Number is the within of all things—­the “first form of Brahman.”  It is the measure of time and space; it lurks in the heart-beat and is blazoned upon the starred canopy of night.  Substance, in a state of vibration, in other words conditioned by number, ceaselessly undergoes the myriad transmutations which produce phenomenal life.  Elements separate and combine chemically according to numerical ratios:  “Moon, plant, gas, crystal, are concrete geometry and number.”  By the Pythagoreans and by the ancient Egyptians sex was attributed to numbers, odd numbers being conceived of as masculine or generating, and even numbers as feminine or parturitive, on account of their infinite divisibility.  Harmonious combinations were those involving the marriage of a masculine and a feminine—­an odd and an even—­number.

[Illustration 72:  A GRAPHIC SYSTEM OF NOTATION]

Numbers progress from unity to infinity, and return again to unity as the soul, defined by Pythagoras as a self-moving number, goes forth from, and returns to God.  These two acts, one of projection and the other of recall; these two forces, centrifugal and centripetal, are symbolized in the operations of addition and subtraction.  Within them is embraced the whole of computation; but because every number, every aggregation of units, is also a new unit capable of being added or subtracted, there are also the operations of multiplication and division, which consists in one case of the addition of several equal numbers together, and in the other, of the subtraction of several equal numbers from a greater until that is exhausted.  In order to think correctly it is necessary to consider the whole of numeration, computation, and all mathematical processes whatsoever as the division of the unit into its component parts and the establishment of relations between these parts.

[Illustration 73]

[Illustration 74]

The progression and retrogression of numbers in groups expressed by the multiplication table gives rise to what may be termed “numerical conjunctions.”  These are analogous to astronomical conjunctions:  the planets, revolving around the sun at different rates of speed, and in widely separated orbits, at certain times come into line with one another and with the sun.  They are then said to be in conjunction.  Similarly, numbers, advancing toward infinity singly and in groups (expressed by the multiplication table), at certain stages of their progression come into relation with one another.  For example, an important conjunction occurs in 12, for of a series of twos it is the sixth, of threes the fourth, of fours the third, and of sixes the second.  It stands to 8 in the ratio of 3:2, and to 9, of 4:3.  It is related to 7 through being the product of 3 and 4, of which numbers 7 is the sum.  The numbers 11 and 13 are not conjunctive; 14 is so in the series of twos, and sevens; 15 is so in the series of fives and threes.  The next conjunction after 12, of 3 and 4 and their first multiples, is in 24, and the next following is in 36, which numbers are respectively the two and three of a series of twelves, each end being but a new beginning.