"Before passing on to the study of the symbol itself it is essential to understand certain aspects of the teaching which makes use of this symbol, as well as the relation of this teaching to other systems which make use of symbolical methods for the transmission of knowledge.
"In order to understand the interrelation of these teachings it must always be remembered that the ways which lead to the cognition of unity approach it like the radii of a circle moving towards the center; the closer they come to the center, the closer they approach one another.
"As a result of this the theoretical statements which form the basis of one line can sometimes be explained from the point of view of statements of another line and vice versa. For this reason it is sometimes possible to form a certain intermediate line between two adjacent lines. But in the absence of a complete knowledge and understanding of the fundamental lines, such intermediate ways may easily lead to a mixing of lines, to confusion and error.
"Of the principal lines, more or less known, four can be named:
1) The Hebraic
2) The Egyptian
3) The Persian
4) The Hindu
"Moreover of the last we know only its philosophy, and of the first three, parts of their theory.
"In addition to these there are two lines known in Europe, namely theosophy and so-called Western occultism, which have resulted from a mixture of the fundamental lines. Both lines bear in themselves grains of truth, but neither of them possesses full knowledge and therefore attempts to bring them to practical realization give only negative results.
"The teaching whose theory is here being set out is completely self-supporting and independent of other lines and it has been completely unknown up to the present time. Like other lines it makes use of the symbolical method and one of its principal symbols is the figure which has been mentioned, that is, the circle divided into nine parts:
"This symbol takes the following form:
| Fig. 44 |
"The circle is divided into nine equal parts. Six points are connected by a figure which is symmetrical in relation to a diameter passing through the uppermost point of the divisions of the circumference. Further, the uppermost point of the divisions is the apex of an equilateral triangle linking together the points of the divisions which do not enter into the construction of the original complicated figure.
"This symbol cannot be met with anywhere in the study of 'occultism,' either in books or in oral transmission. It was given such significance by those who knew, that they considered it necessary to keep the knowledge of it secret.
"Only some hints and partial representations of it can be met with in literature.1 Thus it is possible to meet with a drawing of it like this:
| Fig. 46 |
"The symbol which takes the form of a circle divided into nine parts with lines connecting them together expresses the law of seven in its union with the law of three.
"The octave possesses seven tones and the eighth is a repetition of the
1 In the book Etude sur les origines de la nature du Zohar by S. Karppe, Paris, 1901, pp. 200-201, there is a drawing of a circle divided into nine parts:
with the following description of this circle:
"If we multiply 9X9 the result is shown in the number 8 on the left side and the number 1 on the right side; in the same way 9X8 gives the product shown in number 7 on the left and in number 2 on the right; exactly in the same way with 9X6. Beginning with 9X5 the order becomes reversed, that is, the number representing the units takes the left side and the number representing the tens takes the right."
first. Together with the two 'additional shocks' which fill the 'intervals' mi-fa and si- do, there are nine elements.
"The complete construction of this symbol which connects it with a complete expression of the law of octaves is more complicated than the construction shown. But even this construction shows the inner laws of one octave and it points out a method of cognizing the essential nature of a thing examined in itself.
| Fig. 47 |
| 5 |
| 9 |
| 7 |
| 4 |
| 2 |
"The isolated existence of a thing or phenomenon under examination is the closed circle of an eternally returning and uninterruptedly flowing process. The circle symbolizes this process. The separate points in the division of the circumference symbolize the steps of the process. The symbol as a whole is do, that is, something with an orderly and complete existence. It is a circle—a completed cycle. It is the zero of our decimal system; in its inscription it represents a closed cycle. It contains within itself everything necessary for its own existence. It is isolated from its surroundings. The succession of stages in the process must be connected with the succession of the remaining numbers from 1 to 9. The presence of the ninth step filling up the 'interval' si-do, completes the cycle, that is, it closes the circle, which begins anew at this point. The apex of the triangle closes the duality of its base, making possible the manifold forms of its manifestation in the most diverse triangles, in the same way as the point of the apex of the triangle multiplies itself infinitely in the line of its base. Therefore every beginning and completion of the cycle is situated in the apex of the triangle, in the point where the beginning and the end merge, where the circle is closed, and which sounds in the endlessly flowing cycle as the two do's in the octave. But it is the ninth step that closes and again begins a cycle. Therefore in the upper point of the triangle corresponding to do stands the number 9, and among the remaining points are disposed the numbers 1 to 8.
"Passing on to the examination of the complicated figure inside the circle we should understand the laws of its construction. The laws of unity are reflected in all phenomena. The decimal system is constructed on the basis of the same laws. Taking a unit as one note containing within itself a whole octave we must divide this unit into seven unequal parts in order to arrive at the seven notes of this octave. But in the graphic representation the inequality of the parts is not taken into account and for the construction of the diagram there is taken first a seventh part, then two-sevenths, then three-sevenths, four-sevenths, five-sevenths, six-sevenths, and seven-sevenths. Calculating these parts in decimals we get:
1/7=0.142857 . . .
2/7=0.285714 . . .
3/7=0.428571 . . .
4/7=0.571428 . . .
5/7=0.714285 . . .
6/7=0.857142 . . .
7/7=0.999999 . . .
"In examining the series of periodic decimals obtained we at once see that in all except the last the periods consist of exactly the same six digits which run in a definite sequence, so that, knowing the first digit of the period, it is possible to reconstruct the whole period in full.
"If we now place on the circumference all the nine numbers from 1 to 9 and connect those numbers which are included in the period by straight lines in the same sequence in which the numbers stand in the period, according to which number we start from, we shall obtain the figure found inside the circle. The numbers 3, 6, and 9 are not included in the period. They form the separate triangle—the free trinity of the symbol.