What is Chaos Theory?

Discussion in 'General Philosophy' started by wegs, Sep 1, 2019.

  1. Seattle Valued Senior Member

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    If the answer is "there is no relationship" then there is no "quantum chaos"?

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    What is the relationship between quantum mechanics and classical humor?
     
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  3. sculptor Valued Senior Member

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    gestalt
    (The whole is greater than the sum of its parts.)
     
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  5. wegs Matter and Pixie Dust Valued Senior Member

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    Classical humor?

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  7. Seattle Valued Senior Member

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    If you change the "yess...yess" to "hehe, yes?"
     
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  8. wegs Matter and Pixie Dust Valued Senior Member

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    ''hehe'' isn't as diabolical. This is a diabolical butterfly.

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  9. Seattle Valued Senior Member

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    I could tell that butterfly was up to no good from the first frame. "hehe" is more creepy than diabolical I agree.
     
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  10. wegs Matter and Pixie Dust Valued Senior Member

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    LOL for realz

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  11. Michael 345 New year. PRESENT is 72 years oldl Valued Senior Member

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    To small to make out the fine details but I am guessing a diabolical butterfly has fingers in arch mode and tapping them in sequence

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  12. billvon Valued Senior Member

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    But not "muahahaha" level diabolical.
     
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  13. Yazata Valued Senior Member

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    I tend to think of this in terms of non-linear dynamics.

    Imagine a mathematical function. This is a one-to-one mapping of mathematical objects (typically real numbers) to other mathematical objects (real numbers). It can be thought of as a black box, where if you input a number, another number pops out. Functions can be illustrated in graphs, there the x-axis is the input number and the y-axis the output number.

    All of those mathematical hieroglyphs that theoretical physicists love so much are defining functions that they believe or hypothesize define the relationship between different physical variables.

    Typically, these graphs are lines. Meaning that if we change the x input an infinitesimal amount, the y output only changes an infinitestimal amount. The smaller the change in x, the smaller the change in y.

    But not always. Sometimes the graphs of functions aren't lines at all, but rather dusts. A small difference in x might produce a huge difference in y, such that the points of the graph are scattered all over seemingly randomly.

    It isn't entirely undetermined since if there's still a function defining where each y falls given a particular x, there would still be a deterministic function. But the non-linearity makes extrapolation and interpolation impossible.

    And determining from experimental results that appear random that there's indeed a function determining the outcome might sometimes be more an expression of metaphysical faith than anything that anyone really knows. I'm not sure how one could demonstrate it.

    The bottom line is that with some functions, even an infinitesimal difference in x can be associated with an arbitrarily large difference in y.

    The question then is how many of what seem to be totally random (the word used is stochastic) processes in nature are in fact determined by nonlinear functions?

    Back in the 1990's this kind of stuff created tremendous excitement and many universities created research units to study it. But I don't believe that many useful results ever emerged and much of the excitement has dissipated. They did succeed in producing some interesting (though perhaps not definitive) mathematical tests for chaos though.

    My saying this will probably anger some people (you can guess who), but I don't really distinguish between philosophy, mathematics and physics at the level of fundamentals. This is all three and of interest to all three.

    I can't prove it, but I'm inclined to think (very strongly) yes.

    Quantum mechanics might conceivably have big implications for this. If some of the functions describing the evolution of physical systems and the unfolding of physical reality itself are indeed non-linear, such that even infinitesimal differences in the value of input variable x can be associated with huge differences in how the universe unfolds (the value of subsequent variable y)... and if some physical values on the microscale are undefined and only probabilistic, then we could perhaps argue that there aren't any mathematical functions (in the 'if a particular x, then a particular y' sense) governing these events. They might just be stochastic by their fundamental nature.

    If quantum mechanics makes the idea of precise x's physical existence problematic, and if nonlinear dynamics can amplify even infinitesimal differences in x into big differences in y (in how the universe unfolds), then the 19th century deterministic picture of physical reality might start to collapse.

    That's one reason why I'm not inclined to imagine time as a single one-dimensional line extending from a determined past (what happened happened) to a determined future (what is going to happen must happen precisely that way).

    I'm more inclined to imagine the future as an infinitely branching tree, where countless future states of affairs are consistent with the state of the universe now. I don't see the present state of the universe as determining precisely which branch and twig of the tree the future follows. It probably does put probabilistic constraints on how the future unfolds though. Some possible futures are more probable than others, given how things are now or were in the past.
     
    Last edited: Sep 11, 2019
  14. RainbowSingularity Valued Senior Member

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