Suppose that we were asked to arrange the followingin two categories—distance, mass, electric force, entropy, beauty, melody.I think there are the strongest grounds for placingentropy alongside beauty and melody and not with thefirst three.
Syndication link: https://boffosocko.com/2013/09/26/entropy-beauty-melody/
What it means to be a member of this or that class is a complex, interpretative matter; but tracking how many times a person has been to the opera is not. You can count the latter, and (the bargain goes) facts about those numbers may illuminate facts about the deeper concepts. For example, counting opera-going might be used to measure how immigrants move up the social class ladder across generations. Crucially, operationalization is not definition. A good operationalization does not redefine the concept of interest (it does not say "to be a member of the Russian intelligentsia is just to have gone to the opera at least once"). Rather, it makes an argument for why the concept, as best understood, may lead to certain measurable consequences, and why those measurements might provide a signal of the underlying concept.
This is a good example of the fuzzy sorts of boundaries created by adding probabilities to individuals and putting them into (equivalence) classes. They can provide distributions of likelihoods.
This expands on: https://hypothes.is/a/3FVi6JtXEe2Xwp_BIaCv5g
Signal relationships are (usually) symmetric: if knowledge of X tells you about Y, then knowledge of Y tells you about X.
Reframing signal relationships into probability spaces may mean that signal relationships are symmetric.
How far can this be pressed? They'll also likely be reflexive and transitive (though the probability may be smaller here) and thus make an equivalence relation.
How far can we press this idea of equivalence relations here with respect to our work? Presumably it would work to the level of providing at least good general distribution?