Page:Nature and Life (1934).pdf/47

 region at this durationless instant. This occupation of space is the final real fact, without reference to any other instant, or to any other piece of matter, or to any other region of space. Now, assuming this Newtonian doctrine, we ask — What becomes of velocity at an instant? Again we ask — What becomes of momentum at an instant? These notions are essential for Newtonian physics, and yet they are without any meaning for it. Velocity and momentum require the concept that the state of things at other times and other places enters into the essential character of the material occupancy of space at any selected instant. But the Newtonian concept allows for no such modification of the relation of occupancy. Thus, the cosmological scheme is inherently inconsistent. The mathematical subtleties of the differential calculus afford no help for the removal of this difficulty. We can, indeed, phrase the point at issue in mathematical terms. The