I'm not understanding your point - which may be completely on me - but your example here - why would the "child" universe require more memory than the parent has available?

You don't know the capacity of the host universe to start with though.

Sure you can. There is just noticeable delay and "glitches" in the simulation.

Maybe the host swaps to the disk? ;)

> You can't write a virtual machine with 20 GB of memory running on a real machine with only 10. Simulation isn't magic.

You can, and it will work as long as the memory of the virtual machine can be compressed to less than 10 GB.

Programs compiled to run on current amd64 CPUs have access to 2^48 bits of virtual memory, yet they run on real machines with much much less real memory.

Hey, look, most of the space out there is a vacuum! Gravity may be the hashing/pre-compressor function the simulation we are living in. ;)

As long as not all the memory is actually used, you can pretend that there is 20GB though. Once you actually need to map more than there is, you would need to stop the virtual machine.

If you read e.g. the Bostrom 2003 paper, you will see that this is more or less what they claim: If your simulation technique is good enough, you can just fake most of the universe and only actually perform fine-grained simulations where it matters. This would e.g. assume that you have special simulation rules for brains, large scale chemical reactions etc., which allows you to just skip most of the details and make them up once you need them. You could even automatically detect whether your simulation is fine grained enough by running the same simulation at two different granularities at the same time, readjusting whenever the outcome between the two differs too much.

I think the argument in its original form does not make too much sense (future humans simulating todays humans for research and fun). What you would probably simulate much more, are human-like entities in a much simpler universe (e.g. no weird quantum-mechanics that are really hard to simulate).

So in my opinion, you could take away from the simulation argument that there is a non-zero chance that we are living in a simulation. But the computer that performs the simulation most probably lives in a universe that does not follow the same rules our universe does. It might be a universe with two or more time-like dimensions. It might be one where quantum mechanics are just super-easy to simulate for some reason (maybe in the same way it would be really easy to e.g. build Conways game of life in transistor hardware for us).

I have another counter-example. Why not simulate a smaller part of the universe, not the whole experience?

Suppose you have a real machine with 10 GB. You simulate a world of 1 GB. Inside the world, the universe is contained in 1 GB (say, a smaller version of the universe, simplified physics, etc). Inside the virtual machine, in the simulation world, the perceived universe is 1 GB. They simulation agents don't perceive a short-coming because they have never been exposed to the out-the-simulation experiences.

Why is it so hard to imagine universes bigger than our own?

That's like saying "I only own a computer with 10Gb of memory, so certainly a program using 20Gb is impossible!"

What makes you think beings simulating us are in a universe with resources lesser than us?

OK, there are lots of people here insisting that you can simulate a larger machine inside of a smaller machine, in terms of the total state space. Let me assure you that in general, you cannot. That's absolutely a fact. Windows can fool you into thinking it can simulate a 20GB system inside a 10GB system, because it's using the hard drive as the extra 10GB. Which means you really still have a 20GB+ simulating system! I'm talking about a system in which you don't have some other form of memory to fall back on. Data cannot be infinitely compressed, and state space is finite no matter how it's partitioned into dimensions and so forth.