This dissertation emerges out of an effort to understand the supra-individual aspects of attitudes and tastes, and especially those political attitudes that make up "public opinion." Various theoretical accounts conceive of large-scale attitude systems in terms of fields, shared schemas, cultural logics, or partisan ideologies. Though diverse, these accounts all depict attitudes as structural phenomena, defined by patterns of relations between cultural, cognitive, or social elements. In the three substantive chapters, I draw on network analysis, statistics, information theory, and computer science to create original methods for such structural analyses. I use them to provide new insights on culture as both individual cognition and macro-scale social organization. The first project examines networks of political attitudes. I find that, across subgroups, attitudes either follow the dominant liberal-conservative logic, or lack systemic organization. In the second project, I clarify and extend existing theories of cultural schemas to develop a greatly improved approach to detecting them in surveys. In the final project, I approach political attitudes as a field of competition. If public opinion is a debate between competing ideological camps, do the camps at least agree on which issues they are debating? My analyses of the skill with which individuals at different positions in the opinion space report their attitudes suggests that no such agreement exists.