target system states than model states for any co...

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    Perspectives
    2 (1 for, 1 against)
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