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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that If nonlinear systems are mathematically equivalent to linear systems under Koopman lifting, the nonlinearity/linearity distinction is representationally relative, not ontologically fundamental.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Koopman lifting requires infinite-dimensional spaces; finite physical systems cannot access these lifted spaces, so equivalence is not practically instantiated.
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    • 2.Nonlinearity in state space constrains what initial conditions and measurements are accessible; this constraint is ontologically real regardless of lifting.
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    • 3.Mathematical equivalence doesn't entail ontological equivalence—a map and territory can be equivalent without eliminating territory properties.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematical equivalence under valid transformations typically indicates representational rather than intrinsic differences in formal systems.
      ?

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    • 2.If observers with different state-space embeddings disagree on linearity, the property depends on perspective, not objective reality.
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    • 3.Koopman lifting preserves all dynamical predictions, making the linear/nonlinear distinction pragmatically idle for dynamics.
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