831.00 Sheet of Paper as a System

831.01 Our steel dividers have sharp, straight-edged legs, each tapering into sharp points. We can call these dividers “scissors.” Scissors are dividers of either linear or angular, i.e. circular, differentiation. We can even make our explorations with some superficial accommodation of the Greeks’ propensity for using a plane. For instance, we can take a finite piece of paper, remembering (operationally), however, that it has “thickness” and “edges,” which are in fact small area faces. If it is a rectilinear sheet of typewriter paper, we recognize that it has four minor faces and two major faces. The major faces we call “this side” and “the other side,” but we must go operationally further in our consideration of what the “piece of paper” is. Looking at its edges with a magnifying glass, we find that those surfaces round over rather brokenly, like the shoulders of a hillside leading to a plateau. We find the piece of paper to be fundamentally the same kind of entity as that which we have watched the baker make as he concocts, stirs, and thickens his piecrust dough, which, after powdering with flour, can be formed into a spherical mass and set upon a flour-powdered surface to be progressively rolled into a thick sheet that may be cut into separate increments of the same approximate dimensions as the “sheet” of typewriter paper.