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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?

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    The problem you have is that Duetsch creates a possible situation outside the reach of his simulation machine. If all your chess example does is create an impossible situation, then it is your example which is weaker than Deutsch's, it doesn't counter it – Bug Catcher Nakata Nov 4 '18 at 21:22
  • Duetsch uses infinities to create the "new environment", whether this can be done with actual universes, with finite ages and minimum duration time slices, is not so clear. The chess example shows that in a multiverse, with stable rules and a minimum time slice (one move), every possible scenario is reachable. For Duetsche's argument this means that successive time slices, in the new environment, would not always follow from the preceding one in accordance to natural law. How could that be a possible world? – christo183 Nov 5 '18 at 4:45
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To be honest, I couldn't exactly follow your construction. But I can say that Deutsch is definitely not using an impossible scenario. He is actually adapting the Cantor Diagonalisation Argument which is a well known technique in Pure Mathematics. He is demonstrating that for any infinitely long list of scenarios, there is some scenario (which is a possible scenario) that is not on the list. That is, no such list could possibly be exhaustive, even if it were infinitely long.

I don't see how this proves anything about simulation theory though---to me it just seems to show that you can't list the simulations in a sequence. But I could be wrong.

As a final note, the diagonalisation argument (and it's variant here) rely on the fact that there are infintely many elements that could potentially be changed. For this reason, chess games which consist of finite numbers of moves are not going to work. Deutsch's scenario works because he has infinitely many time slices to alter.

Edit: The wikipedia page actually is not the most accessable description, but there are heaps on maths blogs and stuff.

  • The so called "...CantGoTu Environment takes the ideas embedded in the Diagonal Argument of George Cantor, the Undecidability theorems of Kurt Gödel, and the limits of computability highlighted by Alan Turing, and applies them to Virtual Reality environments" - mixedreality.wikia.com/wiki/Simulated_reality The chess analogy tries to show: a possible world must have a minimum "time slice"(planck time) corrolated to 1 chess move. If all possible games/environments are in a series containing all valid progressions, then any game not in series is an impossible 'world'. Also see edit. – christo183 Nov 3 '18 at 13:11
  • Yes but isn't the claim "all possible games are in a series" proven wrong by diagonalisation? Maybe you'd escape if we had a hard deterministic clockwork universe, but with probabilistic radioactive decay I think its more like infinitely long chess games where pieces respawn randomly – Bug Catcher Nakata Nov 4 '18 at 21:36
  • No, the games have the same rules of progression and progression is by discrete steps math.stackexchange.com/q/35107 Granted chess doesn't quite capture the complexity of the real world, but it shows that granularity and universal determinism prevents us from surety regards simulation/not simulation. Note that while probabilistic decay fits a graph, actual decay is granulated by planck time. – christo183 Nov 5 '18 at 5:17
  • But if the number of scenarios is finite (or temporary finite) this argument does not disprove simulation hypothesis, right? – rus9384 Nov 5 '18 at 11:19
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Deutsch is restating some well known results in the theory of computation discovered by Godel and Turing. The result explains that not all functions can be calculated by a computer. This is not a criticism of the simulation argument.

Deutsch's criticism of the simulation argument can be found on pp. 11-12 of It from Qubit. A universal computer only requires a physical system capable of performing a particular limited set of operations, which can be performed by a very wide range of physical systems, e.g. - vacuum tubes and silicon chips. So if we're a program running on a computer we can't know anything about the underlying hardware, i.e. - the real laws of physics. So the simulation argument is anti-scientific since it sez we can't understand anything about the real laws of physics.

Deutsch points out another problem with the simulation argument in "The Beginning of Infinity": I don't know exactly where, you can look it up in the index at the back of the book. The simulation argument also sez we will be running in many simulations, so it is likely we are in a simulation, but it doesn't specify how those simulations should be counted. For example, the computer on which I am typing this may be using multiple electrons in the same wire to represent the same bit. Should we count all of these redundant instances of the same information as separate simulations of whatever my computer is doing?

  • "For example, the computer on which I am typing this may be using multiple electrons in the same wire to represent the same bit" - I love this sentence, it is such a fertile source for metaphor... i.e. electrons represent bits via movement, position, potential or presence, all relating to different metaphysical perspectives on Reality. - The other question is about a somewhat different aspect than this, very much appreciated, answer address. – christo183 Jul 17 at 8:34
  • @christo183 A metaphor is "a figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable." So whether electrons represent bits by virtue of one measurable physical quantity or another is not a metaphor, since it is a matter of what literally represents the bits. What you wrote is nonsense and you should be more careful in your writing. – alanf Jul 17 at 9:29
  • You may indeed have read nonsense, but there is still hope that if you search for meaning you may find some truth. - Also see @MoziburUllah answer and comments here: philosophy.stackexchange.com/a/64626/33787 – christo183 Jul 18 at 8:33

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