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
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,
_PR__T_ 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, _PR__T_ = Power; this means that the number _PR__T_, 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 = PR__1__ + PR__2__ + PR__3__ + ... + PR__T_;
that is,
(4) _W_ = _R_ ÷ (_R_-1) × (_PR_T - _P_)
It should be noticed that by (2) this expression for _W_ may also be
regarded as the sum of _T_ different powers _PR_, _PR__2_, etc., each
working during one and only one generation; if we divided this sum by _T_,
the quotient would be a power that would have to act through _T_
generations to produce _W_. The reader should not fail to notice very
carefully that the expression (4) for _W_ is an expression for the total
progress made—the total work done—the total wealth produced—in the course
of _T_ generations and he should especially note how the expression
involves the exponential function of time (_T_), namely _PR__T_.
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