Words frequently acquire new senses, but the mental processthat underlies the historical emergence of these senses is oftenopaque. Many have suggested that word meanings develop innon-arbitrary ways, but no attempt has been made to formalizethese proposals and test them against historical data at scale.We propose that word meaning extension should reflect a drivetowards cognitive economy. We test this proposal by exploringa family of computational models that predict the evolution ofword senses, evaluated against a large digitized lexicon thatdates back 1000 years in English language history. Our find-ings suggest that word meanings not only extend in predictableways, but also that they do so following an historical path thattends to minimize cognitive cost - through a process of nearest-neighbor chaining. Our work contributes a formal approach toreverse-engineering mental algorithms of the human lexicon.