I recently learned of the Simulation Argument, which attempts to show that one of three statements is very likely true, paraphrasing:
- Civilizations are unlikely to ever be able to simulate realities.
- Civilizations that are able to simulate realities will almost always choose not to do so.
- We're probably in a simulation already.
To arrive at (3), the argument goes: Suppose that civilizations do manage to simulate realities (with inhabitants) and those simulated inhabitants develop, then eventually those simulated inhabitants will make their own simulations, and on and on until there are many more simulations than there are "real" realities.
My question is:
Is the argument above compatible with the proposition that physical entities have finite information content?
The counterargument would go: Let N be the minimum number of bits required to describe all physical entities in R. (Such an N exists because physical entities have finite information content.) Then the total information content of all realities simulated within and/or nested beneath R, must be less than or equal to N, for if the total were greater than N then the simulation apparatus itself could not be contained in R. As a result, there cannot be an unlimited number (or even very many) simulated realities---Any given "real" reality could contain at most "about one" extra reality of comparable complexity, and then only if the simulation apparatus contained the bulk of the root reality's information content.