Only if it is inside the predictable domain. AFAI remember, predictability breaks down after reynolds numbers become a certain value in fluids at least.
This is fair point. This i precisely what the theory is about. But, it also does say that at certain situations the variations in system given small perturbations is so large it is essentially unpredictable, isn't it?
Anywho, what I wanted to say was that Chaos Theory, Order Theory, and Paradox Theory.... went a little wild by the OP.
You're right about how Reynolds number give an idea about if the flow is laminar or turbulent. It doesn't say anything more than that itself.
"predictability breaks down after reynolds numbers become a certain value in fluids at least" that observation/statement must comes from another source, not the Reynolds number itself because it doesn't claim more than turbulent transition. I'm pretty sure it was an engineering tool for a bunch of scientists to design their pipe sizes and say "oh fuck, the flow is changing shape". I don't have any knowledge to bridge the logic that Re=>unpredictable. Only Re=>turbulent or laminar.
You're right about the fact that laminar flow can be simple enough to have analytical solution. However, engineers are making paintstaking effort to predict turbulent flows thanks to the advance in computer science, saying that turbulent flow just can't be predicted is the same as saying that they should drop their job and do something more useful lol.
"But, it also does say that at certain situations the variations in system given small perturbations is so large it is essentially unpredictable, isn't it?"
I agree for every sensitive systems considered in our physical real world that they are unpredictable from start to finish.
You could write about a fictitious universe where people can control initial condition infinitely perfectly and that doesn't stand true anymore. That world would be pretty easy to predict for the people inside.
Predictability is a spectrum too. It depends on the timeframe and how precise your inputs you are. You could linearize the system and have a close prediction of the real system in the next little timeframe. The more you're accurate in your model and inputs, the longer you can stretch the acceptable predictions.
I'd rephrase your sentence like this: "Chaos theory shows that
real physical systems that are highly sensitive to perturbations/initial conditions are unpredictable in an infinite timeframe
because those quantities cannot be infinitely controlled/measured."
It becomes compatible with the fact that weather can be forecast and why it's shit.
Functions/systems that can give two outputs with the same inputs aren't deterministic. I guess they exist but they aren't the target application of chaos theory.
Yeah agreed, OP went really wild lol
