Thursday, October 22, 2009

An inconceivable analysis

One of my favorite scenes in any movie is the Battle of Wits from The Princess Bride, in which Vizzini (Wallace Shawn) must decide which of two goblets Westley (Cary Elwes) has poisoned. Almost everyone finds the scene amusing and clever, but it has subtleties that are easy to miss. They concern the following questions: What in the name of mutton, lettuce and tomato sandwiches is Vizzini doing in this scene? How did he arrive at the choice he finally makes? And how come he's so confident in that choice when it's so spectacularly wrong?

Consider his opening argument, which makes more sense than anything else he says: a clever man would be tempted to put the poison in his own goblet, except that Westley would have anticipated Vizzini would think so, and therefore he'd put it in Vizzini's goblet instead. (Game theory deals with reasoning such as this, where you try to anticipate not only what your opponent will think, but how much he will anticipate your anticipations. Many games have this dynamic, where it's a race to determine who will do the most determining. Various webpages and books have examined the role of game theory in this scene.)

He eventually sticks with his initial conclusion (that the poison is in his own cup), but not before rambling for an entire minute about Australia and giants and Spaniards, going back and forth on which glass he thinks was poisoned. What he's trying to do, I suspect, is gauge Westley's reactions. Since Westley already knows the poison's location, he will (Vizzini assumes) fear for his life if he thinks Vizzini is guessing correctly. (That's why Vizzini secretly switches the goblets--he figures Westley will forfeit the game rather than voluntarily commit suicide if he realizes Vizzini has won.) Vizzini's strategy, therefore, is to keep changing his answer until Westley's body language betrays the correct one. As Westley observes, "You're trying to trick me into giving away something." In light of Vizzini's sureness when he finally makes his choice, we presume he does manage to detect something in Westley's behavior at crucial moments--nervousness maybe.

Westley indeed is nervous, but for a different reason than Vizzini assumes. He's worried Vizzini will stumble upon his actual secret, that he has poisoned both goblets. Vizzini almost seems to be approaching the truth as he rambles about how he "clearly" can't choose this glass and "clearly" can't choose the other one either. He even says at one point, "You could have put the poison in your own goblet, trusting on your strength to save you." His own rhetoric contains the solution to the puzzle, yet somehow he never notices. He's just bluffing (a recurring theme in The Princess Bride).

He possesses the classic fatal flaw of overconfidence, or hubris. He may in fact be smart enough to figure out what Westley is up to. Immunity-building was a practice known to the Ancient Greeks, whom Vizzini references earlier in the scene when he declares that Plato, Aristotle, and Socrates were "morons." The problem isn't so much that Vizzini is less smart than he imagines as that he discounts other people's intelligence. Truly wise people accept the wisdom of others. Thinking everyone in the world but oneself to be an idiot is folly, not wisdom.

Essential to any game is sizing up one's opponent, and Vizzini seriously underestimates Westley every time the word "Inconceivable!" escapes his lips. He never learns his lesson even as Westley continues to do everything he thought wasn't possible, including defeating a master swordsman and a giant. He reasons that a man who can defeat those "morons" still cannot hold a candle to his perfect mind. As he explains to Westley, "I can't compete with you physically, and you're no match for my brains." It doesn't seem to occur to him that Westley used brains, not brawn, to defeat Inigo and Fezzik. Since he maintains such a low opinion of Westley in spite of all available evidence, he fails to consider there might be a trick up the man's sleeve.

Ironically, his lack of appreciation for other people's minds deprives him of a powerful tool he could use against his enemies. What makes Westley so formidable an opponent is not just that he's versatile and quick-thinking, but that he uses people's natures against them. That's how he handles all his adversaries throughout the movie: he takes immediate advantage of Inigo's fairness, of Fezzik's sportsmanship, of Vizzini's pride, of the palace guards' credulity, and of Prince Humperdinck's cowardice. In contrast, Vizzini is all tactic and no psychology.

You might think I'm reading more into the film than is there, but in the novel it's pretty obvious that the author, William Goldman (who also wrote the screenplay), put considerable thought into the themes, the traditions, and the history this mock fairy tale draws upon. There are many interludes in which he speaks directly to the reader about various plot elements and their significance. Whether in movie or book form, The Princess Bride is not just clever and entertaining, but also well-conceived. It should not be underestimated.

Monday, October 12, 2009

Harry Potter, the jock

I'm sure I'm not the first to have noticed, but quidditch, the imaginary sport from the Harry Potter books, probably wouldn't work very well in the real world even if you had all the technology needed to make the game physically possible--including flying broomsticks, and a ball with a mind of its own.

In this game, each team has a group of players called Chasers who try to get a ball through the other team's goalpost. Of course every team has a goalie. This would all sound like soccer on broomsticks were it not for a couple of really exotic elements. First, there's a heavy, enchanted object called a bludger which tries to knock players off their broomsticks. To protect the players, each team has special players called Beaters, armed with a club for batting away bludgers.

The trouble is, nothing the Chasers, the Beaters, or the goalies do has any effect in moving the game toward its conclusion. A team could go on scoring goals forever, and the game wouldn't end even if the score was 440-0. A team's ultimate fate rests entirely with one player, the Seeker, whose task is to catch a tiny enchanted object called the Golden Snitch which only appears on occasion and tries to elude the Seeker's grasp. Once the Seeker catches the Snitch, his or her team earns 150 extra points and the game ends. Usually his or her team then wins the game. Only if that team is more than 150 points behind at the moment the Snitch is caught does the team lose. One of the later Harry Potter books (I can't remember which) depicts such a game.

Quidditch therefore has one fundamental flaw: the Chasers, who make up the majority of the players and whose actions dominate most of what happens, have a very weak incentive for scoring goals. As long as they manage to remain within 150 points of the other team, they are in little danger of losing. The score could be 140-0, and the team that hasn't scored could still easily win. Most likely, a typical quidditch team would hardly score at all, focusing its energy simply on preventing the other team from scoring.

To compensate for this all-too-obvious flaw, teams get ranked according to points scored rather than number of games won. But that makes it heavily dependent on record-keeping between games. You'd have to commit yourself in advance to playing many games for it to have any impact. It's not the type of sport that lends itself to casual play in the backyard.

In our world, most team sports revolve around one very simple formula: one team tries to relocate a small object (a ball, a puck, etc.), and the other team tries to stop it. That's it. Right there you have the basic description of soccer, hockey, baseball, football, basketball, volleyball, and lacrosse. Soccer and hockey are almost moronically simple games. Baseball and American football have intricate rules of progression, and baseball (along with its cousins such as cricket) is slightly unconventional in that a team's ultimate objective involves the movement of players rather than the movement of the ball. None of these games, however, allow more than one ball on the field at a time, much less more than one type of ball. And a game where regular scoring doesn't count for anything more than a team's record is hard to imagine. In sports, complexity is not necessarily a virtue.

The Potter books, nonetheless, make quidditch out to be the most dazzlingly exciting sport in the history of mankind, far surpassing any of the familiar earth-bound ballgames. No other wizard sport ever gets mentioned, suggesting the wizarding world is quite satisfied with this one. Most readers consider it one of the charms of the series, an example of J.K. Rowling's enduring creativity. Somehow it's fun to read about, even if the rules are probably too unwieldy for it to work in the real world.

Whether it's fun to watch is less clear. Only the first two movies show the game in detail, and the fourth and fifth movie don't show the game at all. The novelty of seeing the magical sport on screen makes it interesting at first. After that, there's little suspense to be generated, apart from hoping Harry doesn't get hit by a bludger. As a Seeker, most of what he does during any game is sit around waiting for the Snitch to appear. As for the other players, since they do not determine the game's ultimate fate, what's the point in watching them play? (It's no wonder the films so often show cheating and other disturbances; they aren't confident the game will be interesting on its own terms.)

Had Rowling eliminated the business with the Seeker and the Snitch, quidditch would be more believable. It would be like soccer in three dimensions rather than two, similar to what Orson Scott Card envisioned in his novel Ender's Game, in which child soldiers conduct simulated space battles in a null-G environment. But the Golden Snitch is just enough to put quidditch over the top as something truly otherworldly. If all the game consisted of was players trying to score goals, it would quickly begin to sound mundane once the novelty of their flying on broomsticks wore off. The bludgers add a level of danger you don't associate with high school athletics, and the Snitch makes the game unlike anything you've heard of.

Quidditch is really part of the whole mystique of the Harry Potter series. In a world where magic dominates and where broken limbs can be mended within seconds, physical prowess is a lot less valued than in our "muggle" world. That's why a kid who looks to us like a class-A dork can get to be the star of his school's sports team. That's why girls can play along with the boys, without anyone turning their head. That's why even the school bully is a pint-sized kid. But considering that the magic in these books is a lot like advanced technology, one must ask: isn't this where our own society is headed?