[Of course there is still a problem if one is to assign prior probability to N via Kolmogorov’s complexity, but it seems to me that it doesn’t make much sense to do so as such f won’t be monotonously decreasing]
I think this is the problem that most people are worried about. What’s more likely, that a big business is sold for $1,000,000,000 or that it’s sold for $945,234,567?
What is more likely, that a big business is worth $1,000,000,000 or that it is worth $945,234,567 ? ;)
We round off the numbers; the 1000 000 000 accumulates some of the values from a range nearby.
Intuitively, complexity of generating and torturing this many beings, is so enormous, that the change in Kolmogorov’s complexity due to their sheer count, is unimportant. (plus I, personally, do not count duplicates, so the N falls well short of 10^(10^30) .
edit: example, the lowest complexity way to torture really many beings could be to simply implement our universe. The number of beings here really is unlikely to be anything as obvious as 3^^^^3 , and probably can’t be generated in any other way than yourself running the universe and counting. edit: or it might well be uncountably infinite. In any case, for Kolmogorov’s complexity as a prior, the super-universe needs infinite computing power. And so do you to calculate that prior.
I think this is the problem that most people are worried about. What’s more likely, that a big business is sold for $1,000,000,000 or that it’s sold for $945,234,567?
What is more likely, that a big business is worth $1,000,000,000 or that it is worth $945,234,567 ? ;)
We round off the numbers; the 1000 000 000 accumulates some of the values from a range nearby.
Intuitively, complexity of generating and torturing this many beings, is so enormous, that the change in Kolmogorov’s complexity due to their sheer count, is unimportant. (plus I, personally, do not count duplicates, so the N falls well short of 10^(10^30) .
edit: example, the lowest complexity way to torture really many beings could be to simply implement our universe. The number of beings here really is unlikely to be anything as obvious as 3^^^^3 , and probably can’t be generated in any other way than yourself running the universe and counting. edit: or it might well be uncountably infinite. In any case, for Kolmogorov’s complexity as a prior, the super-universe needs infinite computing power. And so do you to calculate that prior.