...So, where in this schema does Minimum Message Length fit? Under AIT, or coding theory? Seems like it’d be coding theory, since it relies on your current coding to describe the encoding for the data you’re compressing. But everyone seems to refer to MML as the computable version of Kolmogorov Complexity; and it really does seem fairly equivalent.
It seems to me that KC/SI/AIT explicitly presents the choice of UTM as an unsolved problem, while coding theory and MML implicitly assume that you use your current coding; and that that is the part that gets people into trouble when comparing Zeus and Maxwell. Is that it?
It seems to me that KC/SI/AIT explicitly presents the choice of UTM as an unsolved problem, while coding theory and MML implicitly assume that you use your current coding; and that that is the part that gets people into trouble when comparing Zeus and Maxwell. Is that it?
I think more or less yes, if I understand it. And more seriously, AIT is in some ways meant not to be practical, the interesting results require setting things up so that technically the work is pushed to the “within a constant” part. Which is divorced from praxis. Practical MML intuitions don’t carry over into such extreme domains. That said, the same core intuitions inspire them; there are just other intuitions that emerge depending on what context you’re working in or mathematizing. But this is still conjecture, ’cuz I personally haven’t actually used MML on any project, even if I’m read some results.
...So, where in this schema does Minimum Message Length fit? Under AIT, or coding theory? Seems like it’d be coding theory, since it relies on your current coding to describe the encoding for the data you’re compressing. But everyone seems to refer to MML as the computable version of Kolmogorov Complexity; and it really does seem fairly equivalent.
It seems to me that KC/SI/AIT explicitly presents the choice of UTM as an unsolved problem, while coding theory and MML implicitly assume that you use your current coding; and that that is the part that gets people into trouble when comparing Zeus and Maxwell. Is that it?
I think more or less yes, if I understand it. And more seriously, AIT is in some ways meant not to be practical, the interesting results require setting things up so that technically the work is pushed to the “within a constant” part. Which is divorced from praxis. Practical MML intuitions don’t carry over into such extreme domains. That said, the same core intuitions inspire them; there are just other intuitions that emerge depending on what context you’re working in or mathematizing. But this is still conjecture, ’cuz I personally haven’t actually used MML on any project, even if I’m read some results.