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
    History of complexity theory shows that problems once dee... — Carmelics
    Home
    HistoryEditSee Inverse

    Part of a larger discussion

    Challenges→NC is expected to be properly contained in P (NC ≠ P)

    History of complexity theory shows that problems once deemed inherently hard (e.g., primality testing) later yielded to unexpected algorithmic techniques, undermining inductive confidence in current parallelization barriers.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.AKS primality test and elliptic curve methods were genuinely unexpected breakthroughs, suggesting algorithmic creativity remains underexplored.
      ?

      Think about whether this reason is strong or weak

    • 2.P vs NP remains unsolved; absence of proof for parallelization barriers doesn't establish they are fundamental rather than merely undiscovered.
      ?

      Think about whether this reason is strong or weak

    • 3.Historical pattern shows computational barriers often reflect incomplete technique exploration, not intrinsic problem structure.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Primality testing improvements involved changing problem variants or lowering guarantees, not solving inherent sequential dependencies like NC vs P.
      ?

      Think about whether this reason is strong or weak

    • 2.Some barriers (e.g., logarithmic depth for P-complete problems) have conditional lower bounds independent of algorithm discovery rates.
      ?

      Think about whether this reason is strong or weak

    • 3.Inductive inference from algorithmic breakthroughs to parallelization remains logically weak—historical examples don't establish absence of actual limits.
      ?

      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.

    Key Terms

    Algorithmic techniques(the solutions that unexpectedly made hard problems easier)
    Step-by-step procedures or methods that computers use to solve problems efficiently.
    Complexity theory(where analogous issues might appear)
    A branch of computer science and mathematics that studies how difficult different problems are to solve and how much computational power they require.
    Inductive confidence(confidence that gets undermined when old assumptions turn out wrong)
    Trust in a pattern or belief based on past examples—like assuming the future will work the same way as the past has.
    Parallelization barriers(barriers we currently believe are impossible to overcome, which the statement suggests might be proven wrong)
    Limits or obstacles that seem to prevent us from solving certain computer problems faster by breaking them into smaller tasks and working on them simultaneously.
    Primality testing(given as an example of a problem once thought to be inherently hard)
    The problem of figuring out whether a number is prime (only divisible by 1 and itself), which was long thought to require enormous amounts of computation.

    Connections

    2 topics

    Modality & Possibility1 linkedSkepticism1 linked

    Related

    AKS primality test and elliptic curve methods were genuinely unexpected breakthr...Historical pattern shows computational barriers often reflect incomplete techniq...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit
    Inductive inference from algorithmic breakthroughs to parallelization remains lo...
    NC is expected to be properly contained in P (NC ≠ P)
    +3 moreShow less
    P vs NP remains unsolved; absence of proof for parallelization barriers doesn't ...Primality testing improvements involved changing problem variants or lowering gu...Some barriers (e.g., logarithmic depth for P-complete problems) have conditional...