Talk:Chaos theory/Archive 4

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All publications on Bios Theory

These are all the publications related to Bios Theory and biotic motion mentioned in the Science Citation Index and INSPEC.

• H. Sabelli and L. Kauffman (1999). "The process equation: formulating and testing the process theory of systems". Cybernetics and Systems. 30: 261–294.
• L. Kauffman and H. Sabelli (2002). "Mathematical bios". Kybernetes. 31: 1418–1428.
• L. H. Kauffman and H. C. Sabelli (1998). "The process equation". Cybernetics and Systems. 29: 345–362.
• H. Sabelli (2000). "Complement plots: analyzing opposites reveals mandala-like patterns in human heart beats". International Journal of General Systems. 29: 799–830.
• A. Sugerman and H. Sabelli (2003). "Novelty, diversification and nonrandom complexity define creative processes". Kybernetes. 32: 829–836.
• M. Patel and H. Sabelli (2003). "Autocorrelation and frequency analysis differentiate cardiac and economic bios from 1/f noise". Kybernetes. 32: 692–702.
• H. Sabelli (1998). "The union of opposites: From Taoism to process theory". Systems Research and Behavioral Science. 15: 429–441. (this may be a stretch)

• S. Levy-Carciente and H. Sabelli and K. Jaffe (2004). "Complex patterns in the oil market". Interciencia. 29: 320.

XaosBits 23:26, 17 January 2006 (UTC)

It would be preferable to see papers which Sabelli did not write; as demonstrating the power of the idea (as opposed to, for example, the force of Sabelli's personality). Also, does anyone know how many of these co-authors are Sabelli's graduate students? Septentrionalis 03:29, 18 January 2006 (UTC)

Louis Kauffman is not a graduate student. He is a very well known knot theorist. XaosBits 04:42, 18 January 2006 (UTC)

That is reassuring; thank you. Septentrionalis 05:06, 18 January 2006 (UTC)

(As of early 2006, six researchers distinguish another type of behaviour, biotic motion as a type of motion of a dynamical system, which they claim is distinct from chaotic motion. The six researchers were identified among the authors of articles covered by the Web of Science.)

This is simply false! As of 2006 there are more than 6 researchers. You can say 6 researchers that were indentified by Web of Science.Lakinekaki 05:23, 18 January 2006 (UTC)

Now, Lakinekaki, you want this out of the article. The way to do this is to convince the rest of us that it is not true or not fair. Fallacious arguments about OR are unlikely to do this; OR is intended to prevent what, in the words of Wikipedia's founder Jimbo Wales, would amount to a "novel narrative or historical interpretation". Summarizing secondary data by counting is not an interpretation. Please be brief; rants are less likely to convince. Septentrionalis 05:06, 18 January 2006 (UTC)

Dear Septentrionalis, it is not just counting, the results involve methodology (choosing keywords with certain assumptions), search, and counting. Lakinekaki 05:14, 18 January 2006 (UTC)

Even if you wrote: "There are 765 Nobel prize winners", you would have to provide reference, and not just conduct the search and count. Lakinekaki 05:17, 18 January 2006 (UTC)

This does not suggest that the text you wish to revert is either untrue or unfair. Finding another paper with a seventh aurhor, for example, would. What do you want and why? Persuade me; rules-mongering chiefly antagonizes. Septentrionalis 05:38, 18 January 2006 (UTC)

That's easy! You can see on bios theory page more than 6 authors. Also, it really confuses me that you ask me if something is true, because that is not criteria for Wikipedia. And I do not understand why you say that the burden of proof is on me, when someone else put that line. How can I verify what he said? I really do not know. You get results from Web of Science by typing certain words. What words shell I type? Lakinekaki 05:49, 18 January 2006 (UTC)

Sabelli H., Sugerman A., Kovacevic L., Kauffman L., Carlson-Sabelli L., Patel M., and Konecki J. (2005) Bios Data Analyzer. Nonlinear Dynamics, Psychology and the Life Sciences. 9(4):505-38.

Only this one reference has 7 authors! Lakinekaki 05:57, 18 January 2006 (UTC)

And if others are found, this can be changed. This is a wiki. Septentrionalis 06:35, 18 January 2006 (UTC)

Now, that's much more accurate, at least the second sentence, if it is true. Also, the first sentence may or may not be accurate. It is based on your count from the references provided at this moment. In other words, it is not based on some source but on your research. It is not VERIFIABLE. I am repeating this because you keep ignoring this FACT. To prove you wrong, I will provide you another reference:

• Sabelli, H., and Abouzeid, A. (2003) Definition and Empirical Characterization of Creative Processes. Nonlinear dynamics. 7: 35-47

It is not upon me to prove you wrong, it is upon you to prove that you are right. Provide reference!

(I guess you would change it now to thirteen. Unless if you are superstitious!) Lakinekaki 07:21, 18 January 2006 (UTC)

...authors of articles covered by the Web of Science... does this mean: a) they wrote some article that is there, or b) they wrote bios related article that is there. Sentence sais a). That is false! 65.42.94.166 07:53, 18 January 2006 (UTC)

x researchers distinguish...(To perceive as being different or distinct.) How can you tell the exact number of how many researchers distinguish bios from chaos? Those papers past peer reviews, and therefore, referees also distinguish bios from chaos. Otherwise, they would not give positive reviews. This whole thing about puting the exact number of bios researchers is soo strange. 65.42.94.166 08:13, 18 January 2006 (UTC)

It is strange, I agree. I modified the original line from some researchers to six researchers to make the point that biotic motion is a fringe topic in dynamical systems. It should not be mentioned in an article that can be backed by rigorous results. User Lakinekaki has been very insistent that his chosen area of research be mentioned in the Wikipedia. I feel that having an article in Bios Theory and a See Also link in the Chaos Theory page is a very generous compromise.

The two new citations do not change the researchers-in-print count. The journal Nonlinear Dynamics, Psychology and the Life Sciences is not indexed by the Science Citation Index. As the journal has been around for a few years, this means that its impact is too low to justify inclusion. The reference with H. S., A. Sugerman et al. does not alter the line about six researchers. The other citation must have a typo. The journal Nonlinear Dynamics—An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems does not have an article by Sabelli. The volumes for 2003 were 32, 33, and 34.

XaosBits 12:59, 18 January 2006 (UTC)

You are right about the typo, I googled it and found correct reference. It is Nonlinear Dynamics, Psychology and the Life Sciences.

I suggest this sencentence: (Few researchers distinguish another type of behaviour, biotic motion as a type of motion of a dynamical system, which they claim is distinct from chaotic motion. As of early 2006, six researchers were identified among the authors of articles covered by the Web of Science.)

I would also put the second sentence at the begining of the of the Bios theory page, and not here. (just a suggestion) Lakinekaki 19:32, 18 January 2006 (UTC)

Mediation?

Dear gentlmen, I think that we may need a help here from a mediator. It seems that all of us have certain emotions on the subject and ideas about importance/validity of this line. We are being subjective. Do you agree that we decide on this line thru mediation process?Lakinekaki 16:17, 18 January 2006 (UTC)

Circle map

FYI, I started an article on the circle map; I'll try to add better graphics as the weeks go by, including a devils staircase and the "biotic motion" graph, as well as the subharmonic path to chaos, which will make Lakinekaki spin, because in the subharmonic case, there are three!! branches that period-double in one cell, before eventually going "biotic". However, a non-zero Ω is needed to see that behaviour. Anyone have good refs on these subharmonic routes? linas 19:19, 16 January 2006 (UTC)

Did you mean something like this...Lakinekaki 00:00, 17 January 2006 (UTC)

3 pairs

chirikov equation

Types of behaviour

I feel a bit uneasy with the section "Description of theory". It starts with saying that there are five types of motion. Are these really exhaustive? This is a bit of a difficult question, because the types are not really defined. Is there a theorem behind this?

Perhaps I should try to formulate my problem in another way. How would the Lorenz system be classified? In what sense is the set of periodic conditions dense? -- Jitse Niesen (talk) 14:50, 18 January 2006 (UTC)

Perhaps, we could find an answer to this by citing some reference that defines all kinds of motion. If there are references that present different categorizations, we should try to find concensus, and eventually make a note about these differences. Lakinekaki 19:25, 18 January 2006 (UTC)

Jitse Niesen reverted a biotic motion line edit with the following explanation: Description of the theory - remove bios theory - chaos theory is a huge discipline maths/physics, not all parts can be explained here, and bios theory is just to small to be mentioned here)

It seams to me that you have ignored the whole discussion about biotic motion presented above. Lakinekaki 19:25, 18 January 2006 (UTC)

I have not ignored it. I read all of it and I saw that there are only a handful of people working on biotic motion. There is only a limited amount of material we can include in this article, so we should be selective. I think that a minimum criterion for a topic to be mentioned on this page is that it should be mentioned in the standard text books on chaos theory (which would still give us far too much to write about). The discussion and my experience shows that this is not the case for biotic motion. Therefore, I removed the line. -- Jitse Niesen (talk) 20:25, 18 January 2006 (UTC)

How can recently discovered distinction be mentioned in the standard text books on chaos theory? Besides, this section is about clasification of non-linear motions and it gives references to other types of motions, it is not about chaos.

In how many standard text books can you read about Yoshi Ueda (paragraph that is in the history)? In what text book can you read about movie and book Jurassic Park that is in Popular culture section? Lakinekaki 20:37, 18 January 2006 (UTC)

A few books where Yoshi Ueda is mentioned: The Impact of Chaos on Science & Society by Gregobi and Yorke; or Nonlinear Dynamics and Chaos by Thompson and Stewart; or Vibrations and Stability by Thomsen. Although in the late 1970s and early 1980s Ueda was not recognized worldwide as a pioneer in chaotic dynamics, today he is. Surprisingly, Jurassic Park is mentioned in a few nonlinear dynamics texts, for example, Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers by Hilborn. XaosBits 01:38, 19 January 2006 (UTC)

XaosBits, your bibliographical skills are impressive! If you can also find video game,Tom Clancy's Splinter Cell: Chaos Theory for me, you will be my idol! 64.108.210.62 05:20, 19 January 2006 (UTC)

Actually, I think that the list of different types of motions should be deleted alltogether. As I thought, it is not exhaustive. A simple motion that is not included is converging to a fixed point, as for instance happens with the system $y'=ay$ with $a<0$. So I would replace the list with a sentence like "A dynamical system can exhibit many kind of motions, ranging from the regular to the erratic. Chaos theory studies chaotic motions." (or perhaps delete it without putting anything else in place). -- Jitse Niesen (talk) 14:30, 19 January 2006 (UTC)

Sounds like a good idea to me. Anything that might help this chaotic debate to converge to a steady state is a good idea ! Gandalf61 14:42, 19 January 2006 (UTC)

Now that's a good introduction to chaos theory! Good job XaosBits. Lakinekaki 11:57, 22 January 2006 (UTC)

Chaotic spectrum

If I have a spectrum, is there some way of telling if its "chaotic"? To the eyeballs, the eigenvalues seem to be occurring at "random" values, but I was wondering if there's some better way of classifying beyond just a "gee this looks random" result. linas 14:25, 24 January 2006 (UTC)

I imagine the spectrum is some smooth decaying curve with "noise" in it. If you take your time series, Fourier transform it, replace all the phases by random numbers, transform back, you end up with a series with the same spectrum but with unrelated dynamics. This randomization game shows that there is not enough dynamical information in the spectrum. If the spectrum has a whole bunch of peaks that are not "harmonically" related, then they are a reflection of unstable periodic orbits. XaosBits 17:45, 24 January 2006 (UTC)

Hmm. Not sure I understood. I know that spectra provide incomplete info: "you can't hear the shape of a drum", it turns out. I don't have a time series, I just have a spectrum, and I'm don't know what the corresponding iterated function system/Poincare map is. The spectrum is just a bunch of discrete eigenvalues, each larger than the last; no smooth decaying curve. (This is from a Hamiltonian, and not from a transfer operator). I am assuming that this is indeed a quantized chaotic system; I'm just hunting for tools or "well-known techniques" to characterize it with. Whatever; I'll have to meditate on it some more. linas 01:15, 25 January 2006 (UTC)

XaosBits

I just realized that my scepticism regarding your counting of researchers who distinguish bios in the Web of Science was justified. At the website of the Journal of Nonlinear Dynamics, Psychology, and Life Sciences [1] you can see that this journal IS abstracted in the ISI Web of Science (through PsycINFO). I was right when I claimed that you conducted research (although a very poor one that would not pass peer review), and you were incompetent of finding the journal in the list (although you had access to ISI while I didn't and could not verify your claim). FYI, here [2] they show that NDPLS has an impact factor of 1.90.

NDPLS is currently abstracted in:

PsycINO (American Psychological Association)

ISI Web of Science (through PsycINFO)

JEL/Econlit (American Economic Association)

Medline (National Library of Medicine)

Proquest (1997-2003 issues at the present time)

ScienceDirect (Elsevier)

Scopus (Elsevier)

FYI, Cybernetics and Systems is 7th out of 18 journals in Computer Science, Cybernetics (Science), with an impact factor of 0.768. [3]

It was very interesting for me to observe your (other editors included) behaviour regarding this whole bios thing. (I wanted to see how far you would go, and I was keeping some arguments just in case - like the one with the video game) You were so resistant to this new idea that you were not familiar with that you rewrote the whole section in order to eliminate biotic motion link from it (because you could not find argument that would justify its deletion in the past form). I am certain that anyone who is not specialized in chaos theory would not react like few of you did. If an intelligent person (non-specialized in these areas) would read chaos and bios articles, that person would not had biases that you had. You tried to attack me personally for adding this bios thing (that I did because I was familiar with it - I cannot add things I am not familiar with, while you wanted to substract things you were unfamiliar with!), while it is so obvious that all of you are chaos fans. linas for example goes often to chaos related seminars - so he said. What are chances that he is not doing research in that field? XaosBits has access to ISI, why would non-researcher have this? From his contributions to wikipedia, it is obvious what is his area of research - chaos. Gandalf61 has also contributed with so many chaos related articles.

Linas told me somewhere I should try to make friends on wikipedia. I don't need this kind of friends. What was friendly in your actions. Maybe generosity that XaosBits mentioned by allowing 'Bios theory' to be an article in wikipedia and also a link in 'See also' section here. He is not in a position to be generous. Wikipedia is not his petpedia!

PS. Gandalf61, we had biotic debate, not chaotic. You should know this by now :) Also, convergence to a steady state is rarely a good idea! Constant interaction, feedbacks and generation of novel things (aka bios) is far more appealing.

So much from me. Lakinekaki 00:38, 25 January 2006 (UTC)

NonLinear Dynamics

I have been wondering why nonlinear dynamics is linked to this page? As was stated previously chaos is a specific behavior exhibited by nonlinear dynamical systems, and not all encompassing. I was wondering what everyone thought about giving nonlinear dynamics its own page. The page would include what constitutes a nonlinear system, some common behaviors of such system (of which chaos is one, bifurcations, limit cycles, ect..), what these systems model(ie..predotor prey models, nonlinear vibrations, ect..), solution methods(both graphical and analytical), and some links to ongoing research being conducted in the field. I am new to wikipedia, but I think I can contribute a good article. Any comments would be greatly appreciated. And please answer my original question if anyone can. Why is nonlinear dynamics directed to chaos? Mechj 05:38, 2 February 2006 (UTC)

Contributions are welcome, especially good ones. The original creator of the nonlinear dynamics redirect seems to no longer be around, so we can only speculate why it was created. I hear the expression nonlinear dynamics used by many as a synonym to chaos and related topics. Remember Stan Ulam's quip about “defining the bulk of zoology as the study of non-elephants.” Nonlinear dynamics is most of dynamics, and some of it, linear or nonlinear, is covered in the article on dynamics. The dynamical systems article is written from the geometrical perspective to encompasses nonlinearities.

The chaos theory article could be the anchor to many other topics (time-series analysis, chaotic synchronization, control of chaos, etc...). There are important concepts in dynamical systems that do not yet have an entry in the Wikipedia, such as the stable and unstable manifold. – XaosBits 16:00, 2 February 2006 (UTC)

I read some of the article on dynamical systems, and I think I am going to add a section on nonlinear dynamics in that. If it begins to take on a form of its own I will then give consider giving it its own page. This will be the best way to approach this I think. Thanks for you replies. Mechj 05:10, 3 February 2006 (UTC)