Talk:Chaos theory/Archive 3

message: Your arguments fall into two categories:
1) In the first category I put arguments where you object that bios and biotic motion are not well defined (mathematically) on the Bios theory page, and since I put there something that is relatively new, it is upon me to provide enough information from the references cited in Bios theory article. You provide some good arguments there (single indent) and I give my comments (double indent): 
:*I can't see how "biotic motion" is anything more than a special type of standard chaotic behavior. How exactly can you tell that a system is behaving "biotically" and not just chaotically (in the mathematical sense of the word)? 
:*N.B. The current definition of novelty in the bios theory page must be wrong. The number of isometries as defined is invariant under shuffling. I imagine something else was meant.
::*I acknowledge this, and I have improved descriptions in Bios theory.
:*Maybe Bios is different, but the leading example provided -- An + 1 = An + gsin(An) is the "famous" circle map, studied for some 50-odd years now. To suddenly call this "biotic" is unusual. At+1 = At + g sin(At). Is known as the circle map. 
:*Biotic motion seems to be a slice through the Standard Map, with some of the parameters varied adiabatically over time. Since the standard map is both well-known, heavily studied, and still full of many deep mysteries and surprises, it would be much more comforting if this example of biotic motion was compared to what is already known about the standard map, so that we could tell apart the new results from the parts that are "well known".
:*What I disagree with is the attempt to promote biotic motion to a new type of behaviour, distinct from chaotic motion. I have seen nothing so far that justifies this view. Biotic motion is a sub-type of chaotic motion which arises from a particular family of maps. 
::*What is new is not the circle map, but the new features discovered in it’s specific case, and also in other processes. Authors considered these features fundamental enough to define a new concept and publish papers on the subject. This does not mean that these processes cannot be analyzed with the tools devised for chaos analysis, on the contrary. (In the same manner that periodic series analysis is being applied to the chaotic processes) What this means is that there are additional characteristics in these processes that are not present in every process that can be put in the chaos category. I understand that you are making an argument that bios is only a subclass of chaos. However, in the same manner that periodicities have repeating values, while chaos series always generate variations, chaos always generates recurrences (absence of novelty), while bios always generates novelty. Bios is not subcategory of chaos, but a distinct  concept. (James A. Yorke coined word chaos for processes analyzed for a long time. Recently word bios was given to another class of process that has been also analyzed for a long time and was mixed with chaos.)
:*For biotic motion there is no characterization of the type-of-motion, and consequently, no collection of results. 
	
::*This is simply not true.
:*It is just that in a mature field, such as dynamical systems, the onus is on the discoverer to explain how the work fits in with the rest of knowledge. 
::*I am not discoverer, but authors do explain this. Some explanations on Bios theory page seem quite clear to me. If you think it is not enough you can add more (this is Wikipedia!). 
2) In the second category I put arguments where you object to the actual validity of things presented in papers (or the reputability of the journals), and to this argument I responded by trying to explain from my point of view why bios theory is valid. On this we can agree or disagree, but that is only our personal thing. Guidelines of Wikipedia are very clear in this regard. However, for the sake of clarifying things, I will provide summary of my comments here.
:*I thought I'd made some reasonable statements, and instead of finding reasonable rebuttals, I'm finding lots of histrionics.
::*You did make some reasonable statements, although I don’t see how they relate to the theory of bios (they relate to some equations, but not to the theory). Furthermore, did your statements disproof the theory of bios. If they did, how should that affect articles in Wikipedia? If they did not, what should I refute? Furthermore, I think I did give some reasonable responses.
:*Kolmogorov defined the winding number for this map (I believe) in the 1960's, maybe later, although Feigenbaum's const 4.6 was not yet known at that time, nor was the so-called "period-doubling route to chaos" understood. 
::*Nor was so-called biotic motion known.
:*When the motion is diffusive, I would expect the dynamics to be chaotic. 
::*Bios can be diffusive although it is not it’s fundamental characteristic. 
::*I can see that all of you understood very well the kinetics of the process equation, and I am very glad for that. You mention what would happen when initial conditions originate in different basins of attraction, and I am providing here an image of that case. Six different basins generate this. Although you think that nothing fundamental happens after the point 4.6.. I tend to think that there is significant change happening there.
 
::*I also provide here three more graphs. In your view, left and middle images are different processes which they really are (left is periodicity with many points, while middle is chaos), while middle and right are the same (right is chaos). In my view (and the theory of bios), middle and right are also different processes (right is bios).
thumb|250px|left|periods thumb|250px|left|chaos thumb|250px|none|bios
I don’t think that I have anything more to say on this subject, and since I think that the line that I am adding on the Chaos theory page about biotic motion is in full observance of the Wikipedia policies, I will keep adding this line. You can keep deleting it, but that will only lead to disputes and revert wars.
Verifiability does not mean that editors are expected to verify whether contents of an article are true. In fact, editors are strongly discouraged from conducting this kind of research.
Lakinekaki 06:54, 17 January 2006 (UTC)
thread_title: Summary as I perceive it

message: (In print, nine researchers distinguish a sixth type of behaviour, biotic motion, which they claim is distinct from chaotic motion.)
Maybe I have put references of that many, but there may be more papers on the bios theory that we may not be aware of, and therefore I think that the last solution was better:
(Some researchers distinguish a sixth type of behaviour, biotic motion, which they claim is distinct from chaotic motion.)
Lakinekaki 19:43, 17 January 2006 (UTC)
replies: text: I think that you should also include word bios, as the line refers to biotic motion while biotic motion is part of the bios theory. Authors acknowledging bios would implicitly acknowledge biotic motion. Till then, I reverted your change.Lakinekaki 23:45, 17 January 2006 (UTC)
replies: text:  There are zero articles in the Web of Science mentioning bios theory or bios in the sense of bios theory.  So I'll revert the reverted line.   XaosBits 02:50, 18 January 2006 (UTC)
replies: text:  I am impressed! You really did a good research. Now all you need to do is publish it somewhere (i.e. analysis, methodology used and results - and hopefully you will give me some credit there for telling you how to improve your results, and make your research more sound) so that it becomes verifiable since as we all know here, Wikipedia publishes things that are verifiable! Till then, I'll revert the change. Lakinekaki 03:31, 18 January 2006 (UTC)
thread_title: biotic motion line