Nope, given our current theories time travel is practically impossible. On the other hand we know that chaotic systems are functions and that matrices can approximate any function.
I'm not sure what point you're trying to make. Matrices only perform linear transformations, so matrices only approximate functions linearly, which in general, is a terrible approximation globally.
Especially, if you have complex systems where discretization and linearization aren't computationally achievable and/or numerically accurate ... like predicting global weather patterns or even very small experiments. I think about the phrase: All models are wrong; some models are useful.
I was pretty sure someone was going to focus on the example I gave instead of the idea :), very predictable. Chaotic systems are not just functions, that's why there's an entire discipline that studies them. There are many ways to approximate functions that have been developed during a long time and all have had trouble approximating chaotic functions.
If you’re going to be that pedantic, I’ll see your pedantry and raise you. Time travel is not only possible, but routine, just in the forward direction only. It’s only travel into the past which is probably impossible, and to be even more pedantic and abstract, impossible only in our observable spacetime geometry.
So is with the chaotic systems: we know for sure that approximating them is just a matter of boundary conditions: that is - the more you know about the starting points, the better you approximate the real world.
I mean, there might be a case where we will finally get to the point where we are just "good enough" at measuring the boundary conditions to predict weather for the next year, but it has got nothing to do with obtaining the knowledge about chaotic systems themselves.
