Conundrum: Two Boxes
Researchers in Germany are working on a way to predict the intentions of human subjects by observing their brain activity. Damn!
For some reason it’s a little disturbing to me that something as personal and ephemeral as an intention can have a physiological manifestation that can be measured. Or maybe I’m just disturbed that they are now starting to measure it. What new “mind reading” technologies might be developed from this science? Could it become prosecutable to merely intend to commit a crime? Intent is already used as a legal concept, and attempted murder is considered a crime, even if nobody is hurt as a result. Could market researchers measure the intent of potential consumers? Will we one day have little handheld devices that can measure intent at a poker table or when our daughter’s date arrives to pick her up?
It all reminds me of a thought experiment made popular by Robert Nozick, which will be this week’s Conundrum. Before we get to it, though, it might be helpful to consider another thought experiment known as Kavka’s Toxin.
Let’s say I offer you $100,000 if you can form an intention to drink a particular toxin. This toxin will make you violently ill for about five or six hours, after which you will be perfectly fine. You’d drink it for the money, but you’re not being asked to drink it. You’re being asked to intend to drink it. After you have the money, you are free to change your mind and not drink it. The question is, can you actually form a genuine intention of doing something unpleasant that you will have no motivation to do?
Turn that one over in your mind for a few moments before moving on to this week’s Conundrum, Newcomb’s Problem.
Imagine there are two boxes, Box A and Box B. You will have the option of choosing to take both boxes, or to take Box B alone. You will keep what you find inside. Box A is transparent and contains one thousand dollars. Box B is opaque. A super-intelligent alien scientist with a proven track record of accurately predicting human behavior has analyzed you and has secretly made a prediction about which you will choose. If he believes you will choose Box B alone, he has put one million dollars inside. If he believes you will take both boxes, then he has left Box B empty. Which do you choose?
The super-intelligent scientist has run this trial with several hundred other humans, and has made a correct prediction each time. The only people who have ended up with the million are the ones who chose Box B alone. On the other hand, our alien friend has already made his prediction and left. Your choice can no longer affect the amounts that are in the boxes. You may as well take them both, right?
Fans of game theory might recognize this as a variation of the Prisoner’s Dilemma. Game theory would likely suggest that you flip a coin, so we’re going to disallow that option. You must rely on reasoning alone.
Unlike last week’s math puzzler, this one doesn’t have a right or wrong answer. It’s a thought experiment designed to test your conceptions of free will vs. determinism.
Or as Nozick put it:
To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly.
It will be interesting to hear how people answer this.
Will you take both boxes, or Box B alone?
Feel free to answer the question, or continue the discussion of any of the topics covered above.
April 18th, 2007 at 9:13 pm
Okay, let me give you my own take on the problem.
First of all, I would actually drink Kavka’s Toxin. It’s the only way to form an intent to do so. No matter how afraid I am, no matter how bad it smells, no matter how sick I’ll get, I have to force myself to drink it. That much seems clear. So by that same logic, it seems to make sense to choose Box B alone to collect the million dollars.
But Newcomb’s Problem is more complicated than that. It’s not a matter of finding some mental process to form an intent to choose Box B. Nobody’s asking me to. The only question is whether I have the qualities and internal makeup to make one choice or the other. These factors are entirely out of my control.
Based on the premise, there seem to be two kinds of people – those who take the two boxes and those who take Box B. The Nozick quote reinforces the idea that this aspect of it may actually be true. The premise also implies that there is a way of identifying these two types, even if it’s beyond human capacity to do so. And whichever one of those kinds of people I am, I am that right now. I am that when being analyzed, and I am that when I make my choice. And the first time I’m actually being asked to make a decision is after it has any power to affect the outcome. That’s what makes it different from Kavka’s Toxin. If all we had to do was form an intent to choose B, it would be a variation of the same problem.
So why would anyone choose Box B alone? For that, we turn to John Calvin, the 16th century Protestant reformer.
Calvin takes the ideas of Martin Luther to their logical extreme. Luther said that God has already chosen who would be saved and who would not. So good works were unnecessary, only faith was required. Calvin noted that if God has already made his decision, and nothing we can do change it, then not even faith is required. Those who are already saved would also be granted faith and its manifestations, and it’s not something we have any control over. You may already be a winner!
You’d think that this philosophy would have led to an anything-goes mentality, but it didn’t. Calvinists all wanted to believe that they were among those already saved, so they acted that way.
Look, I’ll be honest with you. I want that million dollars. I have big plans for it. If there are really two kinds of people, I want to be the kind of person who gets the million dollars. And I can choose to be that kind of person by choosing Box B.
But that’s not who I am. When I’m standing there in front of the two boxes, I know that nothing’s going to change about that Box B. To choose it alone would be pure superstition. And what’s more, our alien friend knows that’s who I am, and he has left Box B empty before I even got there. I might as well get the thousand.
I’ll take both boxes. And I’ll probably chicken out before I drink the toxin, too. It wouldn’t be the first promise to myself I’ve broken. But I’m keeping the money because that was the deal.
Total thought experiment currency earned: $101,000
I wonder how much that is in Second Life money.