It seems like if I’m trying to talk about a real-world case with finite support, I’ll say something like “it’s not actually a power law—but it’s well described by one over the relevant range of values.” Meaning that I have some notion of “relevant” which is probably derived from action-relevance, or relevance to my observations, or maybe computational complexity.
If I can’t say that, then the other main option is that I care more and more as the power law gets more extreme, and then as the possibilities reach their physical limit I care most of all. But cases like this are so idiosyncratic that maybe there’s no point in trying to develop a unified language for them.
It seems like if I’m trying to talk about a real-world case with finite support, I’ll say something like “it’s not actually a power law—but it’s well described by one over the relevant range of values.” Meaning that I have some notion of “relevant” which is probably derived from action-relevance, or relevance to my observations, or maybe computational complexity.
If I can’t say that, then the other main option is that I care more and more as the power law gets more extreme, and then as the possibilities reach their physical limit I care most of all. But cases like this are so idiosyncratic that maybe there’s no point in trying to develop a unified language for them.