I read a very disturbing book a while back. "Permutation City", by Greg Egan, explored several concepts that I found unnerving. One of these was the idea that the order in which a system enters various states is irrelevant to an observer contained within that system.
To illustrate this, let me use a simple example. Imagine that you are about to record a speech. You have your speech written on index cards, which you have thoughtfully numbered in case of clumsiness on your part, and let us further suppose that for some strange reason, you have put exactly one word on each card. Finally, you are using a tape recorder that is voice activated.
Sure enough, just before you are about to record your speech, you drop the deck of index cards. However, rather than sort them, you decide to scan through the random deck, possibly many times, and read each word in sequence. Since the recorder is voice activated, the potentially long pauses between words are eliminated. So, to the observer (who listens to the recording later), it makes no difference that the deck was in a random order.
This in itself is unremarkable, but let's take it a step further. Imagine that you have a small film clip of a boy throwing a ball and a dog fetching it. Again, you number each frame just in case you want to do some editing later. When you watch the movie, for all intents and purposes, there is a cause and effect relationship between the boy, the ball, and the dog's actions. The boy seems to exert a force on the ball to throw it, the dog seems to respond to the thrown ball by fetching it, and so on.
Now some mischievous individual (whom I shall call Muffin for reasons best left unstated) gets his hairy mitts on the film and proceeds to spread it, lickedy-split, into a rather large collection of single frames, which he then shakes to randomize. Now, even though Muffin really slicked up the works, no information was lost - it would still be possible to rearrange the frames in their original order. Thus, in some sense, the boy still thinks he is throwing the ball and the dog still thinks he is retrieving it, even though the movie has been savaged by Muffin.
So, to broaden it, what if we ourselves only exist as frames in some large three-dimensional analog of a movie? Would we know or care? What if some hyper-Muffin has blown our hyper-movie to pieces? What if every other frame were discarded? For any given frame, our brains would be in a state of remembering all that had occurred up to that point. How could we notice the missing frames?
What if the only frame that remains is the one that occurs right.... now?
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