Suppose you could enter someone else's dream just as if you were visiting a party. It's not that this is an entirely unpopular idea, there are several movies based on this notion, such as only recently Inception. But let's for the moment leave the elaborate theories presented there aside and examine the basic idea in a more simple setting.
1) Suppose, then, you could enter someone else's dream. Let's call the dreamer 'Joe'. You're now in Joe's dream. What would this be like? Would you just be at the same location, see what Joe sees in his dream? Imagine that Joe is in fact dreaming about a party, and now that you have entered the dream, you're at that party. Just as Joe, when he dreams about being at a party, it's as if he were standing in the room, together with all the other guests, hearing the music and idle chatter, seeing those people, the furniture, some food and drinks on a table, the dimmed light, the stereo in a corner... just as for Joe it feels in his dream as if he were actually there, it now also does for you. You're there with him in that very room, seeing and hearing the same things. But does this mean that you can see everything in the room, including the things that Joe isn't looking at, including the things that Joe hasn't even looked at up to now? Or is what you see restricted to what Joe sees, or at least to what he has seen so far (what his dreaming mind has, so to speak, dreamed up)? For instance, if Joe is just standing near the door, looking into the room — does it mean that all you can see is this room, or can you actually peek out the door and see what happens in the next room, even though Joe has (so far in his dream) never turned round and looked there?
We can only answer that question if we have some account of how dream worlds are built. Who decides what and who is in the room at that party Joe and you have joined? Since Joe is the dreamer, it seems that Joe's dreaming mind must do that job. The moment Joe dreams up a chair standing in the middle of the room, the moment that chair exists in the dream world. As it happens, there are three ways this can look to him. Let's say that Joe hasn't glanced at that spot before; then he either might take it that the chair has been there all the time, or he might think it just appeared out of thin air. On the other hand, if we assume that Joe has been looking there frequently and there's never been any chair, then he might notice that now, suddenly, there is a chair where none was before. (Dreams are like that, such things happen all the time.)
But what does that mean for you, the extra participant? What's going on from your point of view? It seems clear that in the third case you are observing a dream world in which there is an empty spot in the middle of the room and in which suddenly a chair appears in that very spot. But what about the two others? What if Joe has been transfixed by some events in the left part of the room and for quite some while hasn't looked at the middle of the room: what do you see when you do look there? Do you see the chair? Since Joe hasn't imagined (dreamed) it yet, perhaps we should say that you can't see it. Now what if Joe now turns to the middle of the room and calmly imagines a chair there, satisfied that it must have been there all along?
We seem to have run into a dilemma here: on the one hand, if we grant the dreamer authority about the furniture of his dream, its position and its changes of place, then we can only observe what he's already dreamed, so there is literally nothing there at any place until he brings his attention there. And presumably, when he turns his awareness somewhere else, there can't be said to be anything there as well: it's neither that the chair remains there nor that it suddenly disappears, leaving the spot empty again. Somehow, it seems, if we take this point about a dreamer's authority serious, the largest part of the dream world is undefined, for most of the time. If, on the other hand, we relax this strict adherence to the dreamer's attention (and imagination), we might enjoy a much more stable world of the dream, but it would be less clear in what sense this is still the world of that dreamer's dream.
2) At this point we might borrow a trick from the way fiction (another form of unreality) works in order to avoid this kind of trouble. No fiction describes each and every detail of the fictional world it is about — that wouldn't be possible. So what usually happens is that there is a tacit agreement between the author and the audience that the undescribed portions are filled in with appropriate assumptions. Thus if a story starts by telling us that "It was a cold, rainy autumn day in London of the year 19__", we can assume that the big city has many inhabitants who go about their lives, and that there has been a day with some weather before and after that particular day at which the story begins, while none of all this is ever mentioned, and quite probably most of it is also totally irrelevant for the narrated events. We just imagine the relevant parts and assume the rest as suitably fixed.
We mustn't misinterpret this 'filling in', however. When you read such a sentence, you may or may not visualize the streets of London in pouring rain, and to any degree of detail you like. Perhaps you'll take a moment after reading this very first sentence and bring those streets before your mind's eye, one by one, with every house clearly and to the smallest detail specified; but probably not. But then some people read stories without even picturing anything; and still they can take up the general idea of a cold, rainy day in a place like London.) In either case, none of them will have to imagine anything about the weather on the previous day, the day before the story begins, our about all the other people in the city which don't have any bearing on the story. To 'fill in' the necessary detail, then, is not to run through all the small details in your mind and fill them in. It's just to suppose that, as in the real world, there are some facts of the matter about all those things, and to be content that they would be described to us, should they be of any relevance to the story.
How can this stance of 'as close to what you'd expect unless directly specified' help us with the world of the dream party we're attending? Let's go through all the possibilities again. First, let's say Joe has looked several times at the center of the room, never noticing a chair or anything else there, but then suddenly dreams up one standing there; he thinks 'Whoops, there's a chair there!' for a moment, and then turns his attention elsewhere. For you, as an observer, the sequence would be the same: you see an empty spot up to the moment when suddenly a chair pops into existence there; you might have a similar thought about it, and from now the chair just remains standing there. Should Joe at some point turn back to see if the chair is still there and then dream its sudden disappearance, then at that moment the chair will dissolve before your eyes as well. Second, let's say the moment you enter the room you look at that center spot, whereas Joe so far has never as much as even glanced there, transfixed by the events in the left part of the room. If the room is mostly empty, then we wouldn't expect neither a chair nor anything else there, so you don't see a chair. (Of course, if the room is actually like a theatre audience with rows and rows of chairs, then we wouldn't expect a gap at this spot either, and so we would do see a chair there. It all depends on what the reasonable thing to expect is.) When Joe turns his attention to this spot, suddenly imagining a chair there, then the chair will duly appear, and for you as observer it will appear only then, even if Joe thinks that it has been there all the time. (That is, the third option above collapses into the second option — there isn't any difference between them, except in what Joe thinks; that, however, is not part of the dream world's exterior, but only of Joe's awareness of it.)
I think this approach preserves most of the authority of the dreamer while still keeping the dream world somewhat stable. Just as always in dreams, completely surprising things can suddenly happen (such as a totally unmotivated appearance of a chair in the middle of the room), but then that's just what dreams are like. However, only with this extra assumption can there be something like a shared dream world, something that both Joe can dream and you can observe. The minimum is some assumption of stability and filled-in detail. Otherwise, the whole idea of entering someone else's dream wouldn't even be conceivable.
But note that this means that Joe can be wrong about the world of his own dream in some respects: not about its present state, for that is exactly as he imagines it, and there is no way he can be wrong about that. (We still hold on to the idea of the authority of the dreaming mind. You can't be wrong about what you imagine. It is as you imagine it, by stipulation.) What he can be wrong about is what was going on before. The past sequence of dream events must be something stable, for that's not something Joe imagines, but something that he has imagined, and you have perceived. It's not something that can be up to anyone's imagination any more. It can be tracked as if it were an objective fact about the dream world, no longer a subjective element that is in Joe's imagination. (I think there is something wrong about this move, but I won't follow up with this here. I'll reserve that for a later post.)
3) So far, we have only talked about looking around, and what it would be like for you to be an observer in someone else's dream. What about exploring this dream world a little more actively? Think of that door next to which Joe is standing. Since he hasn't yet dreamed about what's behind that door, it could be anything from a yawning abyss to an ordinary floor — or perhaps it's a blind door that is fully blocked by a wall. Assuming what is most likely, we would think that if you looked behind it, you'd probably see another room that appears roughly as one would expect; you'd however step through at your peril, for if Joe focuses on it and imagines a blind door there, then you're suddenly in the middle of nowhere (possibly in an adjacent room, or falling down several stories outside — whatever the most likely scenario would be under the changed circumstance, or alternatively, if Joe dreams anything more about it, then whatever that will be).
The world of someone else's dream is an extremely unstable thing: a dreaming mind will change the surroundings all the time. Remember your own dreams: sudden changes of place, or transformations in your surroundings aren't in the least unusual.
4) This is not yet the end of our difficulties. What happens to the authority of the dreamer when it comes to interaction? Once you're not just an observer, but also take action in the dream world, there is potentially a conflict in everything that happens. Suppose you've spotted a chair in the middle of the room, and that chair is actually dreamed by Joe; now you decide to walk over to that chair and sit down on it. Suppose further that Joe's repeating nightmare is an empty chair that just remains empty however long he stares at it. But this time, you just go there and occupy it. Can we still claim that we're in Joe's dream, when this sequence of events is not something that originated in Joe's mind, when it in fact couldn't even have originated there (assuming that the nightmare pattern is relatively sticky and Joe would go through it all over again if left to his dream).
Now you might perhaps say that there is nothing unusual about this: after all, things happen to us in the real world all the time, we don't have full control over events (not even nearly). So why should a dream be different?
It should be different because dreams are a play of the imagination. You may not be able to control what you dream — in fact, most of the time, our dreaming mind plays wild spectacles for us without us having even the slightest say in matters of the program. But even though it is the arbitrariness of our dreaming mind, it is precisely the arbitrariness of our mind. It's not as if you perceive events going on somewhere. You imagine them. Thus the wildest things may happen indeed, but none of them have originated outside your imagination. There is no such thing as an independent actor, or an independent event. It's all in your head.
Intervening in someone else's dream, then, is probably best taken as indeed breaking up the dream state and fiddling with it from the outside. It belongs in the same category as noises or light effects in the sleeper's room which get through to the sleeping mind and become ad-hoc components of the dream; or talking to someone who is in the process of waking. There's decidedly an outside influence here. Sometimes, this idea is taken to the point of actual therapy: in Dreamscape, for instance, dream researchers enter others' dreams in order to figure out the deep-seated origins of nightmares (typically some repressed idea, a notion from the Freudian tradition of dream theory), and address them from within the dream. It is, as if a helping hand is extended to you from a character in your dream, only that this character is not in fact a character at all (someone imagined by you), but a real person who is projected into your dream. (Is there a way for the dreamer to distinguish between a proper dream character and an impostor, someone who came from the outside world into the dream with an agenda?) In any case, interaction is a further complication that makes the idea of entering someone else's dream a rather difficult setup. (Remember that we still haven't even discussed the question how this might be implemented: we're only talking about the phenomenology, that is, how it appears; or how it would appear, if it were actually possible to implement.)
5) Because of all this, in Inception a wholly different process of dream world creation is used.
The basic idea of the movie is that you can get into another person's dreams and there interact with that person's mind, in particular, steal some information that person wouldn't reveal to you when awake. This notion is probably inspired by the observation that dreams do visualize much of our inner lives, especially our emotional lives, which we wouldn't be willing (or even capable) to expose to others in words. Since you put your deepest secrets into pictures when you dream, you open up to spies there much more than when you're awake.
But your dream world would be much too unstable for anyone to enter it, and thus too dangerous — the plot would be infeasible. Therefore, the spies won't simply put you to sleep and then enter your dreams. Instead, they let you enter the dream of someone from the team; and the world of that dream has been pre-designed. It's not something his dreaming mind creates on the spot, it's something that an 'architect' has carefully drafted and later on explained to the team member who dreams it. Then you are invited into this world, and you start walking around in it. When you encounter a safe place, such as a bank vault, you'll picture your innermost secrets as lying there, safely. (You also 'populate' it, in the film's lingo, with projections of people you know.) The gang of thieves, who don't just know the interior of the world much better than you, but also quite probably have built in some back doors and secret shortcuts, will then 'extract' that information from the safe place, and so in effect steal it from you.
So, in other words, the way Inception solves the problem of the instability of dream worlds is by using worlds which aren't, strictly speaking, dream worlds at all. They resemble much more the worlds of a video game: they're pre-designed, not just in their layout, but also with a specific purpose in mind. You don't enter another person's dream, you enter a virtual-reality playfield. (Revealingly, the dream worlds are called 'dream levels' in Inception jargon, which is probably not a coincidence: the worlds of video games are also structured into 'levels'.) By treating dreams as a kind of shared video game, the creators of Inception have addressed an inherently complicated aspect of a world of unreality to make it plausible that you can 'enter' it, as it were, travel into it. (In this way, the film is also similar to those which play around with the notions of the past and the future, to make it plausible that you can travel there, using a time machine.)
(Side remark: This is basically a more detailed exposition of the line of thought at the end of my earlier posting on Projection, interception, and Inception.)