New Foundations for Physical Geometry: The Theory of Linear Structures

The volume under review is the first of a projected pair in which the author will present a new approach to the geometry of physical space or spacetime. The present volume contains only the purely mathematical apparatus to be applied to physics in the sequel. This being so, to a large extent the evaluation of the book must await that sequel. The introduction announces the theses of the two volumes: (1) The most fundamental geometrical structure that organizes physical points into a space is the [straight or curved] line. (2) What endows spacetime with its geometry is time. How wide a range of approaches to physics can be accommodated from this perspective, and how comfortably, and how profitably? We will have to wait for the second volume to find out the scope and limits of the project. Obviously, failure of the physical application would tend to reduce the mathematical apparatus to the status of a curiosity, or at any rate something of more mathematical than philosophical interest. Since I am writing under space limitations, for a philosophical and not a mathematical journal, I will not attempt to describe what the project looks like as pure mathematics, independent of the applications not yet shown. I do promise that readers of a