One Language, Under Force

I watched the Super Bowl.  Well, "watched" might be putting it a bit strongly.  I watched the first part, a very short part, in which the Broncos seemed as though they might have had a decent chance to win.  After that, I watched mostly to see what other parts could fall off the Denver bandwagon.  Congratulations to Seattle; they thoroughly outclassed their opponents.

That left the halftime show and the commercials.  I have to say that I didn't even watch those very assiduously, though I find the idea that they aren't as good as they used to be to be about a step or two shy of yelling at the neighborhood kids to get off the lawn.  It's Cranky Old Geezer time!

But even through my haze of disappointment in the football game, I did manage to get a look at the Coca-Cola "America the Beautiful" commercial.

The one-minute spot consists of a sequence of short video vignettes of the broad span of Americana, against which is sung "America the Beautiful."  There's nothing at all contentious about that, as far as it goes, of course.  What seems to have gotten lots of people in a lather is the fact that, except for the first and last phrase, the song is sung in several different languages.  No doubt Coca-Cola wanted to evoke the idea that part of what makes America beautiful is the wide variety of people that make it up, and that's what the commercial does.  In fact, Coca-Cola went so far as to follow the commercial up with a tweet, just in case someone missed the point:

Apparently, that's not the message that many people got.  I imagine the reaction of Coca-Cola to the some of the retweets ranged from bemused concern to horrified astonishment.  (Or maybe they're more cynical than that; it's quite plausible.)  I don't have the patience to drag them all out, obviously, so I'll just link to a collection of some of them here.

As might be expected, there's also been a backlash against those reactions, lambasting them as racist or ignorant or condescending, or who knows what.  I won't attempt to characterize them one way or the other; as I like to say, people feel what they feel, and it's pointless to tell them they're "wrong" to feel that way.  But I think it is interesting to try to suss out just why they feel that way.  What is it about diversity, in what seems like such a harmless context, that spooks some people?  Is our sense of national pride so fragile that it relies upon the exclusive use of a language that was brought forth onto this continent for the first time not half a millennium ago?  I have no idea whether one of the languages used in the commercial was an Amerind tongue (maybe someone can tell me), but I wonder what the reaction to that would be.

The melting-pot metaphor used to be a point of pride for us; it's a central point of one of those Schoolhouse Rock shorts, for those of you who remember those.  I don't remember anyone lashing back at those a few decades ago.  Shall we say to those who object to singing "America the Beautiful" in anything other than English that they are simply being too sensitive?

In connection with that possibility, let me introduce another commercial, which aired last year (and was brought back to mind by a friend of mine):

Notice anything out of the ordinary?  I have to admit that the first time I watched this, I didn't.  Then, my friend pointed out, "Look at who's in the box."  My reaction to this was, "Oh, PoCs in a box," since the forward-thinking hotel guest (who incidentally spouts some meaningless marketing mumbo-jumbo, but that's neither here nor there) is a white male, and all the persons of color, along with a white male or two (for variety I suppose), are in the box.  Even the guy who thinks to venture out before scurrying back to the safety of the box is a white male.  (I must say that the look of relief on the woman next to him is hilarious.  She should get a Cleo for that.)

A "natural" reaction by some people, in response to such a comment, might well be "Oh, you're being too sensitive.  They had to put someone outside the box; it just so happens it was a white guy."  In isolation, that point might be arguable.  However, it happens too frequently for it to be just random chance.  The vast majority of business travellers I work with are white males, and it's not surprising that they (the primary target of the commercial, after all) would prefer to see someone like themselves as the hero of the story.

I see too frequently, however, the objection that people of color have an inferiority complex, that they play the race card too readily, that they are too comfortable in the victim role.  Does it really make sense that a group of people who are actually empowered would feel that way, that instead of doing what they're capable of, they would rather lie down and cry foul?  I'm not sure that there's been a significant group of people like that in the history of ever.  Regardless of whether that group is a victim of discrimination as they claim, or for some constitutional reason is less capable, or both, it's utterly implausible to me that they would rather blame someone else than have more power.  Blame may be a salve for what ails them, but equal power is the cure.  A small number of them might miss that, but not the whole group.

Could something similar be at work with the reaction to the Coca-Cola commercial?  Is it that people feel upset about the commercial because it represents a situation they have little or no immediate control over?  Undoubtedly that's part of it.  After all, the tweets are rife with threats to boycott Coke, but these threats would have essentially no impact on Coke's bottom line even were they credible.  As it is, I suspect the vast majority of those would-be boycotters will be back to drinking Coke before the month is out.  Inexpensive habits can be terribly hard to break.  And at any rate, Coca-Cola is here serving only as a proxy for what some evidently see as a distressing trend toward inclusiveness.

Isn't it provocative, though, that each side sees a given cultural portrayal as betraying an awful truth, and often speaks out vigorously against it—something that the other side views as oversensitive and tiresome?  And this may be the crux of the matter: that there is a kind of massive joint cognitive dissonance between the way that the various groups perceive the current cultural situation, and the way that the various groups think the situation should be.  This dissonance is made all the more contentious by the striking symmetry between the views.

There is one thing, however, that distinguishes the two cases, as exemplified by these commercials, and that is the distinction between equality and uniformity, something that has stuck with me ever since it was first explained to me in stark simplicity in Madeleine L'Engle's A Wrinkle in Time.

What is at the root of the desire for uniformity (for I see no other way to describe, as succinctly, the demand that people sing this song in English) that the Coca-Cola tweets share?  It seems to me that it aims for a feeling of security, that if we only trust those people who cleave to the majority culture, then all will be well in this world gone mad.  But if that's so, is it necessary to demand uniformity?  Can't we feel secure without insisting on the elimination of the traces of other cultures?  Why not cut the middle man of uniformity out of the picture entirely?

I fear, though, that this is not likely until people see that this kind of uniformity not only isn't the end goal, but is actually counter-productive as far as any real kind of security is concerned.  I like to say that religion is a laser of the people, by which I mean that it moves people to behave and operate in unison, almost as though they constituted a single being, which can do certain things that the individuals couldn't do, separately.  But that same uniformity has a cost, because if all the individuals uniformly have a weakness, that weakness is passed onto the group as a whole, and is not amortized, so to speak.  I'm reminded of the old Aesop's fable in which an old man, near the end of his life, demonstrates to his sons the value of unity by tying together a bundle of sticks.  That bundle, of course, could not be broken by vigorous effort, even as the individual sticks were easily snapped.  It's ironic to think, though, that one could quickly slice through the bundle if one were to cut lengthwise.

The amortization of weaknesses is what makes diverse groups so robust.  It's why a farm made up of a single strain of high-yield crops is not a good long-term strategy.  It's why a diversified investment portfolio is safer than one that relies on a single kind of asset.  And why shouldn't the same kind of reasoning apply just as well to people as to crops or funds?  Yes, uniformity is good in moderate doses, for it enables feats that could not be achieved otherwise, but in doses large enough to dominate an entire country, it's dangerous.  It's dangerous not only because it makes the country more vulnerable, but also because it is such an appealing dogma.

Who knows if there will come a time when ads like Coca-Cola's will not produce such a strong negative reaction.  But if it does, it will be because people understand, viscerally, the value of diversity, and do not see it for the demise of national security.

The Tip of the Iceberg

A couple of weeks ago, as I write this, Dharun Ravi was found guilty of invasion of privacy and a host of other charges in a sequence of incidents, including spying via webcam, that ultimately culminated in the suicide of his roommate Tyler Clementi (left).  Ravi faces up to ten years' imprisonment, and deportation to his native India.

Now, since it's been a couple of weeks, a lot has already been written about whether or not Ravi was culpable, whether others had a role, what it says about us as a society that we continue to demonize and ridicule homosexuality (or conversely, what it says about us that we are able to demonize and ridicule someone for being a peeping Tom and a loudmouth).  I'm not going to say anything about that.  As is my wont, I'm going to talk about statistics, but with an eye toward how we perceive events like this.

In a way, those who wonder how we can hound Ravi the way we do have a point, even if I disagree with their larger perspective: What Ravi did, as wrong as it was, is probably happening all over the country—or the world—as we speak.  Is Ravi wronger because what he did led to Clementi's suicide?  Should he, in effect, be the scapegoat on which we place all the otherwise indistinguishable wrongs that, by sheer dumb luck, resulted in nothing more than a change of roommates?  I've been following the Ravi/Clementi case for a few months, after Clementi's suicide but before the trial began, and I seem to recall that Clementi did in fact look into switching rooms, but for whatever reason did not manage to do so before his death.  If he had changed rooms, where would we be now?  Would we be up in arms about homophobia and scapegoating?

This is only part of a general problem that human beings have with assessing rare events.  To be sure, it's not simply a matter of placing too great an emphasis on the result of those events, although we do do that.  (Many of us greatly fear the rare airplane crashes, even though they are at least an order of magnitude safer than road travel by practically any metric you care to choose.)  More than that, it's that we just do not have the vocabulary to compare these rare events, and their consequences, with their more typical brethren.

Interestingly, we don't really run into significant roadblocks with their opposite number, the rare non-events.  If someone intentionally shoots a bullet into a crowd, and against incredible odds, manages to hit no one at all, we still find them guilty of reckless endangerment.  The rare non-homicide doesn't conceal from us from the essential wrongness of the act.

But Ravi's case, and others like it, put us in a quandary.  Despite what others have said, I don't believe what Ravi (right) did led inevitably to Clementi's suicide.  We tend to think so because Clementi did in fact die, and what Ravi did is reprehensible and did in fact lead materially to Clementi's death.  But to think that it was the unavoidable outcome of what Ravi did is to assume that his actions are as rare as Clementi's suicide, that whenever this kind of thing happens, we will hear of it.  This strikes me as burying one's head in the sand.  It's not appealing, because many of us really do want to blame Ravi, but one can't consistently believe both that Ravi inevitably caused Clementi's suicide, and that their situation is common. 

But if the opposite is true, and similar situations are playing themselves out all the time (just with much lighter consequences), then what are we, as a society, to do with Ravi?  What are we to do with anyone who does something criminal that then leads, against (let us say) hundred-to-one odds, to someone's death?  Ostensibly, their actions put them in a lottery of sorts.  We punish the lottery losers, and everyone else goes unscathed, perhaps even unnoticed.

Is this justice?  Does the punishment really fit the crime, or is it more that it fits the consequences?  If it fits the crime, what should we do about those who do not lead to any substantive damage?  On a more abstract level, are we doing what we should to protect potential victims?  Even from the point of view of American jurisprudence, in which the results matter, the situation is unclear.  By throwing the book at Ravi, and missing the others, do we send the message that what Ravi did was wrong?  Or do we just send the message that one just needs to avoid getting caught?

Someday, perhaps, situations like Ravi/Clementi will cease to happen.  It seems unlikely to me, but just perhaps!  But in the meantime, we must think hard about the consequences of punishing people for the results of their crimes, when those results are rare.

Square Roots, Lasers, and Mobilization

I promised (threatened) that I would say more about square roots, and so I am. This is me, talking about square roots again. In typical fashion, though, I'm going to start with something else that will seem, for a time, completely unrelated.

Galileo, he of the telescope, the balls rolling down inclined planes (and probably not in actuality from the Tower of Pisa), the sotto voce thumbing of the nose at the Inquisition—Galileo also discovered, or more likely rediscovered, that pendulums mark out roughly even time, no matter how far they swing. It isn't perfectly even time, owing to friction and to the circular track of the pendulum bob (although both of those can be—and were—accounted for, starting with Huygens's employment of cycloid guides). But it's pretty close.

Since the pendulum keeps fairly even time, that must mean that if the pendulum swings in twice as big an arc, it must also be moving twice as fast, in order to keep beating out even time. Now, as it's defined in Newtonian physics, the kinetic energy of the pendulum bob—that is, the energy of the bob due to its motion—goes as the square of its velocity:

KE = ½ mv²

So, twice the arc, twice the velocity, four times the kinetic energy; three times the arc, three times the velocity, nine times the kinetic energy. And so on.

That swinging motion of the pendulum bob is an example of periodic or wave motion, so called by virtue of it swinging back and forth as a water wave swings up and down, if you were to watch it passing by a buoy. Wave motion is primarily characterized by two parameters: its frequency, which is how often it returns to its starting point; and its amplitude, which is how wide it swings. So the arc through which the pendulum bob swings is essentially its amplitude. (Actually, for historical reasons, the amplitude is defined as half of that arc, from the center point of the swing to either of its extremes, but this won't affect our discussion.) So we can say that the pendulum's energy is proportional to the square of its amplitude.


This turns out to be common to many different kinds of waves—including light waves. Light is a wave. (It's also a particle, in many ways, but we'll ignore that for now.) And being a wave, it has an amplitude, which is the extent to which the light oscillates. What is it that's oscillating, anyway? In the case of water waves, it's water, and in the case of sound, it's the molecules in the air. You can't have water waves without the water, and you can't have sound waves without the air; that's why sound doesn't travel in a vacuum. But light does travel in a vacuum, so what's waving the light, so to speak? Well, the answer is that the light itself is waving, or less opaquely (heh heh), the electromagnetic fields that permeate space are waving.

In any event, like other waves, light waves also carry energy that is proportional to the square of the light's amplitude. If you double the amplitude, you quadruple the energy; triple the amplitude, and the energy goes up nine-fold. And so on.

How would light's amplitude be doubled, though? You might imagine that if you put two flashlights, the amplitude of the two together would be twice that of each individual flashlight, and the combined light output—the energy of the two together—would be four times that of each flashlight. But I think, intuitively, we know this to be false, that the combination is only twice as bright as each flashlight. And if you measure the light carefully, in a dark room, this turns out to be perfectly true.

What happened? Light waves, like other waves, have a secondary property, called phase. Two waves of the same frequency are said to be in phase if they swing in the same "direction" (in some not altogether well-defined sense); imagine two pendulums swinging in unison, so that when one swings left, the other does, too. They are out of phase if when one swings left, the other swings right, and vice versa. Or, they may be partly in phase, partly out of phase.

When you combine two light waves of the same frequency and the same amplitude, you get for all intents and purposes a single wave that is the two original waves added together. If they're in phase, the peaks get peakier and the valleys get, err, valleyier, and the amplitude of the waves is in fact doubled. On the other hand, if they're out of phase, the peaks of one get cancelled out by the valleys of the other (and vice versa), and the resultant wave has no amplitude at all.

More typically, though, the two waves are partly in phase and partly out of phase, and the resulting wave's amplitude is somewhere in between zero and two times the original. On average, one can show that the amplitude is the original times √2 . What's more, if you add three waves together at random phases, the amplitude of the sum is the original times √3 . And so on. Aha, the square root!

And since the energy of the final wave is the square of the amplitude, what comes out has two, three, or whatever times the original energy. Which is, of course, exactly what you'd expect. And good thing, too, because if it came out otherwise, we'd have a violation of the conservation of energy. Clearly, it takes n times as much energy to run n flashlights as it does to run one, and if their combined output were something other than n times the original, we'd have to seriously rethink our physics.

You might wonder if there isn't a way to get the waves to line up properly in phase so that the amplitudes do add up in the normal way, and you get a dramatic ramp up in energy. And there is; it's called a laser. A laser essentially gets n individual photons to line up in phase so that what comes out is a sort of super-photon (or super-wave, equivalently) with n² times the energy of any of the input photons. The physics-saving catch is that it takes more energy to line up, or lase, the light than you get as a result.

Nevertheless, that single photon or wave, coordinated as it is, can do things that you couldn't do with the individual photons separately. You can shine a bunch of flashlights at your eye and nothing will happen, other than a rather annoying afterimage and perhaps a headache. But even a modest laser can be used to reshape your cornea and render your eyeglasses superfluous. Of course, it should go without saying that it's not such a great idea to randomly shine lasers into your eye!

Or out, for that matter.

I see in this a kind of metaphor for human nature, and I hasten to say it's only that; as far as I know, one can't really take this and apply it rigorously in any scientific sense. But I think it's a useful metaphor all the same. I like to say that religion, among other things, is a laser of people. What on earth do I mean by that? A single human being can do a certain amount of work (in physics, work is defined as energy applied in furtherance of a force). What happens if you get two human beings together? Well, if they work against each other—if they're out of phase, in other words—less work gets done. Maybe none, if they spend all their time squabbling. Even if they're not exactly out of phase, if they're not particularly coordinated, their combined output is rather less than you might think, like the drunkard making slow and halting progress homeward because he can't put one foot directly in front of the other.

On the other hand, if they cooperate—if they're in phase—they can do twice the work. In fact, maybe they can get even more done, for there's no arguing that a coordinated combination of two people can do things that each individual person couldn't do, even adding their results together. Two people can erect a wall, for instance, that neither person could individually. Maybe, in some sense, those two people can do what it would take four people, working randomly, to achieve. And perhaps three coordinated people can do what it would take nine randomly working people to. And so on.

But it's pretty straightforward to get two or three people to work together, if they're of a mind to. But what about a hundred, or a thousand, or a million? That's where ideologies can be enormously effective; through them, a thousand can achieve what would otherwise require a million. And there may be no ideology better suited for the purpose than religion, although other ideologies—sociological, fiscal, even autocratical—may suffice. That's not to say that all that these various ideologies achieve is beneficial: for every great liberation, there may be a dozen pogroms. But they are part and parcel of a society's capacity for achievement; without them, we get only as far as a drunkard's walk will take us.