This chapter considers the relation between lines and the surfaces on which they are drawn. It explains the foundations for what might be called a comparative anthropology of the line. We have anthropological studies of visual art, of music and dance, of speech and writing, of craft and material culture, but not of the production and significance of lines. Anthropologists have a habit of insisting that there is something essentially linear about the way people in modern Western societies comprehend the passage of history, generations and time. Anthropologists do just the same when they draw genealogical diagrams of kinship and descent. Although the idea of the straight line as a connection between points that has length but no breadth goes back more than two millennia, to the geometry of Euclid, it was perhaps not until the Renaissance that it began to assume the dominance in our thinking about causes, effects and their relations that it does today.