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> This only demonstrates that the system is chaotic, not that there is no closed form solution. This seems a bit off, it seems like[1] an implicit assertion ("
by mistermann 3y ago
> This only demonstrates that the system is chaotic, not that there is no closed form solution.
This seems a bit off, it seems like[1] an implicit assertion ("only(!) demonstrates") that it is not possible for a system that lacks a closed form solution in fact (beyond our ability to discern) to be demonstrated.
To be clear I'm in no way implying this was your intent (I see it as an interesting "quirk" of our culture)...I'm mainly interesting if you can see what I'm getting at.
As a thought experiment, stand up two instances: one is our current situation (inability to discern, indeterminate), the other where we have (somehow) proven out (or, come to believe we have, reality being Indirect but experienced as Direct, thus: "is "proven", thus: "is") that a closed form solution is not possible: would the second instance "be(!) a demonstration that the system has no closed form solution"? (Thinking more....I think maybe the choice of the word "demonstrate" may very well make a path to seeking the truth of the matter ~impossible to achieve in these sorts of cases, especially if one takes cultural forces[2] into consideration).
[1] Using "pedantry", which few people understand the technical meaning of, and tend to flip flop on depending on what is being considered (precision & accuracy in science/physics is good, precision & accuracy in philosophy/metaphysics is bad - no explanation or justification needed: a Cultural Fact).
[2] Which make the 3 body problem in the known to be deterministic physical realm seem like child's play.
- jovial_cavalier 3y agoI'm not sure I understand what you're saying. >As a thought experiment, stand up two instances: one is our current situation ..., the other where we have (somehow) proven out ... that a closed form solution is not possible As far as I understand, this has in fact been proved. Quite a long time ago, too, by Poincare I believe. GP has edited his comment to reflect my feedback, but originally said that his experiment "demonstrates that there is no solution." All I was trying to point out is that the two concepts are not necessarily related. You could imagine some system x' = f(x), where f(x) is some transcendental function. There is no analytic solution to this system, but it's obviously not chaotic. Could you imagine a system that is chaotic but does have an analytical solution? I'm not sure. Closest I could find to answering this was: https://sprott.physics.wisc.edu/pubs/paper496.pdf https://sprott.physics.wisc.edu/pubs/paper496.pdf I'm sure he understood this. I only commented to try and minimize the confusion of others. edit - This article suggests that the logistic map (a system famously used to introduce the concept of chaos) has an analytical solution: https://www.sciencedirect.com/science/article/pii/0378437195001632 https://www.sciencedirect.com/science/article/pii/0378437195...