…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."

The geophysicists base their model on an assumed shape for the bottom of the volcano - a champagne glass. The concrete balls on chains then fill the glass in a way similar to small chains of pearls filling up a real champagne glass. Based on estimates of the size of the "champagne glass" they estimate that they’ll need approximately 1500 balls to manage the mud flow.

No one really know, of course, what will happen when these 1500 balls are dropped in the steaming opening, or whether there is even a champagne glass shape inside the volcano. (I have not seen any info on why this assumptions was made, but I imagine it comes from studying the interior configuration of dormant volcanoes.)

The process started in early 2007. There has been some report of progress: in March the flow stopped for 30 minutes. The BBC report on this stoppage does not indicate how many balls have been dropped so far. Nor does it describe the rate of flow once the mud started flowing again. (If any readers know of links with more info, please post them.) A scientist suggests a reason for the stoppage might be "that a new equilibrium between the concrete balls and the mud pressure is almost established and the mud has absorbed the energy of the balls"

If the Big Ball solution really does work, it will be an amazing feat of modeling, engineering, and chutzpah.

Anyone taking on such a massive project, with potentially dire/fatal consequences if the predictions are wrong, needs to worry about unintended consequences. Modeling, and especially engineering modeling, should never lead to an implementation without an aggressive analysis of these side effects.

So it is not surprising that some critics of the Big Ball Theory had pointed out that by slowing down the mud (which most agree will happen because the balls will clearly take up some volume and block mud flow paths), pressure will build up and the mud will simply "find" another place to go - possibly causing an eruption in some weak-walled part of the volcano. This could be why the mud started flowing again.

But, with nothing working to date and the mud still flowing, there came a time when the engineers, officials, politicians, chose an unusual option that could work - and they ran with it.

So here is a situation where a model - as unorthodox as it sounds - is serving as a way out, a savior from a calamity. It’s in this situation that the role of modeling, and modelers, really becomes apparent. Modelers are usually behind the scenes, but in Porong they have sold the idea of their model, which at first glance seems like an outlandish solution. How this happened is most likely a tale of conviction, science, desperation, charisma, and a bunch of…

… concrete balls. Big ones.

It’s been 8 months since news broke of the US population reaching the 300 million mark, only 39 years after the population reached 200 million in 1967. At the time many news reports claimed that the US growth rate was accelerating. The reason? It had taken 52 years for the US population to double from 100 to 200 million, but only 39 years to go from 200 to 300 million. Hence the accelerated growth rate.

This is totally incorrect reasoning!

Using the Rule of 70 (Growth Rate x Doubling Time ≈ 70),; a 52-year doubling time implies a growth rate of approximately 1.3%. However, the 39-year-span in going from 200 to 300 million is not a doubling time - this is only an increase of 50%. Therefore, the growth rate over the last 39 years (since 1967) is approximately 1.04%, i.e. the US growth rate has declined.

So a lot of media totally botched the message - not unusual given the rampant innumeracy (a wonderful word, and terribly debilitating problem for citizenry as described so well by John Allen Paulos in his book of the same title) in this country.

Is the growth rate still diminishing? This is probably a good bet. Population growth rates in the US dropped for most of the 20 century (see the Historical National Population Estimates for a listing of yearly grown rates form 1900-1999), starting at a value of approximately 2% in 1900. (Not surprisingly, there was a slight blip upwards post-World War II)

But there is every evidence to suggest that innumeracy, at least among the media, is staying level - and maybe growing.

I am always interested in university programs that combine science and writing. The Stevens Institute of Technology has a very unique program titled the Center for Science Writings, which was created in 2005 to "emphasize the vital importance of writing and other forms of communication to science."

With award-winning author and journalist John Horgan as Director, the CSW sponsors a number of exciting and important activities. Two of particular interest to me are a blog that "explore(s) the boundaries between science and the media", and a list of the greatest science books of the 20th century. So far there are 50 books listed, and readers are encouraged to comment and suggest other books. The CSW criteria are that the books "stand out because of their subject matter, their rhetorical style and their impact on science and the rest of culture."

The blog contains a number of interesting posts that are motivated by press reports - something that I occasionally post about here. There are also a few posts written by students, although it is not clear whether these are class assignments. I will be teaching Chaos and Fractals again in Fall 2007, and all students will soon be posting here - most likely in a separate journal on this site. The CSW blog has already given me some a source of interesting readings for my upcoming class and a possible assignment - having my students respond to some of the CSW posts.

The book list is fascinating. Along with standards that all would expect - Einsteins’ The Meaning of Relativity, Kuhn’s Structure of Scientific Revolutions, Dawkins’ Selfish Gene, Popper’s Logic of Scientific Discovery, Watson/Crick’s Double Helix, etc.. - I am really glad to see that Gleick’s Chaos made the list as well as Mandelbrot’s Fractal Geometry of Nature. Then there other books that I probably would never have come up with, but am glad that someone did: Rachel Carson’s Silent Spring, Margaret Mead’s Coming of Age in Samoa, Dianne Ackerman’s A Natural History of the Senses…even Oliver Sacks’ The Man Who Mistook His Wife for a Hat. So be sure to check out the list, and make a suggestion or two. (Don’t Panic - I see that someone has recommended Hitchiker’s Guide to the Universe!)

If there are any readers out there who know of other interesting science & writing programs, please post a comment with a link.

da Vinci catheterized? See below for details. Click to enlargeReaders interested in more of the science-art boundary should check out the review by Bettyann Holtzmann Kevles in the May 2007 Scientific American. Titled The Interplay of Art and Science,the piece is an in-depth look at two books by Martin Kemp:

Leonardo da Vinci: Experience, Experiment and Design and Seen/Unseen: Art, Science, and Intuition from Leonardo to the Hubble Telescope

(Note: Kemp is a frequent contributor to the Science in Culture column in Nature. A leading expert on da Vinci, he is professor of art history at Oxford.)

According to Kevles, a common theme in both books is how art affects imagery in science and science affects imagery in art, which leads to some very interesting and provocative ideas about digital imagery.

Two parts of the review are of particular interest. In one, Kevles describes how Kemp relates D’Arcy Wentworth Thompson’s analysis of the shape and size of living organisms spelled out in his famous work On Growth and Form to the "visual mathematics of fractals, chaos theory and machine-made images."

Continuing with the idea of the connection between visual imagery, art, science, and life, Kevles closes with some of Kemp’s concerns about the imagery produced by science (e.g. in the form of medical imaging technology) and the reality behind it. The following is an excerpt: (See Kevles’ full review for much more)

He (Kemp) questions the validity, interpretation and ultimately the use of computerized, machine-made images extracted, for example, from PET and fMRI brain scans. Suddenly he fears the technology he has been describing. "The more technological the image looks, the more it exudes ... authority," he writes, but a computer is, nonetheless, a man-made tool that "seems to promise a non-human precision." And it would be a mistake to put the tool makers in the privileged position of deciding how their tools should be used. ...Kemp offers us a way of considering how artists and scientists have intuited visual truths in the past, reminds us that the past and the present are connected, and warns us against the potential tyranny of the newest digitized images that, though often beautiful and beguiling, are still man-made and not infallible.

Woman’s Torso by Leonardo. Click to enlargeKemp is describing images that can’t be seen directly (i.e. MRI images), and so his concern is well-taken. Reality is what we see, of course, and indirect views via imagery - hand made or computed - are often the only ones available. The "authority" of an image is a function of how the image was produced, but if we don’t stop to occasionally question the technology behind the image, we may be fooled into accepting a reality that isn’t true. (Oddly, there is a connection here to my earlier post on the Fake Farm Music Machine. )

And I wonder how Kemp would react to learning that Leonardo’s name provides an acronym for a medical-imaging device known as daVinci, which stands for VIsual Navigation of Catheter Insertion. I suppose if you are going to be catheterized, this is better than a "blind" insertion, but I can’t help but be reminded of da Vinci’s own anatomical drawings, which are pretty good for 15th-century work. (The image at the top of this post is a screen shot from the interface.)

The ultimate in modeling occurs when a simulation of physical events is so real that reality pales in comparision.

Consider, for example, the case of the University of Iowa Farm Music Machine, as described in a recent e-mail making the rounds:

This incredible machine was built as a collaborative effort between the Robert M. Trammell Music Conservatory and the Sharon Wick School of Engineering at the University of Iowa. Amazingly, 97% of the machines Components came from John Deere Industries and Irrigation Equipment of Bancroft Iowa, yes farm equipment! It took the team a combined 13,029 hours of set-up, alignment, calibration, and tuning before filming this video but as you can see it was WELL worth the effort. It is now on display in the Matthew Gerhard Alumni Hall at the University and is already slated to be donated to the Smithsonian.

If you haven’t seen/heard this device, check out the video. (Note - this is a wmv file. If your media player can’t play it, try viewing the film at any one of hundreds of websites, e.g. digg)

While this is an amazing video, the Farm Music Machine is obviously not true - it is a brilliant computer animation produced by Animusic titled Pipe Dream. The e-mail describing the FMM may just be the most benign, and popular urban legend listed on Snopes.

In addition to the impossible-to-imagine precision needed to set up such a device, the giveaway is the speed with which the balls fly out of the pipes, follow a parabolic arch, and then land on the drumheads and keys. The rapidity of the notes generated by the balls hitting the keys is much faster than gravity would allow.

It is still fun to watch, though. As a piece of animation, it is brilliantly executed. The fact that it appears real enough to have become an urban legend is testament to the fact that the creators of the film are modeling the physics of the machine close enough to reality that the existence of the machine is almost believable.

Pay careful attention to the above-mentioned parabolic trajectories, or the way the balls bounce off of the mini drumheads. The motion of each of these balls is calculated by using the basic 2-D kinematics of projectile motion typically covered in the first semester of a General Physics course. If this hadn’t been done, the illusion would not have fooled anybody because of our individual experiences watching real projectiles.

It is interesting to note that, before Galileo, scientists believed that projectiles followed circular trajectories. This presents an interesting question - is it possible that 15th-century scientists would immediately see the Farm Machine as false because of their incorrect view of reality? That is, do simulations only fool those with correct views of reality?

Whatever the answer to this paradoxical situation, I am glad to be fooled - over and over. No matter how many times I watch the Fantastic Farm Machine video, I am suckered into believing that the machine does exist, and that the team did spend a "combined 13,029 hours of set-up, alignment, calibration, and tuning before filming this video."

Actually, it is possible to imagine the animators spending this much time to create the film!

For a thorough review of Animusic’s work, including audio and video quality, see DVDActive Reviews.

The need for careful analysis of all assumptions that go into a mathematical model, and a corresponding willingness to investigate the predicted output of a model vs. what is actually observed, is sine qua non for all mathematics modelers.

I mention this because I just heard of the death of Ida Hoos - someone whom I was unfamiliar with, but who published frequently on the potential problems with mathematical modeling in the social sciences.

From the 5/5/2007 NYTimes obit by Katie Hafner:

...Dr. Hoos, a sociologist, was widely recognized as an outspoken critic of systems analysis, which came to prominence after World War II. The approach used mathematical models to perform cost-benefit analyses and risk assessments on complex technologies like radar systems and military aircraft. With the concept strengthening in the 1950s and ’60s, when the use of computers to assess technology grew more popular, she wrote widely on a need to balance it with other considerations like effects on the work force. “A kind of quantomania prevails in the assessment of technologies,” Dr. Hoos wrote in 1979 in the journal Technological Forecasting and Social Change. “What cannot be counted simply doesn't count, and so we systematically ignore large and important areas of concern.” Dr. Hoos urged national decision makers to take such assessments “with a large measure of skepticism lest they lead us to regrettable, if not disastrous, conclusions.” Harold A. Linstone, emeritus professor of systems science at Portland State University and longtime editor in chief of Technological Forecasting and Social Change, said Dr. Hoos was in many ways the intellectual conscience in the field of technology assessment. “She basically pointed out that in a lot of complex social and technical systems, a reliance on these systems analysis approaches couldn’t always do the job,” Dr. Linstone said. “She would not accept the superficial answers or phony arguments.” Dr. Hoos also questioned the usefulness of systems analysis when evaluating public policy. Her 1972 book, “Systems Analysis in Public Policy: A Critique,” cast a critical eye on the prevailing methods for evaluating education, waste management and health care. “These technical-think-tank types were riding high,” and Dr. Hoos “wasn’t averse to pointing out that the king was naked,” said Louis Feldner, an engineer who worked with her on several technical committees over the years. “And she was respected for it.”

All administrations, regardless of party affiliation, use mathematical models to set their agendas, frame their policies, and govern this country. More citizens should be aware of both the extreme care that must be taken in using certain models, and the potential pitfalls of modeling if something is amiss in the assumptions that go into the model - often times this is much harder to spot than problems in analysis or computation. What’s worse is ignoring potential conflicting effects because they are not amenable to mathematization, leading to Hoos’ statement What cannot be counted simply doesn’t count, and so we systematically ignore large and important areas of concern if something is inherently "uncountable."

Certainly today, with the explosive world-wide growth of the discussion of climate models, I read much less about the social effects of climate change than I do about the raging scientific debates. These debates are usually misnamed - they not debates, really, but often self-described "facts"slung from one side to the other. Ida Hoos should be essential reading for anyone attempting to understand the human side of the modeling process, and especially for those who need to make public policy decisions based on these models.

To see whether Ida Hoos’ ideas have made their way into current think-tank modeling efforts, I recommend a for-profit group such as 12 Manage: Rigor and Relevance in Management , where you will find some cost-benefit analyses and much more

For an academic approach, see The Institute for Complex Additive Systems Analysis at New Mexico State. The institute is a "a cooperative alliance among academia, industry, and government" with a focus on understanding "the additive effects—or unintended consequences—of efficient design in interdependent systems of systems…The Institute’s research is characterized by the study of dynamical systems, control theory, mathematical physics, and economics using the tools of theoretical analysis, modeling, and simulation."

Thanks to philosopher and colleague Mike Kerlin of La Salle U. for informing be about Ida Hoos.

Whether or not baseball is still America’s Game has been debated for a long time. For some, its often-glacial pace can’t compete with the speed and physical intensity of the other major sports.

But for others the glacial pace is both comforting and a description of their rate of acceptance of the reality of climate change.

Recently, Sports Illustrated devoted a sizeable part of an issue to the effects of global warming on sports. From Golf courses to ski slopes, the article was a thorough summary of potential changes to sports because of the possible loss of outdoor venues. (See Going, Going Green by Alexander Wolff). A lot of doomsday scenarios to be sure - but some chilling images nonetheless. None more so than a sidebar on The Catch - Willie Mays’ famous steal of Vic Wertz’s shot to center field in the 1954 World Series between the NY Giants and Cleveland.

The story is that with global warming, average temperatures have risen just enough to make Mays’ catch much harder, and quite possibly impossible, even for Willie. This is because the higher temperatures produce air that is less dense, allowing the ball to travel just a little bit farther then it would have otherwise. Compared to average temps of 76° in 1954, today’s average temp of slightly more than 77° would give Wertz’s fly ball an extra two inches of loft. Would Mays still get the ball, or would it hit the tip of the glove’s webbing and bounce off? Would the Giants go on to sweep the Indians?

The physicist behind this model is Alan Nathan of the University of Illinois at Urbana-Champaign. He maintains a fascinating web site on the Physics of Baseball that contains the results of his own research and numerous other links to physics-of-baseball resources. He has published articles on everything from The Physics of the Trampoline Effect in Baseball and Softball Bats to The Effect of Spin on the Flight of a Baseball to How to Hit Home Runs: Optimum Baseball Bat Swing Parameters for Maximum Range Trajectories.

This modeling is pure speculative fun, right?

Not when your opinions of global warming are more informed by politics than by science. Since the March 12 Issue of SI hit the stands, there have been numerous letters to the editor complaining of that old bellwether - "liberal bias." The letters assert that SI and readers who actually believe in Global Warming have no business reading a sports magazine. We are all swallowing (gulp) hook, line, and sinker the left-wing claims about Global Warming..and doesn’t everyone know that it was colder this year than last in my home town, and, oh yeah, what’s the big freakin’ deal about 1° anyway?

On second thought I was being wildly off-target describing their rate of acceptance of the reality of climate change as glacial. There won’t be any change until the golf courses start vanishing - which, should be noted, is one of the main doomsday scenarios in the SI article.

(And for someone who takes warnings of global warming a bit more personally, see Global Traumaning by Tim Blair.)

Is there a better way to reach these folks short of the horror of seeing Green Life Jackets at Augusta?

Maybe. There’s already a blog about discussing climate change. See A Few Things Ill Considered: A layman’s take on the science of Global Warming featuring a guide on How to Talk to a Climate Sceptic. This blog is maintained by Coby Beck - who claims that he is not a climate scientist, but is "rather obsessed with the controversy over Global Warming." Beck’s site is a systematic attempt to answer as many objections as possible about Global Warming, which he neatly characterizes as falling in one of six broad areas:

• Ignorant or Misinformed Arguments
• Socio-Political/Economic arguments
• Scientific FUD*
• Philosophical/Arguments from Higher principals
• Crackpottery
• Underdog Theories

Beck’s site is an amazing collection of arguments against global warming, and his answers to those who recite them. (And it’s more amazing if it really is true that he’s not an atmospheric scientist).

Medieval Warm Period by J. Harris. Click to enlarge. So the next time someone claims that Vikings could not have settled in Greenland without the higher temperatures of the MWP (the Medieval Warm Period) you’ll know what to do…

Call in the center fielder to make the impossible grab, turn quickly, laser the ball to the infield, letting no doubters advance…

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.

(Note: This post is motivated by a marvelous book by David Edmonds and John Eidinow on this incident titled Wittegenstein’s Poker: The Story of a Ten-Minute Argument Between Two Great Philosophers. E&E do a masterful job of explaining the foibles and eccentricities of K and L as shaped by their personal history in the tumultuous first-half of the 20th Century. Read it!)

The main part of the story, as recounted by Edmonds & Eidinow:

Popper put forward a series of what he insisted were real philosophical problems. Wittgenstein summarily dismissed them all. Popper recalled that Wittgenstein "had been nervously playing with the poker," which he used "like a conductor's baton to emphasize his assertions," and when a question came up about the status of ethics, Wittgenstein challenged him to give an example of a moral rule. "I replied: 'Not to threaten visiting lecturers with pokers.' Whereupon Wittgenstein, in a rage, threw the poker down and stormed out of the room, banging the door behind him."

I’m not giving anything away by pointing out that this tale is recounted by Popper, and there are real questions about whether the event transpired as he describes., or has been embellished at the sake of Ludwig, who apparently was known to often leave rooms by storming out in a blaze of philosophical muttering. Read Wittgenstein’s Poker for the definitive forensics of the event.

This story is fascinating to me for reasons beyond the intense personalities that could lead to such an eruption. Both Wittgenstein and Popper were obsessed with the nature of the world and what could be known about it, but both could not be further apart on method. Thus the main seeds of the argument grew from Wittgenstein’s approach to philosophical issues as problems in language, while Popper was a "big issue" guy, with works on everything from the distinction between science and non-science to the dangers of totalitarianism.

Of specific relevance to the Chaos and Fractals course is Popper’s description of falsifiablitiy as a necessary condition for a scientific theory. (We do spend some time reading about the 20th-Century schools of mathematical philosophy, including logical positivism and the verificationist stance of the Vienna Circle - the antithesis of Popper’s falsifiability.) Basically, a falsifiable theory is one for which there is no logical reason why an experimental observation can’t show the theory to be incorrect. Popper necessarily then must have prediction as a major hallmark of any theory - without this, there’s no way to gauge the correctness of the theory. What to make then of Chaos Theory? One of the features of Chaos is that predictions can be notoriously unreliable due to sensitive dependence on initial conditions. Thus the theory itself contains as a prediction its own unpredictability. Does this make Chaos non-scientific because there is then nothing in principle that is observable that would refute this unpredictability?

This dilemma/paradox is typical of any statement that is defined recursively and in which it describes itself - "This sentence is not true" being a standard example. In the case for falsifiability, physical law - one which we believe describes a certain feature of the universe, and which we believe to be an essential feature of the world (e.g. Newton’s Law of Gravitation) occupies a real place of tension between absolute true reality, and a precarious about-to-be-refuted relationship. This convoluted reasoning reminds me of Groucho Marx’s "I refuse to belong to any club that will accept me as a member," and it clearly got to Wittgenstein, whose own views on science are notoriously difficult to parse. Here’s a nice collection of statements from Tractatus Logico-Philosophicus complied by Robert Brow in his interesting essay Wittgenstein, Science, and God:

"The world is everything that is the case. The world is the totality of facts, not of things. The facts in logical space are the world" (1.1-13). In any scientific system "the totality of true propositions is the total natural science (or the totality of the natural sciences)" (4.111). It is the propositions which are possible in our scientific language, which "show the logical form of reality. They exhibit it" (4.121). Which means that "empirical reality is limited by the totality of objects. The boundary appears again in the totality of elementary propositions" (5.5561) "The limits of my language mean the limits of my world" (5.61).

On the other hand, Wittgenstein himself was a master of vertiginous meta-sentences, one of which I have adopted as the underlying theme of the Chaos and Fractals course:

The fact that we can describe the motions of the world using Newtonian mechanics tells us nothing about the world. The fact that we do, does tell us something about the world.

Now back to the story of the poker and its truthiness. Popper no doubt knew that his talk would produce a very agitated Wittgenstein. Given Wittgenstein’s M.O., there’s no way Ludwig would not have done what he did. Therefore the outcome of the exchange between the two Austrians was not falsifiable and thus not scientific. It was, however, a thoroughly fascinating case of two philosoraptors locked in a brief, violent embrace of ideas. As they rumbled off to separate corners of the room, campus, and globe, the reverberations of this death match continue to illuminate the always passionate debates about the foundations of science and mathematics that continue to this day.

A version of it has even made Hollywood: Ryan O’Neal, of Love Story fame, was recently arrested after getting into a bizarre family/drug scene rage with his son Griffin. Both father and son claimed that the other tried to kill him with a - you guessed it - fireplace poker.

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. Professor Kuhn argued in the book that the typical scientist was not an objective, free thinker and skeptic. Rather, he was a somewhat conservative individual who accepted what he was taught and applied his knowledge to solving the problems that came before him. In so doing, Professor Kuhn maintained, these scientists accepted a paradigm, an archetypal solution to a problem, like Ptolemy's theory that the Sun revolves around the Earth. Generally conservative, scientists would tend to solve problems in ways that extended the scope of the paradigm. In such periods, he maintained, scientists tend to resist research that might signal the development of a new paradigm, like the work of the astronomer Aristarchus, who theorized in the third century B.C. that the planets revolve around the Sun. But, Professor Kuhn said, situations arose that the paradigm could not account for or that contradicted it. And then, he said, a revolutionary would appear, a Lavoisier or an Einstein, often a young scientist not indoctrinated in the accepted theories, and sweep the old paradigm away. These revolutions, he said, came only after long periods of tradition-bound normal science. "Frameworks must be lived with and explored before they can be broken," Professor Kuhn said. The new paradigm cannot build on the one that precedes it, he maintained. It can only supplant it. The two, he said, were "incommensurable."

I don’t know whether it was directly due to Gleick’s book, but, shortly after its release, I started hearing about paradigm shifts an amazing number of times, in a wide variety of different settings - almost none of which matched Kuhn’s description. So much so that the original sense of the paradigm shift as envisioned by Kuhn has been lost in all of the "shifting."

My earliest memory of this occurred in the late 80’s at a math/science teaching workshop. The speaker that day used the idea of paradigm shift to describe what needed to happen in order to "change the culture" of mathematics and science teaching at the K-12 level. One may view a different teaching culture and associated methods as an "answer" or way of understanding something in a completely new light, which in this case is a different understanding of how student learning can be affected by different pedagogy. Now this is stretch from Kuhn’s paradigm idea, but one that is not out of line - I took it as a metaphor that did have some illuminating power.

Then there was the case of Sony Betamx vs. VHS, an interesting, huge-money skirmish to determine which format would dominate the video recording market in the early days of TV video recorders. Even though Sony beta was considered the better format from a technical standpoint, VHS won out for a variety of reasons - most due to the recording length of Betamax tapes and the relative availability of films in the vying formats. Remarkably, I have heard this "locking in" of VHS to the detriment and ultimate demise of Sony Beta as a paradigm shift. I always thought that this was an inappropriate example of a paradigm shift as envisioned by Kuhn, because it wasn’t the wholesale replacement of an idea by one that was apparently better. Beta lost because the consuming public chose VHS.

This is clearly nowhere near Kuhn’s vision - it was simply the contingencies of the market, aided and abetted by smart and dumb business practices, good fortune and rotten luck - no paradigm’s here.

Which by the way explains the title of this post. In the ongoing war of DVD formats for High Def - Blu-Ray vs. HD-DVD, you can find sources that claim one side or the other are "winning." (There are several good sites that keep tabs on the format war, with ign and Gzmodo two of the very best.) Now Sony is one of the backers - in fact the principal developer - of the BLU-Ray format. Maybe to ensure good electronic karma for the fateful decision of the DVD-buying public, SONY execs are using the term paradigm shift to describe all of its high-def efforts, including Blu-ray. According to SONY Electronics CEO Michael Fasulo, “HD is a huge paradigm shift. It’s a huge opportunity. We haven’t seen this since black and white went to color." Then there is Fortis Investments - a global investment firm that calls its research publication Paradigm Shift. Their rationale for this name:

As the research publication of Fortis Investments, Paradigm Shift seeks to identify recent or imminent changes in dominant investment paradigms that have direct consequences for our clients. In doing so we aim to demonstrate the intellectual basis of our investment processes and to argue the case for our innovation.

What would Kuhn think about this? Short of Buy High and Sell Low, the idea of maximizing investment earnings still seems to be the overarching paradigm in the word of investments - one that will not shift anytime soon - although dropping the PShift name may make more clients willing to sink their $’s in Fortis.

Now, just when I had lost any hope that paradigm shift would ever be used to describe phenomena correctly, I finally heard a reference that did ring true - just today on sport-talk radio I heard one of the hosts describe the need for the Philadelphia Eagles to undergo a paradigm shift in their offensive philosophy, from more passing to more running plays.

I’m sure that Kuhn would agree such a switch to be archetypal, the ur-paradigm shift of paradigm shifts.

If the Eagles do switch I’ll have to record the entire season on Blu-Ray…

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 preference that moves them to act is not the preference that they prefer having, in contrast, "sheds light." To be in the grip of crummy preferences is to rationally act and to still be respected as a "whole." In addition, it permits normative evaluation of market shortcomings (markets are ill equipped to create preferences that we prefer having) while at the same time not particularly suited for making predictions. The two-selves models, in contrast, do not have the same normative weight. My point: assumptions matter if we are to gain "understanding."

OK, I totally agree that assumptions are crucial to a true understanding of any phenomena via modeling. But, and this was my point in my original post about the economic modeling of religion, if there is no predictive power, I question what the model provides other than an explanation for why things are the way they are. I’ll even go so far as to say that, if there is no prediction, there is no understanding.

Now, with apologies to D. George, this is a pretty harsh view. I am lead to it, however, by wondering where the belief that the model provides understanding comes from if not from some "test" of the model via prediction. Maybe it’s the word model that has me going here. A model that provides understanding ONLY is really only an explanation of the current situation - one that might "sound right," but which is lacking any inductive way of measuring its merit as compared to another "model."

There’s an interesting connection to Chaos Theory here. Because of sensitive dependence on initial conditions that is the hallmark of many a non-linear dynamical system, it would appear that one could have complete understanding of a system (i.e. the equations that determine the interactions among the system members are know to be exact) but no predictive power. So doesn’t this blow away my argument about the need for prediction? How can Chaos Theory be used to model anything at all if non-predictability is built in? The difference is that Chaos Theory, in a nicely recursive way, predicts its own unpredictability. Not only that, but because of the constrained randomness that is the best way of describing the output of many a chaotic system, it does so pretty accurately.

So I challenge anyone to come up with a model that only yields understanding, but no prediction.

I predict that, in all cases the "model" is better described as an explanation of the current state.