If we live in a simulation, what does that imply about the world of our simulators and our relationship to them? [1]

Here are some proposals, often mutually contradictory, none stated with anything near certainty.

1. The simulators are much like us, or at least are our post-human descendants.

Drawing on some of the key points in Bostrom's Simulation Argument:

Today, we often simulate our human ancestors' lives, e.g., Civilization. Our descendants will likely want to simulate their own ancestors, namely us, and they may have much-improved simulation technology which support sentience. So, our simulators are likely to be our (post-)human descendants.

2. Our world is smaller than we think.

Robin Hanson has said that computational power will be dedicated to running only a small part of the simulation at low resolution, including  the part which we are in. Other parts of the simulation will be run at a lower resolution. Everything outside our vicinity, e.g., outside our solar system, will be calculated planetarium-style, and not from the level of particle physics.

(I wonder what it would be like if we are in the low-res part of the simulation.)

3. The world is likely to end soon.

There is no a priori reason for an base-level (unsimulated) universe to flicker out of existence. In fact, it would merely add complexity to the laws of physics for time to suddenly end with no particular cause.

But a simulator may decide that they have learned all they wanted to from their simulation; or that acausal trade has been completed; or that they are bored with the game; and that continuing the simulation is not  worth the computational cost.

The previous point was that the world is spatially smaller than we think. This point is that the world is temporally smaller than we hope.

4. We are living in a particularly interesting part of our universe.

The small part of the universe which the simulators would choose to focus on is the part which is interesting or entertaining to  them. Today's video games are mostly about war, fighting, or various other challenges to be overcome. Some, like the Sims, are about everyday life, but even in those, the players want to see something interesting. 

So, you are likely to be playing a pivotal role in our (simulated) world. Moreover, if you want to continue to be simulated, do what you can to make a difference in the world, or at least to do something entertaining.

5. Our simulators want to trade with us.

One reason to simulate another agent is to trade acausally with it.

Alexander Kruel's blog entry and this LW Wiki entry summarize the concept. In brief, agent P simulates or otherwise analyzes agent Q and learns that Q does  something that P wants, and also learns that the symmetrical statement is true: Q can simulate or analyze P well enough to know that P likewise does something that Q wants. 

This process may involves simulating the other agent for the purpose of learning its expected behavior. Moreover, for P to "pay" Q, it may well run Q -- i.e., simulate it. 

So, if we live in a simulation, maybe our simulators are going to get some benefit from us humans, and we from them. (The latter will occur when we simulate these other intelligences).

In Jaan Tallinn's talk at Singularity Summit 2012, he gave an anthropic argument for our apparently unusual position at the cusp of the Singularity. If post-Singularity superintelligences across causally disconnected parts of the multiverse are trying to communicate with each other by mutual simulation, perhaps for the purpose of acausal trade, then they might simulate the entire history of the universe from the Big Bang to find the other superintelligences in mindspace. A depth-first search across all histories would spend most of the time where we are, right before the point at which superintelligences emerge.

6. We are part of a multiverse.

Today, we run many simulations in our world. Similarly, says Bostrom, our descendants are likely to be running many simulations of our universe: A multiverse.

Max Tegmark's Level IV multiverse theory is motivated partly by the idea that, following Occam's Razor, simpler universes are more likely. Treating the multiverse as a computation, among the most likely computations is one that generates all possible strings/programs/universes.

The idea of the universe/multiverse as computation is still philosophically controversial. But if we live in a simulation, then our universe is indeed a computation, and Tegmarks' Level IV argument applies.

However, this is  very different from the ancestor simulation described in points 1-3 above. That argument relies on the lower conditional complexity of the scenario -- we and our descendants are similar enough that if one exists, the other is not too improbable. 

A brute-force universal simulation is an abstract possibility that specifies no role for simulators. In addition, if the simulators are anything like us,  not enough computational power exists, nor would it be the most interesting possibility.

But we don't know what computational power is available to our simulators, what their goals are, nor even if their universe is constrained by laws of physics remotely similar to ours.

7. [Added] The simulations are stacked.

If we are in a simulation, then (a) at least one universe, ours, is a simulation; and (b) at least one world includes a simulation with sentience. This gives some evidence that being simulated or being a simulator are not too unusual. The stack may lead way down to the basement world, the ultimate unsimulated simulator; or else the stack may go down forever; or [H/T Pentashagon], all universes may be considered to be simulating all others.

Are there any other conclusions about our world that we can reach from the idea that we live in a simulation?

[1] If there is a stack of simulators, with one world simulating another, the "basement level" is the world in which the stack bottoms out, the one which is simulating and not simulated. This uses a metaphor in which the simulators are below the simulated. An alternative metaphor, in which the simulators "look down" on the simulated, is also used.