Archive for May, 2005

And then, on sixth down, the Eagles gained 4 yards

“It has nothing to do with football,” [Mildred] Bazemore said. “It has to do with the mathematical concepts that you’re studying.”

GRRRRAAAAAGGGHHH!

That’s approximately how I reacted to the above quote, taken from a news report about a particularly boneheaded standardized test question devised by the geniuses at the North Carolina Department of Public Instruction (hat tip: FO). The question asks students to determine a football team’s average gain on the first six plays of some hypothetical football game. Unfortunately, this hypothetical game doesn’t abide by the most basic of football’s rules:

The team opened with a 6-yard loss, a 3-yard gain and a 2-yard loss, which would have made it fourth down with 15 yards to go for a first down. The team’s fourth play was just a 7-yard gain, yet it maintained possession for a 12-yard gain and a 4-yard gain on two additional plays.

Now, it doesn’t particularly bother me that the test question is badly written (and pretty much guaranteed to confuse anybody with an ounce of football awareness); these things, though unfortunate, do happen, no matter how much editorial oversight there is,1 as anybody with an ounce of teaching experience will tell you.

No, what gets my blood boiling is the nonchalant response on the part of Ms. Bazemore, the chief of the DPI‘s test development section. This notion that such a subjunctive test question “makes sense mathematically” and “has nothing to do with football” is, I submit, symptomatic of the educational institution’s generalized and deplorable mistreatment of mathematics at both the primary and secondary levels.

Okay, admittedly, I’m being a bit hyperbolic here, but the basic point is this: Bazemore’s comments suggest that she believes that there is a disjunction between “mathematics” and “the real world” (here embodied by football), that the platonic ideal of (-6+3–2+7+12+4)/6 = 2.67 is only sullied by the interference of words and ambiguous readings. In other words, she seems to think that mathematics is (or, at least, should be) purely abstract, purely computational and, as a result, utterly boring to anybody that isn’t autistic.

Again, interpolating all of this from some throwaway comment to some undoubtedly bored reporter is a bit extreme, except for the fact that virtually every public school teacher and administrator I’ve had the extremely mitigated pleasure to interact with holds this exact view (I went to public school K-12, so I couldn’t tell you about private school teachers or administrators). This is especially true of elementary school teachers, who either secretly hate math or are exactly the sort of detail-oriented obsessive-compulsives who loved memorizing their multiplication tables as a kid but hated word problems and philosophy classes, but it also tends to hold among middle- and high-school math teachers (somewhat more surprising, since these people teach math exclusively, in contrast to their primary-school counterparts).

This all derives, I think, from a poor understanding of what mathematics really is, which is certainly understandable, but the end result is that the misunderstanding is propagated to the next generation for pretty much the same reason it got propagated to the last generation: teachers make math classes miserable, so students not unreasonably conclude that math is miserable.

So what’s the misunderstanding? Basically, the notion that math is conceptually equivalent to memorizing formulas and plugging numbers into them. Certainly, this is the bulk of the content of your average math class in both primary and secondary schools and even in most college math classes below about the 300 level (which range, needless to say, encompasses the totality of the majority of the population’s experience with formal mathematics education). Rare indeed is the math teacher who seems to understand and, more importantly, can communicate that mathematics is fundamentally not about plugging numbers into formulas but rather about coming up with those formulas in the first place. No matter which branch of mathematics we look at, from the purely theoretical to the applied, the mathematicians or scientists working in that branch are, fundamentally, taking what they know and trying to synthesize it in some original and creative way to produce some new theorem or formula that better describes the situation. The data that goes into this synthesis may range from the completely abstract to the completely concrete, but the basic process is pretty much the same and totally at odds with the plug-and-chug process, which produces nothing conceptually original.

And yes, I know the traditional objection of the public schools: “That all sounds great in theory, but you can’t even get to that point without memorizing your multiplication tables or simple integrals.” Which is all true, in a sense, but also completely false. It’s probably true that you won’t ever prove the Riemann Hypothesis if you don’t know that 8×9=72 or that ∫cos x dx = sin x + C (though there’s no theoretical impediment), but such a perspective ignores the fact that, at some point in the course of human history, such “elementary” questions were just as mysterious, even to the intelligentsia, as the Riemann Hypothesis currently is and their solutions were just as exciting as a proof of the Riemann Hypothesis would be today.2 Whether the actual history of such problems is formally introduced into the course of instruction or not (and, despite generally being in favor of such an approach, I do have mixed feelings about it), there’s certainly no reason not at least to try to impart the same sense of mystery and discovery into the proceedings that the original discoverers/inventors of the material experienced. In other words, rather than taking the attitude that “I have a bunch of facts which I will try to cram into your head,” one would like to see more math teachers take the attitude that “I am going to try to give you the support and the tools you need to discover a bunch of interesting and useful facts for yourself” (with the additional side benefit that the students may discover more of those facts than appear on the curriculum). Admittedly, this is supposedly what “New Math” was (partially) about, but the methodology there was (or at least became) entirely wrong; a student’s feelings about math are pedagogically null to his fellow students.

The first step in this path, needless to say, is to try to view “word problems” less as particularly inefficiently coded messages (wherein we encode the “real problem,” which is something like (-6+3–2+7+12+4)/6=2.67, into this ambiguous cipher we call the English language) to be decrypted by the student and more as examples of actual, conceivable problems that might arise in the student’s experience and which can be attacked using various mathematical tools and tricks which he has (or, at least, should have) at his disposal.3


1. Though Colby Cosh makes an interesting point in the context of journalism that too much editorial oversight may actually be a bad thing. His entire perspective is extremely interesting, especially since he is both a professional journalist and an experienced and widely-read blogger.
2. Although there’s some question as to whether anybody would actually recognize a proof of the Riemann Hypothesis even if it slapped him in the face, an issue addressed, more or less, in the provocatively-titled “Definitional Drift: Math Goes Postmodern.”
3. And yes, I know I’ve addressed this issue several times before (see “From politics to mathematics and back,” “A beginner’s guide to producing new results in mathematics,” “…you just get used to them” and, tangentially, “Mathematics and sex” for four of the more recent examples), but, as something of a math teacher myself, this is an issue that I think a lot about and, more importantly, I think I’m getting closer and closer to actually expressing myself clearly on the subject.

To be or not to be done with all this

Allow me to say what I hope will be my final words on the whole Iraq debacle. Those who have been reading this site from its inception will know that my views on this subject have changed on more than one occaison, which I don’t hold to be anything to be ashamed about in regards to a subject so inherently volatile, since it seems to me that only someone totally intransigent would have remained completely unperturbed through the entire course of it. I have tried to reconcile my sympathy for the hypothesis that the world is almost always better off when the number of megalomaniacal dictators is reduced with my disapproval of the manifest incompetence which has poisoned the effectiveness of this whole adventure to a surprising extent. I suppose in the end I fall in with that whole group that I have often mocked in the past that is fairly supportive of the ostensible goal of ridding the world of said murderous regime while remaining extremely skeptical of the method by which it has actually been carried out.

Let me make the following analogy: suppose a man leaves his house and murders several neighbors one day. The government in response puts him under house arrest. Then a bit later on someone else alleges that he left his home and procured a number of pistols and other firearms. The police demand to enter his house and he refuses, then relents. They show up, don’t find anything, have some arguments with him about where they are and are not allowed to search, and then leave. Two weeks later they show up with a judges’ decree condemning him for uncooperativeness and cut his head off. If this is not the most lurching, inconsistent, arbitrary sort of justice imaginable, I would like to see what is, even if everybody, most especially the neighbors, would be better off if he were removed from their proximity. Of course the U.S. military is not exactly an accepted world governing body, but since it is essentially assuming the prerogative of enforcer of “international law” then it might at least act as a responsible government and propogate a coherent set of policies, infractions, consequences, etc. This is purely practical self-interest, since the single greatest consequence of this whole mess for the U.S. is that America is seen as the aggressor by the rest of the world. I can understand the point of view of those who hold, as the above example suggests, that the whole thing was actually a defense of international laws or principles or whatever, but that’s trying to have it both ways: the American government is exempt from being constrained in any way, but it can enforce “international regulations” whenever it chooses, no matter how inconsistently.

I think that the end of the Iraqi regime has been beneficial to Iraq, and the world, as a whole, especially when one considers that all the terrorism and violence since then has been largely, in my view, a continuation of that regime’s attempt to regain power by setting off a civil war, and that this would almost certainly have been the result no matter how or when the regime fell. However, ironically enough it seems to me that America has incurred the most needless damage in this whole thing, what with the military commitment and the cost and the overall degradation of its image abroad. As one of my friends said the other day: “Do you remember when Americans were popular in the world?” It is in the interest, as well as being the obligation, of any peaceful nation to remain at peace until threatened by an aggressor, and above all never to become the aggressor. I can understand that aggression can come in more subtle forms these days than tanks overriding a frontier, but if arms stockpiling is the new standard, than that must at least coalesce into a clear principle, and of course even then it must fall within the bounds of reason.

Saul Alinsky said that the price of a successful attack is a constructive alternative, but I don’t think that those who approve of the dictatorship coming down but still deplore the circumstances are liable for inconsistency or even obligated to propose an alternative means by which it could have been destroyed. After all, everyone wishes for things for which they are not willing to sacrifice everything, and I wouldn’t have spent the price of the last three years for the questionable benefits that Iraqis may have gained by it, just as the forty years of the Cold War were preferable to some sort of Ragnarok with the Soviet Union in the late ’40′s. These types of governments have a tendency to implode sooner or later, and since the U.S. is much more stable and powerful than any of them, time is always on its side. There is no reason to squander that advantage by bringing matters to a head and subjecting everything to the perfidies of fortune. Freedom is a cause worth fighting for, but likewise a people that desires freedom should fight for it themselves, because only they can ultimately adjudicate the best form of social organization for themselves. This was as true for Russia as it is for Iraq.

Towards the peaks

From this article, about the Russian satirist Vladimir Voinovich, the entirety of which I recommend the reading for the other little tidbits of his wit that are included, I can’t resist posting a little excerpt, since my brother was elsewhere talking about the mixture of the sacred and profane. In this case it’s more like the learned, the poetic and the profane in sublime satire, which to me recalls nothing so much as Le Neveu de Rameau (Rameau’s Nephew), by Diderot, which I also greatly recommend, with its erudite jokes about in stolchim regit (not sure about the Latin, since I don’t have the text with me) and an arrogant ecclesiastical prelate sitting come un maestoso cazzo fra due coglioni. Anyway, here it is:

“Naturally, in these little sheds (the younger generations perhaps cannot even picture this) on both the M side and the W side the wooden floor was embellished with a dozen or so large holes in a long row and soft heaps deposited haphazardly around them….

The visitors squatted in a row, like sheaves of wheat standing in the field, and I recall with particular sympathy the old men suffering from arthritic joints, constipation and hemorrhoids, who strained until they turned blue, wheezing and moaning and groaning as if they were in a nativity home.

[The narrator's friend] used to say that if it was up to him to decide what monument to erect to our Soviet era, he would not have commemorated Stalin or Lenin or anyone else, but the Unknown Soviet Man squatting like an eagle on the peak of a tall mountain (Mount Communism) deposited by himself.”

p.s. The title of the post is the title of an old Vladimir Vissotsky song about mountaineering, which is also about communism in a subtle way.

addendum 7/12: now that I actually have a copy of Le neveu de Rameau in front of me, I can provide the passages from Diderot in full (translations mine):

“On s’enrichit à chaque instant. Un jour de moins à vivre, ou un écu de plus; c’est tout un. Le point important est d’aller aisément, librement, agréablement, copieusement tous les soirs à la garde-robe. O stercus pretiosum. Voilà le grand résultat de la vie dans tous les états” (“One enriches oneself constantly. One day less to live, or a dollar more; it’s all the same. The important thing is to go easily, freely and copiously to the bathroom. Oh precious manure! That’s the major result of life in all its forms”).

“Comment, l’abbé, lui dis-je, vous présidez? violà qui est fort bien pour aujourd’hui; mais demain, vous descendrez, s’il vous plaît, d’une assiette; après-demain, d’une autre assiette; et ainsi d’assiette en assiette, soit à droite, soit à gauche, jusqu’à ce que de la place que j’ai occupée une fois avant vous, Fréron une fois après moi, Dorat une fois après Fréron, Palissot une fois après Dorat, vous deveniez stationnaire, à côté de moi, pauvre plat bougre comme vous, qui siedo sempre come un maestoso cazzo fra duoi coglioni” (“‘How now, priest,’ I say to him, ‘are you presiding? That’s all well and good for today; but tomorrow you will descend a seat; the day after tomorrow, another seat; and so on from seat to seat, whether to the right or the left, until you come to the seat that I once occupied before you, and Fréron before me, Dorat before Fréron, Palissot before Dorat, and you will finally stop beside me, poor little bugger that you are, sitting like a majestic penis between two testicles’”).

Sex through plate glass

While reading about various Catholic saints on Wikipedia today (don’t ask), I skimmed through the entry on San Juan de la Cruz, the Spanish mystic and poet. I couldn’t help but be amused by the analysis offered therein of San Juan’s famous poem “La Noche Oscura”:

Dark Night of the Soul narrates the journey of the soul from her bodily jail to her union with God. It happens during the night, which represents the hardships and difficulties she meets in detachment from the world and reaching the light of the union with the Creator. There are several steps in this night, which are related in successive stanzas.

Not that this is necessarily wrong (it’s certainly the orthodox interpretation and the one San Juan de la Cruz himself gave to justify himself to the Inquisition), but it’s definitely the interpretation of someone who’s only read “La Noche Oscura” in stilted translation and not someone who has read one of the most erotic poems ever written in the Spanish language (which is no mean feat; after all, this is the language about which Heinlein once said “the Spanish language is so beautiful that much of its poetry sounds best if the listener does not understand the meaning”). As always, I’m reminded of one of the favorite sayings of the late, great Bill Bonds:

Reading poetry in translation is like having sex through plate glass: you can more or less see what’s going on, but you won’t feel anything.

Mathematics and sex

In reference to Curt’s latest post, I feel obligated to make a quick comment on the linked discussion between Steven Pinker and Elizabeth Spelke, specifically Spelke’s comments on mathematical aptitude. Now, I’m not (yet) a card-carrying member of the mathematical establishment, but I like to think two years in an Ivy League Ph.D. program has given me some insight into how mathematics works, certainly more than I think Spelke, despite her apparently solid reputation as a psychologist, demonstrates. Her argument is that any difference between men and women in performance in the hard sciences and mathematics is socially, not biologically, determined.1 Okay, as valid a hypothesis as any other. What’s her evidence?

Well, it turns out to be surprisingly elusive, especially coming on the heels of Pinker’s well-reasoned argument that there is some biological basis for the difference of performance between men and women. Of course, she’s right that it’s misleading to look at, e.g., the SAT math test to provide a definitive answer, because the writers of that test can tweak it to get pretty much any result they want (although it is interesting to note that she apparently doesn’t even consider the possibility that the writers of the test are trying to create a test that most closely tests mathematical aptitude, whatever that is, instead talking about how “they can create a test that makes women look like better mathematicians, or a test that makes men look like better mathematicians”). That having been said, it seems downright disingenuous to me for her to acknowledge that males and females tend to have different cognitive profiles, while denying that there’s any chance that has an effect on aptitude for mathematics:2

Finally, the mathematical word problems on the SAT-M very often allow multiple solutions. Both item analyses and studies of high school students engaged in the act of solving such problems suggest that when students have the choice of solving a problem by plugging in a formula or by doing Ven [sic] diagram-like spatial reasoning, girls tend to do the first and boys tend to do the second.

This comes as a continual surprise to non-mathematicians (who imagine that mathematicians sit around doing more and more complicated arithmetic and calculus problems all day), but plugging into a formula is virtually worthless from a mathematical perspective, whereas “Ven[n] diagram-like spatial reasoning” is fundamentally similar to the sort of thinking that a professional mathematician does. Thus, if women tend to be plug-and-chug types, it shouldn’t really be a surprise that they are underrepresented in mathematics departments. Of course, this doesn’t demonstrate that there’s any biological basis to the difference, but Spelke’s apparent contention that plug-and-chug methodology and more abstract reasoning constitute equivalent levels of mathematical aptitude seems pretty naïve.

That having been said, she does make a strong argument when she points out that women and men get equal grades in math classes in college and are math majors in roughly equal numbers. However, it needs to be pointed out that undergraduate math courses and professional mathematics are qualitatively different, not just quantitatively, which Spelke implicitly assumes:

I suggest the following experiment. We should take a large number of male students and a large number of female students who have equal educational backgrounds, and present them with the kinds of tasks that real mathematicians face. We should give them new mathematical material that they have not yet mastered, and allow them to learn it over an extended period of time: the kind of time scale that real mathematicians work on. We should ask, how well do the students master this material? The good news is, this experiment is done all the time. It’s called high school and college.

The qualitative difference is the following: in undergraduate math courses (at least in my experience), performance is based largely on one’s ability to internalize a few examples and follow their template in solving other (relatively easy) problems; the professional mathematician must take known results and integrate them in a novel way to solve problems nobody has ever solved before (which, given that they are unsolved, are pretty much universally very, very difficult). The former is, needless to say, much more amenable to the plug-and-chug mindset than the latter.

Spelke summarizes this section of her argument as follows:

The outcome of this large-scale experiment gives us every reason to conclude that men and women have equal talent for mathematics. Here, I too would like to quote Diane Halpern. Halpern reviews much evidence for sex differences, but she concludes, “differences are not deficiencies.” Men and women have equal aptitude for mathematics. Yes, there are sex differences, but they don’t add up to an overall advantage for one sex over the other.

Again, this is just disingenuous. The outcome of this large-scale experiment is not that men and women have equal talent for “mathematics”; it is that they have equal talent for undergraduate mathematics classes. Certainly, high performance in undergraduate math classes is a prerequisite for getting into graduate school, which is, in turn, a prerequisite for getting a Ph.D. and becoming a math professor, but, as untold grad school dropouts can tell you, there’s a hell of a difference between the sort of thinking that you do as an undergrad and the sort of thinking you must do as a “real” mathematician (in this context, it’s telling that Spelke uses the fact that 57% of accountants are women as evidence that women have the same mathematical aptitude as men). Of course, maybe it shouldn’t be a surprise that a psychologist has an apparently naïve view of what constitutes professional-grade mathematical aptitude when psychology styles itself (these days, anyway) as an empirical science, which is to say an analytic discipline, while mathematics is practically the definition of a synthetic discipline.

Now, this is not to say that there aren’t significant social causes of the male/female discrepancy in the hard sciences and mathematics (in fact, I really haven’t said anything at all about biology; it’s certainly possible that all of the above differences are due to social factors). Spelke makes good points about how parents seem to perceive the performance and capabilities of male vs. female children differently and how faculty hiring committees tend to receive male candidates more favorably than equally qualified female candidates (this latter should come as no surprise to readers of Malcolm Gladwell’s Blink, which touches on the fact that a significant contributor to the increasing gender balance of classical symphonies in the last few decades is the fact that virtually all reputable symphonies these days conduct auditions with the candidate performing behind a screen). These and probably many other social factors almost certainly play a role in women’s under-representation in math and science; as may be, Spelke’s apparent ignorance of mathematics makes it hard to accept her position on the issue which is, as Pinker rightly points out at the beginning of his presentation, extreme.


1. I’m quite aware that in this post I’m cherry-picking from Spelke’s argument by addressing only that component of it which I feel like I have some expertise in. I’m not trying to offer a comprehensive rebuttal of her argument and just because I disagree with what is essentially one point in a larger argument do I mean to suggest that the other points are also wrong. As usual, it’s probably best to read it for yourself and draw your own conclusions.
2. The usual caveat applies: when I talk about men or women having more or less aptitude for something, I’m speaking of statistical averages (to whatever degree those even make sense), not of individual people. There are plenty of women who are wonderful mathematicians (some of whom I’m lucky enough to know) and countless men who are abject morons (many of whom I also know); the old adage that statistics lie and liars use statistics is never more true than when someone tries to use statistics to “prove” statements about individuals.

Finally I get to use the “sex” category!

Steven Pinker and Elizabeth Spelke debating the issue of the day at Harvard, probably the only issue of any importance in the world, as Pinker implies, if your view of the universe begins and ends in Harvard Yard. It seems to me that Pinker has the better case, since, as he points out, Spelke’s evidence is largely about general mundane mental activity, not the sort of highly specialized and possibly male-favorable kind of work that is specific to university-level scientists. However, there is really nothing the least bit conclusive about any of it, and I am inclined to side with Pinker only because his claim is the more modest and intuitive one. In other words, I can’t understand how any of these very tentative hypotheses are being taken as having immediate implications on public policy, and not just within the university. After all, what do Pinker and Spelke disagree on at the practical level? He calls himself a feminist, with her it pretty much goes without saying. They both no doubt wish to end discrimination, and hopefully not only against women, and make scientific merit the criterion in hiring and admissions.

But I imagine that this assumption of immediate applicability comes about precisely because at least one faction, probably the one to which Pres. Summers was addressing his comments in the first place, has taken an absolutist and extremely over-deterministic attitude, predicated on the view that not only are there no differences in cognitive ability between the sexes (which are obviously just social constructs anyway), and not only is a rigid 50-50 parity in employment desirable, but a failure to attain this goal is itself prima facie evidence of discrimination. In the way of opposing this notion it perhaps behooves me to criticize the whole notion of using statistical blocks as specific social goals in this way, since the practice transcends this particular issue. My hometown, for example, has apparently decided to institute a monthly harvest–sorry, I mean quota–of DUI arrests.

In this case the folly of such quotas is perhaps more evident. For example, suppose hypothetically that there simply are not as many drunk drivers to be accosted as are called for in the quota (hardly an absurd possibility, since it simply takes a couple of over-zealous bureaucrats inflating statistics and/or possibility). Logically, some non-drunk drivers would have to be arbitrarily arrested to fulfill the quota. If the officers had consciences they probably wouldn’t do it, but the very issue proves the cleft between the actual goal (hopefully), which is apprehending criminals and reducing crime, and the artificial authoritarian goal, which is attaining a monthly haul of arrests. In academia I don’t think it is any more ludicrous to presume that, even should men and women be fundamentally “equal” in scientific ability, in any given year there will surely almost never be an exactly equal number of qualified candidates from both genders. This is usually not a problem, since statistics are simply meant to more or less reflect reality, not prescribe it. But as any quantum physicist will tell you, the statistical fuzziness is never as precise as we would desire it, and if the point gets pushed it will result in some less-qualified candidates being hired. I would go further and assert that while incidental discrimination may be a result of the present system, a quota system is virtually the only way to institutionally mandate it.

Why should this be the case? Well, why don’t scientists write up their conclusions before performing the experiments? Assuming an outcome in advance, no matter what it is, betrays a fundamental inflexibility to reality. Even if police set a quota of arrests which decreases every year, they really can’t guarantee a commensurate decrease in crime. The reason that fuzziness is built into statistical analysis is because there is an implicit assumption that it is only an approximation, that reality can always exceed or disappoint expectations, etc. So if one wishes to remain “within the conditions of life,” as Flaubert would say, then one must, like a scientist, focus on the methodology, but not presume the outcome. So perhaps if there is a reason scientists are rushing to try to resolve an issue that they know well (and say so on several occaisons in the transcript) cannot be decided with any competent degree of certainty at the present, it is probably in response to those that made up their minds at the very outset.

Untitled (pretentious art snobbery)

The (un)title of Curt’s latest entry reminded me of a thought that crossed my mind as I was wandering around the artistic wasteland that is the fourth floor of the obsessively weird Centre Pompidou last week: untitled works of art almost universally suck. Now, I’m sure some of you e.e. cummings and Jackson Pollock fans will be outraged by this assertion (though it’s telling that Pollock’s most famous painting is known colloquially as Lavender Mist, not Number 1, 1950), but even granting that there are probably exceptions, I think an honest reflection on the various untitled works of art one has experienced must invariably lead to the conclusion that most of them are garbage.1

Why? Well, it’s not necessarily clear why this should be the case. After all, if Don Quijote or Das Wohltemperierte Klavier or La Gioconda had gone untitled, they would still be recognized as great works of art; after all, what we find beautiful about those works are their content, not their names (especially in the case of Don Quijote, which could be loosely, but not entirely inaccurately, translated as Sir Cheesy). That having been said, it seems to me that, given that a title usually reflects the sensibilities of both the author and the work, there may be some common themes to untitled works of art that might explain why they tend to suck.

For one thing, many such works are so abstract as to admit no titular description (both Pollock and certain minimalist works especially come to mind). Still, modernist naïf that I am, it seems to me that the better abstract works evoke something outside themselves instead of being hermetically sealed, self-contained objects. And a title usually gives some insight into whatever it was the author was trying to evoke (e.g. Alexander Calder), even if one ultimately rejects that interpretation. Perhaps more importantly, the sort of work that is so hermetic as to be totally resistant to titling probably isn’t going to strike that evocative chord.

That isn’t to say that there isn’t something to Rothko’s justification that “Silence is so accurate” when explaining why he used generic or non-existent titles for his later works (he feared, or at least claimed to, that more descriptive titles would paralyze the viewer’s imagination).2 This is, of course, a common refrain among modern artists, but in most cases it’s a cop-out from lesser artists who want to conceal the fact that they really just don’t have anything to say.

Which brings me to my second point, which is that, in my limited experience as a writer, coming up with a good title is often significantly harder (at least, relative to the semantic/syntactic “size” of title vs. content) than producing, e.g., a well-written essay (not that either is particularly good, but the title/content of this particular post illustrate this point quite admirably, I think).3 As hinted above, I suspect a goodly number of artists are simply taking the easy way out when leaving their works untitled; and let’s face it: the sort of artist who’s willing to take the easy way out on the most recognizable (rightly or wrongly) aspect of his work probably isn’t going to produce a lot of really earth-shattering art. In other words, while there may be excellent reasons for art to be untitled, those reasons are invoked considerably more often than is really justified.


On what may or may not be an unrelated note (the perceived independence of the following observation from the above probably depends on whether your opinion of the Pompidou’s fourth floor agrees with mine or not), I feel, as someone who’s been in at least five internationally renowned art museums in the last week (the Louvre, the Pompidou, the Orsay, the Marmottan and the Musée National Picasso), qualified to pass the following judgment on art museums: they suck (and yes, that’s three uses of the word “suck” in this post, which might give one the false impression that I had a really bad time in France; I didn’t, of course, it’s just that cynical complaining is much more up my rhetorical alley than enthusiastic paeans).4 Don’t get me wrong, I love art museums, but I’m convinced that, by their very nature, they’re antithetical to their purported purpose. What do I mean by that? Well, it’s actually quite simple: after four hours in your third art museum of the last two days, it’s virtually impossible to appreciate any work of art that you haven’t already seen and dissected on slides or prints (and even in the case of those works you have seen in, say, an art history class, it’s still pretty tough to see the painting itself as opposed to your professor’s description of it). When your feet hurt, your back aches, and you’ve already seen 300 works of art that could legitimately be called masterpieces, it’s very difficult to have any reaction to yet another painting other than “Oh, that’s nice.” The Louvre, of course, is the most egregious example of this, given the size and quality of its collection, but any sufficiently large and well-stocked museum (the Prado, the National Gallery, etc.) is capable of evoking this reaction all by itself, and the smaller museums devoted to a single artist (the Marmottan, the Sorolla museum in Madrid, etc.) or a single movement (the D’Orsay, the Pompidou, the Reina Sofia) are arguably worse, given the relative homogeneity of their collections.

In this context, one really begins to appreciate the presentation of El entierro del Conde de Orgaz in the church of Santo Tomé in Toledo. El Greco’s masterpiece has a room entirely to itself in a church that offers no other great artistic works aside from itself (in particular, its mudéjar tower); this, along with the fact that one has to pay an entrance fee just to see the painting, really forces you to linger over El entierro, to devote some time to looking at it and thinking about it (of course, given that the annex in which it’s housed is usually quite crowded with Japanese tourists, it helps that the painting is pretty large and visible even from a good distance away). Whereas if you wanted to do the same with each significant painting in the Louvre, you’d be there for months (a viable option for those who live in Paris, perhaps, but not for those of us ingrates who like having bacon for breakfast).


1. Of course, most works of art, untitled or not, are garbage, but here I’m restricting my attention to those works of art deemed worthy of appearing in prestigious art museums.
2. I have a print of Rothko’s Orange and Yellow hanging in my living room, so of course I’m going to be somewhat sympathetic to his perspective.
3. Requisite “meta” moment.
4. Since this sentence is already irrevocably tangled by parentheses, I might as well add the further parenthetical observation (except I hate nested parentheses, so it goes in a footnote instead) that my overuse of the word “suck” might also be seen as some sort of sexually-frustrated cry for help, but, at this point, that practically goes without saying.

Untitled #9 (perhaps lazy painters are on to something)

Tolerance is a very over-rated value, and the way in which it is bandied about in our society is very stupid. Make no mistake, one of the aphorisms I live by is J.M. Coetzee’s (fictionalized) declaration that “I have beliefs, but I don’t believe in them.” Which is to say, I believe that most of the beliefs I find most valid are simply those which have not thoroughly been discredited yet. But I can no more cease to hold them or act on them in the absence of a better alternative than can scientists in the possession of a deficient paradigm. What I can’t stand are those that rail, for example, of “activist judges” trying to imposing their values on the administration of justice, or how the religious should essentially refrain from imposing their views on others, which is to say acting on their beliefs, or even Edward Gibbon’s scornful remark of the Byzantine emperors that “it was held to be the duty of a prince, to impose on his subjects the dictates of his own conscience.” He is talking, of course, about the enforcement of religious orthodoxy, but somehow I don’t believe he would have such a baleful view of imposing the “dictates of [own's] own conscience” if that concerns the equitable administration of justice or the fostering of peace and trade. In other words, it is the values themselves, not the commitment to them, that provokes animosity.

This value-neutrality is ultimately as paralyzing and impossible as the objectivity by which journalists try to scourge themselves (or don’t, but never honestly). But the irony, obviously, is that this is itself a value, and the resulting confusion creates such absurdities as the assassin of Gandhi, who believed that Muslims could not and should not be permitted to exist in a tolerant society. I don’t believe that anyone’s conscience is flexible enough to be truly tolerant of that which they believe to be wrong, nor do I believe that it would be very admirable even if they could. Is not lack of opposition to that which is wrong a form of complicity in wrong-doing? Yes, I think people of different religions should tolerate each other, and yes, I believe that scripture should be kept out of our judicial law, but that is because I don’t have any religious views myself. But I cannot go along with this duplicity of sanctioning people’s religious beliefs and then condemning them for acting upon them.

I understand the appeal and the theoretical value of this sort of attempt to transcend specific values and inculcate some sort of reciprocal universal tolerance, but to be honest I find the idea of some sort of value-neutral intellectual space to be chimerical and preposterous, and the fact that so many people seem to believe in it probably indicates how cocooned our intellectual life is. Do you think the raft of tolerance is big enough for the members of al-Qaida? Sadly, some do, but their version of tolerance is pretty much the appeasement of the strong by the feeble. I would say any issue on which mutual tolerance among the proponents of the various sides is regarded by someone as the most important thing is probably an issue on which that person simply does not care enough to have a positive or negative opinion, or one in which none of the pertinent opinions seem adequate or right. Religion is somewhere between the two for me, so I am all for tolerance in that area, but I would never accuse myself of some sort of universal and indiscriminate tolerance for all that is both right and wrong. You won’t see me calling terrorists victims of intolerance, let’s put it that way, in fact quite the opposite.

Jason Giambi and Bill Clinton, separated at Perth?

“If only these folks in Congress showed as much passion about campaign finance reform, seeing how soft money is politics’ equivalent of steroids.” –Dan Shanoff, ESPN.com

I agree. Both are phony moral issues in which people who otherwise claim to believe in free competition try to force other people that are more apt than they from increasing their competiteveness, despite the fact that this preparation violates no one else’s rights. I note that no amount of political funding or advertising can force anyone to vote a certain way, and that steroids are (or should be) equally available to anyone. But I’m sure that both politicians and athletes will save themselves from sinking to hypocrisy and lying by either defending their undoubted right to indulge in both or honestly forswearing the practice, instead of paying lip service to a questionable value and going about secretly violating it just as before.