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Monday, December 18, 2006

So an alien with a million bucks walks into a bar...

Boingboing recently linked to a description of a paradox called "Newcomb's Paradox", with the description:
A highly superior being from another part of the galaxy presents you with two boxes, one open and one closed. In the open box there is a thousand-dollar bill. In the closed box there is either one million dollars or there is nothing. You are to choose between taking both boxes or taking the closed box only.

But there's a catch. The being claims that he is able to predict what any human being will decide to do. If he predicted you would take only the closed box, then he placed a million dollars in it. But if he predicted you would take both boxes, he left the closed box empty.

Furthermore, he has run this experiment with 999 people before, and has been right every time. What do you do?

On the one hand, the evidence is fairly obvious that if you choose to take only the closed box you will get one million dollars, whereas if you take both boxes you get only a measly thousand. You'd be stupid to take both boxes.

On the other hand, at the time you make your decision, the closed box already is empty or else contains a million dollars. Either way, if you take both boxes you get a thousand dollars more than if you take the closed box only.
The puzzle was apparently popularized by Scientific American columnist Martin Gardner and Harvard philosopher Robert Nozick, both of whom declared that they would take both boxes; Nozick figured that since your choice can't affect the prediction the alien made in the past, your hope that the alien predicted generously and your desire to grab the extra $1k are unrelated. Franz Kiekeben, who wrote the above summary, disagrees, arguing that if you behave like Nozick, then surely the alien predicted this and didn't put the $1m in the box; therefore your only chance at the $1m is to have already been the kind of person who would take the $1m.

But there's a difference between the problem as Kiekeben originally poses it and the problem as he solves it. The original phrasing suggests that you first begin to think about the puzzle when the alien appears to you--that is, after it has made its prediction already. At that point, you are powerless to affect the alien's decision. As Nozick points out, you delude yourself if you think that your choice to pick just the $1m box will encourage the alien, in the past, to predict this. Kiekeben concludes that "Nozick and Gardner's choice to take both boxes... make them much less likely to make a million." Assuming that the alien's predictions are very likely to be correct, Kiekeben is correct that Nozick and Gardner's choice now to take both boxes would hurt them were such an alien ever to appear to them. But does that mean they should, like Kiekeben, believe that it is wiser to take just the one box? That is, should they take on a belief solely because it is advantageous (and let's hope that no aliens ever appear who reward takers of both boxes instead!), rather than because it is true?

A thread on the puzzle has attracted some excellent comments, including this from Brad Templeton, chairman of the board of the Electronic Frontier Foundation:
In the context of this problem, you do not _make_ a choice. You _are_ a choice. The alien's accuracy suggests that a human's conclusion that she is weighing two options here is a false one. From the alien's viewpoint, you are no more likely to choose differently than the prediction than you will choose to suddenly freeze because of a bizarre entropic coincidence. (It could happen, but it's really unlikely.)

So there is no paradox. Predictable beings are presented with a problem and answer it just as predicted. The only paradox is in their illusion that they might do otherwise. The trick is the question asks you to decide which choice to take, when in fact the premise says you don't have that freedom.
Taking both boxes does mean hoping that the alien predicted incorrectly, which seems like a long shot. But at this point, the degree to which you are the kind of person who takes one box or the kind that takes two is set. It may be likely that the alien predicted correctly, but it isn't absolute; as one commenter in the forum points out, you could render the alien's prediction useless by just flipping a coin. You are no more a slave to the alien's past odds than you are a miracle worker by plucking a blade of grass (because hey, what are the odds that you'd have picked that particular blade!?). You should take a deep breath, hope that you seem like the kind of person who would take just the $1m box, and take both boxes.

(Better yet, decide to flip a coin and to interpret heads as instructing you to take both boxes, and be lucky enough to have a friend who will slip a heads-only coin into your pocket without your knowledge. The alien's prediction will still be useless, but you'll be guaranteed to make the most profitable decision!)