> wouldn't be surprised if predicting climate + weather 12 months out is a simpler problem than most medical problems at which AI is currently being pointed
Simple systems can be famously unpredictable [1]. Our bodies manage entropy; that should make them complex but predictable. The weather, on the other hand, has no governors or raison d'être.
The three body problem lacks a closed form solution. How does that mean it's unpredictable, though? I thought that numerical methods can be used to make n-body predictions to arbitrary precision. Are these simulations less accurate than I am thinking? How do engineers and scientists working on space probes plan their trajectories and such?
> numerical methods can be used to make n-body predictions to arbitrary precision
Arbitrary precision, not arbitrary length. Even "from [a] mathematical viewpoint, given an exact initial condition, we can gain mathematically reliable trajectories of chaotic dynamic systems" to only a "finite...interval" [1]. (This is due to "numerical noises, i.e. truncation and round-off error, where truncation error is determined by numerical algorithms and round-off error is due to the limited precision of numerical data, respectively.")
For a physical system like the weather, uncertainty "mainly comes from limited precision of measurement," though there is also the "inherently uncertain/random property of nature, caused by such as thermal fluctuation, wave-particle duality of de Broglie’s wave, and so on."
> Finite interval doesn’t mean it can’t be arbitrary
Skim the paper. Numerical noise means you cannot calculate the 3-body problem to an arbitrary length. There is a finite, mathematical limit even with perfect knowledge of initial conditions.
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.
You can solve to arbitrary precision but you can't measure and specify initial conditions to arbitrary precision, making the solution wrong outside of a small time interval.
Simple systems can be famously unpredictable [1]. Our bodies manage entropy; that should make them complex but predictable. The weather, on the other hand, has no governors or raison d'être.
[1] https://en.wikipedia.org/wiki/Three-body_problem