Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Formal definitions of chaos may not be applicable to actu... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Skepticism
    HistoryEditSee Inverse

    Formal definitions of chaos may not be applicable to actual physical and biological target 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
    ?
    • 1.Lyapunov exponents—the standard mathematical measure of SDIC—are defined only in the limit as time approaches infinity.
      ?

      Think about whether this reason is strong or weak

    • 2.No physical or biological system operates over an infinite time horizon, making Lyapunov exponents strictly inapplicable to real systems.
      ?

      Think about whether this reason is strong or weak

    • 3.Finite-time Lyapunov exponents are system- and trajectory-dependent approximations that lack the universality required for rigorous classification of chaos.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.As Suppes and Winsberg have argued, mathematical models and their target systems inhabit distinct ontological domains, requiring explicit correspondence rules to bridge them.
      ?

      Think about whether this reason is strong or weak

    • 2.No established correspondence rules successfully map idealized properties like topological transitivity or dense periodic orbits onto measurable quantities in finite physical systems.
      ?

      Think about whether this reason is strong or weak

    • 3.The absence of such bridge principles means chaos attributions remain confined to the model, constituting what Cartwright calls a 'lying law'—accurate of the model but silent on the world.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Formal definitions seek to fully characterize chaotic behavior in mathematical models
      ?

      Think about whether this reason is strong or weak

    • 2.Target systems run for only a finite amount of time
      ?

      Think about whether this reason is strong or weak

    • 3.Uncertainties in target systems are always larger than infinitesimal
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Topics

    SkepticismTruth & Knowledge

    Connections

    2 topics

    Causation2 linkedModality & Possibility1 linked

    Related

    As Suppes and Winsberg have argued, mathematical models and their target systems...Deriving sensitive dependence on initial conditions (SDIC) requires assumptions ...Finite-time Lyapunov exponents are system- and trajectory-dependent approximatio...Formal definitions seek to fully characterize chaotic behavior in mathematical m...
    +6 moreShow less
    Lyapunov exponents—the standard mathematical measure of SDIC—are defined only in...No established correspondence rules successfully map idealized properties like t...No physical or biological system operates over an infinite time horizon, making ...

    Similar

    Classical chaos itself has no fully agreed-upon definition and involve...83%Varying definitions of chaos have varying strengths and weaknesses82%Quantum mechanics cannot exhibit chaos in the classical sense77%A mark of chaos merely identifies that chaos is present, but does not ...77%

    Source

    AI-extracted1/3 agreementValid
    SEP: chaos
    View source passageHide passage
    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
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Target systems run for only a finite amount of time
    The absence of such bridge principles means chaos attributions remain confined t...
    Uncertainties in target systems are always larger than infinitesimal
    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit