The part about the reasoners having an arbitrary amount of time to think wasn’t obvious to me. The TM can run for arbitrarily long but if it is simulating a universe and using the universe to determine its output then the TM needs to specify a system for reading from the universe.
If that system involves a start-to-read time that is long enough for the in-universe life to reason about the universal prior then that time specification alone would take a huge number of bits.
On the other hand, I could imagine a scheme that looks for a specific short trigger sequence at a particular spatial location then starts reading out. If this trigger sequence is unlikely to occur naturally then the civilization would have as long as they want to reason about the prior. So overall it does seem plausible to me now to allow for arbitrarily long in-universe time.
I want to add that the intended generator TM also needs to specify a start-to-read time, so there is symmetry there. Whatever method a TM needs to use to select the camera start time in the intended generator for the real world samples, it can also use in the simulated world with alien life, since for the scheme to work only the difference in complexity between the two matters.
There is additional flex in that unlike the intended generator, the reasoner TM can sample its universe simulation at any cheaply computable interval, giving the civilisation the option of choosing any amount of thinking they can perform between outputs, if they so choose.
The part about the reasoners having an arbitrary amount of time to think wasn’t obvious to me. The TM can run for arbitrarily long but if it is simulating a universe and using the universe to determine its output then the TM needs to specify a system for reading from the universe.
If that system involves a start-to-read time that is long enough for the in-universe life to reason about the universal prior then that time specification alone would take a huge number of bits.
On the other hand, I could imagine a scheme that looks for a specific short trigger sequence at a particular spatial location then starts reading out. If this trigger sequence is unlikely to occur naturally then the civilization would have as long as they want to reason about the prior. So overall it does seem plausible to me now to allow for arbitrarily long in-universe time.
The trigger sequence is a cool idea.
I want to add that the intended generator TM also needs to specify a start-to-read time, so there is symmetry there. Whatever method a TM needs to use to select the camera start time in the intended generator for the real world samples, it can also use in the simulated world with alien life, since for the scheme to work only the difference in complexity between the two matters.
There is additional flex in that unlike the intended generator, the reasoner TM can sample its universe simulation at any cheaply computable interval, giving the civilisation the option of choosing any amount of thinking they can perform between outputs, if they so choose.