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 PRT where PR denotes the ending progress made in the generation with which we [pg 111] agree to start our reckoning, R denotes the ratio increase, and T denotes the number of generations after the chosen “start.” The quantity, PRT 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.
Nature is the source of all energy. Plants, the lowest form of life, have a definite rôle to perform in the economy of nature. Their function is the forming of albuminoids and other substances for higher purposes. All of their nitrates are high-explosives, or low explosives, but explosives anyway. They are powerful sources of some new energy. Animal life uses these “explosives” as food and is correspondingly more dynamic, but in animal life time does not play the rôle it plays in human life. Animals are limited by death permanently. If animals make any progress from generation to generation, it is so small as to be negligible. A beaver, for example, is a remarkable builder of dams, but he does not progress in the way of inventions or further development. A beaver dam is always a beaver dam.
Finally humanity, the highest known class of life, has time-binding capacity as its characteristic, its discriminant, its peculiar and definitive mark. It is an unrealized fact that in this higher class of [pg 112] life, the law of organic growth develops into the law of energy-growth—the mind—the time-binding energy—an increasing exponential function of time. That fact is of basic importance for the science and art of Human Engineering. In mechanics we have the well-known formula
(1) Work ÷ Time = Power.
We have seen that, in accordance with the law of geometric progression, PRT represents the progress made—the work done—in the Tth generation (T being counted from some generation taken as starting point of reckoning); this progress, achievement, or work, being done in one generation, we have by (1)
(2) ( Work = PRT ) / ( Time = 1) = Power,
that is, PRT = Power; this means that the number PRT, which measures the work done in a given generation, is also the measure of the power that does the work. Now, the total work, W, done in the T generations is
(3) W = PR1 + PR2 + PR3 + ... + PRT;
that is,
(4) W = R ÷ (R-1) × (PRT - P)