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
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that TIME(t1(n)) is a proper subset of TIME(t2(n)) when t2(n) grows sufficiently faster than t1(n)

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The time-hierarchy theorem's proof relies on a universal Turing machine simulation with logarithmic overhead, presupposing a specific machine model.
      ?

      Think about whether this reason is strong or weak

    • 2.Different computational models (e.g., multi-tape vs. single-tape TMs) yield non-equivalent complexity hierarchies for identical time bounds.
      ?

      Think about whether this reason is strong or weak

    • 3.Therefore, 'proper subset' relations are model-relative artifacts, not intrinsic mathematical facts about computational difficulty.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The theorem's diagonalization construction produces a language that is deliberately pathological and not representative of natural computational problems.
      ?

      Think about whether this reason is strong or weak

    • 2.Benacerraf and Putnam's structuralist critiques suggest that mathematical existence claims require more than diagonal constructions to establish genuine ontological distinctions.
      ?

      Think about whether this reason is strong or weak

    • 3.A proper subset relation demonstrated only via diagonalization may establish a formal separation without revealing any substantive difference in computational power.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.t1(n) and t2(n) are time constructible functions with t2(n) >= t1(n) >= n
      ?

      Think about whether this reason is strong or weak

    • 2.The limit of t1(n)*log(t1(n)) / t2(n) as n approaches infinity equals 0
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

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