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    Global Lyapunov exponents may lack physical significance ... — Carmelics
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    Global Lyapunov exponents may lack physical significance for real-world systems

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Global Lyapunov exponents are computed as time-averages over infinite trajectories, but physically realizable observations are always finite-duration.
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    • 2.Eckmann and Ruelle (1985) acknowledge that ergodic theory's infinite-time limits need not converge to physically observable rates on measurable timescales.
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    • 3.A quantity defined only in an idealized infinite limit cannot straightforwardly characterize the finite-time behavior of systems embedded in physical reality.
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    Reason for 2 of 2
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    • 1.Suppes and Winsberg's arguments on model-world gaps entail that mathematical invariants of abstract systems need not correspond to measurable physical quantities.
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    • 2.The Lyapunov exponent presupposes a fixed, smooth invariant measure, but real systems subject to noise and perturbation do not preserve such measures exactly.
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    • 3.When the theoretical preconditions of a formal quantity fail to obtain in target physical systems, that quantity loses its claim to physical significance.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Global Lyapunov exponents only apply to infinitesimal uncertainties
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    • 2.Uncertainties in physical systems are always larger than infinitesimal
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    • 3.Any growth in uncertainties between neighboring trajectories can be fitted with an exponential function
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    Related

    A quantity defined only in an idealized infinite limit cannot straightforwardly ...Any growth in uncertainties between neighboring trajectories can be fitted with ...Eckmann and Ruelle (1985) acknowledge that ergodic theory's infinite-time limits...Global Lyapunov exponents are computed as time-averages over infinite trajectori...
    +6 moreShow less
    Global Lyapunov exponents only apply to infinitesimal uncertaintiesIf any exponential can be fitted to the data, the choice of parameter is arbitra...Suppes and Winsberg's arguments on model-world gaps entail that mathematical inv...The Lyapunov exponent presupposes a fixed, smooth invariant measure, but real sy...Uncertainties in physical systems are always larger than infinitesimalWhen the theoretical preconditions of a formal quantity fail to obtain in target...

    Similar

    Global Lyapunov exponents only apply to infinitesimal uncertainties76%Feasible numbers should not be regarded as closed under exponentiation...73%Feasible numbers should not be closed under exponentiation under stric...71%Van Dantzig holds feasible numbers are closed under addition and multi...71%

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    SEP: chaos
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    The other worry is that the definitions we have been considering may only hold for our mathematical models, but may not be applicable to actual target systems. The formal definitions seek to fully characterize chaotic behavior in mathematical models, but we are also interested in capturing chaotic behavior in physical and biological systems as well. Phenomenologically, the kinds of chaotic behaviors we see in actual-world systems exhibit features such as SDIC, aperiodicity, unpredictability, ins
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    Details

    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit