Ted,
I was responding because often it seems to me that people throw around
terms like Chaos Theory (or more appropriately non-linear dynamics) and
really don't understand it. The point of my post was to show that
1. Long term prediction of a chaotic system is problematic
2. The system is perfect deterministic (i.e. not random)
3. It is very very easy to confuse a chaotic system with a random one.
Number 3 above relates to the gif. In looking at the data one might
conclude that the two series are both AR(1) series and try to model them
both that way and in one case would be quite wrong. Now, if you agree
with my junk science post that insufficient information can be bad then
you'd want to be somewhat careful in how you analyzed those two time
series.
Regarding your statistician's comments. Fantastic! I agree completely.
I know that in economics for instance Chaos Theory is not a big research
area because nobody can seem to find any. If you were to go into a PhD
program and specialize in Choas and how it applies to economics you'd a)
be writing to a very small audience and b) be working primarily in the
theoretical field.
Steve
--- Ted Mosquin <[log in to unmask]> wrote:
> Steve from: Steve <[log in to unmask]> wrote:
>
> > Stella-Maria wrote:
>
> > If nature is ruled by chaos and randomness, if determinism is just a
>
> > > stupid construction (which may well be) why then so much hussle to
> start
> > > burning the few forests left in order to manage them (why= ethically
> i
> > > mean, not scientifically). There is absolutely no reason to do
> prescribed
> > > burning on ethical grounds.
>
> And Ted responded:
>
> > Interesting question. We could all do well to read more on systems
> > theory, complexity theory, chaos theory and the idea of the
> self-organization
> > (self-realization?) of matter. I know this sounds odd for a long
> practicing research
> > biologist and ecologist but I continue to be puzzled at the idea that
> > "Nature is ruled by chaos and randomness" - as the system is so
> complex, harmonious
> > and cooperative)
>
> To Steve: In the above I was only questioning Stella-Maria's statement
> on "Nature ruled by chaos and randomness." You have clarified the
> matter, but
> a lay person would find it impossible to comprehend just what you mean.
> So I am adding to an explanation to your response (see below).
>
> And Steve wrote:
>
> > Problem: A chaotic system *is* deterministic. It appears random over
> various values.
> >
> > Example:
> > http://www.geocities.com/recursive_1/image002.gif
> >
> > One series is chaotic the other is an autoregressive (of order 1)
> time
> > series. Cany you tell which is which?
> >
> > Since I created the chaotic series I know with certainty the initial
> > condition and can predict with 100% accuracy the evolution of the
> system.
> > Nobody else can, unless they just happen to know the initial starting
> > value (exactly).
>
> Ted here:
> Steve, I looked at the above .gif file and can't tell the difference. I
> don't see why anyone would need to, or what it has to do with
> enviroethics.
> So I consulted with a statistician who offered the following comment on
> your post. Here it is:
> _____________
>
> "Well, I can try to explain what Steve is saying. How much relevance it
> has to ecospheric ethics is another issue. (not much, to me!)
>
> "Think of a sine wave where you know the amplitude and frequency of the
> cycles. If you know where a certain point on the wave is located then
> it is easy enough to compute the rest of the wave.
>
> "The same is true for chaotic systems, although in this case the line
> drawn does not look at all regular, like in the graph on Steve's web
> page.
> However, the noisy line is completely deterministic as he says in that
> you can find any value on the line once you know a starting value.
>
> "So his point is that something that appears completely random can in
> fact be completely deterministic.
>
> "How this matters from an ecological/ethical point of view is not so
> clear to me, as there is a big jump from a simple Cartesian plot to a
> fully functioning ecosystem. My understanding (very limited) of these
> things is that the iterative equations used for making such plots have
> generally little scientific interpretation, so if you could match up a
> real world plot to a chaotic plot, and fully understand the state of
> the system, would you gain from it scientifically?
>
> "In addition, I do not think that the people interested in these ideas
> could cite an actual real world example where a non-trivial natural
> system was found to be deterministic in the chaotic way he
> describes.... There is a big jump between developing a mathematics
> that can deterministically produce the appearance of randomness, and
> taking actual data and showing that it was generated by such a
> deterministic system. For example, maybe the chaotic plot he gives is
> "similar in features" (perhaps similar mean variance, etc.) to a plot
> of rainfall fluctuations in the Amazon for the spring season. This
> would by no means mean that Amazon rainfall is deterministic, as I
> could easily generate another plot from a truely random process with
> the same features (his autoregressive plot being a possible example).
>
> "To show that a natural system is deterministically chaotic you would
> need to get exactly the same curve in nature as from your equations,
> and this is really asking alot!
>
> "Anyway chaotic systems are certainly interesting to think about, and
> philosophically they put a new twist on determinism, so its all just
> grist in the mill of interesting enviroethics debate.
>
> END of invited comment.
> ______________
>
> Ted here again:
> Well, good for statisticians! What interests me is not pure randomness,
> but complex systems that repeatedly produce order -- such as the
> Ecosphere
> (system) has done for over 3.5 billion years, and in a necessary
> earlier form (according to some - ever since the moment of the Big
> Bang). Of
> course, in the case of the Earth's Ecosphere the process of
> complexification has been grossly interrupted (smashed) particularly by
> 3 or 4 huge
> asteroids which wiped out the emerging ecosystems and a lot of lines of
> evolution completely. But the astounding thing is that the "Gaian
> system"
> (the Ecosphere) started right up there with what was left and once again
> began to create an ordered, and ever more complex Nature. While the
> creation of order in Nature, no doubt involves some random phenomena
> (mutation, selection, etc.), something of far greater significance was
> going on
> -- ever more order was arising out of a complex, dynamic system.
>
> It seems to me that a ligitimate question in enviroethics is whether the
> actions of humans are heterotelic or homeotelic to the complexifying
> ecospheric system which produced us - because this should help govern
> our ethical thinking and conduct. Heterotelic refers to abnormal or
> misdirected behaviour which, though it may, partly at least, satisfy the
> requirements of the individual, does not satisfy those of the larger
> systems
> of which it is a part - i.e. the Gaian hierarchy as a whole. Such
> behaviour therefore reduces stability and integrity of the Gaian system.
> Or, in
> contrast, the behaviour and actions can be homeotelic - normal behaviour
> that serves to maintain the critical order of the whole Gaian hierarchy.
> Thus, to behave ethically to the Earth's environment, humans would have
> to promote stability rather than do things which destablize and
> impoverish
> planetary ecosystems. Here, Maria Stella's comment (right at the top of
> this post) on prescribed burning of forests is very relevant - but it is
> only
> one tiny example. More graphic (and serious) examples of heterotelic
> behaviour of humans would be clearcutting, mega-trawling, industrial
> agricultural practices, the generation of anti-environmentalism hate
> literature, mega-pollution, and all the other huge kinds of destruction
> of the
> Earth's evolved, ordered system that are taking place (driven by a
> massive overpopulation of humans). With a small (normal) population, I
> believe
> that humans too could once again behave in a homeotelic manner (as have
> many smaller-scale cultures in the past), but while retaining
> "ecologically
> friendly" technologies ( see
> <http://www.ecospherics.net/pages/RoTechEcol.htm>). This is a topic for
> another time.
> [The complete definitions and full discussion of homeotelic and
> heterotelic behaviour are found in the excellent book by Edward
> Goldsmith "The Way:
> An Ecological World View." U. of Georgia Press, Athens (1998), 541 pp.
> (which I read last spring while sitting on a stump making maple syrup in
> the
> woods of Lanark County, where I live].
>
> Ted
=====
"In a nutshell, he [Steve] is 100% unadulterated evil. I do not believe in a 'Satan', but this man is as close to 'the real McCoy' as they come."
--Jamey Lee West
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