Since the first days of civilization, humans have been known to entertain themselves with virtual reality games. The 6th century saw the birth of chess, a game where a few carved figures placed on a checkered board are supposed to mimic human social hierarchy.  Later, the technological breakthroughs of the 20th century allowed creation of games which were significantly more sophisticated. For instance, the highly addictive “Civilization” allowed players to create a history for an entire nation, guiding it from the initial troubles of wheel invention and to the headaches of global warming. Here is a quick summary of the virtual reality games features.

1)     The “reality” of the game, while being superficially similar to the reality of the player, must at the same time be much simpler. Hence three-dimensional humans play in the two-dimensional world.

2)     The laws of the game must be largely deterministic to allow a meaningful intervention by the player. Yet, in order not to make it too predictable and hence boring, an element of chance must be introduced.

3)     The game protagonists must appear to have freedom of movement and yet be limited to the borders of the screen/allocated memory size. The limits of this virtual freedom are usually low at the early stages of the game, but grow as the scenario develops.

4)     The game scenario must end before it reaches the limit of the allocated resources.

I now propose a little Gedanken experiment. Imagine the existence of a four-dimensional world hosting a civilization whose technology is way ahead of ours. Is there a strong reason to think that such civilization is impossible or that members of this civilization would not play virtual reality games?  If the answer is no, how may these games look like? Using the analogy with our own games, we might expect the following.

1)     The game protagonists would resemble the players. Yet, the need for simplification would require them to be three-dimensional.

2)     To satisfy the second rule we need to combine determinism and chance. In the three-dimensional universe quantum mechanics is known to do the trick.

3)     At the early stages of the game, protagonists’ freedom of movement is constrained by low technological development. At later stages a physical limit may be required (speed of light?).

4)     This point may have something to do with the Fermi Paradox.

I’m interested in other possible analogies. If somebody can suggest a way to rule out the whole idea that would be even greater.

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This is a very narrow segment of the space of Simulation Hypotheses, and I don't see any reason to foreground it in particular. Further, I think that this is too off-topic for Less Wrong at this time.

Carl and Michael,

I certainly had no intention to claim that I invented the underlying idea of Simulism. It certainly has been around for many years. My immediate motivation for posting was to discuss whether “talking snakes” from the previous post could have rational explanations, which can not be easily dismissed. I did not want to spell this outright lest I immediately provoke the flame of some people here.

The “reality” of the game, while being superficially similar to the reality of the player, must at the same time be much simpler. Hence three-dimensional humans play in the two-dimensional world.

I disagree with this "axiom". Most VR games that exist today simulate or model a 3D environment. It's only the "rendering" that eventually becomes 2D because most of us have 2D monitors. But the model itself is in 3D, and as our display technology improves, we may eventually render to 3D, without needing to change anything about our model.

1) The game protagonists would resemble the players. Yet, the need for simplification would require them to be three-dimensional.

And so I suspect that creatures in a 4D world playing VR games would have their games model a 4D world, but perhaps would only render to 3D (because that's what their "flat" screens are capable of displaying). If our universe were merely a simulated model in their game, we would expect our universe to be 4D.

"I disagree with this "axiom". Most VR games that exist today simulate or model a 3D environment. "

I suppose what I had in mind are games that model entire civilizations, rather than track the movements of one or several protagonists. In the latter case the “horizon” of the protagonists is very limited, allowing 3-D, but at the price of limiting the available space. However, if you want your protagonists to avoid bumping into the wall (remember “Truman Show”?), you might still need to give up one dimension.

See games such as Homeworld or Sins of the Solar Empire. These take place in 3D environments (outer space) with no "hard walls": rather than explicitly forbidding you from leaving the "game zone", there simply is no point to. There's so much empty space between galaxies that you would never be able to fly from one galaxy to another before getting terribly bored with the game. So players are strongly motivated to stay within the star systems where the real action is.

Also, in the same way you can construct a finite but boundary-less 2D universe for your game (e.g. a universe on the surface of a sphere, or a universe on the surface of a torus), you can also construct a finite but boundary-less 3D universe for your game.

If you think that we are a simulation built by a world that has "real" continuous, non-quantized mechanics, there is a simpler explanation. A particle in such a world would take an infinite amount of information to describe. By using quantum mechanics in their simulations, they could create an infinite number of simulations of their world. Supposing that things on the Planck scale of their "real" world (pun!) are unimportant, these simulations would be just as good as their world. They could also build infinitely larger simulated universes out of their real world, and move into them.

(The number of quantized simulations that you could build in a real world is the number of times that the integers fit into the reals.)

The speed of light is also a necessary limit for these simulations; otherwise, velocities could go towards infinity, requiring an unlimited amount of information for a particle.

Thanks for your comment.

1) The infinity seems unlikely to be a problem. Our own three-dimensional space can be subdivided into an infinite number of two-dimensional subspaces. That does not mean we would want to move into them, even if we could.

2) My own personal opinion is that all talks about things on the Planck scale, rarely amount to more than a wild speculation, even if we restrict ourselves to our own “unreal” three-dimensional world. I would not presume even to speculate how an additional dimension might affect this problem.

I’m interested in other possible analogies.

I'll avoid rehashing the arguments here, but if anyone interested in the above post hasn't heard of simulism or the Simulation Argument I encourage them to check out these links.

As for the above idea, there are plenty of specific possible scenarios like this which you can find plenty of circumstantial evidence for if you look hard enough, so we probably should demand much stronger evidence to make it worth focusing on this one hypothesis in partucular.