directed to the design of the old Colonial bed-spread shown in Figure
3. Adjacent to this, in the upper right hand corner, is a magic
square of four. That is, all of the columns of figures of which it is
composed: vertical, horizontal and diagonal add to the same sum: 34.
An analysis of this square reveals the fact that it is made up of
the figures of two different orders of counting: the ordinary order,
beginning at the left hand upper corner and reading across and down in
the usual way, and the reverse-ordinary, beginning at the lower right
hand corner and reading across and up. The figures in the four central
cells and in the four outside corner cells are discovered to belong
in the first category, and the remaining figures in the second. Now
if the ordinary order cells be represented by white, and the reverse
ordinary by black, just such a pattern has been created as forms the
decorative motif of the quilt.

It may be claimed that these two examples of a relation between
ornament and mathematics are accidental and therefore prove nothing,
but they at least furnish a clue which the artist would be foolish not
to follow up. Let him attack his problem this time directly, and
see if number may not be made to yield the thing he seeks: namely,
space-rhythms which are beautiful and new.

We know that there is a beauty inherent in _order_, that necessity of
one sort or another is the parent of beauty. Beauty in architecture
is largely the result of structural necessity; beauty in ornament
may spring from a necessity which is numerical. It is clear that the
arrangement of numbers in a magic square is necessitous--they must be
placed in a certain way in order that the summation of every column
shall be the same. The problem then becomes to make that necessity
reveal itself to the eye. Now most magic squares contain a _magic