[Illustration 75]

It will be seen that this discovery of numerical conjunctions consists merely of resolving numbers into their prime factors, and that a conjunctive number is a common multiple; but by naming it so, to dismiss the entire subject as known and exhausted, is to miss a sense of the wonder, beauty and rhythm of it all:  a mental impression analogous to that made upon the eye by the swift-glancing balls of a 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 expression in the Tuscan, the Doric, and the Ionic orders according to Vignole, for in