4 ms·

Quantity of information - a simulator whose state itself can be expressed in X bits can't possibly have a simulation with X+1 bits of incompressible state.

vidarh 3y ago
Yes, but assuming much incompressible state is already assuming to know a lot about the nature of the simulation, ranging from size, longevity, to the extent which the structure of our perceived universe is the way it is to enable an outside simulator to take shortcuts we don't know about.
- FartyMcFarter 3y ago
  That assumption is baked into the question being asked though. When we talk about X bits of storage it's generally accepted that this means being able to store any bit string of length X, not just compressible ones.
  - vidarh 3y ago
    The question was: > What's the reason for the simulation to be smaller than the simulator? And the answer to that is that there's no reason. There's no reason to assume the state of a simulation isn't compressible, because have no knowledge about whether or not it is, and we do have plenty of knowledge of how to create simulations that appear complex but that reduces to easily computable sequences "from the outside". The more restricted question isn't meaningful because we have no basis for assuming we can restrict ourselves to consider incompressible state, because we have no way of determining if the state is incompressible. There would be any number of sets of possible simulations that would indeed be smaller than their simulators, but given that within two similarly sized universes, you would be able to fit more simulations that are reducible, the probability that any given simulation is an approximation that allows for shortcuts ought to be higher than that it is a simulation of an irreducible set of data. So much so, that perhaps if we were able to somehow demonstrate aspects that would prove incompressibility (and I'm not convinced that is possible, or even meaningful) that might indicate that we're more likely to be in the "outer" universe. Conversely, the more compressible our universe looks, the more we might want to consider that it's an indication that we're more likely to be in a simulation.
    - PeterisP 3y ago
      I'd (obviously? perhaps not) define the "size" of the simulation as the amount of information (i.e. uncompressible state) it contains, simply because for other measures of size many trivial simulations are infinitely large while having tiny incompressible information, so these other measures of size are not useful and not used. So a more compressible i.e. more regular, simpler simulation is the smaller one, and the simulation still has to be smaller than the simulator, and we literally don't care about the compressibility or incompressibility or uncompressed size, because why would we, that's not information-theory information.

vidarh 3y ago

Yes, but assuming much incompressible state is already assuming to know a lot about the nature of the simulation, ranging from size, longevity, to the extent which the structure of our perceived universe is the way it is to enable an outside simulator to take shortcuts we don't know about.

FartyMcFarter 3y ago
That assumption is baked into the question being asked though. When we talk about X bits of storage it's generally accepted that this means being able to store any bit string of length X, not just compressible ones.
- vidarh 3y ago
  The question was: > What's the reason for the simulation to be smaller than the simulator? And the answer to that is that there's no reason. There's no reason to assume the state of a simulation isn't compressible, because have no knowledge about whether or not it is, and we do have plenty of knowledge of how to create simulations that appear complex but that reduces to easily computable sequences "from the outside". The more restricted question isn't meaningful because we have no basis for assuming we can restrict ourselves to consider incompressible state, because we have no way of determining if the state is incompressible. There would be any number of sets of possible simulations that would indeed be smaller than their simulators, but given that within two similarly sized universes, you would be able to fit more simulations that are reducible, the probability that any given simulation is an approximation that allows for shortcuts ought to be higher than that it is a simulation of an irreducible set of data. So much so, that perhaps if we were able to somehow demonstrate aspects that would prove incompressibility (and I'm not convinced that is possible, or even meaningful) that might indicate that we're more likely to be in the "outer" universe. Conversely, the more compressible our universe looks, the more we might want to consider that it's an indication that we're more likely to be in a simulation.
  - PeterisP 3y ago
    I'd (obviously? perhaps not) define the "size" of the simulation as the amount of information (i.e. uncompressible state) it contains, simply because for other measures of size many trivial simulations are infinitely large while having tiny incompressible information, so these other measures of size are not useful and not used. So a more compressible i.e. more regular, simpler simulation is the smaller one, and the simulation still has to be smaller than the simulator, and we literally don't care about the compressibility or incompressibility or uncompressed size, because why would we, that's not information-theory information.