EXCERPT Chomsky and others have rightly made a big deal of the fact that a good number of the sentences produced by the speakers of any given language are unique, as in, they’ve never been spoken before in the history of that language. I’d wager that when you take into account writing, this proportion becomes even larger, just because we tend to write longer sentences. It’s all about how big the possibility space is. Let’s take an extreme example: What are the chances that, if you took a number of Spanish words at random, the same length as Don Quixote, you would somehow recreate the novel? As Pierre Menard understood, the chances are infinitesimally small unless one can discover some principle through which to generate it, something better than mere randomness, something like Cervantes’s original inspiration. Some problems are like finding a rule, and some problems are like following a rule. Some are unavoidably confronted with a space of possibility and some can collapse this space into necessity. It’s immeasurably harder to discover a novel mathematical proof than it is to check one. It’s far harder to write a great novel than it is to read one, and far harder to compose a brilliant song than to enjoy one. In case it looks like this is always an asymmetry between production and consumption, here’s something that seems to go in the opposite direction: it’s far harder to decrypt something than to encrypt it. But wait, this only works if you haven’t got the encryption key, which means you have to find the rule! The lesson is that in asymmetric interactions the sender and receiver can play different roles.…