"Instance"? Instance of what? Are you talking about the existence of an instance of your nondeterministic mathematically linked/dependent dwarf simulation not precluding, say, Mr. Conway holding an instance of a deterministic mathematically isolated Life-game simulation? Of course I've ascertained that. Or are you claiming that the instance of your nondeterministic mathematically linked/dependent dwarf simulation on your hard drive, and the hypothetical instance of a deterministic mathematically isolated dwarf simulation with different initial conditions on my hard drive, are the same system?
I am claiming none of the above.
I am claiming that the mathematically isolated dwarf simulation on your hard drive that uses
the same initial conditions as the mathematically isolated instance of the same on my hard drive are in fact the same system, on account of their shared identity within the bounds of their mathematical isolation. They are the same thing independent of where they happen.
Okay, I guess that's a reasonable claim. But they are not the same system as the non-isolated system that had dwarves dying when you intervened to kill them, correct?
I don't know who this Conway person is you mention.
Conway was a mathematician who studied cellular automata.
Now, on a secondary note, I also argue that if you are going to treat the non-isolated series of invocations as a result of an infinite normal, a "just-so" of the initial condition, even seemingly non-isolated finite systems are represented as deterministic mathematically isolated systems.
I don't know what "an infinite normal" or "a just-so" mean.
At any rate, it's been well supported that a mathematically isolated system can be used to demonstrate the sensibility of super-nature as their nature is clearly a sub-nature, and one implies the other, that we are super-nature to their sub-nature.
I see no support for that claim. And how could it have been well-supported when your claim uses the word "nature" five times and you still haven't offered a definition of "nature"?
In any event, you don't appear to have even supported the sensibility of mathematically isolated sub-systems and super-systems. You are attributing these "sub" and "super" properties to certain mathematically isolated systems, but if you've supplied any justification for those attributions, please point out where. And your above reasonable claim, "They are the same thing independent of where they happen.", appears on its face to rule out the possibility of any objective "super" or "sub" status to a mathematically isolated system, or at any rate to any sufficiently powerful mathematically isolated system.
As you note, "they don't even have to run the same instruction set or have the same registers." Mathematical isomorphism is all it takes to make two "instances" the same system. Well then, suppose "System A" is a universal Turing machine running a program that systematically generates and by time-sharing simulates all possible computations. Infinitely many of those are simulations of the "Life" cellular automaton, with all possible finite initial conditions. Infinitely many of those "Life" instances contain configurations of "Glider guns" that collectively form implementations of Turing machines. (Yes, the "Life" cellular automaton has been proven to be Turing-equivalent.) In at least one of those instances, "System B", the initial state of its simulated tape is a program that systematically generates and by time-sharing simulates all possible computations. Among those computations it simulates is, inevitably, an instance of System A. So, simultaneously, System A is simulating system B and system B is simulating System A. And, as you point out, the simulated instance of System A and the original postulated instance of System A
are the same system. Likewise, the System B "Life" pattern and the instance of the same "Life" pattern created by the simulated instance of System A are also the same system. So System A and System B cannot be assigned any objective order that makes one of them "sub" and the other "super". "Sub" and "super" are relations between
instances of systems, not relations between
systems.
Consequently, any claim that a denizen of a mathematically isolated system makes about some other mathematically isolated system being "sub" or "super" to her own system can have no objective truth or falsity to it. Such a claim is not even wrong. It's a type-mismatch error.
If we look at it, there are at least two related Cosmologies, between the isolated system on your drive and the isolated system on my drive, which lead to creation of the same mathematically isolated system's existence.
If the denizens of the system running on both our drives form two competing religions, asserting that their system was created by super-system beings respectively named Jarhyn and Bomb#20, it isn't possible that it's the Jarhynists on your drive are who are right while the Bomb#20ists are wrong, while it's the other way around on my drive. Because, as you note, those are the same system. The prophet of Jarhynism on your drive is the same person as the prophet of Jarhynism on my drive, and his claim on your drive is the same claim as his claim on my drive. His claim can't be both true and false. The two related cosmologies are both metaphysics, i.e., bunk. In a correct cosmology -- a physics cosmology -- mathematically isolated systems are just mathematically isolated, not mathematically isolated and sub or mathematically isolated and super.
Which goes to my claim that saying "there is only one god" is also a misnomer.
There are zero or more.
What's a "god"?