Ted Hoffman

This thread is a continuation from a pevious thread with Ender which you can see <a href="http://iidb.org/cgi-bin/ultimatebb.cgi?ubb=get_topic&f=56&t=000135&p=5" target="_blank">Here</a> Ender attributed the chaotic nature of our universe to the eternal flux in it.

First of all, I find the use of the word chaotic a misnomer in describing the phenomena that scientists have observed in the world over. I also find it inaccurate and baseless. Is it enough to call something chaotic just because minute initial conditions result in colossal differences in observed outcome?

Lets look at the following definition from
<a href="http://herkules.oulu.fi/isbn9514250133/html/x238.html" target="_blank">here</a>
Chaos is more easily understood through a comparison with randomness and periodicity. Random behaviour never repeats itself and is inherently unpredictable and disorganised. Unlike random behaviour, periodic behaviour is highly predictable, because it always repeats itself over some finite time interval. A sine wave is a typical example. If we know the amplitude, frequency and phase of a sine wave at any instant, we can predict the wave perfectly at any other point in time. Chaos is distinct from periodicity and randomness, but has characteristics of both. It looks disorganised, but is actually organised. The most important criteria for chaotic behaviour are summarised as follows: 1. Chaos is deterministic and aperiodic and it never repeats itself exactly. There are no identifiable cycles that recur at regular intervals. 2. Most chaotic systems have sensitive dependence on the initial conditions. In other words, very small differences in the initial conditions will later result in large differences in behaviour.3. Chaotic behaviour is constrained. Although a system appears random, the behaviour is bounded, and does not wander off to infinity. 4. Chaotic behaviour has a definite form. The behaviour is constrained, and there is a particular pattern to the behaviour (Crutchfield et al. 1987, Gleick 1987, Ruelle 1979, Grassberger & Procaccia 1984, Procaccia 1988).

I will provide scientific findings that support the chaos theory and debunk them. This is basically a war between classical physics (which provided a deterministic universe from Newtons laws) and quantum physics (whose "chaos theory" is enshrined in Heisenbergs uncertainty principle).
The first example:

Edward Lorenz, a meteorologist, programmed a model of the weather into a computer, he got strange results. Lorenz found that minute differences in initial weather conditions produced drastic changes in the outcome. Some Meteorologists had long suspected this was so. In fact, they had given the idea a name — ‘the butterfly effect’. The name was based on ‘the half-whimsical belief that a butterfly flapping its wings in Asia could affect the weather in New York a few days or weeks later.

Here, I attribute the inaccurate nature of the experiment to lack of constant and accurate initial conditions as the cause of the chaos - thus the non-predictability of the system resulted from different initial conditions. We could conclude that the universe (or weather patterns) is random if We could ensure infinite accuracy in the model. Our model remains flawed and thus its baseless to blame the unpredictability on the universe.

Next Example
Ary Goldberger of Harvard Medical School believes he has discovered not only that the rhythm of the human heart is chaotic, but that chaos in the heart is necessary. When he compared the variations in the heartbeats of a healthy person to those of one suffering from heart disease, the healthy heartbeat was actually the more chaotic.
To expound:
I quote
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The normal heart rate time series is fractal-like and seems to display the fractal property of self-similarity over different time scales without a characteristic time scale. The power spectra of heart rate time series have been shown to concur with 1/f behaviour, which is essential for fractal-like behaviour and also characteristic of chaotic behaviour. Normal heart rate time series have been shown to demonstrate a “strangelike” attractor, which is characteristic of chaotic as opposed to random or periodic signals. Based on this Ary Goldberger has concluded that “the most compelling clinical example of cardiac chaos is paradoxically found in the dynamics of the normal sinus rhythm”. These chaotic, fractal and nonlinear qualities of heartbeat behaviour have inspired investigators to develop new analysing methods of heart rate behaviour (Mandelbrot 1982, Goldberger 1996, Goldberger & West 1987, Yamamoto et al. 1995).
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Even in this example, heart rate can be attributed to many factors:
1. Health status of a subject
2. Mental status (excited, calm, stressed etc)
3. Biochemical status ( adrenaline, sex hormones (eg when aroused) other hormones etc )
4. Lung status (breathing rhythm, respiratory problems etc)
5. Weather conditions like temperature (which affect metabolic rate hence heartbeat)

I am not a doctor but I believe it would be naive to expect these factors (and the ones I have not included) to be constant or to vary proportionately. It is logical for there to be more activity (hence chaotic rate) in a healthy individuals heart than in a sick individual because the healthy heart is able to respond to all "messages" from the diferent parts of the body compared to a "sick" heart.
So I hold that the heart is not displaying an irregular heartbeat. Its the other "factors" that are not regular.

The backbone of "chaos theory" is marked by the way that predictive errors evolve with time (like in a swinging pendulum) newtons laws can be adequately used to predict outcome.

In a chaotic system, a small starting difference between two identical systems will rapidly grow. In fact, the hallmark of chaos is that the motions diverge exponentially fast. Translated into a prediction problem, this means that any input error multiplies itself at an escalating rate as a function of prediction time, so that before long it engulfs the calculation, and all predictive power is lost. Small input errors thus swell to calculation-wrecking size in very short order.

My contention is that first the word "chaotic" reflects the anthropocentric nature of the researches: I find it extreme and inaccurate in describing systems that magnify initial errors.

Two, I believe it would only be logical to call the systems "chaotic" if even with the same initial conditions and control factors, radically different outcomes were observed.

Without that, I believe our instruments and approach are still too flawed to capture some workings of our universe. Hence we need to refine them.

Three, even if those few experiments were correct in saying those systems were chaotic, What about the solar system - the way planets revolve on their axis, the way the earth rotates on its axis, the way the earth wobbles without spinning out of control - is that the nature of chaos - cell division and growth - is it chaotic?

Is it practical to project our incapacity to detect a pattern in the workings of out universe as a sign of chaos? Shouldnt we rather doubt our abilities and focus on improving them?

Does the amount of "chaos" outsize the amount of order observable in the universe? Isnt the idea that the universe is chaotic antithetical to science and empiricism?

And finally, if the universe is chaotic, does that mean we are operating under blind chance?
If that is truly so, what are the implications?

[ April 26, 2002: Message edited by: IntenSity ]</p>

moon

The short answer is no.

The longer answer is no, but...

There is a distinction between chaos and "blind chance." Chaos does not mean an abrogation of the law of cause and effect. It just means that slight differences in initial conditions can mean enormous differences in the condition at a later time. A classical example is that of mixing red and white paint. If you take an equal amount of red and white paint, and put it into a pail, and mix it up, you end up with, eventually, a pail of pink paint. If you look at an initial point, it is either red or white, and if you follow it in time, it follows strict rules of causality, and ends up at some determined point later on. But, if you look at a point arbitrarily close to it, it may end up at a distance from its neighboring initial point that is on the scale of the pail itself. The system is chaotic, in that you cannot predict where a point will end up, if you only specify that it starts in a little blob. But, you can predict the final global state--it is pink.

Chaos is distinct from indeterminacy. In an indeterminate system, you cannot determine what the final outcome of a point will be under the evolution. Quantum mechanics is an indeterminate theory, in that you can only specify probabilities of outcome, strict causality does not apply. This does not mean "blind chance," however, just that matter obeys probabilistic laws, as opposed to laws of strict causality.

phaedrus

Would the pinball machine qualify for being chaotic system ???

The ball's movements are precisely governed by laws of gravitational rolling and elastic collisions—both fully understood—yet the final outcome is unpredictable.

Lorenz and his butterfly

[ April 26, 2002: Message edited by: phaedrus ]</p>

Ender

short answer: Mistaking austere models of mathematics (science) with reality is why common sense tells us there is order in the universe.

Long answer to come!

~WiGGiN~

boneyard bill

Intensity writes:

But how do we know that the radically different outcomes are due to tiny differences in initial conditions? The differences in initial conditions are so tiny that they are immeasurable. If they were measurable then, presumably, they outcomes could be mathematically modeled and predicted. But if the initial conditions are immeasurable, how do we know that any differences exist at all? Are we imposing a scientific model on the world? Isn't chaos theory just an unsubstantiated assumption?

Secondly, is it possible for initial conditions ever to be identical? If the earth is rotating on its axis and revolving around the sun which is revolving around the glaxay, etc. and everything is in constant motion; then how is it possible to say that absolutely identical initial conditions can ever obtain? And is it not reasonable to assume that at some point this constant motion and constant change in space will have an influence on earth?

In other words, can we ever get away from chaos even in terms of your definition? The most you can say is that it is theoretically possible that initial conditions will produce the same result and that it is unlikely than planetary and stellar motion are relevant to the initial earthly conditions. You can make those claims. But is there any reason why we should believe them?

At what point should we say that scientific and mathematical models have reached the limit of their usefulness and (gasp!) can't explain everything?

boneyard bill

Intensity writes:

This is only a problem if one assumes a materialist (or its currently deceptive substitute-"naturalist") view of the universe. The current opinion (totally unsubstantiated in my view) is that for the world to be explained "scientifically" it must be explained without reference to mental language such as "mind," "intelligence," "purpose," or "will."

At the biological level this is quite impossible. Researchers cannot even describe the behavior of genes without using mental language.

So if God changes his mind, is it an example of chaos? It has to be if God is not part of your explanatory vocabulary. The point is that there is a huge difference between reality and a necessarily language-based description of reality.

Our description of the world will always be constrained by the limits of our language, but modern scientific dogmatism refuses even to acknowledge the need for all of the language tools that are currently available.

owleye

I tend to agree with moon in his distinction between indeterminacy and chaos, however, I don't make much of this. If initial conditions are effectively hidden from us, we will select probabilistic models of outcomes. It is how the world is presented to us that matters, not how the world is in itself. The reason that particle physicists search for deterministic models is because there are anomolies of one sort or another in the patterns of data as compared to existing models, especially as our instruments get more precise, and these anomolies need to be explained. We just can't let it be that chance explains anomolies.

BTW, despite that the weather is difficult to predict, and even if it is true that chaos plays a significant role in it, I think there is an expectation that increasingly better weather models will be developed that provide advance notice of weather systems with more pinpoint accuracy. It science fails in this endeavor (and living here in the Seattle area, I'd say science is doing poorly by us), and I know they've been at it for at least 65 years, with the last 50-60 through the use of computer models, I suspect it will not fare well for science generally. But I could be wrong.

owleye

boneyard bill

owleye writes:

Really? So what is important is that we maintain faith in our theories, not whether or not the theories are right.

Ender

Thank you for creating this thread, Intensity. As promised, here is the long answer- i hope to flex my meandering thoughts on chaos, as well as what the great thinkers have said on this matter.

What follows is an interpretation of existence, and a philosophical one, at that- not fact. Instead of arguing for facts, I mean to show that chaos is not what the world really is before it is conceptualized by us- but as an atheological and antiessentialist interpretation. It is not a matter of separating the real from the perceptible, but identifying the alternate ways of constructing perceptible worlds. By denying metaphysical realism, I am arguing that there is no fact of the matter that could be ascertained by an accurate understanding of the universe in itself but only a bunch of rival interpretations.

As a "speaker for the death of God" I aim to abolish all "shadows of God" such as "efficient causes" in theology (God as causa prima) formal causes (the world-as-organism/cycle/machine/melody/law-abiding), final causes (equilibrium, progress, happiness), or material causes (materialistic atomism, pantheism). Any attempt to inhere the world with the mentioned causes is always a means of escaping one's perspective, and step outside in order to see the natural, internal features as representations of some grander plan. There is no such position that enables any possible judging, measuring comparing or sentencing the entire universe, because that is a superfluous perspective that lies outside of life and nature, one that is not afforded to living creatures such as ourselves.

A neo-Kantian could argue that knowledge is an imposition upon "chaos" that applies regularities and forms according to our practical nature. I am exploring whether this is a viable merging of Nietzschean epistemology with the positive programme of Kant- that the world we know- our experience- is built upon another, unknowable, primary, pre-given world of becoming or chaos. There is a common epistemological strain in Kant, Nietzsche and F. A. Lange- their ontologies are eerily similar: if the phenomenal world (whatever world exists for a particular perspective) is a "mediated" world, a world of representations," or "appearances" by inference there should be some "real" "unmediated" or "original" world that these perspectives distort, filter, or represent. Kant said that this is the noumenal world where the things in themselves is apprehended by the sensuous intuition and deciphered by the categories of the understanding in order to be knowable. Lange said that this was the "original" world, an "evanescent stream" of "unknowable becoming" a "presumed chaotic 'manifold' of sensory impressions." A host of Nietzschean commentators have argued that he maintained the view that the world in itself is a "becoming" "chaos" a world devoid of definition or organization. The parameters of our perspective imposes order upon this irrational " becoming" and contributes to our chances for survival.

However, there is prima facie evidence against such a Kantian reading of Nietzsche, with his constant criticism of the "thing-in-itself." In the book Gay Science, a proper reading of the passages 322 and 109 lends substance to the notion that Nietzsche means "chaos" not as an absolute lack of order, but as a "set of irregular" or "contradictory movements." The chaotic universe is not one that moves teleologically, but errantly- no simple linear or cyclical path but a "labyrinthine" one. Chaos also includes a perspectival or interpretive multiplicity. Gilles Deleuze reads Nietzsche as a "posttheological Leibniz." If God exists, he by definition guaranteed a single world-trajectory, and a world-interpretation. With the death of God, a series of "irregular" and "contradictory" movements are grounds for "interpretive multiplicity." Leibniz' God creates an infinite number of divergent and incongruent worlds only to actualize "the best." Nietzsche atheological perspectivism, as well as "becoming" deny the existence of a privileged worldview and affirm the coexistence of irreducible worldviews. Deleuze defines Nietzsche's chaos as the "complication of these divergent worlds and worldviews in their coexistence within the same world." A better word Deleuze coins- chaosmos.


As opposed to the naïve anthropomorphisms of the physicists' conception of nature's conformity to law, I advocate a picture of the universe as indifferent, tyrannical, and inconsiderate, lacking in laws or aims. There is no order and a fortiori no moral order in the universe. There are only points of origin for perspectives, which are occupied by active wills that seek to organize the world from its own perspective, and each are locked in combat with one another.

The ontological structure of the Heraclitean "flux" is a world of becoming" or "chaos." Frozen concepts like "Being" are grounds for order, whereas a dynamic term as in "becoming" translates to "chaos." I conclude a conception of the world itself as "becoming or "chaos" or a dynamic force- a fluid, impermanent and undifferentiated Urwelt where the categories of knowledge [as in identity, substance, or causality] no longer apply.

I leave you with a nice byline on Heraclitus:
"Heraclitus will always be right in this, that being is an empty fiction."
~WiGGiN~

Vorkosigan

This is only a problem if one assumes a materialist (or its currently deceptive substitute-"naturalist") view of the universe.

BB, a world without god is only a problem for theists. Metaphysical naturalists find it a meaningful, interesting and beautiful place.

The current opinion (totally unsubstantiated in my view) is that for the world to be explained "scientifically" it must be explained without reference to mental language such as "mind," "intelligence," "purpose," or "will."

What do you mean by this? The current view in science is methodological naturalism; one cannot invoke the supernatural to explain events in the world.

Vorkosigan