Where There's Smoke There's Hot Air: Prediction Without Understanding

Montgolfier Balloon over Paris, 1783. Click to enlarge.Sometimes prediction is easy without any understanding.  Take driving a car, for example.  Stepping on the gas causes the car to accelerate if it is in gear.  How many drivers actually understand why this happens, short of the basic guess that "more gas" somehow got to the engine?  Clearly one doesn't have to understand anything about internal combustion engines to predict what will happen when the engine gets more gas, or gets the wrong octane gas, and so forth.

So Prediction without Understanding is a common occurrence. 

A related happenstance is when accurate prediction occurs even with a totally incorrect understanding.

Consider the first human flight, which occurred on Nov. 21, 1783 when two Frenchmen ascended above Paris in a hot air balloon.  The balloon was designed by the Montgolfier brothers, who believed that thick smoke caused the balloon to stay in the air.  Of course, the thick smoke was a byproduct of whatever they burned in the fire at the throat of the balloon , but it was the hot air (less dense air)  caused by the fire that actually led to the balloon floating.

OK, so the Montgolfiers weren't that far off - you don't have to dig too far to find the connection between thick smoke and hot air, after all.  But this example does raise a more interesting question:  when is it the case that understanding is totally lacking, yet predictions are right on? 

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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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The Economic Modeling of Religion

I usually view economic modeling as a more asymmetric activity than, modeling in physics. In physics, models are used to both understand why something happened or happens, and predict what will happen in future circumstances - the twin pieces of understanding and prediction. This is probably a biased view on my part, or a woeful lack of knowledge of the predictive power of economic modeling, but it seems to me that most economic models I read about are more useful in explaining the past. Any extrapolation of the model into the future basically depends on assuming similar conditions. Physics models are often tested by finding out what they predict for future situations under different conditions. (I am not including econometric modeling here, which I consider to be a qualitatively different activity - it is modeling that is more empirical in the sense that data crunching is used to establish the coefficients of the model equations.)

Again, my opinion may be totally nearsighted. If it is, let me know.

I write this because of a recent book titled The Marketplace of Christianity by R.  Ekelund, Jr., R. Hebert, and R. Tollision, which was described in a recent issue of the Chronicle of Higher Ed. (Nov. 3, 2006, page A13) In the book the authors use economic analysis to describe such things as the number of different Christian churches through the centuries and the different acceptance rates of the Protestant Reformation.

Some of the models, at least as reported by the Chronicle, seem very far-fetched - a huge, Procrustean stretch, if you will.

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Copenhagen, Quantum Mechanics, and a Shot of Glen Livet

The tag line for this blog, indeed the overarching theme of the Chaos and Fractals course is the fuzzy three-legged monster of Modeling, Understanding, and Prediction. Fuzzy because the boundaries are never clear; they are themselves fractal-like. Suffice it to say that the non-linear dynamic modeling of most systems is used for both the understanding the models provide about why something happens the way that it does as well as the prediction of future states.

Which brings me to quantum mechanics - a field where models routinely predict experimental results with extraordinary accuracy, yet there is still debate on what it all means. Taking this to an extreme, if there is disagreement among physicists on the meaning of quantum mechanics (specifically, the meaning of the quantum mechanical wave function and the nature of observation) then there is a lack of understanding. Whether one considers this "good prediction, no understanding" scenario unsatisfying or not comes down to one's proclivity for philosophizing.

Actually, for me I developed a "proclivity for philosophizing" because of Quantum Mechanics.

I remember as a physics student being totally mystified at and angry with quantum mechanics. Sure I could do the mathematics, but I really had no clue as to what a stationary state was, or what it meant for a wavefunction to collapse. Even after getting very good grades in both semesters of quantum, I really couldn't articulate the connection between the mathematics and reality in a reasonable way, or at least not in the tangible way that I could describe the (apparent) reality of Newtonian physics.

Click to enlarge the Quantum CatGrad school and a post-doc in solid state physics finally did bring some aha! quantum moments; I could finally talk-the-talk of quantum mechanics interpretation as well as theory. Like most students, I was taught the Copenhagen Interpretation of Quantum Mechanics as promulgated by Bohr and Heisenberg in the 1920's. I adopted it whole heartedly, and soon Schrödinger Cats and Wave-Particle Duality were common topics of late-night sessions, often fueled by single-malt ...

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To Drill or Not to Drill: Modeling Oil Production in the Arctic National Wildlife Refuge

Click to enlarge mapThe Arctic National Wildlife Refuge is a flash point for environmental and energy issues, combined in a volatile atmosphere of anti-terrorism. If only the U.S. could start drilling for oil there, the up to 8 billion estimated recoverable barrels of oil would surely lower our dependance on foreign oil, especially from the Middle East.

Or so proclaim those in favor of opening the refuge for drilling. (See ANWR.org - with a tag line of "Jobs and Energy For America" - for a collection of pro-drilling arguments.)

Currently, ANWR drilling is not permitted by federal statute. Over the past few years there have been several attempts in Congress to allow drilling - on some occasions from the House, only to be turned down by the Senate, and then from the Senate, shot down by the house.  (Click here for more details.)

Even though it appears as if those against drilling are currently holding their own, the no-end-in-sight Iraqi situation combined with the explosion of jihadist sentiment and activity could tip things enough so that both the Senate and House finally agree to open up the slopes for drilling. (Which is just one of the reasons that the upcoming mid-term elections, and possilbe change in majority party in both the Senate and the House, are extremely significant for the ANWR.)

The Sierra Club is one of the more public groups leading the charge against ANWR drilling.

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On the Increase in Greenland Ice Loss

Iceberg in Jacobshavn Isfjord, Greenland. Photo by Evert Wesker.Greenland holds an important place on the frontier - both of the habitable world, and of global warming. Greenland is where sudden climate changes have been mapped, a phenomenon that was one of the first markers of global warming to be widely accepted. (Click here for a previous post.)

Greenland is back in the global warming news: the rate at which ice is leaving Greenland (through meltwater and ice shearing) is apparently accelerating.

The study was done by Eric Rignot (NASA's Jet Propulsion Laboratory) and and Pannir Kanagaratnam (Univ. of Kansas Center for Remote Sensing of Ice Sheets.)

Ten years ago Greenland was losing ice at a rate of 22 cubic miles/year. It has now increased to 53 cubic miles/year. The size of this number is staggering. (22 cubic miles/year was already incomprehensible.) 53 cubic miles has a weight of approximately 2.4 trillion tons. To put this number in perspective, an asteroid that is totally iron would be over a mile in diameter to have the same weight!

Glaciers at the edge of Greenland have

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Uncertainty, Impossibility, and Reality: Heisenberg, Gödel, Einstein

Click for the Heisenberg CafeThe underlying structure of the Chaos and Fractals course is the understanding-prediction continuum. Starting with the Chaos Game and proceeding through all of the readings and Classroom Chaos exercises, the elusiveness of true understanding of non-linear dynamical systems and the need to "settle" for mere prediction is common and unsettling.

One can only wonder, then, about the possibility of true understanding of anything more complex than linear processes. Maybe this inability to understand is a symptom of a world that is fundamentally unknowable.

Now I should know better than to leave the understanding-prediction axis and question the fundamental nature of reality. Jumping into the philosopher's sandbox is often a prescription that leads one to lose sight of the day-to-day business of actually doing science or mathematics. So let me turn to those who really could live in that sandbox, mix it up with the philosophers, and jump out again to do their science and mathematics.

The defining work of 20th Century science and mathematics may just be the development of theories that posit fundamental limits to what we can do, what we can measure, and what we can know. Einstein's relativity rests on the postulate that the speed of light is constant in all reference frames; a result that leads to limits on the velocity of particles with mass, and destroys the notion of absolute time and simultaneity. Heisenberg's Uncertainty Principle puts an inviolable restriction on what we can measure and therefore know about a physical system. Gödel's Incompleteness Theorem denies us the possibility of knowing or proving all mathematical truths.

Do these limits tell us something about the world, or just about our ability to understand the world? Einstein, Heisenberg, and Gödel were very clear on this question: they believed that they were discovering the true nature of the world.

This point is espoused by philosopher Palle Yourgrau in his book "A World Without Time: The Forgotten Legacy of Gödel and Einstein":

Einstein, Gödel, Heisenberg: three men whose fundamental scientific results opened up new horizons, paradoxically, by setting limits to thought or reality. Together they embodied the zeitgeist, the spirit of the age. Mysteriously, each had reached an ontological conclusion about reality through the employment of an epistemic principle concerning knowledge. The dance or dialectic of knowledge and reality -- of limit and limitlessness -- would become a dominant theme of the 20th century.

Ok. Back out of the sandbox and back to work. If the world is unknowable, I don't want to know it. In fact I don't want to think about it - it's time to get back to modeling and prediction. And if I don't really understand what's going on in my dynamical system, or why my predictions work, who is going to know it?

(Heisenberg cartoon by Mark Stivers)

Solar Activity Modeling: Great Predictions, Lousy Understanding?

Click to enlarge view of sunplumeA number of news sources reported yesterday that scientists had predicted more intense activity in the coming cycle of sun spots, solar flares, and other solar phenomena. This prediction was accompanied by another prediction on timing - the solar activity would be somewhat "delayed."

These statements naturally got me wondering about a number of issues - how is solar activity modeled? How accurate are the predictions? Is the underlying physics that causes the upsurge in activity understood?

First, it's clear why accurate predictions are needed: increased solar activity can really do a number on communication and navigation electronics, causing satellites to go awry - and in some cases causing delays of planned rocket launches.

Now to the "delayed" issue - the basic lore is that the sun goes through an 11-year cycle of low-to-high activity, culminating in a significant number of sunspots appearing on the sun's surface. In reality, there is a spread in this: cycles run from 9 to 14 years, with 11-years being the mode of the distribution of solar cycle lengths. (Solar cycles and their lenghts have been tabulated since approx. 1760. We are currently in Cycle 23, which started in May 1996. Click here for a histogram of cycle lengths .) Most solar cycles are near the 11-year length, so any delay is with respect to 11 years (i.e. the next cycle is expected to start sometime in 2008). The delay, then, is nothing out of the ordinary.

Even with this spread in cycle lengths, the regularity is amazing, given the incredibly non-linear processes at work in the stellar interior - a hellish cauldron

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Global Warming & Prediction of Water Shortages

Click on glacier to enlargeMost Global Warming (GW ) scenarios predict melting of polar ice caps, leading to massive seaboard flooding as sea levels increase. A fact often overlooked (at least in the popular press) is that GW will most likely produce water shortages for many, even while other areas are inundated with too-much water.

A recent account was picked up by the major newspapers: Tim Barnett of the Scripps Institution of Oceanography (La Jolla, CA) has developed a mathematical model predicting that up to 1/6th of the world population could face water shortages because of GW.

So, if there is too much water, why the water shortage? The answer is that the water shortage is a fresh-water shortage. Fresh water will be lost due to GW in several ways:

• Evaporation from fresh-water sources, such as rivers, may occur at a faster rate than any higher precipitated caused by GW.
• GW will cause glaciers to melt. Glaciers are estimated to contain up to 70 percent of the world's fresh water reserves. (And they are the natural feeders of rivers)

Island countries will be the hardest hit by GW because of the flooding and the fresh-water loss. There are already numerous calls around the world for action. The United Nations Environment Programme has recently released an urgent call for world attention to Water Shortages and Global Warming Risks for Indian Ocean Islands, where the potential for future tsunami is very real.

We are at least at a point where most agree that GW is occurring, even though there is still much debate (ideological/political) about whether GW is caused by the effects of mankind. Usually these debates center on the mathematical model used. Mathematical modeling always involves compromise. Decisions are made to simplify the model by keeping the number of variables (and equations) manageable, and the interaction of these variables (e.g. solar energy and ocean condition) is usually done heuristically. With the models necessarily non-linear, the potential for chaotic behavior , especially SDIC, is very real. Because of this erratic-output, it then becomes very easy for some (and some governments) to blame the model, or the modeler for the bad news of GW, losing sight of the occuring phonemona of GW.

GW still remains very real, however, whether or not a model can convince all of what what causes GW. But the models for water shortage due to GW are much simpler because of the basic correlation that more heat = more ice melting, and should be trusted by all.

Predictions of severe water shortages due to GW are not new - they just don't make it into MSM - until now. Is anyone listening?

The Why vs. When of Weather

It has been a relatively mild January in the Philadelphia area, with high temperatures significantly above the normal temperature range for this time of year. This type of occurrence is often thought to be a sign of global warming. This is not obvious - in fact there have been very large changes in January temperatures, both high and low, throughout the past century. (And January of 2005 was hotter than the current month!) This means that we cannot look at at our temperature record alone as a signature of global warming. This is true even if there is a string of higher-than-average-temperature days, months, or even years. Repeatability in weather patterns is certainly nothing one can count on.

Edward Lorenz did show that a simplistic weather model based on three coupled non-linear differential equations produces weather patterns that never repeat. He used this fact, coupled with the sensitive dependence on initial conditions (SDIC) to make strong claims against the impossibility of accurate weather prediction. His model also predicted sudden swings in weather patterns - similar to what we are now experiencing.

Jim Laver, the director of the Climate Prediction Center is quoted in today's Inquirer, explaining why the weather has been warmer - it is due to easterly winds from the Pacific as opposed to cold Canadian air dominating our area this month. But why the shift in winds? There is this follow-up quote from Jim Poirer of the National Weather Service in Mount Holly, NJ: "If we knew why, we'd make money."

What's wrong with this statement?

According to Lorenz, we do know why - weather is a non-linear system that displays SDIC, and its phase-space trajectory is a strange attractor. It is the when that we don't know. This is a case where we do understand, but cannot predict with reasonable accuracy.