Isn’t the paper about the uncertainties that inherently exist with physical systems?
There isn’t any claim that mathematically exact starting values can’t be propagated with arbitrary precision to arbitrary length, and I would claim that this is possible (but not practical due to compute being limited, of course).
But there’s no hard limit of precision and length where a simulation can’t be made if the starting conditions are exact. The point of the paper is that starting conditions are never exact which limits the length you can propagate.
> Isn’t the paper about the uncertainties that inherently exist with physical systems?
It talks about that. Which is relevant when we're talking about the weather. But it opens by discussing the hard mathematical limits to numerical methods.
> there’s no hard limit of precision and length where a simulation can’t be made if the starting conditions are exact
Wrong.
Read. The. Paper. Numerical methods for chaotic systems are inherently, mathematically uncertain.
Beyond a certain number of steps, adding precision doesn't yield a more precise answer, it just produces a different one. At a certain point, the difference between the different answers you get with more precision covers the entire solution space.
There isn’t any claim that mathematically exact starting values can’t be propagated with arbitrary precision to arbitrary length, and I would claim that this is possible (but not practical due to compute being limited, of course).
But there’s no hard limit of precision and length where a simulation can’t be made if the starting conditions are exact. The point of the paper is that starting conditions are never exact which limits the length you can propagate.