In The Fabric of Reality (1997) by David Deutsch, he says:
Imagine a computer built to render every possible Virtual Reality. Suppose all possible environments produced by this generator can be laid out sequentially, as Environment 1, Environment 2, etc. Take time slices through each of these of equal duration. (Deutsch specifies one minute, but this could, in principle be anything, e.g. Planck time.) Now construct a new environment as follows. In the first time-period, generate in the environment anything which is different from Environment 1, and in the second time period, anything different from Environment 2, and so on. This new environment cannot be found in the sequential layout of environments specified earlier, as it differs from all possible environments by what happens in one particular time-slice. Hence this means that no such universal VR generator can be created, and there are environments which effectively can never be rendered by any means (since there are infinitely many).
Lets take the Game of Chess. We create Series 1 by sequentially playing every possible game and call every game Environment 1, Environment 2, etc... Now Series 1 will have every possible game position, further (and except for first and last position in each Environment): every position will have immediately before it every possible position that can lead to it, and after it every possible position that can follow from it. Also most positions will exist in many Environments, with earlier positions appearing more frequently.
Lets create a second series and call it Environment X. We take positions sequentially from sequential Environments: position 1 from Environment 1, position 2 from Environment 2, and so on. It is obvious that there are two possible results for Environment X, depending on how the Environments in Series 1 was arranged: A) Position 1 Environment 1 is followed P2E2 which is a possible successor to P1E1, P2E2 is followed by its possible successor P3E3, etc. - It is thus guaranteed that Environment X will be a possible game somewhere in Series 1. B) The arrangement of Environments are such that each position in successive Environments are not always possible from the preceding position in the preceding environment. - Here it may well be that Environment X is an impossible game.
Now we create Environment X along the lines of Deutsch's "new environment". A) We use a random position(time slice) from successive Environments. - In this case it would be possible to have Environment X such that it is absent in Series 1, but not guaranteed. B) (exactly as Deutsch) We specifically choose each position (n) in Environment X such that it doesn't exist in Environment (n). - This leaves us with a thoroughly impossible game.
I'm not sure what to make of this. Is Deutsch using an impossible scenario to prove that all possible scenario's cannot be simulated? Is he saying external agency is the only way we can be sure we are not in a simulation?
Am I missing something?
EDIT: Some more digging into "cantgotu environments"- http://www.liquisearch.com/simulated_reality/arguments/cantgotu_environments - reveals that Deutsch's argument is not in fact meant to refute the simulation hypothesis, rather it purports to prove that certain worlds cannot be created by a "universal possible worlds generator". I still don't quite grasp how his argument proves anything beyond the tautology: A possible worlds generator cannot produce impossible worlds.
Two lines of inquiry presents to me: 1) There are some sort of conflagration of possibilities - impossibilities, infinitesimals/infinities - physically possible objects. 2) A single generator isn't sufficient to create all worlds; something I attempt to explore here: Should we think twice about dualism? and Is Reality an intersection of Incompatible Ontologies?