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Enigma of the butterfly effect

  1. Feb 28, 2008 #1
    I am trying to understand the so called "butterfly effect".

    By wording used to describe it, audience gains an intuitive impression that a small initial action of some sort can produce very large changes in system including unleashing storms that have built up.

    However the original writing seems to claim something else. Initial degree of certainty drops exponentially and system although deterministic, can not be predicted further on. What lies at the beginning of the sensitive reaction is a small initial uncertainty - a value which has physical units but doesn't seem to connect to the chain of cause and effect as a physical reality. It introduces a large amount of randomness into system and it is puzzling how that is treated as a physical mechanism.

    If I presume that in some concrete case exists a real, fundamental physical quantity, does it have a possibility to cause major events beyond it's own energy-momentum?

    At the first glance due to energy conservation, all the laws of mechanics and friction there is no such thing. The implications are mind-boggling. Going back to the past and altering anything appears to the intuition as something that would change everything in the present time - but it won't - everything in it's fundamental nature would remain the same. And yet at the same time, there is absolutely nothing accurate that can be said about the future.

    Do you believe there is some specific physical quantity that is at least conserved as information throughout the event of first initial action to which a system reacts sensitively?

    And finally, is a stored mechanical potential something that can fluently give the momentum to a small particle to release the potential in the system?
  2. jcsd
  3. Feb 28, 2008 #2


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    It seems that you have spent some time and effort delving into this. If you can, I would suggest that you locate a copy of "Chaos" by James Gleick and give it a good read - maybe 2 times through. It's an old book, but there are some foundational concepts expressed there.
  4. Feb 29, 2008 #3
    (I thinks books won't help for now because I'm browsing them and I'm waiting for something great but go ahead with ideas.)

    I'm currently thinking of the following schematic. Although the most intriguing questions I posed continue on, I invented brand new postulates of the new physics of dynamical systems. Behold...

    1. natural laws are attractors that freely float, spreading out their influence into chaos
    2. clap of the butterfly's wings will remain forever emanating into infinity in all dimensions and directions as a constant, undifferentiated, infinitely small and untraceable influence which adds a random amount of data into the chaotic system.

    (I rock :-)
  5. Feb 29, 2008 #4
    A more simple example of chaos is the three body problem.

    Applications of the three body problem to space flight are discussed in the following thread:

    http://www.newmars.com/forums/viewtopic.php?t=2410 [Broken]
    Last edited by a moderator: May 3, 2017
  6. Feb 29, 2008 #5
    Last edited: Feb 29, 2008
  7. Feb 29, 2008 #6
    Can you describe this more?
  8. Feb 29, 2008 #7
    This is amazing example to study. The most notable feature is how they call it the zero-energy trajectories in solar system. That just might have something to do with my invention of the first law. Just like the first Newton's law, the motion is postulated to last for ever at no expense until collision or other interaction. In that respect the distance in space and time between close proximity to one or another planet appear to be what I called non-physical. Spacecraft could gain potential from either planet and start falling in some case if that is the plan but between the two passes and two such possibilities there is a partial free motion between gravitational fields.
    Last edited by a moderator: May 3, 2017
  9. Feb 29, 2008 #8
  10. Feb 29, 2008 #9
    I'm new here, but not new to science. I think Lojzek's explanation is a very good one. I think you missed the subtlty of his explanation.

    Maybe another way of saying it is that chaos doesn't create energy. So, when you clap your hands (wherever you are), it doesn't have enough strength to reach me here in the U.S. Chaos does not say the strength of the signal will increase. It says random fluctuations in the signal make it impossible to predict the exact state of that energy in the future.

    So, when you clap your hands, people in the room will hear it because we know the AVERAGE effect. However, we can't predict which particular air particle will reach the ear of the person listening.
  11. Mar 1, 2008 #10
    I'm calling it a second law now instead of first and I AM LOVING IT :-)) Lorentz had in mind the quadratic attractive iterating formula - one simple equation. It's fixed form reminds me of a physical law. It is ideal in a limited way. What you can do with it is run two sets of iteration with a slightest possible difference in starting point - and then when the two graphs are compared they start to differ even more great until they're incomparable.

    So if were expecting to obtain from a finite set of physical laws the deterministic fate - I do get that as far as there is energetic connectedness - at least in principle of cause and effect and equation for flow. However if I imagine a localized system from which is emanating a radiation (on which to base one law) then the similarity emerges.

    Partially that must be true - but the classical mold for a law with equal sign being a deity, giver of the result doesn't match my invention; someone will know to find a flaw in idea that laws are attractors.

    With the first law I'm thinking in line of the first Newton's law but for dynamical systems: initial cause that is a motion or work of force will continue to exist indefinitely (as energy - you know that) and it will be untraceable and will add a random amount of low-energy data (stream of bits) into system depending from conditions.
  12. Mar 1, 2008 #11
    I'm trying to see a statement here but? Lets see those trajectories around Lagrange points. We send a spacecraft at minimal expense to travel via low gravity areas and occasional favorable curve. With a little error the craft goes into orbit around some planet which would take another rocket to escape. Hence, it was easy to send people to Mars. The minimum fuel energy for that is E>0.

    Sensitive? Yes, sure - but energy never drops to zero and no planet moves.

    Hearing is very sensitive to harmonics present and speech recognition is something special. The whole system can be broken into more statistical subsystems until atoms! I don't see a point.

    Do you think that avalanche qualifies as butterfly effect? Is that something that really starts off as one connected system from one show ball? Is snow ball conserved as information in the valley?
  13. Mar 1, 2008 #12
    Wow. You really don't get it. We'd have to step back and try something simpler before this is going to go anywhere.

    I'm not saying my explanation was flawless, but ... maybe it's a language barrier.
  14. Mar 1, 2008 #13

    I don't see any answer at all from you. I bet a million of anything that if you ask any student if a small pinball can cause avalanche they'll say yes. Whats the word then? :-))
  15. Mar 1, 2008 #14
    Im not really sure how to answer you. Im having trouble understanding what you are saying. Im not familiar with HOW you are using familiar terms common to nonlinear dynamics and chaos theory.

    Can you back up your 'law' witb any experiment or numerical simulation? Newton's laws have stood the test of time.

    Can you explain what an attractor and a physical law is? I dont see the connection.
  16. Mar 2, 2008 #15

    I understand :-)) Why don't I leave aside my invented laws just for the moment so that I don't kill the base for all this. We can discuss that later for creative approach...

    Well, how should I simplify? Butterflies around the world don't cause hurricanes, they don't stop them, their whole contribution is nothing but a smallest fraction of one Joule of energy to the planet earth. Butterfly effect doesn't exist. One thing on my mind is if there is somewhere in physics such effect after all.

    In daily life we are confronted with handy user interfaces that operate machines such as Windows. Although it is highly accessible to erase whole Windows in a moment, this does not qualify as a basic physical phenomenon or basic system.

    Just to make sure that it really is not a simple system - imagine the opposite. Starting with few basic laws I would be able to prove beyond doubt that my Windows system, me and you, and everything else would be produced in another universe if we restarted the whole universe. But we can't prove that because we need to add more energy and act more to make sure that would be truly so. It doesn't arise from simple curves or graphs of Newton's force for example. It does arise from all that in principle within some reasonable limits of certainty. I would like to talk about it better but I can't. I have read on the nature of the physical law and similar topics so I won't try to get into that.

    However, what I learned from thinking about all this is to ask better questions: Can I learn the boundary between the basic system and the very first complex system that follows after the simple one?
  17. Mar 2, 2008 #16
    In numerical analysis, you can study the condition of a problem. The condition gives a measure of how a small perturbation on the input can result in a bigger perturbation in the output, independently of the algorithm used to solve the problem. An example of an ill-conditioned problem is finding the roots of a polynomial. Whatever method you use, even the algorithm is perfect, a small perturbation in the input will result in a big difference on the result.
    I have a feeling that this is somehow related to the butterfly effect, in the sense that nature is an ill-conditioned "problem". This is just a small remark that may be interesting. It occurred to me when I had a course on numerical analysis previous semester.
  18. Mar 2, 2008 #17
    Ok, to my knowledge, the butterfly effect is a poetic way of describing a fundamental idea of chaotic systems. It is an appealing analogy, it sparks interest, it invokes discussion, it is intuitive, and brings about thought.

    I don't believe anybody is arguing that realistically a butterfly will cause or stop a hurricane. What is being said is that chaotic systems are extremely sensitive to initial conditions.

    First, not all systems exhibit chaos. Linear systems do NOT exhibit chaos. Nonlinear systems CAN exhibit chaos, but do not necessarily do.

    First, what is your definition of a system? To you, what does it mean for a system to exhibit chaos?

    Lets look at a system that exhibits the "butterfly effect". It is called Chua's circuit. Here is a link:

    Now, this system can be MODELED with nonlinear differential equations, and guess what? The system is extremely sensitive to initial conditions, hence it has the "butterfly effect", and this implies that it is a chaotic system. This is a real device! You can setup an experiment and see this chaotic behavior.

    You could also look at a system such as a car. You could model a car, lets say moving in one direction with nonlinear differential equations. But guess what? It will not exhibit chaos!

    So, my point is this. There are real devices that exhibit chaos. These occur in systems that are nonlinear, but not all nonlinear systems are chaotic.
  19. Mar 2, 2008 #18
    It's interesting to note that you could look at a system such as the logistic map:

    The system can be shown to demonstrate chaotic outputs. This relates that small perturbations in the input cause drastic output changes, just like you can see in numerical analysis. However, there are certain parameters that you can set, that whatever input conditions you choose, the system is NOT chaotic.

    There are these thresholds that if you set the parameter just before some number the system is not chaotic, but then as soon as you reach that the number, the system become chaotic. I could explain this better, or just check out:

    1: bifurcation
    2: http://en.wikipedia.org/wiki/Mitchell_Feigenbaum
  20. Mar 2, 2008 #19
    I don't understand what is "ill-conditioned" problem. In Newton's method solutions come out really quickly:
    x_n+1 = x_n - f(x)'/f(x)
    That speed is the "sensitivity", something exponential. So picking a starting point is sensitive. Very close points lead to different possible solutions. The main problem would be to do it by hand and miss 60% of solutions because of initial guessing. However it is very precise method because it reaches solution quickly

    Computers plot the whole set of possibilities (coloring where all starting points lead and how quickly) so you get an interesting pictures but not damn interesting pictures.

    Now I don't see a point but I can invent one perhaps? Pendulums maybe have sensitive initial positions and if I plot each result after 10seconds I get what? Maybe no two are alike so it would be many colors... approximately I don't know.
  21. Mar 2, 2008 #20
    The system is connected or bound physically like a mechanism, or heat engine, a rock, one zone of entropy in phase space, or a planet... I don't care for chaos I am simply thinking of order within or combined with a large amount of additional data, extra motions that are random, unpredictable etc.

    Well the problem is that in some cases chaos originates from complexity and logical gates or the domino effect. Thats fun - and I don't know what tech can achieve ... (Hope to see no problem). Its just that its not entirely a physics; the exciting question is in the case if that is fundamental property that originates from atoms for example in *simple* systems.

    Lets say, a snowball can not cause avalanches because it has no energy for that not even after rolling downhill. At the same time dynamite can. If I drive in with snow plowing machine thats not that fundamental physics.
  22. Mar 2, 2008 #21
    The condition of a problem is independent of the algorithm/method used to solve it. Maybe I presented it a little too abstract. For a polynomial of degree n, the input are the coefficients of the polynomial. The output are the roots. That the problem is ill-conditioned means that a small change in the coefficients of a polynomial can lead to big differences in the roots of the functions. One historical discovery in numerical analysis is http://en.wikipedia.org/wiki/Wilkinson%27s_polynomial" [Broken]. No matter how stable your algorithm is for errors, the problem will always be ill-conditioned. This is an extremely important fact since computers don't have infinite memory and thus they can't represent numbers exactly. There are always rounding-errors that occur and those errors result in changes in the input.
    Last edited by a moderator: May 3, 2017
  23. Mar 2, 2008 #22

    Looks deep and I promise to get a degree on that. My point simplified was that algorythms are easy to point out when if fact of the reality, IF the fact of the reality is that no ENERGY will ever travel, change like that and ever leave out of the standard equation for flow (conservation). mean, I am thinking it for real, thoughts have always been real :-)
    Last edited by a moderator: May 3, 2017
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