January 24, 2006

Politically incorrect fashion II: Sex

In Part I, we addressed the racial make-up of the fashion design world, which is mostly European and East Asian. A key variable is general intelligence, or g (measured by IQ tests), in particular the visuospatial (VS) "flavor of g," often tested by tasks that require mental rotation of 3-D objects (a crucial part of conceptualizing a garment before constructing it). We now address how sex and VS differences affect the fashion world. But first, let's emphasize that while the g-loadedness of a discipline may make its practitioners more impressive objectively, it doesn't necessarily make their work more satisfying subjectively. We can all agree that master designer Yohji Yamamoto has greater mental agility than a local craftswoman who quilts, but whom to celebrate is of course in the eye of the beholder. I am only interested in the empirical question of why males dominate the visual art & design world.

First, we remain agnostic on sex differences in median IQ. In The g Factor, Arthur Jensen reports no significant such sex difference, though IQ tests are crafted so that no such differences emerge. What no one debates, however, is greater male variance: the male curve is more spread out than the female one, meaning males will be overrepresented at both the high and the low ends. Also, while some sex differences aren't pronounced, the difference in VS ability is the most pronounced of all: Jensen reports only about 25% of women are above the male median (for a 0.67 standard deviation difference in medians), while a 1993 meta-analysis suggests a 0.9 SD difference in medians (19% of females above the male median).

Now, no one knows for sure what cutoff level of VS skills a noteworthy designer must meet, but let's conservatively estimate it at 2 SD above the male median: not insanely high, but enough to weed out the merely above-average. Assuming normal distributions and equal variances, at this level of VS skills the ratio of men to women (M:W) would be at least 6 to 1 (using the 0.67 SD difference) and up to 12 to 1 (using the 0.9 SD difference). This ratio becomes more lop-sided toward men if male variance is greater (which it is) and as we look at higher cutoff levels (which we would for Big Names). This also assumes men and women are, on average, equally likely to pursue fashion (probably not true), so the above ratios are expected for the visual arts & design fields in general (painting, architecture, etc.). As for fashion itself, here are some interesting ratios to ponder:

1) At the most basic Level 1, "students at top fashion design schools," we observe a M:W of about 1 to 13 at Parsons and about 1 to 5.7 at FIT, among the most prestigious schools internationally. So here, women far outnumber men. (See footnote [1] for references throughout this list of statistics.)

2) Moving up to Level 2, "good enough to be showcased," the M:W is 1.29 to 1 among members of the Council of Fashion Designers of America. Sartorial encyclopedias Who's Who in Fashion and The Encyclopedia of Clothing and Fashion -- both edited by women -- show a M:W of 1.5 to 1 and 1.9 to 1, respectively, among those featured. I did some original research on Vogue's website, and there are 151 entries for ready-to-wear labels in Spring 2006. Of these, 12 were designed by a mix of men & women; 50 by women alone; and 89 by men alone (list available by email). Setting aside the mixed category (since it's difficult to tell who does what), the M:W is 1.8 to 1. These four separate ways of calcuating M:W at Level 2 converge on values between 1 to 1 and 2 to 1 -- significantly reversing the pattern of Level 1.

3) At the top Level 3, "fashion's elite," we count those great enough to win top awards, to enter The Canon, etc. The winners of the CFDA's Perry Ellis awards for emerging talent show a M:W of 3.6 to 1, nearly triple the M:W of its membership. I came up with a pretty objective (though as always somewhat subjective) list of the most influential female designers and got 9: Vionnet, Lanvin, Chanel, Schiaparelli, Sander, Prada, Westwood, Karan, and Kawakubo. I then listed the male designers at least as influential and got 24. To save space, see the appendix for the men. This gives a M:W of 2.7 to 1. Let's say, then, that M:W at Level 3 is about 3 to 1.

So, these data confirm that examining higher cutoff levels skews M:W more towards males. But the actual M:W at Level 3 (3 to 1) is half our predicted lower bound for even Level 1 (6 to 1), though still favoring males. Why the discrepancy? Recall one crucial assumption: that visuospatially gifted men & women are equally likely to go into fashion. To foreshadow Part III of this series, in fact very few men so gifted drift toward fashion; most male fashion designers are gay. Most estimates of gay men in the male population range from 1% to 5% -- we'll assume 3%, or 1.5% of all people. However, they represent 54% of all Perry Ellis award winners and 33% of all in my most influential list. Thus, they are from 22 to 36 times more frequent at fashion's Level 3 than they are in the general population. Lesbians are typically estimated at half the frequency of gay men, meaning straight women represent about 49% of the population at large. All females at Level 3 are straight and comprise 22% of Perry Ellis award winners and 27% of my most influential list, meaning they are only about half as frequent here as they are in the general population.

In light of Steve Sailer's observation that unlike straight men, gay men tend to prefer more people-oriented fields (fashion, PR) than thing-oriented fields (mechanical engineering), we interpret the data as showing that males will not dominate a visual art field to the extent expected by VS differences if the field is too people-oriented for the average male (who is typically straight) with high VS skills. Men will still dominate, just not so heavily. However, the corollary is that if a visual art field is quite thing-oriented, thus not turning off straight men with high VS skills, it will be even more male-dominated. Case in point: architecture. The M:W for winners of the most prestigious awards in architecture, the Pritzker Prize and the AIA Gold Medal, are 27 to 1 and 61 to 0, respectively.

Are there other explanations for the male-female disparity? In polite society, the only acceptable one is sex discrimination. Tara Subkoff of avant-garde label Imitation of Christ suggests that " 'Gay men stick together like a band of brothers ... whereas a woman would be threatened' to promote another woman" [1]. Ah, the old Old Boys Network charge. While I'm sure gay men find one another more entertaining than women, just watch Project Runway and see gay men Michael Kors (top designer) and Tim Gunn (Chair of Fashion at Parsons) critique fellow gay men when they screw up and praise straight women when they hit the mark. Plus it's straight women like Anna Wintour at Vogue and PR judge & ELLE fashion editor Nina Garcia who editorially promote some designers over others in their publications.

Moreover, of the 9 elite female designers I listed, only 2 are from time-places influenced by radical feminism (Donna Karan and Vivienne Westwood), contra FIT museum curator Valerie Steele's hypothesis that males took over in the 1950s due to the "feminine mystique" that shackled women [1]. But she has forgotten the history of women's liberation movements in the developed countries beginning in the late '60s. Though Karan and Westwood came of age as designers in rad fem-influenced America and England, respectively, Prada, Sander, and Kawakubo came of age in equity feminist Italy, West Germany, and Japan, respectively. No elite designers hail from feminist bastions in Scandinavia.

Informally I notice that, where there are sufficient numbers to judge (almost no top designers are black), East Asian top designers have a M:W that's the least male-skewed -- part of an apparent pattern of less sexual dimorphism among East Asians (Ctrl F "physical"). Or it could be that their top competition -- gay men -- is less frequent among East Asians, though I was unable to find data for or against this hypothesis. Indeed, all 3 East Asians on season 2 of PR are female. This is despite the greater "gender rigidity" of East Asian cultures. And not to slight Karan and Westwood, but Prada, Sander, and Kawakubo are much more central to fashion history. To be clear, I don't think increased rigidity of a culture's gender roles causes better female designers to emerge; a confounding variable is the real & apparent differences in VS skills between groups.

And anyway, gay men make up a large chunk of influential designers, so why haven't they been discriminated against? After all, gay men have historically been much more fiercely persecuted than straight women have. Why did investors not withhold funds? Why did straight female celebrities not boycott their boutiques? Why did straight female fashion editors not blackout their collections? Evidently the only discrimination is from the Lauren Bacalls and the Anna Wintours, which falsifies the sexist patriarch hypothesis. Again, this is the good kind of discrimination -- by merit -- as when we say that Bacall has "discriminating" tastes.

But fact-free theories aside, what about the sensible alternative that women struggle to balance career and family priorities, the latter weighing more on a woman's mind than a man's? That would keep out deserving women, by personal choice if not by discrimination. I agree and sympathize: to satisfy my softy parental instinct, I prefer teaching cute little kids and adolescents, even if this means that status-wise I'll never amount to anything. Nevertheless, I doubt this accounts for a majority of the variance in visual art accomplishment. For comparison with the Pritzker and AIA Gold Medal, consider the winners of the Booker Prize, an elite literary award given since radical 1969 -- the M:W here is a measly 17 to 12, i.e. still male majority but quite far from the utter domination of architecture prizes. (A cursory look at the Nobel Lit winners shows their M:W is not as pretty, though.) Given that the Pritzker and Booker have been awarded within the same time-places, societal factors alone cannot account for the different patterns. If personal choice is so strong, the prediction is that Pritzker-capable females are much more likely to cave in to their maternal instincts and forego fame, whereas Booker-capable females on the whole are either uninterested in families or are better at silencing their maternal instinct.

However, in The Essential Difference, Simon Baron-Cohen shows the obvious: women on average like people & babies more than men do and have better verbal skills, while men are on average more interested in things and have better VS skills. He argues that a large piece of the puzzle is exposure to testosterone in utero, with male levels making the brain more thing-oriented and VS-friendly. So, the above prediction is likely backwards: Booker-capable females are likely more susceptible to caving in to a need for people, feelings, and family, precluding fame. There's a simple test to check whether elite female visual designers are more masculinized than elite female wordsmiths. The ratio between the lengths of one's index finger and ring finger (the 2D:4D ratio) correlates well with exposure to androgens in utero -- the ratio is typically lower for men (index notably smaller than ring) and more balanced for women. The prediction is that, for female architects vs. female novelists, the average 2D:4D of the former would be closer to the male population mean than the latter's would be to the male mean. It's simple and non-invasive, thus not difficult to conduct.

So, the large sex differences in fashion accomplishment reflect underlying biological differences in VS skills (both in median and variance), and though personal choice may exacerbate this, overt discrimination is an unconvincing and glib explanation. When trying to compare M:W in fashion, we suggest keeping in mind the expected value for men and women, since the actual values alone -- though skewed towards males -- don't take into account the question: well, how many men did you expect to devote their lives to making women beautiful?! For a more satisfying picture, we consider the entirety of the visuospatial design & art world. As of yet, we know of no sub-field where females dominate -- indeed, in one of the most people-oriented sub-fields (fashion), men still rule. And to reiterate: the mental agility required to excel in a field, while it may impress, doesn't necessarily make those who possess more of it any more aesthetically worthy than those who possess less of it. Paraphrasing Steven Pinker in The Blank Slate: sameness in constitution is not a prerequisite for fairness in judgment.

[1] Data from Eric Wilson, "In Fashion, Who Really Gets Ahead?" NYT, 12/8/2005, Sec G p 1 col 5. Unfortunately now in the pay archives. Viewable if you click the 'Cached' option of this google search.

Update: I wanted to focus on the arts, so I didn't mention the Larry Summers controversy, as more eloquent people have said what I think (2nd list). However, I might as well mention that because science and art both require higher levels of g, and because some sciences and arts favor female-typical flavors of g (verbal) and others male-typical flavors (VS), the above discussion is mirrored in the sciences. Females are equally or overrepresented in the most people-oriented and verbal-friendly disciplines (psychology, literature), and shrink as one moves to more thing-oriented and VS-friendly disciplines (mechanical engineering, architecture). While some mech-engin-capable females may opt out due to family concerns, I doubt this accounts for a majority of the variance. Paralleling the faulty prediction that Pritzker-capable females are more swayed by family and feelings than Booker-capable females, the strong version of the personal choice argument predicts that females talented at mech engin are more likely to cave in to their maternal instinct compared to females talented at psychology. Again, this prediction likely has it backwards: psychologists probably feel a stronger need to deal with their own or surrogate families. The 2D:4D test we proposed would work here as well to see whether female mech engineers are more masculinized than female psychologists.

Elite male designers

The 24 male designers I found at least as influential as the 9 women in the post above: Cardin, Dior (PG), Saint-Laurent (G), Ellis (G), Gautier (G), Armani (G), Versace (G), Tom Ford (G), Klein, Lauren, Miyake, Yamamoto, Galliano (G), Slimane, McQueen (G), Balenciaga (PG), Dolce & Gabbana (G; counted only once), Lagerfeld (G), Helmut Lang, Givenchy, Chalayan, Valentino (G), Alaïa, Poiret. "G" indicates openly gay, "PG" probably gay. I chose them based on overall contributions -- for example, I excluded gay male designer Roger Vivier, credited with inventing the omnipresent stiletto heel.

January 19, 2006

Politically incorrect fashion I: Race

No, I don't mean a t-shirt with a Fred Reed slogan on it.

Having caught last night's Project Runway 2, the fashion designer competition show, allow me to admit one of my guilty TV pleasures: the couture-based reality shows. I never miss Isaac Mizrahi's talk show; I less frequently tune in to What Not to Wear; I'll watch a few minutes of How Do I Look? just to catch half-Italian host Finola Hughes; but I haven't bothered with Queer Eye for about a year. And for the curious: I happen to be one of the few straight guys who are interested in such things. What really strikes me as I watch these shows, PR in particular, is that, for all its cosmopolitanism and obsession with female beauty, the fashion world is largely ruled by gay men of European extraction. Let me clarify: I refer only to the visual design aspect -- not, e.g., the journalistic work that goes into promoting or criticizing a designer's work. In an intellectual climate dominated by "kill the Canon" fashion statements, the world of couture shows clearly just how much European -- and Asian -- males rock! Part I will consider race, part II sex, and part III sexual orientation. Full disclosure: straight, male, 3/4 northern European & 1/4 Japanese.

I don't have access to the ethnic background of all the members of the Council of Fashion Designers of America, but a quick check of global designers hot enough to be featured on Vogue's website shows that there are few if any of sub-Saharan African origin. Indeed, on both seasons 1 and 2 of PR only 1 of 12 and 1 of 16 designers, respectively, have been black, although season 1's Kara Saun (straight, black, female) deservedly went to the finals and only slightly lost to Jay McCarroll (gay, white, male), indicating that as everywhere, overlapping bell curves don't imply zero members of the lower-average group succeeding -- just that the ratio of higher-average members to lower-average members will increase the further one goes out into the tail. Make no mistake: IQ, or at least the visuospatial subcomponent of it, matters a lot here. You try creating a mental image of a garment that fits and flatters the human form, while adhering to some coherent concept, mentally rotating that 3-D image to see what it would look like from various angles and during movement, reasoning hypothetically about which additions or subtractions would have which effects, and then keeping track of all these things while executing your wearable sculpture!

Predictably, many of the Big Names belong to those of European extraction. However, the pattern is more subtle than that. There are very few Eastern or Central European designers, even though these areas have given us many great works of literature and music. Also fairly absent are the Scandinavians (although they have produced many great furniture designers), as well as the English -- the UK's three Big Names are ethnically Turkish Cypriot (Hussein Chalayan), Irish (Alexander McQueen), and English (Neil Barrett, though he's from Devon, a county next to Celtic Cornwall). Most of the avant-garde types are from Belgium (the "Antwerp Six"), France (Jean-Paul Gautier), or Austria & Germany (Helmut Lang, Karl Lagerfeld). France and Italy vie for status as fashion center of the world, with the French tending more toward the notion of nonchalant "chic" (the original Christian Dior and Yves Saint-Laurent), and the Italians more toward a sensually imposing presence (the original Gianni Versace). And while there aren't many Big Names from Spain, superstar designer John Galliano (who currently designs Christian Dior) is half-Spanish from Gibraltar; and a number of mostly-white Hispanics are included among the Canon, such as Oscar de la Renta and Narciso Rodriguez. The Iberians also tend to emphasize sensuality like the Italians. America's most important designer is Tom Ford, a non-Hispanic white whose exact origin I'm unable to locate, and who until recently designed the collections for both Gucci and YSL. Now, how much of this variation within the intracontinental European racial group is due to genetic differences, I couldn't say -- culture could matter for sure, but it's striking that the centers of fashion design in Europe also largely overlap with the historical and current centers of the visual arts, architecture, and furniture design, so the cultural feedback loop (or whatever mechanism is proposed) would have to operate at a much higher level than simply fashion design.

However, far from being a white boys network, the fashion design world boasts many East Asian designers, especially among the more avant-garde. While the West spiraled further downward into the sartorial quagmire that was the 1980s, three Japanese designers -- who had been working since the 1970s -- offered an intellectual, minimal, and monochromatic alternative, which by the end of the decade became the life-preserver to which the moribund Western fashion world clung to pull themselves out of the zaniness of the '80s and into the sleekness of the '90s. Those three -- whose approach was dubbed "Hiroshima Chic" -- were Rei Kawakubo of Comme des Garçons, Yohji Yamamoto, and Issey Miyake. Hanae Mori also proved influential. Among more recent designers, Asian-Americans Peter Som, Anna Sui, and Vera Wang deserve mention. And on the current season of PR, 3 of 16 are Asian-American (Guadalupe, Chloe, and Diana). So, contra Richard Nisbett, far from reflecting their mastery of ideographic scripts, their excellent visuospatial skills appear to have a substantial genetic component. Indeed, the higher average IQ that East Asians enjoy largely derives from having much higher visuospatial skills (despite not-too-hot verbal skills), a pattern evident among Korean adoptees in Belgium as well (Ctrl F "belgium-koreans"; 2nd item), who certainly don't read ideographs or follow an Asian diet.

Still, one generally brainy, high-achieving ethnic group is curiously... well, not absent, but represented merely on the same order as they are in the general population -- Ashkenazi Jews. (Blacks, by contrast, are underrepresented.) The ethnic group with the highest average IQ (about 115), they also show lopsidedness like Asians but in another direction: higher verbal & quantitative skills, but middling or slightly below-average visuospatial skills. Gregory Cochran, Henry Harpending, and Jason Hardy theorize that this reflects a selection for such skills in the social niche that the Ashkenazim occupied during roughly 900 AD to 1750 AD, namely as money-lenders, estate farmers, etc. And sure enough, "Jewish fashion designer" doesn't just sound odd. While Ashkenazi Jews comprise only about 2% of the US population, they account for about 28% of our Nobel Prize-winning scientists. But the only Ashkenazi Jewish name among the Canon of couture is Calvin Klein (maybe Donna Karan). While Marc Jacobs, Ralph Lauren, and Michael Kors (half) may go down in the annals as well, they won't do so in such percentages as Nobel winners. Two other highly regarded Jewish designers are Diane von Furstenburg and Isaac Mizrahi, host of Isaac. However, as the latter's surname indicates, he is not Ashkenazi but Syrian; and though I cannot find data on von Furstenburg, she is half-Greek, suggesting her Jewish parent may be Sephardic as well. Just as we may not soon see a Japanese Woody Allen, we may have to wait some time for an Ashkenazi Yohji Yamamoto.

As a concluding sidenote, the design world more impressively showcases the talents of East Asians than the world of science or fine arts. With such great visuospatial skills, they might be expected to have discovered geometry, or to have dominated much of the history of painting and sculpture. Yet, as Charles Murray points out in his Human Accomplishment, Asians aren't so overrepresented among Big Names in the sciences and arts. In fact, he says he began the project hoping to unearth their underestimated accomplishments. As it turned out, though, those darned Europeans have had far greater influence. What Murray missed as an academic, though, was the practical, profitable world of design, where IQ still matters: fashion design, graphic design, architecture / interior design, furniture design, and so on. In fairness, Murray stopped investigating once he hit 1950, so his surprise at the lack of Asian Big Names might have changed had he looked up to the present -- not just in the design world, but also in the sub-area of the fine arts world which is arguably the most practical and profitable: film. East Asian directors, directors of photography, and cinematographers could give Franco-Germans and Mediterraneans a run for their money any day when it comes to the purely visual and spatial aspect of artistic filmmaking. This is again probably due to the visuospatial flavor of g, since we note a relative dearth of visually artsy Ashkenazi or black filmmakers, both of whom tend to focus more on the verbal aspect of storytelling.

Take-home message: IQ matters just about everywhere; and when investigating IQ, it's important not to leave any area unmined of data.

January 10, 2006

Linguistic vignettes I: Negative polarity items

The first in the series I described below will be from semantics, which deals with meaning, a field rarely covered by popular works. A separate post below will provide formalization for the math nerds. Following convention, an asterisk indicates an ill-formed sentence. Now, suppose you're a 1980's pop culture prof. I ask you, "How many students showed up for the Who's the Boss marathon?", which everyone skipped, and "How many came to Weird Science?", which some attended. Your respective answer sounds good in 1i) but bad in 1ii):

1i) No students showed up at all.
1ii) * Some students showed up at all.

Curious as to why no one showed up for the WTB marathon, you ask a student why they ditched WTB but caught WS. 2i) sounds good but 2ii) bad.

2i) I don't give a flying fuck about Tony Danza sitcoms.
2ii) * I give a flying fuck about John Hughes movies.

What do 1i) and 2i) share which distinguish them from 1ii) and 2ii)? Think for a sec.
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The good sentences have a negative like "no" or "don't." Stubborn items like "at all" and "give a flying fuck" are happy only at the negative pole, thus negative polarity items (NPIs). Others include "ever," "any," and phrases like "drink a drop," "lift a finger," etc. Convince yourself by trying them in negative & positive sentences. (Yes, linguists really do study "give a flying fuck" -- Paul Postal has an interesting essay on vulgar NPIs here, Chap. 5). But wait, where's the negative element:

3i) Every student who liked '80s movies at all showed up for WS.

Plainly, there is no negative in 3i). Worse, why does a recast of 3i) sound bad here:

3ii) * Every student who likes '80s movies gives a flying fuck about WS.

Take another look if you want at 1i), 2i), and 3i) vs 1ii), 2ii), and 3ii), but warning: you probably won't see it. Lucky for us Bill Ladusaw, who broke a lot of ground on NPIs, went into linguistics rather than something else. Before we get to the punchline, let's look at a related property of the positive, negative, and "every" sentences. We were all taught that each sentence has a subject and a predicate: "Plants" is the subject and "love sunshine" the predicate in the sentence that joins them in that order. Simplifying somewhat, we can model the meaning of the subject "plants" as just a set, namely the set of all plant-like things (tulips, grass, etc.), and the meaning of the predicate "love sunshine" also as a set, namely the set of all sunshine-loving things (plants, beach babes, etc.). The sentence "Plants love sunshine" means that the plant set is a subset of the sunshine-loving set.

Our NPI sentences also have the bits "no," "some," or "every" in front. Let's see how substituting arbitrary subsets or supersets of both the subject and predicate affect the truth conditions -- that is, does our initial sentence imply the new sentence? Let's start with "no" and alter the set denoted by the subject:

4i) No students liked Who's the Boss.
4ii) No male students liked Who's the Boss.
4iii) No people liked Who's the Boss.

The 1st implies the 2nd (subset), but not the 3rd (superset). Let's change the predicate's set:

5i) No students loved Who's the Boss.
5ii) No students saw Who's the Boss.

Again, our initial sentence implies 5i) (subset), but not 5ii) (superset). So substituting a subset for subject or predicate works. For brevity, you can convince yourself that starting the sentence with "some" results in the opposite: it implies the sentences which substitute a superset of the subject or predicate. The key is the "every" sentence:

6i) Every student liked WS.
6ii) Every male student liked WS.
6iii) Every person liked WS.
6iv) Every student loved WS.
6v) Every student saw WS.

The 1st implies the 2nd (subset of subject) but not the 3rd (superset of subject), as well as the 5th (superset of predicate) but not the 4th (subset of predicate). So "every" sentences behave like "no" sentences w.r.t. the subject (subset works) but like "some" sentences w.r.t. the predicate (superset works). Now look back at where the NPIs were allowed. Notice anything?
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NPIs are allowed where substituting a subset is implied by the original sentence, dubbed "downward-entailing" environments: both parts of a "no" sentence, neither part of a "some" sentence, and the subject but not the predicate of an "every" sentence.

So, in just this one nook of the linguistic world we've discovered a bit about human language. The meaning of a garden variety subject and predicate can be modeled as a set of things. We're unconsciously aware of whether altering this set to a subset or superset is entailed by the original sentence, and we use this to discriminate whether a quirky class of items sounds good there or not. Given that these data are all from casual speech, it shows how complex the ordinary really is and how prosaic an intimidating language like first-order logic or C++ is. Moreover, this sort of knowledge is incredibly flexible. If a new NPI entered the language, say, "dial a digit" used in negative sentences to swear to your mate that you haven't been calling other girls (or guys) -- e.g., your partner asks whether you were chatting last night with so-and-so, and you respond:

7i) Honey I swear, I didn't dial a (single) digit!

-- then we would immediately know it wouldn't work in a positive sentence, say, when your partner tells you to make an appointment with your doctor:

7ii) * OK, I'll dial a digit and book it for Friday.

Because our unconscious knowledge of language is so abstract and sophisticated, we'd have no trouble classifying "dial a digit" as an NPI given the context we heard it in, probably after just one exposure; and we'd be able to do the typical NPI things with it, all despite lack of overt instruction. Try building such quirks into an AI language faculty -- I'm not denying the computational theory of mind, but just showing how primitive the really existing anthropic AI is compared to the supposed sluggard shlepping away between our ears.

NPI math appendix

For those who desire more formal detail or want formal convincing, we formalize the above account. Simplifying, think of the meaning of the words "no," "some," and "every" as functions n, s, and e, which take the meaning of a partial-sentence, x -- basically, containing a full predicate but an unquantified subject like "dog barks" -- and return a full (quantified) sentence, y. More stuffily: they are a subset of the Cartesian product P x F of the set of partial-sentences, P, and full sentences F. I'm going to fudge a little to keep from proliferating even more formal machinery -- this'll sacrifice total accuracy for the sake of conveying the gist in brief blog form. I'll pretend the meaning of partial "student passed the test" is the same as full "a student passed the test," the rationale being that sans quantifier, we remain agnostic and assume "a" unless told otherwise -- then our n, s, and e will remove this place-holder and supply the true quantifier.

The entailment relation is defined on sentences x and y in P (or F) thus: sentence x entails sentence y iff in all possible worlds in which x is true, y is also true. For example, "John drove to school today" entails "John drove today." For want of fancy characters, we use |- to represent entailment. For all sentences x, y, z in P (or F), x |- x (every sentence entails itself); if x |- y and y |- z, then x |- z (easy to check); and the sole case where x |- y and y |- x is where x and y are synonymous (x = y semantically). Entailment is therefore a partial order on P (or F). We now define the functions: n is the "no" function which takes a partial-sentence x and replaces the assumed place-holding quantifier "a" with "no." If b is the subject and c the predicate, then "No b c" is true iff the sets denoted by the subject and predicate are disjoint. Next, s is the "some" function which does likewise; "Some b c" is true iff the intersection of the sets is non-empty. And e is the "every" function which does likewise; "Every b c" is true iff the subject set is a subset of the predicate set.

The functions n and s are monotically decreasing and increasing, respectively. Let x = "male student passed the test" and y = "student passed the test." Then left alone, x |- y. After passed through n, though, "no student passed the test" |- "no male student passed the test," or n(y) |- n(x). So n is antitone or "entailment-reversing." But if passed through s, "some male student passed the test" |- "some student passed the test," or s(x) |- s(y). So s is entailment-preserving. We chose x so that its subject was a subset of that of y, but the reader can verify that the same works for n and s if we choose x so that its predicate is a subset of that of y (e.g., x = "student aced the test," y = "student passed the test"). "Every," recall, is split. If we choose x so that its subject is a subset of that of y (e.g., x = "male student passed the test," y = "student passed the test"), then e is entailment-reversing like n; but if we choose x so that its predicate was a subset of that of y (e.g., x = "student passed the test," y = "student took the test"), then e is entailment-preserving like s. Thus, NPIs are allowed in sentences with an entailment-reversing function: either case of "no," neither case of "some," and the afore-mentioned case of "every" but not the other. Again, I simplified and fudged just a bit, but it conveys how NPIs relate to monotonic functions while keeping the discussion brief.

January 7, 2006

Linguistic vignettes 0: Background

For some reason, many people from diverse backgrounds are interested in human language, perhaps because it is one of our species' defining traits. As my training is in linguistics, I thought I'd start an occasional series that presents an impressionistic sketch of some narrow topic in linguistics that illuminates part of the big picture of the human language faculty and mind. Thus, the goal will always be modest rather than exhaustive. The only popular renderings of modern linguistics with any appreciable readership are those of Steven Pinker: The Language Instinct and Words and Rules. I've read both, so I'll make sure to instruct via examples not covered therein, while still attempting to delight as he does. To inaugurate the series, I've chosen a topic from semantics, a subfield of linguistics barely covered in popular renderings -- for example, TLI is an overview of linguistics yet contains no proper chapter on semantics and only fleetingly referes to it elsewhere. But first, here is the rough geography of the major subfields within linguistics, just so you know which one deals with what primary concerns before I discuss particular topics from them (there is overlap of course). I've cited the accompanying chapter in TLI for reference (since many own it).

Syntax is the study of how words combine into phrases, and phrases into sentences -- those tree diagrams that analyze how the parts of "John walks the dog" combine. TLI chapter "How Language Works." Investigates a question like: when you negate something, e.g. with "not" or "doesn't," where does this negative thingy go, no matter what the sentence?

Semantics is the study of how the meaning of the individual words and their combination gives you the meaning of the entire grouping of words. No TLI chapter. Investigates questions like: how does the meaning of the word "black" and the meaning of the word "dog", plus their grouping together in the larger unit "black dog," tell us what "black dog" means.

Morphology is the study of how smaller bits of words like roots and suffixes combine together to form entire words. TLI chapter "Words, Words, Words," as well as much of WR. Investigates questions like: why isn't it OK to call a "ville" where many "losers" hang out a "losersville," and why is the correct form "loserville," even though more than one "loser" hangs out there?

Phonology is the study of sound structure -- not how you produce sound with your tongue and lungs or perceive it with your ears (which is phonetics), but what sound combinations are allowed in a language; or how individual sounds like /s/ or /t/ combine into syllables, and syllables into words, for example. TLI chapter "The Sounds of Silence." Investigates questions like: why is "brick" an actual English word, and "blick" a possible English word, while "bnick" is an impossible English word?

These are the basic four food groups of linguistics. Awhile ago Julius Moravcsik pointed out that these resemble the "constitutive factor" -- or "what stuff it's made of" factor -- in Aristotle's group of causes, or aitia (hat-tip to Razib for the aitia link). For now, I'm leaving out subfields that approach language from a different angle -- e.g., historical linguistics looks at how changes in the above take place over time; processing looks at how we string together speech or parse someone else's speech in real time; acquisition looks at how the entire language faculty develops during childhood; and evolutionary linguistics asks how and why language evolved in humans. Linguistic superstars Noam Chomsky and Steven Pinker pointed out that these latter resemble Nikolas Tinbergen's four why's of animal behavior, as well as Ernst Mayr's distinction between proximate and ultimate causes.

January 4, 2006

Dangerous Ideas round-up II: The behavior genetics of art

Below I discussed why I'm skeptical that art criticism will ever take off scientifically, but in the spirit of Dutton, I'd like to borrow some findings in behavior genetics (BG) to throw light upon an issue in the arts, namely the nature of artistic inspiration and creation. My goal is very modest: to show informally that a finding from a hard science can provide useful analogies when investigating the arts. I don't claim there is no cleaning up to do, but this is just a first pass. The two entries from Edge's dangerous ideas collection that provide the impetus are those of Judith Rich Harris and April Gornik. Harris summarizes findings of BG, which Eric Turkheimer has condensed into three neat Laws of BG (from the "Three Laws..." pdf):
1) All human behavioral traits are heritable.
2) The effect of being raised in the same family is smaller than the effect of the genes.
3) A substantial portion of the variation in complex human behavioral traits is not accounted for by the effects of genes or families.
Harris mentions that, in fact, the shared environment (families) accounts for a miniscule portion of the variation. Turkheimer's pdf assigns ~50% of the variation to the nonshared (or unique) environment, which comprises the things which happen to one sibling but not the other, and which are not an effect of genetic differences -- so, this would exclude differentially treating two children due to one being genetically predisposed to crybaby-ness and the other to being well behaved. As such, this can include things like the open slot left in a child's peer group, pathogenic contagion, and other chance affairs. I assume most reading this have already heard this and refer any readers who haven't to the accessible papers at Turkheimer's site & the references therein, or to the wonderfully written chapter on "Children" in Steven Pinker's The Blank Slate.

So what does this have to do with art? Harris' claim that normal parenting has little influence on how children turn out, and that chance events are key, sounds a lot like Gornik's view that "the exact effect of art can't be controlled or fully anticipated." I thought of how BG could relate to artistic creation in 2004 when I was reading a lot of interviews of David Lynch, who consistently drives home how his works come to fruition -- the ideas come to or call him, and he is but a faithful attendant to them, like a gardener who waters seeds that will grow into different creatures, depending in large part on what their genes specify. See here, here, and here. For example, in describing how a work gets its features like sound, style, characters, etc., he says (first link above): "...everything comes out of ideas. Never go against the ideas, stay true to them. And it will always tell you the way you go." Now, Lynch is hardly to first artist to liken their ideas to children, but what is unusual is his insistence that they play a larger role in how the final work turns out than any deliberate nurturing on his part -- again, separate from the effect of how the idea's nature evokes a certain treatment. Well, there's that whole history of artists who believe they're possessed by foreign thoughts and only give birth to their art rather than calculatingly shaping a lump of undifferentiated thought-clay. But it's the first I recall hearing it from a major modern or avant-garde figure.

So let's explore this traditional view of artistic creation and what BG would predict. Again, I don't commit to fine-grained quantities, as this is art crit, but here goes. The original idea is like a child, born of inspiration in the unconscious mind -- say, two bees in the bonnet of the artist's uncosciousness connect, one fertilizes the other, and eureka! an inspirational idea is born. The idea-child, like all children, needs a healthy environment to nourish it into maturity, and this is the role of the artist's conscious action during the development stage. However, just as BG suggests, the effects of parental nurture are limited and mostly consist of helping the idea-child grow into what it wants to be, rather than trying to manipulate it against its predispositions. As all idea-children are reared by the same conscious mind, the deliberate part of the artist's thinking is like the shared environment; the unique environment includes things like the peer group of fellow idea-children with whom an idea socializes, chance occurrences in the artist's brain-home, as well as chance occurrences outside -- say, it's introduced to new idea-peers by a collaborator. The genetic endowment consists of the union of various unconscious sparks that gel together, forming a single idea-fetus. Ever felt your unconscious sparking but not resulting in anything solid? Not every mingling results in conception. Once fully developed, the idea instructs the artist how to behave (i.e., use this hue, weave in unrequited love, etc.).

What about the adoption & twin studies which BG researchers use? In brief, the findings are that unrelated siblings reared in the same adoptive home are no more similar than strangers despite their shared environment; identical twins separated at birth & reared apart are pretty similar but not terribly so; and identical twins reared together are no more similar than if they were raised apart. So again, genes & unique environments explain most of the variation, parental nurture very little. The adoption analogy would be ideas conceived within two separate unconscious minds with little genetic relatedness but reared in the same brain-home. Say, Mozart gives early-era Stravinsky an undeveloped idea for a composition, which is reared alongside one of Stravinsky's own. Assuming normal development -- i.e., assuming he isn't a wicked stepparent who maliciously bends the idea-child's nature -- wouldn't you think the compositions would be quite different? I'm sure they'd be somewhat similar as well, but I'd attribute it more to how Mozart's idea-child interacts with its newfound idea-peers that inhabit Stravinsky's brain (i.e., unique environment), since to get Mozart to sound strongly like early Stravinsky would require abusive / pathological upbringing. BG also shows that parental influence can have a noticeable effect during childhood, but once children grow into full adults and leave their homes, their genetic nature starts asserting itself and the effects of upbringing wane as parents no longer wield the whip over their children's heads. So part of the similarity could also be due to the fact that Mozart's idea can't escape Stravinsky's brain-home -- though if it did and found a more understanding parent (like a humble songwriter), it would end up more like a Mozart composition.

As for the identical twins separated at birth, let's assume that Mozart kept and raised his original idea but also made a clone (i.e. identical twin) which he then let Stravinsky adopt and raise -- a classical cover song, not unlike those of the latter's Neo-Classical period. Continuing to assume normal parental upbringing, wouldn't you expect them to sound pretty similar, even if not completely so? And wouldn't you account for the differences in the Stravinsky version by its interaction with its fellow idea-peers that inhabit Stavinsky's brain-home but not Mozart's, such as those still left over from the former's Primitive period, or those for orchestral techniques developed only after Mozart's death during the Romantic movement?

And what about the identical twins reared together, who in the BG literature are no more similar than twins reared apart? It's hard to think of how this would play out, since typically Stravinsky is contemplating how to develop just one copy of his idea-child, not an identical copy of it as well. But perhaps a close analogy would be that of the same parental conscious rearing the idea at one point in time, and then returning to it far later on to redevelop an identical copy of it in some new direction. It's as if a human parent raised a child a particular way, had a clone made of it 20 years later, and tried to raise it in the same encouraging fashion. But after 20 years of comings and goings from the peer group, the younger twin of Stravinsky's original idea may have a substantially different peer group from its older twin. We still expect them to turn out similarly given their common origin, but given differences in the unique environments, they wouldn't be indistinguishable. For example, say the idea is telling Stravinsky to compose a work on a pagan theme -- developed during his early Primitive period, it might sound like The Rite of Spring, whereas developed later during his Neo-Classical period after his brain-home's begun to house a somewhat different population of idea-peers, it might sound more like Orpheus. As for the non-peer aspect of the unique environment, say a whim strikes him which directs his conscious thought down a different path than that which originally occurred to him. This idea-peer / whim interaction often strikes many people when pondering how they'd re-do their work if given a second chance -- the "Oh! You know what I should've done there...?!" moment.

Well, I could go on, but you get the idea. The take-home message is that the BG picture of development, as well as the usually concomitant prescription to parents that they should encourage their children to find themselves, corresponds pretty closely to the traditional idea of artistic inspiration and creation -- that the original endowment and unique environment matter a lot, while conscious nurture (separate from genetic effects) seems to matter little. So, there really is something special about Mozart's brain that makes it capable of producing such singularly amazing works, not that he's simply a harder working parent to his idea-children -- in fact, if we believe the popular portrayal of him and his rival Salieri in Amadeus, Mozart's offspring are like the children of smarties who on average grow up smart, more or less no matter what assuming basic nutrition is met; whereas the offspring of duller folks on average don't reach the same level despite a heavily orchestrated campaign of nurture to force them in that direction. I've left out two things in this discussion. First, the nature of scientific output -- I think that, aside from the exceptional "Aha!" insight of a genius, a lot of scientific output comes from being a wicked stepparent who through trial-and-error strives to mold one's idea-children this way or that until something works, and if not, try again with a different child until one of them ends up explaining something interesting. Artists do this too but are more likely to "listen to their ideas" no matter what since no empirical issues are at stake. Second, I haven't discussed memetics because the ideas I'm discussing here look more like children that a parent raises into maturity, and less like genes (or how I see them, pathogens -- something distinct).

January 3, 2006

Dangerous Ideas round-up I: The limits of science & wonder

Steve Sailer and GNXP alert me that Edge has just unleashed its plague of dangerous ideas upon mankind. One thing that struck me was that many of them, viewed by a impartial observer, would be no more than nuisances. We don't have souls? Oh well, big whoop, time to get back to doing whatever I was doing before I heard the news. The Earth goes around the sun? Meh. The fact that such ideas can spark such fire-breathing retaliation speaks to how powerful the moralistic fallacy can be -- that is, if the world ought to be such-and-such a way, then it is in fact that way. For example, if human nature ought to be on the whole benevolent, then it is in fact on the whole benevolent -- malevolent acts arise primarily from contamination by the corrupting environment (bad parents, bad schools, civilization, Hollywood, etc.). Once informed that the world is not that way, they apply modus tollens and get: therefore, it's not the case that the world ought to be that way... but -- but -- but imagine just what would happen if we withdrew a moral claim about ideal existence based merely on an empirical finding?! And that's when the alarm bells are sounded, as Steven Pinker shows in The Blank Slate. The real solution is of course not to silence the modus-tollens-setter-uppers but rather to not hitch one's moral claims about ideal existence to the wild, wayward wagon of science.

That said, I'd like to highlight two of these nuisances, the first of which I'll call the limits of science and wonder. Trehub's brief entry sums it up. Hauser and Dehaene (scroll down) mention the computational property that accounts for this, namely that human cognition seems to like "discrete infinity" -- endless variation within constrained pathways, a prime example being the linguistic diversity observed within universal tendencies. In plain English: many solutions are possible, but only within certain boundaries. Sabbagh, Strogatz, and Fischl lament the Explanation of Everything leaving one unsatisfied now that there are no more deeply fulfilling areas left to explore scientifically. Dutton, however, suggests that Darwinian thinking can be fruitfully applied to unblazed trails like aesthetics.

Everyone with an interest in both science and the arts has at one time or another hoped to themselves, "What if I tried to scientifically describe and explain the arts, with the same rigor as physicists?" However, pretty soon the realization sets in that, "Ah shit, people have been trying to rigorously theorize about art and literature forever and haven't gotten any juicy results." Indeed, though rocky, the progress of the more physical & mathematical sciences over the past 2000 or so years has been pretty impressive; whereas essentially no astounding progress has been made in explaining works of art. That is, not why people paint or sing (perhaps it's to get mates), nor why this character backstabs that character (perhaps to avenge a close family member). I mean, minutely analyze the work of art formally and explain in fine, mathematical detail why the work of art ended up having those properties of the description instead of possible other properties -- and get results anywhere near the level of physics.

The nuisance is that we humans can't theorize about just anything and get the same level of sophistication for each object of inquiry (OI), precisely because our Theory-Forming Faculty (TFF) is a product of our evolved brain. The TFF may just be parasitic off of our more primitive "intuitive physics," but the point remains that it itself or the thing it uses for scaffolding evolved for some particular purpose, not every possible purpose. Think of the TFF as a super-duper version of our visual faculty; after all, we commonly refer to scientific "insights," say that Newton "unveiled" the laws of gravity, or mention that so-and-so can "see" things that others can't. Now, our visual faculty has evolved to be terrific at perceiving the wavelengths of light from roughly 400 nm to 700 nm (ROYGBIV); it can vaguely intuit what infrared or ultraviolet light might look like, just outside of the perceivable range on either side; but when it goes past them in either direction (gamma rays on the UV side, radio waves on the IR side), perception utterly collapses. For visual comparison, here is a graph of the light spectrum, in which only a tiny sliver (1/3 of the way from the top) is occupied by light visible to humans -- almost everything is an impenetrable enigma, and we're damn fortunate to see anything at all.

Notice that within that tiny canal of biologically constrained perception, we still see an infinite continuum of colors. What physicists use to describe color is the light's wavelength (~400 nm for blue vs ~700 nm for red), and since the wavelengths' values are real numbers, the set of colors is uncountably infinite, even if human language or thought bundles them into fuzzy chunks. The same appears to be true of scientific "perception" -- it peaks when the TFF is looking at the many OI studied in physics and chemistry, so-so when it comes to those of biology / biological psychology, pathetic when looking at the arts, before tailing off into utter ignorance of the regions beyond. But then, doesn't this give the pessimists some unknown to wonder at? I think so. We don't even know what those OI are, though perhaps an intelligent extraterrestrial race whose intelligence evolved for other purposes might have laid down a physics of the arts while remaining wholly confused as to how their planet orbits its star, just as honeybees see UV light but we don't. But what if, by developing an aid like a spectrometer -- a "science spectrometer" that listed all the regions in the spectrum of "objects of scientific inquiry" -- we became aware of what aspects of the world lie beyond? Wouldn't that spoil the wonder? I don't think so. We're well aware of gamma rays and radio waves, but we can't actually see them, even vaguely. So even if some science spectrometer returned the results of scientifically perceiving OI we're not even aware of, that would hardly be a gut-satisfying substitution for scientifically perceiving them by ourselves. The spectrometer would have no sense of wonder, but we still would.

Lastly, maybe we just haven't waited long enough for a physics of the arts to be worked out by someone's TFF. Maybe. But given that the complete lack of deep understanding is not a quirk of some particular area of artistic study (like most probability and statistics were not formulated until recently within mathematics) but rather a general feature, I wouldn't get your hopes up. Of course, just as selection pressures could budge human nature into being capable of perceiving radio waves, so it might budge our TFF into scientifically explaining the arts and beyond. But there are two problems here. First, don't hold your breath, since not even your great-grandchildren would see it. Second, if selection pushes us in one direction, it usually pulls us away from wherever we were before -- or at least, the set of conditions that would drive selection to engineer a visual faculty capable of perceiving all wavelengths of light is vashingly smaller than the set of conditions that would drive it to fit it to a localized region like UV or gamma rays. More likely is that we'd perceive radio waves but then lose our ability to perceive ROYGBIV. Likewise, being able to scientifically explain the arts would probably cost us our physical sciences. They'd still be written down, but they'd be just as incomprehensible to future generations as if we were to currently stumble upon a "physics of the arts" textbook written by the previously mentioned alien race. What would you give up for what else?