I discovered a little while ago that at least one intelligent and well-informed person who sometimes reads this stuff had never come across Newcomb's paradox before. It's worth knowing about, if only because it will make your head spin.
Imagine that there is some being (call it Bill) with a well-established ability to predict people's behaviour. In particular, Bill has demonstrated to your satisfaction that he can predict, hours in advance and very reliably (let's say well over 99%), what you will do in a wide variety of situations, and he has demonstrated a similar ability to predict other people's behaviour in the exact situation you're about to be placed in, which is this:
In front of you are two boxes. One is made of glass; you can see into it. It contains a cheque for £1000. The other is made of steel, and welded shut; you can't tell what's in it. Bill has put in it either a blank piece of paper or a cheque for £1000000. You may take (and keep) both boxes, or just the opaque one. But here's the rub: Bill has used his pred1cti0n sk1llz and has put the big cheque in the steel box if he thinks you'll take only that box, and the blank piece of paper if he thinks you'll take both. What do you do?
Let me recap, in two different ways suggestive of two different answers.
- There is almost certainly £1000000 in the steel box if you choose to take only that box, and almost certainly nothing of value in it if you choose to take both boxes. (Therefore: Take only the steel box. Obviously.)
- There may or may not be £1000000 in the steel box, but there is certainly £1000 in the glass box, and whatever is in the steel box there is therefore £1000 more in the two boxes together than in the steel box alone. (Therefore: Take both boxes. Obviously.)
Almost everyone finds it entirely obvious what it's rational to do in this peculiar situation. Unfortunately, there is no agreement on which of the two courses of action is the obviously rational one.
When we ask questions like "What should I do in this situation?", I think we are implicitly operating with a possibly-naïve notion of how the world works, and if Bill's predictive skills are possible then it's definitely too naïve. That notion is as follows: There are various ways the world (past and present) could be, all of which look just like the actual world in the past, and which differ in the future according to your choice; all the future differences are consequences of your choice and could in principle be traced back to that choice itself, via causes flowing forward in time.
Generally, this view of things works well. But in a world containing Bill, it breaks down: your future choices are strongly correlated somehow with things in the past, and by Bill's clairvoyant or simulatory prowess those things in the past are in turn strongly correlated with something else contemporary with (even preceding) your choice, with macroscopic consequences. Thus, our key assumption – that all the differences between the hypothetical futures of the world in which you chose differently flow from that choice – fails.
(Very likely it fails in the real world too, but so far as we can tell it generally fails benignly, or at least in ways we don't see because our powers of perception and prediction are unlike Bill's.)
But that assumption is a fundamental part of what we mean by asking questions like "What should you do?". It's hard to answer this question when it concerns Newcomb's situation because one of the question's presuppositions is false. It's like asking what colour electrons are.
You may notice that the question I actually asked was "What do you do?". Not being Bill, of course, I don't really know, even if "you" means me. But I'm pretty sure that I take only the steel box. Is that a rational decision? I think the question has little meaning. But it's rational at least in this sense: making that decision is strongly predictive of getting £1000000 instead of £1000.
I think the distinction between backward causation and really reliable prediction is dubious.
If a tiny chance of having the satisfaction of proving Bill wrong is worth a near-certainty of giving up a million Generic Currency Units, then by all means go for it; my priorities differ.
I've never had a problem with this; I just open box B. Ashley is never going to get the satisfaction of proving Bill wrong since even we, without Bill's magic powers, can predict his action perfectly reliably. But more generally, any argument for opening both boxes must assume that there's no backwards (in time) causality. The experimental data show that Bill's predictions *do* involve backwards causality, so the argument breaks down. It's simply no good saying that we don't believe in backwards causality because we've never seen anything like it before; the fact is we've never seen anything like Bill, either. When we do we'll have to update our world model.
And if it wasn't true backwards causality, but modelling the whole physical universe including my brain to see what I would decide -- well I don't see that that really changes anything. It's still clear that if I open both boxes the million won't be there.
(And note that some of those earlier people on whom Bill demonstrated his prowess surely thought of the obvious idea of tossing a coin to decide, which is as near as dammit a random choice, and if Bill was still scoring well over 99% -- well, it seems worth having a degree of respect for his powers of foresight.)
By the way, are you particularly attached to this blogging software? If not perhaps you might start using your livejournal instead. I mean I dare say they're ev1l in all kinds of ways, but my god is this HaloScan stuff annoying.
(After writing the above I hit "preview" and got a blank page ... thanks, HaloScan ... ah no it seems to have worked this time. Thankfully the "back" button worked.)
I agree with you, with (as I mentioned) the proviso that I think the distinction between backwards causality and really good prediction is basically bogus; indeed the whole notion of causality is at best an approximation to the truth.
Yeah, HaloScan is horrible. I'm thinking about it...
Backwards causality I understand, there are models of the universe in which this ("closed time-like loops") is possible. If it looks like that is the case, then go ahead and pick just the steel box.
Really good prediction is another matter. A coin is one thing, but can Bill predict "quantum events", such as atomic nucleus decay? If so, we have to throw out quantum mechanics. Can bill predict thermodynamic noise? If so, Bill has some reality simulator that is sufficiently accurate between the time he puts the money in and the time you make your choice. He must also thermodynamically isolate the money in the steel box.
...Or perhaps not, since I don't really have any sort of model of the physics of a universe where Bill can predict nuclear decay and also we have various experimental results which originally gave rise to quantum theory.
Um, so generally I agree with your analysis 'It's hard to answer "What should you do?", because one of the question's presuppositions is false.'.
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Bill seems to violate causality, so the obvious question is, is a world with a Bill even possible? If so, it rather depends on the nature of Bill. If he's a time-travelling visitor from the future, take just the steel box. If he's guessing based on his understanding of your behaviour, you have a choice of gaining either a $1000 or the satisfaction of proving Bill wrong.