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• Blue_Morpho@lemmy.world ⁨1⁩ ⁨month⁩ ago

  A double pendulum is bound by definition! It is a fixed point, a line with a 2 axis joint, and another line. That’s the definition.

  Just because a system is chaotic doesn’t mean it can move in unlimited ways. A chaotic pendulum cannot move outside it’s predefined limits of its geometry despite being chaotic.

  The real world imposes far more constraints. A pendulum starts out in a known state. It gets pushed. It moves chaotically for a minute, then returns to its original rest state.

  In the context of Hitler’s parents, you shove the dad, he moves chaotically for a second, then goes back to walking. No long term change has happened.

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  • vrighter@discuss.tchncs.de ⁨1⁩ ⁨month⁩ ago

    I completely agree with what this comment says. It’s still irrelevant though. Where did I say it has to be unbounded? You are countering an argument I did not make. Whether the result is divergent or not is irrelevant. The point is that “not having a closed form solution” is not the meaning of chaos, which was your original wrong statement.

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    • Blue_Morpho@lemmy.world ⁨1⁩ ⁨month⁩ ago

      No closed form solution is one property. It’s not wrong, only incomplete. But if a system of equations had a closed form solution, it wouldn’t be called chaotic. For example any exponential equation like x^y is extremely sensitive to initial conditions yet it isn’t chaotic.

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      • vrighter@discuss.tchncs.de ⁨1⁩ ⁨month⁩ ago

        oh really?

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