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This question assumes the following is true:

  • Our universe is simulated
  • We will eventually have the capacity and ability to easily simulate our own universe
  • Every point in time at every place will be generated and observable from outside the simulation

Question It has always been a great source of existential dread to think about the very real possibility of our universe being a simulation, but it also got me thinking that perhaps eventually we will be able to simulate a universe ourselves. Essentially a simulation within a simulation, so feasibly if we are discussing in terms of data and physical size, when (if at all) would there be an end to the simulations? A simulation rock-bottom, if you will.

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    $\begingroup$ In computing it this is quite common; you could for example run a program written in an interpreted language, the interpreter itself being written for example in Java and thus running on the Java Virtual Machine, itself running in a full-blown virtual machine on some host system. That's the entire point of a virtual machine: to the programs running on it the VM appears to be a physical computer. IBM used to make a lot of money from operating systems which contained virtual machines running older operating systems and so on, to the effect that a modern computer could run 60 years old software. $\endgroup$ – AlexP Sep 23 '17 at 18:09
  • $\begingroup$ Do note that there is a tremendous difference between simulating "our" universe and simulating "a" universe. The former has all sorts of twists to it, like infinite descending sets and stationary points which make the arguments very hard. $\endgroup$ – Cort Ammon Sep 24 '17 at 6:07
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    $\begingroup$ Also, it has not always been a source of existential dread. It's predecessor, Plato's Allegory of the Cave, brought great inspiration and hope to its creator, demonstrating the value philosophy brings to the world. $\endgroup$ – Cort Ammon Sep 24 '17 at 6:07
  • $\begingroup$ you can create a copy of a universe and embedded in itself people have made games in other games, given enough time, you can make the same game within the game. $\endgroup$ – A. C. A. C. Sep 29 '17 at 19:42
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There seems to be no way to iterate too many times the "simulate a simulation" game (it can be done and it has been done, though).

The simulating system needs to have, at the very least, as many different states as the represented (simulated) universe (in practice the simulating universe will have to be much more complex than the simulated one).

This means that simulated universes will rapidly become simpler; after a (short) while the simulated "universe" will be too simple to to sustain a simulation.

To reiterate: simulating universe will have, as distinct states, all the states of the simulated world. plus many more of its own. In order to do some simulation you need to use up some of the "degrees of freedom" of your universe to fuel the simulated.

Simulating something with the same level of complexity of the simulator would require an infinite simulator; unfortunately(?) "infinite" and "infinitesimal" are two very useful mathematical concepts, but they don't seem to have a physical existence in our universe.

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  • $\begingroup$ "The simulating universe will have, as distinct states, all the states of the simulated world": only if we assume that the programmers are incompetent. A basic optimization technique in computer simulation is to have various levels of detail for various aspects of the simulated system. For example, suppose we lived in a simulated universe; there is no reason for the simulation to maintain a detailed state of the far side of the moon; only if and when a probe is sent to photograph it will the far side of the moon acquire a defined state, based on the previous stored state plus random impacts. $\endgroup$ – AlexP Sep 23 '17 at 22:36
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    $\begingroup$ @AlexP: nevertheless all represented states in the simulation must have at least the equivalent representation in the simulating equipment. This means the simulating equipment is at the very least as complex (i.e.: it may be in, at the very least, as many distinguishable states) as the simulated universe. We can safely assume the simulating environment is a small fraction of the universe where it lives; which is what I was driving to: at each simulation round universes lose a huge part of their complexity, you cannot continue the chain long. This has nothing to do with optimization. $\endgroup$ – ZioByte Sep 24 '17 at 7:31
  • $\begingroup$ +1 @ZioByte, Excellent point. If you can see a simulation from outside the simulation, that implies the simulation 'layer' contains less information than the 'layer' in which the simulation resides. Thus there is a monotonic descent of informational content, layer by layer, and information is not infinitely divisible. Thus eventually the content must decline to zero. $\endgroup$ – Amadeus Sep 24 '17 at 15:21
  • $\begingroup$ This answer relies on the fact that we can not implement infinite memmory in finite space. While this seams to hold true in our universe it does not have to hold in the hypotetical universe simulating ours or any universe above that. Given infinite storage in finite space we can implement arbritrary nesting, thing ideal turing machine with infonite tape. It may be that our universe is a simulation exploring what happens if any point can only have finite information. Another way would be if the universe allowed decreasing entropy, then infinite space could be used for storage. $\endgroup$ – lijat Sep 25 '17 at 7:02
  • $\begingroup$ @lijat: in purely speculative terms you might be right. I strongly believe certain concepts are nothing but useful generalizations that we use to describe something, but have no province in the "real" universe. Our brain is built to recognize patterns and apply them whenever possible, extrapolating too far is one of the main mistake sources (the other is generalizing too much). "infinite", "infinitesimal", "fractal" are a few examples of concepts extrapolated "at libitum"; IMNSHO they are very useful as mathematical devices, but I won't use them in anything related to (our) reality. $\endgroup$ – ZioByte Sep 25 '17 at 7:20
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I don't have a final-final answer for you, but let's dig a little.

In theory, you can have as many layers of simulation as you want. But you know the difference between theory and practice? In theory, nothing. ;D There are limitations caused by the substrate the simulation runs on. It needs to have enough processing power and -- importantly -- storage to host this new universe. Think of computer systems ... you can't have a recursive function run indefinitely, because it'll run out of stack space.

Also critical is that the simulation can't be exact -- your simulation can't account for every particle in the real universe, because that would require our entire universe to be used to build the simulation. I'm suggesting therefore that as you go deeper into simulations you get less and less complexity in terms of data storage or # of particles represented.

You can play with this. Is there a final Simulation Omega which is the deepest one able to portray viable life (and that's what you need to construct the next layer down, right)? Wouldn't it be embarrassing if we were Simulation Omega?

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