There is a certain thesis that is loosely related to the view that nature is finite downward, namely, that an explanation of the universe is possible in which we start with small scale things, and explain large scale phenomena in terms of their small scale constituents, the thesis, in other words, that all the properties of the large are contained in the properties of the small and that the large may be constructed out of the small. Some such thesis as this seems implied in the general attitude of many physicists. Let us examine the physical basis for this. To maintain this thesis would demand that aggregates of things never acquire properties in virtue of their numbers which they do not already possess as individuals. Is this true? Consider, for example, the two-dimensional geometry on the surface of a sphere. This is non-Euclidean. Is the geometry of the individual elements of the surface of the sphere non-Euclidean, or do they acquire this property in changing scale? Is the kinetic energy of a number of electrons all moving together in such a way as to constitute an electric current the sum of the kinetic energies of the individual electrons, or is there an additional term? Is the mass of an electron the sum of the masses of its elements? A mathematical consideration is suggestive here. Those properties of a system which can be described in terms of linear differential equations have the property of additivity; the effect of a number of elements is the sum of the effects separately, and no new properties appear in the aggregate which were not present in the individual elements. But if there are combination terms (as in the electrical energy, which contains the square of the field), then the sum is more than (or different from) its parts, and new effects may appear in the aggregate. Now of course the linear equation is of enormous importance in describing nature, but many examples of systems with other types of equation can be found, as that above for electromagnetic mass. In expecting to find in nature such non-additive effects, we need not commit ourselves at all to the view that nature is governed by differential equations, but by analogy may expect similar effects if difference equations, for instance, should prove to be fundamental, or even something beyond present mathematical formulation.