If, for example, we look at one of those white flakes, which we get by mixing soap solution with common salt, we at first see its surface sharply outlined, but the nearer we approach to it, the more indistinct the outline becomes. The eye gradually finds it impossible to draw a tangent to a point of the surface; a straight line which, viewed superficially, seems to run tangentially, is found on closer examination to be oblique or even perpendicular to the surface. No microscope succeeds in dispelling this uncertainty. On the contrary, whenever the magnification is increased, new unevennesses seem to appear, and we never succeed in arriving at a continuous picture. Such a flake furnishes us with a model for the general conception of a function which has no differential coefficient. When, with the help of the microscope, we observe the so-called Brownian movement, which is molecular by nature, we have a parallel to the curve which has no tangent, and the observer is left only with the idea of a function devoid of a differential coefficient.... We find ourselves obliged, ultimately, to give up the hope of discovering homogeneity at all in studying matter. The farther we penetrate into its secrets, the more we see that it, matter, is spongy by nature and infinitely complex; all indications tend to show that closer examination will reveal only more discontinuities. I have not yet had an opportunity of seeing these Brownian movements under the microscope, but I must mention that Einstein has repeatedly spoken to me of them with great enthusiasm, of an objective kind, as it were, for he betrayed neither by word nor by look that he himself has done research leading to definite laws that have a recognized place in the history of molecular theory. As soon as we approach the question of molecular irregularities we recognize that, when we earlier spoke of the figure of the earth in discussing the principle of "approximation," we were still very far from the limit that may be imagined. We had set up the three stages: plane--sphere--ellipsoid of revolution, as relative geometrical steps, beyond which there must be still further geometrical approximations. If we imagine all differences of level due to mountains and valleys to be eliminated, for example, and if we suppose the earth's surface to consist entirely of liquid, undisturbed by the slightest breath of wind, even then, the ellipsoid is by no means the final description. For now the discontinuities from molecule to molecule begin, the infinite number of configurations without tangents, the macroscopic parallels of what the white flake soap solution showed as microscopically, and no conceivable geometry would ever be adequate to grasp these phenomena. We arrive at a never-to-be-completed list of functions which can never be described either in words or in symbolic expressions of analysis.