Stanislas Dehaene, in his fascinating book The Number Sense, describes an experiment with the Sheba, a chimp who not only learned to count accurately but learned to order the Arabic numerals by size from 1 to 9, and could accurately compute the inequality between any two of them presented to her and pick the larger one, which shows extremely impressive symbolic and mathematical understanding.  After Sheba demonstrated all this sophistication, her trainer, Sarah Boysen, tried something else, having to do with theory of mind. Here's Dehaene on

the curious difficulties that Sheba met when she had to pick the smaller of two numbers. The experimental situation seemed quite simple: The animal was shown two sets of food, and when it pointed to one, the experimenter gave it to another chimp while Sheba received the other food set. In this novel situation, it was in Sheba's interests to designate the smaller quantity, so that she would then receive the larger one. However, the chimpanzee never succeeded. She continued to point to the larger set, as if choosing the maximum amount of food was an irrepressible response. Sarah Boysen then thought of replacing the actual piles of food with corresponding Arabic digits. Immediately, from the first trial, Sheba chose the smaller digit! Numerical symbols seemed to liberate Sheba from immediately material contingencies. They enabled her to act without being influenced by the parasitic impulse that otherwise compelled her to always pick out the larger amount of food.

So the fascinating thing about this is that as soon as Sheba is thinking symbolically she's also thinking about the experience of the other chimp. When it's only food, she's pointing to what she wants, pure and simple. When it's a symbol she's pointing to what she wants the other chimp to get. Symbols aren't only 'for others' in the sense of my communicating with them through some sort of code. Symbols are also what I am willing to give away to others, what I can think about offering to others. They not only allow me to contrast my point of view with that of another (which a lot of primates can do without symbols: they can lie or affect ignorance about where food is hidden). They allow me to compare my perspective and my desires with someone else's. That's not what the number sense is for originally ("the number sense" is Dehaene's name for an undernoticed and surprising innate capacity to estimate quantities, one we share with a lot of mammals and birds) but it is what actual counting comes to be for, at least when it is rendered symbolic. When I see a numeral, I needn't be distracted too much by the real presence of the thing symbolized. I can think symbolically about the fate of another and about my own, without the actual material objects hijacking my thought. I can think of minds instead of bodies.

I suspect this - or its converse - has something to do with the knock-down persuasiveness of two completely opposite analyses of Newcomb's Problem, offered by Robert Nozick in his original introduction of the paradox. If it's just you and the Martian (the stunningly accurate predictor), it may easily seem right to ratify her prediction that you'll only take one box by taking only one box: her expectation that you would think this is what was right is what you're now ratifying, and the reason you're ratifying it. If, however, you know a friend can see into the opaque box through a window on the other side, you know that your friend already knows what's in both boxes, and will be rooting for you to take both, since he can see directly that taking both gives you a thousand more bananas than taking just the one box, opaque to you but not to him.  (I've changed the money to bananas to make the parallel with Sheba's situation clearer; I am, as all analysts of Newcomb's do, assuming that bananas have a linear utility, so that two bananas is always twice as preferable as one banana, and 1000n bananas a thousand times as good as n bananas.  That is: even if stomachs have a finite capacity, eyes may be arbitrarily bigger than them.)

So the difference between the two scenarios is this:  1) the million bananas are already there, or not, but only notionally; and 2) the bananas are already there, or not, and your friend is looking right at them if they're there, or at their absence if they aren't.  He can see the sum of the bananas in both boxes put together, and can see therefore that there are more a thousand more bananas in both boxes put together than in just the large box.  So you know that he knows that taking both boxes gives you a thousand more bananas than taking just the large opaque box.  But if, as in the first scenario, you have no friend looking directly at the sum of what's in the two boxes, the opaque box is symbolic, its contents not yet realized, and what it symbolizes is the Martian's prediction of whether you will take it.   So I think that when the opaque box is genuinely opaque to everyone, you are much more likely to treat it as symbolic; but when your friend is looking right at its contents what Dehaene calls the "parasitic impulse" kicks in: grab for the real and not the backwards-causing, past-affecting symbol.

Of course this already assumes a vicarious relation to your friend too, but not vicarious in the way that's interesting me here - not vicarious through symbolism. I think the truer analogy is between acting on parasitic impulse and acting through the actuality-deferring medium of symbols.  When the box isn't truly opaque - when your friend can see what's in it - its contents are actual, right there, not to be put by, and this is something we know because we know that part of the world we see, we experience ourselves as seeing, we see through other eyes, fully knowing that others are seeing something even if we don't see it directly. (As I suggested above, most primates seem to know this too). This is one of the most basic facts about how we construct the spatial world through interacting with others, and it essential to how almost all narrative film works: it's the visual analogue to implicature.

(Parenthsis: For a movie which is entirely made up of shots of people seeing, rather than the thing seen, try Kiarostami's amazing Shirin -- here's a scene:

 

or this classic Saturday Night Live skit):

 

...after which I end my long parenthesis to return to Sheba and Newcomb.)

When the box is truly opaque, it's a symbol of its contents. But what it symbolizes to you, its interpreter, is your accurately predicted interpretation of it. There is nothing yet quite gelling into actuality in this recursive toggling, so it becomes metastable as a symbol of the choice you're about to make: just that box. As with Sheba, symbolic thinking can trump the attraction of the actual bananas.

And as with Sheba this symbolic thinking is vicarious thinking: for her, of the other chimp's experience; for the chooser in a Newcomb's problem, of the Martian's prediction.