adily in mind.

Energy, we have noted, is the capacity to do work. In human economy work
may be (1) _useful_ or (2) _neutral_ or (3) _harmful_. These words have no
significance except in human economy. The energy of the human intellect is
a time-binding energy, for it is able to direct, to use, to transform
other energies. This time-binding energy is of higher rank--of higher
dimensionality--than the other natural energies which it directs, controls,
uses, and transforms. This higher energy--which is commonly called the
mental or spiritual power of man--_is_ time-binding because it makes past
achievements live in the present and present activities in time-to-come.
It is an energy that initiates; it is an energy that creates; it is an
energy that can understand the past and foretell the future--it is both
historian and prophet; it is an energy that loads _abstract_ time--the
vehicle of events--with an ever-increasing burden of intellectual
achievements, of spiritual wealth, destined for the civilization of
posterity. And what is the natural law of the increase? What is the
natural law of human advancements in all great matters of human concern?

The question is of utmost importance both theoretically and practically,
for the law--whatever it be--is a _natural_ law--a law of human nature--a law
of the time-binding energy of man. What _is_ the law? We have already
noted the law of arithmetical progression and the law of geometric
progression; we have seen the immense difference between them; and we have
seen that the natural law of human progress in each and every cardinal
matter is a law like that of a rapidly increasing geometric progression.
In other words, the natural law of human progress--the natural law of
amelioration in human affairs--the fundamental law of human nature--the
basic law of the time-binding energy peculiar to man--is a Logarithmic
law--a law of logarithmic increase. I beg the reader not to let the term
bewilder him but to make it his own. It is easy to understand; and its
significance is mighty and everlasting. Even its mathematical formulation
can be understood by boys and girls. Let us see how the formulation looks.

Suppose _PR_ to denote the amount of progress made in some important field
by a given generation--which we may call the "first" generation; where _R_
denotes the common ratio--the ratio of improvement--that is, the number by
which the progress of one generation must be multiplied to gi