Chaos and Compatibilism

Chaos Theory is often cited as a way out of the determinsim-free will paradox. The explanation usually goes like this: OK, everything is determined by physical law, but the laws themselves are non-linear and the output of a particular equation that codifies a law often leads to a pseudo-random process and/or sensitive dependence on initial conditions. Ergo while we are governed by strict physical laws, our behavior - and by implication our decisions - do not give the appearance of being constrained in any way.

The philosophical position that free will can co-exist with determinism pre-dates chaos theory, with Hume and Hobbes early proponents. Known as compatibilism, it stands on its own without chaos theory. Much of the compatibilist argument rests on a careful definition of what it means to act freely, leading to a so-called category error.

The compatibilist definition of free will states that free will is not the ability to choose as an agent independent of prior cause, but as an agent who is not forced to make a certain choice. Determinists argue that all acts that take place are predetermined by prior causes. Because human decision is an act that is not exempt from prior cause, by this definition, some determinists known as hard determinists believe that free will thus becomes an illusion.

A compatibilist, or soft determinist, in contrast, will define a free act in a way that does not hinge on causal necessitation. For them, an act is free unless it involves compulsion by another person. Since the physical universe and the laws of nature are not persons, they argue that it is a category error to speak of our actions being forced on us by the laws of nature, and therefore it is wrong to conclude that universal determinism would mean we are never free.

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Turbulence in Space

Turbulence in SpaceTrying to model and understand turbulence is one of the main thrusts of chaos theory. So it may be a good thing or bad, depending on where you are chaotically, that more turbulence has been found - this time in deep space.

As reported in APS Physics News for 2006:

If you think chaos is complicated in the case of simple objects (such as our inability to predict the long-term velocities and positions of planets owing to their nonlinear interactions with the sun and other planets) it's far worse for systems with essentially an infinite number of degrees of freedom such as fluids or plasmas under the stress of nonlinear forces. Then the word turbulence is fully justified. Turbulence can be studied on Earth easily by mapping such things as the density or velocity of fluids in a tank. In space, however, where we expect turbulence to occur in such settings as solar wind, interstellar space, and the accretion disks around black holes, it's not so easy to measure fluids in time and space. Now, a suite of four plasma-watching satellites, referred to as Cluster, has provided the first definitive study of turbulence in space. The fluid in question is the wind of particles streaming toward the Earth from the sun, while the location in question is the region just upstream of Earth's bow shock, the place where the solar wind gets disturbed and passes by the Earth's magnetosphere. The waves in the shock-upstream plasma, pushed around by complex magnetic fields, are observed to behave a lot like fluid turbulence on Earth. One of the Cluster researchers, Yasuhito Narita (y.narita@tu-bs.de) of the Institute of Geophysics and Extraterrestrial Physics in Braunschweig, Germany, says that the data is primarily in accord with the leading theory of fluid turbulence, the so called Kolmogorov's model of turbulence. (Narita et al., Physical Review Letters, 10 November)

Kolmogorov is one of the famous trio Kolmogorov - Arnold - Moser. after whom the KAM theorem is named. Ironically, the KAM theorem shows the existence of quasi-periodic orbits in a chaotic solar system. The idea of stability within turbulence is an archetypal chaos construct.

Poker, Popper, and Wittgenstein - This Ain't No Love Story

It's hard to imagine a time when big-time philosophers roamed the earth as true public figures, in search of weighty issues, faculty positions, and total intellectual superiority over fellow philosophers who dared to argue with them.

Such was the time in the first half of the 20th Century, with one of the main battlegrounds the post-war scene at Cambridge University, home base of Bertrand Russel, GE Moore, and of course Ludwig Wittgenstein - the iconoclastic bad boy of philosophy, cult figure, and master of cryptic utterances who had a devastating penchant for eviscerating the work of philosophers he disagreed with - which was most other philosophers without the initials LW.

The scene was the Moral Science Society, which was was holding their monthly meeting on October 25, 1946. Karl Popper - at that time just starting a position at the London School of Economics, was already causing a stir with his The Logic of Scientific Discovery - was in town presenting a talk titled Are There Philosophical Problems?

The head of the MSD was none other than Ludwig W. Wittgenstein, scion of one of the wealthiest families in pre-war Austria, who had renounced all his wealth to live an ascetic life of the mind, spirit, and body that is so improbably eccentric that he and his ideas are recurring figures and themes in many fictional stories that need a touch of the bizarre (e.g. The World As I Found It, by Bruce Duffy, A Philosophical Investigation by Philip Kerr, Wittgensteins' Mistress by David Markson).

Apparently Popper was no no shrinking violet either : a truly fesity, take-no-philosophical-prisoner scold according to many contemporaries.

Back to the dom's room at Cambridge. You get the picture: smoky, with drab walls, scuffed, darkened oak chairs and table, leaded glass separators on the casement windows, bottles of port, an old fireplace with soot-covered bricks inside, and... a fireplace poker soon to be infamous for the briefest of philosophical battles. What happened in that room is the stuff of philosophical lore - 10-minute argument that flashed between Wittgenstein and Popper that is still recounted and debated today.

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Thomas Kuhn in High Def - Paradigm Shifts, Blu-Rays, and the NFL

Until I read James Gleick's Chaos: The Making of a New Science in 1987, I had only a passing knowledge of  paradigm shifts, one of the defining features of science described by Thomas Kuhn in his Structures of Scientific Revolution. Gleick used the paradigm shift idea to describe the break with the overly linear science brought on by the new discoveries of Chaos Theory - a usage of the paradigm shift concept that seems to adhere to Kuhn's definition.

A concise summary of  Kuhn's ideas can be found in Lawrence van Gelder's June 19, 1996 NYTimes obit:

His thesis was that science was not a steady, cumulative acquisition of knowledge. Instead, he wrote, it is "a series of peaceful interludes punctuated by intellectually violent revolutions." And in those revolutions, he wrote, "one conceptual world view is replaced by another."

Thus, Einstein's theory of relativity could challenge Newton's concepts of physics. Lavoisier's discovery of oxygen could sweep away earlier ideas about phlogiston, the imaginary element believed to cause combustion. Galileo's supposed experiments with wood and lead balls dropped from the Leaning Tower of Pisa could banish the Aristotelian theory that bodies fell at a speed proportional to their weight. And Darwin's theory of natural selection could overthrow theories of a world governed by design.

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No Prediction, No Soup For You...

There has been an intermittent dialogue taking place in response to my previous post on The Economic Modeling of Religion, in which Bob Ekelund, one of the authors of The Marketplace of Christianity and a professor of Economics of Auburn U responded to misgivings about the applicability of the economic model. Recently David George - a colleague at La Salle known for his work in meta-preferences (see his Preference Pollution: How Markets Create the Desires we Dislike) has added a provocative comment to the mix.

So I am starting a new thread here with a top-level post for two reasons: to make sure that newer viewers are award of the dialogue, and particularly Bob Ekelund's responses and defense of the economic model of religion, and to answer David George's point concerning understanding and prediction, which will give me more of chance to discuss this continuum.

An excerpt from D. George's response:

Second, I must disagree with both of you that, to quote Bob Ekelund, "any model must have predictive power." As you, Rich, appear to point out in an earlier entry, "understanding" is also of great importance. Work that I have done tends to focus on exactly such understand[sic] without claiming to be able to predict. The late Milton Friedman brought economics to its present sorry methodological state by asserting in an early 1950s article that "assumptions don't matter." I have seen first-hand the mischief that this can cause. Beginning, I believe, with Thaler and Sheffrin around 1980, attempts to explain internal conflict have begun with the assumption of "two-selves" (or "multiple-selves") residing within each individual. If pressed, advocates of these models will probably stress that person isn’t really “two-selves” but simply behaves "as if" he is. As I have argued extensively, this does little to further our understanding of internal conflict. To tell someone trying to understand her internal conflict that she has more than one self begs the question, to put it mildly. To explain that the

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M.C. Escher: Chaos and Order and Back Again

Order and Chaos. Click to enlarge.

In an earlier post I commented on the ability of M.C. Escher to capture the infinity of time and space in his woodcuts, drawings, and lithographs.

Another common thread in many of Escher's works is the sense of order arising out of chaos - or is it chaos out of order? A master of graphic puns that simultaneously emphasize and blur the demarcation between figure and ground, Escher does seem to lean more in the direction of order out of chaos. In The Magic of M.C. Escher , a fabulous compendium of Escher's works that includes unpublished sketches from his workbooks and excerpts from his correspondence with family and colleagues, this direction is clear:

The consistency of the phenomena around us, order, regularity, cyclical repetitions and renewals, have started to speak to me more and more strongly all the time. The awareness of their presence brings me repose and gives me support. In my pictures I try to bear witness that we are living in a beautiful, ordered world, and not in a chaos without standards, as it sometimes seems.

For a very good intro to a broad selection of Escher's most famous works, visit the M.C. Escher - Life and Work on-line tour at the National Gallery of Art. From the program notes for the Order and Chaos lithograph pictured in this post:

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Coping with Chaotic Climate Models

Model prediction of Arctic sea ice loss - 2000 (L) vs. 2040 (R). From BBC news. Click to Enlarge.Now that the IPCC has released the summary of it's upcoming study report Climate Change 2007: The Physical Science Basis , strongly stating that global warming is man-made, it is still important for scientists to clearly enumerate any issues surrounding the accuracy and reliability of their models.

Because if they don't, global warming deniers, or those who believe that we need still more time for convincing proof will focus on the slightest inaccuracy in a model's prediction in classic red herring fashion. (In a way similar to anti-evolutionists, they will neglect the hundreds of accurate predictions and claim that the one that doesn't quite fit calls for total abandonment of a theory.)

Climate models are by their very nature prone to chaotic behavior. This behavior must be accounted for when using climate models for any type of prediction.  An excellent article on how chaotic models are handled has been provided recently by Cecilia Bitz of the Univ. of Washington. In her Real Climate article Arctic Sea Ice decline in the 21st Century, Bitz describes work she did with colleagues Marika Holland and Bruno Tremblay, which culminated in a paper for the Dec. 2006 Geophysical Research Letters. I want to focus on two aspects of Bitz's commentary: the presence of chaos in the climate models, and the overall accuracy of the modeling process. Bitz recounts:

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Prediction, Fiction, and Science Policy: The Jurassic Park Syndrome

Michael Crichton needs to visit an ER for an arrogancectomy...

It's amazing to me how global warming is now accepted as fact, when not too long ago it was still being described as possibly a climate condition that appears, and has appeared, from time to time in the course of the lifespan of the earth.  There now seems to be an article every week in the major press about the latest discoveries confirming a warming trend that does not appear to be part of some grand cycle through earth's history.  This has led several countries and continents  to proclaim global warming to be the BIGGEST threat to humanity in the not-so-long term, enacting legislation and controls that will stem the tide of further warming.  

The U.S. is not one of them, of course.  Hopefully, this sad state of affairs will begin to change with the  new makeup of Congress.   If so, it will be those who aren't fans of Michael Crichton that may make the difference.

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A chaotic test for Parkinson's

Originally Posted by Matt Venanzi

In an article from New Scientist - 11 April 2006

CHAOS theory could help monitor the effectiveness of treatment for Parkinson's disease and aid in earlier diagnosis, according to physicists who have developed a method to monitor how much sufferers tremor.

There is still no definitive test to identify Parkinson's disease in its onset. Now Renat Yulmetyev at Kazan State University in Russia and colleagues have adapted a statistical technique based on chaos theory, and used to study earthquake vibrations, to monitor the distinctive progression of symptoms such as tremors.

Sixteen people in Canada who had Parkinson's disease held their index fingers in the path of a laser beam for measurements of tremor frequency in their fingers and the team analysed the results. In patients in the early stages of the disease, the tremor pattern is more chaotic, says Yulmetyev. As the disease takes hold, the tremors not only become more pronounced, but they become much more periodic and regular. Medication with the drug L-dopa causes the tremor patterns to become more chaotic again (Physica A, DOI: 10.1016/j.physa.2006.01.077).

Click here for the full 20-page PDF of the report.
(Physica A, DOI: 10.1016/j.physa.2006.01.077)

For more information on Parkinson's disease, click here.

Update to Reflections of Chaos

Originally Posted by Jeremiah Noll

Click on image to enlarge

At the beginning of this course I was much more certain of things! I have learned quite a bit, but with this learning came new mysteries. Studying chaos has expanded my mind and taught me things I never would have dreamed. When you sit and think about the concept and the principles which founded chaos it just makes sense. Butterflies can start El Niño's and the stock market is predictable to a small degree. But sensitive dependence on initial conditions is not the only principle of chaos, there is also the fact that extremely simple rules can produce infinitely complex results. Who would have thought a couple lines of computer code could produce the Serpinsky Triangle or model the population growth of a small nation. But the coolest things I have ever seen are fractals. Through this course I have developed a great understanding of the image, mapping, and product of fractal code. Simple functions and an imaginary plane can model infinity in the most accurate and beautiful way. I enjoyed fractals so much I decided to make them my semester project. The value of this course is a tremendous amount of insight into how the world works and how things thought to be random can really be very simple. I feel as if I have been shown a piece of how God put this universe together and how he made it so complex in only six days. Like deciphering the human genome code chaos makes us more able to predict, heal, and understand the way things work and why events happen.

I still use fractal software today and it is still interesting and novel even though I have been exposed to it for some time. I still have my own fractals on my website so that I can, hopefully, get others interested in math and science too. My friends never thought Math could be so intriguing. Since the Fall semester I have progressed in the ability to create lifelike landscapes from fractal software.