The potential of social media to give insight into the dynamic evolution of public conversations, and into their reactive and constitutive role in political activities, has to date been underdeveloped. While topic modeling can give static insight into the structure of a conversation, and keyword volume tracking can show how engagement with a specific idea varies over time, there is need for a method of analysis able to understand how conversations about societal values evolve and react to events in the world by incorporating new ideas and relating them to existing themes. In this article, we propose a method for analyzing social media messages that formalizes the structure of public conversations and allows the sociologist to study the evolution of public discourse in a rigorous, replicable, and data-driven fashion. This approach may be useful to those studying the social construction of meaning, the origins of factionalism and internecine conflict, or boundary-setting and group-identification exercises and has potential implications.