ly
hypothetical, the case supposed has always been actual and is actual
to-day on a vaster scale than ever before. My contention is that while
progress in some of the great matters of human concern has been long
proceeding in accordance with the law of a rapidly increasing geometric
progression, progress in the other matters of no less importance has
advanced only at the rate of an arithmetical progression or at best at the
rate of some geometric progression of relatively slow growth. To see it
and to understand it we have to pay the small price of a little
observation and a little meditation.

Some technological invention is made, like that of a steam engine or a
printing press, for example; or some discovery of scientific method, like
that of analytical geometry or the infinitesimal calculus; or some
discovery of natural law, like that of falling bodies or the Newtonian law
of gravitation. What happens? What is the effect upon the progress of
knowledge and invention? The effect is stimulation. Each invention leads
to new inventions and each discovery to new discoveries; invention breeds
invention, science begets science, the children of knowledge produce their
kind in larger and larger families; the process goes on from decade to
decade, from generation to generation, and the spectacle we behold is that
of advancement in scientific knowledge and technological power according
to the law and rate of a rapidly increasing geometric progression or
logarithmic function.

And now what must we say of the so-called sciences--the pseudo sciences--of
ethics and jurisprudence and economics and politics and government? For
the answer we have only to open our eyes and behold the world. By virtue
of the advancement that has long been going on with ever accelerated
logarithmic rapidity in invention, in mathematics, in physics, in
chemistry, in biology, in astronomy and in applications of them, time and
space and matter have been already conquered to such an extent that our
globe, once so seemingly vast, has virtually shrunken to the dimensions of
an ancient province; and manifold peoples of divers tongues and traditions
and customs and institutions are now constrained to live together as in a
single community. There is thus demanded a new ethical wisdom, a new legal
wisdom, a new economical wisdom, a new political wisdom, a new wisdom in
the affairs of government. For the new visions our anguished times cry
aloud but the only answer