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.
The butterfly effect refers to divergent chaotic systems. Chaos in math isn’t the layman’s chaos. It doesn’t mean wild. It only means there is no closed form mathematical solution. For example stepping on a butterfly can’t affect the weather such that the moon would crash into the Earth.
Bumping into Hitler’s parents wouldn’t necessarily change anything. You have to do something drastic such that he was conceived days to weeks apart such that the sperm was completely different. Even a minor delay wouldn’t affect it because the sperm that fertilizes an egg isn’t random. There are selection hurdles in mobility that the sperm passes such that the most “fit” is likely the one that fertilizes the egg.
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?
'Robert L. Devaney, says that to classify a dynamical system as chaotic, it must have these properties:[22]
it must be sensitive to initial conditions, it must be topologically transitive, it must have dense periodic orbits. " https://en.m.wikipedia.org/wiki/Chaos_theory
f(x)=x^y doesn’t satisfy those 3 conditions. Nor does the paper you linked say that x^y is a chaotic equation.
That function in the paper cannot be solved for an input because of its sensitivity to initial input. He used a computer to simulate the time steps. He couldn’t immediately calculate any point on the the plot like y^x.
Chaos means that a small change in initial conditions can lead to drastically different places in the long term, so I think OP was using the idea correctly. Though I agree that just bumping into the parents may not be enough to push the system into another trajectory.
Yes, what I was trying to explain is that it could (no closed form) but doesn’t necessarily mean that is must. A chain with 2 segments is a double pendulum, the classic simple chaotic system. If you hold a piece of chain and give it a light tap, it will move chaotically for a few seconds and then come back to rest. The system will not have changed. Even with a hard push, the chain can’t move beyond the limit of the links.
If you gave Hitler’s dad a push, he would stumble for a second (chaotically), then go back to walking (return to initial state). Nothing would change.
Kick his dad in the nards!