Formal plane geometry has been contrasted with an unformalized and quite unfamiliar geometry of surfaces. But the latter is more appropriate for describing the environment in which we perceive and behave, because a surface can be seen whereas a plane cannot. The differences between a plane and a surface have been pointed out.
A tentative list of the main features of surface layout has been proposed. The definitions are subject to revision, but terms of this sort are needed in ecology, architecture, design, the biology of behavior, and the social sciences instead of the planes, forms, lines, and points of geometry. The term object, especially, has been defined so as to give it a strictly limited application unlike the general meaning it has in philosophy and psychology.
The fundamental ways in which surfaces are laid out have an intrinsic meaning for behavior unlike the abstract, formal, intellectual concepts of mathematical space.