[Illustration:  Figure 1.]

Suppose that we determine to divest ourselves of these and other precious inheritances, not because they have lost their beauty and meaning, but rather on account of their manifold associations with a past which the war makes suddenly more remote than slow centuries have done; suppose that we determine to supplant these symbols with others no less charged with beauty and meaning, but more directly drawn from the inexhaustible well of mathematical truth—­how shall we set to work?

We need not set to work, because we have done that already, we are always doing it, unknowingly, and without knowing the reason why.  All ornamentalists are subjective mathematicians—­an amazing statement, perhaps, but one susceptible of confirmation in countless amusing ways, of which two will be shown.

[Illustration:  Figure 2.]

Consider first your calendar—­your calendar whose commonplace face, having yielded you information as to pay day, due day, and holiday, you obliterate at the end of each month without a qualm, oblivious to the fact that were your interests less sordid and personal it would speak to you of that order which pervades the universe; would make you realize something of the music of the spheres.  For on that familiar checkerboard of the days are numerical arrangements which are mysterious, “magical”; each separate number is as a spider at the center of an amazing mathematical web.  That is to say, every number is discovered to be half of the sum of the pairs of numbers which surround it, vertically, horizontally, and diagonally:  all of the pairs add to the same sum, and the central number divides this sum by two.  A graphic indication of this fact on the calendar face by means of a system of intersecting lines yields that form of classic grille dear to the heart of every tyro draughtsman. [Figure 2.] Here is an evident relation between mathematical fact and ornamental mode, whether the result of accident, or by reason of some subconscious connection between the creative and the reasoning part of the mind.

To show, by means of an example other than this acrostic of the days, how the pattern-making instinct follows unconsciously in the groove traced out for it by mathematics, the attention of the reader is 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.