(2) The rich are those who have possession and control of most of the _material_ wealth produced by the toil of bygone generations—wealth that is dead unless animated and transformed by the time-binding labor of the living. (3) The poor are those who have neither the knowledge possessed by the intellectuals nor the material wealth possessed by the rich and who, moreover, because nearly all their efforts, under present conditions, are limited to the struggle for mere existence, have little or no opportunity to exercise their time-binding capacity. Let us now try to ascertain the rôle of the time-binding class of life as a whole. We have by necessity, to go back to the beginning—back to the savage. We have seen what were the conditions of his work and progress; we saw that for each successful achievement he often had to wrestle with a very large number of unsuccessful achievements, and his lifetime being so limited, the total of his successful achievements was very limited, so that he was able to give to his child only a few useful objects and the sum of his experience. Generally speaking, each successor did not start his life at the point where his father started; he started somewhere near where his father left off. His father gave, say, fifty years to discover two truths in nature and succeeded in making two or three simple objects; but the son does not need to give fifty years to discover and create the same achievements, and so he has time to achieve something _new_. He thus adds his own achievements to those of his father in tools and experience; this is the mathematical equivalent of adding his parent’s years of life to his own. His mother’s work and experience are of course included—the name father and son being only used representatively. This stupendous fact is the definitive mark of humanity—the power to roll up continuously the ever-increasing achievements of generation after generation endlessly. We have seen that this time-binding power is an exponential power or function of time. Time flows on, increasing in arithmetical progression, adding generation unto generation; but the results of human energies working in time do not go on arithmetically; they pile up or roll up more and more rapidly, augmenting in accordance with the law of a more and more rapidly increasing geometric progression. The typical term of the progression is _PR__T_ where _PR_ denotes the ending progress made in the generation with which we agree to start our reckoning, _R_ denotes the ratio increase, and _T_ denotes the number of generations after the chosen “start.” The quantity, _PR__T_ of progress made in the _Tth_ generation contains _T_ as an exponent, and so the quantity, varying as time _T_ passes, is called an exponential function of the time.