hmm yes, i took “the laws of nature” to mean something like laws giving what we canonically understand to be our universe, and not to include laws giving some weird other simple cellular automaton on which some aliens live who are hacking into our predictor, but maybe i misunderstood what you meant.
But even if you say “our world”, arguably that still works: if I’m living on a computer run by aliens, then arguably the base reality where the computer sits is my world
hmm, interesting point. if the aliens are building giant antimatter statues with your predicted inputs and the shortest program is looking at those, then i think the shortest program isn’t a simulation of your world with a pointer at you, because you aren’t a being at these statues? there could be a computer inside this alien world running a simulation of you and reading off your raw inputs with a pointer, but that’s not what is getting directly pointed at in these malign predictors. however, i guess if pointing at the malign statues is the best predictor, then pointing to your inputs inside the computer on which you are simulated by these malign aliens would be not too far behind, because one can point at it via the statues (appending “now look for the same thing on a computer in the same universe”), and then maybe we should think that you live there more than in what we would naively consider base reality or other kinds of simulations of base reality. my intuitive guess is that you’re not actually (mostly) living on a computer in this malign alien world even if they are the best predictors, but i’ll need to think more about this. anyway, even if you mostly live on a computer in the malign alien world, i still think that a pointer to the malign statues is not a pointer to your location in the universe
I’m interested though why you believe there are shorter good predictors than world + pointer. I agree it’s possible, I just can’t think of one. How would they look like?
tbh mostly the argument that there are incredibly many different programs and there’s some really clever constructions in there, and from that starting point i’d need a strong reason to think the best program looks like a world+pointer, and i don’t really see any strong reason. i don’t know what the best programs look like, mostly i don’t think any of the good programs are intelligible to us, and i can’t really tell you a better one. to state a hyperparam: my guess is that there are better programs that look somewhat more like clever guys thinking about what next bits to guess, than like worlds + pointers. i don’t have a specific better program in mind though, so i’m unable to give a great answer. i’ll keep the question in mind and try to write another comment in the future if i think or hear of something.
one point i can make: i think that for most reasonable input streams, you can’t have an actual full simulation because (given our current best understanding of physics) the specification length of the initial conditions and quantum branching (i mean the part of these in our past lightcone) is greater than the length of even the uncompressed raw input stream itself (of course the optimal compression won’t be the raw stream, because one can compress it a lot; this just means one can’t compress it this way). however this doesn’t rule out some sort of partial simulation
hmm yes, i took “the laws of nature” to mean something like laws giving what we canonically understand to be our universe, and not to include laws giving some weird other simple cellular automaton on which some aliens live who are hacking into our predictor, but maybe i misunderstood what you meant.
hmm, interesting point. if the aliens are building giant antimatter statues with your predicted inputs and the shortest program is looking at those, then i think the shortest program isn’t a simulation of your world with a pointer at you, because you aren’t a being at these statues? there could be a computer inside this alien world running a simulation of you and reading off your raw inputs with a pointer, but that’s not what is getting directly pointed at in these malign predictors. however, i guess if pointing at the malign statues is the best predictor, then pointing to your inputs inside the computer on which you are simulated by these malign aliens would be not too far behind, because one can point at it via the statues (appending “now look for the same thing on a computer in the same universe”), and then maybe we should think that you live there more than in what we would naively consider base reality or other kinds of simulations of base reality. my intuitive guess is that you’re not actually (mostly) living on a computer in this malign alien world even if they are the best predictors, but i’ll need to think more about this. anyway, even if you mostly live on a computer in the malign alien world, i still think that a pointer to the malign statues is not a pointer to your location in the universe
tbh mostly the argument that there are incredibly many different programs and there’s some really clever constructions in there, and from that starting point i’d need a strong reason to think the best program looks like a world+pointer, and i don’t really see any strong reason. i don’t know what the best programs look like, mostly i don’t think any of the good programs are intelligible to us, and i can’t really tell you a better one. to state a hyperparam: my guess is that there are better programs that look somewhat more like clever guys thinking about what next bits to guess, than like worlds + pointers. i don’t have a specific better program in mind though, so i’m unable to give a great answer. i’ll keep the question in mind and try to write another comment in the future if i think or hear of something.
one point i can make: i think that for most reasonable input streams, you can’t have an actual full simulation because (given our current best understanding of physics) the specification length of the initial conditions and quantum branching (i mean the part of these in our past lightcone) is greater than the length of even the uncompressed raw input stream itself (of course the optimal compression won’t be the raw stream, because one can compress it a lot; this just means one can’t compress it this way). however this doesn’t rule out some sort of partial simulation