But what about the all-zero universe, 0000000...? The program must loop forever. We can’t tell we’re in the all-zero universe by examining any finite number of bits. You don’t know whether you will eventually push the button.
An infinite loop may be a paradox. Perhaps the paradox exists only because of the infinity, or some confusion stemming from it or how it is used?*
What is the difference between 0.9999 that goes on forever, and 1? In the real numbers, 0.
How do you determine this? If you know the process generating the numbers you can tell.
Practically?
1. If only a finite number of digits is relevant to your decision it doesn’t matter. (Additionally, if a theory isn’t falsifiable, a) should we consider the hypothesis?, and b) is there lower hanging fruit we should pick before trying to solve a potentially unsolvable problem?)
2. Wait. Where did you get an infinite number of bits (which you are unable to analyze because they are infinite) from? (Computability sounds nice, but absent arbitrarily large computing resources (i.e. infinite), in this universe, past a certain point, computability don’t seem to exist in a practical sense.)
*It isn’t necessarily clear that the environment must be computable. (Even if there is some proof of this, an agent unaware of the proof a) must function without it, b) decide whether it is worth investing the time to try and find/create it.)
The requirement about computability:
An infinite loop may be a paradox. Perhaps the paradox exists only because of the infinity, or some confusion stemming from it or how it is used?*
What is the difference between 0.9999 that goes on forever, and 1? In the real numbers, 0.
How do you determine this? If you know the process generating the numbers you can tell.
Practically?
1. If only a finite number of digits is relevant to your decision it doesn’t matter. (Additionally, if a theory isn’t falsifiable, a) should we consider the hypothesis?, and b) is there lower hanging fruit we should pick before trying to solve a potentially unsolvable problem?)
2. Wait. Where did you get an infinite number of bits (which you are unable to analyze because they are infinite) from? (Computability sounds nice, but absent arbitrarily large computing resources (i.e. infinite), in this universe, past a certain point, computability don’t seem to exist in a practical sense.)
*It isn’t necessarily clear that the environment must be computable. (Even if there is some proof of this, an agent unaware of the proof a) must function without it, b) decide whether it is worth investing the time to try and find/create it.)