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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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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Woodstock and Superconductivity

Physicist lowers body temperature to achieve a superconducting state.

I came upon a child of god
He was walking along the road
And I asked him, where are you going
And this he told me
I'm going on down to Yasgur's farm
- Joni Mitchell

I never made it to Yasgur's farm - I was just too young in 1969 to head to New York to catch all of the acts that I loved. Later that summer I did make it to the Atlantic City Pop Festival , which was a much-sanitized version. No rain, no mud slides, no babies born...and there was certainly no one making movies or disclaiming about the AC Pop Festival Generation.

Many years later I finally made amends for my serious cultural lapse in '69 and attended the next Woodstock - the Woodstock of Physics. This 1987 event was a wild affair as the news of high-temperature superconductivity was just breaking, along with promises of a Jetson-like future soon to be commonplace. There were thousands at the session in NYC, with most (including this author) watching the presentations via monitors in the corridors, straining to hear every word, to make out every blurred overhead with a hastily sketched graph, waiting to hear what would be the next latest (and higher) superconducting temperature...

We are stardust
We are golden
And we've got to get ourselves
Back to the garden

A surprising fact about HTSC is that discovers  Karl Müller and Johannes Bednorz received the Nobel Prize that same year -an amazingly short time for the Nobel committee to name an award winner. (They had first noticed the effect only a year earlier.) Typically it is many years between discovery and award, with other experimenters and theorists demonstrating that the original discovery was both true, and truly significant for physics. More amazing, there was no consensus on why HTSC occurs.

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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.

Modeling Pandemic Strategies

Spanish Flu in SpokaneModeling how a disease progresses in a pandemic, and the related modeling of the effects of different strategies on stopping the pandemic, are, next to perhaps nuclear attack modeling, some of the most sensitive mathematics being done today.

Consider the difficulties of determining pandemic-containment strategies by looking to past pandemics.

Efforts of several cities to halt the spread of the 1918 Spanish flu have now been analyzed and modeled by several research teams. One technique that appears promising is "social distancing" - referred to a s a non-pharmaceutical intervention (NPI) - a fairly obvious strategy of reducing the potential contact between members of the community by closing schools, churches, stores, etc.

I wrote "fairly obvious" - but is it? There are so many contingencies that affected each city that it is hard to draw conclusions. Consider the report of the studies as described by Maryn McKenna of the Center for Infectious Disease Research & Policy at U. Minnesota

But while NPIs make intuitive sense, actual evidence for their ability to block or slow flu transmission has been limited. An Institute of Medicine report released last December concluded that the measures might help in a pandemic but should not be oversold.

"It is almost impossible to say that any of the community interventions have been proven ineffective," the report said. "However, it is also almost impossible to say that the interventions, either individually or in combination, will be effective in mitigating an influenza pandemic."

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How to read a REAL Climate Modeling article

Diagram of General Circulatin ModelBolstered by the anti-climate-modeling stance of Michael Crichton, there are many out there who claim that climate modeling that predicts global warming is somehow "bad science." I'm not sure many of these folks have ever read a real climate modeling paper (or any who believe that climate change is occurring, for that matter)

It is instructive to try to wade through a serious paper that points out the difficulties of modeling on the one hand, but also presents very confident predictions of the model described in the paper..

By chance I recently came across a paper written almost 2 years ago by Jian Yuan, Qiang Fu (Department of Atmospheric Sciences, University of Washington) and Norman McFarlane (Canadian Centre for Climate Modeling and Analysis, Victoria, British Columbia). The name of the article is forbidding: Tests and improvements of GCM cloud parameterizations using the CCCMA SCM with the SHEBA data set.

(Note: GCM is General Circulation Model, or Global Climate Model - the bellwether of climate modeling)

The article describes the wide variability of different models of the Arctic, and how the authors re-formulated cloud interactions, yielding a model whose output is much closer to actual recorded data.

For the uninitiated, trying to read this type of paper seems impossible. You can get a lot from it, though, by reading the abstract, intro, and conclusion. (This is something I do in the Chaos and Fractals course - i.e. have students read and dense papers in areas outside of their majors - an essential activity for all scientists).

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Improve Your Home Run Chances - Walk Softly But Swing a Small Stick

From Baseball Physics: Anatomy of a Home Run by Davin Coburn in the June 2007 issue of Popular Mechanics, comes some interesting data/trends on home runs. Some of these are contrary to baseball-lifers' opinions, but I assume that some players will take heed of the predictions. After all, one thing not in the article because it is obvious is the direct relation between salary and home-run prowess.

Check out the article for some interesting graphs that illustrate the following findings:

• The sweet spot is larger than previously thought
• Batted Ball Speed (BBS) is more of a determining factor in home runs. This leads to a prediction that increasing the swing speed is better than increasing the bat weight. A corollary to this is that lighter bats (31-32 oz) are ideal bats for pro players.
• Because of the direction of spin when they reach the plate, curve balls can be hit farther than fast balls, even though fast balls leave the bat traveling faster.

Other interesting facts that can be derived in an introductory physics class is that the average pro swing imparts 4145 pounds of force to the ball, and the farthest a ball can be hit (with no wind to help it, and no rarefied air such as in Colorado) is approx 475 ft.

Although no physicist is quoted by name in the article, I believe that some, if not all, of the topics discussed come from Alan Nathan's Physics of Baseball work, described in my earlier post on Willie Mays and Global Warming.

Solar Cycle 24 Predictions

Cycle 23-24 sun-spot predictions. Click to enlargeIn a post last year titled Solar Activity Modeling: Great Predictions, Lousy Understanding? I described the current state of solar cycle modeling. Solar storm cycles are approximately 11 years in length.

We are now entering Cycle 24, which will start in March 2008, and reach a peak in 2015. The prediction from the NOAA (National Oceanic And Atmospheric Administration) is that "the Earth will soon experience a period of intense solar storms and the exact number of solar storms expected will become clearer in time."

Read the NOAA release of these findings here.  This is an excellent article that describes how sunspots form, the nature of the 11-year cycles, and how the predictions are made. Sun spot activity can be extremely deleterious to transportation and communication infrastructure, and therefore predictions have to be accurate. The care with which the predictions are made is evident in the statement by solar-physicist Doug Biesecker:

“...there are approximately six techniques used to predict the intensity of a solar cycle,” said Biesecker. “The first three are based on statistics and provide a sound historical baseline upon which to forecast future cycles. The other three are based on physics and the sun’s dynamo conveyer belt theory.”

An overview of these techniques can be found in last year's post.

There's Danger in Them Thar Equations

A very interesting piece by Howard Wainer in the latest American Scientist (May-June 2007) concerns dangerous equations, which he describes as falling into two classes:

• equations that are dangerous because we know them - they "may pose danger because the secrets within its bounds open doors behind which lies terrible peril," with E=mc² the most obvious candidate
• equations that are dangerous because we don't know them - mot because there is no theory that has yet yielded these equations, but rather because they are not known by those who need to know them. This is especially true for policy makers that base their decision on mathematical models, and specifically statistical models.

Wainer's top choice for most dangerous statistical equation is due to Abraham de Moivre, who showed in 1730 that the standard error of the mean of a sample is the standard error of the mean of the population divided by the square root of the sample size. A significant prediction of this equation is that small sample sizes lead to large fluctuations in sample means. It is this simple statement:

small samples → large fluctuations in sample means,

that provides the biggest danger when not used, or not understood, by both policy makers and the average citizen.

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Killing the Mud Softly With...

...concrete balls. Big ones.

The mud volcano in Porong, Indonesia, has now been spewing its thick ooze for almost a year  (since May 29, 2006). The stats on how much mud is flowing is scary.  Reports claim that mud flows of up to 126,000 cubic meters (that's 164,801 cubic yards) a day are being recorded.

This is a lot of mud. To put this number into some perspective, it would fill up a 13-story office building with a footprint of 50x50 yards.

Each day.

And there's no sign that the volcano will be stopping anytime soon, if ever. Given the estimated size of the mud source below the volcano and current flow rates, this mud pie could be emptying out for 10's, if not 100's of years!

With nothing traditional working so far (e.g. walls or berms), a radical plan to stop the mud is now underway - thanks to some interesting modeling. The plan, designed by geophysicists, consists of dropping giant concrete balls (weighing up to 250 lbs), linked together on a chain, with four to a chain, into the mouth of the volcano (the largest balls are 16" in diameter). The idea is to "is to make the channel smaller ...narrowing it enough to slow the mud's rise and so decrease its flow rate by up to three-quarters. Forced to go around the chains and balls, the mud will give up some of its energy to friction, vibration and rotation."

The net result is beautifully described: "It will make the mud tired. We're killing the mud softly."

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