Is it possible for an entity that exists only in a computer simulation to run an accurate computer simulation of the ‘higher’ entity that simulated them?
If the answer is ‘no’, then whatever we contemplate in our universe is only a small subset of what can be known by those who reside higher in the sequence of more complex simulations. And if the answer is ‘no’, it would mean that there are deep aspects of reality that we cannot even imagine.
Of course, the answer to this question depends on the precise definitions of terms such as ‘simulation’ and ‘computer’. Formal systems theory and computer science provide many theorems that suggest that, whatever definitions we adopt, the answer to the question is indeed ‘no’. However, rather than expounding on these theorems that suggest our cognitive abilities are limited, I’d like to take a step back. These theorems are examples of the content of our mathematics, examples of our mathematical ability and ideas. Much of this content already suggests our cognitive abilities are too limited to fully engage with reality. But what about other aspects of our mathematics?