length of an arc, and all that need be done is to inscribe in the arc a sequence of rectilinear contours of an increasing number of sides. When these contours approach a limit, the length of the arc becomes the limit of this sequence. The older method of determining volumes by liquid displacement is thus translated into abstract visual terms by calculus. The principles regarding the concept of length apply also to notions of areas, volumes, masses, moments, pressures, forces, stresses and strains, velocities and accelerations. The miracle-maker, the sheer function of the infinitely fragmented and repeatable, became the means of making visually flat, straight, and uniform all that was nonvisual: the skew, the curved, and the bumpy. In the same way, the phonetic alphabet had, centuries before, invaded the discontinuous cultures of the barbarians, and translated their