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Wednesday, March 24, 2010

A pay raise for congress

The horrible health bill Obama signed Tuesday is a brutal demonstration of our congressmen's ignorance of economics and constitutional law. We should reward them with a pay raise. The current congressional salary is $175,000. A congressman receiving this salary must maintain two households, one in DC and one in his home district. He leads a life which is extremely harsh for family life, often enduring a commuting marriage. Successful professionals in many fields earn comparable or larger salaries without a massive disruption of family life and without having to listen to Nancy Pelosi every day. Hence, in the absence of a significant greed motive, who is attracted to serve in Congress?
  • Those who love power
  • Those who actually enjoy committee work
  • Those who are unable to succeed in other professions
  • Those with no family life
  • The independently wealthy
  • Saints and retirees
I would like to see more honestly greedy, successful, intelligent candidates attracted to office.

As long as we are attracting more talent with monetary incentives, why not introduce a reward structure that encourages positive outcomes. Let's double congressional salaries to $350,000, but let's make the last $125,000 a bonus for work well done. For example, to earn the bonus, Congress must balance the budget. Perhaps a segment of the bonus should also depend on rising GDP (although given the time lag between votes and economic outcomes that idea has some equity issues.)

I like this bonus idea. Let's extend it to Social Security. Let's raise the social security payments significantly, but only as a bonus. The bonus is once again dependent upon a balanced federal budget. I suppose this abuses the usual concept of bonus, since our seniors are not all intimately involved in setting our economic policy. On the other hand, it would certainly provide a strong incentive for seniors to vote for sound fiscal policy. (Of course, in order to balance the budget, they would probably first vote to exclude my generation from social security.) Should we introduce welfare bonuses next?

Perhaps these ideas are more suitable for an essay by Swift than a policy prescription, but contemplating them is more fun this week than imagining the future of my family's medical care.

Sunday, March 21, 2010

Women in Mathematics

After posting my note on Math and Gender Bias, I received numerous comments which indirectly echoed Larry Summers' famous remarks in 2005 suggesting that innate biological differences limited the role of women in mathematics and science. Even in 2005, Summers' remark was somewhat disconnected from the data. I thought it might be useful to compile a few relevant numbers to dispel misconceptions about the role of women in mathematics.

According to the Notices of the AMS, (vol 51, no. 7), by 2003, women received 21% of Ph.D.s granted by the top 48 U.S. mathematics departments (as ranked by the National Research Council), 27% of the Ph.D.s granted by the next (ranked) 56 departments, and 26% of all mathematics Ph.D.s. Last year, 16% of the (over 800) job applicants to our department were female, and women comprise receive a comparable percentage of our job offers.

What do these numbers suggest about biology and mathematical ability? For the ten years preceding 1991, women received approximately 17% of doctorates in mathematics. Anyone positing that the fact that women represent only 26% of all mathematics Ph.D.s is evidence of a significant biological difference must also argue for dramatic genetic changes over a 12 year time period leading to a 50% increase in women's representation among Ph.D. recipients. It is hard to avoid the conclusion that social influences play a dominant role in these numbers.

Looking beyond these numbers, it is also true that there are ever more women who are the - or among the - leaders in their fields. So, the numbers are not merely evidence of competence. The impact of women on the field is continuing to grow.

The hot political question is: "Do universities discriminate either for or against women in their hiring?" I have certainly not seen evidence of institutional discrimination against women. A decade or more ago, I was occasionally annoyed by letters of recommendation which compared female job applicants only against other women. These were probably clumsy attempts to aid women, which I viewed as counterproductive. I haven't seen such letters in recent years. I do believe that there is a premium paid for female candidates. There are two simple ways to pay such a premium: cash or prestige. A candidate may earn a higher salary or gain a more prestigious position than might be predicted by research accomplishments alone. There is no reasonable way to measure the latter; so, I will not consider it here. I have, however, heard university administrators advocate the cash premium. My conservative colleagues can have little quarrel with this premium. There is competition for the best female job candidates, which drives up their salaries. A university donor, a trustee, or tuition paying student may argue whether or not having more women on the science faculty is worth a small salary premium, but if the premium is not paid in prestige, it does not affect the department's research reputation. I think this is ultimately a nonissue, not really deserving significant attention from conservative thinkers.

Thursday, March 18, 2010

Sloppy conservative critics of universities

In an incredibly intellectually sloppy analysis, Peter Berkowitz launches another confused attack on universities, careening from Climategate, to core curricula, to inadequacies of the peer review process. His discussion suffers severely from his attempt simultaneously to treat disparate fields from the humanities to the hard sciences.

I greatly enjoy the Climategate spectacle and have no particular opinion on common reading requirements. (I have no objection to students being well guided in their bedtime reading.) Berkowitz's discussion of curricular issues is too incoherent to address. So, I will focus today on the refereeing, hiring, and promotion processes.

Unlike Berkowitz, I have only been involved in refereeing for mathematics and physics journals. I do not share his apparently all encompassing expertise in the different review standards practised in the humanities, the social sciences, engineering, and medical journals - although I do hear some gossip. I defer to the fascinating tales of Alan Sokal for insight into the publication standards in cultural studies. In mathematics, most papers submitted to journals are sent to one or two referees. The chosen referees are experts in the fields germane to the submitted paper. If they were not experts, how could they possibly assess the correctness, importance, and originality of the paper? This can be an extremely difficult job - even for the expert. Berkowitz asserts that their expertise disqualifies them from impartiality because they are necessarily competitors. Scientists are human, and there are a few bad apples, but in mathematics they are rare. Most mathematicians I know have one or two stories of referee abuse. I have my own, but a handful of negative experiences over decades of work does not suggest the enterprise is corrupt - merely human. More common than abuse is simple human error. I have had authors complain about my understanding of the importance or accuracy of some argument, and amazingly, sometimes I decide that they are correct. Despite my expertise, I have made an error. I communicate my error to the editor, and the paper gets published. More often, the author of a rejected paper simply submits it to a different, perhaps less prestigious, journal. It is worth noting that in the internet age, there is less incentive for a referee to engage in hanky panky. Mathematical scientists of many stripes post their papers first on the arxiv , where it is rapidly disseminated throughout the community. Discarding refereeing because of the occasional failures is like the left condemning all business because an occasional Enron blows up.

Berkowitz is correct in stating that
"departmental colleagues are regularly asked to evaluate scholarly work in which they have little more expertise than the man or woman on the street. Often unable to form independent professional judgments—but unwilling to recuse themselves from important personnel decisions—faculty members routinely rely on confidential letters of evaluation from scholars at other universities."
In fact, in my department this is more often the case than not, for both hiring and promotion. (Well, the statement about the man or woman on the street is clearly a gross exaggeration). Rather than hiring our intellectual clones, we try to expand the expertise of the department by hiring scholars whose expertise is different from our own. We absolutely depend on the advice of the leaders in the field. Amusingly, an important part of our expertise is now social. We need to know which leaders are consistently overgenerous in their praise, which push their own students, and who is sparing in their praise. If we recused ourselves, who would make the hiring decisions - our office staff?

Berkowitz's piece achieves a level of incoherence I expect from the left, but I expect better from my conservative colleagues. For many (read the NRO for example), their upset with the undeniable (far) left tilt of academe leads them to ill informed and poorly argued attacks on the universities. It ill serves them. Editors stop using referees when they are given reason to suspect their judgment; so too do readers stop attending to writers who weaken their credibility by spouting nonsense.

Wednesday, March 10, 2010

A mathematical perspective on snowflakes and global warming

Surprisingly, I have never heard support in the Mathematics faculty lounge for the global warming prognosticators of doom. I admit to baiting my colleagues on occasion with the standard game - attributing assorted random, ridiculous phenomena to global warming. None take the bait. My colleagues have been inoculated against much of the global warming hype by their prior exposure to bad mathematical modelling.

In the '90s, many applied mathematics groups wanted to hire experts in scientific computing. Computing power had increased so greatly that approximate solutions to many previously intractable problems became computable. Our department invited numerous experts in scientific computation to interview for a faculty position. Many talks took the following form. The speaker would discuss an algorithm for modelling some phenomenon, such as the formation of snowflakes, where the macro level physics was well understood, but how the basic physical laws translated into the observed structure of snowflakes was unknown. The speaker would postulate various mathematical rules for interpolating between the known physical regime and the unknown regime. The origin of these rules was usually obscure or ad hoc, and (key point!) involved numerous free parameters. The speaker would then run his algorithm, showing us many beautiful computer generated pictures, with many choices of the free parameters. The initial pictures looked as much like the Pillsbury Dough Boy as a snowflake. Finally, we would see a series of pictures where the parameters had been tuned to values so that the pictures looked like actual snowflakes, not Rorschach ink blots. The speaker declared victory.

The majority of our faculty agreed that these exercises had no scientific merit. Given any flexible model with enough free parameters, you can tune the parameters to obtain any desired result. It has no predictive value and no explanatory value. We made no hires of these parameter tuners. Most of them ended up working on Wall Street.

Turn now to global warming. What are the issues in the debate?
  1. Does CO_2 cause warming?
  2. Has there been significantly more warming post increase in CO_2 production than before?
  3. If there has been recent warming, is it due to CO_2?
  4. Will CO_2 induced warming lead to harmful consequences?
I have not heard disagreement on the first point. CO_2 has a warming affect. The second point is a question of data, and is the primary focus of most of the Climate Gate scandal. The integrity of the data on whether any significant warming has actually been measured is now suspect. The favorite alternate hypothesis to CO_2 induced warming is that warming is more likely to be a function of variation in solar output. My favorite analogy is that of lighting a match in a room with a furnace. Yes, the match increases the warmth of the room, but it is not as important as the furnace turning on and off. If clean data is ever produced showing there has actually been recent unusual warming, it has no weight unless it is demonstrated that it is caused by CO_2.

Finally we turn to the fourth item, which is closer to my expertise. The actual effect of CO_2 on the vastly complicated climate currently can't be directly known. The system is too large and too many details of the interactions are currently unknown. Hence the global warming brigade produces computer models with numerous ad hoc mathematical rules and many free parameters. They then tune the parameters until they get a snowflake! No, until they obtain any result they desire, from a 20 foot increase in sea level to a prediction of the winner of the World Series. Currently it is unknown if simple models of simple fluid flow give correct long time solutions. There is a million dollar prize for solving this problem. There is no scientific reason to respect these CO_2 models treating a vastly more complex system. Of course, if you want to test a model, the first question is: does it accurately predict the future? (They are constructed so that they always correctly 'predict' the past.) The global warming models have all failed this test.

Until the many microlevel details on how CO_2 and the environment interact (such as the various feedback mechanisms), no computer model can carry much weight. Of course, if one is designed that makes fantastically accurate long term predictions, then we have reason to put aside our doubts. Until these problems are overcome, vote down carbon taxes. If you want to hedge your bets, invest in Canadian real estate.

Saturday, March 6, 2010

Health Care and the Resolution of Cognitive Dissonance

The conservative punditry (eg. Steyn) frequently asserts that once a government healthcare bill passes, it will be virtually impossible to roll back. The American population will rapidly degenerate to a passive, infantile state more commonly associated with European serfs than American pioneers. Our great northern neighbors constitute Exhibit A. According to many polls, Canadians massively support their national healthcare system, even though it enforces severe rationing by means of long queues for basic services. Why will we be different?

Certainly our history with the programs of the Great Society (which struck me as such abominations in my youth but no longer excite the same levels of indignation in my middle years) supports this dismal viewpoint. As an eternal optimist, however, I note several essentially different features of the current situation.

Quoth Wikipedia, "Cognitive dissonance is an uncomfortable feeling caused by holding two contradictory ideas simultaneously. The theory of cognitive dissonance proposes that people have a motivational drive to reduce dissonance by changing their attitudes, beliefs, and behaviors, or by justifying or rationalizing them."

Voters supported the Great Society legislation but were subsequently faced by its manifold failures, such as the creation of a permanent underclass in America. The simplest way to resolve the conflict between their initial enthusiasm and the subsequent disappointing reality was to ignore the failures and inflate the benefits. Similarly, a Canadian (self-definition: not American) takes great pride in his government healthcare. It is one of the primary ways he distinguishes himself from his southern neighbors. When he is treated to extortionate tax rates, multiyear waits for simple surgical procedures, and surgery without anesthesia (as happened to one of my Canadian acquaintances) - when even his elected officials go to the U.S. for their healthcare, he preserves his belief in the the superiority of his system by exaggerating the problems in U.S. healthcare. He believes stories of Americans dying in the streets unable to access healthcare.

The American public has loudly and clearly expressed its hostility to the looming destruction of our healthcare system. Currently, most Americans have no psychological investment in the success of the new government mandates. In fact, the majority, who have been fighting against statist health policies, will view through a microscope every failure of the Democrats' Rube Goldberg creation. They will note every new tax, every premium increase, and every loss of service. If there are any benefits, they are more likely to be minimized than emphasized. It is the nature of the beast. In such an environment, the Republicans taking over Congress this November still have time to reverse the government takeover of the health sector of the economy.

I am not sure what means our new Republican Congress will employ in 2011 to roll back the implementation of the Democratic plan, if it is forced down our throats. I do think we have more time than generally claimed before we turn into a flock of Eurosheep.

Wednesday, March 3, 2010

Politics in the Classroom

Question: should faculty discuss politics in their classrooms, when it is unrelated to the course material?

Students at my University have told me that they have a simple rule for determining the political leanings of their professors: if the professor discusses politics in class, he is a liberal; if he doesn't discuss politics, he is a conservative. Is it unilateral disarmament for the conservative faculty to omit political discussion, or simply responsible pedagogy? I hold the latter view. I feel it is an abuse of the students' time and money to transform a multivariable calculus class into a political rant, and there is not enough time to have both an intelligent discussion of political issues and teach Stoke's theorem.

I have read studies that assert students leave college more conservative than they entered. I have read studies claiming they emerge more liberal. Conservative students who discuss these matters with me tell me that the bulk of the political indoctrination they receive in class consists (for the previous 8 years) of snide remarks about Bush, the stupidity of prominent conservatives, and standard leftist anti-American rants. Students who are influenced by such lowbrow fare are not likely to become great shapers of public opinion, and I suspect will conform to the opinions of their peers in their subsequent business and social spheres. So, I doubt there is much harm done.

In my early career, I did indulge in one minor bit of liberal bashing in my calculus classes. An important concept in physics is that of a conservative force. These forces are distinguished by the property that zero work is done by an object travelling in a closed loop when the object is acted on (only) by a conservative force. After defining this concept, I then dubbed nonconservative forces, liberal forces (not a conventional usage). I then would always observe that when subjected to a liberal force, you generally did work even when you went nowhere (net). Moreover, the most frequently encountered liberal forces, such as friction, work against you, no matter what direction you travel.

With mathematical political humor at this low level, I think it is clear that the propagation of conservative political principles is best served by my leaving politics out of my classroom.