Basically I think you’re confused. You correctly begin to identify the core of the problem and then don’t engage with it here
Agreed, good catch.
I think that when I proposed that definition, I quickly thought “Well nothing like that could exist” then swapped out the definition with something very vague like, “A perfectly accurate simulation would be a thing that feels reasonable to call a perfect simulation, yet not as powerful as what I just described”, and then carried on reasoning from there.
Giving it more thought, I find the original definition of perfect simulation to be a good fit, and the original question is now resolved.
Though I no longer see the sub-string problem I proposed as relating to the original problem, I’m curious about what you think would be a meaningful definition of a “perfect encoding”.
I’m curious about what you think would be a meaningful definition of a “perfect encoding”.
Part of the point of the excerpt you quoted from Aaronson is that in any notion of an encoding, some of the computational work is being done by the decoding procedure, whatever that is. So e.g. you can specify a programming language, and build a compiler that will compile and execute programs in that programming language, and then talk about a program perfectly encoding something if it outputs that thing when run. Some of the computational work is being done by the program but some of it’s being done by the compiler.
Thanks for the feedback!
Agreed, good catch.
I think that when I proposed that definition, I quickly thought “Well nothing like that could exist” then swapped out the definition with something very vague like, “A perfectly accurate simulation would be a thing that feels reasonable to call a perfect simulation, yet not as powerful as what I just described”, and then carried on reasoning from there.
Giving it more thought, I find the original definition of perfect simulation to be a good fit, and the original question is now resolved.
Though I no longer see the sub-string problem I proposed as relating to the original problem, I’m curious about what you think would be a meaningful definition of a “perfect encoding”.
Part of the point of the excerpt you quoted from Aaronson is that in any notion of an encoding, some of the computational work is being done by the decoding procedure, whatever that is. So e.g. you can specify a programming language, and build a compiler that will compile and execute programs in that programming language, and then talk about a program perfectly encoding something if it outputs that thing when run. Some of the computational work is being done by the program but some of it’s being done by the compiler.