juggler, the evolutions of drilling troops, or the intricate figures
of a dance; for these things are number concrete and animate in time
and space.

[Illustration 76]

The truths of number are of all truths the most interior, abstract
and difficult of apprehension, and since knowledge becomes clear and
definite to the extent that it can be made to enter the mind through
the channels of physical sense, it is well to accustom oneself to
conceiving of number graphically, by means of geometrical symbols
(Illustration 72), rather than in terms of the familiar arabic
notation which though admirable for purposes of computation, is of
too condensed and arbitrary a character to reveal the properties of
individual numbers. To state, for example, that 4 is the first square,
and 8 the first cube, conveys but a vague idea to most persons, but if
4 be represented as a square enclosing four smaller squares, and 8
as a cube containing eight smaller cubes, the idea is apprehended
immediately and without effort. The number 3 is of course the
triangle; the irregular and vital beauty of the number 5 appears
clearly in the heptalpha, or five-pointed star; the faultless symmetry
of 6, its relation to 3 and 2, and its regular division of the circle,
are portrayed in the familiar hexagram known as the Shield of David.
Seven, when represented as a compact group of circles reveals itself
as a number of singular beauty and perfection, worthy of the important
place accorded to it in all mystical philosophy (Illustration 73). It
is a curious fact that when asked to think of any number less than 10,
most persons will choose 7.

[Illustration 77]

Every form of art, though primarily a vehicle for the expression and
transmission of particular ideas and emotions, has subsidiary offices,
just as a musical tone has harmonics which render it more sweet.
Painting reveals the nature of color; music, of sound--in wood,
in brass, and in stretched strings; architecture shows forth the
qualities of light, and the strength and beauty of materials. All
of the arts, and particularly music and architecture, portray in
different manners and degrees the truths of number. Architecture does
this in two ways: esoterically as it were in the form of harmonic
proportions; and exoterically in the form of symbols which represent
numbers and groups of numbers. The fact that a series of threes and
a series of fours mutually conjoin in 12, finds an architectural
expres