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Even encoding schemes themselves have an information theoretic entropy level regardless of universe. Encoding schemes with less entropy can be considered more

Even encoding schemes themselves have an information theoretic entropy level regardless of universe. Encoding schemes with less entropy can be considered more 'natural' - it's possible to come up with a measure of the 'naturalness' of encoding schemes in a pure mathematical sense without having to take into account entities beyond the mathematical realm.

whatshisface 9y ago
If my understanding is right, a bijective function won't change the entropy of the strings it acts on. So, as long as I can find enough states in my grain of sand (quite possibly undoable, so imagine I'm talking about a few photons in space instead!), I can map them on to my universe and be no worse-off, from an information entropy standpoint.
- jblow 9y ago
  A mapping is a computation. If your mapping is very complex compared to the ostensible simulator, then the mapping is actually doing most of the simulation. So the simulation is not mostly running when the ostensible simulator runs, it is running when you perform the mapping. If you are inside the universe being simulated and think you can do that mapping, it seems unlikely that there exist enough time and space for it.
  - whatshisface 9y ago
    Right, but if the role of the mapping is just to make the status of the simulation make sense to you, (after all, that's the only thing you would be able to observe it doing), then the inhabitant wouldn't care if the mapping was ever computed. So, it's fine if the mappings would be ridiculously impossible to compute. (Extra note: it is extremely hard to simulate the chaotic motion of nearly every physical system. Does that mean they are doing lots of hard computation? If so, does that make them "more likely" to be interpretable as simulating universes?)
    - jblow 9y ago
      It's not that "the mapping" makes "the simulation" make sense. You have moved most of "the simulation" into "the mapping". So if you don't do the mapping, the simulation mostly does not happen, so there is nothing to make sense of.

whatshisface 9y ago

If my understanding is right, a bijective function won't change the entropy of the strings it acts on. So, as long as I can find enough states in my grain of sand (quite possibly undoable, so imagine I'm talking about a few photons in space instead!), I can map them on to my universe and be no worse-off, from an information entropy standpoint.

jblow 9y ago
A mapping is a computation. If your mapping is very complex compared to the ostensible simulator, then the mapping is actually doing most of the simulation. So the simulation is not mostly running when the ostensible simulator runs, it is running when you perform the mapping. If you are inside the universe being simulated and think you can do that mapping, it seems unlikely that there exist enough time and space for it.
- whatshisface 9y ago
  Right, but if the role of the mapping is just to make the status of the simulation make sense to you, (after all, that's the only thing you would be able to observe it doing), then the inhabitant wouldn't care if the mapping was ever computed. So, it's fine if the mappings would be ridiculously impossible to compute. (Extra note: it is extremely hard to simulate the chaotic motion of nearly every physical system. Does that mean they are doing lots of hard computation? If so, does that make them "more likely" to be interpretable as simulating universes?)
  - jblow 9y ago
    It's not that "the mapping" makes "the simulation" make sense. You have moved most of "the simulation" into "the mapping". So if you don't do the mapping, the simulation mostly does not happen, so there is nothing to make sense of.