If cross-cultural researchers hope to contribute to cultural evolutionary theory, methods must be developed to describe and explain cultural processes. The distinction made by Boas between historical and comparative methods limited scholarly interest in the analysis of patterned historical change. Numerous techniques have been developed to draw diachronic inferences from synchronic ethnographic data, with varying degrees of success. The use of archaeological and historical data to draw diachronic inferences similarly has had mixed results, but requires fewer assumptions and allows a more direct comparison of cultural change. Shifting the unit of analysis from the culture to the event allows events to be compared to one another. A case study from the evolution of numerical notation systems shows the potential of rigorous diachronic methodologies to complement synchronic ones. While synchronic analysis is highly useful for studying correlations between traits, diachronic analysis is far better for analyzing processes of change.