Talk:Chaos theory

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Latest comment: 15 years ago by Incompetnce in topic Definition of chaos theory

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Phase diagrams

"Phase diagram for a damped driven pendulum, with double period motion" is of poor quality. The plot is not doubly periodic (possibly due to a large integration step). Digitalslice 13:51, 4 June 2007 (UTC)Reply

From the description, this plot seems to be generated from experimental data rather than a numerical simulation - thus the inexact measurements. Chrisjohnson (talk) 01:52, 30 January 2008 (UTC)Reply

The relation between chaos theory, systems and systems theory

The importance rate of this article for the WikiProject Systems has been uprated from high to top allready two weeks ago on 10 June 2007. I could have referted it because importance rates are set by the WikiProjects themselves and these rates have a particular objective meaning: The importance rate is not about the objective importance of the article, but of the relative difference from the article to the hart of the WikiProject. Now formaly the hart of the WikiProject Systems is in a way the category:systems. The items in this category get a top-importance, the items in the first subcategories are of high-importance.

Instead of referting this I kept wondering about the relation between chaos theory and systems and systems theory. Is or isn't chaos theory in the first place about chaos and not about systems. And aren't systems in the first place about organization and not about chaos? I know a bit more about systems theory, a little about chaos theory but even less about the role of systems and systems theory in chaos theory. Can somebody explain this to me? - Mdd 19:41, 25 June 2007 (UTC)Reply

I can't really answer the question, and would encourage others to do so, because it is an interesting and important question, but I should make some comments about changing the ratings.
  • First of all, I shouldn't have changed the systems theory importance rating, because this is the importance of the article for WikiProject Systems, and I don't know how that project assigns these ratings. Please change it back to "High" if you think it is appropriate: different projects can of course have different ratings for the same article.
  • Second, some background. At the Mathematics WikiProject, we are finding that too many articles are getting Mid and High importance ratings compared to Top and Low. In particular, this makes it harder to prioritise which Stub and Start-Class articles at the top end most need expansion. So we have been trying to improve the situation, and have developed more detailed importance criteria to help us.
  • Third, my changes here. I uprated the Mathematics importance from High to Top (by the above reasoning). Now, WikiProject physics is rather inactive right now, and I figured this article is at least as important in physics as maths, so uprated the physics importance too. Then I went a bit far by thinking "Well, if it is top for maths and physics, it probably is for systems too"!
  • Fourth, a comment. From what you have said, I understand that WikiProject Systems assesses importance in an absolute sense, i.e., only the main items in Category:Systems can hope to be top priority and so on. We discussed this quite a lot at the mathematics project, and have come to the conclusion that:
    • it is more helpful to assess the importance of an article within context rather than in absolute terms
    • Wikipedia 1.0 actually recommends this approach.
Now I am very impressed that your response to my mistake was not to revert it, but to think about it and raise such interesting questions. Maybe you might want to take some of the maths project thoughts on importance ratings back to WikiProject Systems and initiate a debate. All the best, anyway. Geometry guy 20:19, 25 June 2007 (UTC)Reply

I will answer the questions refering to the assesment of article further on the talk page of the WikiProject Systems. And I would like to leave my question about the relation between chaos theory and systems and systems theory here for others to respond. So if anybody can help me out? - Mdd 22:22, 25 June 2007 (UTC)Reply

The role of systems theory in chaos theory

I am not sure that systems and systems theory can be said to have a role in chaos theory. I think it is rather the other way around; chaos theory has a role in systems and systems theory (from chaos emerges order and/or a system). In economics, notably, this is exposed through the concept of spontaneous order. See also Complex system#Complexity and chaos theory which has some info, although probably not perfect. --Childhood's End 13:56, 26 June 2007 (UTC)Reply

Thanks for this perspective. This brings me all kind of questions. Is chaos theory a new paradigm in the field of systems theory. Should you in the first place name that field systems theory? Did or didn't the chaos scientists thought that chaos theory was a field on it's own. What did they think about the relation to systems theory? Now I am going to read the parts you mentioned and probably come up with questions? We'll see? - Mdd 14:58, 26 June 2007 (UTC)Reply
I'm still wondering about the question is chaos theory can be seen as a form of systems theory? I found only partly an answer in a discussion here from March 2006, see [1]. - Mdd 00:12, 27 June 2007 (UTC)Reply
hi mdd, my below post was partly in response to you. as described in the chaos theory wiki and in the dynamical systems wiki chaos theory is a fairly well defined island of mathematics. It has it's own language and its own set of tools used to get results. As such it is a good LANGUAGE and TOOL that can help discussion of systems theory (what ever THAT grab bag might be). Notice in the talk page for dynamical systems they are choosing to include only systems acting on what is called a smooth mathematical space, and therefore leaving out such topics as (discrete) cellular automata and networks etc... Again, this makes that chunk of tools very specific, these mathematicians have developed many tools that work on giving results in these smooth systems, but DON'T KNOW yet how to get results in the discrete systems. Leaving again, complex systems, general systems, emergence... to be more general more varied topics.
So, not every complex system is approachable yet by the mathematical tools of dynamical systems theory, and remember, not every complex system exhibits chaos.
One more point: chaos theory and the more general dynamical systems theory are deterministic systems, they do NOT involve chance or random input. That is yet a whole other body of mathematics! Many of the systems under the topics of complex systems and general systems, i presume, include random elements. they require other tools.
Certainly SOME of the systems explored in systems theory and complex systems have served as inspiration to people developing the mathematical results of chaotic dynamical systems, but they necessarily have to choose very simplified examples in order to do their work.
Remember that most of this stuff has only been developed in earnest in the last 50 years! It is uncharted territory, still in flux. that is why i still stand by my conclusion that ALL OF THIS might best be approached for an encyclopedia as a set of very separate topics each with their own approach and insight and let the reader make his own connections. Otherwise we will end up in very strongly point of viewed personal ramblings, as i have done in my attempts to bring this stuff together in my own mind these past 20 years, resulting in my decision for my own writings to write 60 separate lab manual entries for each kind of system/topic.
however this is exciting that you guys are attempting this and i will mull this all over in the coming weeks.Wikiskimmer 19:37, 29 June 2007 (UTC)Reply

Bleach on the term chaos theory - what a nest of hornets

bleach on the term chaos theory! the concepts described in this wiki are basically a solid body of well defined MATHEMATICS. It describes a subset of the area of mathematics called dynamical systems. as such it is an excellent tool for some other more complicated human endevours like complexity, systems theory etc... as a body of mathematics it stands on its own two feet.

i've just started looking at all these related wikis. my god. what a nest of hornets! Wikiskimmer 05:40, 29 June 2007 (UTC)Reply

And again, in English? -- GWO
the name chaos theory sounds too mush brains. i think the term used by mathematicians is chaotic dynamical systems. Wikiskimmer 19:39, 29 June 2007 (UTC)Reply
What about these 1500 books that call it "chaos theory"? Dicklyon 20:12, 29 June 2007 (UTC)Reply
The body of this wiki fairly clearly discusses the specific body of mathematical work on chaotic dynamical systems. perhaps a mention at the beginning can be made of the broader usages of the term in science, engineering and pop culture. i am exploring the tangle that all the wiki articles related to 'systems' is in. i think in an encyclopedia, the less tangle the better. Wikiskimmer 21:34, 29 June 2007 (UTC)Reply

to redirect

Mdd, if you put brackets around chaotic dynamical systems then make the thing redirect to chaos theory because THAT article IS chaotic dynamical systems. I don't know how to redirect.Wikiskimmer 05:47, 3 July 2007 (UTC)Reply

To redirect you just click on the red-lighted word chaotic dynamical systems, then a new page starts. In the text field you then write #REDIRECT [[chaos theory]]. Next time you see the chaotic dynamical systems it's turned blue. You then created a new page: a redirect page I call them. A good thing is to search in the Wikipedia for this word in articles and there putt brackets around them. Better you do this before you make a redirection page.
Now I did some searching for you and found that in the article Floris Takens the term chaotic dynamical systems is redirected in an other way, like chaotic dynamical systems or in plain nowiki-text [[chaos theory|chaotic dynamical systems]]. It all that's some time getting use to. You should just try different times. Good luck with it. - Mdd 11:38, 3 July 2007 (UTC)Reply
ok, i did that. but here's another question. can i do it the other way around? can i change the name of the chaos theory article to "chaotic dynamical systems" and have chaos theory redirect to IT? That would be a minor esthetic improvement, as in english the term "chaos theory" still sounds to wishy washy, a theory of (general) "chaos", as in what my bedroom looks like, while "chaotic dynamical systems" refers to the mathematically defined systems that exhibit "mathematically defined chaos".Wikiskimmer 14:14, 3 July 2007 (UTC)Reply

Wikiskimmer, if I understand you correctly, you are proposing to move chaos theory to chaotic dynamical systems. I see two problems with this. Firstly, a small problem - WP:NAME says "In general only create page titles that are in the singular", so the new name would have to be chaotic dynamical system. Secondly, a bigger problem - WP:NAME also says "Except where other accepted Wikipedia naming conventions give a different indication, use the most common name of a person or thing that does not conflict with the names of other people or things". Like it or not, chaos theory is a more common name for the subject of this article than chaotic dynamical systems. Anyway, before you change anything, I suggest you mention your proposed name change at Wikipedia talk:WikiProject Mathematics and see what the general reaction is. Gandalf61 16:12, 3 July 2007 (UTC)Reply

if the goal is to be a POPULAR encyclopedia instead of a MATHEMATICAL encyclopedia, then i suppose chaos theory might be the most popular term. but the popular notion probably points to a broader category than the math that's in our chaos theory article. and all of a sudden i'm wondering, in the grand scheme of things, just how important is this anyway?Wikiskimmer 16:41, 3 July 2007 (UTC)Reply
I oppose such a move. The topic is widely known as chaos theory, and there's no reason to mess with it. Dicklyon 00:08, 4 July 2007 (UTC)Reply

A reorganisation of this article

Today 16 july 2007 I made a rather large reorganization of this article. The main idea behind it is:

  1. In the first place an introduction as it was.
  2. Second an part about the history
  3. And in a third part all theoretical parts together
  4. And the ending with references is reorganized according to Wikipedia standaards

I hereby kind of followed the example of the featured article Electrical engineering. Following this example also gives an idea how this article can be further improved. It looks to me that improvements can be made o points like: Education, Practicing & Applications!? - Mdd 12:50, 16 July 2007 (UTC)Reply




"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. Gleick (1988, p. 306) notes that "No one [of the chaos scientists he interviewed] could quite agree on [a definition of] the word itself," and so instead gives descriptions from a number of practitioners in the field. For example, he quotes Philip Holmes (apparently defining "chaotic") as, "The complicated aperiodic attracting orbits of certain, usually low-dimensional dynamical systems." Similarly, he quotes Bai-Lin Hao describing chaos (roughly) as "a kind of order without periodicity." It turns out that even textbooks devoted to chaos do not really define the term. For example, Wiggins (1990, p. 437) says, "A dynamical system displaying sensitive dependence on initial conditions on a closed invariant set (which consists of more than one orbit) will be called chaotic." Tabor (1989, p. 34) says, "By a chaotic solution to a deterministic equation we mean a solution whose outcome is very sensitive to initial conditions (i.e., small changes in initial conditions lead to great differences in outcome) and whose evolution through phase space appears to be quite random." Finally, Rasband (1990, p. 1) says, "The very use of the word 'chaos' implies some observation of a system, perhaps through measurement, and that these observations or measurements vary unpredictably. We often say observations are chaotic when there is no discernible regularity or order." So a simple, if slightly imprecise, way of describing chaos is "chaotic systems are distinguished by sensitive dependence on initial conditions and by having evolution through phase space that appears to be quite random." In particular, a chaotic dynamical system is generally characterized by 1. Having a dense collection of points with periodic orbits, 2. Being sensitive to the initial condition of the system (so that initially nearby points can evolve quickly into very different states), a property sometimes known as the butterfly effect, and 3. Being topologically transitive. However, it should be noted that despite its "random" appearance, chaos is a deterministic evolution. In addition, there are chaotic systems that do not have periodic orbits (periodic orbits only survive in the boundaries of KAM tori, and for sufficiently strong perturbations from the integrable case, islands do not necessarily survive). Furthermore, in so-called quantum chaos, trajectories do not diverge exponentially because they are constrained by the fact that the entire evolution must be unitary. The boundary between regular and chaotic behavior is often characterized by period doubling, followed by quadrupling, etc., although other routes to chaos are also possible (Abarbanel et al. 1993; Hilborn 1994; Strogatz 1994, pp. 363-365). An example of a simple physical system which displays chaotic behavior is the motion of a magnetic pendulum over a plane containing two or more attractive magnets. The magnet over which the pendulum ultimately comes to rest (due to frictional damping) is highly dependent on the starting position and velocity of the pendulum (Dickau). Another such system is a double pendulum (a pendulum with another pendulum attached to its end). M. Tabor and F. Calogero have advocated an interpretation of chaos as motion on Riemann surfaces (Tabor and Weiss 1981, Fournier et al. 1988, Bountis et al. 1993, Bountis 1995).

Chad Miller Chadman8000 (talk) 00:12, 4 March 2009 (UTC)Reply

its periodic orbits must be dense.

I think that's about where my tigerdilly should go. It's an inversion of an escape-time fractal (a complication of the Mandelbrot Set), so a large area of periodic orbits is in it, but the sparse, textured area of escapes finds difficulty in analysis. Brewhaha@edmc.net 18:45, 26 August 2007 (UTC)Reply

A essay about chaos theory

Tonight User:71.185.153.98 dumped an essay "Chaos Theory: A Brief Introduction" into this article. I for the moment moved it back to User talk:71.185.153.98 page. Maybe someone wants to take a look at it. - Mdd 20:13, 9 October 2007 (UTC)Reply

Infinity and Circular views

Hi, I am very new here. This is the first time I do this. I hope I don't mess anything up. I have read this passage in the article.

"Sensitivity to initial conditions is often confused with chaos in popular accounts. It can also be a subtle property, since it depends on a choice of metric, or the notion of distance in the phase space of the system. For example, consider the simple dynamical system produced by repeatedly doubling an initial value (defined by the mapping on the real line from x to 2x). This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points will eventually become widely separated. However, it has extremely simple behaviour, as all points except 0 tend to infinity. If instead we use the bounded metric on the line obtained by adding the point at infinity and viewing the result as a circle, the system no longer is sensitive to initial conditions. For this reason, in defining chaos, attention is normally restricted to systems with bounded metrics, or closed, bounded invariant subsets of unbounded systems."

I understand it completely until the part where it talks about using bounded metric on the line obtained by adding the point at infinity and viewing the result as a circle. I think I have an idea of what it means but it seems rather far fetched to me and I woul much rather hear some explanations before looking like a fool. What is the difference between bounded and unbounded metrics? I wish to get some clarification on this as well.

Again, sorry if I did this wrong and if I didn't do it wrong then thanks for your input!

Alkaroth 11:41, 18 October 2007 (UTC)Reply

I will attempt an explanation. Each point on a unit circle C is defined by an angle θ, which we take to be in the interval -π < θ <= π. We can map the real line R to the circle C in various ways. One way is to define a function θ:R->C such that θ(x)=2tan-1(x). This is an bijection between R and the subset -π < θ < π of C. It is also a continuous function (although it is not uniformly continuous). The only point on C that is not an image of a point in R is the point θ=π, that is "opposite" to 0. If we add a "point at infinity" to R with the convention that tan-1(infinity) = π/2 then we have a bijection between R+{infinity} and C. With this mapping, C is called the real projective line.
The dynamical system x->2x is a dynamical system on R. But if we map it from R to C then the behaviour of every point (except for the fixed point 0) is identical - they all converge to the point θ=π. So this dynamical system is clearly not "chaotic" on C. As we have used a continuous mapping, we can reasonably argue that we have not changed any fundamental property of the dynamical system by this mapping - and we would like "chaotic" to be a fundamental property that is not changed by a continuous transformation. So the dynamical system x->2x is not usually described as being "chaotic", even though it could be said to exhbit "sensitivity to initial conditions" when considered as a dynamical system on R. Gandalf61 12:57, 18 October 2007 (UTC)Reply
Gandalf, Thanks a bunch for the explanation. I understood it better and it was similar to what I had in mind. Thanks again for your help Gandalf. Alkaroth 13:31, 18 October 2007 (UTC)Reply

Chaos analysis software

It would be nice to explain in the article which software tools or languages are available for the analysis of chaotic systems. —Preceding unsigned comment added by 83.34.43.235 (talk) 18:55, 11 November 2007 (UTC)Reply

Finally I find a nice software to study chaos: TISEAN. —Preceding unsigned comment added by 81.35.123.125 (talk) 17:56, 24 April 2008 (UTC)Reply

Distinguishing random from chaotic data

I'd like to add another reference Physics Letters A, Volume 210, Issues 4-5, 15 January 1996, Pages 290-300 Reconstructing the state space of continuous time chaotic systems using power spectra J. M. Lipton and K. P. Dabke (at the very end of this section) but as a co-author I'm conflicted. Anyone keen to confirm this as a reasonable citation and add it? Thanks Jmlipton (talk) 05:14, 18 December 2007 (UTC)Reply

A section a simpler terms?

Could it be possible to add a small section that pretty much stated the chaos theory in 'plain English'? Stepshep (talk) 02:07, 8 December 2007 (UTC)Reply

The first sentence of the article has a high-level informal definition of chaos theory: "... chaos theory describes the behavior of certain nonlinear dynamical systems that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect)". Follow the links to find out more about dynamical systems and the butterfly effect. There is an expanded introduction in the Simple English wiki here. But if you want to know exactly what chaos theory is about (i.e. what exactly is known about the behaviour of chaotic systems and how do we know it) then you have to understand some of the mathematics behind it. Gandalf61 (talk) 12:24, 9 December 2007 (UTC)Reply

I agree with Stepshep. Whoever wrote this article was high on chaos-related jargon and low on writing skills and communication ability. For the purposes of your FIRST SENTENCE, you should probably avoid multiple other articles that must be read. That becomes a slippery slope (i.e. what if those articles also require more reading) that makes encyclopedias useless.

Example...the phrase "certain nonlinear dynamical systems" can be simplified to just "certain systems." It means the same thing, and you can add exactly what type of systems later. Likewise, you can replace "may exhibit dynamics that are highly sensitive" with "may be highly sensitive." You don't need the excess detail, especially in the first sentence which is supposed to plainly state what you're discussing.69.232.97.150 (talk) 02:49, 6 February 2008 (UTC)Reply

Possible consequences

The way, I've always been told the chaos theory, is when a butterfly flaps its wings, disaster strikes. Obviously, these are pretty extreme circumstances, and I am currently unaware of the full details, but if anyone could possibly let me know, about the reprimands of chaos theory, I would be very grateful. —Preceding unsigned comment added by Hammerandclaw (talkcontribs) 21:17, 29 December 2007 (UTC)Reply

It is not that bad, fortunately. Most of the time, when a butterfly flaps its wings, no disaster strikes. The idea is, rather, that the effect is unpredictable, and that we cannot fully 100% guarantee that such a tiny and seemingly insignificant thing cannot lead to a large-scale effect, which, if we are unlucky, might be disaster. This does not only apply to butterflies flapping their wings right now, but also to someone scratching their nose, and the large-scale results we see are the combined effect of many such things over long periods, including Julius Caesar scratching his nose, and all flapping of wings by Jurassic butterflies 200 million years ago; each and any of that may be the difference between rain or sunshine tomorrow. See also Butterfly effect.  --Lambiam 23:28, 29 December 2007 (UTC)Reply

Chaos in Every day life

What about how chaos underpins such subjects as sociology, biology, politics, etc? 194.73.99.107 (talk) 11:31, 12 January 2008 (UTC)Reply

Underpins? Sounds like someone's fanciful imagination. Dicklyon (talk) 17:44, 12 January 2008 (UTC)Reply
Actually, it's not so fanciful. There have been studies into chaos in the behavior of stock markets, see also here. Biological systems are complex systems which have been described as "anti-chaotic" (see Stuart Kauffman's work, for example). The presence or absence of chaotic heartbeats have been implicated in human health (here and here). SteveChervitzTrutane (talk) 07:11, 9 April 2009 (UTC)Reply

Quick suggestions

The lead and general introduction should perhaps provide more concrete & practical examples of the so-called "Butterfly effect" (pendullum, etc.) History of discovery of this new "paradigm" should be more developed (here it seems everything is brought back to the "first discoverer of chaos", and then comes the computer... James Gleick's book might be of some help here in retracing the various discoveries and time needed to take them together). Technical information should come last. Right now the article is at the same time too short and too complex to provide a useful introduction to a reader totally unfamiliar with the subject (simple example: sensitivity to initial conditions & Butterfly effect is easy to understand for anyone familiar to this theory, but should be explained better here. An example from population dynamics could comes in handy (low fertility: extinction; medium fertility; regular increase; high fertility=phase 3 implies chaos...) Mandelbrot sets, fractals and the creative dimension in some fractals should also be depicted. Difference between chaotic & stable systems with non-chaotic stable systems should be explained. Lapaz (talk) 13:56, 17 January 2008 (UTC)Reply

Removed "philosophical" paragraph

I removed the following paragraph from the History section of the article:

"Philosophically, Chaos theory demonstrated that Laplace's demon deterministic assumptions were erroneous, as various outcomes could originate from the same initial situation. Furthermore, it showed the possibility of self-organizational systems, thus defying the second law of thermodynamics of increasing entropy. Chaos theory did not, however, reject all forms of determinism, but only Laplacian or classical determinism, which assumed that if one knew perfectly all of the coordinates of the universe at one point of time, one could predict all its past and future history. To the contrary, Chaos theory showed that if emergent properties arose from disorder and non-linear systems, thus creating novelty and dismissing the Laplacian hypothesis, the appearance of disorder itself and of non-regularity could themselves be predicted, in particular by using iterated function systems."

I believe this paragraph is incorrect. Firstly, chaos theory studies deterministic systems, so a given initial situation can only give rise to one outcome at a given later time. Laplace's demon could happily predict the behaviour of a chaotic system as long as it had exact knowledge of the initial conditions. What prevents Laplace's demon predicting the behaviour of actual physical systems is the inherently non-deterministic nature of quantum physics - but this aspect of reality is not studied by chaos theory, which only considers classical deterministic systems (except in the rather separate and specialised field of quantum chaos). Secondly, self-organizational systems do not defy the second law of thermodynamics. They are either open systems which decrease their local entropy by exporting entropy to the surrounding environment (typically by cooling, and so heating their environment), or they are closed systems which are initially prepared in a very specific state, and so have an extremely low initial entropy anyway. This is discussed in Self-organization#Self-organization vs. entropy. Gandalf61 (talk) 11:03, 18 January 2008 (UTC)Reply

I agree it was too quickly formulated. Perhaps another formulation could be given to it, namely the distinction between determinism (maintained by chaos theory) and previsibility. Various views appears to spring up here: Jean Bricmont, for example, alleges that Laplace did not claim that determinism implied previsibility [2]. On the other hand, Bernard Piettre, director of studies at the College International de Philosophie, maintains exactly the reverse (link lamentably in French, maybe an automatic translator could work). Whatever the way, I think the philosophical issue should be adressed, and if various point of views supported, these one given. Maybe you have some other, not too technical, sources in English concerning philosophical implications of this chaos theory (which, we agree, is deterministic)? Lapaz (talk) 19:42, 23 January 2008 (UTC)Reply
Stephen Kellert's 1993 (called, I think "In the wake of chaos") book argues that in a sense chaos theory does undermine the assumption of determinism. But I find his argument unconvincing. This paragraph should be left out as any philosophy related to chaos theory is almost certainly original research. The field is a mess, and there is lamentably little written on chaos from a philosophical perspective. 158.143.86.159 (talk) 14:27, 28 July 2009 (UTC)Reply

"Renewed" physiology

I removed User:Lapaz's addition of the sentence "The emergence of chaos theory renewed physiology in the 1980s." from Physiology. I wasn't aware the physiology needed any renewing in the 1980s. I see a similar sentence here, although there is more detail (the sentence here is "Chaos theory thereafter renewed physiology in the 1980s, for example in the study of pathological cardiac cycles." Is it possible to add a reference for this fact, and maybe change the wording a bit, to avoid implying that physiology was dead? - Enuja (talk) 00:46, 19 January 2008 (UTC)Reply

Formulation may have been poorly chosen, but chaos theory did impact physiology and modify approaches, in particular by boosting mathematical researches. There is a source concerning the eye tracking disorder here in this article. My original source was James Gleick's Chaos: Making a New Science, the chapter at the end on "Internal Rythms". Lapaz (talk) 19:50, 23 January 2008 (UTC)Reply
I suggest you cite the source, then. In this article, how about "Chaos theory provided new computational approaches for physiology, for example in the study of pathological cardiac cycles.[1]"
  1. ^ Gleick, J. Chaos: Making a New Science 1987.
  2. You can name the ref and easily re-use it for everything that comes from that book. I regularly go look at WP:Footnotes to figure all that out. - Enuja (talk) 20:06, 23 January 2008 (UTC)Reply

    Statistics?

    The article contains the sentence:

    As well as being orderly in the sense of being deterministic, chaotic systems usually have well defined statistics.

    What is the meaning of the term "statistics" here? A measure of the average amount of time the system state is, on the long run, in a Lebesgue-measurable subset of phase space? It seems that this would contradict a statement on pp. 168–169 of Gleick (1988 Penguin paperback edition). Does anyone have a citable source for this statement?  --Lambiam 18:42, 28 March 2008 (UTC)Reply

    English, please!

    Could somebody please translate the very first sentences of this article. As soon as I got to 'nonlinear' it was like digging underground in the dark with the earth coming in on you. Fuck, if some of you lads had your way this entire article would be a stream of equations! I just want to know the broader applications of this chaos theory stuff in simple English. Tanks. 86.42.102.87 (talk) 14:09, 18 April 2008 (UTC)Reply

    See the information under A section a simpler terms? above. Gandalf61 (talk) 14:28, 18 April 2008 (UTC)Reply
    I have taken a look at the first sentence:
    • In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect).
    Couldn't this be in simple English:
    I do think such an introduction would Wikipedia: The first sentences and introduction should be understandable to a larger audience.-- Mdd (talk) 19:58, 18 April 2008 (UTC)Reply
    The words "specific kind" would be potentially misleading; it is in general not possible to tell whether a given system is chaotic or has merely very complex, but nevertheless non-chaotic, dynamics.
    It is essential that the systems are dynamical. For example, it would be nonsensical to consider the question whether a given coordinate system is chaotic. The word "dynamical" must therefore not be omitted from the first sentence. We might add an explanatory phrase (e.g., "dynamical systems – that is, systems whose state evolves with time –"), although I agree with Gandalf61 that a reader who does not understand the term should either just ignore it, or follow the link. (However, the lede of Dynamical system is, unfortunately, not as accessible as it should be. Until that is fixed, a slightly better article to link to is perhaps Dynamical system (definition).)
    The word "nonlinear" is less essential and could be omitted from the lede; in fact, it is more informative to state, somewhere in the body of the article, the theorem that linear dynamic systems are not chaotic, which implies that chaotic systems are nonlinear. There are more theorems that could be mentioned, such as (if I'm not mistaken) that the phase space has to have dimension ≥ 3 for chaos to arise. A natural place for this is the section Chaotic dynamics.
    In my opinion, the words "in physics" could also be struck, just as we also do not state: "In mathematics and physics, spectral theory is ...", even though spectral theory has applications in physics, as in the models of the hydrogen atom. The theory is mathematical, and as far as chaos theory relates to physics, it is actually to mathematical models embodying theories of physics. The apparent chaotic behaviour of various natural systems may be explained by a chaos-theoretical analysis of such mathematical models.  --Lambiam 07:17, 25 April 2008 (UTC)Reply
    I agree with Lambian's points. Minor clarification - a continuous dynamical system on a plane space must have a phase space with at least 3 dimensions to exhibit chaotic behaviour - this is a consequence of the Poincaré–Bendixson theorem. However, a discrete dynamical system (such as the logistic map) or a continuous dynamical system on, for example, a torus can exhibit chaotic behaviour in a phase space of 1 or 2 dimensions. Gandalf61 (talk) 08:25, 25 April 2008 (UTC)Reply
    Thanks, my proposal wasn't such a good idea. I only just noticed that there actually is a Chaos theory article in simple English. This makes a difference to me, because this gives the opportunity to make a difference in a simple and more complicated description.
    Now I do agree with Lambian, that we should loose the "In mathematics and physics" frase in both descriptions. The introduction should state that chaos theory "has mayor applications in physics", and that "the theory is mathematical" or as Lambian states "it is to mathematical models embodying theories of physics". -- Mdd (talk) 11:51, 25 April 2008 (UTC)Reply

    Dasavathaaram

    The first question is copied from User talk:Mdd

    The film's theme is based upon the chaos theory. Why do you insist on removing it? Universal Hero (talk) 19:46, 15 June 2008 (UTC)Reply

    There are good reasons why this movie is removed from the list already some seven times here: There are tons of movies about chaos theory. At least a dozend movies have been removed there before the last year. Now there is one new film Dasavathaaram, which is a Tamil language feature film...!? What does that mean...? Certainly not that we should mention it all at once. No. The listing of movies here is just selection of the most important movies ever made. The Dasavathaaram movie certainly isn't (yet). I will make you a deal. If he receives an Oscar next year, we will add the movie to the list. Until then I consider it just linkspam to get any attention to this what ever Tamil language feature film...!? -- Marcel Douwe Dekker (talk) 20:21, 15 June 2008 (UTC)Reply

    Double standards- Because Jurasic park is an American dream, it gets a position in Wikipedia!! Dasavatharam is more apt to be there.Wikipedia is a dynamic knowledge portal and has to be nutural to reality. Sad commentary that it ignores Dasavaatharam.Ramesh

    It is rather foolish of you to dismisss a Tamil film as you have done. Dasvathaaram is the most expensive Indian film ever to be produced (inc. Bollywood etc) and features the lead actor in ten roles, breaking the world record for the highest amount of roles in a feature film. Furthermore the film is being distributed by Walt Disney and Sony, becoming the biggest film in Indian cinema ever. the film is the turning point in the non-Western belief of the chaos theory, becoming the first film to explore this issue in the non-Western world. Universal Hero (talk) 23:07, 15 June 2008 (UTC)Reply
    Ok, why the rush. We look at it next year. The Wikipedia is not to promote all greater things to come. -- Marcel Douwe Dekker (talk) 23:16, 15 June 2008 (UTC)Reply
    When the people who have watched and understood the plot and could genuinely relate it to the Chaos theory, why would you not listen to the so many credible people are vouching for it? Oscars alone don't rule the movie world. Any movie - good or bad, significant or not, whether you know the language or not, if it has to have a place on the WIki, it has to be there. Since you have not watched Dasa, it does not become any less important. A movie a MOVIE wherever it is made and Oscar or Hollywood alone don't hold the bastion. Dasavatharam deserves a place is a loud call. If you are refuting, go watch the movie. 207.229.184.110 (talk) 02:38, 23 June 2008 (UTC)Reply
    It doesn't matter whether anyone is refuting it; it's just that you can't make wikipedia content out of WP:OR; what's required is WP:V, WP:RS. Re-read those and let us know what you think. Dicklyon (talk) 03:24, 23 June 2008 (UTC)Reply
    In what way exactly is the film based upon chaos theory ? Reading the plot synopsis in our Dasavathaaram article, I can see no connection at all. Do you have a reliable source that discussses the film's connection with chaos theory ? Gandalf61 (talk) 21:22, 15 June 2008 (UTC)Reply
    The plot section is still under active construction. If you see the film, the element of chaos theory is mentioned by the characters several times, as well as mentioning the butterfly effect. Furthermore, why don't you opt for a Google search on "dasavathaaram chaos theory" - I'm sure that'll give you the needed info. Universal Hero (talk) 23:07, 15 June 2008 (UTC)Reply
    Even if this isn't a googlebomb, it's likely that none of those pages is both reliable and actually says the movie is related to chaos theory. It's the job of the editor adding information to support it, not the job of reviewing editors to find support for factoids. — Arthur Rubin (talk) 01:23, 16 June 2008 (UTC)Reply
    Several attempts have been made to add this film to The Butterfly Effect article as well. The lack of sources, the inability to explain just what the relevance of the film is (I notice that theme has turned into mentioned several times above), and the repeated attempts to add without bothering to discuss make this look more and more like spam to me. Gandalf61 (talk) 06:48, 17 June 2008 (UTC)Reply
    What is the chaos in adding Dasavathaaram or any other film that relates to chaos theory into the article? Adding Dasavatharam to the list isn't going to be touted as promoting the film nor is there a special rule on adding films that win the Oscars to be mentioned in articles. A film is a film, whether good or bad. Dasavathaaram perfectly portrays the Chaos Theory and Butterfly Effect in a well organized manner to the locals of India in the three prominent local languages of the country: Tamil, Hindi, and Telugu. I highly doubt those films that are mentioned in the article already would be known to Wikipedia users in those regional areas. Wikipedia is used by everyone all over the world, knowing its part of the World Wide Web and we must keep it usable for everyone. Dasavathaaram doesn't need the Oscars to prove it an honourable mention. If you search videos of Dasavathaaram Soundtrack Audio Launch you can see yourself how even Jackie Chan speaks about the film in the function. Bottom line, adding Dasavatharam to the list is NOT spam or vandalism, it is only the implementation of the article itself and of course, Wikipedia. It is something that exists in the world and must be mentioned, and the only encyclopedia ever to explain the most stuff in the world is Wikipedia. What some of you are doing is just hogging the article to yourself which is pretty selfish. Respect the willingness of other Wikipedians to add viable and reasonable information and do not prevent them from doing so. Eelam Stylez (talk) 03:06, 21 June 2008 (UTC)Reply


    Dasavathaaram is a movie whose plot is STRICTLY based on chaos theory. As you see one of its initial scenes starts with a butterfly symbolic to the butterfly effect. The Scriptwriter explains what is the theory and his story is based on this theory, and i see it's much more relevant than theButterfly Effect and its stupid that you consider it as an ordinary regional tamil movie. Why Indians are treated so? So can you only approve a hollywood movie? That is RIDICULOUS! Harikrishnan (talk) 03:06, 21 June 2008 (UTC)?Reply


    So provide a source. That is all that is required. Provide just one independent reliable source that discusses the importance of chaos theory as a theme of this film, and then there should be no objections to its inclusion in the article. Gandalf61 (talk) 16:13, 21 June 2008 (UTC)Reply

    This movie has a much bigger profile than any of the hollywood movies listed as examples of the "Chaos theory" in popular media. The opposition of these American editors is based on little other than bigotry against anything that is Indian.There is no other explanation --59.189.44.116 (talk) 06:00, 25 June 2008 (UTC)Reply

    So supply a source, even a Tamil language source. It hasn't been done, yet. — Arthur Rubin (talk) 06:52, 25 June 2008 (UTC)Reply

    This edit shows the attitude of the anti-Indian bigots who control this page. I added a source for Dasavatharam showing how it relates to the Chaos Theory and added fact tags to the other movies, yet User:Arthur Rubin reverted the edits without so much as an explanation. Funnily enough, these people who are foaming at the mouth over the inclusion of Dasavatharam don't require sources for the American/English langauge movies and books. It speaks for itself--59.189.44.116 (talk) 07:09, 25 June 2008 (UTC)Reply

    The movie has been added and removed about 50 times in the past two weeks. -- Marcel Douwe Dekker (talk) 09:32, 25 June 2008 (UTC)Reply
    The other movies mention Chaos theory in their article, and the information is sourced there. Your article had mentioned it, but without sources, even Tamil language sources. — Arthur Rubin (talk) 12:20, 25 June 2008 (UTC)Reply

    I'm a bit baffled by this. 59.189.44.116 is doing himself no favours by ranting; but whats all this about asking for RS to demonstrate that films are indeed about the effect? I've just perused the butterfly effect film page; I see no RS there saying its about BE. This smells of double standards. If the objection is that we've got enough films about BE and Das is non-notable then lets stick to that argument, and not invent implausible new arguments William M. Connolley (talk) 22:36, 25 June 2008 (UTC)Reply

    And I've just looked at The Science of Sleep which is liked from Chaos theory. WTF!?! Why? It doesn't even claim any connection William M. Connolley (talk) 22:39, 25 June 2008 (UTC)Reply

    That only means that it too, may be challenged and removed if no reliable source can be found. Every film that has a central plot revolved around World War II is not listed on that page, nor articles for cowboy, murder or love, much more popular themes. Finding one or two reliable source to back a claim is not too much to ask. Requests to establish some notability are made for a purpose, to verify to other editors the significance of a link, in this case, between an unreleased, Indian film and a mathematical theory. My preferences would be to only list documentaries that are about chaos theory. - Shiftchange (talk) 23:19, 25 June 2008 (UTC)Reply

    Well I've tested what seems to me a rather odd idea, by rm'ing all films that don't have RS to link them to chaos. Thats leaves only one. I was tempted to do the books too, but that would have meant taking out Gleick, which would be veeeeerry odd. I'll leave that to the people who actually believe what they've written above William M. Connolley (talk) 18:11, 26 June 2008 (UTC)Reply

    "The butterfly effect" is not exactly related to chaos theory, only to the assertion that small actions can lead to large unpredictable effects. — Arthur Rubin (talk) 18:33, 26 June 2008 (UTC)Reply
    So, are you going to take out Gleicks book? William M. Connolley (talk) 18:42, 26 June 2008 (UTC)Reply
    Maybe the best way to integrate wikilinks to related films is either in a Cultural references section, or better yet in a template at the bottom of the page. A good example would be Template:Peak oil listing films, books and people related to peak oil. Having a template for chaos theory would also clear the large see also list on this page. - Shiftchange (talk) 05:12, 27 June 2008 (UTC)Reply
    The template/Cultural References section sounds good. I request the Wikipedians who maintain this article consider that to clear the controversy over Dasavathaaram. Eelam Stylez (talk) 3:11, 30 June 2008 (UTC)
    I started the {{Peak oil}} template, and I will probably start another template for films relating to the general topic of Energy, since there are other films such as Who Killed the Electric Car? that are not strictly about Peak oil but relate peripherally to it. I recommend that Chaos theory enthusiasts should start a navigation template for media relating to chaos theory. The template can have separate groups for fiction films, documentary films, books, etc. Navigation templates can clean up main articles on a topic, by eliminating many "See also" links, and they add value to the linked-to articles, because editors can quickly add a single template to many articles, thereby sparing the need to repeat introductory material in every article having something to do with a topic such as chaos theory. Navigation templates look nice and give a more professional appearance to Wikipedia. A navigation template itself can serve as a comprehensive outline of a subject; for example, someone who reads all the articles linked from {{Peak oil}} will have a solid introduction to that topic. Navigation templates are helpful for avoiding edit wars, since we only have to find consensus once, with respect to what goes on the template, rather than argue about every link in every topic-related article. To learn how to make them, see WP:EIW#Series, Help:Template, {{Navbox}}, WP:DOC, and of course just copy and paste an existing template you like into a user sandbox and edit it. I also have some notes in User:Teratornis/Energy#Energy templates, which record how I researched and developed some templates. --Teratornis (talk) 20:16, 17 August 2008 (UTC)Reply

    Hash functions

    Maybe the arcticle should mention hash functions and the avalanche effect, as somewhat related topics. Just an idea. --Azazell0 (talk) 19:49, 9 July 2008 (UTC)Reply

    why does nonlinear dynamics redirect here?

    All chaotic systems are nonlinear, but not all nonlinear systems are chaotic. Only non-linear systems with positive feedback are chaotic (i.e. they must have a positive Lyapunov exponent). Systems that do not have feedback are linear systems. Systems that have feedback are non-linear systems. Systems that do not have any positive lyapunov exponents (i.e. have only negative feedback) are categorically NOT chaotic (per definition in chaos theory). Chaos theory only deals with systems that are chaotic (per definition in chaos theory). Therefore, re-directing nonlinear systems to chaos theory is categorically wrong. And I presume that, by the same mistake, much of this article's content has nothing to do with chaos theory proper (i.e. should be in the (non-existent) article on nonlinear dynamics).

    To put it another way, systems that have feedback but do not have any positive lyapunov exponents -- such as, oh say, the planets orbiting around the sun, lasers, predator-prey relationships, and the microprocessor inside the very computer that i'm typing this on -- are categorically NOT linear dynamical systems and categorically NOT chaotic dynamical systems. So where do they go? Well I can tell you two places that they clearly DON'T go:

    • an article on linear dynamics
    • an article on chaotic dynamics

    Kevin Baastalk 17:06, 18 July 2008 (UTC)Reply

    Non-linear dynamical system redirects to dynamical system. In the absence of an actual article on non-linear dynamics (as distinct from chaos theory), I am changing non-linear dynamics to redirect to dynamical system as well. Gandalf61 (talk) 17:59, 18 July 2008 (UTC)Reply

    Reference #35 is a broken link. —Preceding unsigned comment added by 70.168.46.253 (talk) 14:25, 26 August 2008 (UTC)Reply

    Deleting page "Chaos (physics)"

    I was planning on merging Chaos (physics) into this page. Having read the Chaos (physics) article in more detail, I can't see anything in it worth keeping that isn't duplication of the Chaos theory page - however, I don't know enough about the subject to really be sure. The text of the Chaos (physics) article is below in case anyone wants to add anything from it into this article.

    Chaos in physics is often considered analogous to thermodynamic entropy. Chaos is a poetic or metaphysical concept evoking a sense of discord, whereas entropy is a concretely defined function of a physical system. See entropy for the mathematical quantification of the disorder in a system.
    The term "chaos", as commonly used, denotes utter confusion, an incomprehensible and heterogeneous mess. This intuitive notion is at odds with the famous Second Law of Thermodynamics, which states that entropy cannot decrease in a closed system. Maximized entropy always corresponds to apparent homogeneity in a system. Any random disturbance of a homogeneous system results in no meaningful change, therefore scientists will say the randomness, i.e. chaos, is maximized. Such systems are observed as being isotropic.
    As with any scientific concept or mathematical abstraction, entropy may not be equally applicable in every situation. For example, it is unknown whether protons may remain forever free and unchanged, or whether they are subject to destruction by cosmological randomness.
    Chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. Among the characteristics of chaotic systems, described below, is sensitivity to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, the behavior of systems that exhibit chaos appears to be random, even though the system is deterministic in the sense that it is well defined and contains no random parameters.
    However, chaos as defined in physics is strongly contrasted with the common definition of chaos. Chaotic systems, with no central control, are able to create "order"; that is to say, they may form a pattern that humans recognize. Biological systems are well-known examples. Potential applications are found in nanotechnology, where self-assembling systems have been developed.
    ==See also==

    Thanks! Djr32 (talk) 17:55, 25 October 2008 (UTC)Reply

    Introductory Paragraph

    The introductory paragraph is merely a clumsy fanboy exercise in jargon-dropping. It is not an honest attempt to explain a concept to someone unfamiliar with it, in familiar terms. Some half-dozen technical concepts are referred to, but left unexplained and unreferenced [probably just as well as an uninitiated reader would never get to the end this paragraph]. This paragraph is at best redundant. Anyone familiar with these concepts already has some notion of what "chaos theory" is. Those that don’t will be none the wiser, and will probably stop reading. This paragraph does define nor explain one single concept.

    Chaos is not confined to dynamical systems, so the reference to that subject in an introductory paragraph is unenlightening and relevant. Surely the "May" in "May exhibit dynamics …", shouldn’t be there, as this sensitivity is a defining feature of so-called chaotic systems. Not all "exponential growth of perturbations in the initial conditions blah blah …" is indicative of chaos, so this statement is both pretentious and irrelevant. The second paragraph is no more enlightening. It doesn’t really say anything, but terms like "chaos-theoretic analysis" sound oh so-good, and I’ll resist the temptation to say "its information-theoretic content is null". Moreover the term "chaos theory" better describes a zeitgeist, now terminal, that produced a lot of flaky pretentious nonsense, and should be avoided, unless trying to impress girls at parties.TitusCarus (talk) 09:51, 13 November 2008 (UTC)Reply

    Regardless of the merits of either the old lead or your proposed replacement, your tone is really not helping your case here. Wikipedia is all about collaboratve editing and consensus. Phrases like "clumsy fanboy exercise", "not an honest attempt" and "pretentious and irrelevant" and your rhetorical devices such as "I’ll resist the temptation to say ..." are unlikely to encourage other editors to work with you on improving this article. I suggest that you politely ask TheRingess (an experienced editor) to explain why they thought your replacement lead was not an improvement, and then work together to develop a compromise text that works for both of you. I am confident that you will find this alternative approach is more productive in the long run. Gandalf61 (talk) 10:36, 13 November 2008 (UTC)Reply

    Thanks for the time spent taken to comment, but that was a validictory one. I've deleted my pass-word, so I cannot use my account. Editing Wikipedia articles is not an efficient use of my time. PS. I'm always polite. Mr Lucretius. —Preceding unsigned comment added by 86.27.192.219 (talk) 11:55, 13 November 2008 (UTC)Reply

    "chaotic"

    humans call everything that's transcendent to us or out of our observational reach, "chaotic". it's a ridiculous, overused term. 68.46.139.114 (talk) 03:30, 22 November 2008 (UTC)Reply

    Subject of article does not exist

    I am dead serious! There is no branch of mathematics (despite what the Mathematics article says) called "Chaos Theory".

    The relevant branch of mathematics is Dynamical Systems, in which "chaos" is a concept. Period.

    It's not even a well-defined mathematical concept, since there a several closely related but distinct concepts that have been used to convey the idea of chaos.

    This article perpetuates the myth that there is such a branch of mathematics. The fact that the phrase "chaos theory" has appeared many times in print (and perhaps has been mentioned several times on the NUMB3RS TV show) is not evidence that there is such a branch of mathematics.

    It's fine to have an article that discusses this concept. But it's not fine to perpetuate a myth by making it appear as fact.75.61.110.161 (talk) 17:25, 5 March 2009 (UTC)Reply

    As far as I can see, this article doesn't say anywhere that chaos theory is a "branch of mathematics". If you disagree with the contents of the Mathematics article, then you could take this up at Talk:Mathematics. Gandalf61 (talk) 17:40, 5 March 2009 (UTC)Reply

    Maybe a reference to Jurassic park?

    About how Ian Malcolm was obsessed with it? Or perhaps its not needed, just getting my two cents in —Preceding unsigned comment added by 59.92.57.171 (talk) 16:40, 15 March 2009 (UTC)Reply

    Definition of chaos theory

    As I understand it, the definition of chaotic dynamics given here is contentious. It is a modified version of that found in Devaney's 1989 book Introduction to Chaotic Dynamical Systems. This definition has been criticised by, for example, Peter Smith in his 1998 Explaining Chaos. As far as I am aware there is no such thing as a canonical formal definition of what it means for something to be a chaotic system. This should perhaps be reflected in the tone of that section. Incompetnce (talk) 14:37, 28 July 2009 (UTC)Reply