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Tuesday, December 28, 2010

Overproduction of Ph.Ds

The Economist has another article on the overproduction of Ph.Ds. There is no question that many students who enroll in graduate school would be better served pursuing other career paths. The Economist, however, minimizes and dismisses the passion that leads so many mathematicians and other scientists to gamble years of their lives on the wager that they will be the successful researchers who ultimately capture a tenured position. Most mathematicians I have known love mathematics. The Economist says that
"Academics tend to regard asking whether a Ph.D. is worthwhile as analogous to wondering whether there is too much art or culture in the world." This assertion does not ring true to me. To most passionate mathematicians, their love of mathematics is more important than any abstract notion of whether or not there is too much mathematics in the world. In order for an outsider to understand the mindset, imagine the budding mathematician as a close relative of the aspiring musician, athlete, writer, or actor. Each of these knows that only a small fraction of their number will become famous artists or athletes, etc.; yet their love of their craft (or their thirst for fame) drives them to risk years of their lives in pursuit of their dreams. Graduate students in the sciences face far better odds of success than the aspiring actresses and writers who bus tables while waiting for their big break. Moreover, their education buys graduate students an excellent insurance policy. Should they fail to secure a tenured position, many employers are happy to hire these highly educated, driven, and tenacious workers .

In my pretenure days I viewed the academic job market as a meat market. Departments blithely terminated the appointments of anyone whose research did not sufficiently advance the departments' reputations. Criteria for 'sufficiently' were strongly influenced by a department's view of how readily they could hire a better researcher on the open market. My comrades in graduate school all knew the cut throat market we faced, and we each believed (or hoped, depending on personality) that we would be the ones to succeed. Fewer than a quarter of us ended up as research mathematicians. Those who changed career paths included some who seemed to be extremely intellectually gifted, but their personalities or intellectual strengths were not compatible with a career as a mathematician.

As in athletics, the excess of strivers over available positions works to ensure the high quality of the resulting research community. I do not understand how economists and numerous conservative bloggers can understand the virtues of competition (and creative destruction) in business but yet be so appalled by its manifestations in science. I suspect, however, that one constributor to their cloudy vision is that they do not appreciate the sheer joy of doing mathematics and science. It is difficult to monetize joy, especially as this particular joy requires hours of effort incompatible with holding a more remunerative but nonscientific 8AM-6PM job. Conservatives and libertarians object to the intrusion of government into our lives, in part because most big government programs require the noxious implicit assumption that we all (should?) have the same values and priorities as our federal overseers. It ill behooves these same conservatives and libertarians to be distressed by individuals who are willing to make economic sacrifices in order to pursue goals more prized by them than by the staff of the Economist. Let's leave the worship of uniformity in the hands of statists where it belongs.

Sunday, December 12, 2010

Unbundling Health Insurance

Last month I read Mark Pauly's Health Reform without Side Effects, a short book analyzing our health care system. As a recipient of generous employer provided health insurance for most of my adult life, I found Pauly's discussion of the inefficiencies of the individual insurance market the most illuminating section of the book. The treatment of coverage for high risk individuals was also careful, but it led me to realize that health insurance policies contain a hidden component which I have not yet seen analyzed and did not include in my prior post on health insurance. In addition to claims administration, benefit coupons, and insurance against catastrophic illness, insurers are required to include, as part of their insurance plans, an option for the insured to purchase insurance at a later date at a (strike) price that does not take into account the individual's health history subsequent to acquisition of the option. It would be interesting to see how this option would be priced if it were unbundled from the rest of the health care plan.

If I buy healthcare insurance while I am in good health, and then have a heart attack, I feel betrayed if my insurance premiums rise precipitously the subsequent year. Thus I expect my yearly insurance premium to pay both for protection against any catastrophic illness in the policy year and for an option to purchase insurance in subsequent years at rates set for healthy adults of my age. If this option feature of insurance were made explicit, more carefully defined, and separated from the rest of the policy, people could decide exactly what such an option is worth. Insurers might then offer `points' on insurance like bankers do on mortgages. Paying a certain number of points in advance, one can lower the nominal interest rate on a mortgage. Insurers could sell points that allowed one to buy insurance at rates set for lower risk individuals. What purpose could such points serve since insurers would have no incentive to sell points at a lower cost than the difference between the premiums for the buyer's actual risk level and the desired lower risk level? Points introduce the possibility that an entity other than the insurer could sell the option contracts. Options would essentially become options to purchase points. Assuming competition kept point costs fairly uniform, sellers could offer `universal' options which could be exercised at many large insurers. An immediate benefit of such an unbundled system would be increased portability of insurance. If an employer's insurance plan provided an explicit option, then a high risk employee who wished to leave his job need not worry about a subsequent dramatic increase in insurance costs. He would simply exercise his option at his new place of employment (or in the less efficient individual insurance market).

Unbundling of options might lower their cost. If you wish to purchase an option today which cannot be exercised for ten years, then the seller of the option will factor in ten years of returns on investing the option premium when pricing the option. (Of course you must also consider your loss of use of the funds for ten years in valuing the purchase.) In buying insurance, we know we should rationally only purchase insurance for catastrophic events unless our insurance is subsidized. If you can afford to pay 2 years of the higher insurance premium charged to high risk individuals, perhaps you would only wish to purchase options which cannot be exercised until three years after the date of purchase, decreasing their cost further.

None of the potential savings consequent to the decoupling of options from insurance plans is large enough to offset the price inflation associated with third party payment of basic medical services, but the concept introduces numerous ways to decrease cost and increase flexibility.

Sunday, December 5, 2010

Leroux and Global Warming

For a change of pace I have added Marcel Leroux's Global Warming - Myth Or Reality? to my bedtime reading. I don't recall why I chose this particular climate book from the shelf, but it is published by Springer, a publishing house respected by most mathematicians. In general it is difficult for an outsider to establish the reliability of a putative expert in a distant field. In fields in which I have some expertise, I frequently see the media promote extremely marginal scientists as expert spokesmen. Given the extent to which climatology appears to foster charlatanism, I am wary of all authors in the field.

I was especially eager to read Leroux's treatment of climate modelling. I have already written on why mathematicians are wary of the computer simulations responsible for the alarmist gloom and doom scenarios which lead so many people to advocate wrecking the world economy, abandoning democracy if necessary, in order to limit CO_2 output. My post on this subject dealt only with those universal features of the simulations that one could address without delving into the details of the models. I hope Leroux will shed more light on the nuts and bolts of the models.

Leroux's treatment of models (Chapter 7 of his book) is tinged with an antipathy to models qua models, which I consider misplaced. My objections are simply to the abuse of models. Leroux does provide us with more information about the models and their defects, although I assume that details such as grid sizes change monthly or yearly. I will rephrase and repackage Leroux's more coherent criticisms into a more mathematical framework.

Computer simulations of climate phenomena require dividing the atmosphere into a collection of volumes known as cells and assigning numerical data to each cell representing 'average' climate data for that cell for some time interval. At the time Leroux was writing, typical cell size ranged from hundreds to tens of thousands of cubic kilometers. He does not mention the typical time interval involved. Obviously, the smaller the cell and time step, the more reasonable is approximation of the climate within by some average. Ever increasing computer power is the only inherent limit on the number and therefore the size of the cells. Ideally, we would like to start with some initial approximate climate state, and compute the approximate evolution of the system by numerically approximating the solutions to the complex nonlinear fluid dynamics and other equations governing the system. Any phenomena which take place at smaller time or space scales than the time intervals or cells of our simulation cannot be modelled. Of course one can model such phenomena with a simulation adapted to the given phenomenon. Thus one could not use a simulation designed to model a century of global climate evolution to model the path of a hurricane. Instead, one uses a model adapted to the time and space scale of the hurricane, and corrects the simulation with new information several times a day.

In addition to errors arising from cell size and absence of real world initial data, climate evolution includes too many interactions to include in a realistic deterministic model. For example, the quantity of the main greenhouse gas, water vapor, depends on temperature, pressure, particulate matter, surface water, plant respiration, etc. These do not all admit simple modelling with numerical partial differential equations. Those features which are too complex for current deterministic models are ignored (the most honest path) or added into simulations by ad hoc mechanisms. These latter admit fine tuning to reach any desired conclusion.

Another source of error in simulations is the fact that the earth is not a closed system. Time varying solar radiation is the fundamental driver of our climate, but I am unaware of the existence of climate models that include realistic simulations of the complex dynamics of the sun's nuclear reactions.

Leroux appears to be bothered by the deterministic attitude of the climate modellers, a concern which I do not share. It seems reasonable to me that the extremely complex large scale dynamics of our climate stem result from small scale fundamental physical and chemical processes. Nonetheless, it is clear that since current climate models that are adapted to short time predictions are only crudely accurate for a few days, long term predictions have no value.

The more of Leroux I read, the less reliable he appears. His logic is generally quite poor. He frequently points out some weakness in the arguments of proponents of anthropogenic global warming, and then immediately concludes that CO_2 does not cause global warming, when, in fact, he has only countered an argument in support not actually presented an argument against. He also has a worrisome single factor explanation for most features of our climate. All phenomena of interest can be explained (according to Leroux) by his contribution to climatology: mobile polar highs. I have checked out a few books on atmospheric physics to make myself somewhat better able to analyze his claims. From my currently inexpert position, many of his assertions seem to be the atmospheric equivalent to the assertion that water runs down a mountain into a valley because the mountain is higher than the valley, and not because the valley is lower than the mountain. Such a distinction makes no sense to me; so, I need to learn more. Fortunately climate books are much lighter reading than math books, and hence can be read before bed without stimulating the brain enough to interfere with sleep.

Sunday, November 7, 2010

Liberal Outpost

Well, we won nationally but were thumped locally. After the election returns were in, I remembered one of the reasons I had been inactive in local politics in previous years: it is hard to feel like you can make a difference in such an extremely Democratic district. There did not seem to be much return on months of canvassing. We did, however, do better than we have in any year since 1994. It will be interesting to see if the bump outlasts the Obama presidency. If the Democrats stay this far to the left, then perhaps the local GOP can win some elections.

This is the first canvass free/conference free weekend in months. It feels great. I will have my week's lectures written by Sunday evening. I expect a pop in math output too. Clearly politics do not mix brilliantly with research - too distracting.

Amazingly I have heard nothing about the election in the faculty lounge for months. Perhaps my colleagues simply preferred not to think about the approaching wave. Wednesday I heard exactly zero comments about the election at work.

In one last attempt to help the candidates, I volunteered to electioneer for 4 hours on Tuesday, after my various University commitments were fulfilled. I was sent to pass out GOP literature at a polling site uncomfortably close to campus. I saw one overt Republican all evening. I arrived hours before the evening rush, too early for electioneering. I was not joined by other electioneers for over an hour. All the others represented liberal groups. Most were pleasant, and perhaps amused at my quixotic efforts. One lady, however, responded to my pleasantries with the revealing question: ''How can someone be a Republican?" I told her that it was difficult for anyone who understood economics or who objected to the government dictating the minutiae of his life to to be otherwise. She then launched on 'the Party of No' and castigated the GOP for opposing the healthcare bill. The discussion reminded me of grad school days. When I pointed to specific features of the bill I found objectionable (although I am opposed in principle to more or less the whole package) she would more often than not deny the existence of the offending feature. Clearly ignorance and denial are essential features for maintaining the liberal belief system.

Unfortunately, her belief system triumphed over mine in the local elections that night.

Sunday, October 31, 2010

Fraud in the Voting Booth?

My county, like so many Democratic counties, has a long history of voting irregularities. It is hard to guess what impact this has on elections since the Democrats massively outnumber the Republicans anyway. This is my first year experiencing this first hand, and I am not sure how to interpret what I see.

Last weekend was the end of canvassing walks. This weekend I decided to substitute phone banking for walking. I am not overly fond of the phone and would rather contribute in most any other way to retiring the Democrats this election, but clearly phoning voters and urging them to the polls was the way to contribute yesterday. I settled in at GOP HQ with a bounded but seemingly infinite list of phone numbers to call. Shortly after I began calling to urge voters to the polls, a distraught woman dashed into headquarters. She was a designated GOP poll observer at the nearby polling site (early voting). She had arrived a quarter of an hour before the legal opening of the polls to find voters already filling the voting booths marking their ballots. When she identified herself and asked what was going on, the Democratic election officials barred her from the polling place. Happy for a reason to leave my phone, I trotted up the hill to the polling site and asked the GOP electioneers whether things were proceeding appropriately. They were (appropriately) barred from the actual polling site, but were able to confirm that the polls had opened early. I returned to HQ and phoned the county GOP chair to have him file a complaint.

Was anything wrong actually taking place? I don't know. Election officials may have decided to open early to accommodate the long lines of voters waiting to cast their votes. On the other hand, they may have opened early in order to open before the GOP observers and judges were in place. Perhaps ballots sans voters were fed into the machine before the GOP witnesses arrived. Perhaps not, but years of Democrats cheating at the ballot box makes a man paranoid. I have not yet heard the outcome of our chairman's complaint.

I returned to my phone and my finite but large list of GOP voters. I have learned on my walks not to identify myself as a GOP volunteer after hearing one time too many, ''Which ones are they, the Republicans or Democrats?" I now identify myself as an X County Republican volunteer. A few score calls later, the X County GOP secretary arrived at HQ. I had a bone to pick with her. Earlier that week I committed a cardinal error of life in our modern world; I sent her an email with my analysis of the vote numbers we had seen so far and their implications for our candidate (better than other people believed). Included in the email was a sarcastic comment about one of our underperforming candidates. The secretary liked the analysis and emailed it to the entire X County GOP, all the candidates, and our district officers too. Perhaps she emailed it to the WSJ too, but I haven't checked.
I was too amused to be really annoyed, but I did have to ask what the underperforming candidate said. Apparently he was not pleased, but he has a good sense of humor, and I am sure he will find it funny (but perhaps not for several weeks). I asked the secretary, tongue in cheek, if she was trying to get me kicked out of another GOP organization.

If you are a Republican (and a U.S. citizen and registered voter) and haven't voted yet, get out and vote Tuesday. If you are a Democrat, spend Tuesday curled up with a good economics text. If you are a visitor from Europe, Asia, Australia, or Africa, I am not sure why you read my blog entries on local politics, but hello, glad to have you here.

Sunday, October 24, 2010

Milton Friedman's Twist on Hayek

Milton Friedman's Capitalism and Freedom has succeeded Boaz as my political bedtime reading. In my political readings thus far, I have been impressed and educated by Hayek's careful analysis of socialism, aggravated by Von Mises' sloppy analysis of liberalism, and much provoked to thought by Boaz's modern presentation of libertarian principles and their applications. Friedman, however, has been less exciting. Reading Friedman reminds me of reading Shakespeare and remarking on all the 'cliches'. Perhaps Friedman's impact on our current economic thinking has been so strong that his analysis now seems commonplace. I was, however, struck by an observation in Chapter II: The Role of Government in a Free Society. Friedman notes that government action, unlike market action, imposes conformity. The greater the scope of government action, the more areas in which people are forced to conform. Extending the range of the imposed conformity too far works to undermine social cohesion and generate conflict. This is reminiscent of Hayek's assertion that the massive legislation required to implement socialist economic policy is incompatible with democracy: the vast scope of the legislation makes it exceedingly unlikely that a majority can agree on any economic plan, leading socialist proponents to circumvent the democratic process in order to impose their program. (Of course, our current congressional leadership has obviated this obstacle by the simple expedient of convincing the Democratic majority to vote for enormous bills without actually reading them.) Friedman transfers Hayek's assertion from the House and Senate to the electorate: the greater the number and impact of government intrusions into citizens' lives, the more likely any given individual will be strongly opposed to some aspect of government action, with possible consequent disruption of society.

While I find Friedman's extension of Hayek's assertions intriguing, I have not seen much evidence of consequent social disruption. The Tea Party movement suggests that large numbers of Americans have decided that government intrusion into their lives has indeed exceeded their tolerance. Observe, however, that the response is political rather than social. I am not sure what form social disruption is supposed to take, although visions of rioting and striking French workers come to mind. Of course Europeans accept with little protest dramatically greater government control over their lives than Americans endure. Their history, however, differs from ours; in particular, they have never experienced the degree of individual liberty that Americans have long enjoyed and taken for granted. A great conservative fear at the time of the passage of Obamacare was that Americans could be lured into the same servile attitude towards the government.

When wondering how much government intervention American voters will tolerate, one is led to ask to what extent voters accept government impositions simply because they are advocated by their 'team' (i.e. political party)? In the same vein, as most of us ask as soon as we become politically aware, why are attitudes toward homosexuality, immigration, carbonophobia, class warfare, etc. linked? Presumably people choose their positions on issues based on their party affiliation at least as often as they choose their party affiliation based on their stands on issues. Perhaps the rise of the unaffiliated voter is important to consider in this context. As government reach expands, political parties must take stands on an ever wider variety of issues. Perhaps it is becoming ever harder for many Americans to affiliate with either major party; there are simply too many axes of potential disagreement. Unfortunately, opting out is a poor choice. The unaffiliated have little impact at the primary level; so, they share responsibility - through inaction - for the poor choices we often face in general elections. Once again I am led to appreciate the increased voter participation represented by the rise of the Tea Party movement. If the Tea Partiers are successful in rolling back government overreach (admittedly a long term project), then an amusing consequence could be a rise in voter identification with both parties. When the Republicans and Democrats no longer need to take stands on whether it is better to allow a hip replacement at age 70 instead of state of the art cancer drugs at age 75, it will be easier for voters to find a party with which he has no deal breaking disagreements.

Monday, October 11, 2010

"Let all things be done decently and in order."

Both Democrats and Republicans exhibit peculiarities in their candidate selection. Democrats have strong servile tendencies. They like to elect aristocrats, and they refer to their elected representatives as 'rulers'. With the name Kennedy, any charlatan is eligible for Democratic nomination to high office. The Bush dynasty shows the GOP shares this tendency to a lesser degree. The Democrats swoon for their candidates; their candidates "make their knees weak." Before the Tea Party, on the other hand, the GOP often seemed to regard nominations as a reward for services rendered; there almost seemed to be a queue, with candidates 'entitled' to the nomination, simply because they were, by some measure, next in line. How else can you explain nominating candidates like Bob Dole or John McCain, who seemed embarrassed by political principles?

Perhaps the 'reward for services rendered' interpretation was naive. As I became more active in the local GOP this year, I learned to appreciate the great power of name recognition in seeking support from an often uninterested electorate. Perhaps the 'next in line' were simply the best known.

The rise of the Tea Party promised an overthrow of the queue. In primary after primary, the 'entitled' GOP candidates were rejected. Unfortunately, in my county GOP, I have witnessed precisely the entitlement mentality that I had naively speculated was the source of Bob Dolian candidates. An important function of our county organization is to endorse candidates in nonpartisan races. In one nonpartisan race we considered recently, we had two Republicans competing. Our evaluation committee reported that one candidate had previously held the position, but was removed from office after committing a criminal offense. The other candidate was new to politics but boasted the sort of business and professional background which usually appeals to GOP voters. I was the only vote opposing the candidate with the criminal background. His appeal? He had more experience.
It was uncharitable to hold his prior offenses against him. I was unaware that the county GOP was a charity. I was appalled. After the meeting was over, I realized that not only were we rejecting a promising new candidate, but that our endorsement of the criminal could potentially cast doubt on all our endorsements of strong candidates. What happens to our credibility when a careful voter sees that we recommend criminals?

I felt culpable afterwards for failing to successfully convince my fellow Republicans. I have learned that the manner of argument suitable for faculty debate is not very successful in political forums. Oh well, maybe next time.

Sunday, October 3, 2010

Crypto vouchers and For-Profit Colleges

This weekend I had so many deadlines piling up on me that I decided it was the optimal time to research the for-profit colleges, which have been crowding the educational policy sector of the blogosphere of late. Many conservatives and libertarians, while deploring the distortions caused by government funding of (for-profit and traditional) college education, express an interest in the for-profit education sector - an interest which I suspect is nurtured by their distaste for the liberal academics dominating traditional universities.

I had no prior knowledge of for-profit colleges other than the emails they occasionally send me asking me to recommend potential math faculty to them. My biases are what you might expect - I assumed that these were just diploma mills providing little or no education. My research topic was : what does a math major look like at a for-profit? My research tools went no further than Google. I only looked at a few of the larger for-profits, such as Phoenix and DeVry.

My first discovery was that the larger for-profits I examined are amazingly opaque. You cannot find the lists of courses readily available on traditional universities' web sites. Faculty lists at Phoenix are arranged by college rather than by department, meaning you have to sift through a data dump, if you want to determine who teaches math. Even finding what math courses they offer is difficult. Every query on their website seems to offer different answers. I felt like an accountant hired to assess Enron. The only consistent answer to my queries was : every math course I found was no higher than the level of courses offered by a large public high school; the descriptions sounded lower level than what you would find at a good public high school. Conclusion: within my area of expertise and my narrow investigation, these schools are essentially high schools.

This discovery puts the discussion of government funding of for-profit education in a rather different light. We should really view it as a vast federal government experiment in educational vouchers for private high schools. I have long advocated state funding for voucher programs; federal funding is perhaps constitutional overreach. I think this program, if continued, would be greatly improved if it was extended to all private high schools, and not restricted to those labelling themselves as universities. This would allow students to use the tuition money to obtain an excellent education before college.
(My apologies to all those for-profit colleges of higher quality than the handful I probed.)

Sunday, September 26, 2010

Marriage Buffet: A Solution in Search of a Problem

I generally prefer to steer clear of social issues here, especially as a mathematical perspective does not often add illumination to them. Discussions of same sex marriage, however, always lead to the question: what harm does it cause? The answer I most often hear is that legalizing marriage between same sex couples will degrade the institution of heterosexual marriage. My attempts to analyze this answer thus far leads only to the creation of spherical horses.

In order to understand the threat to marriage posed by a government action, we first must consider marriage's relation to the government. Libertarians often argue that government should play no role in matters as inherently personal as love and marriage. A natural libertarian position might then be that the government should recognize no marriage - heterosexual or straight. In fact, libertarians often argue that marriage should exist solely as a religious sacrament. I think this argument is attractive on the surface, but fundamentally incorrect.

Every libertarian I have read asserts that government should protect citizens' property rights. Consequently, the government must prevent fraud and help enforce contracts. From my perspective, the most important contract most people enter into is the marriage contract. Unfortunately, the terms and conditions of the contract have become so weak and vague that it is now essentially ceremonial. Question: does this loss of a clear marriage contract fundamentally degrade the institution of marriage? One way to approach this question is to ask what form an optimal marriage contract should take. What sanction does our society impose - what sanction should it impose - on the man who blithely discards his wife of twenty years and three children, replacing her with a younger lady who catches his eye? Should inability to conceive or bear children constitute grounds for dissolution of a marriage? I don't pretend to have answers for such questions and doubt a satisfactory single answer exists in our pluralistic society, but if a couple is be able to agree to the answer before they wed, then why shouldn't the government help enforce that contract like any other? Of course prenuptial agreements exist, but are generally considered distinct from the marriage contract. Perhaps the Catholic and Presbyterian churches should each offer their own approved marriage contract. Perhaps the Sierra Club and National Public Radio could offer their own approved standard marriage contracts too, each with its own list of duties, grounds for dissolution, and penalties for violation. If corporate America can impose noncompete contracts, why can't similar terms be included in a marriage contract: if you leave without grounds, you can't remarry for n years. The possibilities are endless and entertaining to contemplate.

Unfortunately, I do not see what current difficulty such a buffet of personalized choices remedies. I suppose that many engagements would terminate short of marriage when the loving couple is unable to agree on what type of marriage they are entering. When I began toying with the idea of more specific and varied marital contracts, I was thinking of the negative effects of the current very loose divorce laws. However, I'm not sure I would want my spouse to remain with me out of fear of contractual penalties rather than from delight in our mutual companionship. (Of course, someone else may feel differently, in which case the lack of resonance of the idea with my personal situation actually supports the argument for more species of marriage.)

So, I haven't managed to shed any light on any of the questions raised. Classes have begun here. Perhaps I will have to wait until the next class break to actually solve any (nonmathematical) problems.

Sunday, September 19, 2010

Extracting Splinters or No Mathematician Need Apply

For the second time in my life I have been asked to leave a volunteer organization. Ouch. The chairman of our local GOP splinter group, the NXC GOP, has requested that I never again attend one of their meetings. This has been the occasion of much hilarity at home and in my county GOP organization.

The first time I was evicted from a political organization, I was a young assistant professor in my first tenure track faculty position. I joined a group of conservative faculty members who met regularly to discuss politics. The leader of the group was a chain smoking Polish emigre professor, who was obsessed with communism and the USSR. We met in his house just a few blocks from campus, its walls yellowed by the never ending plumes of smoke rising from his cigarettes. I was as happy to discuss the USSR as the next person, but it was not my sole interest in life. I pushed to broaden our discussion and activism (in this group, I recall the activism never graduated beyond tongue wagging) to include other issues. In particular, I broached the issue of educational vouchers. Professor Chimney was initially casually dismissive of my suggestion but was subsequently shocked to see that most of the group expressed interest. At the meeting he suggested I research vouchers and lead a discussion at our next meeting. A few days later he called me up and said he did not want 'country club' Republicans like me at his meetings and invited me to leave his group, which I did. Never before or since have I heard the claim that interest in educational vouchers was a defining feature of 'country club' Republicans. Nonetheless, as the group never actually did anything other than talk, I did not mind my forced exit.

Two decades later I have been dismissed from another political group. I have been attending meetings of the Northern X County GOP (NXC GOP). The chairwoman of the NXC GOP is a former campaign director for the loser in the GOP congressional primary in my district. As I have written before, her candidate was an unappealing nativist whose possible nomination I considered harmful to the local GOP. I believe that her goal is to create an organization which can rapidly transform into a campaign organization for him should the current GOP nominee lose. She is hostile to efforts to aid the duly nominated candidate and always structures the NXCGOP's efforts so that they exclude our congressional candidate. With less than a month and a half left before the election, her agenda for our last meeting was the recruitment of candidates for the 2011 municipal elections. (She had neglected to observe that half her membership did not even live in the city limits and therefore could not even vote in the municipal elections.) I have been attending these meetings with the goal of keeping the group in the GOP camp. I frequently announce opportunities for its members to participate in canvassing and other services for our duly nominated candidates. I did not believe the chair wished to make her hostility to the nominated congressional candidate explicit to the group's members, who are not generally partisans for the loser. This left me with room to promote our nominee. Last Thursday, I apparently exhausted her patience. At the beginning of the meeting, I observed that I had not seen many members of the group canvassing on Saturday mornings. The room turned to ice, but little more was said on the subject, except for the reasonable observation that many of the members were working on other campaigns (but for 2012?). I thought no more of it until the next morning when I received an email :
Thank You for showing an interest in our organization. Regretfully, you and the
NXC GOP are not a good fit. We respectfully request that you not
attend any future NXC GOP meetings.

Oh well, at least she didn't accuse me of being 'country club'. My family and the county GOP have been ribbing me ever since. My family observes that I am the only one they know who was threatened with violence by a high school teacher after disagreeing with him on a school advisory committee. So, perhaps my willingness to disagree with people (endemic in the mathematics community) also played a role in my latest expulsion. Luckily, I can counter with the observation that I was not expelled until I brought my wife to a meeting. (She attended her first NXC GOP meeting last Thursday). Perhaps her attendance precipitated my forced departure. She has agreed to test this hypothesis if the county organization gives me too many assignments. If I become overburdened, she has offered to attend her first county meeting and see if this leads to expulsion number 3.

Sunday, September 12, 2010

Walking the Streets: First Time Canvassing

The last two Saturday mornings I have been walking the streets of my precinct with lists of Republican voters with a history of skipping midterm elections. My assigned task is to ring doorbells and encourage the targeted voter to pledge to vote early; secondarily, I provide information about our congressional candidate. The goal of early voting is simple. During the early voting period, the GOP congressional campaign checks its list of each day's voters against its list of all GOP voters, especially pledged early voters. Volunteers then email or call to harass pledged voters who are procrastinating. The more voters who vote before election day, the easier the Get Out The Vote effort on November 2nd.

My first time out, approximately half of the voters I visited answered their doors. I assume many more were there but did not answer a stranger ringing their doorbell. I often refuse to open for visitors bearing clipboards; so, I can't fault others for ignoring me. I decided it was a bad idea to ring twice after this produced a few women not yet dressed for the day and obviously annoyed at being pulled to the door dishabille. I won no new voters at those houses. Those who did answer their doors (on the first ring) were almost uniformly enthusiastic. They pledged to support the GOP candidate. They pledged to vote early. When probed, however, they were unable to identify their polling sites; so, subsequent monitoring appears to be desirable. The exception to the enthusiasts were the Democrats who had moved into the houses of some Republicans on our lists. Of course, I didn't encourage them to vote early (or at all). They were all polite, however, and did not harass the poor volunteer.

The next Saturday I hit the streets again. The targeted neighborhood looked economically depressed compared to the previous week's walk. This time very few doors opened, and nobody pledged to vote early. Most had never even heard the name of our congressional candidate. I have no idea whether the difference between week one and week two was random, a function of the calendar, or a function of socioeconomic differences. I'll collect a few more data points in the coming weeks before I offer an opinion. Like the previous week, everyone was polite, including the Democrats living in former Republican houses. I had a few amusing interactions. At one house, I asked if Mrs. Jone's lived there. The woman who answered the door thought for a minute and then said, 'No, I don't think so - not really.' I wondered what partial state of residence could make the question subject to internal debate. At another house, I asked the elderly grey haired woman who answered the door if she was Jane Smith. She said no, and then called: 'Momma. There's someone here to see you.' Henceforth I'll reserve 'elderly' for the white haired. At the last house on my list, the door was answered by a portly bare chested (and bellied) man, who told me his wife was a Republican, but he was registered as a Democrat. He said, 'I'm actually a Republican, but have to register as a Democrat for personal reasons.' In a liberal town like ours, it's easy to imagine his reasons, including a desire to prevent politics from hurting his business prospects. Perhaps he contracts with the government. I didn't probe but left curious.

Unsurprisingly, my doorstep spiel became more fluent with each new house. By the time November rolls around, I will be so comfortable with cold calling strangers that I can become a vacuum salesman should I ever have to quit mathematics.

Sunday, September 5, 2010

How much is a college diploma worth?

Recent weeks have produced a constant stream of articles and blog posts attacking the value of a college diploma. Given the low quality instruction my children endured at various points in their middle and high school careers, I can at least recommend many colleges as a good place to get a decent high school education. To support their assertion that college diplomas are overvalued, the blog discussions generally cite anecdotes of college graduates who are waiting tables or are otherwise underemployed. The terms of the discussion are always too vague to support a coherent argument; so, let's see if we can add clarity to the noise.

A quick internet search yields the following useful Wall Street Journal data on salaries by college major.
Undergraduate Major Starting Median Salary Mid-Career Median Salary
Mid-Career 10th Percentile Salary Mid-Career 25th Percentile Salary Mid-Career 75th Percentile Salary
Accounting $46,000.00 $77,100.00
$42,200.00 $56,100.00 $108,000.00
Aerospace Engineering $57,700.00
$64,300.00 $82,100.00 $127,000.00
Agriculture $42,600.00 $71,900.00
$36,300.00 $52,100.00 $96,300.00
Anthropology $36,800.00 $61,500.00
$33,800.00 $45,500.00 $89,300.00
Architecture $41,600.00 $76,800.00
$50,600.00 $62,200.00 $97,000.00
Art History $35,800.00 $64,900.00
$28,800.00 $42,200.00 $87,400.00
Biology $38,800.00 $64,800.00
$36,900.00 $47,400.00 $94,500.00
Business Management $43,000.00 $72,100.00
$38,800.00 $51,500.00 $102,000.00
Chemical Engineering $63,200.00 $107,000.00
$71,900.00 $87,300.00 $143,000.00
Chemistry $42,600.00 $79,900.00
$45,300.00 $60,700.00 $108,000.00
Civil Engineering $53,900.00 $90,500.00
$63,400.00 $75,100.00 $115,000.00
Computer Science $55,900.00 $95,500.00
$56,000.00 $74,900.00 $122,000.00
Drama $35,900.00 $56,900.00
$36,700.00 $41,300.00 $79,100.00
Economics $50,100.00 $98,600.00
$50,600.00 $70,600.00 $145,000.00
Education $34,900.00 $52,000.00
$29,300.00 $37,900.00 $73,400.00
Electrical Engineering $60,900.00 $103,000.00
$69,300.00 $83,800.00 $130,000.00
English $38,000.00 $64,700.00
$33,400.00 $44,800.00 $93,200.00
Film $37,900.00 $68,500.00
$33,900.00 $45,500.00 $100,000.00
Finance $47,900.00 $88,300.00
$47,200.00 $62,100.00 $128,000.00
Forestry $39,100.00 $62,600.00
$41,000.00 $49,300.00 $78,200.00
Geology $43,500.00 $79,500.00
$45,000.00 $59,600.00 $101,000.00
History $39,200.00 $71,000.00
$37,000.00 $49,200.00 $103,000.00
Industrial Engineering $57,700.00 $94,700.00
$57,100.00 $72,300.00 $132,000.00
Journalism $35,600.00 $66,700.00
$38,400.00 $48,300.00 $97,700.00
Marketing $40,800.00 $79,600.00
$42,100.00 $55,600.00 $119,000.00
Math $45,400.00 $92,400.00
$45,200.00 $64,200.00 $128,000.00
Mechanical Engineering $57,900.00 $93,600.00
$63,700.00 $76,200.00 $120,000.00
Music $35,900.00 $55,000.00
$26,700.00 $40,200.00 $88,000.00
Philosophy $39,900.00 $81,200.00
$35,500.00 $52,800.00 $127,000.00
Physics $50,300.00 $97,300.00
$56,000.00 $74,200.00 $132,000.00
Political Science $40,800.00 $78,200.00
$41,200.00 $55,300.00 $114,000.00
Psychology $35,900.00 $60,400.00
$31,600.00 $42,100.00 $87,500.00
Religion $34,100.00 $52,000.00
$29,700.00 $36,500.00 $70,900.00
Sociology $36,500.00 $58,200.00
$30,700.00 $40,400.00 $81,200.00
Spanish $34,000.00 $53,100.00
$31,000.00 $40,000.00 $76,800.00

One source gives the median high school salary as $32,000 for adults aged 25-34, a weak approximation to 'midcareer'. I suspect a better approximation to the Journal's midcareer category would add several thousand dollars to this.

Assuming the high school versus college data is roughly comparable, it is easy to see that for most college graduates who are now midcareer, the college degree is certainly strongly correlated with greater earning power. (Of course, we cannot exclude the possibility that for this cohort, the college degree is a proxy for a lower bound on their IQ.) With the exception of a few fields like education and religion, it should take little more than a decade or so to pay back college costs (including the cost of delaying entrance into the work force). The data becomes more interesting when we look at the bottom 10% of earners (by major) among college graduates. We see that for many majors, including Anthropology, Art History, Education, English, Film, Music, Psychology, Religion, Sociology, and Spanish, occupants of the lowest decile do not recoup the cost of the college degree.

Let's make a strong assumption that the bottom 10% of wage earners in each major are roughly the same group as the bottom 10% of students in the major (defined by some incredible nonexistent linear measure of academic ability). Of course, this assumption has terrible holes, for example, women who temporarily drop out of the workforce to raise children. Nonetheless, we will assume until otherwise informed that the correlation between poor student performance and lower subsequent wages is strong. We further assume that the majority of people who did not attend college would have been weaker students than those who did. Similar caveats obviously apply to this assumption, but I suspect it is accurate on average. We then see that the push to encourage higher rates of college attendance for students who would have been unlikely to attend otherwise, is likely to lead to poor economic results for the majority of those new students, if they major in the Arts or Humanities. On the other hand, the above data is brighter for those who choose to major in Engineering, Math, Physics, and Economics. Even the 10th percentile of earners with degrees in these majors have room to recoup the costs of college. So, if one discovers a subset of students who have strong mathematical skills but would not traditionally attend college, then perhaps they should be encouraged to attend. Otherwise, the push to continue to enlarge the population of college students does not appear likely to be economically rewarding for lower performing students.

We see that the loud corner of the blogosphere that asserts that a college degree has lost its value is obscuring the main issue. A college degree in many fields is strongly correlated with subsequent higher earnings, but our above commonsense (but unproven) assumptions suggest that the more precise statement is: for good students a college degree in many fields is likely to lead to higher earnings. For weaker students, it is likely to be a money pit.

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.

Monday, July 12, 2010

How the internet has changed mathematical research

Many years ago I told a science librarian that electronic journals would never replace paper journals. Reading papers on a computer screen was simply too uncomfortable, and printing paper copies simply transferred costs from the library budget to the departmental budget. I was completely wrong. Not only has the advent of laptop computers made reading on computer screens comfortable (now I can read them in bed), but the ubiquity of electronic journals, internet mathematics archives, web course notes, and even Wikipedia has dramatically accelerated the pace of mathematical research and lowered barriers to entering new fields.

Before the internet, whenever I encountered an unfamiliar mathematical concept, I traipsed to the library, pulled books on related topics, and searched though their indices for a discussion of the concept in question. If the concept was too young to be covered in a monograph, I would chase through a maze of references in journals, one paper leading me to another until I mastered the desired concept. Now Google replaces this many hour endeavor with a rapid download of pdf files of relevant materials. Reading the papers might still be time consuming for complicated theoretical constructions, but finding the materials requires vanishingly little time. For a forgotten elementary definition, Wikipedia does the trick.

The advent of the mathematics arxiv led to an explosion of papers, often with results many might deem too insignificant to merit a paper. The downside is clutter on the web. The upside for my work is that with a quick flick of Google, I can find useful mathematical building blocks, which even though not deep, may save me from spending a week or more working out the details myself. Effectively, this makes research more collaborative.

The publication of minor results coupled to a rapidly searchable arxiv has dramatically quickened the pace of research. A researcher can now spend the bulk of his time at the leading edge of discovery (where admittedly the pace of progress often slows again), instead of trudging back and forth from the library.

Monday, July 5, 2010

Republican outpost in hostile territory

My community hosts an arts festival each summer. My county GOP decided to sponsor a booth in this year's festival. These festivals are fun to attend, but the crowds are dominated by long (grey) hair and tie dyed tee shirts. I have always assumed that Republicans constitute a miniscule minority at these events. One of my more indomitable colleagues in the county GOP observed that as the Republicans were outnumbered 3-1 in the county, if we were unwilling to venture into Democratic territory, we might as well give up. I decided to further my political education and convictions by contributing a Sunday morning and afternoon to manning the booth.

As usual, our organization was poor. I arrived at the appointed time with no instructions, only to find an unmanned booth. I found sacks of materials inside the booth and dug through them looking for materials to place on our table. Our materials were a bit skimpy. Many people are drawn to the booths seeking stickers and buttons. Lesson 1: Keep an ample supply of goodies on hand. Shortly after my co worker arrived (30 minutes late), a representative of the festival visited to warn us that we were not allowed to give water to passers by; we were only allowed to offer information. We would be expelled if we left our booth to offer information. Apparently we had violated both rules on the preceding day. I assume that the Democrats were bound by similar restrictions but would like to be able to confirm that.

For most of the day my coworkers were two judicial candidates, one running for the state court of appeals and one for the state supreme court. I asked them if it was difficult campaigning for a nominally nonpartisan office and explaining to voters the differences between their judicial philosophies and that of their opponents. They told me that the main goal of campaigning for nonpartisan office was to establish name recognition. If people were familiar with their names, they would vote for them. They rarely discussed judicial philosophy with voters. They even said that some names were better than other names simply because they appealed to various demographics. We couldn't improve their names; so, we focused on name recognition. We asked all visitors to wear stickers with the judges' names. I was also asked to plaster myself with name stickers and pins. Lesson 2: Name recognition is key.

The visitors to our booth were a heterogeneous group. Some simply wanted to discuss politics and to learn about local races. I enjoyed chatting with these folk. Others wanted to discuss their encounters with local government and to seek help in overcoming governmental obstacles. I happily turned these over to my better informed colleagues. Others simply wanted to collect pens, pins, and stickers. Now I understand that these folk aid the candidates too, especially when we can induce them to display the candidates's names while they are at the festival.

Of course no Republican booth in a sea of aging hippies could escape without encountering a few hecklers. Our first heckler was actually quite polite. My usual slow, careful style of discussion, however, was completely useless in dealing with a hostile audience. Clearly I need a stock of short pithy responses. Lesson 3: Do your homework, and prepare soundbite responses.

Our final heckler was quite abusive. He approached the booth and asked what we thought about "Drill baby, drill," now? What could I say to that given the current tragedy in the Gulf? I simply said that it was a shame that regulations had pushed drilling into such deep water that it was nearly impossible to cap the well. I did not mention Obama's rigid adherence to the Jones Act or other manifestations of the Obama administration's mishandling of the disaster. My answer, even though I neglected to indict the Obama administration, infuriated the visitor. He started flinging f* words at us. I reminded him that there were ladies present and told him not to speak that way in front of them. He departed, flinging a few more f* words at us as he left. The judges appeared to be somewhat bothered by the encounter. They had been worried that the aging hippie would become violent. I had not sensed any incipient violence and thought their worries were unfounded. By the next day the story had grown. By the next meeting of the county Republicans, I expect to hear that I had to wrestle to the ground a drug crazed hippie who was foaming at the mouth and trying to attack the judges. I will disabuse people of the more colorful story - eventually.

Sunday, June 27, 2010

Grade inflation: The View from the Trenches

When I began teaching at my current university, I received precise instructions governing grades for multisection calculus classes and no guidance for grading upper level classes. The multisection classes have many sections with different instructors but share a common syllabus and a common final exam. Department policy aims to ensure that grading is uniform across all sections; students with comparable performance should receive comparable grades, even if they are in different sections. The method for approximating this uniformity of grades is simple. Final exams are graded in common, and the exam grades are submitted to an administrator. The administrator looks at historical grade distributions, consults with senior instructors, and sets a curve for the final exam. Individual instructors are then required to set a grade distribution for their sections which approximates their sections' grade distribution on the final. Thus, if 10% of my students make an A on the final, I should award A's to approximately 10% of my students (not necessarily the same 10% who scored an A on the final). Grade inflation is minimal in courses subject to this grading regimen.

Upper level courses are an entirely different game. When I began teaching here, I approached prior instructors of my assigned upper level courses and asked them what grade distributions they had assigned when they taught the course. Upper level courses typically have a computational component, a knowledge component, and a proof component. Grading proofs has a significant subjective element. It is easy to decide that an argument is wrong; incompleteness or clumsiness, however, are much more subjective. There is no universal meter stick to use to decide what grade to assign. It is, however, usually easy to partially order the students. This clump is better than that clump. What I have to decide is whether the clumps are B's and C's or A's and A-'s. So, when I teach calculus classes, I feel virtuous for keeping grade inflation so far below what we see in the humanities. When I teach upper level courses, I sometimes have grades concentrated in the nosebleed territory between B- and A. I don't know how I would distribute grades in a humanities class where so much of the grading is subjective.

What is the harm in grade inflation? The most interesting argument I have heard is an economic one: if grades are inflated, students are not pushed to migrate to majors where they hold a relative competitive advantage. Thus a student who is not gifted in, say English, may major in English and receive grades on a par with more gifted writers, rather than being pushed into a business or econ class, where they may earn a lower grade than in their English class, but outperform more of their peers. I also imagine grade inflation makes college transcripts less useful for employers in hiring recent graduates. When I write letters of recommendation for unspectacular students, I always tell the employer not only what grades the student earned in my classes but also where he ranked in the class, in order to obviate the grade inflation problems. I suppose we would need more data about the correlation between academic success and job success to understand whether grade inflation inconveniences employers.

If grade inflation is accompanied by a watering down of the course material, the harm to students is obvious. In my department, I have seen little evidence of decreasing course rigor. In fact, I believe that mathematics courses have become more rather than less rigorous during my time here.

What are the causes of grade inflation? Economists offer one of the most amusing explanations of the fact that grades in the humanities are so much higher than in mathematics, chemistry, and economics departments. They observe that the average mathematician's midcareer salary is approximately 50 % higher than that of a psychology major. They conclude that a good grade in a psych class is worth less than a good grade in a mathematics class. The good grade in psych should therefore cost less. The relevant currency is student effort. This leads to inflation of grades if psych is to retain enrollments. I like the argument because it makes math look good (or at least profitable), but I have met few students who know average salaries by major and fewer still who don't think they will be the exceptions. Hence, I don't believe the economic argument explains the reality. On the other hand, it is very believable that instructors inflate grades in order to keep enrollments up and course evaluation numbers high. When faculty have low enrollments or poor evaluations from their students, the department administration notices and seeks explanation. Consistently poor enrollment and evaluation numbers can lower chances of promotion of junior faculty and can depress salaries for tenured faculty. Strict grading policies can lead to low enrollment and lower evaluations. The resulting pressure to inflate grades is real.

Because many of the incentives to inflate grades stem from worries about administration response to the possible consequences of tougher grading, the administration can easily tighten grading standards if it chooses to do so. If the departmental administration requests that its faculty assign certain grade distributions, then enough faculty will cooperate to slash grade inflation. Departmental administrations, however, also worry about overall departmental enrollments. Hence they are unlikely to act alone unless they are over enrolled. If the university requests that all departments enact tighter grading standards, then much departmental resistance would disappear. Unfortunately, there is a significant faction of the humanities faculty that opposes tighter grading for political/philosophical reasons which I have never understood and will not, therefore, try to explain here.

Though, grade inflation is real, I am unsure of its negative consequences. It is, however, easily addressed if the university administration is willing to buck the politics of a minority of faculty opposed to rigorous grades.

Sunday, June 20, 2010

A Newcomer's Guide to State Political Conventions

I recently attended my first state GOP political convention. The convention occupied the better part of a weekend, and I never strayed far from the question: is this activity worth my time? In this post, I will describe aspects of the convention and my answer to the preceding question.

Before the convention, I assumed that the main business of the meeting would be working out the party platform. One of my colleagues in the county GOP, however, told me that the resolutions would be more interesting than the platform. As homework before the convention, I studied the platform proposed by the Platform Committee and sought and identified logical inconsistencies, incoherent statements, violations of my idea of small government conservatism, and impolitic planks. I was unsure how one addressed these at the convention.

Day 1: The convention met in a large hall. The delegates were seated by county. I was the only delegate from my county. We began with a prayer, the presentation of colors, the Pledge of Allegiance, the National Anthem, and a welcome speech from the state party chairman. A large part of the work of the convention then focused on the rules for running the convention itself. The state party chairman appointed the convention officers. In particular, the party chairman does not chair the convention. I assume the rationale for this is that the party chairman generates so much animosity in his capacity as chairman that it makes for a friendlier convention if an outsider is appointed chair of the convention. The next order of business is the report of the Credentials Committee. This committee rules on which people have passed the necessary hurdles to become delegates (and therefore given voting rights). Amusingly, the prospective delegates are asked to vote to accept this report; i.e., we vote on whether we have the right to vote. This process takes a surprisingly large amount of time, especially as there were inevitable omissions which needed to be corrected. Now that we had voted to grant ourselves voting rights, the Rules Committee proposed rules for running the convention, in particular, rules for voting and rules for debating. There was little debate over the rules of debate, and we quickly passed the proposed rules.

I assumed, as a naive newcomer, that the next item on the agenda, amending the state GOP rules of organization, would be comparably pro forma. Apparently, rules changes are the outgrowth of old internecine party fights. There was extended debate about the proposed rules. I had no opinion on (or understanding of) the issues and simply listened and watched the nature of floor debate. The final item on the agenda for the day was voting on the party platform.

My assumption that the party platform would be the heart of the convention was mistaken. There were few proposed amendments. I decided to address a substantive issue. Although I am comfortable speaking before large audiences of mathematicians, I was self conscious addressing the convention. There were microphones spaced along the four aisles dividing the hall. I approached a mike and received permission to speak from the chairman. I gave my name and county and then suggested we amend one of the social planks to delete federal references. I believe it will lead to better electoral prospects for Republicans if we stick to our constitutional principles and treat most social issues as the proper domain of the state governments - not the federal government. My amendment was promptly seconded, and then I was given a second opportunity to approach the mike and take two minutes to argue my case. I had not observed this part of the process and was unready with additional rhetoric. I merely added that conservatives were always ill served when social issues were federalized. I then returned to my seat. At this point other delegates had the opportunity to approach a microphone and argue for or against the amendment. Before any substantive discussion began, a delegate from a nearby county proposed postponing indefinitely debate on the amendment. The convention chairman then explained to us that this was a parliamentary procedure to kill an amendment without expressing an opinion on it. This motion passed killing my amendment. A few minutes later, someone proposed voting to cut off all further debate on the platform. This passed by the required two thirds majority, and we shortly thereafter approved the platform, warts and all. We then adjourned for the day.

The judicial candidates invited the delegates to visit their 'hospitality suite' in the evening. This consisted of a suite in a hotel with free booze and hors d'oeuvres. You had to pass a phalanx of candidates to reach the refreshments. The rooms were too packed with bodies for me to bother to enter.

Day 2 began like day 1: prayer, the presentation of colors, the Pledge of Allegiance, the National Anthem, and welcome speeches. Various candidates for statewide offices were paraded across the stage and allowed to make a few remarks. The top of the ticket (whom I had met that morning) made a long speech. We then broke out for various 'training sessions', addressing topics such as how to employ facebook and twitter in campaigns. Lunch followed. Lunch with the top of the ticket was an (expensive) option.

After lunch we reconvened in the convention hall. After numerous speeches, many quite good, we once again heard from the Credentials Committee. Once again it took quite a bit of time to vote on who could vote. My county delegation swelled to eight people on day 2. The rest of the day was devoted to voting on resolutions. The Resolutions Committee had prepared a list of proposed resolutions covering numerous topics such as repealing Obamacare, opposing a VAT, and calling for sanctions against Iran. Several handouts proposing resolutions, not supported by the committee, also circulated.

The debate over resolutions was much more heated than the debate over platform. Delegates formed long lines at the microphones, waiting their turn to speak. I was extremely impressed by the informed and thoughtful arguments, articulate speeches, and mastery of parliamentary maneuvers. Of course some delegates made statements I thought absurd, but it was heartening hearing so many concerned citizens from so many different walks of life making subtle and intelligent arguments - even if I did disagree with many of them. The silent majority of delegates, however, seemed to prefer to accept the committee reports essentially unaltered.

By the time 5:30 rolled around, I was ready to join a vote to close discussion and accept the amended report. The convention ended, and I went home. Because this was my first convention, I had looked at every aspect of it with a view to answering the question: is this worth my time? At times I wondered if the convention is primarily a vehicle for rallying the troops, rather than seeking their input. I am sure this is one objective of the convention (and a reasonable one), but my current assessment is that the debate over issues and platform is more important than merely adding an egg to a cake mix. I will try to return next year.