May 25, 2007

Visualizing the fourth dimension, Part 2

Part 1 here. To construct a 4-D hypercube, we first need to make a slight detour into graph theory. All proofs are secluded in an Appendix at the end, for the math nerds -- and for my own benefit, since I need to get back into the habit of writing proofs. We're going to use Hasse diagrams, which can be seen below.

What these two diagrams show is a set of elements and a relationship among the elements. To pick a familiar example, I chose some natural numbers {1, 2, 3, 6}, and the "divides" relation. We say "a divides b" and write a | b if and only if b = a*n, for some integer n. For example, 2 | 6 because 6 = 2*3. To show a | b in the graph, we draw an edge between a and b, with an arrow going from a to b. We get the graph on the left. For all a, a | a since a = a*1, so this relation is reflexive. For all a and b, if a | b and b | a, this implies that a = b (see Appendix), so this relation is antisymmetric. And for all a, b, and c, if a | b and b | c, this implies that a | c (see Appendix), so the relation is transitive. So, the "divides" relation is a partial order on the set of natural numbers.

Anytime the relation is a partial order of the set of elements, then a lot of the detail in the graph is superfluous. We don't need the self-loops, which only state what's true by definition, namely that a | a. We also don't need the arrows, since we can orient the graph so that we understand that the arrows always point upward -- they can never point back downward since that would imply a | b and b | a for distinct a and b, a violation of the antisymmetry property. And we don't need the extra edges that demonstrate transitivity, such as the edge going from 1 to 6 -- we could go from 1 to 6 indirectly through either 2 or 3. The result is a Hasse diagram, shown on the right in the picture above. Much cleaner. To cut to the chase, I chose 1 as the "origin" since 1 divides any natural number, and I chose 2 and 3 as the first numbers to branch out from the origin since they are co-prime -- they don't have any common factors aside from 1. This makes their axes go in different directions. Then, 2 and 3 bend into their least common multiple, 2*3 = 6. This is also the "terminal" point.

To move into 3-D, we need another axis that will be relatively prime to the two we already have -- the simplest way is to pick the next prime number for each new axis. So that would be 5, and our 3-D cube is the Hasse diagram below. We start with the same origin, 1, and we now have 3 co-prime axes which hit 2, 3, and 5 in the first step of branching. Then, 2 and 3 bend into their lcm = 6, 3 and 5 bend into their lcm = 15, and 2 and 5 bend into their lcm = 10. Each pair of "intermediate points" -- 6 and 10, 15 and 10, and 6 and 15 -- bend into the same lcm = 30, which terminates the branching and bending.

Now, this 2-D picture only allows us to see a single cube within all of 3-D space. If we wanted to improve our vision beyond extreme myopia, we'd need to allow each prime axis to continue infinitely, rather than stop after the first multiple of 2, 3, and 5. It's tedious to draw lots of these cubes, so I just drew one more cube in our 3-D space that we can visualize in our 2-D picture:

Because we went two steps instead of just one along the 2-axis, we can see one cube further in that direction. If you have nothing better to do, you can draw out what the cubes would be if we went one more step in along the 3-axis and the 5-axis, giving you four cubes in total (the original plus one new one in each direction). If you were really bored, you could then fill in the remaining four cubes to see a 2-by-2-by-2 cube. (As a guide for the bored, the axes would branch to 4, 9, and 25, and the terminal point of the entire cube would be their lcm = 900).

As an aside, what if we relabled the vertices logarithmically, so that each coordinate along the n-axis was just the exponent to which n is raised in the prime factorization of that vertex? For example, 4 = (2^2)*(3^0)*(5^0), and we'd re-label 4 as (2, 0, 0), where the 1st coordinate is the power of 2, the 2nd is that of 3, and the 3rd is that of 5. In the same way, 15 = (2^0)*(3^1)*(5^1), and we'd label 15 as (0, 1, 1). If we treat a vertex as a vector that starts at the origin and ends at that vertex, we could take the dot product of 4 and 15 = (2, 0, 0) x (0, 1, 1) = 2*0 + 0*1 + 0*1 = 0 + 0 + 0 = 0, implying that 4 and 15 are "perpendicular" or orthogonal. That is, the angle from 4 to 1 to 15 is a right angle. In our graph, being co-prime implies being orthogonal and vice versa (see Appendix).

In the next part of this series, we'll analogize these ideas to draw a Hasse diagram of a 4-D hypercube. I'm going to wait a bit since this post itself has eaten up enough of my time today, and since readers may want to see if they can do it on their own first. It's also worth taking time to let everything sink in.

Appendix. To prove the transitivity of "divides," assume a | b and b | c. Then b = a*n and c = b*m, where n and m are natural numbers. Replacing b with a*n, the second equation says c = (a*n)*m, and since multiplication is associative for natural numbers, we can write c = a*(n*m). Because the natural numbers are closed under multiplication, (n*m) is also a natural number; call it q. Then we have c = a*q, which we can rewrite as a | c, as required. (_)(_)

To prove the antisymmetry of "divides," assume a | b and b | a. Then b = a*n and a = b*m, where n and m are natural numbers. Replacing b with a*n, the second equation says a = (a*n)*m, which by associativity implies a = a*(n*m). Since a = a*1, we can rewrite this as a*1 = a*(n*m), which by cancellation implies that 1 = n*m. Since 1 is the identity element for multiplication in natural numbers, and since the natural numbers don't have multiplicative inverses except in the case of 1, whose inverse is 1, this implies that n*m = 1*1, or n = 1 and m = 1. Substituting into the original equations, we get b = a*1 and a = b*1, or a = b, as required. (_)(_)

To prove that co-prime numbers are orthogonal (and vice versa) in our Hasse diagram with logarithmically scaled axes, assume we have a n-dimensional cube, infinite in dimension since there are infinitely many prime numbers. Assume two natural numbers a and b are co-prime: by definition they have no factors other than 1 in common. That implies that they cannot both have a non-zero coordinate along the n-th axis (otherwise they would share prime factor n). So, if a = (a_1, a_2, ... , a_n) and b = (b_1, b_2, ..., b_n), then for all a_n and b_n, either a_n = 0 and b_n =/= 0, or a_n =/= 0 and b_n = 0, or both a_n = 0 and b_n = 0. No matter which case we have, (a_n)*(b_n) = 0 for all a_n and b_n in the respective vectors, so that the dot product a x b = 0 + 0 + ... + 0 = 0, indicating that a and b are indeed orthogonal.

Conversely, assume that a and b are orthogonal, which means their dot product a x b = 0. Expanding the dot product, we have (a_1)*(b_1) + (a_2)*(b_2) + ... + (a_n)*(b_n) = 0. Because the vertices in our graph are natural numbers, and because the vertices along a given axis represent multiples of a (prime) natural number, none of the a_n or b_n can be negative. Let's see why not. The a_n (or b_n) can be 0 if the prime factorization of a (or b) includes a 0-th power along the n-axis. But if we assume that a negative power were allowed, then along this n-th axis, we would have n^(-m), for m a positive integer, in the prime factorization of a (or b). Since n^(-m) = 1/(n^m), somewhere within the rest of the product of the prime factorization there would have to be a positive integer multiple of (n^m) in order for the entire product to multiply to an integer, rather than a non-integer rational number. But we have already accounted for the power along the n-th axis when we stipulated that it was (-m), and since all axes are mutually co-prime (they are distinct prime numbers), there is no axis along which we can retrieve more powers of n. Our prime factorization would then be a non-integer, contradicting our choice that it represented a natural number; so, all of the a_n and b_n are non-negative integers.

Now, if the sum of products of pairs of non-negative integers adds up to 0, it is not possible for the elements of a given pair (a_n)*(b_n) to both be positive. Assume it were possible, i.e., that both (a_n) and (b_n) in the term (a_n)*(b_n) were positive. Then for the entire sum to add up to 0, somewhere in the rest of the sum there would have to be elements (a_m) and (b_m) such that (a_m)*(b_m) = -1*(a_n)*(b_n). Both sides of this equation are negative under our assumption, implying that either (a_m) is negative or (b_m) is negative (but not both). However, we've already shown that negative values for the a_n and b_n are impossible, making a contradiction. Therefore, we have that both elements of a product must be non-negative, and that at most one of them may be positive, implying that either a_n = 0 and b_n =/= 0, or a_n =/= 0 and b_n = 0, or both a_n = 0 and b_n = 0. Since these represent powers of the prime number along the n-th axis, this implies that a and b have no factors in common other than 1 -- that is, they are co-prime. Combining this with our previous result, we have proved that natural numbers a and b are co-prime if and only if they are orthogonal in our suitably scaled Hasse diagram. (_)(_)

I've seen Hasse diagrams using prime number axes and the "divides" relation before, but I don't know of any comment on co-prime-ness and orthogonality implying each other when the axes are scaled logarithmically -- just drawing the axes perpendicularly doesn't make them so. I searched Google but didn't find anything to this effect, so I hope I'm the first person to prove this observation. Realistically, it's not that hard to see if you were paid to think about this stuff all day, so I'm sure some professional mathemitician somewhere has figured it out, and that the results are in an article or book chapter that didn't show up on a Google search.

Addendum 6/19: I just realized I probably got myself into trouble by introducing infinite vector spaces (one dimension for each prime number), as I haven't finished an analysis course yet. So let me water down the model to one where the vector space is finite in dimension, though as large as you want it to be. Good enough for the present purposes.

Visualizing the fourth dimension, Part 1

Via Uncertain Principles, here is a neat PowerPoint presentation on visualizing a hypercube. I don't promise that any of this series will be easy reading because 1) we're talking about weird stuff, and 2) I'm not getting paid for this, so it may not be as perfectly polished as a textbook would be. But who said visualizing a 4-D object would be easy?

Before getting to how to visualize a hypercube, let's note that this is not the same thing as "visualizing in four dimensions." Allow me to rain on the parade as follows -- see picture below: by visualing a 2-D cube (that is, a square), we can proceed to visualize all of 2-D space by fusing together the (n-1) dimensional "faces" of a square with those of another square (that is, the line segments that make up the perimeter). Say we fused the right side of square A with the left side of square B, making two squares side-by-side; we could do this infinitely in the left-right dimension. Then we could fuse the top of square A with the bottom of a third square C, and again stack as many others as we wanted in the up-down dimension. In this way, we'd fill out all of a 2-D coordinate system, like everyday graph paper.

To visualize all of 3-D space -- see picture below -- we'd start with the (n-1) dimensional faces of a cube (that is, the squares making up the surface) and fuse them just as we did before. Since there are 3 dimensions we can travel in, we'd fuse the square sides of a bunch of cubes left or right, up or down, and toward or away from our viewpoint, filling up 3-D space. Note that the picture only shows this in one dimension to minimize clutter -- the top of the left-hand cube would be fused with the bottom of a cube on top of it, and the back of the left-hand cube would be fused with the front of a cube behind it.

The problem comes when we try to do this in 4-D: the "faces" of a hypercube are (n-1) dimensional cubes -- that is, 3-D cubes -- and we have to fuse these between adjacent hypercubes in four dimensions. You can't do this in 2-D, anymore than you could visualize 3-D space using only 1-D, so you'd need to build a 3-D model. The trouble is that, unlike fusing a bunch of square faces in a 2-D picture to imagine what 3-D would look like, which you can do with a special kind of graph paper, building a 3-D model of a 4-D coordinate system in the same way would require too much effort to be worth it, unless you were a real geek. So, the best we can do without really slaving away is to visualize just a 4-D (hyper)cube -- as if we could only visualize one cube in 3-D or one square on 2-D graph paper. Pretty myopic, but do-able.

In Part 2, we'll take a necessary detour through some graph theory, which will greatly aid us in thinking about how to go from 3-D to 4-D, which we'll do later on still.

May 19, 2007

Retiring "exotic" the word but not the idea

In a previous post, I suggested that most men who are vociferous about expanding the scope of interracial dating are, if they were to be honest with themselves, mostly interested in dating exotic babes, rather than broadening their appreciation of the world's cultures. Unfortunately for them, many such girls are turned off by the idea that a guy would be attracted to her in virtue of her ethnicity, as opposed to her individual qualities. She doesn't want to be the guy's most recent addition to his menagerie of Hot Babes of the World. Men are different, though, and most wouldn't care on the basis of what reasons a cute girl was interested in them sexually. Still, that leaves half of a sub-population that's cautious of dating outside their group.

At first, this was mostly a problem for White guys who had an (East) "Asian fetish" . How much of this hubbub came from concerned East Asian girls vs. East Asian guys who were trying to scare away potential poonanny poachers, I don't know. Anecdotally, though, East Asian women rarely participate in feminism of any stripe, while East Asian men have formed internet groups devoted to their bitterness. In the Wikipedia link above, it's mostly males who decry White male / Asian female relationships, while females are in favor of interracial dating or feel resentful that slang like "Asian fetish" has made them feel guilty about being attracted to White guys [1]. However, there has emerged an independent "don't exotify us" movement within the South Asian community, and in this case a lot of the sentiment does come from the females themselves and so cannot be dismissed as the envious slandering of one's competition.

Unlike the East Asian case, then, this puts White Guys Who Like Brown Girls in a very sticky situation: the former must conspicuously prove to the latter that they do not have a "curry fetish" (or however the slang has it). A post at SepiaMutiny features a hint of the comic strip Questionable Content, including this example that illustrates the matter clearly: White guys with a taste for the exotic are overly eager to denigrate other White guys for using the word "exotic." In reality, White guys who say stuff like Steve in the comic are just a special case of the general pattern of "Guy who feigns empathy with girl's problems to get closer to her," part of the criteria for Byronic bad-boy. For instance, some guys pound the table about 3rd-order feminist concerns (e.g., how high heels are torture devices). All hot air amongst those jockeying for status. The same goes for the White trust-funding indie-rocker who pretends that a Brown girl wouldn't have been a rarity where he grew up. In fact, Northampton, Mass., where the comic is set (and home to Smith College), is 90% White and barely 3% Asian, of whom only a fraction are South Asians.

What we see in Steve's strategy is a churning of the euphemism treadmill, whereby words for sensitive topics become contaminated by association with their touchy subject matter and are jettisoned in favor of new terms that refer to the same thing. You're not supposed to refer to the Japanese as Oriental anymore, since that word is associated with something bad (I'm not sure what). So, White guys who like Oriental girls say instead, "Dude, did you see all those hot Asian chicks at the party?!" Only the sound-containers have changed, not the thoughts they convey. And now that the word "exotic" is officially démodé, we will soon see its replacement by a more palatable phrase. This changing of the linguistic guard will not change the reality that novelty-seeking is variable among individuals, and that in some cases it will take the shape of a guy who prefers hot girls from an ethnically dissimilar group over hot girls from his own group. This is as true for White guys as for Brown, Black, or Yellow guys.

Skimming through the thesaurus entries for "exotic," I can't see any of them catching on: alien, foreign, non-native, strange, mysterious, etc. Then what will likely happen is that guys will have to perform their ritual cleansing in more roundabout ways. For example, joking to a Brown girl, "Don't you hate it when goofy White people ask you what your favorite Ravi Shankar CD is?" Or perhaps, "Isn't it annoying when goofy White people see Bride and Prejudice and think they're suddenly experts on Bollywood?" Or, as we've seen in the comic strip above, casting aspersions on guys who use the word "exotic" to refer to people -- perfectly paralleling the taboo use of "Oriental" to refer to people (though it's fine when referring to carpets or cutlery).

I hate euphemism treadmills because they often force into retirement words that do their job better than their insipid successors. Consider "Semitic" -- "Jewish good looks" just won't do. And while I'm not quite sure what it means, the title of the Smashing Pumpkins album Siamese Dream is more alluring than Thai Dream. So how best to proceed? Well, first, the idea that there are men for whom South Asian (or fill-in-the-blank) ancestry is a sufficient condition for attractiveness is simply a red herring. The people we're talking about would list "ancestry" as a high priority, competing with other highly ranked priorities, including all the ones we're used to hearing about. Seen in this way, it's no more loathsome than a preference for tall women, who have no control over their height, and some of whom may wonder about whether men are in love with them or their height.

Moreover, I don't even see anything wrong with affectionate nicknames that refer to the girl's ancestry -- no more than if a guy with a preference for choleric exhibitionists referred to his girlfriend as a "firecracker." Indeed, Latin-American girls seem quite proud of describing themselves as having "fiery blood" or a "Latin temper." I have even seen a pornographic video in which the guy asks what language the actress is speaking, whereupon she shouts "Portuguese!" and begins to chant -- while being plowed -- a Brazilian version of "U.S.A! U.S.A!" They are that proud of being renowned as the world's sex-bombs.

One thing's for sure: if a girl would become visibly agitated upon learning that her ancestry was one component among many that attracted you to her, it is unlikely she would have been very open to dating outside her group in the first place. So, to the girls who don't fret about being exotified in the comic book way that rarely happens, your linguistic tip-toe-ing will just make you look like a namby-pamby. And obfuscation notwithstanding, girls don't dig pantywaists. Just don't behave like a colonial official, and you'll be fine. Recall also that some groups aren't so concerned about exotification -- the Latins for sure, and Persians are not yet up in arms about it either. But once the word gets out that Persian girls tend to be much better looking than the average American, something similar to the South Asian case could well happen. So chat up those Persian princesses (their term) with impunity while you still can.

[1] As the indirect product of a Japanese / French-American relationship on my paternal grandparents' side, I'm glad my Japanese grandmother had kids by a White guy. Don't get me wrong: I'm glad that I could outperform probably 29,999 out of every 30,000 people in visual problem-solving. But I'd be even shorter, skinnier, and more introverted than I already am if she'd married a Japanese guy. One of my father's brothers returned to Japan and married a Japanese woman, and that's fine; but I'm glad my father married my Scotch-Irish mother, who grew up on a farm in Appalachia, since I wouldn't have such a rascally hillbilly temperament otherwise.

May 17, 2007

Migrating to find The One

Inductivist has two posts (here and here) on the value of seeking out women in "Slavic" countries. I put Slavic in quotes since I think he'd include Lithuanians, Hungarians, and other non-Slavs in the less developed parts of Europe. I don't have much to add, so I'll just link to a similar post of mine on this topic. Of course, my target would be Iberia rather than Muscovy, but some guys prefer the tall, skinny blonde look. Actually, most of the Southern Slavs (e.g., the former Yugoslavian countries) have more than a hint of the Mediterranean in their appearance. For example, see the delegates to Miss Universe from these countries, the composite face of the Balkan Slav vs. other Slavic women at the bottom of this report by Dienekes, or compare Donald Trump's first wife (who is Czech) with his new wife (who is Slovenian).

Remember: to increase the probability of getting a hot girlfriend (regardless of whatever else you look for, and regardless of who you are), target a group whose mean is greater and whose variance is slighter than the American for physical attractiveness. That way, an objective 8 will perceive herself subjectively as a 5, and thus demand less at the bargaining table. With less variance, the gap between hot and not won't be as salient, so even if she is in the right tail, she won't percieve herself as standing heads and shoulders above the uglies, which also serves to make her more modest.

Addendum: If you live where there are lots of international women, you may not even have to migrate. E.g., any large metropolis or a university with international students.

May 15, 2007

How to make a top-performing school

From an NYT article on the ingredients for molding adolescent behavior in desirable ways at school:

There is no question that the Briarcliff school starts out with many advantages. It is part of a district in Westchester County that spends $24,738 per student, or more than one and a half times the New York State average, and can afford to buy extra sets of classroom textbooks so that students can leave their own copies at home. Its student body is relatively homogenous -- 91.8 percent are white -- and so well off that less than 1 percent qualify for free or reduced lunches. In contrast, in nearby New York City, 72 percent of the population qualifies.

You mean that's all it takes? Great, let's get started! Even if you threw a bunch of money at the problem, that wouldn't raise IQ. Wealth can be redistributed, brains can't.

So the school strives to develop critical thinking, teach organizational skills, and instill social and moral values.

Bullshit. Among the 6 or 7 high school students I knew who took the SAT in March (or maybe April), all but one wrote the exact same essay for the Writing test -- and not because they cheated. Rather, they are jaded enough to have realized that most essays like this are color-by-numbers assignments in which they drip platitudes into the allowed spaces. The goal was to write a persuasive essay on whether it was better to conform or stand out from the crowd, and damn near every student I talked to wrote an essay about "What if Martin Luther King had conformed?" Nothing wrong with the choice of evidence per se, but gimme a break, this is the real-life instantiation of the Chris Rock joke about how his answer to every question in African history class was "Martin Luther King" (watch here starting at 5:25).

So let's all embody the virtues of non-conformity by chanting identical, canned responses in unison. What a goddamn joke high school English classes are. It's also a shame that logic is taught in geometry class: almost none of the kids will ever study mathematics at a level where they'll need to rigorously prove anything, whereas they'll be making verbal arguments for as long as they're in school and perhaps beyond. So, you know, as long as you can tub-thump persuasively, who the hell cares if what you're saying makes any sense or not? I'm sure the little dears will make fine politicians or PR representatives some day.

Harry Zimmerman, 13, a seventh-grade student, said that managing his impulsivity during a social studies discussion stopped him from blurting out that he did not like Senator Hillary Rodham Clinton, who lives in nearby Chappaqua. "I realized that there might be people in the room who might be offended by that, and I didn't say it," he said.

Harry, stop being such a royal pussy. Jesus, he wasn't even about to say anything profane, only that he didn't like her. There's "critical thinking" for you: "I've figured out that slightly upsetting these panicky pukes will result in my tar & feathering, so I'd better just keep my big yapper shut." If I went to Briarcliff, I'd graffitti-tag the hell out the sterile hallways with portraits of Dead White Males and whistle Beethoven at the top of my lungs while they carted me away. Liven the joint up a little bit.

"This town needs an enema!" -- The Joker, Batman.

May 12, 2007

Mongolian visual IQ and throat singing

Last year I wrote up some suggestive evidence that in order for a group's musical style to emphasize harmony (or the "vertical" aspect of music), a necessary but not sufficient condition was a cognitive profile that either was lopsided toward Spatial rather than Verbal IQ or was balanced. Emphasis on melody (or the "horizontal" aspect) appears universal and is likely parasitic off of Verbal skills.

To reiterate the key groups and their exemplary musical genres: Africans with Hip-Hop and Jazz, Ashkenazi Jews with Klezmer and Jazz (and a little Hip-Hop), Germans with Baroque and Classical music, and Arctic peoples with throat singing. So, pretty much what I just said about Verbal-dominant groups pioneering more melodic genres and Spatial-dominant or balanced groups pioneering genres with a greater emphasis on harmony. Remember that I'm talking about composition, not performance / interpretation.

Now, throat singing is most strongly associated with Tuva and Central Asia in general (listen to an example), although data on the cognitive profiles of Central Asians was lacking at the time, so I made the obvious prediction that Central Asians must have IQ profiles favoring Spatial over Verbal skills. Richard Lynn has a new article out that reviews two large studies* of the IQs of Mongolians and Han Chinese in the regions of China near Mongolia. The first study used an IQ test that only tests raw pattern-recognition, without sub-tests for Verbal and Spatial skills. However, the second study did measure both, and they found that not only did Mongolians show the lopsidedness toward Spatial skills that characterizes East Asians broadly, but that on Spatial sub-tests they actually outperformed the Chinese on average by about 2 IQ points! This is despite scoring on average 10 points below the Chinese on Verbal and 5 points below the Chinese in overall IQ (combining both studies). So, it looks like the hypothesis about cognitive profiles and musical styles holds up for now.

* The studies were carried out by Chinese researchers and published in Chinese.

May 11, 2007

Photoshop makeovers -- so what?

Via 2blowhards, here's one of many clips showing how "easily" an expert Photoshopper can mold a fat, ugly dog into a slender, stunning fox. Apologies for the scarequotes, but they're there to contradict the facile conclusions that many non-slender non-foxes draw from such YouTube demonstrations -- namely, that we shouldn't believe our eyes when we see a Victoria's Secret ad, given how airbrushed it must be. "No one is that beautiful in real life," the likeminded Dove Real Beauty ad campaign implies.

Well, maybe not that beautiful, but the margin of error is likely to be negligible, and the reason (as always with such whining) is very simple: if the ad agency has a particular goal "look" in mind, they will choose models who are closest to the goal without Photoshopping, in order to minimize cost and effort (Cindy Crawford in her prime might have required no touching up, to a first approximation), as well as to maintain credibility were the model to make a public appearance attending an award show, promoting the brand on a talk show, and so on. To check this hunch, let's have a look at a few professionally touched up photos taken from real published work. Here are two safe examples (one, another), as well as a more provocative, full-body one. Drag the mouse pointer over the image to see its "before" look: most of the changes are accounted for by changes in lighting and contrast, not severely warping the woman's form as if it were Play-doh. The women "before" are clearly all very good-looking. (To see more examples, substitute other numbers just before the ".html" part of the URLs above.)

The logical error in casting aspersions on print models is confounding "the possible" with "the common." Rather than commit this fallacy, attempts at consciousness-raising should highlight how a typical viewer will be lured into thinking that flawless bikini models are common due to the quirks of human reasoning: even when we know that a group of 20 women has been selected to be hot babes, it's hard to perceive them as a non-random sample, leading us to believe that such alluring women are an order of magnitude or more common than they actually are. As we can't will this quirk of ours away, the best we can do is simply not consume these materials in the first place. Readers may be expecting me to say something like, "After all, it won't kill you to listen to a Bach concerto rather than stare at your idiot box," and while this is true, you can find plenty of more mundane ways to entertain yourself other than watching TV or visiting celebrity-themed internet sites. Work on your car, bake a batch of brownies -- anything, really. Of course, the male sex won't mind looking at an unrepresentative group of gorgeous women in the first place.

Added: For examples of the "facile conclusions" I referred to above, just look at the comments on the YouTube video (click "Oldest" to skip the bickering):

"This video really makes [you] think about what there is behind all the photos with those super-thin-and-beautiful models..."

"Makes you wonder if any pictures you see online are true to your eyes! good job on video!"

I know -- I feel like Plato's prisoner who has realized that all he has seen before were mere shadows on a cave wall! Puh-lease.

May 8, 2007

Mass immigration is bad for interracial dating

Most of the reasons that the Open Borders enthusiasts trot out are selfish: cheap labor for large corporations, cheap labor for home renovations / housekeeping / maid service, and so on. If the children of these illegal immigrants will have more difficulty in school due to lack of knowledge of English or lower mean IQ, the enthusiasts don't care since their own children won't attend the same schools as those of immigrants -- and probably won't even live within 20 minutes driving distance of each other. So, someone else can shoulder the negative externalities.

One of the few reasons that appears prima facie not selfish -- the desire for all the world's cultures to "come together and get along" -- probably is selfish, even if to a far lesser extent. Women who say this tend to be interested in bragging about how multicultural they are, the better to make their female peers envious. The men who insist on this benefit, though, almost surely have something else in mind: the opportunity to date, marry, or just have sex with exotic babes. In most discussions of interracial relationships, the men in favor just seem a bit too eager to be guided by a dispassionate principle such as "It would be good if we could transcend race."

The trouble is that mass immigration makes interracial relationships less likely, as Steve has noted in his recent VDare column. The reason is pretty simple: people tend to prefer to date within their own group, but we all have standards -- if you're a Mexican girl who lives in a community where there are only 5 Mexican guys, it's unlikely that you'll find a guy who fits your preferences within your own ethnic group. Therefore, you'll be more likely to look elsewhere. But if you're looking for a 1-in-100 Mexican guy in a community made up of thousands of Mexicans, you're more likely to find him, or at least someone pretty close.

So, if you consider increasing the frequency of interracial relationships a good thing (for whatever reason -- although, be honest, it's probably out of a hope to date exotic hotties), then you should favor immigration restrictions. On a personal note, my first girlfriend was Central American (probably Salvadorean), and she sought me out -- girls asking out guys is rare in itself, let alone across racial boundaries! That was in 6th grade, or 1992, about six years after the 1986 amnesty; if I had been born five to ten years later, I probably would have experienced no such thing, since the ranks of Central Americans in the US had swelled by then. In high school, a south Indian girl and I had a light mutual crush on each other, which didn't go anywhere, though she ended up dating a White guy still. That seems much less likely these days, since there are cities where South Asians congregate to raise their kids; and upon graduation, many South Asians end up in the same big cities, where they have plenty of opportunities to date within their race.

My second girlfriend, in 1997, was half-Anglo and half-Persian; I would guess her parents met in the mid-to-late 1970s. Although there are a lot of Persians in Los Angeles, it's hard to think of many towns that are predominantly Persian, to the same extent that some towns are highly South Asian. At the same time, I do notice that the Persian high schoolers I've tutored, as well as the Persian friends they tell me about, are more ethnically conscious (they have more "Persian pride"). Ten years ago, you wouldn't have known who the Persians were at high school, even when there were quite a few (like where I went). Today, Persians are more "out" as a group, and so high school kids know who the Persians are, even ascribing stereotypes to them (which seem pretty true, as far as I can tell). Nevertheless, immigration from Iran is far less than from South Asia, and the pool of potential Iranian immigrants is swamped in size by the pool of potential South Asian immigrants. So, interracial dating between Persians and other groups seems pretty protected in most areas.

Now, dating prospects are just one force that might pull an immigrant out of their community; others are job prospects (where English may vs may not be required), and so on. All of these forces tend to cause a small body of immigrants to disperse into the larger community, in the same way that a tiny asteroid tossed into Jupiter's orbit would be torn apart and scattered by the tidal forces of Jupiter itself and its numerous large moons. Once the immigrant community attains a certain critcial mass, it can withstand these forces and maintain cohesion -- this simple logic is not lost on ethnic boosterists, whose primary goal is to increase the sheer numbers of their group. This is not out of a concern for the well-being of the individual particles composing the immigrant body, since they will continue to be constituted of the same elements even if the body is broken apart. Assimilation rarely means "fusion" or blending. This is most true at the level of genetics: inheritance is particulate, so immigrant genes will persist into future generations, rather than be blended into a homogenous mix with the native genes. I conclude that "maintaining group cohesion" arguments serve group interests, obviously enough. That's what we need less of, though: chauvinism.

I concede that aspects of the group's culture may be diminished, language being the most susceptible to loss, but we're not talking about the vanishing of such cultural elements -- they will persist as long as they will in the group's home country. Whether they vanish upon immigration to the US (or wherever) is of little concern to the preservation of such elements per se. Again we are led to conclude that if you consider preservation of a diversity of languages (or other cultural elements) a good thing, then you should favor immigration restrictions. After all, it's easier to preserve the Farsi language if most of its speakers form a country of their own, such as Iran, rather than immigrate en masse to a large non-Farsi-speaking country, where the language will be embattled at best. No matter how you look at it, all of the plausibly laudable goals that naive pro-immigration folks espouse would be better served by a far more limited immigration policy. The fortunate thing is that these don't-know-any-betters outnumber the cynical shills for corporate and elite interests, who would prefer to amass even greater wealth by exploiting imported peasants while socializing the costs onto the bottom 90% of the native population. That makes the solution to the problem rather feasible.

May 4, 2007

Visualizing music to increase appreciation

Lots of people who should be, but are not interested in Western classical music would probably have their brain tickled more if they saw the "visual pattern" appeal of many interacting musical voices. As I was searching YouTube, I came across the videos of a guy who uses an animation program to visualize the melodic and harmonic aspects of several pieces. These aspects are implicit in sheet music, but you have to be trained to read musical notation, whereas his animations are incredibly intuitive. A trained musician or music lover might be able to hear all of the different voices and their interactions, but in order to reel in those who aren't already aficionados, something less demanding has to do the job.

For example, one reason why classical music snobs (of whom I'm not one) deplore much popular music, including film music, is that it lacks the richness that only comes from interacting voices, as opposed to the single line of melody, perhaps backed up by slavish accompaniment, that dominates most popular music. Since those who don't prefer classical music don't get what the "richness of interactions" argument is about -- which is understandable, given how vague a lot of the explanations are -- here are some visuals to the rescue. Let's start off with a simple example of counterpoint (a common method of producing interacting voices), namely a round:

Frog Round

The four lines are going in their own particular directions, but at each point in time they harmonize or produce agreeable sounds. However, the "particular directions" are really the same pattern, only shifted a little to the right as each "new" voice is added. As the lines go by, you can actually see this "same voice but shifted rightward" idea on the screen at once: watch the 1st and 3rd lines or the 2nd and 4th lines. So what we have is a single quirky pattern, then several copies of that pattern, and then shifting these copies to dovetail with the original and with each other. In other words, it's like a tessellation (some examples). Although popular among geeks, M.C. Escher prints ain't exactly the summit of visual art for at least three reasons: first, they don't appear to express much. And they are easily copied -- you can make your own tessellations with "how-to" websites on the internet. Furthermore, it's hard for them to sustain the audience's interest for very long after the initial appeal of "Wow, look at that repeating pattern!" has waned. Still, much more interesting than comic book or billboard art.

Let's have a look at more complicated examples from Baroque counterpoint, in which the two voices aren't just independent shifts of each other but are distinct patterns:

Scarlatti, Sonata K. 455
Bach, Toccata & Fugue in D Minor

Off the top of my head I can't think of a good art or math analogy for what the difference is between these and the round [1], but consider a dancing / martial arts analogy. Fill an otherwise empty room with people, so that each one is about three feet from their neighbors (let's say the room has a chessboard grid on the floor, with each person in one square). It would be pretty hard for each person to swing their fists without at least someone (probably lots of them) getting injured. The round's basic solution to this is to have everyone do the exact same thing -- say, stick your arms out in an "on the cross" pose, and spin your body in place -- but in such a way that the parts dovetail (i.e., in the opposite clock direction as your neighbors; try this with pens or toothpicks if that's not clear). So, when my neighbors have their arms pointed at me, mine are pointed perpendicularly to theirs, and by the time my arms are pointed at them, they have turned their arms to be perpendicular to mine. From the ceiling, it would look like a bunch of gears were turning, each gear with two teeth (a person's arms). No injuries! Cool -- but still, a pretty boring sight.

The voices in the Baroque counterpoint, especially the fugue, are like capoeira dancers, each of whom performs his own complicated dance moves, and who are doing so in close proximity to each other, but who have coreographed the dance so that they never hit each other. That's damn hard, and therefore it wouldn't look boring at all. Pedestrians could watch all day. Now, imagine four people doing this in close proximity, for nearly an hour and without repeating that much, and then you get a hint of the genius that produced The Art of the Fugue.

Even in the realm of popular music, some compositions are animated by more counterpoint than others. To provide two examples, consider the bass playing of Paul Simonon of The Clash vs Dee Dee Ramone of The Ramones. Or take the video game music in Castlevania 2 vs Gradius. The former parts sound richer than the latter parts since the accompanying voices don't merely "prop up" the main voice but instead do their own thing. Audiences readily recognize which music is richer than the other, so the potential is there for a better popular appreciation of what Western classical music has to offer. And with the more widespread use of visually intuitive aids such as the animation program used to generate the videos above, more potential art music lovers will become actual art music lovers.

[1] Here is my attempt. The idea is that each shape does something unique, but that they all blend together continuously -- leaving no gaps. The "no gaps" condition isn't so hard to meet with a tessellation, but it gets tricky when you use different, irregular shapes. For example, imagine trying to make a circle and square dovetail -- the aesthetically unpleasing, "pull it out of your ass" solution would be to inscribe one inside the other, and fill in the gaps with shapes that were tailored (stipulated) to fit them. That strategy is for Procrustes. I can't think of a good example on-the-fly, again since it's so hard, but it would look like three or four wacky 3-D shapes that meet together in a gapless knot.