The mind discerns geometric designs

The mind discerns geometric designs and principles of spatial organization in the environment. For example, Dakota Indians find evidence of circular forms in nature nearly everywhere, from the shape of birds' nests to the course of the stars. In contrast, the Pueblo Indians of the American South-west tend to see spaces of rectangular geometry. These are examples of the construed space, which depends on the power of the mind to extrapolate far beyond the sense data. Such spaces lie at the conceptual end of the experiential continuum. Three principal types, with large areas of overlap, exist-the mythical, the pragmatic, and the abstract or theoretical. Mythical space is a conceptual schema, but it is also pragmatic space in the sense that within the schema a large number of practical activities, such as the planting and harvesting of crops, are ordered. A difference between mythical and pragmatic space is that the latter is defined by a more limited set of economic activities. The recognition of pragmatic space, such as belts of poor and rich soil, is of course an intellectual achievement. When an ingenious person tries to describe the soil pattern cartographically, by means of symbols, a further move toward the conceptual mode occurs. In the Western world systems of geometry—that is, highly abstract spaces—have been created out of primal spatial experiences. Thus sensorimotor and tactile experiences would seem to lie at the root of Euclid's theorems concerning shape congruence and the parallelism of distant lines; and visual perception is the basis for projective geometry.