A tiny change could mean a big change but it doesn’t mean that change is unlimited. For example a double pendulum is a classic chaotic system. There is no solution but that doesn’t mean the pendulum can move greater than the length of its segments. It’s still a bound system.
vrighter@discuss.tchncs.de 1 week ago
what does any of that have to do with anything I said? By the way, that wikepedia page doesn’t contain the word “closed” anywhere in it. just saying
Blue_Morpho@lemmy.world 1 week 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.
vrighter@discuss.tchncs.de 1 week 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.
Blue_Morpho@lemmy.world 1 week 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.