Therefore, if the Predictor has, in fact, always been right, then the best choice is to open box one, collect the million dollars and use it to fund your research into the workings of this puzzle. You will then have plenty of time to experiment with opening both boxes.

From an economic standpoint, anyone can come up with a thousand dollars if they work hard and save, and most people could just whip out the old credit card if they needed to make a purchase of that size, but a million is much harder to come by, so why even bother taking chances for a mere thousand dollars? Open box one and have a chance at the million.

In either case, I think the box with the thousand in it is a waste of time.

The puzzle should be re-worded so as to offer more of an incentive to risk it all and open both boxes.

And what you’re saying is that, if this holds true, then the only way it can be true is if we are part of God (again, as an idea) – thus having our free will and exercising it will influence the outcome and the knowledge. So, insofar as we know what we do, God (or whatever word you choose to replace the idea of an omniscient entity that still offers us free will) shall know as well, because we are part of it, and its omniscience occurs as a result of the sum of partial knowledges, our own partial knowledge (resulting from and resulting in our own free will) included.

Well, yeah
Well put, however. And thanks for mentioning Newcomb’s problem, I didn’t know of it before – I do indeed have a social life, regrettably (or not)

Aristus: No, if the Predictor wants anything, it’s to give you $1,000,000 if you take the first box only, or $1,000 if you take both. If it wanted to give you as little money as possible, then presumably it wouldn’t put anything in either box.

But there is still a difference between you and the Predictor: whether or not it knows your intentions, you don’t know *its* intentions. Everyone seems to assume that it wants to give you as little money a possible. Why?

No, so that the real you could take only the first real box (just like the simulated you, who’s actually “the same” person), but have there be $1,000,000 in that box.

And then I would take the red pill.

Wait, something’s not right….

Intention does crop up in science in a couple of places. First off, there is the Bayes versus Fisher debate on statistical inference. Must we commit to a stopping rule for taking data and stick with this rule in order to have scientifically reasonable conclusions? A few years back, the philosophers were all on the Bayes bandwagon, and the scientists were Fishereans — but the two camps seem to be reversing allegiance today.

The second puzzle is Polchinski’s interpretation of Weinberg’s nonlinear quantum mechanics. Polchinski forbids faster than light communication by imposing a condition on the observables of the system, but he says that a result of this move things in one (Everett world) affect things in another (Everett world) depending on the intentions of the experimenter. The problem goes something like this:

A spin 1/2 ion enters a Stern-Gerlach machine, which measures the z component of the spin. Things are arranged such that the deflected beam is rejoined to the undeflected beam, and will continue on. If the observer saw spin up, he does nothing. If he saw spin down, he makes a firm intention to either (1) does nothing or (2) rotate the spin by use of a field coupled to the y direction (this is not a measurement). The ion then enters a region of a field coupled to a quadratic x spin (it evolves nonlinearily). Now, if you measure the z spin after the nonlinear evolution (after having observed spin-up earlier), you will ALWAYS see an up spin if you had intended to take Action (1), and you will ALWAYS see a down spin if you had intended Action (2), in the case that you had observed a down spin earlier (if you didn’t observe spin up in step one, do nothing in this step). It seems that your intentions — about what you would do in situations that haven’t arisen — have an effect on the world. Actually, the discussion in John Preskill’s lecture notes is clearer than Polchinski’s.

For Polchinski (and Preskill), this is an argument against nonlinear quantum mechanics — for me, it is an argument against the many worlds interpretation — but the question remains, what is the scientific status of an intention? We philosophers have talked a lot about this question with regard to beliefs and cognitive science, but compartively little ink has been spilled with regard to intention.

I’m not surprised this problem (along with the issues of Baysean convergence) finds its way into your work.