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I was watching the following video: https://youtube.com/shorts/fK1VmX9mzRw?feature=share

In the video, they claim that a double pendulum is not "random" but "chaotic". The future trajectory of the double pendulum is unpredictable at any time, and can only be loosely predicted using postions at immediately preceding time points.

Doesn't that effectively make it random?

Thanks!

stats_noob
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  • I know close to nothing about this subject. According to this post "Random behavior is non-deterministic: even if you knew everything that can be known about a system at a given time in perfect detail, you would still not be able to predict the state at a future time. – Bumblebee Dec 28 '21 at 07:21
  • Chaotic behavior on the other hand is fully deterministic if you know the initial state in perfect detail, but any imprecision in the initial state, no matter how small, grows quickly (exponentially) with time." – Bumblebee Dec 28 '21 at 07:21
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    Very casually speaking, it is not random, because the equations of motion are known and completely deterministic, but it is chaotic, because an arbitrarily small perturbation can change the whole course. – dxiv Dec 28 '21 at 07:21
  • May I point out that randomness does not entail utter unpredictability. P.S. Do consider accepting (and/or upvoting) answers to your questions. – ryang Dec 28 '21 at 08:17
  • @ ryang: I routinely accept answers on stackoverflow when there is code involved, because I can check and see if the code provided runs. When it comes to math, I am in no position to really comment on the answers - i greatly appreciate the answers and find them very useful, but I am not sure if I can accept them because I have no way of "checking to see if they are correct" (unlike the answers on stackoverflow that are code), because I am not a mathematician. – stats_noob Dec 28 '21 at 08:20

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