seen that man is a natural being, a part of nature
literally, then it will be seen that the laws of human nature--the only
possible rules for ethical conduct--are no more _super_natural and no more
_man_-made than is the law of gravitation, for example, or any other
natural law.

It is no cause for wonder that mathematical thinking should lead to such a
result; for Man is a _natural_ being, man's mind is a _natural agency_,
and the results of rigorous thinking, far from being artificial fictions,
are natural facts--natural revelations of natural law.

I hope I have not given the impression, by repeated allusion to
mathematical science, that this book is to be in any technical sense a
mathematical treatise. I have merely wished to indicate that the task is
conceived and undertaken in the mathematical spirit, which must be the
guiding spirit of Human Engineering; for no thought, if it be
non-mathematical in spirit, can be trusted, and, although mathematicians
sometimes make mistakes, the spirit of mathematics is always right and
always sound.

Whilst I do not intend to trouble the reader with any highly technical
mathematical arguments, there are a few simple mathematical considerations
which anyone of fair education can understand, which are of exceedingly
great importance for our purpose, and to which, therefore, I ask the
reader's best attention. One of the ideas is that of an _arithmetical
progression_; another one is that of a _geometrical progression_. Neither
of them involves anything more difficult than the most ordinary arithmetic
of the secondary school or the counting house, but it will be seen that
they throw a flood of light upon many of the most important human
concerns.

Because we are human beings we are all of us interested in what we call
progress--progress in law, in government, in jurisprudence, in ethics, in
philosophy, in the natural sciences, in economics, in the fine arts, in
the practical arts, in the production and distribution of wealth, in all
the affairs affecting the welfare of mankind. It is a fact that all these
great matters are interdependent and interlocking; it is therefore a fact
of the utmost importance that progress in each of the cardinal matters
must keep abreast of progress in the other cardinal matters in order to
keep a just equilibrium, a proper balance, and so to maintain the
integrity and continued prosperity of the whole complex body of our social
life; it is a fact, a f