Warning! Almost assuredly blithering nonsense: Hm, is this more informative if instead we consider programs between 10^100 and 10^120 bits in length? Should it matter all that much how long they are? If we can show convergence upon characteristic output distributions by various reasonably large sets of all programs of bit lengths a to b, a < b, between 0 and infinity, then we can perhaps make some weak claims about “attractive” outputs for programs of arbitrary length. I speculated in my other comment reply to your comment that after maximally compressing all of the outputs we might get some neat distribution (whatever the equivalent of the normal distribution is for enough arbitrary program outputs in a given language after compression), though it’s probably something useless that doesn’t explain anything, like, I’m not sure that compressing the results doesn’t just destroy the entire point of getting the outputs. (Instead maybe we’d run all the outputs as programs repeatedly; side question: if you keep doing this how quickly does the algorithm weed out non-halting programs?) Chaitin would smile upon such methods, I think, even if he’d be horrified at my complete bastardization of pretend math, let alone math?
Warning! Almost assuredly blithering nonsense: Hm, is this more informative if instead we consider programs between 10^100 and 10^120 bits in length? Should it matter all that much how long they are? If we can show convergence upon characteristic output distributions by various reasonably large sets of all programs of bit lengths a to b, a < b, between 0 and infinity, then we can perhaps make some weak claims about “attractive” outputs for programs of arbitrary length. I speculated in my other comment reply to your comment that after maximally compressing all of the outputs we might get some neat distribution (whatever the equivalent of the normal distribution is for enough arbitrary program outputs in a given language after compression), though it’s probably something useless that doesn’t explain anything, like, I’m not sure that compressing the results doesn’t just destroy the entire point of getting the outputs. (Instead maybe we’d run all the outputs as programs repeatedly; side question: if you keep doing this how quickly does the algorithm weed out non-halting programs?) Chaitin would smile upon such methods, I think, even if he’d be horrified at my complete bastardization of pretend math, let alone math?