Words frequently acquire new senses, but the mental process that underlies the historical emergence of these senses is often opaque. Many have suggested that word meanings develop in non-arbitrary ways, but no attempt has been made to formalize these proposals and test them against historical data at scale. We propose that word meaning extension should reflect a drive towards cognitive economy. We test this proposal by exploring a family of computational models that predict the evolution of word senses, evaluated against a large digitized lexicon that dates back 1000 years in English language history. Our findings suggest that word meanings not only extend in predictable ways, but also that they do so following an historical path that tends to minimize cognitive cost - through a process of nearest-neighbor chaining. Our work contributes a formal approach to reverse-engineering mental algorithms of the human lexicon.