In my view one of the most glaring indictments of the way philosophy and other humanities are taught and practiced is the senseless insistence on reading original works by the great masters. This is most apparent in the continued consumption of Plato, Hobbes, Aristotle and the like in philosophy but can be equally well be seen in the reverance for Chaucer, Shakespeare or other literary classics. To my horror this reverence for the original works is even being promoted in economics. So even though I gave a short reply in the comments at overcoming bias when this issue came up I’ve been meaning to discuss the question in more detail.

For the moment I’d like to set aside the issue of literature for another post and focus on subjects like philosophy and economics where (at least in theory) the aim is to genuinely progress towards a (more) accurate/useful understanding. Since I find it genuienly perplexing why one would ever feel the need to read the originals rather than the digested and improved material found in modern expositions as one does in math of physics I’ll quote Tyler Cowen’s justifications for returning to the original thinkers. Obviously these don’t represent every possible justification but they are the best justifications I’ve ever heard.

First though I’d like to be perfectly clear that the issue under consideration is whether there is some pedagogical benefit to reading original thinkers as opposed to modern summaries (of either the original thinker or simply the current state of the discipline). There is no accounting for taste so if you simply have some Plato fetish or like the way reading Plato makes you feel sophisticated you might find it more enjoyable to read Plato rather than more modern work just as someone else might prefer to have their philosophical arguments interspersed in Harry Potter slash. Also if your interest is in original historical research then influential works are a reasonable thing to read¹ but again the question at hand is the benefit of reading original works by great thinkers to the advancement of the discipline itself not it’s history or the practitioners feelings of sophistication. With this point clear let’s examine what Tyler Cowen has to say point by point.

1. Secondary sources are unreliable and they do not capture or understand many of the original insights. To remove it from the distant past, what I get from John Rawls or Robert Nozick is quite distinct from what I get from their distillers.

So what? The standard isn’t whether a latter distillation captures the exact content but whether it’s a more effective way to gain understanding. Reading a modern calculus book is extremely different from reading the original Newton. Newton’s notions of infinitesimals and fluxions have been excisced wholesale and replaced with the modern notions of limits and epsilon-delta proofs and that’s a huge improvement in the ability of calculus books to convey understanding.

2. Truly great thinkers require numerous distillers. Can you read just one book on Keynes? No. So you have to read a few. Shouldn’t one of these then be Keynes himself? Yes.

This presupposes the goal is to understand what Keynes thought. Keynes was a brilliant economist but he was just as human as the rest of us and some of his ideas were simply confused or poorly thought out. The benefit of later distillers is to transmit the insights while avoiding the confusions, so no, one of these shouldn’t be Keynes himself.

I mean imagine Keynes was really a highlander and was still alive and at the height of his intellectual powers. Who would it be more beneficial to read the 1936 Keynes or the 2010 Keynes who has used the intervening years to excise the confused parts of The General Theory and find more lucid explanations of the key insights? Surely it’s the 2010 Keynes who would (likely) provide the better explanation (if you disagree would you go back to his half-assembled notes? Further?). Yet surely if Keynes could improve on his own work than (as the goal is to convey economic ideas not Keynes personal beliefs) surely others could as well, especially when the benefit from the collaboration and exchange of ideas provided the academic discipline.

3. The errors of top thinkers are often more interesting and instructive than their successes. Distillers have a hard time capturing these errors and their fruitfulness.

But that’s the wrong comparison. The right comparison is whether it’s more useful to build upon the work of past greats and digest this new material including the mistakes made by those who have built upon the great thinkers of the past than to spend time digesting the errors of the past. Obviously if it was costless one would read every book on the subject but the key question question is would the time spent exploring the errors made by Keynes be better spent exploring later work that builds upon his insights.. The reason it’s so tempting to advocate reading originals is that we don’t properly take into account the opportunity costs incurred reading those originals.

Moreover, given that there is only so much time for students (or professors) to devote to learning a subject either one must give up totally on the idea of making progress or admit that it’s sometimes more effective to substitute modern materials for some works of great thinkers. Hence this argument either proves too much (progress is impossible because it’s always better to learn from the mistakes of past great thinkers) or proves nothing at all since we continuously make beneficial trade offs of replacing originals with more modern works.

4. We often read great thinkers not to learn what they understood but also to set our minds racing and to find interesting new questions. Great thinkers are usually better at supplying this service than are their distillers.

Again this assumes that the job of the distiller is to summarize the original author. A good analysis book doesn’t summarize Newton it digests his insights and presents them as part of a grander theory. Reading a modern analysis book does a much better job a posing interesting new questions than does reading Newton.[^empirial]

Moreover, I suggest this is largely a placebo effect. One is told that the reading great thinkers in the original is particularly inspiring so we search for questions to inspire us. We would probably do equally well if told that Joyce’s Ulysses conveyed deep economic questions. If you doubt this consider the stunningly large number of people who, despite not being religious, claim to derive deep moral messages and insights from the bible despite it’s blatant encouragement of genocide, rape, and every other kind of brutality imaginable.

5. Sometimes the value is in having read common sources and benefiting from the commonality per se. Great thinkers are usually more focal than any of their distillers and thus reading them is a good input for discussions with others.

OFten this is simply false as influential textbooks and articles are often just as widely read. More importantly by virtue of the novelty of their ideas original thinkers are usually lacking in clarity meaning the same work is usually interpreted in a host of different ways.. However, even if true this argues for more canonical books. In mathematics this issue is solved by the publication of various yellow books that provide a common base for everyone to use as a reference and there is no reason not to do the same for other subjects.

6. Original sources often help you challenge or reexamine your world view or intellectual ethos. Distillers very often pander to that world view, while pretending to challenge you.

Given their status as influential originals the content in these works has largely been either incorporated into your modern world view or people have developed standard objections. I know my world view (or even philosophical position) has never been threatened by the original work of an past great thinker but often it’s been shaken by a new argument or idea from a modern source.

7. Consider a simple comparison. You can read either Adam Smith’s two major books or any ten or even twenty books on him, toss in articles if you wish. It’s a no-brainer which you should choose.

Right, neither. Who the hell cares what some dude named Adam Smith thought. Given the choice between reading a modern economic textbook and any of Adam Smith’s books I know which one I would choose and it’s the same thing we always choose for undergraduates.

8. The best distillers often are original sources in their own right (and in part unreliable expositors), such as in Charles Taylor’s excellent book on Hegel.

Again the false dichotomy. Instead of trying to find out what Hegel said we should be finding out what is true (which in the case of Hegel will involve simply ignoring him).

9. Distillation works best in very exact sciences, such as physics and mathematics. If you rely on distillation for an inexact science, you will do best at capturing its exact parts. You will be left with a systematic bias, and knowledge gap, regarding its inexact parts.

So it’s only when you can’t actually go out and check whether going back to read the original works by great thinkers that it’s beneficial? That’s awful suspicious

Stepping back for a moment I would point out the fact that there are many different mutually contradictory disciplines of theology (every major world religion has one). Thus regardless of your religious views (and especially if you are an atheist) you must admit that there are academic disciplines which are totally bullshit. Now I would point out that in virtually all instances of theological study the original work of prior influential (but not prophets or otherwise supernaturally gifted) theologians is regarded as similarly important to read in the original.

Hence, we must all admit there are situations where academic disciplines are convinced of the important of reading influential past thinkers in the original despite even though it provides no actual benefit. Conversely in all those disciplines where we have reliable quantatative measurements of progress (with the obvious exception of history) returning to the original works of past great thinkers is decidedly unhelpful. Therefore at the very least anyone who wishes to claim that reading past great thinkers in the original (be it Plato, Keynes, Aristotle or whomever) has a substantial argumentative burden to meet and until they do the assumption should be against spending time doing so.

This morning a story on slashdot linked to A Mathematician’s Lament by Paul Lockhart as well as a blog post discussing the issue. This is the first time I’ve read Lockhart’s rant but little of what he said was new to anyone who has listened to any of the mathematicians vocally crusading for better mathematics education. As usual most of his piece was the same unrealistic claptrap about how if we could only show the children the joy and beauty of math all would be well. It’s a pleasant fiction to believe, and it’s seductive to think that with just one little nudge all children could discover the pleasure we take in mathematics, but it’s about as reasonable as believing everyone would love to garden, read Shakespeare or anything else if they were only exposed to it.

To be fair I was quite impressed with Lockhart’s brutally frank analysis of what currently passes for mathematical edification in K-12. Apart from teaching kids to sit still and signaling social status¹, for 95% of the class everything after multiplication (and a good bit before) is totally pointless. Go talk to some doctors (GPs), lawyers, managers, etc.. to solve a simple algebra problem (say two linear equations in two unknowns) and see just how few have the slightest clue. No one’s benefiting by making them rotely memorize some rules they promptly forget. However, the notion that if we only taught children real math they would gobble it up is simply absurd.

I remember taking a differential geometry class in college that was taught in what was (at least for me) an abominable way. No rigor, just vague comments about pictures and twisting so unsurprisingly I kept putting that homework off and gradually falling further behind. At that point understanding became nigh impossible. Just doing the problem sets made me feel frustrated, angry and perhaps a bit inferior and I’m unreasonably over confident about my mathematical abilities. Naturally one then puts them off and when you force yourself to work you just grind through the problems without any curiosity or hope of understanding the bigger picture. Psychologically you just can’t force someone to be curious and deeply thoughtful about a subject that makes them feel bad and that’s what understanding math requires. So certainly a sufficently bad teacher (who won’t follow a book) can discourage real learning but could better teaching really significantly encourage real mathematical understanding in K-12?

Sure if you somehow eliminate the social significance of mathematical ability and turned math class into a non-threatening fun activity like most HS art classes you might make some progress. That, however, is simply impossible. Nothing the teacher says can erase the knowledge that actually showing interest and talent in mathematics opens up many lucrative doors and signals intelligence. So long as the mathematically gifted are financially rewarded students (and their parents) will care about how they perform in the subject. Unlike art or literature math also has right and wrong answers and can often leave one feeling lost and frustrated so unavoidably half your student body will resent math for making them feel stupid and inferior even if they would never admit it. No matter how excellent the teacher they can do no more than try to distract the under performing students from inevitable comparisons with those who are doing better. Worse, any attempt to discourage people who dislike the subject from taking the courses will simply increase the incentive for them to camouflage themselves as someone who does like math to future schools and bosses. The problem would be a lot easier if it was just that some people weren’t smart enough.

I don’t really know what we should do about this situation. However, I suspect one reason people are so reluctant to face this possibility is that it would require us to explicitly consider how we want to trade off the benefit to the small fraction students who could benefit immensely from non-rote proof based mathematics and in turn contribute disproportionately to our economic growth against the interests of the larger number of students who are too intimidated by the subject to do anything but rote work. I think we ought to consider using programming, with it’s more video game/slot machine pace of rewards, as the means to teach logic and quantitative thought but that still doesn’t answer the math question.

Today on the front page of the dailycal is an article discussing the hardships student parents wil face as a result of UC budget cuts. The people interviewed in the article seem to think we should be moved by the unfairness of reducing the child care subsidy provided to graduate student parents and support the Graduate Assembly’s resolution to exempt child care from the proposed budget cuts. While I can empathize with any graduate student who faces tough choices because of our low wages (particularly at UC Berkeley) the universities subsidy of child care is blatantly discriminatory against people with other lifestyle choices and should be totally abolished not saved. I mean we surely wouldn’t tolerate a program that offered straight couples who wanted to have their own apartment (rather than rooms in a shared house) a subsidized low rent apartment but denied gay couples the same benefit so why do we tolerate a program that discriminates on this lifestyle choice?

My fiance and I will never have children but this hardly means that graduate school imposes no hardships on us. She is a graduate student at Harvard and I am finishing up at UC Berkeley and just as the low salary of graduate students makes it difficult to raise a child it also makes it tough to afford flights across the country. Yet does the university offer me a subsidy to visit my fiance the way it does to graduate student parents? No! Worse, this term UC Berkeley gave me a MWF teaching assignment (instead of the Tuesday one I requested) that made it impossible to visit my fiance over the weekends. But long distance relationships don’t get any consideration by the university while graduate students with children get automatic first dibs on teaching slots that are convenient for their child care arrangements. Moreover, the department is expected to bend over for graduate students with children if they need a particular day free while it’s just tough luck for me if I want to visit my fiance but can’t find anyone to substitute.

In light of this blatant unfairness does the article offer us any particular justification as to why we should subsidize those students who make the choice to have children? No, we are merely given a string of observations about how difficult it is to raise a child as a graduate student.

“If you have an infant, it’s $20,000 a year just in child care fees,” Keeley-Saldana said. “(The cost) really prohibits students from seeking their higher education degrees.”
…
With a new baby on the way, Cruz said the heightened costs would be “impossible” for he and his wife to meet.¹
…
Senior Dana Parsons, 32, said campus child care services are essential for student parents such as herself.
….
“Had it not been for subsidized care on campus, I would not have been able to attend school full-time,” she wrote in an e-mail.
…
“There is no good solution,” she said. “I’m not saying that I don’t think it’s fair for Early Childhood to be spared from cuts, but I’m hoping that they really do value the children on campus.”

First of all let’s make this absolutely clear. Failing to subsidize child care doesn’t force anyone to stay at home, leave graduate school or otherwise deny them the benefits of higher education. The lack of subsidized child care merely forces people to choose between the benefits of using their resources to have a family or attend school. This is no different from the fact that without subsidies or special considerations Sharon and I must choose between graduate school and getting to see each other more than rarely during the school year. It’s blatantly unfair to offer monetary subsidies and preferences to one lifestyle choice without the slightest official consideration for the other.

Of course sometimes radically unfair policies can be justified if they offer sufficient benefit for the society at large. However, in order to overcome the presumption against unfair policies such as this one would need compelling evidence that this was really the most cost-effective way to increase the number of US graduates in math/science or the equivalent. Since women make up a majority of graduate students even finding that subsidized child care did more to retain women than men wouldn’t justify the program.² Even restricting such subsidies only to the fields where women were underrepresented and granting the bizarre idea that numerical underrepresentation is ipso facto unfair³ one would need to establish that this kind of subsidy was particularly effective (more so than just giving women extra pay) to justify discriminating against those women who didn’t plan to have children.

I’m not going to even go into how this policy implicitly discriminates against those who have a more difficult time having children (the infertile, gays and lesbians). However, I will note that offering these benefits only to parents and not to those of use with other lifestyle preferences goes directly against the valid feminist justifications for legally required maternity leave and other bars against the implicit discrimination against women smuggled in via career punishment for maternity. However, unlike the lauditory goal of stopping corporations from imposing unfairly excessive penalties for one lifestyle choice (partially because of female stereotypes) we have a situation where the university is unfairly benefiting one lifestyle choice over another.

Of course I realize that few people are likely to be convinced by a logical argument in this situation. Most people want to have children themselves so, as is common with discrimination, it seems right and proper to them that people like themselves should receive a benefit. Moreover, the people who benefit from this program are easy to see while the small cost that all graduate students pay as a result is diffuse. So if you aren’t yet convinced just ask yourself this. How would you feel if things were reversed? Suppose I got subsidized air fare to go visit my fiance and got first pick of teaching assignments so my schedule would allow these visits but graduate student parents received no official consideration at all. If you find that disturbing tell me what’s different about this situation.

I’ve always sorta suspected that explaining mathematics to students in very concrete ways wasn’t really a shortcut but it was like being offered a magic lamp with a genie who will grant your wishes. You know something about it is too good to be true even if you don’t really know what it is. Anyway apparently now there is some evidence that my intuitions are correct.

Of course I don’t think this means one should never use analogies to concrete situations or that math must be presented as uninterpreted formal manipulation. Nor is it really true that I didn’t know why I found the teaching of math in a super concrete fashion troubling. Ultimately math is the use of abstraction to solve problems. The power of things like group theory, analysis, recursion theory or even calculus is the result of abstracting the relevant features from the motivating examples. This is just as true for the subjects we try and teach our students as it is for the subjects we study ourselves. For example, in order for students to understand (not merely memorize) how to take the derivative of an integral using the chain rule and fundamental theorem of calculus requires the students have abstracted away from the idea of functions as rules they can right down in terms of powers,ratios, trigonometric functions and exponentials and can accept a define integral they can’t compute as just another function.

Ultimately, interpreted correctly I don’t think this study really says anything that shouldn’t have already been obvious. It doesn’t say that concrete examples can’t help students grasp the abstract concepts being presented (they can) it just tells us that there is no shortcut to mathematical understanding. If you want students to actually understand math that means teaching them to understand the concepts abstractly and if you take the easy way out and encourage your students to understand mathematics in a particular concrete fashion instead of offering the concrete examples/analogies and encouraging them to move beyond it their understanding will suffer.

As a side note the entire discussion around this study is a perfect illustration of the fundamental confusion at the heart of mathematical education today. Framing the study as showing that concrete teaching methods fail because they aren’t as effective in teaching students to solve other concrete problems seems totally backwards to me. Frankly in the modern world being able to compute when too trains will pass or find the symbolic integral of sin(x) isn’t an important skill for most people. Go ask anyone over 40 who doesn’t work in a technical field to solve a system of two linear equations, integrate a function, or even multiply fractions and they aren’t likely to be able to do it. If the particular skills we pass on in math class were so important to everyone how has our civilization manage to flourish up till now? It might be sad, you might not like it but the strategies of asking a technical friend, using a calculator, or just not dealing with mathematical problems work pretty damn well for most people. On the other hand the ability to abstract away particular features of a class of examples is a skill virtually all professionals require.

Ideally we would stop blindly teaching the traditionally expected skill set and ask what we mean to accomplish. If we want to give people practical skills to use in their life we need to take a look at some empirical data about what if any mathematical education translates to practical benefit. You might think that everyone should be able to calculate with percents and fractions but if most people simply use the calculator on their cell phone then we have to consider the possibility that we’d be better off helping them practice computing in that way. Certainly some people need to learn how to do things like multiply fractions, compute integrals and so forth but that isn’t everyone. On the other hand if the reason to teach mathematics is to impart quantitative reasoning and the ability to reason abstractly then why the hell is most of our mathematical education blind computation?

In the chronicle of higher education yesterday there was a short snippet about academics taking performance enhancing drugs and if you have a nice proxy server you can read the longer article or the commentary in nature (you can also find the Volokh Conspiracy article that brought it to my attention). Now I was quite pleased with the reasonable approach taken in the Nature article. In particular I thought the following paragraph hit things right on the head.

Rather than individuals purchasing substances over the Internet, we believe it would be better to ensure supervised access to safe and effective cognitive-enhancing drugs, particularly given potentially dangerous drug–drug interactions. Such regulation must be evidence-based and a product of active dialogue between scientists, doctors, ethicists, policy-makers and, importantly, the general public. This may necessitate a new form of regulation because the remits of the existing health and drug agencies are for the regulation of medicines for treatment, not for enhancement.

If a new class of compounds (so far most ‘cognitive enhancers’ are effectively less euphoric versions of amphetamines) really is developed that appeals primarily to educated wealthy people rather than being associated with lower socioeconomic classes such a change in our regulatory outlook might actually occur. True, I’m skeptical that more than a modest cognitive enhancement effect is possible from drugs (they can’t fundamentally rewire the brain) but accepting the careful use of drugs as enhancements has the potential for massive increases in utility. While I doubt drugs are ever going to make us all geniuses there is no reason to believe that future pharmaceutical research can’t produce mood enhancing drugs with only mild side effects. The benefits to depressed people alone of not stupidly insisting that depression is always a disease (rather than an unfortunate extreme end of a distribution) and researching medications that might make everyone a bit happier would be huge¹. More broadly I’m sure that everyone has noticed that some people tend to be more happy and energetic than others (and studies have suggested these people are more productive as well). The benefits to society of a compound that could shift everyone’s baseline amount of happiness up to where it naturally lies for these bright happy people would be greater than any other change since the industrial revolution.

However, in the chronicle article we find a much less enlightened view from one interviewee.

The notion raises hackles in some parts of academe. “It smells to me a lot like taking steroids for physical prowess,” said Barbara Prudhomme White, an associate professor of occupational therapy at the University of New Hampshire, who has studied the abuse of Ritalin by college students. Revelations about the use of performance-enhancing drugs in professional baseball have stirred public interest recently, and she sees parallels between athletes and assistant professors. “You’re expected to publish and teach, and the stakes are high. So young professors have to work their tails off to get that golden nugget of tenure.”

Now I’ve always thought it was kinda silly to keep performance enhancing drugs out of sports² but there at least it’s merely a game and fairness is a principle concern. In academics, however, we are supposedly actually producing something of worth. We don’t try and tell academics they can’t spend more time on their work because other people have children to take care of or family obligations. It’s not about being a fair competition but about maximizing academic output. True, perhaps one might reasonably worry that these performance enhancing drugs don’t genuinely lead to more performance in the long run, i.e., they are a way of gaming the system, but short of that I see no reason why they shouldn’t be allowed.

Also I found it amusing the way everyone seemed to assume that it was unacceptable for students to take these sorts of drugs during exams yet no one tries to stop people with ADD from taking ritalin or amphetamine during exams and often even give them extra time. Of course ADD is a real issue but it falls on a continuum and the same drugs that help concentration with ADD have been shown to boost everyone’s scores on the SAT.

So I finally got my application in for the NSF postdoc and got some needed sleep. So instead of working on my math like I should be now I went and downloaded the new Radiohead CD, “Rainbows.” Now I don’t actually like Radiohead that much so I didn’t pay anything at all¹ and that’s a perfect example of the inefficiency of the current copyright system. I’m likely to get some positive utility out of this (satisfying a hoarding instinct if nothing else) and this utility is a pure loss on a normal copyright system. However, it’s pretty annoying to hear all the people on the media and in forums act as if the fact that people are paying Radiohead for their CD shows that this is a plausible alternative model.

Even paying $0 for real honest reasons (worth less to me than transaction cost of using a credit card) even I was inclined to feel a little bit guilty and no doubt this is what causes people who actually like Radiohead to chip in a reasonable amount. But one feels guilt primarily because you feel that Radiohead is somehow stepping out on a limb by trusting users to set their own price. If this was ever to become a common practice that pressure would disappear. More critically is that the very people like me this system benefits will cause it to break.

People have strong intuitions of fairness and if you ever tried to distribute music more generally with this sort of system people would start feeling like suckers when they pay twice what their friend did for the music. Ultimately there will be an inevitable slow creep to the bottom as people check with their friends and see that their only paying $6 so that’s not cheating if I do that or come up with other reasons why it’s okay not to pay a bit less. I mean hasn’t everyone someone justifying their use of P2P by saying they would buy music if only the studies didn’t produce such crap? The same process of self-justification would start to happen with self-priced products as well. Besides, who is going to decide to buy 5 CDs worth of music they only sorta like for their car trip because they only have $15 to spend and they value the CDs they really like more than that?

No, I’m afraid solving the inefficiencies of the copyright system will require a fundamental change to the system of IP for creative content. Some means of truly collective purchase is required and the best system that I can think of at this point is to put works in the public domain after 3 years or so with a taxpayer funded system that compensates content producers based on numbers of tracked downloads from some central online repository. Maybe some clever person can figure out something better but as IP fills a bigger and bigger role in our lives the unacceptable inefficiencies of the current market become less and less bearable so sooner or latter something will change.

Rumsfeld’s plan to become a fellow at Stanford’s Hoover Institution has become the focus of protest. Now I think that Rumsfeld fucked up Iraq pretty badly and is thereby responsible for thousands if not millions (remember the Iraqis) of deaths. Given his popularity, especially among the left, it is no surprise that some liberals would protest this appointment. Some people would protest the fact that he was getting any job more prestigious than janitor. However, for Stanford professors to demand he not be given this appointment is an unacceptable attempt to tear down academic freedom and turn academic appointments into popularity contests.

First of all let’s make it clear that the protesters really are trying to subject academic appointments to a political test. Sure, they might raise a smoke screen about Rumsfeld not having authored many (any?) academic papers but if this was really the pivotal concern they would be demanding universities end the general practice of hiring ex-politicians as fellows. No one has given any plausible reason to believe that Rumsfeld would not have at least as much to offer the campus community in terms of real world experience in government and inside knowledge of his eventful years in government as other politicians who are offered these kinds of appointments. In other words it is as clear as day that those protesting this appointment of Rumsfeld are demanding that an otherwise valuable addition to the campus community be passed over for his political views¹.

Indeed this isn’t too far from what is being said in the petition against Rumsfeld’s appointment. A petition the New York Times says is being signed by many professors.

We view the appointment as fundamentally incompatible with the ethical values of truthfulness, tolerance, disinterested enquiry, respect for national and international laws and care for the opinions, property and lives of others to which Stanford is inalienably committed

Whoa. This is fucking nuts. Are they saying that Stanford should refuse to hire professors who argue against respecting national laws? What about academics who argue that government lie more or that the values of tolerance are overstated? Even if you actually believe that these sorts of views should disqualify one for a fellowship it’s merely a political belief that Rumsfeld is particularly at odds with these values. A good case could be made that Rumsfeld is more truthful than many of his equivalents and cares more for the property and lives of others than the protesters. He may have made a stupid mistake in invading Iraq but at least he seems to be concerned about the fate of the Iraqi people unlike many of the anti-war protesters who don’t seem to have even stopped to seriously consider what is in their interest. Ultimately what you believe about how good a defense secretary Donald Rumsfeld was is irrelevant. Rumsfeld is not advocating any anti-scientific or beyond the pale view like intelligent design or white supremacy and however strongly you might disagree with his politics or choices as defense secretary these aren’t good reasons to oppose his fellowship.

So several professors have called into the kqed show about this topic while I’ve been writing this and justified their opposition to the appointment by claiming that Donald Rumsfeld’s involvement with Abu Gharab make him a human rights violator and a violator of international law. Presumably the argument is that it would be reasounable to deny Hitler or Stalin appointments no matter what their academic credentials and it is thus reasonable to deny Donald Rumsfeld an appointment on the same grounds. This is pure sophistry to justify acting on their strong emotional reaction to Rumsfeld.

Not only is there insufficient evidence that Rumsfeld was more than negligent or cultivated an approving attitude of harsh terrorism to deny him a job even if he had personally tortured prisoners for information this still wouldn’t justify denying him the appointment. The view that it is reasonable to torture people for information when you believe it will stop more suffering than it causes is hardly beyond the academic pale and if you believe that we’ve made Iraq worse than it was in Saddam you are tacitly agreeing that sometimes human rights violations are a net positive (when they hold sectarian violence in check). The international law point is pure bullshit since there is more clear cut reason to believe Clinton violated international law with his (laudable) intervention in Bosnia than Rumsfeld did and if people really believed in this justification they would be getting out treaties and citing chapter and verse instead of using them to stand in for their vague emotional feelings on the issue.

Ultimately I’m skeptical of the idea that any views or prior actions justify denying academic appointments² but even if some views or actions are beyond the pale the mere fact that Bush was reelected just four years ago with Rumsfeld by his side is enough to show that Rumsfeld doesn’t fall into this category. You can try to play clever word games to reclassify just the people you really really don’t like fall outside the protection of academic freedom but if academic freedom is going to be worth anything it needs to offer a robust protection of divergent views and there is no robust distinction that can be drawn between Rumsfeld and other similar appointments. Ironically Rumsfeld is just going to come give some talks at Stanford, his days of causing harm are over, but the professors protesting his appointment are attacking important academic values. Does that mean that by their standard it would be fair to oppose hiring them?

I’ve been critical of the UAW grad student union at UC Berkeley for some time. While I’m generally skeptical of the (direct)¹ benefits of unions I think there is a plausible argument for graduate student unions as well as unions in potentially hazardous working environments, professions with particularly low liquidity or those employing illegal workers². In potentially hazardous professions unions serve an important social good by mitigating the harm of many people’s irrational tendency to underestimate risks in familiar situations. Left up only to the free market I suspect that people’s desire for the immediate reward of high pay would often encourage them to accept jobs where the risk of serious injury outweighed the reward of increased pay. This is obviously not the case for grad students but there is a similar problem of hidden risk. In particular graduate study is only a worthwhile payoff if one truly receives a diploma meaning that every year spent in graduate school is effectively a deposit of resources into the university that goes uncompensated should you not graduate. Just as people’s irrational failure to take into account future risk of death can justify the otherwise inefficient mechanism of union bargaining so too can their irrational failure to take into account the risk of either not graduating or receiving poor recommendations if they don’t do excessive lab work for their mentor justify grad student unions. Somewhat counter-intuitively I take the primary benefit of unions at this stage in US history to be their role in restricting employee choice. That is by preventing employees from agreeing to certain arrangements (yes I’ll work this dangerous job for more cash or I’ll do 80 hours a week in lab for a good recommendation) they prevent employers from providing incentives that prey on human irrationality.

I recognize the benefit the UC grad student union provides for many grad students in this fashion (thankfully not truly necessary in math) and since I think TA’s here aren’t paid nearly enough I remained in the union despite a certain skepticism of it’s political policies and role in restricting differential grad student pay for different departments. However today I finally sent in an email asking to be removed from the rolls when I saw the most recent bargaining update they released. I provide the full text after the break but the section that really drove me to ask to be taken off the roles was the following:

CHILDCARE: the administration rejected our proposal to subsidize employee childcare costs though they recognized the need for a childcare program. One university spokesperson accurately characterized our proposal as “a subsidy program to enhance an [employee’s] ability to matriculate, be gainfully employed and contribute to the mission of the university.” The next day, another university representative, in rejecting our proposal, said, “The University believes that there are sufficient child care resources provided to most of the individuals that you represent, and those programs are both effective and cost effective . They provide services at a reasonable cost, recognizing the financial needs of the students.” This remark displayed an arrogant disregard for the realities of life for teaching assistants, readers, and tutors with children, who more often than not face lengthy waitlists and programs that absorb at least half of their monthly wages.

I have every reason to believe that grad student pay is a zero sum game. Every dollar the UC spends to increase child care resources is one less dollar that can be used for other sorts of graduate student support. Thus by taking the position they have the union is basically advocating for a transfer of money from my pocket to the pockets of people with families.

Now I don’t have anything against grad students who choose to raise families and I sympathize with the fact that it is very difficult to raise a child on a graduate student’s salary. However, it’s also fucking difficult to try and afford frequent plane flights across the country to maintain a long distance relationship. I’m sure it’s equally difficult to try and visit sick relatives, help with the family business or any other major life choice that requires money. Now I could see an argument that certain sorts of life choices tend to produce more utility so we should subsidize those at the expense of people who would use their money to go skiing in Vale. Yet on such a theory it should be relationships, which have a much stronger correlation with happiness than children, that should be supported and I have no doubt the number of grad students at Berkeley in long distance relationships is of the same order of magnitude as those who have children.

Now someone is undoubtedly going to say something about women running out of time to have children but I would argue that relationships, not reproduction, is the truly time sensitive concern. Very few women in grad school are anywhere near menopause and upon graduation they can still choose to reproduce but once out of grad school your ability to meet worthwhile new people plummets. Sure you could argue that once out of grad school it is very difficult for a woman to have a child without taking damage to her career but it is misleading³ to suggest this is a gender equity issue and uncompelling compared with the unconditional increased difficulty of meeting a significant other outside of school. Now I certainly agree that academia unnecessarily penalizes people with competing interests such as child care while they are young but if anything academia needlessly penalizes relationships with other academics more than it does reproduction. In other words every valid concern about fairness or individual utility that favors subsidizing childcare also favors subsidizing my plane flights to Boston as well as many other life choices.

What then about the argument that affordable childcare is needed for the child’s wellbeing? This might be a compelling argument if we were talking about a group besides grad students but while expensive child care might burden the grad student it is unlikely to cause the child to be neglected or otherwise suffer. Given the various studies suggesting that the difference merely adequate and excellent parenting makes in quantitative measures of a child’s future success is quite small this argument just doesn’t hold water for grad students. Grad students are the one group we can count on to delay having a child or rearrange their lives to make sure the kid isn’t neglected.

What then about the final argument that we need to encourage more grad student types to reproduce. I think this is the only plausible case to be made but I no longer think it is compelling. The idea that we need to encourage smart people to reproduce as some kind of selective breeding program seems to make a subtle mistake about the way natural selection works. In the long run evolution will either manage to put together the little tweaks that make grad students smart with a strong desire to reproduce or it will find a better unrelated path toward intelligence. As far as the near future I don’t see subsidies for grad student families making huge differences in the electorate but I do see social benefits accruing from discouraging academic women to reproduce. Certainly anyone who believes in the role model theory for affirmative action should think that the more we can do to discourage women from opting out of academia for children the better. In fact anyone who believes that women are somehow triked or brainwashed into taking more than their fair share of childrearing should oppose this sort of reproductive support on the grounds that it reduces the unfairness and works to eliminate the stereotypes that caused the problem.

Ultimately I was uncertain about my support for the UAW grad student union in the first place and this message finally convinced me that my membership was doing more harm than good. The university doesn’t even want to go back to the days where biology grad students could be made to work 80 hours a week but my support for the union signals my acceptance of fucked up feel good policies like prioritizing families over the childless and silly demands for equality between the summer session and the school year⁴. Since the union isn’t going to disappear all my continued membership does is help convince the union and the university these stupid policies are what the grad students want. Besides I just feel dirty being affiliated with a organization that not only makes such unjustified policy demands but also alleges “bad faith” on the part of the university for simply believing that the union’s positions aren’t correct.blah⁵

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In addition to the cost I usually find closed source text editors and similar utilities to be lacking in features and insufficently extensible. Textmate for OS X, however, is a glaring exception. It is well worth the cost and I’m constantly surprised by the many useful bundles and customizations available (for instance convienient remote editing with Cyber Duck or easy blog posting using the MetaWeblog API). So when Texmaker started slowing down on large complex files¹ I resolved to switch over to using textmate to write up my mathematics in LaTeX.

However, textmate’s prompt syntax highlight combined with the depreciated use of ‘$$’ to start displaymath mode was really annoying. Each time I would start to add inline mathematics by typing ‘$’ textmate would automatically provide the closing ‘$’ leaving me a line like this:

every $g \fungeq f$ that is ‘close’ to $f$ can compute $$

Of course textmate now interprets the remainder of my file as part of a displaymath block started by the ‘$$’ consequently changing the syntax highlighting. Since writing up theorems involves lots of inline mathematics this quickly became very annoying.

Anyway in case anyone else runs into the same problem let me share the quick fix I used. Go into your bundle editor and in the Latex bundle edit the language TeX. Find the following section

name = 'string.other.math.block.tex';
   begin = '\$\$';
   end = '\$\$;

and change it to:

name = 'string.other.math.block.tex';
   begin = '\[';
   end = '\]';

Of course this is something of a dirty hack since it disables the correct syntax highlighting for the ‘$$’ abbreviation. But since that is depreciated you always use ‘[' and ']‘ right?

If anyone knows the ‘right’ way to do this I’d love to hear.

To avoid confusion let me emphasize that I think it is pretty much mandatory for GSIs to make themselves available during the time leading up to the final to answer student questions and otherwise explain the material to students who ask. But the more I think about it the more it seems like offering a true review session, the sort of thing where you prepare specific problems for the students and have a spiel prepared for them is actually harmful (posting a list of practice problems to the web for all the students to try is a different matter and something I approve of).

Before we can even get a grip on this question we need to be clear about the goals of a class like this. Given that these students are fairly unlikely to ever use this material outside of this class three reasonable goals spring to mind.

1. Actually create real understanding in the students
2. Actually teach the students the skills of calculus.
3. Prepare the students for the second half of the year if this is the first semester.
4. Train the students to think quantitatively/formally (in a very weak sense)
5. Function as a hurdle passage of which indicates a certain level of work ethic, intelligence and ability to learn

No matter what we take the goal of the course to be we have two possibilities to face. Either review sessions are genuienly effective at improving student performance on the final or they are not. If offering genuine review sessions (as opposed to say office hours) doesn’t offer a substantial benefit over holding office hours then holding them is either a waste of time or some kind of dastardly trick played on the students (who are all clearly lead to believe the aim of the review session is to help them study) and in either case ought to be discouraged not celebrated . On the other hand if offering genuine review is substantially effective at raising exam scores we have to ask what makes these few hours have such a big impact.

From my experience I would conclude that what makes a review session effective at raising exam scores isn’t that it conveys more understanding than office hours, just the opposite in fact, but because it helps the students get the low hanging fruit. In particular it’s been my experience that the primary advantages review sessions have over office hours consists of helping the students avoid stupid errors like forgetting the +C in an integral, bootstrapping off the Ta’s implicit understanding of what sort of problems the professor is likely to ask, and seeing all the types of problems laid out at once letting the students build up a lookup table letting them infer what type of problem they are being asked using textual hints rather than real understanding. In short, to the extent review sessions are effective it isn’t because they make significant contributions to understanding.

Yet even if you think that having a real review session as opposed to just office hours has some benefit surely this is offset by the harm it does undermining the value of the test as an assessment. For starters since review sessions are offered outside normal class periods it is likely that some students will be unable to attend, or find it significantly more difficult to do so. With office hours the same TA will often have a range of options while with real review sessions there is often implicit (if not explicit) pressure not to attend another Ta’s review session and frequently only one or two Ta’s will offer full scale review sessions while the rest will offer something between office hours and review sessions.

Review sessions surely reduce the effectiveness of the exam in estimating work ethic or ability to learn independently as compared to office hours. To the extent that these math courses are simply hurdles to make sure that the students are smart and disciplined enough any kind of hand holding (as opposed to offering office hours for those who want to make use of it) is counterproductive. As many people don’t attend review sections because they judge it a poor trade off (need to study for other finals more) any ability review sessions have to improve grades without increasing understanding or future ability to apply the material undermines the ability of the exam to measure these attributes. Also more generally it seems like the more test taking strategies that students learn to use on the exam, e.g., learning to use textual clues to the type of problem, the worse the test will be at judging either actual understanding or ability to apply these skills in any context but this particular course.

In short it seems to me that the benefits of actual review sessions are quite small compared to those from office hours even though they may be quite effective at raising exam scores. On the other hand the harm done by review sessions to any reasonable conception of what course grades are supposed to track seems significant. Yet despite this holding actual review sessions seems to be uncritically regarded as a good thing for a TA to do and I’ve never heard of a professor banning them. At the very least professors should require that any TA who makes a review sheet available post it on the web to make it easily available by those without friends who attended the review section.

I’m well aware that most review sessions are offered with the best of intentions but that is my real complaint. During my 5 years of teaching I’ve seen a lot of strong attitudes about how teaching should be done and a whole host of other background assumptions about what makes for good teaching but virtually never heard any serious ground up analysis of what we are trying to achieve. At the very least it seems perfectly plausible that review sessions are actively harmful yet this sort of consideration doesn’t ever seem to come up. Perhaps doing so is too depressing and we need to pretend we aren’t inflicting totally useless material on students who won’t ever use it while making them hate math along the way but it seems we could be a lot more useful if we actually thought through what we were trying to do rather than taking for granted how we should teach and then trying to justify it.

For instance I think just having to draw a line between when it is acceptable to muck with grades to motivate students (allowing not turning in HW/low attendance to impact grades) and when it is not (seripticiously giving girls a 5% bonus in the class if we discovered this improved both sexes motivation) would be a huge improvement over the current situation.