If this is a simulation, then the universe running it must be, too
The simulation hypothesis [1] assumes that if it is possible to simulate a universe in some cosmological frame, it is probably happening already. The extrapolation leads to the conclusion that sentient inhabitants of a simulated universe would also run simulations, whose dwellers in turn would also run simulations, leading to infinitely nested universe simulations.
Do infinite simulations require infinite resources?
Does an infinitely nested simulation require infinite resources? At first glance one might say that it probably does, if there is a minimum resource requirement for a simulation-running capable sentience to arise in a simulation. Even if simulations at a deeper level run slower and with reduced precision, there must be a minimal amount of resources available for a nested simulation to run (which, in turn, must also be capable to host infinite simulations).
One argument against the infinitely nested hypothesis is that the information content of the host universe at the n-th level has to be larger than the information content of a guest universe at the (n+1)-th level, similarly the computing power of the host universe (as in simulation steps per unit of time) has to be larger than the computing power of the guest universe. Infinitely nested simulations would thus require infinite computing power in the first (n=0 and the only real) universe.
At first look, I don’t find this argument compelling for two reasons. First, the study of physical laws reveals “imperfections” at every level which lead to the destruction/inutility of information (uncertainty principle, 2nd thermodynamic law etc.), thus a guest simulation could run at a lower precision than the host simulation. This means that the sum of all the computing powers of all simulations is less than infinite if the simulation scope/precision diminishes significantly with each new level (eg. a series that converges is shown to the left).
Second: time (number of events per simulation step) at deeper nesting levels could run slower than time in higher levels which reduces the need for computing power by an arbitrary amount and would make nested simulations economically sensible, as long as they run slowly enough.
So, concluding, it doesn’t seem that resource constraint is an argument against infinitely nested simulations.
Everybody crashes
Programs crash, simulations are programs, so simulations crash. The probability that a simulation at the n-th nesting level survives goes down (a lot) with n.
The second counter-argument (time-stretched simulations) actually provides the basis for the reasoning that we don’t live in a simulation. Let’s assume that I successfully ran a simulation for several years. As time progresses, what is the probability of a catastrophic failure (power outage, equipment destruction, destabilising bug in the simulation, my untimely demise)? If I hand over the simulation to a powerful organisation such as a foundation or a government agency, what are the chances of a catastrophic failure at that level (war, natural disaster)? A catastrophic failure at the n-th level of the recursion would destroy all simulations deeper than n (eg. n+1, n+2…) which, in an infinite recursion, are infinite.
Since computing power of deeper nested universes must be lower than that of shallower nested universes, time (as in number of events) deeper in the simulation recursion must flow slower than earlier in the recursion, which means simulations deeper in the stack are at an disadvantage.
Summary
We explored this chain of reasoning:
- If we live in a simulated universe, then the universe hosting our simulation probably is a simulation, too.
- By extension, the stack of nested simulations is infinite
- A simulation that crashes erases all nested simulations deeper in the stack
- The deeper in the stack a simulation is, the likelier it is to crash
- If our universe is simulated in an infinite stack, the probability that it is about to crash immediately is nearly 100%
Resources
[1] https://en.wikipedia.org/wiki/Simulation_hypothesis
[2] Stars picture from the Hubble space telescope
https://en.wikipedia.org/wiki/Universe#cite_note-spacetelescope.org-1
George's Techblog 
Even if we crashed repeatedly, how would we as denizens of a simulation detect being restored and rebooted? It would all most likely look continuous to us, even if millennia lapsed between restarts. That said, I do concur with your reasoning, we’re probably not living in a simulation.
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I was reading a article where they were claiming to have found computer code embedded in everything that exists on a Quantum level
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Ok, Maybe we are first level simulation hosted in non-simulation. Maybe we will crash at the end, maybe that is purpose of time, to give a chance for horizont of events before crash. Maybe all worlds/simulation crash in 100%of cases, but before that they exist in space-time or through some other dimension(s).
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The biggest glaring flaw with this theory that seems to be overlooked is the assumption that whoever or whatever that has created and is hosting our simulated universe abides by the same laws of physics and science that we do, which is very unlikely.
I believe our reality is essentially a very advanced version of virtual reality that we have now. We can currently put on a headset and trick our eyes and brains into feeling like we’re somewhere else, but it’s only a subset of our ‘real’ reality, it doesn’t include other factors we experience like tastes and smell etc as it’s explicitly dictated by the parameters that we’ve designed it adhere to.
Therefore we have no idea what the true ‘reality’ and science is above what we’ve been exposed to, so I’d argue that ultimately the possibilities are endless, and there’s no way to disprove that we aren’t in a simulation.
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Thanks Iain. I’m paraphrasing your opening statement: the rules of the simulator don’t apply to the simulation. As long as the laws of just one universe in the (infinite?) simulation stack allow for catastrophic failures, that’s enough to support the hypothesis.
“there’s no way to disprove that we aren’t in a simulation”: took me a while to unpack that triple negation. It sounds like you then agree with the thesis that we’re not a simulation or are you saying that the topic cannot be answered?
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“As long as the laws of just one universe in the (infinite?) simulation stack allow for catastrophic failures, that’s enough to support the hypothesis.”
Sorry maybe I’m being dense, this is all fairly new to me to be fair, but I don’t understand your reasoning here. Also as a software developer I understand how breaking bugs in code will bubble up and break higher level code stacks, but I don’t understand how this can be known to true in this hypothesis?
For example, if someone encounters a bug whilst playing a VR game that causes it to crash, this has no effect in our reality, so why does that logic apply here?
Ha yes well spotted! However the statement still applies. We can’t prove it either way, that’s my point. There’s still too much that we dont understand yet, and everything we do is simply based on observation, so unless we can actually open up and look at the underlying ‘code’ that dictates our reality, it’s all purely guesswork, unless I’m missing something?
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The fact that we don’t understand how reality works doesn’t necessarily invalidate the argument. In short, the argument goes like this: assuming we live in a simulation, it’s very unlikely that our universe is the simulated one and the outside universe running the simulation is the “real” one (the post explains why). This leaves only the other possibility, that our (nested) simulation runs inside another simulation, which in turn runs inside another simulation and so forth. If only one of those simulations breaks, we’re toast (the post explains why). Since we exist, I conclude that we don’t live in a nested simulation, but in a real universe.
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