with 1) it seems like what you're saying is that given a closed system, you cannot accurately observe and record the whole state of that system within the syste

with 1) it seems like what you're saying is that given a closed system, you cannot accurately observe and record the whole state of that system within the system itself. This feels right on the surface, but is it actually true? A quine contains a complete record of itself. That's an extreme case to be sure, but it does seem to provide at least one counterexample . . . (of a system that contains itself, not necessarily a system that actually observes and records itself) A recording of a system does not need to contain everything in order for that recording to by played back, as long as the replay system is deterministic -- you just need to record the random inputs. E.g. see the way they do it in video games [http://www.gamedev.net/topic/439336-replay-system/ http://www.gamedev.net/topic/439336-replay-system/] I'm not saying that it is possible, just it shouldn't be dismissed out of hand just because it feels like it should be impossible.