Thursday, October 23, 2003

Kill Bill and 3 dirty faces

Tarantino movies always have that "movie about movies" reflexivity that can be either intriguing or just a pain. This time he mixes revenge movies and the French New Wave's preoccupation with audience manipulation.

Directors are concerned with staying one step ahead of their audience in a way similar to someone wanting revenge seeks to outwit their foe. And if any director has set themselves up as having to stay ahead of their (film-wise) audience it is Tarantino.

But any game of strategy runs the risk of what is called in film theory "mise en abyme". Infinite regress. We know Tarantino will be referring to other movies, he knows that we know this and we know that he knows that we know etc etc into the abyss of reflecting mirrors.

And similarly with revenge. An act at of revenge is only effective if the person on the receiving end knows that they have brought this on themselves. One has to know that the other person knows that it is payback time.

In Game Theory there is the following puzzle that deals with this issue of levels of common knowledge.

Three young siblings, Alice, Sue and Bob, all turn up at home, after playing separately, with dirty faces.

Each does not know and cannot determine if their own face is clean or dirty but can see that the other two have dirty faces. (They do not talk or otherwise communicate with each other and there is nothing tricky like mirrors on the wall etc).

Their mother enters the room and says: "Not all your faces are clean" (Or, if you prefer, "Some of your faces are dirty").

The mother then asks "Put your hand up if you know your face is dirty".

How many times does she ask this same question before they all put their hands up?


Once you see that this is actually a valid question it becomes very intriguing and/or annoying.

One way of approaching the problem is to think of, for example, what Alice might think that Bob might think that Sue thinks. I couldn't work it out that way, it just gave me a headache. Its somewhat easier to start with less people and work up. (Or if you want to use symbolic formalism look at the last question here).

You might think that this is all mildly interesting but greatly irrelevant. But this sort of thing is a common feature of all adversarial relationships, from the personal level right up to the level of nation states. It leads to problems in conflict resolution that are independent of the amount of goodwill on either side. In the above puzzle it is an external agent, the mother, who makes a critical difference by telling the kids something they already know, which is a bit counter-intuitive.

There is lots of this sort of trickiness in Kill Bill. ("Entropy" is no doubt a nod to Pynchon.) I eventually got a bit bored with the fight scenes but found that the movie ended too soon. If nothing else it is a magnificent example of film making virtuosity.

But it is a lot more than that. It is not a celebration of violence, it is not mere pastiche and does actually have a huge psychological depth - deliberately masked by an ironic distance reminiscent of Kubrick at his best. Its too bad Tarantino didn't direct AI.

But aside from all that it is quite funny and very stylish. And of course great music.

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