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.

Signal relationships are (usually) symmetric: if knowledge of X tells you about Y, then knowledge of Y tells you about X.

Running this simulation over many time steps, Lilian Weng of OSoMe found that as agents' attention became increasingly limited, the propagation of memes came to reflect the power-law distribution of actual social media: the probability that a meme would be shared a given number of times was roughly an inverse power of that number. For example, the likelihood of a meme being shared three times was approximately nine times less than that of its being shared once.

Special Complexity Zoo Exhibit: Classes of Quantum States and Probability Distributions 24 classes and counting! A whole new phylum of the Complexity kingdom has recently been identified. This phylum consists of classes, not of problems or languages, but of quantum states and probability distributions. Well, actually, infinite families of states and distributions, one for each number of bits n. Admittedly, computer scientists have been talking about the complexity of sampling from probability distributions for years, but they haven't tended to organize those distributions into classes designated by inscrutable sequences of capital letters. This needs to change.