a non-linear space for students of chaos and fractals....


Modeling Acts of God, Part 2 - Earthquakes

parkfield.jpgThis is #2 in a series. (Click here for #1 on modeling hurricanes)

Earthquake modeling seems to generate a wide range of emotions, vitriol, successes, and failures - so wide as to need a logarithmic scale, a la Richter.

The Parkfield Earthquake Experiment, now running for over 22 years, has been the development test bed and experimental "lab" for US Geological Survey/State of California efforts to develop  physical models of earthquakes that will lead to viable predictions. The USGS site contains a wealth of information on the experiment, and good background on the history of earthquake prediction, which is still highly hit or miss. An interesting excerpt from the site neatly illuminates the need for prediction based on an understanding of physical causes as opposed to one based on statistical correlation only:

Early scientific efforts toward earthquake prediction in the U.S. were directed primarily toward the measurement of physical parameters in areas where earthquakes occur, including seismicity, crustal structure, heat flow, geomagnetism, electrical potential and conductivity, gas chemistry. Central to these efforts was the concept that a precursor might be observed in one or more of these measurements. However, the connection between a commonly accepted precursor and the earthquake was often speculative and uncertain. A coherent physical model was lacking.

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Constructal Theory of Everything?

air_routes.jpgA very interesting text that describes what appears to be a bold new approach to modeling many possible systems - even human ones - is about to be released. Titled Constructal Theory of Social Dynamics and  edited by Adrian Bejan and Gilbert W. Merkx, the text "brings together for the first time social scientists and engineers to develop a predictive theory of social organization, as a conglomerate of mating flows that morph in time to flow more easily (people, goods, money, energy, information). These flows have objectives (e.g., minimization of effort, travel time, cost), and the objectives clash with global constraints (space, time, resources). The result is organization (flow architecture) derived from one principle of configuration evolution in time (the constructal law): "for a flow system to persist in time, its configuration must morph such that it provides easier access to its streams."

Begin and Merkx are from Duke. The Duke press release  is very enticing - this is certainly a text that will serve as a reference for the chaos and fractals course, or perhaps a primary source.

Some tantalizing tidbits:

Why does a railway network look like a river? Why do the streets of old Rome look like a leaf? Because whether their shape is determined by the interactions of molecules or the choices made by individual humans, all of these systems of flow are governed by a relatively simple new principle of thermodynamics.

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In Search of the Fastest Rubik's Quark in the World

Magnetic/Acrylic Rubik by NTronics
There's a great scene in the Pursuit of Happyness in which Christopher, the protagonist played by Will Smith, becomes infatuated with his son's Rubik's Cube, and ultimately goes on to be a Cube Solver. In a chance encounter with a stockbroker he is trying to impress, Chris/Will solves the cube - a feat that blows away the broker, and which leads to an interview, and then...I won't go on here - rent the movie, it is a good one, and based on a true story.

Back to the Cube. Jessica Fridrich of SUNY Binghamton, who completed a Ph.D. in non-linear dynamics (Removing observational uncertainty from orbits of nonlinear dynamical systems) is something of a cube speed freak. Consider that she won the First Czechoslovak Championship in Rubik's Cube in 1982. At the top of her game she " routinely solved the cube in an average time of 17 seconds...actively using more than 100 algorithms." You'll find some of her solution techniques and algorithms here. You'll also find links to other speeders, including sage advice on how to grease your cube.

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Cosmic Legos

Escher Legos. Click to enlarge.
In his book God's Universe, Harvard astronomer Owen Gingerich attempts to reconcile intelligent-design and evolution. This seems to be an almost impossible task, so I was curious as to how Gingerich would approach this division.

Unfortunately, the reviews and descriptions I have read leave me bewildered because Gingerich's argument seem to be of an anticipated form, namely that God created the laws and then let everything develop on their own.

Gingerich does riff on the idea that the physical constants and various energy levels of appropriate atoms are so fine-tuned as to allow life - (shades of the anthropic principle!) that there is some "higher purpose." So what then is different in his argument from intelligent-design? God created the building blocks and the physical laws and just stood back and watched. This is not so different from the views of many scientists, so I'm not sure where Gingerich is headed that adds anything to the debate. Unfortunately, in the quotes I have read, he does seem to rely on an unsubstantiated claim of an underlying imperative for the existence of our universe, and, by extension, all of us:

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Bad News Polar Bears with Business Intelligence

Bad News: Walter Matthau and Bear
Modeling can't exist as an urgent, necessary, and successful activity without some agreement about the data that is used to verify the model. Monitoring the loss of Arctic sea ice is a relatively unambiguous measurement: take some pictures and measure what you see over a stretch of time, looking for a trend.

For anyone not themselves lost in the Arctic for the past year or so, the sight of polar bears hopelessly afloat on shrinking bergs is an iconic image that is a powerful image of the immediate consequences of global warming.

A natural question needs to be asked - if the arctic ice is shrinking, does that mean that each polar bear has less ice as the arctic approaches the population density of New Jersey, or does the number of polar bears decrease to match the decrease in ice?

Counting bears is much more ambiguous - and dangerous - than measuring photos of ice. What's needed is a protocol that doesn't miss any old bears, and new bears, and especially the lack of bears that brings bad news.

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Newtonian Determinism and Pathological Aloneness

Newton's Alchemical manuscript. Click to  enlarge.
Newton's Laws applied to physical situations describe a Universe that is totally deterministic. For scientist-modelers, the canonical methodology for predicting future events is based on Newton's process: stuff the initial conditions of a system into the appropriate "laws", and let time increase in the resulting equations of motion. Here's your prediction as a time series extending as far out into the future as you need. Next problem!

Chaos theory does not violate this Newtonian modeling process. Instead, chaos demonstrates that the equations of motion are so non-linear that small inaccuracies in the initial conditions lead to wildly varying future predictions - the so-called sensitive dependence on initial conditions that is the foundation of the butterfly effect. In effect prediction becomes limited in many situations, with weather one of the chief systems where predictability is desperately needed, but often leaves all of us wondering where the TV weather people ever got their degrees...So prediction is diminished, even though determinism is as strong as ever.

I was thinking about Newton's legacy of determinism as I read a piece on Newton written several years ago by James Gleick for Slate, titled Isaac Newton's Gravity. Gleick, the author of the text that brought Chaos to the masses (Chaos - The making of a new Science) is also the author of a well-received 2003 bio of Sir Isaac.

Gleick argues convincingly for the need to display Newton's achievements in the context of his rather bizarre life (of which the pathological aloneness in the title of this post is one of Gleick's signature descriptions). In this his approach reminds me very much of the recent biographies of Einstein.

Was Newton as methodical as the way physics is now presented seems to suggest? Were his life, beliefs, etc., a product of immutable beliefs and processes?

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Empirical Prayers & Logical Fallacies

hezekiahs_prayer_woodcut622x600.jpgIn Prayer: A Neurological Inquiry Skeptical Inquirer author David Haas asks "Are silent prayers transmissible to, or readable by, a supernatural being?" He then attempts to answer this question using "modern information about the brain."

Haas makes a distinction between thoughts and prayers and the underlying brain activity, stressing the non-naturalness of the prayer processes:

"The brain, an electrochemical organ, consists of matter and energy, but the mental states that are the epiphenomena of its physiological processes are neither material substances nor forms of energy ...If thoughts—including silent prayers—are not a form of energy, then there is no known natural means by which they could be transmitted beyond ourselves or read within us. "

Haas then gets to his main question - "Though thoughts and prayers are neither transmissible nor readable by any natural means, could they be known to a supernatural being?"

This is a provocative, $64,000 Question, one which cannot be answered to anyone's satisfaction, but one that leads to all sorts of meta-issues involving all-knowing and all-powerful deities.

Unfortunately, Haas trips up immediately. Here's how he wishes to answer the question of whether prayers can be known to a supernatural being:"Evidence for or against this can be obtained by determining whether prayers are followed by what was solicited by them."

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Strange Bedfellows in the Climate Change Debate

Chaos Theory by click to enlarge
An excellent web site titled The Discovery of Global Warming is provided by the Center for History of Physics of the American Institute of Physics.

Created by Spencer Weart, the Director of the Center, this is the best site I have seen on climate modeling and climate change by far. Fully hypertextual, you'll find everything from the first mention of greenhouse gases to political ramifications and chicanery, to a very detailed description of General circulation models.

But the best is the section on Chaos in the Atmosphere , which provides an enormous amount of detail on atmospheric modeling well before Lorenz, and well beyond. From the intro: the 1950s, work with slightly more complex physical and computer models turned up hints that even quite simple systems could lurch in unexpected ways. During the 1960s, computer experts working on weather prediction realized that such surprises were common in systems with realistic feedbacks. The climate system in particular might wobble all on its own without any external push, in a "chaotic" fashion that by its very nature was unforeseeable.

Skeptics of global warming usually fixate on the idea behind the statement "the climate system in...might wobble all on its own without any external push, in a "chaotic" fashion that by its very nature was unforeseeable." They'll use this to discount any effect of carbon emissions, i.e. human-produced climate change.

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Cross-Species DNA and Accelerated Evolution

Protein molecular evolution. From M. Deem.
A recent article in the May 2007 APS News describes the use of a physics model to understand accelerations in evolution that occurred between the appearance of 1-celled organisms 3.5 billion years ago, multi-celled organisms 1 billion years ago, and everything other organism that has since appeared on earth in only the last billion years.

The modeling is by Michael Deem of Rice U. His model allows for  "cross-species genetic exchange" - in effect DNA from one species is adopted by another which then realizes an evolutionary advantage. Successful DNA adoption is called HGT - Horizontal Gene Transfer. Deem's approach is based on field-theoretic techniques. The net result: species can evolve much quicker because they contain fully-functioning "genetic modules" from another species. The implications for our own genome are startling, and it may be that a "significant portion of our DNA was donated by viruses and bacteria that infected our ancestors" over millennia.

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The Terrible Tao of Chaotic Career Moves

Myron Cope and his Terrible Towel: Pittsburgh broadcaster or Chaos Theorist?
With a field of study as rich in language and imagery as chaos and fractals, it is inevitable that whole bodies of research will develop that find the theory and results of chaos & fractals applicable in totally improbable situations. It used to be that quantum physics was the leader in this phenomena, with the Tao of Physics  by Fritjof Capra the ur-text that promised a much more balanced outlook on life informed by wave/particle duality. (And I will note that I still have my copy.) Given the history of this text, I need to introduce a new category of post, which I openly steal from all Pittsburgh friends and readers - The Terrible Tao. The T-Tao designation is given to applications of chaos and fractals - and I might as well throw in complexity - to the most unlikely social situation.

My goal here is not to criticize these efforts, because they represent attempts to find models for social behavior that are grounded in a well-established field - chaos and fractals - that just happens to yield a range of behaviors that are remarkably similar to human and institutional behavior. Actually, with many of the articles appearing in journals well outside of the natural sciences, the writing often contains a self-contained expository section on nonlinear dynamics because a general knowledge of chaos and fractal theory on the part of the journal's audience cannot be assumed. So I am glad that the ideas of chaos and fractals reach a larger audience.

With that said, I often find that the modeling is more a use of chaos and fractals as metaphor - a way to describe human situations with exotic terms such as bifurcation, or homoclinic tangle. As a result, I rarely see any predictive value in the modeling, which, as a result, leaves me no farther along in understanding the situation being modeled.

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