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Sunday, August 29, 2010

Crypto Conservatives?

Do conservative faculty on liberal campuses have an obligation to fight the campus left? I have always been extremely vocal in matters of departmental policy, but as noted in a comment on one of my posts, I have, at times, held back in matters concerning the larger university. Is restraint judicious or cowardly?

The argument against restraint is simple. If conservatives do not speak out on campus, the left wins every argument; at the university, the left is both numerous and outspoken.

The reasons for restraint are numerous and range from the selfish to the practical. Most of the conservatives I know in the sciences put their energy into their work - not into political battles. Not everyone is willing to devote time and resources to political battles that do not affect them directly. In the sciences, I doubt that outspoken conservative politics affects promotion and tenure, but I can sympathize with the cautious junior faculty member who prefers to keep his head low before tenure.

My primary calculation when I consider addressing a worthwhile issue is: will my public position on this issue make me less effective in dealing with future issues of greater importance? This is a tricky calculation, which leaves room for never ending postponement and avoidance. To illuminate components of the calculation, I recall a formative period from my early faculty days. In the late '80's, the National Association of Scholars (NAS) appeared on many campuses. At that time the NAS was opposed to trivialized curricula, restrictive speech codes, post-modernist humanities scholarship, and similar anti-intellectual university trends. Not long after the NAS appeared, prominent humanities professors at major universities demanded that their university administrations adopt policies prohibiting members of the NAS from serving on any university governing committee. I never heard of any university publicly adopting such a policy, but the threat was clear: publicly endorse conservative positions and be branded a whacko unfit for positions of responsibility.

My response to this threat has been twofold. Sometimes I simply chose not to fight a battle that I had no hope of winning. I don't stand in front of a train. When I choose to fight, I fight on narrow grounds rather than in the context of broader conservative vs. leftist ideological battles. For example, recently, my university surreptitiously changed the selection criteria for one of our primary merit scholarships, reducing the emphasis on raw academic talent in favor of greater attention to community service and similar drivel. The justification was the standard social engineering blather. I (with allies) successfully argued for the reversal of this sacrifice of academic standards. We did not argue on ideological grounds but instead argued in terms of the negative effects on the recruitment of potential undergraduate stars for our science program. Opposition on such practical (and self interested) grounds does not generate the heat that ideological opposition does, and is therefore more successful.

The preceding paragraphs may suggest that the conservative faculty member frequently faces ideological battles on campus, but I have not found this to be the case. For those of us not frequently involved in broader university governance (and with our heads in our books), these issues arise infrequently. None the less, I assume that all conservative faculty face them occasionally and are then faced with the choice: fight today or postpone the fight for the future.

Sunday, August 22, 2010

Politics and the Fields Medal

Last week, quite a few visitors came to my blog via a mathematical/political discussion on the website, conservapedia, with which I was unacquainted. As I am otherwise uninspired this week, I will make a few comments on the subject of their discussion: the influence of politics on the awarding of the Fields Medal.

The Fields Medal is often likened to the Nobel Prize. It is a prize awarded every four years to four or fewer mathematicians for outstanding contributions to mathematics. The (perhaps apocryphal) story told by mathematicians is that Swedish mathematician Mittag-Leffler had stolen Alfred Nobel's lover. When establishing his award, Nobel asked prominent mathematicians who would be the likely recipient of the first Nobel Prize in Mathematics. When told that Mittag-Leffler was a leading candidate, Nobel decided there would be no Nobel Prize in Mathematics. Nobel never did marry, and he never endowed a prize in mathematics. Mathematicians all believe this story because they are keenly aware that nothing attracts the opposite sex like mathematical expertise. John Fields subsequently established his prize to correct this unfortunate state of affairs.

The question raised on the above mentioned political site was: what role does politics play in the selection of the Fields Medalist? We are all keenly aware of the role of politics in awarding the Nobel Peace Prize to such great humanitarians as Yasser Arafat and Al Gore. Moreover, many mathematicians and physicists have suggested to me that politics plays a strong role in the selection of MacArthur Prize winners. Does politics play a similar role in selection of the Fields Medalists?

I have never seen evidence of nor heard any mathematician voice suspicion of statist versus individualist, left versus right, etc. politics in the selection of the Fields Medalists. (The location of the award ceremony, however, is a different story). There is, however, no abstract linear ordering of mathematical achievement. Some work is so spectacular that there is no question that it merits a Fields Medal. In other cases, choices have to be made among several excellent candidates. I have heard complaints from mathematicians working in fields whose practitioners have rarely been recognized with Fields Medals. They note that the prize committee is dominated by mathematicians in fields X,Y, and Z, and that fields X,Y, and Z receive most of the prizes. If these fields are the most important and the most active, then it is natural and appropriate that they dominate both committee and prize, but who decides that this is the case? Various committees have to make these decisions, and we should not be surprised to learn that there is lobbying for various fields of mathematics to be given greater consideration. I do not consider recognition of the existence of such politics to be a criticism. It is simply the observation, once again, that mathematics is a human enterprise and therefore subject to the dynamics of human interaction.

Sunday, August 15, 2010

Spontaneous Order vs Locality and some inane analogies

As I continue my bedtime reading in political science (currently Boaz's The Libertarian Reader), I keep returning to the steepest descent metaphor for economic systems. I want to revisit this analogy to explore its different facets.

First, recall the concept of spontaneous order, associated with the Austrian School of Economics. Spontaneous order refers to the development of complex social and economic relations arising, not from a guiding intelligence, but from the separate actions of many individuals acting in their own self interest. In mathematics and physics, we frequently see similar phenomena: a system's dynamics are dictated by some energy functional. The system evolves in such a way as to minimize the energy. For the analogy to be apt, however, we do not consider arbitrary energy functionals. We consider only those which are defined by summing (integrating) a local energy. By 'local', I mean that the energy contribution at each point is computed from information that can be measured near that point (e.g. slopes). Then the energy minimizing dynamics at each point require information available at that point, and not global information. A mathematician can construct physically unreasonable systems which do not possess this locality property. Then the analogy with spontaneous order breaks down. So, the relevant correspondence here is

spontaneous order <-> locality of energy.

Viewed as the dynamics of a system determined by a local energy, the emergence of spontaneous order is essentially tautological. To recast it as a nontrivial statement, you need to turn it into the assertion that the socioeconomic dynamics are determined by a local energy. Then the emergence of spontaneous order follows from hypotheses such as the absence of a strong central government. Extracting political implications requires an assertion that a local energy functional is better than a nonlocal one, the latter being the natural model for a socioeconomic arrangement based on a guiding state or elite. This returns one to the perpetual conflict between small government conservatives and statists: should individuals or a governing elite determine the choice of energy functional (and thus definition of optimal state) for the society? Should individual happiness or the progress of the collective be regarded as the greater good?

Now we pause to enjoy cheap analogies. In partial differential equations class, we study the most fundamental and ubiquitous energy functional: the local energy of a function f defined on some region M and taking values in some constraint space N is defined to be the square of its derivative, |df|^2 (simply a measure of steepness of slope). If the accessible values, N, are completely unconstrained, then the system evolves to a utopian state where every point has the same value - the resources are equally distributed. When there are constraints on values, however, the dynamics are very complicated. Consider a utopia where every member of M is exactly the same; geometrically we model such a system by assuming M is a sphere (we require it to be a compact connected manifold). If we assume N is a finite size constraint space (a compact manifold), then the dynamics are unstable. Generically, one can always lower the total energy by concentrating all the energy (resources) at a single point. So for my all time cheapest mathematical analogy, we find generically that a completely homogeneous society evolves to one where a single member controls all the resources. Fortunately (think Stalin) these dynamics do not lead to stable equilibria.

Jumping from a cheap analogy to one that I find more instructive, I pass to the numerical approximation of the preceding dynamics. If you wish to model these dynamics on a computer, you have to approximate the infinite number of points on your space M by some finite grid, use the grid to compute approximate energies, and from this data, compute an approximate flow. The finer your grid, the better your approximation is to the optimal energy minimizing flow. The longer you run your approximation, the more you deviate from the optimal dynamics. When designing and executing statist policies, the government divides the population into categories, creating a coarse grid. If we assumed, counterfactually, that Congress understood economics, then we could pretend that it could compute an approximate energy for this grid and a consequent approximate energy minimizing flow. Passage to a grid, however, still entails a loss of data; hence, the approximation deviates from the optimal flow, and the deviation increases the longer the statist policies run, rendering the society ever less prosperous than its optimal state. The primary weakness of this analogy is the pretense that Congress actually includes economic analysis into its policy. With our current Congress, one can discard this pretty dynamics picture, replacing it with a discussion of the downside of pouring sugar into your gas tank.

Monday, August 9, 2010

Fraud in the Ivory Tower

Mathematics leaves very little room for fraud. Work can be incorrect, but the errors are generally on full display for the discerning reader to find. The most common fraud is stealing credit for another mathematician's work. It happens occasionally, but probably more often from sloppy literature searches than intent to deceive. The most interesting case of mathematical fraud that I have personally encountered arose in the humanities, in the course of a promotion review.

At most universities the promotion and tenure process has multiple stages. The candidate must first be approved by his department; after departmental approval, a broader university committee considers the candidate. The university Appointments and Promotions committee has less expertise than the departmental committee, but allows the university to monitor the departments' quality control, guarding against friendship overriding scholarly judgment and against mediocrity reproducing itself. Over a decade ago, I was asked by such a committee to help review a promotion decision at the university where I was then employed. The candidate was a tenured associate professor in the humanities being considered for promotion to full professor. To protect the guilty, let's name the candidate John Smith and pretend his field was intergalactic psychology. I was brought on to the case because the candidate's most important contribution, according to the outside letter writers, was his introduction of `new and important mathematical techniques' to intergalactic psychology, a field previously lacking in mathematical sophistication.

I read the candidate's book on mathematical intergalactic psychology. It introduced techniques from group theory (algebra) and catastrophe theory (topology) into intergalactic psychology.

For the nonmathematical reader, I note that group theory can be thought of as the study of symmetries of various sets. For example, consider a square with vertices in counter clockwise order: A,B,C,D. The simplest symmetry is rotation. For example, we can rotate the square, moving vertex A to vertex B's position, vertex B to vertex C's position, C to D's position, and D to A's position. Call that rotation, R. If I make the same rotation a second time, then I now have rotated vertex A to vertex C's position, B to D's position, C to A's position, and D to A's position. Symbolically, we write this new symmetry as RR, or better, R^2. The group of symmetries then consists of the set of all symmetries, with a multiplication defined on the elements of the set. The multiplication of two symmetries is defined simply by performing one symmetry after the other.

I immediately found a problem in the candidate's book. In his application of group theory to his theory of intergalactic psychological interactions, the candidate merely counted the number of members in the interaction. He defined no multiplication table on the interactions. Then he said that because the number of members was the same as the number of elements of some group, it must have the same multiplication defined as the group. Totally bogus. This half of the book had no intellectual merit whatsoever. It was gross academic negligence.

The second half of the book was devoted to the introduction of topological techniques to intergalactic psychology. Here I found a new problem. The first chapter of Part II was gibberish. Mathematical words were juxtaposed in a meaningless jumble. I couldn't make any sense of it. Perplexed, I looked up the references. Finally, I discovered what had occurred. It was the most bizarre form of plagiarism I had ever encountered. Prof. Smith had copied verbatim a popular article of a famous topologist, then recast it "in his own words" after the fashion of a grade school child writing a paper based on an encyclopedia entry. He had simply altered one or two words in each sentence, leaving most of the rest unchanged from the original. Unfortunately for Prof. Smith, mathematics is a very precise language. In his casual word substitution, he had rendered the entire article into gibberish. It made no sense. To make matters worse, he had not indicated that he was paraphrasing (?) published work. He merely listed the source in his bibliography.

So, I returned to the Appointment and Promotion Committee with the information that the candidate was a plagiarist and was guilty of either gross academic fraud or indefensible stupidity. The literature professors on the commttee were not bothered by the candidate writing gibberish. They thought it was simply creative to find new - albeit unknown - meanings for mathematical terms. Many of the committee members observed that the fraud had occurred in the work previously evaluated for tenure; our job was to evaluate the subsequent work, which the outside reviewers had praised. I argued that we should remove a fraud whenever discovered. Moreover, the outside reviewers had praised the fraudulent work above all the rest. Didn't this impeach the reviewer's judgment of the subsequent work? Many committee members felt we should not place our own judgment above that of the outside reviewers. Finally, I prevailed. The committee voted against promotion.

The University overruled us, and the professor was promoted.

Sunday, August 1, 2010

GOP politics and religion

Disarray in my local county GOP has led to the formation of a new GOP splinter group, the Northern X County GOP. I attended the NXC GOP's second meeting and was disturbed by what I saw. The bulk of the meeting was devoted to a presentation on the dangers of Islam. I assumed that the discussion would focus on the history of radical Islam or perhaps on recent American confrontations with distinctly un American aspects of Islam such as the American Academy of Pediatrics' flirtation with ritual Islamic female genital mutilation. I was wrong. Instead, the speaker focused on doctrinal distinctions between Islam and Christianity, such as Islam's rejection of trinitarianism and its relegation of Jesus to mere prophet status. The speaker's rhetoric assumed that every person in the room was a Protestant Christian. The discussion was saturated with an us (conservative Protestants) versus them (everyone else) mentality. Adding insult to injury, the speaker was remarkably ill informed.

As a professor, I am daily surrounded by people who aren't conservative Christians. Is it necessary for the GOP to alienate these people on religious grounds? This season of extreme voter upset with Democratic policies is probably the best opportunity in decades to expand the GOP base. Requiring Republican recruits to adhere to a particular religious dogma is foolish in the extreme. Christian conservatives need to remember two principles which will allow them to maximize their political impact.

Principle (i): If your allies agree with your policy, they need not agree with your reasons for the policy.

Principle (ii): Treat the bulk of social issues as state issues. This is both consonant with the founding principles of our country and is effectively a socially conservative position. Most of the left's attacks on traditional social arrangements begin with federalization of the issue. Adhering to the constitutional principle that social issues are state issues allows conservative Republicans to broaden their support at the national level without significant policy sacrifice.

I'll return to the NXC GOP for its third meeting. If I can't persuade them to hold meetings to which I can invite my Muslim, Jewish, and secular neighbors (this is a college town), I will at least push them to rename the group the NXC Christian GOP so that they do not inadvertently discourage potential secular and other non Christian, Republican recruits.