rather than, say, assigning equal probability to all strings of bits we might observe
If the space of possibilities is not arbitrarily capped at a certain length, then such a distribution would have to favor shorter strings over longer ones in much the same way as the Solomonoff prior over programs (because if it doesn’t, then its sum will diverge, etc.). But then this yields a prior that is constantly predicting that the universe will end at every moment, and is continually surprised when it keeps on existing. I’m not sure if this is logically inconsistent, but at least it seems useless for any practical purpose.
If the space of possibilities is not arbitrarily capped at a certain length, then such a distribution would have to favor shorter strings over longer ones in much the same way as the Solomonoff prior over programs (because if it doesn’t, then its sum will diverge, etc.). But then this yields a prior that is constantly predicting that the universe will end at every moment, and is continually surprised when it keeps on existing. I’m not sure if this is logically inconsistent, but at least it seems useless for any practical purpose.