Ida Hoos - On The Perils of Mathematical Modeling and Public Policy

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.”

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

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

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

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

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

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

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

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No Prediction, No Soup For You...

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

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

An excerpt from D. George's response:

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

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Modeling Acts of God, Part 1

Hurricane structure. Click to enlarge.

This post is the first in a series of the state of modeling very powerful, nasty natural phenomena such as hurricanes, earthquakes, and tsunami.

Depending on where you live you may have trouble acquiring or affording insurance protection form these so-called "acts of God. "  Whatever these AOG's might be, they are often home- and life-threatening.  Can these AOG's be modeled successfully, i.e. how well are they understood and can their generation, properties, and behavior be predicted with any accuracy?

Along with the understanding and prediction provided by standard models for these event, it is natural to wonder how global warming contributes to these phenomena. Do models for these AOG's compensate for GW's effect? This is a very pressing question. Anecdotally, many claim that the events are both more frequent and more severe, with natural tendency to assign blame to global warming.

Consider hurricanes. Hurricanes are pretty well "understood" in terms of how they start and move. Proto-hurricanes start as small tropical vortices , which themselves originate because of rotational effects of the earth on atmospheric gases. Kerry Emanuel, Professor of atmospheric sciences at MIT explains this in Hurricanes: Tempests in a Greenhouse:

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As the World Turns - Foucault's Eco

Feb. 3rd marked the 156th anniversary of Léon Foucault's demonstration that the earth revolved on its axis. The experiment was brilliantly simple: let a large pendulum swing back and forth over the course of a day, with a sharp tip hanging off of the pendulum bob making patterns in a bed of sand below it. As the pendulum bob moves back and fort in a vertical plane the earth rotates beneath it, and this rotation can be measured by the marks in the sand. (For a nice intro to Foucault's Pendulum, check out the scriptographic booklet on the subject at the California Academy of Sciences.)

Foucault did not stop with simply showing that the earth rotates. He was able to predict how fast the pendulum would appear to rotate because of the fact that the rate at which the marks carve out a pattern depends on the latitude of the pendulum. So, for example, at one of the poles the earth will spin once in 24 hours, while at the equator the earth does not spin with respect to the plane of the pendulum. Anywhere in between the amount of time it takes for the pendulum to make one complete rotation is given by

T = 24/sin L

Here T is the time for the pendulum to return to its original position (in hours), and L is the latitude at which the experiment is carried out.

The pendulum demonstration was a huge success, showing as it did in a very simple way what could not be felt by earthly inhabitants - the rotation of the earth they were standing on. (It was also a majestic demonstration, being conducted in the the Panthéon in Paris.) The fact that Foucault could actually predict the exact timing of the rotation made him akin to the explorers who mesmerized remote villagers with abilities to predict eclipses, and he achieved physics rock-star status - maybe the most until Einstein.

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Luminiferously Aethereal Dark Matter and Energy

Star Traveler from Angelbert Metoyer's Dark Energy Splitting the Universe . Click to enlarge.At the end of the 19th Century century many physicists were still searching for the luminiferous aether - the mysterious, invisible substance that permeated the universe - the medium that (it was presumed) needed to exist in order to support light waves.

At that time, waves were understood to be mechanical disturbances in a medium - in effect, shapes that propagate through the medium transporting energy from source to receiver with a speed dependant on the medium itself . Water waves, waves on a string, sound waves in a column of air - all of these phenomena relied on matter to support these moving shapes.

The Aether was supposed to be the invisible stuff that somehow oscillated as the shapes of light waves passed from point A to point B. It had to be really odd stuff - invisible, for one thing, and also incredibly resilient, because it had to support an unbelievable speed - the speed of light.

Nevertheless, by this point the mechanical qualities of the aether had become more and more magical: it had to be a fluid in order to fill space, but one that was millions of times more rigid than steel in order to support the high frequencies of light waves. It also had to be massless and without viscosity, otherwise it would visibly affect the orbits of planets. Additionally it appeared it had to be completely transparent, non-dispersive, incompressible, and continuous at a very small scale. (wikipedia)

In other words, aether couldn't be seen, weighed, touched or tasted, but it was stronger than anything known to man. And it was everywhere - in your shoes, hair, mouth, nose, and subway tunnels. A really strange thing for physicists to believe in.

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Pi-Brained Schemas & Savants: Who's Normal Now?

Meesh Pi. Click to enlargeA most peculiar feat was reported in yesterday's Philadelphia Inquirer:  Marc Umile, a filing clerk from the Philly area, was able to recite the first 12,887 digits of π from memory - an American record. (The current verified world record is for 43,000 digits by Krishan Chahal of India.)

In an odd twist, Umile performed his prodigious feat at a law office, and not for the Guiness Book folks. In these litigious times, it is obviously prudent to be prepared for intellectual property infringement in any activity such as this, which in this case comes under the heading of π's and torts ...

While Umile's feat is incredible, I am more intrigued by the physical/mental issues involved in the data entry, storage and retrieval of these digits. The actual amount of data is not the issue - 12,000 is a very small number of single digits when compared to the potential of the human brain.  Data entry is not hard to comprehend, either, with Umile spending two-plus years memorizing the digits. (I am not commenting on motivation or sanity here.  See the Inquirer piece for this!)

How in the world are the values recalled/retrieved?

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Locally Localized Gravity, or If I Only Had a Brane

The Institute of Contemporary Art (ICA), at the University of Pennsylvania will be running a very interesting show titled Locally Localized Gravity from January 20 - March 25, 2007.  From the ICA website description:

Locally Localized Gravity responds to an alternative mode of art making wherein artists produce events, run collectives and galleries, publish zines and small artist's books—generally acting as catalysts in their communities. In other words, they rarely focus only on traditional object-based practices. The exhibition, which will include over 100 artists, musicians, designers, lecturers, performers, and creators from Philadelphia and other cities, will be one non-stop event and on view in ICA's first floor galleries and terrace.

...

The title is borrowed from string theory, a complex scientific term describing four-dimensional gravity (three dimensions of space and one of time). It was suggested to the curators by artist Matthew Ritchie, whose own work explores ideas of string theory, among many things. The term locally localized gravity can be applied to art scenes where artists, by generating a huge amount of energy, can create centers of gravity.

This description of the meaning of LLG is maximally condensed for public consumption.  It is not the point of the exhibit, nor the role of ICA to give a detailed explanation.  However, because I have participated in an ICA in the past, I was asked to send them a more detailed blurb on locally localized gravity. While my piece might not make the ICA material, I am posting my submission here because LLG touches on the most extreme questions one can ask of any physical model, namely what is the ultimate nature of the universe?

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It's No Fluke: When Mandates Meet Models

In today's news, NJ & NY fishermen are understandably upset because the allowed number of fluke permitted to be caught in the upcoming season has been reduced by 28%.  Just as the number of deer is regulated, with certain numbers of permits issued during deer season, several fish species, and spawning and feeding areas are tightly controlled.  Both of these "game" species are subject to three often irreconcilable forces: scientific predictions in the form of regulatory commissions, local needs of those relying on the game for a livelihood, and the contingencies of politics.

The amount of any species permitted to be caught ("harvested" in the parlance of population minders and modelers) is chosen with one of two possible goals:

1. to keep the overall population in a steady state, i.e. the harvesting rate is basically the net birth rate  (absolute birth rate - death rate)
2. to increase the overall population - i.e. the harvesting rate is greater than the net birth rate 

Presumably the 3rd option - harvesting faster than the series can regenerate, is not a consideration in game or food species, or there soon would be no species left.

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Predicting Nothing and Next - to - Nothing: A Nobel Thought

Temperature fluctuations in CMB. Click to enlarge.John Mather and George Smoot were named winners of the 2006 Nobel Prize in Physics this past month.  Their work on the NASA Cosmic Background Explorer (COBE) is primarily experimental.  The accuracy of their instruments and subsequent precision of their results are remarkable achievements.

What the measurements imply is even more remarkable, and is a great example of the deep interplay between understanding and prediction that happens when things break the right way, when theory and experiment mutually reinforce each other illuminating a deep secret about the universe.  ( Hence the Nobel prize...)

Mather and Smoot were checking on the two major predictions of inflationary Big Bang theory:

• The cosmic microwave background (CMB) - a measure of the intensity of radiation present in the universe as a function of wavelength.  Theory predicted that the measured radiation should follow an almost-perfect blackbody spectrum. (i.e. should follow the mathematical form first determined by Planck in 1900 - the beginning of Quantum Mechanics).  The major parameter used to fit CMB to a blackbody spectrum is temperature, hence finding an experimental blackbody curve can be a very accurate thermometer
• The temperature  of the CMB should vary very slightly for different portions of the sky, i.e. the universe.  It is only with these fluctuations that inflationary theory predicts the eventual clumping of interstellar matter to form stars, proto-galaxies and ultimately the solar system and planets.

Measured vs. Theoretical CMB. Click to enlarge.Click on the graph to the left to see a fit that's "almost perfect"  It is a graph of the experimentally measured spectrum superimposed on a black body function. The size of the data squares represent the uncertainties in measurement. The fit is astonishingly good - as perfect a fit as has ever been seen in an experiment as complex as the COBE. So the first piece of the puzzle came in as desired.  What about the temperature fluctuations?

The figure at the top of this post shows the temperature variation of the CMB over a certain region of the sky. Mather and Smoot measured incredibly tiny temperature variations - approx. 30 microkelvin, again, in line with theory.

So the Nobel goes to experimenters who measured "nothing" - i.e. no measurable deviation from a perfect black-body spectrum, and next-to-nothing - temperature variations so miniscule that a few clusters of atoms moving with slightly different velocities would throw off the results.

What to make of these results?  By themselves, the results are merely facts - interesting facts, to be sure, but simply facts.  It is only in coordination with theoretical predictions that these facts come alive - stating for all that there is something to the theory in the first place.  And, because of that very positive reinforcement, the data+theory yields an understanding about the universe that is much deeper, and stronger, than at any other stage in the history of the cosmological beliefs of Earth's inhabitants.