The butterfly effects would add up and and any zygote formed would not be the hitler-as-we-know anymore, since it would be a different combination of sperm and eggs.
Who needs guns when you got a time machine? Don’t like your highschool bully, just bump into their parents back in time. Or you know, “bump” ( ͡° ͜ʖ ͡°) into their parents.
No it doesn’t mean that. It means that tiny changes in input result in big changes in the output.
By your definition, a simple ellipse is chaotic. Which it clearly isn’t. Tiny changes in the axes result in tiny changes to its shape, and by extension its perimeter. Yet there is no closed form formula for the perimiter of an ellipse.
This could also be verified using a simple dictionary, not even a math textbook.
A tiny change could mean a big change but it doesn’t mean that change must be 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.
https://en.m.wikipedia.org/wiki/Chaos_theory
More importantly, in the real world, if you push a double pendulum, it won’t flail endlessly. It will eventually converge to the single state of rest.
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
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 double 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.
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.
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.
oh really?