Talk:Chaos theory

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[edit] 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)

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)

[edit] 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)

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)

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)

[edit] 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)

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)
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)
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)

[edit] 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)

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)
What about these 1500 books that call it "chaos theory"? Dicklyon 20:12, 29 June 2007 (UTC)
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)

[edit] 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)

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)
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)

[edit] Moving chaos theory to chaotic dynamical systems ??

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)

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)
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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

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)
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)

[edit] 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)

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)

[edit] 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)

[edit] 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)

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)

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)

[edit] 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 (talk • contribs) 21:17, 29 December 2007 (UTC)

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)

[edit] 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)

Underpins? Sounds like someone's fanciful imagination. Dicklyon (talk) 17:44, 12 January 2008 (UTC)

[edit] 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)

[edit] 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)

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)

[edit] "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)

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)
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.
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)

[edit] 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)

[edit] 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)

See the information under A section a simpler terms? above. Gandalf61 (talk) 14:28, 18 April 2008 (UTC)
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)
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)
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)
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)