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.