3 ms·

Finite interval doesn’t mean it can’t be arbitrary. I’m not saying it can be in this example but your counterpoint doesn’t follow from the quote. For example,

Finite interval doesn’t mean it can’t be arbitrary. I’m not saying it can be in this example but your counterpoint doesn’t follow from the quote. For example, I can calculate the Fibonacci sequence to an arbitrary length but not infinite.

JumpCrisscross 2y ago
> 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.
- echoangle 2y ago
  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.
  - JumpCrisscross 2y ago
    > 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.

JumpCrisscross 2y ago

> 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.

echoangle 2y ago
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.
- JumpCrisscross 2y ago
  > 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.