o 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.

Nature is the source of all energy. Plants, the lowest form of life, have
a definite role 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 role 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