(surface) will
not be 5, it will be 25; and the 25 will not be 25 linear units but 25
square or surface units. If upon this square we build a cube, this cube
will have neither 5 nor 25 for its measure; it will have 125, and this
number will not be so many units of length nor of surface but so many
solid or cubic units.

It is as plain as a pike staff that, if we confused _dimensions_ when
computing lengths and areas and volumes, we would wreck all the
architectural and engineering structures of the world, and at the same
time show ourselves stupider than block-heads.

To analyse the classes of life we have to consider two very different
kinds of phenomena: the one embraced under the collective name--Inorganic
chemistry--the other under the collective name--Organic chemistry, or the
chemistry of hydro-carbons. These divisions are made because of the
peculiar properties of the elements chiefly involved in the second class.
The properties of matter are so distributed among the elements that three
of them--Oxygen, Hydrogen, and Carbon--possess an ensemble of unique
characteristics. The number of reactions in inorganic chemistry are
relatively few, but in organic chemistry--in the chemistry of these three
elements the number of different compounds is practically unlimited. Up to
1910, we knew of more than 79 elements of which the whole number of
reactions amounted to only a few hundreds, but among the remaining three
elements--Carbon, Hydrogen and Oxygen--the reactions were known to be
practically unlimited in number and possibilities; this fact must have
very far reaching consequences. As far as energies are concerned, we have
to take them as nature reveals them to us. Here more than ever,
mathematical thinking is essential and will help enormously. The reactions
in inorganic chemistry always involve the phenomenon of heat, sometimes
light, and in some instances an unusual energy is produced called
electricity. Until now, the radioactive elements represent a group too
insufficiently known for an enlargement here upon this subject.

The organic compounds being unlimited in number and possibilities and with
their unique characteristics, represent of course, a different class of
phenomena, but being, at the same time, _chemical_ they include the basic
chemical phenomena involved in all chemical reactions, but being unique in
many other respects, they also have an infinitely vast field of unique
characteristics. Among the en