Of all the comments in this block, byrnema’s seems the most on-track, having the most ingredients of the solution, in my view. A few points:
I prefer to suppose that Omega has a powerful, detailed model of the local world, or whatever parts of the universe are ultimately factors in Joe’s decision. It isn’t just the contents of Joe’s brain. Omega’s track record is strong evidence that his model takes enough into account.
I do not see any backwards-in-time causality in this problem at all. That Joe’s state causes both Omega’s prediction and Joe’s choice is not the same as the choice causing the prediction.
In fact, that’s what seems wrong to me about most of the other comments right here. People keep talking about the choice causing something, but the problem says nothing about this at all. Joe’s choice doesn’t need to cause anything. Instead, Joe’s choice and Omega’s (prediction->money-hiding) have common causes.
The way I see it, the sleight-of-hand in this problem occurs when we ask what Joe “should” do. I think focusing on Joe’s choice leads people to imagine that the choice is free in the sense of being unconnected to Omega’s prediction (since the prediction has already happened). But it is not unconnected, because our choices are not un-caused. Neither are they connected backwards-in-time. Omega’s actions and Joe’s choice are connected because they share common causes.
EDIT: To make this a bit more concrete: Make this a question of what you “should” do if you meet Omega someday. Consider that your decision might be highly influenced by all the musings on the blog, or on Eliezer’s or another poster’s arguments. If these arguments convince you that you should one-box, then they also cause Omega to predict that you’ll one-box. If these arguments fail to convince you, then that circumstance also causes Omega to predict you will two-box.
You’ve got to resist thinking of the machinery of human decision-making as primary or transcendent. See Thou Art Physics.
Of all the comments in this block, byrnema’s seems the most on-track, having the most ingredients of the solution, in my view. A few points:
I prefer to suppose that Omega has a powerful, detailed model of the local world, or whatever parts of the universe are ultimately factors in Joe’s decision. It isn’t just the contents of Joe’s brain. Omega’s track record is strong evidence that his model takes enough into account.
I do not see any backwards-in-time causality in this problem at all. That Joe’s state causes both Omega’s prediction and Joe’s choice is not the same as the choice causing the prediction.
In fact, that’s what seems wrong to me about most of the other comments right here. People keep talking about the choice causing something, but the problem says nothing about this at all. Joe’s choice doesn’t need to cause anything. Instead, Joe’s choice and Omega’s (prediction->money-hiding) have common causes.
The way I see it, the sleight-of-hand in this problem occurs when we ask what Joe “should” do. I think focusing on Joe’s choice leads people to imagine that the choice is free in the sense of being unconnected to Omega’s prediction (since the prediction has already happened). But it is not unconnected, because our choices are not un-caused. Neither are they connected backwards-in-time. Omega’s actions and Joe’s choice are connected because they share common causes.
EDIT: To make this a bit more concrete: Make this a question of what you “should” do if you meet Omega someday. Consider that your decision might be highly influenced by all the musings on the blog, or on Eliezer’s or another poster’s arguments. If these arguments convince you that you should one-box, then they also cause Omega to predict that you’ll one-box. If these arguments fail to convince you, then that circumstance also causes Omega to predict you will two-box.
You’ve got to resist thinking of the machinery of human decision-making as primary or transcendent. See Thou Art Physics.