Permutation City is a great novel with a very interesting philosophical argument embedded inside it. Many people don’t want to read the whole novel, so here is my short explanation of Egan’s Dust Theory.
If you think experience is simulatable, you buy computational or “patternist” theories of identity, there are some very strange implications that are not commonly brought up.
Because computation is sort of subjective, just a set of relations that can be usefully interpreted as representing a function, this seems to imply that the function you identify with can be interpreted as being simulated by any sufficiently complex set of relations.
That is, for any random set of relations with enough complexity to represent a human mind, Egan claims, there exists an exotic encoding scheme that can interpret this set of relations as representing any arbitrary function, including the function that you would call “I”.
Now you cannot access this information usefully, so most functions can be said to not usefully exist within this randomness. But if you buy the whole “I think therefore I am” business this does not matter for those functions that are conscious, because consciousness is self-justifying.
So the function that is you is being “run” far more often in random noise than engineered computers or ‘real’ physical reality. This is sort of like the Boltzmann brain idea but even worse because it applies to any set of relations. According to Egan’s argument all possible experiences that can be computed by any sufficiently complex set of relations are in fact computed by them.
In fact, even if you imagine a static set of relations that do not evolve in time there still exists encoding schemes that can interpret this set of relations as any arbitrary function, so in some sense the set of mathematical objects that represent “you” and “me” and all possible minds can be said to exist in these timeless relations.
Egan discusses some counterarguments to the idea here: https://www.gregegan.net/PERMUTATION/FAQ/FAQ.html