Occupy the faculty lounge for the cultural revolution

The school year is back in full swing, and my colleagues continue to educate me on the finer points of liberal economics. Last week, a conversation with  Professor XYZ about the economic stresses in the Eurozone evolved into a discussion of U.S. tax policy.  XYZ asked why couldn't we dramatically raise tax rates on the rich in order to reduce our deficit. I made the usual observations that raising tax rates did not necessarily result in the expected increase in revenues and that, in fact, tax revenue as a percent of GDP was fairly stable in the 15-20% range over the past half century, despite tremendous variation in tax rates. He responded that, yes, he had heard about 'some curve' which said that raising tax rates eventually led to a decrease in tax receipts. I asked him if he meant the Laffer curve; he guessed that might be what he was referring to. He believed, however, that the Laffer curve was mathematically better defined than I had ever heard. He told me that he had heard that the Laffer curve had more than one optimum: if the top tax brackets were sufficiently high, the government could eventually recapture the revenue that it collected at much lower rates. Independent of the truth of such an assertion, I was staggered by his notion that if we could generate the same tax revenues by choosing either a moderate tax rate or a punitive tax rate, we should choose the punitive one. Progressive tax rates as a tool of persecution of a minority (the rich) rather than as a tool for generating revenue never seems far beneath the surface of leftist economics.

 This week I passed some junior colleagues in the hall while they were discussing economics. One observed that he didn't see why the government didn't simply cap incomes. (I have no idea what generated this comment). I quipped that I would be happy to take his excess income off his hands if he didn't want it. He said, no thanks, he would prefer to have mine. I said yes, that was always the case with such schemes. I then asked him how he would define income for such a system to be fair. I observed that mathematics was so much fun that that you could argue that we were paid, in part, with the pure pleasure of doing research mathematics. Most of us would reject dramatically more remunerative jobs, because we would not be paid in the coin we most valued. If someone else was paid triple our income to perform some task we found odious (proctologist?), should we somehow put a monetary value on the sheer joy of mathematics before we compared total compensation and plotted redistribution schemes? Hearing about idle Wall Street protesters brings the same thought to mind. They clearly have much more leisure time on their hands than the average corporate mogul. Perhaps their redistributionist schemes should include redistribution of their leisure time. I suppose that is an old communist idea, last seen on a large scale with Mao's Cultural Revolution, during which China's intelligentsia was sent to work camps. 

I am becoming more enamored of a flat tax with every week these incoherent protests continue.

The Rule of Law: a naive perspective

As a mathematician who has never taken a course in political science, I am occasionally impressed by the shallowness of my understanding of fundamental political concepts. Watching the rise of crony capitalism under the Obama administration led me to realize I needed to understand better the concept known as "the rule of law."

In The Constitution of Liberty, Hayek frequently returns to the elaboration of the meaning of the simple term: "the rule of law." This broad phrase encompasses many ideas, including the following.
(i) You cannot have committed a crime unless you have violated a previously existing law.
(ii) There can be no ex post facto laws;
(iii) Laws cannot be targeted at individuals. In particular, proscriptive laws must be sufficiently general that any individual can easily avoid violating them.
(iv) Everyone is subject to the same law. Hayek weakens this to allow, for example, different rules to apply, for example, to women. Most important to the preservation of liberty, legislators should be subject to the laws that they create.
(v) The laws should written by a different group of men than those who administer them. This prevents laws being narrowly designed to fit particular cases.
(vi) Laws should be "known and certain." It should be (reasonably) clear whether or not you are complying with the law.

Rules that state, in effect, that you must do what a particular individual commands are a common violation of the spirit of (iii), (v), and (vi). The most common and least objectionable example is probably the ease with which we are punished for violating the commands of a policeman. Nonetheless, the ease with which a corrupt policeman can use such rules to create mischief show how wary we must be about making such exceptions.


Hayek further notes that the limitations on government power inherent in the idea of the rule of law must come from some law superior to the legislative; otherwise legislators could simply legislate the removal of these limitations. In the United States, the Constitution provides precisely such a superior law.

The rule of law has been weakened by both Republicans and Democrats in recent decades. The Congress has crafted ever vaguer laws, delegating the details to administrators in agencies or, in the case of laws like the "honest services" law to the ambition and imagination of district attorneys. This abuse achieved new depths with the passage of Pelosi Care. Even the passage of this law required violations of the democratic process. Sibelius's famous vast list of Obama friendly businesses exempted from various requirements of the law shows how incredibly quickly weakening the rule of law introduces rampant crony capitalism and other corruptions of our society.

Sibelius's infamous list led me to examine Hayek's discussion of the rule of law mentioned above. I was most interested to learn (revealing my political science ignorance) that socialists have long been opposed to the rule of law. In my youth, I had assumed that the Democrats' frequent attempts to avoid the restrictions of the constitution were merely a short sighted impatience with democracy itself, linked to the ubiquitous leftist conceit that their intelligentsia know better than the hoi polloi how society ought to be organized. According to Hayek, the socialists have long been opposed to the rule of law itself, because it restricts the ad hoc and intrusive government power necessary to control the economy. As the Constitution is the principal guarantor of the rule of law, the Democratic Party's long standing attempt to obviate constitutional limitations has much deeper roots than I had previously understood.

Conservatives like to note the similarities between socialist and fascist governments. Less inflammatory, and therefore perhaps more useful an observation when trying to influence educable Democrats, is the (old) observation that the weakening of individual liberties required to usher in the government powers attendant to the "progressive" agenda also weakens our defenses against other pernicious (even to the left) assaults on our liberty. As Hayek and others remind us again and again, despite the ideological differences between the socialists and the Nazi socialists, it was the weakening of the rule of law championed by the German socialists that paved the way for the triumph of the Nazis.

State Conventions - The Sequel

I have now been involved in my local Republican party long enough to have attended my second state convention. Before each one, I have asked myself, "Does this serve any purpose or is it just a waste of time?" Once again, I have decided that although there is a great deal of time wasted during the convention, it is worthwhile for serious people to attend and to provide their input.

This year is not a national election year; so, instead of hearing candidates' speeches, one of the primary jobs of this year's convention was to choose party officers, including chairman and vice chairman for the state party. Last year I had no idea who these people were. By this year, I had enough data to know who I definitely did not want running my state party and voted accordingly. The vote was so close - a difference of fewer than 10 out of a 1000 - that I felt my vote made a difference. Most amusing to me was the assiduous attention I received before the vote from one of the candidates who had always been rude and abrupt with me in previous dealings.

This year I was prepared for the fact that the delegates seem to treat the party platform as a matter of small concern. I was pleasantly surprised, however, to see the handiwork of a Libertarian colleague on the platform committee, removing some of the more noxious sentences from last year's platform. The improved platform passed with little fight. The Convention always (2/2) seems to be much more concerned about resolutions than the platform. Resolution debates always seem to suggest undercurrents of discontent and suspicion in the party. There are always groups who feel their voice is squelched by the leadership. Probably there is some truth in this. When you administer, you generally focus resources (including time) on efforts which you think most likely to succeed, help the group, and which coincide with your goals. Perhaps this seems devious to those who are not heard, but to some extent it is unavoidable. It is obnoxiously amusing, however, how the leadership manages to waste just enough time so that we don't have the time or quorum left at the end of the convention to hear the unsanctioned resolutions.

Even though there were no candidate speeches, there were quite a few newcomers already beginning the long slog toward congressional (and other) nominations, who were eager to chat in the convention halls. Some personal exposure can be quite helpful in deciding whom to support. I met one local congressional candidate who rapidly convinced me to support his opponents (whoever they may be) in the primary.

Outside the election of officers, the bulk of the convention dealt with the same bookkeeping matters we handled in last year's convention, as discussed here; I won't repeat their description.

My personal convention resolution passed unanimously: I resolve that I will attend next year's convention, but I will keep the latest Wall Street Journal handy to read during the most boring parts.

University Wars Continue

In recent months the direction of the conservative attack on the nation's universities has shifted its focus. For decades we have heard about the undeniable strong leftward tilt of the faculty and classroom. For the last year or two we have heard about the waste of time and money when college tuition for the academically unprepared is subsidized by the government. Now the blogosphere and newspapers are filled with commentary attacking the dual role of the university professor - part teacher, part researcher. This time the conservative attack misses its mark.

All of the attacks I have read conflate so many different issues that their analysis is essentially meaningless. I will try here to tease out some of the issues. First let's consider money. Research professors are more expensive than teaching faculty. Their job description (in the sciences) usually assumes that at least half of their time is devoted to research. Their promotion is more tightly coupled to the prominence of their research program than to their teaching prowess (although the attention to the latter has dramatically increased since I was an assistant professor). Moreover, there is greater competition for top researchers than for teachers. Consequently the salary for an internationally renowned research professor may double that of nonresearch faculty. Thus, the cost per classroom hour of a research professor may easily be quadruple the cost of teaching faculty. Is it worth it? How do we decide? One way to approach this difficult question is to examine what the market says.

The most prestigious private universities primarily hire research professors. Premium private four year colleges typically hire faculty with a respectable research program but give them less time to pursue their research and offer somewhat lower salaries. Teaching loads are typically 50% to 100% higher than at the top research universities. Which gives the better deal to students? Let's look at two examples, Stanford and Swarthmore. Tuition and board at Stanford currently costs approximately $53,000 per year. Tuition and board at Swarthmore will run you approximately $53,000 per year. So, we see that in name brand schools, increasing the number of faculty hours in the classroom per salary dollar does not lower student expenses. This reflects two facts: (i) faculty salaries are not the main driver of college costs, and (ii) class sizes are flexible. Four year colleges will definitely offer fewer 200 student lectures than state research universities and fewer 100 student lectures than private research universities. Class sizes are more elastic than tuition.


Some students choose to attend 4 year colleges, and others choose to attend research institutions. Putting aside the question of whether all these students are gaining admission into their preferred school, we see that some students (and their parents) value the smaller class size offered by 4 year colleges; others value the opportunity to interact with and possibly work with leading researchers. Moreover, many students at research institutions whose aptitudes and goals make them unlikely to benefit directly from the presence of active scientists still receive a second order benefit: the extremely academically focused students who are attracted to the research environment enrich the university experience for their less academically focused peers. Both types of environments have significant strengths. I find it highly amusing that the conservative commentators opposed to the research university seem opposed to allowing consumers to choose the product most suited to their tastes and needs.

If we focus on taxpayer supported public universities, then the fact that the best students in their states prefer the research university to the research inactive community colleges is not as decisive an argument in favor of supporting the former as it is in the case of private universities. I have discussed this public funding question elsewhere. We must leave that fundamental value judgement to the voters of each state. I, however, will advocate for supporting the research universities in my state.

Too Much Information

Most people are, I hope, familiar with the incredible universality of mathematics. At the most primitive level, they learn this in first grade when they learn that the observation that three apples plus two apples gives them 5 apples is a special case of the arithmetic result 3+2=5. Less well known is a common beautiful mathematical phenomenon: many problems are hard to solve until they are generalized. In other words, it may be easier to simultaneously solve infinitely many different but related problems than to solve a single one alone. The reason for this varies. Sometimes the salient features of a problem only become visible when viewed from a sufficient distance.

In government the same phenomenon holds. It is often impossible to decide rationally whether to support or oppose particular legislation unless one has a governing rule guiding one's support or opposition to large classes of legislation. There are simply too many plausible ways to spend taxes, too many unintended consequences, too many opportunities to feed sweets to a diabetic, and too many "slippery slopes" for a rational legislator to decide issues in isolation. A rational theoretic framework for deciding issues is often called an ideology. For some reason, many view this term negatively, with the subscribers to an ideology called ideologues, and the latter term synonymous with unreasoning dogmatism and inflexibility. Hayek, in The Constitution of Liberty observes,
" A government that claims to be committed to no principles and to judge every problem on its own merits usually finds itself obeying principles not of its own choosing and being led into action it had never contemplated."
This statement applies equally to individual legislators, and by extension, to individual voters.

In my canvassing work, I have encountered many unaffiliated voters who proclaim proudly that they adhere to no party; they always "vote for the man - not the party." Invariably, these voters are dramatically less informed about the issues and candidates than their partisan colleagues on both the left and the right. It seems their position is simply an excuse for intellectual laziness.

Life is too messy to fit into any axiomatic framework (which is another way of saying again that I am not a Libertarian), but in politics as in mathematics, the attempt to frame all issues within broader theoretical/philosophical contexts is an essential exercise for informing our views on the issues and conversely for testing and developing our ideology.

Inane Mathematical Metaphors

I haven't abused any mathematical metaphors on this blog for some time. To atone for this deficiency, today I will introduce some mathematical concepts that beg to be misapplied to political discourse.

Let's start with geometry. The first three geometries one usually encounters are
Euclidean, Spherical, and Hyperbolic. Euclidean is the geometry we all learn in grade school. It is the geometry of flat space. Spherical geometry is the geometry of the surface of a ball. We learn a few aspects of spherical geometry in grade school. Given the reasonable approximation of the surface of the Earth as a sphere, spherical geometry enters into many planetary scale computations. Unless you major in mathematics or physics, you are unlikely to encounter the third classical geometry: hyperbolic space. One feature of hyperbolic space which makes it useful for metaphor abuse is the fact that in hyperbolic n-space, the volume of a ball of radius R grows like e^{(n-1)R} instead of like R^n as in Euclidean space. (Volume growth of balls in spheres for R greater than half the circumference of the sphere is obviously not particularly interesting.) Equivalently, the volume of a sphere of radius R grows like e^{(n-1)R} in hyperbolic space as opposed to growing like R^{n-1} in Euclidean space. As we often do, we turn to Hayek to develop our metaphors.

In Hayek's Road to Serfdom, Hayek discusses at great length the undirected emergence of complex economic organizations from the individual actions of billions of people. In The Constitution of Liberty, Hayek extends his reflections on the spontaneous emergence of complex phenomena from the realm of economic organization to social. He notes that complex social conventions, like complex economic arrangements, arise undirected; they are the product of the experiences and the experiments - both successful and failed - of all our predecessors. He implies that we should therefore be wary of challenging established custom because we are not simply opposing our reason and experience to that of our neighbors, but also to the accumulated knowledge and experience of all of our predecessors. On the other hand, his analysis contains the implicit assumption that people will continue to experiment and modify social conventions, contributing incremental improvements.

Hayek's fundamentally conservative viewpoint on challenging social norms is based on the assumption that the accumulated experience of our predecessors is greater in magnitude than the new experience of the current generation. So, for Hayek, a Euclidean ball of radius T is a better model for the accumulation of experience in time T than a hyperbolic ball. In Euclidean space, the sphere contains only a small fraction (1/T) of the total knowledge of the ball; in hyperbolic space the sphere and the ball contain comparable data. Therefore, those who believe the experience of their generation outweighs that of all their predecessors might prefer a hyperbolic model of accumulation of experience. I suppose the more extreme conservative position would be one from spherical geometry: after a fixed finite time (presumably already passed) no new knowledge is gained.

So, on social issues, then, we can divide people into spherical, flat, and hyperbolic. We will have to work harder, however, to tie these models to Hayek's more fundamental concern - the spontaneous rise of structure from the independent actions of millions of people (as opposed to the directing hand of government). Actually that seems to be too tall an order, if we wish these structures to differentiate scenarios supporting or opposing the spontaneous rise of structure. In geometry, almost all interesting natural structures arise from optimizing some local energy condition. In two dimensions, spherical, Euclidean, and hyperbolic geometries can all be created from uglier geometries by allowing the geometric structure to flow locally, subject to the instruction to minimize some locally defined energy. So the spontaneous rise of order is hardwired into much of geometry, as I have discussed elsewhere.

There is a subtler (and even sillier) link between these geometric structures and the political spectrum. If you traverse a small circle counterclockwise while holding a small ruler pointing in a fixed direction as you travel (modelled by a covariant constant vectorfield along the curve, for those of you who want precision), then in Euclidean geometry, when you have returned to your starting point, the ruler will be in its original position. In hyperbolic geometry it will have shifted to the left. In spherical, it will have shifted to the right. On these grounds, we will award hyperbolic geometry to the liberal side of the political spectrum and spherical to the conservative side.

If this assignment does not match your politics with your preferred geometry, simply replace counterclockwise travel with clockwise travel to reverse the political spectrum.

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.

The intersection of Medicare and the Death Tax

The GOP suddenly learned to love Medicare when Pelosi et al decided to sacrifice seniors' healthcare in order to move several steps closer to socialized medicine. This Republican change of heart is destined to be short lived. When the fickle GOP returns to its senses, perhaps the Republicans can enlist the Democrats in transforming Medicare from a middle class subsidy to a program for the needy. Attracting the Democrats to the table requires powerful bait. I recommend the Death Tax.

When I turn 65, I am 'entitled' to have the government subsidize my health care costs. Of course, when I say 'the government subsidize' what I really mean is have hardworking taxpayers subsidize my costs, even those who are less financially successful. When I am 65, I will have no kids to support, no mortgage to pay, and hope to have many years of work ahead of me. Years of picking up chalk, pen, and mouse may have taken their toll on my health, but why should those saving to buy a house, to put their kids through college, or to pay off their credit cards and student loans subsidize my health care? The old answer is that the left has always wanted entitlement programs to extend to the middle class so that they get broad voter support.

The current Death Tax compromise is a rate of 35% after an exemption of $5 million dollars. The ability to pass on the fruits of your labors to your children maddens Democrats almost as much socialized medicine delights them. Let's compromise. Tell the left that you will tax my estate at 100% (not until after my wife passes please) until you have recovered 100% of the subsidy the taxpayers have contributed to my healthcare. Then you revert to 35% of [remainder - ($5 million - subsidy)]. If I have saved less than $5 million, then my Death Tax is simply the cost of the subsidy. I have, of course, been paying Medicare taxes for years, but more fool I, if I really believed they were linked to my own welfare.

Now comes the fun part. How do we determine the cost of the subsidy? Is this more of a political or an economic question? Any Democratic leveler will want the subsidy to be priced as high as possible to prevent robber baron math faculty from paying for their grandchildrens' college tuition instead of relying on the state to subsidize it. To prevent the robber barons from being gouged, we have to allow them to opt out of Medicare and fund their own health care. I doubt the left will have the self control to undervalue the subsidy. If we are lucky, the true costs of Medicare become clearer and more people will opt out. I haven't crunched any numbers (we need to find some employment opportunities for economists), but a death tax/Medicare compromise seems worth exploring on the road to weaning the middle class from entitlements.

Quantum Field Theory For Toddlers

Last week, headlines in the newspapers and blogosphere blared:
American Students Struggle with Science. Skimming the articles, we quickly learn that 99% of American fourth graders do not perform at an advanced level in science, according to a Department of Education report. The report also condemns (less laughably) the performance of our 8th graders and 12th graders, but fourth graders? How seriously can you take 'education experts' who worry about the science expertise of fourth graders? Do they have any concept of the nature of science?

Science in elementary school serves two purposes: (i) allay the concerns of pushy parents who erroneously believe elementary school science has content, and (ii) excite the interest of young children so that when they have the necessary mathematical tools, they are eager to study science. A bad elementary school science course is far worse than no science course at all. For, while neither imparts significant knowledge or lays the groundwork for subsequent courses, a bad course gives the young child the mistaken impression that science is dreary drudgery rather than an exciting pursuit.

Mathematicians often speak of the verticality of our discipline. By this, we mean that, for example, in order to understand partial differential equations, you need to understand functional analysis, real analysis, and complex analysis. In order to understand real analysis and complex analysis, you need to understand basic analysis. In order to understand basic analysis and functional analysis, you need to understand linear algebra and calculus. In order to understand linear algebra you need to understand algebra. Each subject rests on an edifice of one or more more basic subjects. Thus the earlier you learn mathematics the higher you can scale the tower of mathematical knowledge. Physics is similarly vertical. Fields which are significantly less vertical are sometimes referred to as "butterfly collecting." This is a disparaging term (often applied when the speaker does not know a field well enough to know its vertical structure). It refers to fields which are largely descriptive; the idea is that describing a swallowtail does not contribute significantly to the description of a sulphur.

At the elementary and middle school level all science must be taught as butterfly collecting. No real physics can be taught without calculus. A good deal of descriptive chemistry can be taught with a modicum of algebra, but a deeper understanding requires physics, which requires calculus. A great deal of descriptive biology can be taught, but a deeper understanding requires chemistry, etc. Teaching biology and chemistry at this level is useful; most students are not destined to become scientists or engineers. If they learn descriptive science, they are better able to understand their world and, as a bonus, are better able to evaluate the junk science pushed by Hollywood, Washington, and the media. There is nothing, however, that can be taught to a prealgebra (precalculus!) fourth grader that will not have to be relearned at a more advanced level by any student wishing to apply science in his work.

So, what are Washington's education experts telling us? Most importantly, they are telling us they have no concept of how best to spend our children's precious classroom hours (which were largely filled by Disney videos in my children's public schools). If you want to improve American's science performance, replace vacuous fourth grade science courses with more math to prepare them to learn real science while in high school. If more math does not fit the bill, foreign language instruction is a better use of their time at that age than playing with circuit boards.

Amendment 28

Following last week's suggestion, today I make a feeble first attempt to formulate an amendment to the Constitution, which simultaneously legalizes our current Social Security laws and reins in the federal government.

Proposed Amendment 28:


Section 1. In defining the powers of the Congress, the phrase 'general Welfare of the United States' in Article 1 Section 8 will be understood to grant no additional powers beyond those specifically enumerated either subsequently in Article 1 Section 8 or elsewhere in the Constitution. Instead, this phrase will be understood to prohibit the Congress from authorizing funds for purposes not benefitting all of the states.


Section 2. The Congress is authorized, but not required, to provide funds for the support of the aged.

Section 3. The Congress is authorized to promote the Progress of Science and useful Arts.

The second sentence of Section 1 returns 'general Welfare of the United States' to its original Madisonian meaning, and incidentally clarifies the unconstitutional nature of most earmarks. Last week I discussed the motivation for Section 2 of the amendment. Weaker, strictly political arguments might suggest changing 'the aged' to 'aged and the indigent' or 'aged and the infirm.' I added Section 3 in honor of the Tevatron and NASA. Such endeavors clearly do not lie in the domains of the individual states. I am sure the number of such (self serving) sections will grow rapidly if people seriously consider how much retrenchment of the federal government they truly desire. Ultimately, Article 1 Section 8 should probably be rewritten in its entirety. The primary goal of this exercise is to make constitutional those unconstitutional laws already enacted which neither party has the political will to repeal. Although this entrenches laws repugnant to most libertarians and many conservatives, the degradation of constitutional governance resulting from systematically ignoring constitutional violations (has been and) will be more detrimental to the long term health of our republic than any legitimization of the currently constituted welfare state.


I include below the text of Article 1 Section 8 for the convenience of the reader.

Article 1 Section 8:
The Congress shall have Power to lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;

To borrow money on the credit of the United States;

To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;

To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;

To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;

To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;

To establish Post Offices and Post Roads ;

To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;

To constitute Tribunals inferior to the supreme Court;

To define and punish Piracies and Felonies committed on the high Seas, and Offenses against the Law of Nations;

To declare War, grant Letters of Marque and Reprisal , and make Rules concerning Captures on Land and Water;

To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;

To provide and maintain a Navy;

To make Rules for the Government and Regulation of the land and naval Forces;

To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;

To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;

To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings; And

To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.

Constitutional Quick Sand and Social Security

The Tea Party has forcefully reminded the GOP of the constitutional limits on the powers of the federal government; the Republican majority in the House has responded with promises to adhere more closely to its oath of allegiance to the Constitution. On the other hand, the electorate largely favors many New Deal and Great Society social welfare programs whose constitutional bases are hotly contested (most often by people not running for office) . This places our newly empowered constitutional conservatives in a weak position. When conservatives oppose legislation which violates the Tenth Amendment's stricture:
"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people,"
the left can always respond that the same argument would apply to Social Security and challenge its opponents either to repudiate Social Security (and the sea of baby boomer voters with low net retirement savings) or to abandon their constitutional principles. Social Security sits as a massive counter example to most claims of strict adherence to the Constitution.

The constitutional conservative has two principled responses to the Social Security challenge. He can repudiate Social Security and hope that this does not lead to decades of governance by Obama clones. A politically powerful, albeit less fiscally responsible alternative, is to propose a constitutional amendment that simultaneously narrowly legalizes (constitutionalizes?) Social Security while further clarifying the limits of federal power. I have no yet formulated what form such an amendment should take (and welcome suggestions). Certainly such an amendment should at most permit a social security plan and not mandate one. In debating such an amendment, we would necessarily revisit the rationale for such a program, and likely redesign it. If we grant, for the sake of discussion, the desirability of offering government pensions, we may perhaps justify removing them from state control by the simple observation that the freedom to move between states would lead a rational citizen to spend his productive years in a low tax state and then move to a high benefit (and presumably therefore higher tax) state upon retirement.

My proposed amendment does not imply that the current Social Security program is an intelligent use of our limited resources. I have saved for my retirement and do not understand why less comfortable workers should augment my income when I retire in a few decades. At the very least, I think we should have some means test for Social Security, even though that will introduce new issues of moral hazard.
Nonetheless, the integrity of our Constitution requires us to legitimize the status quo, as we are exceedingly unlikely to repeal Social Security in the current political and demographic climate. The current willful avoidance of the issue simply encourages further erosion of respect for the Constitution and its restrictions on federal power.

Politics and Party Purity

In one nonpartisan state race this year, my county GOP endorsed a Republican candidate with a criminal record. I fought against this choice and lost. All my arguments fell on deaf ears. My opponents on this issue (essentially everyone else in the county party) cited only the candidate's greater experience in his favor. I objected that endorsing this candidate would taint our recommendations in other races with stronger candidates. The race is now over. There is no evidence that our endorsement tainted our other recommendations. In a large field, the flawed Republican candidate edged out a Democratic candidate by a few thousand votes. If our county GOP had endorsed my preferred candidate, the Democrat probably would have won. I prefer a flawed Republican to a liberal Democrat; should I therefore be glad that I was unable to sway my colleagues? I am still unsure what lesson this experience teaches. Contending lessons include:
(i) My political intuition is much poorer than my colleagues.
(ii) When my colleagues say 'experience', they really mean 'electable.'
(iii) My colleagues' political sensibilities are much closer to the general electorate's than mine are.

I was not upset this election cycle to see the GOP risk losing a few races nationally by discarding some experienced candidates who were all but indistinguishable from liberal Democrats. I think the long term health of the party is better served when it represents strong principles rather than a desire for power. Unfortunately, the line between supporting party principles and pursuing self defeating ideological purity, is not well marked on any map. In my nonpartisan state race, my objections were to a character flaw rather than a disagreement over principles; hence, I doubt the GOP (and therefore the public) would have been better served by a liberal Democratic win. On the other hand, my Republican colleagues now tell me that the losing Democrat is not particularly liberal and may, in fact, have been better qualified for the nonpartisan position in question.

As politics moves from the national to the local level, issues and the meaning of party labels become much fuzzier.