ve nature, the
defining mark, of man; we know that the mental power, the time-binding
capacity, of our pre-historic ancestors, was the same in _kind_ as our
own, if not in degree; we know that it is natural for this capacity, the
highest known agency of Nature, to produce ideas, inventions, insights,
doctrines, knowledge and other forms of wealth; we know that progress in
what we call civilization, which is nothing but progress in the production
and right use of material and spiritual wealth, has been possible and
actual simply and solely because the products of time-binding work not
only _survive_, but naturally tend to propagate their kind--ideas begetting
ideas, inventions leading to other inventions, knowledge breeding
knowledge; we therefore, know that the amount of progress which a single
generation can make, if it have an adequate supply of raw material and be
unhampered by hostile circumstances, depends, not only upon its native
capacity for binding time, but also--and this is of the utmost
importance--upon the total progress made by preceding generations--upon the
inherited fruit, that is, of the time-binding toil of the dead;
accordingly we know that the amount of progress a single generation can
thus make is what mathematicians call an increasing function of time, and
not only an increasing function but an increasing _exponential_ function
of time--a function like _PR__T_, as already explained; we know, too, that
the _total_ progress which _T_ successive generations can thus make is:

_R/R-1_(_PR__T-P_)

which is also an increasing exponential function of time; we know from the
differential calculus that these functions--which represent natural laws,
laws of human _nature_, laws of the time-binding energies of man--are very
remarkable functions--not only do they increase with time but their _rates_
of increase are also exponential functions of time and so the rates of
increase themselves increase at rates which are, again, exponential
functions, and so on and on without limit; that, I say, is a marvelous
fact, and it is for us a fact of immeasurable significance; for it means
that the time-binding power of man is such that, if it be allowed to
operate naturally, civilization--the production and right use of material
and spiritual wealth--will not only grow towards infinity (as
mathematicians say), but will thus grow with a _swiftness_ which is not
constant but which itself grows towards infinity with a swiftn