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Completely out of curiosity: what's the most shocking example of chaos you know? Something that shows (to a non-expert audience) how quickly errors grow in a chaotic system.

For example, I was thinking of something along these lines:

If you simulate a frictionless billiards table with 1000 balls, but you omit the gravitational pull of Pluto, your simulation will be completely wrong in less than a minute.

This particular example is probably not true, but that's the type of statement I'm looking for. Can you think of any examples?

References, or even back-of-the-envelope calculations are appreciated.

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closed as primarily opinion-based by StephenG, G. Smith, Aaron Stevens, Qmechanic Apr 27 at 4:11

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This question will likely be closed soon since opinion-based questions are not suited for this forum. You might want to rephrase it into a question that has a more definite answer like "What actual physical chaotic system is most chaotic?" $\endgroup$ – Anders Sandberg Apr 26 at 22:19
  • $\begingroup$ @AndersSandberg thanks for the heads-up. I'm looking for appropriate examples for an outreach talk, which (I would imagine) is a legitimate question for this SE. Would a re-write along these lines work? $\endgroup$ – Pedro Mediano Apr 26 at 22:45
  • $\begingroup$ No matter how interesting and legitimate a question is, @AndersSandberg is right, at least because of the "shocking" in the question - it really makes it too subjective for the site (which qualifies "opinion-based" questions as off-topic). I think Anders' suggestion for a question is good and, since its answer is probably unknown/unclear, you still might end up with enough different examples. $\endgroup$ – stafusa Apr 26 at 23:33
  • $\begingroup$ I'm performing a rollback to V1 because I think that neither of the existing answers attempts to claim that the systems described are the 'most chaotic'. In my opinion, V2 is a different question. $\endgroup$ – user191954 Apr 27 at 16:31
  • $\begingroup$ @Chair I understand your point that V2 is a different question, but I was following Anders' suggestion to avoid my question being closed. Is there any way we can move out of this impasse, either by rephrasing or just reopening the question? If anyone could edit the question to avoid having it closed, I would really appreciate it! $\endgroup$ – Pedro Mediano Apr 27 at 20:30
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there is a coupled-pendulum system which dramatically demonstrates the development of chaos, as follows.

Imagine the capital letter "T" that has a pivot joint at each of its three ends. Suspended from each pivot is a short bar that is free to swing or rotate around its pivot. Another pivot is provided in the vertical stroke of the "T", near its junction with the horizontal stroke, around which the whole arrangement can freely rotate.

Position the apparatus so the "T" is in the vertical plane and all three sub-pivoted bars are pointing down under the influence of gravity.

Rotate the apparatus around the main pivot- spin it up fast enough that all three bars are thrown fully outward- then allow its speed to decay. At some point the bars will not follow the rotation of the whole assembly but will begin rotating on their own.

As they do they will apply reaction forces to the "T" which perturb its rotation, and soon the three bars and the central "T" will be rotating one way, then the other in a bizarre dance which is random and unpredictable.

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  • $\begingroup$ "Diamond Dogs" by Alastair Reynolds is a nice yarn, with a computer trying to outwit a chaotic system precisely the same as the one you have described. $\endgroup$ – StudyStudy Apr 27 at 17:55
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    $\begingroup$ I believe it can be done- having watched the demo at the Fresno Museum science basement 25 years ago. You have an angle encoder at each pivot point and a locking mechanism next to it. Whenever the encoder registers zero relative angular velocity at that pivot, the lock engages and subtracts a degree of freedom from the dynamics. I think it is worth trying... $\endgroup$ – niels nielsen Apr 27 at 18:35
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When I was reading about chaos and the world of Lorentz, the book I was reading had a fascinating example about trying to predict the weather.

Let's say you have created a meteorological sensor which can capture all of the information you could ever want about the weather, in perfect precision. You lay these out in a 1 meter cubic grid through the entire atmosphere, nevermind the challenges in making this a reality.

Let's say at 12:00 midnight on Jan 1, you feed all of the information from these sensors into the most perfect supercomputer imaginable, capable of as many calculations as you could possibly need to predict the weather.

By 12:01, you are already wrong. Vertices which fit between your 1 meter gridded sensors have expanded, affecting some of the sensors.

By Jan 4, those errors have grown so much that your predictive capabilities are not that much better than weathermen today.

By Jan 31st, the errors have had such an astonishing effect that you basically cannot predict whether Tokyo will have rain or shine any better than a Farmer with their almanac could have.

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  • $\begingroup$ Interesting. Which book though? $\endgroup$ – exp ikx Apr 27 at 15:51

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