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Paradox & Proof

Statements that stay true while contradicting themselves.

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    Paradox & Proof Entry #0168

    The reason a backup can lower reliability

    A second unit adds a component, a switch, a test and an assumption. Each is a new way to fail, and one of them fails silently.

    Novice
    The hidden part #0168

    Redundancy adds components, switching and an unobserved state. The standby’s failure produces no signal until the moment it is needed.

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    Paradox & Proof Entry #0167

    Why proving a negative is harder than proving a positive

    A single instance settles an existence claim. A non-existence claim requires exhausting a space, and spaces are rarely exhaustible.

    Adept
    The hidden part #0167

    One instance settles existence. Non-existence requires exhausting a space, so the claim is really a report about the search that was performed.

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    Paradox & Proof Entry #1119

    Why two losing bets can win when you alternate them

    Parrondo paradox shows why two losing bets can win when you alternate them: the switching itself changes the state distribution the games are played from.

    Master
    The hidden part #1119

    Two losing games can win together when the switching changes the states they are played from.

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    Paradox & Proof Entry #1118

    Why a treatment that works in trials can fail in practice

    The efficacy-effectiveness gap explains why a treatment that works in trials can fail in practice: trials strip out the patients and conditions ordinary care contains.

    Adept
    The hidden part #1118

    A trial measures what a treatment can do; practice measures what it does do.

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    Paradox & Proof Entry #1117

    Why a more efficient engine can burn more fuel

    The Jevons paradox explains why a more efficient engine can burn more fuel: cheaper work invites so much extra use that total consumption rises.

    Adept
    The hidden part #1117

    Efficiency makes each unit cheaper, and cheaper units get used until the saving is spent.

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