3 ms·

Sorry if I misunderstand your point, but the point about chaotic systems are AFAIK this: 1 there are always measurement errors(nothing is perfect) 2 a chaotic

Sorry if I misunderstand your point, but the point about chaotic systems are AFAIK this: 1 there are always measurement errors(nothing is perfect) 2 a chaotic system is predictable but the problem is that is super sensitive to the initial state so the error of the final state will be exponential larger but probably not infinite.

kwhitefoot 7y ago
your use of the word chaotic is from the jargon science. This is not what is meant by chaotic in general conversaton.
- DanBC 7y ago
  But since this discussion is about chaos dynamics it's relevant.
thaumasiotes 7y ago
It's only "super sensitive" to the initial state if you take a very narrow view of what the possible states are. You can start at any point in an infinite Cartesian space and, after enough time has passed for you to reach the small orbital area, you'll stay there forever. Viewed in those terms, not only can you make accurate predictions about the future, but there are sharp bounds on the maximum error those predictions can have. Imagine rolling a bowling ball over an x,y plane with iron rods of positive radius fixed at all the points with integer coordinates. The ball bounces off rods as it hits them in much the same way a real bowling ball would if you rolled it into a stop sign post. Where's that ball going to end up after you roll it in a given direction? Compared to that, a Lorentz system is a model of easy predictability. When you want the particle, you know exactly where to look. The bowling ball could be _anywhere_. The Lorentz particle is guaranteed to be in its orbital, because, unlike the bowling ball system, the Lorentz system is extremely insensitive to initial conditions -- if you view the problem that way.
- simion314 7y ago
  I think you are missing teh point 1 Is all about errors in measurement In the ball example, if it was in some chaotic system, a 1mm measuring error could translate in 1km error for the final point, you could calculate that it will not ever be larger then 1KM if error is under 1 mm but you will nevedr land that ball on the exact spot because you always have errors in the real world.

kwhitefoot 7y ago

your use of the word chaotic is from the jargon science. This is not what is meant by chaotic in general conversaton.

DanBC 7y ago
But since this discussion is about chaos dynamics it's relevant.

thaumasiotes 7y ago

It's only "super sensitive" to the initial state if you take a very narrow view of what the possible states are. You can start at any point in an infinite Cartesian space and, after enough time has passed for you to reach the small orbital area, you'll stay there forever. Viewed in those terms, not only can you make accurate predictions about the future, but there are sharp bounds on the maximum error those predictions can have. Imagine rolling a bowling ball over an x,y plane with iron rods of positive radius fixed at all the points with integer coordinates. The ball bounces off rods as it hits them in much the same way a real bowling ball would if you rolled it into a stop sign post. Where's that ball going to end up after you roll it in a given direction? Compared to that, a Lorentz system is a model of easy predictability. When you want the particle, you know exactly where to look. The bowling ball could be _anywhere_. The Lorentz particle is guaranteed to be in its orbital, because, unlike the bowling ball system, the Lorentz system is extremely insensitive to initial conditions -- if you view the problem that way.

simion314 7y ago
I think you are missing teh point 1 Is all about errors in measurement In the ball example, if it was in some chaotic system, a 1mm measuring error could translate in 1km error for the final point, you could calculate that it will not ever be larger then 1KM if error is under 1 mm but you will nevedr land that ball on the exact spot because you always have errors in the real world.