Frogs, Cigarettes, and Libertarians

I often ask my friends of the Libertarian persuasion,
Question: 'What do you call a Libertarian who wants to get elected?'
Answer: 'A Republican.'
Of course most Republicans are not Libertarians, but the GOP is far and away the natural home for any rational Libertarian. The Republican Liberty Caucus is the home of one subgroup of self identified libertarian Republicans. I have detailed aspects of both my philosophical differences and my agreements with the Libertarians in numerous posts such as Libertarians vs Conservatives, Steepest Descent, Vouchers, Libertarians, and Our Failing Public Schools. Despite my differences with my libertarian colleagues, I am probably viewed by them as a fellow traveler or an ally and am occasionally invited to Libertarian functions. Last week, I attended a state Republican Liberty Caucus (RLC) function and left the event with a burning question: are Libertarians disproportionately smokers? In (American!) Mathematics circles, I do not encounter many smokers and was under the impression that the habit was dying among professionals and, perhaps even more generally, among the college educated. In fact, a quick Googling asserts that smoking has dropped to around 9% of college grads (vs. 27% for high school grads). Yet, at the state RLC function, interesting conversations were frequently interrupted by the departure of one or more participants, heading outside to smoke. (No. They were not simply fleeing me.) At the one district GOP convention I have attended, RLC delegates pushed resolutions attacking smoking bans. The erosion of our liberties at the hands of the nanny state, although upsetting, is still somewhat abstract to me. This week I finally realized the obvious: the erosion of liberty is very real to smokers. Laws have been passed greatly restricting their rights. I greatly enjoy the consequences of these laws, no longer encountering smoking in public places, but here, I use the term public loosely, including privately owned restaurants which are not allowed to permit smoking on their premises (and which I am free to avoid should smoking be permitted there).

Seeing how strongly smokers feel the curtailment of their freedom, I wondered what abridgement of liberty would pinch me similarly. What current painful abridgements can I identify? According to another quick Google, I work from 1/3 to 1/2 or more of the year for the federal government. Since I love my work (and often work through vacations if I am not careful), I don't resent this loss of my time. If I translate this loss of time into a loss of income, the loss remains abstract unless I think about how I might have spent money lost to excessive taxes. The first thought that came to mind was how nice it would have been to send my children to excellent private schools with the taxes spent to maintain bad public schools. This example is not compelling, however, because (i) I could have always sacrificed some other good in order to send my children to a good private school, and (ii) there were not any obviously excellent private schools available. The first weakness illustrates the fact that infringement of liberty by means of taxation is the optimal means of infringement because it allows the victim/taxpayer to forfeit what he values least rather than having the government decide what material good (can a good education be called a material good since it costs money?) he must forfeit. The impending loss of my freedom to allocate as much of my income as I desire to pay for healthcare for my family will likely be my first exposure to a loss of liberty sharp enough to cause strong discomfort. I imagine small business owners have no end of more immediate examples.

Republican speakers endlessly repeat the metaphor of boiling a live frog in a pot to describe the gradual erosion of our liberties. They assert that if you put a frog in a pot of warm water and gradually turn up the heat, the frog will not jump out, whereas he will jump immediately if thrown into a pot of hot water. This sounds unlikely to me, and I don't know why Republican speakers spend so much time boiling live frogs (having steadfastly declined my French hosts' occasional offers of frog legs). Nonetheless, it is clear that if erosion of liberty occurs through taxation, the taxpayer will always eliminate his least valued good first, and is thus more easily lured into accepting ever increasing encroachments on his sphere of activity.

Conservative Marxists?

I have very limited exposure to research in the Humanities. From a distance, I have simply heard some of the words describing popular theoretical perspectives: Marxism, Structuralism, Ethnic Studies, Postcolonial Criticism, Gender Studies, Queer Theory, etc. I have always assumed that these terms mean what they appear to mean to the uninitiated. A colleague of mine from the social sciences, however, recently told me that she suspected that, with respect to Marxism, this is no longer completely true. I have been told that Marxist analysis is somewhat old fashioned. So, who does Marxist analysis now? My social science colleague told me that in addition to being the home of a gaggle of ancient Marxists, Marxism seems to have become a refuge for the politically conservative in the Humanities. If you are a politically conservative Humanities prof, then you can label any economic analysis as Marxist, no matter how far removed from the class struggle. The Marxist label protects you from being outed as politically conservative, and you may pursue your studies unmolested.

This is outside my expertise; so, I may be guilty of posting an inaccurate, third hand report. Perhaps I will not be the first blogger to be guilty of this sin. Nonetheless, the possibility that Marxism has become the conservatives' refuge in the Humanities is a joke too amusing to keep locked in the ivory tower.

Tiger Mom

This spring, I couldn't escape the Tiger Mom in newspapers and the blogosphere. For those of you who missed the phenomenon, Tiger Mom was an Asian American woman (a.k.a. Amy Chua) who wrote a book about her mothering style, which fell just short of waterboarding her children if they paused for a bathroom break during their daily seven hour violin practice. I only read her essay in the Wall Street Journal, excerpted from her book. The essay evoked a loud outcry. While the mothering style Chua described in her essay struck me as harsh and counter productive, it did raise a basic question: Do Americans demand too little from their children?

For me, the answer is unquestionably, yes. I am not concerned with ensuring that every American child become a concert violinist, but I am entirely convinced that our public schools waste years of our children's lives, teaching them so little in school, especially middle school, that we stunt their intellectual growth. This is one of the reasons I would like to see school vouchers. Surely in large metropolitan areas there would be enough parents who believed that education was not merely an exercise in building self esteem to create a demand for strong schools. It is impossible to miss the extreme outperformance of home schooled children, covering subjects at twice the depth and range of public school students. Like Tiger Mom, home schooling parents I have known, respond to underperforming children by making them work harder. Yes, their child may not have a strong aptitude for mathematics, but instead of immediately surrendering and restricting the child to a diet of pablum math, they simply double down, increase the number of exercises until their child becomes competent. We all believe that exercise can make the 90 pound weakling a well muscled, albeit slight of stature 120 pounder, but we rarely admit the same opportunity for growth beyond our immediate limits in intellectual matters. I am not saying that it is worthwhile making all students learn calculus. Nor do I expect a career in mathematical sciences for the student who began life as the 90 pound weakling in mathematics. Nonetheless, giving up on the 90 pounders unnecessarily limits their intellectual growth. Limiting math limits science and economics. Imagine how much stronger our society would be if reporters knew enough basic mathematics to understand economics and the reality of our federal budgets.

While I agree with Chua that we demand too little of our children, I share the basic American fear of imposing my goals on my children. Perhaps in earlier societies, sons generally entered into their father's professions, but not in our country. I did not follow my father's profession, and I do not expect my children to follow mine. If, like Chua, I dictated my children's careers, they would gain the advantage of early preparation. I could have them ready for graduate level mathematics before they began college. On the other hand, they would lose the opportunity to discover their comparative advantage - the natural skills and inclinations which would lead them to outperform their peers in their chosen field, if they were allowed more freedom to explore and discover their strengths and intellectual loves. Every year I meet freshman upon freshman, children of Generic Tiger Mom, telling me that they love subject X or Y, but their parents require them to be premeds. Large number of these manage to underperform as premeds, until their parents release them to study a field which plays to their comparative advantage (or unfortunately, sometimes they never discover such a field).

In graduate school, I met numerous students who had been 'hot housed'. Some were taught advanced mathematics at a very young age, mastering calculus in fifth grade, and moving on to higher mathematics in middle school. None of these went on to successful careers in mathematics. Many, but not all, were emotionally or socially fractured. I know hot housing worked for Norbert Weiner and several other notable polymaths, but making such a choice for one's children seems a step too far to me. So, as in most aspects of life, there is a fundamental tension. Make our children work hard enough so that they can ultimately be good citizens and succeed at their choice of career, but don't push them to live our fantasies for us, breaking them in the process.

Government Funding of the Sciences

The press paints conservatives as mentally challenged whenever they support candidates whose policy proposals will hurt the conservatives' pocket books. The conservatives, of course, simply view themselves as principled. In the last election, I supported a fiscally conservative candidate who opposed most National Science Foundation funding. This was not, however, a selfless manifestation of principle on my part. I simply assumed that the candidate's anti-NSF position was so far from the mainstream that I could support him (for his generally fiscally conservative stance) without endangering my own (and my colleagues') NSF support. This does raise an obvious question, which I have previously avoided here: what is the proper role of government funding in science? I am too close to this question to give a dispassionate analysis, but at least I can try to frame the discussion.

There are several arguments for funding fundamental science research:
(i) economic,
(ii) infrastructure, and
(iii) national pride.
The economic argument is simple. Even Libertarians agree that it is proper for government to fund public goods. Recall, public goods refer to goods which have the properties that (a) one person's use does not limit another person's use of the good, and (b) it is not practical to restrict access to the good. Fundamental scientific knowledge certainly falls into this category. If I use Maxwell's equations describing electromagnetism, it does not limit your use of these equations. Unless we turn science into a mystery religion guarded by secret rituals and high priests, it is not feasible to charge a toll every time someone applies Maxwell's equations (although rumors abound that this was next on Pelosi's agenda before she lost the majority). Observe that the closer science is to engineering, the less likely the public good label will apply. Science leading to patentable products should violate condition (b), essentially by definition. Hence, the public goods argument applies primarily to basic or fundamental science. These terms are used to describe research aimed at understanding aspects of the nature of existence without an immediate eye to application. Politics tends to reverse the natural order here. Politicians are often more willing to fund research if it has immediate applications, even though such research can be profitably funded (and more deftly guided) by private industry.

Classifying science as a public good makes it eligible for public funding from a conservative perspective, but does not require the government to fund it. The decision to fund science then requires the voters to believe there is a significant benefit to funding science and then to decide, given the amount of money they are willing to surrender to the government in taxes, that science stands sufficiently far forward in the queue of priorities that it should be funded rather than some other programs. There is no doubt that advances in basic science have dramatically changed our lives. Who would prefer to live in a world where electromagnetism, chemistry, and quantum physics were unknown? While the patentable iPad is the product of private industrial research teams, it rests on hundreds of years of basic research.

As a nation, we could decide to be a free rider. Let other nations invest in basic research, and we will wait until our private industries see a profitable application. Let France, Russia, and China pay while we profit. If you feel comfortable with this scenario, imagine a world where we waited for the Nazis and Soviets to keep us up to date on nuclear fission. Without a deep bench of our own scientists, there is no doubt we would rapidly become a second rate economic and military power.

An overlooked feature of the scientific infrastructure is the manner in which scientists communicate up and down the scientific ladder. Industrial scientists study under and frequently communicate with basic scientists, basic science is informed by industrial questions, and industrial scientists benefit, of course, from all progress in basic science. Hi tech industry blooms near research universities. I suppose this latter observation suggests that some funding for basic science might be shoved from the federal to the state government. Many state governments have observed the synergy between the universities and hi tech industries and used this to justify high levels of support for state university systems, but in an age of email and skype, I can't predict how important proximity is in the future of this relationship. If proximity becomes less important, some states may hope to become free riders within the U.S. by defunding their research universities.

On a noneconomic note, I would be saddened if the U.S. was no longer a leader in science. It is fine to invest small change in great Olympic sports teams. If a few dollars more helps secure us Nobel Prizes and Fields Medals, it can be money well spent if there is a budget line for national pride. At least it is a better use of resources than lowering the age of eligibility for Social Security benefits.

Sausage, Donuts, and Paperwork in Triplicate

This semester I attended my first county GOP convention. The convention provided a close view of grass roots politics. The goals of the convention in a non-election year were to choose the county GOP leadership for the next two years and to update the rules governing the county party organization.

In our county, the Republican party is a small minority, and it can be difficult to convince people that local participation is worthwhile. About 50% of the eligible delegates from my precinct attended the convention, and that was considered an exceptionally high turn out. When trying to encourage my neighbors to attend, I encountered many excuses for not attending. The prize for the most annoying response goes to those people who told me that they did not want to participate because the people who did take the time to participate were moving the party in directions antithetical to the nonparticipants. This response was particularly nettlesome this year because our leadership race pitted our politically inoffensive current chairman against a newcomer with a record of attacking opponents on religious grounds. Note that I am not complaining that he attacked policies on religious grounds but that he impugned the faith of the proponents of liberal policies. In fact, on one occasion he even made public remarks that appeared to me and my neighbors to attack members of other religious groups regardless of their policy positions. My neighbors most exercised by such religious attacks did not attend the convention. The newcomer won.

Although the focus of the convention was the election of new leadership, the bulk of the time was devoted to changing the rules governing the party. There were no significant areas of contention, but a room full of people in the grip of Robert's Rules of Order can have trouble reaching a common goal. In addition, an occasional freelancer would offer an ill considered amendment that would send the group into strange byways that strongly testified against the reputed wisdom of crowds.

As the convention dragged into the afternoon, the assembled became hungry and restless. A GOP auxillary group offered water and snacks for sale. Unfortunately, election law has become so ridiculous that the purchase of a donut is regarded as a political contribution. In order to avoid corrupting our political process by hordes of conventioneers receiving lucrative government contracts in return for a cruller, the purchase of a donut or bottle of water required the buyer to fill out forms providing employer, address, phone number, and endless other nonsense.

The county convention was definitely messier than the state convention I attended last summer. There were fewer experts to guide us along. Nonetheless, despite the crudeness of the process, I admire those who are willing to give up a beautiful weekend morning in order to make political sausage, and maybe, if they are lucky, leverage a box of glazed donuts into ill gotten government largesse.

Love of Linearity

A function F is said to be linear if it satisfies
(i) F(x+y) = F(x) + F(y), and
(ii) F(sx) = sF(x).
Heuristically, a linear function satisfies a generalized distributive property.
A function G(x) is called affine if G(x)=F(x)+c, where F is linear and c is a constant. Mathematicians and the general public often apply the term linear to any affine function. History is probably on the side of this broader usage, as the graph of an affine function (of one variable) is a line.

Mathematicians love linear functions because they are so easy to analyze. An entire semester college course is typically devoted to their study. Moreover, the object of a differential calculus course is to study the approximation of functions by linear functions. Crudely, a function is differentiable, if in sufficiently small regions, it is well approximated by affine functions (the requisite affine function depending on the small region in question).

We spend several years in elementary school teaching children that multiplication satisfies properties (i) and (ii). We then spend several years in high school (occasionally spilling over into college) convincing students that most functions are not linear. Our success in this latter effort is clearly limited. For example, we often see data analysis accompanied by a computation of the affine function which best approximates the data, even when there is no theoretical or experimental reason to suspect the underlying phenomenon is described by a linear function. In fact, in most natural systems, linearity seems highly unlikely. Remember, the graph of a one dimensional affine function is a line marching onward in perpetuity. If you do not think that a stock price or a population of herring is likely to increase (or decrease) at a constant rate forever, then a linear model is clearly ruled out. Nonetheless, our affinity for linearity is extremely strong, as demonstrated by our tendency to see straight rows in scatter planted corn fields.

I was drawn to think about our bias toward linearity, by a WSJ article,
Balanced Budget vs. the Brain. The focus of the article is the putative irrationality of the average economic actor, who fears risk more than he values gain. The author cites psychologists Daniel Kahneman and Amos Tversky who asked students to bet on coin flips.

"If the coin landed on heads, the students had to pay the professors $20. Messrs. Kahneman and Tversky wanted to know how big a potential payoff their students would demand for exposing themselves to this risk. Would they accept a $21 payoff for tails? What about $30?

If the students were rational agents, they would have accepted any payoff larger than the potential $20 cost. But that's not what happened. Instead, the psychologists found that, when people were asked to risk $20 on the toss of a coin, they demanded a possible payoff of nearly $40. "

Question: why is it rational to value a $20 dollar gain to be worth the risk of a $20 dollar loss? If you own one house (and do not have a large bank account), is it a rational gamble to risk it in an even bet in exchange for an additional house? Are we irrational if we do not view the prospect of owning two houses to be worth the risk of becoming homeless? It is easy to construct numerous examples of this kind. I think the correct interpretation of the study is the pair of observations :
(1) the value we place on assets is not a linear function of their dollar value, and
(2) Jonah Lehrer, the author of the WSJ piece, has an irrational expectation that linearity is ubiquitous in our highly nonlinear world.

I bet (but not $20) that if the students were risking a 20 cent loss, their acceptable payoff would be closer to 20 cents. This is an expression of my irrational expectation that differentiability can frequently be found in our highly nonsmooth world.

As the French are wont to say, "Vive la nonlinearity."

Study Abroad: A Free Lunch for American Universities?

I have often wondered why universities promote their study abroad programs so heavily. Brochures proclaim:
"Come to Wonder University, where we allow you to study somewhere else!"
At first I thought this was simply a marketing ploy. Prospective students learn that if they matriculate at Wonder University, the University will help them to convince their parents that funding a semester long vacation in Europe will further their education. Wonder University becomes more attractive to students desiring a long European vacation, and applications rise. Wonder's competitors then have to promote study abroad so that they don't lose the best tourists to Wonder.

I have, however, heard numerous stories of colleagues fighting with students and the administration over overseas mathematics courses. My colleagues assert that most mathematics courses available to our students in study abroad programs are so much weaker than our own courses that they cannot be allowed to count towards our major. Again and again students are devastated to hear that their "grand tour" will actually slow their progress toward a degree. The more such stories I hear, the less I believe my marketing explanation. Although there often seems to be a chasm between the concerns of the faculty and the attitudes of the student life administration, perhaps something other than marketing is at play here. When trying to understand strange behavior, a common dictum is to follow the money trail. What financial incentives do colleges have to push study abroad programs?

The Wall Street Journal recently published an article on the growing numbers of Americans eschewing American universities, enrolling in European universities instead. The driver: money. Tuition and fees at Oxford are around $5500 for Brits and around $20,500 for Americans. St. Andrews charges approximately $3000 for Brits and $20,500 for Americans. The University of Chicago and Stanford University, for example, both charge around $40,000. The difference is significant to most of us. Given this large financial gap, how much money do students save when they study abroad? At Stanford, the tuition for a year's study in California is $40,500. Their study abroad program charges $40,500. Chicago also charges its students the same tuition to study in balmy Chicago or in Scotland. Who pockets the $20,000 difference? Perhaps the American universities and their overseas partners split the difference. It would be amusing to know the details. Clearly there is enough money to be made to make everyone happy. Even the students are not losing financially, unless their foreign adventure forces them to pay for an extra semester of tuition in the U.S. Perhaps there is an occasional free lunch after all.