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Does Chaos Really Exist ?

  1. Oct 27, 2014 #1
    So I get the gist of Chaos Theory, and I read through another thread on this forum stating that Chaos does exist, which quotes Chaos Theory.

    Does this not seem to be a tad counter intuitive ?

    Chaos theory simply states not knowing the starting attributes of a mathematical system that you can't really predict the outcome.

    Thing is, Chaos doesn't seem to be a fitting adjective, it just sort of reasserts that we have no real clue LOL

    Correct if I'm misunderstanding but there are ALOT of things we don't know, however what we do know seems to be rather provable and reproducible mathematical systems of describing behavior under certain conditions.

    Of course we can write a system of equations to describe how a feather would fall in IDEAL conditions, but real conditions are never ideal.

    But lets say we did have the ability to measure and predict every aspect of air flow and the initial starting point of the feather etc.

    It could be said that in that case we could predict its landing spot from a certain height, at a certain gravity, given its mass, volume, shape and initial displacement above the ground, and any other factor that would even affect it, like the sun shining more or less, no matter how small of an effect that would have.

    Point is, I don't feel in an ordered universe that Chaos really exists, its just a concept that is thoroughly human relating to our lack of ultimate knowledge causing something to go other than expected. So I suppose my question is, does any branch of science really have any way of proving the existence of randomness ?
     
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  3. Oct 27, 2014 #2
    Chaos is an extreme dependence of the dynamics of a system on the initial conditions of the system. A infinitesimal difference in initial conditions can lead to arbitrarily large deviations in a finite amount of time. It is not about randomness, and no one ever said it was. The point is that because you are limited in your ability to measure the initial conditions of a system, then realistically systems which exhibit chaotic behaviour can not be easily predicted.

    Yes, chaos is a very real phenomenon and there are many many real-world examples.
     
  4. Oct 27, 2014 #3

    Dale

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    Chaos and randomness are two completely different things. Chaos is a system that is not random, it is deterministic, but it is highly sensitive to small perturbations in the initial conditions. Randomness is where the exact same initial conditions can lead to different outcomes.

    That said, I am not sure if you are interested in chaos or randomness, but either way "I don't feel ..." is not a valid scientific proposition.
     
  5. Oct 27, 2014 #4
    Well, the beginning of a hypothesis begins with 'I feel" or "I perceive", so I will rephrase. In the sense that chaos, as we understand it outside of science, so equating to randomness, has their been any proof or disproof that true random occurrences happen ?

    There are willed actions, that we perform, celestial bodies and their interaction could be pretty well predicted, gravity can be measured at various points on the globe, if we had a sophisticated enough array of sensors we could measure wind velocity at varying levels, air pressure etc.

    I suppose we're leaning more towards philosophy at this point.

    The idea that we are not knowledgeable enough to predict with precision certain events and that a small numerical modifier on a system will gradually increase to a vary large one over time, as the effect would most likely have a recurring or rate related meaning, as in the case of say introducing energy into the equation with an x-axis bent, is definitely true.

    But is it randomness proper ? Or is it lack of total knowledge ?

    From my understanding the goal of science is to grow and expand until all knowledge of the mind, body, matter, energy, movement, heat, chemical reactions, neurons, etc etc etc has been so thoroughly recorded and proofed into absolute scientific law that no aspect of the universe remains a mystery (obviously we'll probably be extinct before that happens).

    I mean forming a hypothesis I could say. That TRUE randomness does not exist, because in controlled experiments isolating the object of study from external influences not relating to the principle being studied, that I can reproduce the same effect or result continually, if my hypothesis is correct. This is true of many things.

    This would suggest absolute order, not randomness, with randomness being our mind's perception of the event as random, simply because we are not sophisticated enough as human beings to recognize or see all forces or principles acting on the object which effects its overall path of motion or change of state.

    Because of this thought, my main interest, and perhaps I should have been more clear, is whether any scientist has ever been able to find anything, or currently undergoing any study which in fact does prove that there is at least SOMETHING that displays true randomness in the universe and cannot be tied down to a cause and effect standard.

    I mean even psychology works off cause and effect... even if its very hard to create hard and fast laws in psychology, many principles hold true.
     
  6. Oct 27, 2014 #5

    Dale

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    Again, you are mixing up two separate concepts, chaos and randomness.

    Classical mechanics is deterministic. Given perfect knowledge of the state at one time you can predict the outcome of any measurement perfectly. Nevertheless there are systems which classically exhibit chaos. Since our knowledge is never perfect our prediction errors can grow arbitrarily large.

    Quantum mechanics is random. Even given perfect knowledge of the state we cannot predict the outcome of some measurements perfectly.
     
    Last edited: Oct 27, 2014
  7. Oct 27, 2014 #6
    For a chaotic system, see:
    http://en.wikipedia.org/wiki/Lorenz_system
    For a random system, see:
    http://en.wikipedia.org/wiki/Brownian_motion
    In a chaotic system, infinitesimal changes in the starting position can lead to completely different outcomes.
    In a random system, you don't even know the starting position, or the forces that determine the change in the system, nor is there the possibility to know them. For a deterministic description of Brownian motion, you would need to be able to compute the trajectories of all the molecules that interact with the Brownian particle, which is not possible (physically. not because the human mind hasn't come up with a solution yet).
     
  8. Oct 29, 2014 #7

    Danger

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    When in doubt, blame it on Heisenberg. That little bugger ruined it for all of us. :mad:
     
  9. Oct 29, 2014 #8
    I could never quite grasp why men of Newton's time saw the n-body problem (then, specifically the 3 body problem) as a randomness problem rather than a chaos exercise, and assumed it unsolvable. Then again, we do have the advantage of hindsight.
     
  10. Oct 29, 2014 #9

    Danger

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    Bigfooted, I am in no condition right now to read your links (I really need to sleep), but will do so tomorrow. Meanwhile, though... I always thought that quantum randomness is the driving force behind chaos. Is that mistaken?

    edit: Oh... I just looked back in the thread and noticed that you're currently off-line. Probably sleeping yourself, you lucky bugger. Fine, then... I'll just wait until tomorrow. :p
     
  11. Oct 29, 2014 #10

    Filip Larsen

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    As it has been mentioned a few times in this thread already, chaos (i.e. the phenomena that Chaos Theory describes) is a purely deterministic phenomenon that exhibits its complexity through non-linear effects. The precise state of a chaotic system in classical physics (i.e. without quantum effects) would be considered unpredictable after some time, even without any source of randomness. This unpredictability comes from amplification of state (and parameter) uncertainty and not from any inherent random process. Or in other words, in classical physics there are no true sources of randomness, its all "just" uncertainty (the distinction between "uncertainty" and "randomness" in classical physics is probably a meta-physical discussion).

    Note that all this does not mean that the behavior of a chaotic deterministic system is unknown. It is still possible to analyze and calculate a lot of interesting measures and similar for such systems, even if you cant predict the precise state arbitrarily long into the future.
     
  12. Oct 29, 2014 #11

    Danger

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    Thank you, Filip. That clears things up a bit. It also, unfortunately, convolutes things by about the same bit. (I should mention that I am now not only exhausted, but also somewhat inebriated, so bear with me. I seem to react to a dozen beers more vehemently than I did in my youth.)
    Part of the problem is that I didn't realize that Determinism still existed as a theory, let alone a belief. Or am I mistaking it for Superdeterminism, which I'm pretty sure was shot in the head decades ago? (I don't know now whether or not they're the same thing; I always thought so.)
    Mainly, though, I simply cannot get through my head how a deterministic state can become unravelled without the input of quantum effects. The whole point of it is that every single thing is predestined based upon original conditions, which hence precludes the possibility of "free will".
     
  13. Oct 29, 2014 #12

    anorlunda

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    Last edited by a moderator: May 7, 2017
  14. Oct 29, 2014 #13

    DaveC426913

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    Chaos is a classical system. It is more coarse than the quantum level.


    This double pendulum exhibits chaotic behaviour, yet it has nothing to do with QM.

    From the Wiki page:
    "Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions."

    Lorenz summarized it eloquently, thus:
    Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
     
    Last edited by a moderator: Apr 28, 2017
  15. Oct 29, 2014 #14

    Danger

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    I have it. My cousin gave it to me for that December holiday that I don't celebrate some 20 or more years ago (whenever it was published). I absolutely loved it. In fact, this thread makes me really want to read it again, but I have to overcome my physical difficulties enough to get to my optometrist and order a new pair of glasses. I lost mine about 6 months ago. I had some nice $1.99 reading glasses from the pharmacy, but my ex-wife buggered off with them last week. Leaving my house to get another pair would entail even more hardship than going to the optometrist, since the walk to the pharmacy is about 2 km longer, so I might as well just go for the good ones. Besides, the reading glasses cost $1.99, and the real trifocals are free. (I'm on AISH, so I'm allowed a new pair about every year if needed. This will be my second in several years, and I don't really feel guilty about losing the last pair because the prescription was no longer valid.)
    Anyhow... Great book. I'll read it again when I'm physically able to.
    Dave, I've always loved watching those pendulums. I just can't quite figure out how they're non-deterministic within the confines of being deterministic. It's like a Catch-22. (Let's see how long it takes the kids to figure that one out.) From what I understand of Determinism, it precludes, by it's very nature, the possibility of randomness. It also precludes free-will, because everything that has happened or will happen is predestined. If I walk out of my house and into the path of a truck, it's because I have no choice in the matter. It's like believing in a supreme being. (Well, there's no point in studying astronomy because the guy upstairs can change the gravitational constant whenever he wants. :rolleyes:)
     
  16. Oct 29, 2014 #15

    DaveC426913

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  17. Oct 29, 2014 #16

    DaveC426913

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    I don't know why you think of it as non-deterministic. If you set the system up exactly as before, you will get the exact same results. The fact that it is practically impossible to do so does not preclude it being deterministic.

    An easy way to see this is to do it programmatically. With a digital simulation, you can set the system up identically every single time (because your simulation has a finite limit on coordinate resolution, even if it's 100 decimal places). You will get the exact same results, every single time you run the sim.

    But change that hundredth decimal from a zero to a one and you get a completely different outcome.

    So chaotic, yet deterministic.

    Which, I suspect, is why a lot of people are beginning to wonder if consciousness is a quantum effect.
     
  18. Oct 29, 2014 #17

    Danger

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    Right there in that first bit is what I'm having trouble with. "Practically impossible" implies that it can be done. And if it is done, the result, as you said, will be the same. That means that every single subatomic particle and the interactions among them will be in exactly the same relationship and position that they were in the first place. I maintain that such a repetition is absolutely not possible as opposed to "practically impossible".
    As for consciousness, I don't believe that it could be possible without quantum effects. I could be wrong about that, but the fact is that quantum effects exist and therefore there isn't much point in debating what life would be like without them.
     
  19. Oct 29, 2014 #18

    Dale

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    Free will and consciousness are off topic. Please stick to the physical and mathematical aspects of chaos and randomness and not their philosophical and psychological implications.
     
  20. Oct 29, 2014 #19

    DaveC426913

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    No. The sensitivity does not have to be infinitely fine.

    The computer simulation is a perfect (if virtual) example. The sensitivity only extends to the limit of the resolution. In that example, no changes smaller than the 100th decimal will have any effect on the outcome. If you make a really coarse sim, say, 3 decimal places, then having your initial condition within a tolerance of a mere 0.1% will be sufficient to reproduce the outcome repeatedly.

    There is no reason not to think that this could be the case in nature as well, though it might be harder to find examples.

    Biological Populations levels often follow chaotic theory, the population of one year will have an impact of the next year's population. Sometimes this is a steady progression, but sometimes it dissolves into chaos. It's not easy to describe succinctly here, but it has been well-studied.

    v13im8.gif

    The point is that initial conditions (the pop. in year n) will lead to a deterministic outcome (the pop in year n+1), but initial conditions might be coarse (eg. hypothetically a population between 4031 and 4044 will always result in a 10% increase in pop next year, while a population between 4045 and up will result in a chaotic value next year.)

    So, in this hypothetical case, sensitivity of the system is less than 12 individuals. You can have realistic variations in initial conditions without having the system reacting infinitely chaotic.
     
  21. Oct 29, 2014 #20

    Danger

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    Okay. Sorry for the inadvertent derailment, but I find it a bit difficult to separate those elements. I know nothing of math (the only trouble that I ever got into in high school was for assaulting a math teacher at the beginning of grade 10 and I never took the subject since (and it was richly deserved, lest you wonder).
    Now, be sure to realize that this is an honest question rather than a confrontational snipe. Just exactly how is one supposed to separate the concepts of determinism and the lack of free-will when they are exactly the same thing? Determinism means that every single thought in your head was destined to be there since before the beginning of time. I'm willing to treat them as separate subjects if you can tell me how to.
     
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