Paper short abstract:

Geometries of anthropology elucidate how things and the world appear to living beings. This paper overviews four geometries of anthropology and includes a case study framed by Steinbock's analysis of the lifeworld in terms of two transcendental modalities: world-as-horizon and earth-as-ground

Paper long abstract:

Geometries of anthropology support investigations of how things and the world appear to living beings. They inquire into how surfaces, lines and points emerge and grow in the course of working with materials, travelling through and inhabiting places, crossing boundaries, and practically measuring the extent of things. Such geometries, which are both relational and continuous, invite us to interweave core geometrical ideas, such as of parallelism, horizon, surface, infinitude and curvature, with lived experiences, affects and traditions. I briefly overview four geometries of anthropology: 1) Euclid's Optics, which is the oldest surviving text about the mathematics of optics, 2) Projective Geometry, the study of projective transformations between surfaces, 3) Optical Flow, an approach pioneered by Gibson, focused on apparent flows in the visual field, and 4) Differential Geometry, as it pertains to local studies of surfaces and curvature. I shall outline some major lines of research that bring together geometries and anthropology, by way of an exploratory case study focusing specifically on philosophies and experiences of the horizon. The study is framed by Steinbock's (1995) interpretation of the lifeworld as encompassing two transcendental modalities: world-as-horizon and earth-as-ground. I draw on video-notes compiled during activities with university students in a course on projective geometry. These notes document students' experiences and reflections in projecting large curves traced with a rope on a football field. The behavior of the projected curves, as they approach and depart from the horizon, prompts students to cultivate new intuitions on the nature of horizon and projective transformations.