This document discusses ideas for studying information diffusion on online social networks like Twitter. It provides background on lexical diffusion and how words can change pronunciation gradually over time. Prior research has found that high frequency words tend to change faster than low frequency words. The document also discusses how social networks can influence information spread, with central and well-connected users playing an important role. Methods are proposed for collecting Twitter data through its public API and crawling the network in a constrained way to study topics that spread through hashtags and retweets.