3 ms·

Try it with a chaotic system like a double pendulum you’ll see the dynamics are not predictive in the long term.

• adrianN 2y ago
  Is that true? It was my understanding that chaotic systems (with a known initial state) could be predicted to arbitrary precision by throwing enough compute at the problem. Of course knowing the initial state is impossible in the real world, „enough“ compute might not fit in the observable universe, and quantum mechanics contains true randomness…
  • philipov 2y ago
    Yes, chaotic systems can be simulated, and that's the only way to find out what happens with them. The thing one can't do is reduce them to a closed-form function of x and compute their value for any point along their domain. The only thing we can do is inductively figure out the next x from the current x.
    • mitthrowaway2 2y ago
      The issue is more that simulations diverge exponentially with time from any nonzero error in the initial state. With perfect knowledge of the initial conditions and parameters you could simulate the system perfectly, but you'd also need to accumulate zero numerical error along the way. If you don't demand perfection, then in practice you can do pretty well for short times.