When man essays the rôle of creator he cannot do otherwise than
follow similar sequences: it is easy to discern dimensional
progression in the products of man's ingenuity and skill. Consider,
for example, the evolution of a building from its inception to its
completion. It exists first of all in the mind of the architect, and
there it is indubitably higher-spatial, for he can interpenetrate
and examine every part, and he can consider it all at once, viewing
it simultaneously from without and from within, just as one would be
able to do in a space of four dimensions. He begins to give his idea
physical embodiment by making with a pencil-_point, lines_ on a
_plane_ (a piece of paper), the third dimension being represented
by means of the other two. Next (if he is careful and wise) he makes
a three-dimensional model. From the architect's drawings the engineer
establishes his points, lays out his angles, and runs his lines upon
the site itself. The mason follows, and with his footing courses
makes ponderable and permanent the lines of the engineer. These
lines become in due course walls--vertical planes. Floors and
roofs--horizontal planes--follow, until some portion of
three-dimensional space has been enclosed.
Substantially the same sequence holds, whatever the kind of building
or the character of the construction--whether a steel-framed
skyscraper or a wooden shanty. A line system, represented by columns
and girders in the one case, and by studs and rafters in the other,
becomes, by overlay or interposition, a system of planes, so
assembled and correlated as to define a solid.
With nearly everything of man's creating--be it a bureau or a
battleship--the process is as above described. First, a pattern to
scale; next, an actual linear framework; then planes defining a solid.
Consider almost any of the industries practiced throughout the ages:
they may be conceived of thus in terms of dimensions; for example,
those ancient ones of weaving and basket making. _Lines_ (threads in
the one case, rushes in the other) are wrought into _planes_ to
clothe a body or to contain a burden. Or think, if you choose, of
the modern industry of book-making, wherein types are assembled,
impressed upon sheets of paper, and these bound into volumes--
_points, lines, planes, solids_. The book in turn becomes the unit
of another dimensional order, in the library whose serried shelves
form lines, which, combined into planes, define the lateral limits
of the room.