Do we live in a simulation? There are a lot of arguments to answer this question with yes or no. Much less efforts are spend in trying to understand what the question actually means and if it makes any sense at all.
So what exactly it means “to live in a simulation”? A common notion is that “to live” means to live consciously and “simulation” implies performing calculations on a computer according formulas of some physical model.
But then to answer the original question one has to agree that consciousness can be described by a physical model. Only with such assumption one can start to consider if our world is original one or a simulation.
This assumption is a matter of a belief. Strong arguments against it is that physical models describe neither free will nor the perception of time flow, two essential attributes of consciousness.
Yet let’s assume for the sake of arguments that consciousness is reducible to formulas of a physical model. With that assumption what can we say about simulating that?
Presumably the model should be complex and is out of reach of modern computers. It can also be that model will be so complex that it will be out of reach of any computers that can be built in our world. There are various estimates on the physical limits of computations and it can be that the model will exceed those.
So let’s made another assumption that consciousness is not only reducible to a physical model but also that physics allows to run the model on some future computer. Then under such assumptions can we argue that we live in a simulation?
The standard answer is yes. Since there can be a series of nested simulations, then the probability that we live in the outermost one goes to zero. But this is not so interesting since our assumptions made the implication of living in a nested simulation boring.
In particularly the first assumption ruled out free will. Then even the outermost world that started the simulation chain is fully deterministic and is govern by physical laws. The second assumption that such laws can describe a computer that can simulate conscious part of the world just tells that physical laws are fractal in nature.
But we already know that the world is such. Galaxies, stars, atoms and protons have important similarities like forces that keep stuff together without collapsing even if the nature of those forces is different. So living in a simulation will be another unsurprising example of fractal behavior of physical laws.