Stones into the future

How Something Can Be Within Our Power Even Though We Can Have No Causal Effect On It, Or Maybe Not, With Apologies To Newcomb

A time traveller appears to you. (He really is one, you believe that he is, and you believe it for good reasons). He tells you that he is from the future. He just visited tomorrow, and saw that a certain man (call him Steve) is going to play the lottery. Steve is going to receive some number of millions of dollars. This number could be zero. It could be 100. It could be any other number. The time traveler does not specify.

The time traveller also indicates a box nearby, and points out all the stones on the ground around where you are. (You’ve been walking on the beach or something). The time traveller says he has also visited later today, and knows exactly how many stones are going to be in the box at that time. That number could be zero, or it could be any other number. The time traveller doesn’t specify. He does specify, however, that the number of stones that will be in the box is equal to the number of stones you are going to put in the box in the next five minutes.

The time traveller tells you it happens to be the case that the number of stones that will end up in the box is the same as the number of millions that Steve is going to receive. The time traveller also tells you that Steve is a very good, deserving individual who is sure to do a lot of genuine good with any amount of money he might receive.

“So,” you ask, “Whatever number of stones I put in the box, if any, that’s how much money Steve will get, if any?”

The time traveler hesitates. He doesn’t know that he would put it quite that way. The fact is that the number of stones that are going to be in the box is the same as the number of millions Steve is going to receive. But the time traveller clarifies that he isn’t saying you somehow cause Steve to win that amount of money by doing things with the box and the stones. Rather, Steve’s lottery results are completely the result of whatever the normal causal processes are that go into the determination of lottery results. The balls jiggle around in the basket, and are picked out one at a time, and so on. At no point is there a way for facts about this box and these rocks to have an effect on facts about the winning lottery numbers and the number of contestants playing and so on. It’s just a coincidence that Steve is going to get a number of millions equal to the number of rocks in the box. But it’s no less a fact for that.

So there you are–there’s a box nearby, and some stones. You could put some stones in that box if you wanted to.

The question is, do you want to? More specifically, does anything the traveller has just told you make you want to put stones in the box? Or perhaps, even make you think you should put stones in the box?

Having thought about this for a bit, try to pretend you had never read the above story. Now imagine the very same scenario, but imagine that the lottery takes place the day before, not the day after, your conversation with the time traveller. Does this change your intuition at all?

There are obvious similarities between these two scenarios and that found in Newcomb’s Problem. Do your intuitions about these scenarios match your intuitions about the Newcomb scenario? Should it? (There are also important differences, of course. The time travel element of these scenarios makes the relationship between the prediction and the thing predicted very different than in Newcomb’s problem. Is this a very important difference?).

I have no idea what this shows.

Kris Rhodes

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2 responses to “Stones into the future

  1. So we’ve got a scenario in which a guy who we take to be highly reliable predicts something and we’re trying to figure out what’s rational to do. And we’re told that the choice we make is causally independent from the predication. But we’re also told that the indicative conditional (if you put n stones in, he’ll get n million) is true. In this regard, the scenario you describe has lots in common with the Newcomb problem.

    “The time travel element of these scenarios makes the relationship between the prediction and the thing predicted very different than in Newcomb’s problem”

    I’m no expert, but I thought that it was generally acknowledged that what was important was that the predictor is highly reliable, which might arise for various reasons, including clairvoyance, omniscience and including time travel?

  2. Given how little effort it would be to put stones in the box, wouldn’t you do that? Steve has so much to gain, for so little effort on my part… But I suppose that is beside the point. The question is “Is it rational to put stones in a box, on the off-chance that that action might result in someone winning a lot of money?”

    How about if instead of stones in a box, the time traveller told you that it was YOU who was going to win the lottery, and you jackpot win will be (10-n)*10 million, where n is the number of fingers you have when the balls are drawn. So if you have 10 fingers you win nothing, 9 fingers 10m and so on… Is it rational to cut off your fingers to win money?

    I suppose quite a lot depends on one’s views on time and causality. And how highly you value your fingers.

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