Talk:Chaos theory/Archive 5

message: Why is so much space spent in this article on the concept of an attractor? That's a general dynamical systems concept that doesn't have an inherent connection to chaos. Could it be refactored into a separate article, which could then be referenced when talking about strange attractors?
:There are separate articles onm attractor and strange attractors. Why are they so detailed here, and not referenced?Lakinekaki 04:36, 7 April 2006 (UTC)
thread_title:  Verbiage on Attractors 

message: Recent update added:
:Consider the dynamical system defined on the real line by mapping x to 2x. This system has sensitive dependence on initial conditions everywhere ...
Hmmm ... I don't think this is true. The map x->2x has two fixed points - a repelling fixed point at 0 and an attractive fixed point at infinity. All initial points apart from 0 head towards infinity. With an appropriate metric (e.g. by mapping projective real line onto a circle) we can even say that any trajectory that does not start at 0 converges to infinity. That doesn't look like sensitive dependence to me. Maybe another example would be a better illustration of the point being made ? Gandalf61 17:08, 3 March 2006 (UTC)
replies: text: I assumed we were using the usual metric on the real line, and that it did not include the point at infinity. Doesn't this go without saying? Maybe not... if that really seems unclear, I can state it explicitly. --Experiment123 19:07, 3 March 2006 (UTC)
replies: text: You're both right. The x->2x is a terrible example; although one may argue it has a positve lyapunov exponent, the system is not a bounded system, duhh, so the positive exponent does not imply topological mixing or even ergodicity, so it sure won't be chaotic. linas 23:12, 3 March 2006 (UTC)

text: The point of the x->2x example is exactly what you're saying: it's clearly not chaotic, so sensitive dependence on initial conditions does not imply chaos. That's why it's a good example, not a terrible one! --Experiment123 02:21, 4 March 2006 (UTC)
replies: text: I have added the definition of sensitive dependence on initial conditions to the page butterfly effect.  It's from Devaney's book. — XaosBits 03:13, 4 March 2006 (UTC)

text: The systems behave identically only if their initial configurations are exactly the same.
First, I think it should read "system behaves."  It refers to the trajectory after two different initial points, yet within the same chaotic system.
Second, I think that the words "behave(s) identically" is slightly misleading.  The word "behavior" seems to invoke a concept of what the system does after it has been seeded with an initial condition.  I think we should take care to avoid the implication that what follows from two different initial conditions cannot be identical.
Thoughts? --afuturehead 18:13, 26 June 2006 (UTC)
thread_title:  Sensitive dependence 

message: I just googled to find some more info on "chaos theory" in conjunction with dissipative structures.
I found an old cached version of this article there, but that info has been deleted from this section, and the old cached version did not say much. Perhaps one of you experts on the area could direct me to a suitable website or book? I have some familiarity with both, but I am looking for some more examples here.DanielDemaret 11:06, 5 March 2006 (UTC)
thread_title:  Dissipative 

message: I just take a brief look to this topic, and I found something to review about categorization. I only add an external link to Santa Fe Institute, but I thing that the links between "chaos theory" and "complex systems theory" are really deeper and that their topics and sub-topics deserve much more cross-linking (perhaps in a common category) just to make browsing easier (I can't do it by myself, since I am far from competent about and I'm working about "very complex system" of horsemanship...)--Alex brollo 15:39, 9 March 2006 (UTC)
replies: text: I beleive that maybe 20 or 30 years ago, "chaos theory" and "complex systems" were almost synonyms. I don't beleive that's true anymore; chaos has a much narrower definition: these days, it tends to focus on simple systems, not complex systems.  This is in part needed to make headway: one wants to study the simplest possible system that is still chaotic. By contrast, in the field of "complex systems", one is instead looking for ways of discerning the simple parts of a complex system. These simple parts may, or may not be chaotic. So they'r two differnt fields of study. linas 02:01, 10 March 2006 (UTC)
replies: text: This is part of why mathematicians increasingly prefer the term nonlinear dynamics rather than chaos theory to describe what they study: it's less likely to be confused with something else, in addition to sounding less metaphysical. --Delirium 08:44, 15 March 2006 (UTC)
thread_title:  Chaos theory and complex systems 

message: * David Kernow 19:53, 14 March 2006 (UTC)
thread_title: Option 1: 'See also' section should include [[Bios theory]] link.

message: *Experiment123 19:09, 14 March 2006 (UTC)
thread_title: Option 2: 'See also' section should not include [[Bios theory]] link.

message: Look out!  In Talk:Bios theory, I have just listed troubling evidence suggesting serious problems with the claims made in Bios theory and an apparent conflict of interest on the part of User:Lakinekaki.  See also WP:NPOV [[WP:VAIN WP:VERIFY and WP:RS.  ---CH 06:36, 12 May 2006 (UTC)
thread_title: Serious problems concerning [[Bios theory]] and [[User:Lakinekaki]]

message: I just wanted to voice my opposition to merging bios theory with this article. Bios theory is such a fringe topic, if anything at all, that it does not deserve that much attention in an article on such a broad field as chaos theory. -- Jitse Niesen (talk) 11:08, 18 March 2006 (UTC)
thread_title:  Merging 

message: Guys, although Chaos and Bios theories may be treated as related they are slightly different in scope, how they are used and their targets. They themselves and articles about them will likely evolve further, possibly away from one another in actual subject area. As such these two articles should not be merged. 
Should they be listed in one another's "see also" section? Well, tell me, in general, what needs to be listed in any article's "See also" section and then we'll be able to give an answer. I don't have a clear definition myself, but can say that "See also" entries are as frequently useful as they are not and that is quite OK. It is supposed to be that way because of different interests. "See also" sections frequently include sub-classifications, uses or similarly related articles not listed anywhere else in the article we started from. Chaos theory is used for many things and it does not hurt to mention it. It gives the reader more ways to comprehend why it is there and what purposes it serves. In this regard, I think "Bios" theory should be included in the See also section of this article. 
"See also" section should also be short. Having too many entries defies its main purpose - giving the reader a finite set of paths to follow up. In that regard, if we have articles A, B and C such that article B appears in A's "see also" list and C appears in B's "see also" list, then we might not need to also list C in A if the list is already long. Example? See, for example, article Bird. One can probably find better examples, but this is the one I just thought of.
Since "See also" of this article is not that long yet, I still don't see any problem in including "Bios" in its "See also" list. When and if it starts growing, this may need to be reconsidered and, perhaps, more infrastructure articles added for this alone - e.g. "List of theories based on Chaos Theory" vs. "List of direct uses Chaos theory", etc. Until then just cool down.
--Aleksandar Šušnjar 18:25, 21 March 2006 (UTC)
replies: text: Did you actually read the page on bios theory? Maybe there is such a thing, but the current WP page on it is utter bunkum. Until someone can describe bios theory so that it doesn't sound like pseudoscience, it certainly should not be referenced here. linas 15:49, 22 March 2006 (UTC)
thread_title: Wow - what a discussion

message: Shell we have the link on Tuesdays, Thursdays and Saturdays, and not have it on Mondays, Wednesdays, Fridays and Sundays? :O) Lakinekaki
:Let's see. You called a poll; it came out 6-3 against you, and your efforts to suggest a merge for your faorite theory are consistently overridden. You now want equal time. No, we shall not violate WP:NPOV#Undue weight. Verbum sap. sufficit. Septentrionalis 05:51, 5 April 2006 (UTC)
replies: text: It's more like 6-5 (if you count Aleksandar's and my vote), or 8-5 if option 3 (improve) votes are considered against. From WP:NPOV#Undue weight: ...Articles that compare views need not give minority views as much or as detailed a description as more popular views... Noone is comparing views here, or trying to put description of bios in chaos article. We are talking about a link in a See also section.Lakinekaki 16:01, 5 April 2006 (UTC)
replies: text: No matter which way you cut it, the majority result of the poll was a decision not to include a link to the bios theory article. Why did you propose a poll if you are not prepared to accept its result ? Are you simply trying to stir up controversy ? Gandalf61 09:05, 6 April 2006 (UTC)
replies: text: I am accepting result of the poll. I was just hoping more people would vote and give some option significant majority. This way it's more like no concensus.Lakinekaki 14:48, 6 April 2006 (UTC)
thread_title: What shell we do now?

message: Did I misplaced the sentence about 3 body problem? Are they behaving as chaotic attractor, or just chaotic? I know that Solar system is attractor. Lakinekaki 06:04, 7 April 2006 (UTC)
replies: text: The word chaotic often substitutes for another technical term.  Different dynamical systems are chaotic in different ways: as  Axiom A systems, as  mixing systems, as  uniform hyperbolic, etc.  So when one reads in non-technical discussions that the three body problem is a chaotic dynamical system, what is meant is that the phase space of the three body problem is a mixed phase space with regions of periodic behavior and regions that have embedded horseshoes.  That means that there is a neighborhood of initial conditions of the three body problem that behave just like a uniform hyperbolic system.  So rather than say all this, it is common to say that the system is chaotic.  It is similar to usage of smooth when referring to differentiable functions. — XaosBits 22:35, 7 April 2006 (UTC)
thread_title: 3 body and attractors

message: The text that was moved:
Gleick (1989, p. 306) wrote that No one [of the chaos scientists he interviewed] could quite agree on [a definition of] the word [chaos] itself,. That's why he gave descriptions from a number of practitioners in the field some of which are: the complicated aperiodic attracting orbits of certain, usually low-dimensional dynamical systems (refering to "chaotic" behaviour); a kind of order without periodicity (refering to chaos), etc.
Textbooks devoted to chaos do not really define the term. Some descriptions include: 
*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.
*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."
*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. 
*Chaotic behavior can be predicted only if the initial conditions are known to an infinite degree of accuracy, which is impossible.(Jerry Gollub and Thomas Solomon, Academic American Encyclopedia.)
Rather than to give a precise definition of chaos it is much easier to list properties that a system described as "chaotic" has.
(Moved by XaosBits 22:49, 7 April 2006 (UTC)
replies: text: The text that XaosBits has removed is very close to a straight lift from mathworld, and so could be copyvio. If we are going to include a discussion of the definition of chaos, at least let's find our own quotes. Gandalf61 11:05, 8 April 2006 (UTC)
thread_title:  Commentary on definition 

message: There is a book that has a refrence to Chaos theory. I think it was Jurrasic Park (god I hope I spelt that right). 68.228.33.74 08:00, 30 May 2006 (UTC)
thread_title:  Shall we have a Cultural Refrences Section? 

message: I removed the following external links, which I considered to be irrelevant:
:*Nonlinear Dynamics at Drexel
:*Bristol Centre for Applied Nonlinear Mathematics
:*Linear and Nonlinear Dynamics and Vibrations Laboratory at the University of Illinois
If anyone disagrees, let me know.  If these links are to be used at all, I would recommend putting them in some kind of "list of Nonlinear Dynamics research groups" or something.  I don't think they would be immediately useful to someone looking up information about chaos theory. --BryanD 20:04, 6 June 2006 (UTC)
thread_title: Irrelevant links

message: If you could calculate the chaos of one person, could you determine ones future?
:I guess in theory you could, but then again no one knows if chaos theory even exists. That's why it's called chaos theory, not the Law of Chaos or something. It would also be impossible to predict the "chaos" of a person. Chaos is usually figured around things that have set paths to choose. For instance, the water mill example. The water mill, even if it's chaotically rotating from left to right when the water flow is increased to a high amount, the mill only has two directions to turn no matter what. It can only turn left and right, so the chaos of which direction is contained within those two directions. Humans, however, having freedom of choice, always have many options to choose from. For instance, let's say you were in a room and there were two doors leading separate ways. You could go through one of the doors, you could go into a door then come back out, you could use the other door, you could open a door and then shut it without going through it, you could do nothing at all, you could jog in place, etc. As you can see, the possibilities for us are endless, and thus the chaos is not contained by any specific perameters. Thus, even if chaos theory were true, it would be impossible to actually read one's future by determining their "chaos". 24.15.53.225 02:38, 3 June 2007 (UTC)
thread_title:  Chaos for the future 

message: I have tried to find articles about how Chaos Theory can be applied on Evolution.
I wish to use an argument that Evolution by Natural Selection from a Common decent is possible because certain systems in physics bring Chaos from Order as the Double Pendulum.
Is this a valid argument?
--Msitua 17:33, 6 August 2006 (UTC)
thread_title:  Chaos theory and Theory of biological evolution 

message: I find that the GIF animation illustrating the three body problem adds very little to the text, so I have removed it.  The three body problem played an important role in the development of dynamical systems and it could provide a great illustration.  A direct simulation may be interesting, if run for a longer time.  This may be impractical with a GIF, but there may be other solutions that do not overload the page. – XaosBits 02:56, 7 August 2006 (UTC)
thread_title:  Three body GIF