Well, a chain of Boltzmann brain snapshots may very well be my brain. It includes ALL aspects of brain what constitutes me as me: my childhood memory, the hot cap of coffee in my hand right now, stars in the sky I observe, my current thinking about this text… anything what my brain perceives as reality, the reality it is part of... Apparently, it does not require the reality to actually be, it requires only Boltzmann brain to be in such state as it perceives to be part of some reality. The assembly of identical Boltzmann brains is essentially not an assembly of many but a single sample since identical copies cannot be distinguished; therefore, the collection of different/unique snapshots of Boltzmann brain constitutes such assembly. The subset of such assembly which is a composition of “slightly” different from each other snapshots and the order on such subset may represent the time evolution of one of Boltzmann brains (for example my brain). The open question is: in what way it should be different and at what magnitude of “slightness” and what order on subset should be to have a “sane” Boltzmann brain along its timeline/evolution???
Two Kurt Gödel’ theorems:
1) Any consistent axiomatic is not complete. (*)
2) The consistency of axiomatic is not provable within its frame. (**)
Any observation is a true predicate (observations represented by false predicates are not observable). A sane Boltzmann brain must be capable to make observations. Some subsets of Boltzmann brains assembly and the orders on these subsets may represent the Boltzmann brains capable to have observations along its timeline/evolution; therefore, all Boltzmann brains snapshots which violate this “abilities” get excluded/extinct since they cannot constitute a “sane” Boltzmann brain. According to first Gödel’ theorem (*) there is no way to have/predefine a complete subset & order of snapshots of Boltzmann brains which represent a defined “sane” Boltzmann brain along its timeline/evolution – such subset must be open and redefine itself along its time evolution to comply with second Gödel’ theorem (**). This process resembles the natural selection where the environment is presented by Kurt Gödel’ theorems (*/**) and the ability to make observation represents survival. I would call i : Gödel’s natural selection of Boltzmann brains ;o) Apparently, the neighborhood of particular sane Boltzmann brain may represent the superposition of quantum states of macro body (shalom to Everett’s relative state).