We show how to predict the basic word-order facts of a novel language, and even obtain approximate syntactic parses, given only a corpus of part-of-speech (POS) sequences. We are motivated by the longstanding challenge of determining the structure of a language from its superficial features. While this is usually regarded as an unsupervised learning problem, there are good reasons that generic unsupervised learners are not up to the challenge. We do much better with a supervised approach where we train a system -- a kind of language acquisition device -- to predict how linguists will annotate a language. Our system uses a neural network to extract predictions from a large collection of numerical measurements. We train it on a mixture of real treebanks and synthetic treebanks obtained by systematically permuting the real trees, which we can motivate as sampling from an approximate prior over possible human languages.