CHAPTER XXI Determination of Elements in the Representation of the Being
In the preceding chapter, the universalization of our geometrical symbol has been carried to the farthest limits conceivable (or rather, imaginable, since it is always a representation of the sensible order that is involved) ; and this has been done by gradually introducing into it, in a number of successive phases (or, to speak more exactly, phases successively envisaged in the course of this study), an increasirgly greater indetermination, answering to what we have called the increasingly higher powers of the indefinite, but always without departing from three-dimensional space. On arriving at this point, it will be necessary to retrace the same path, as it were, in order to determine positively all the elements in the figure, for without such determination, although the figure exists quite complete in the virtual state, it cannot be actually traced. But this determination, which at the outset was envisaged only hypothetically so to speak, and as a mere possibility, will now become real, for we shall be able to show the exact significance of each of the elements that constitute the cruciform symbol.
What will first be considered is not the universality of beings, but one single being in its totality; the vertical axis will be assumed to be given, and hence the plane passing through that axis and containing the extreme points of the modalities of each state. We shall thus get back to the vertical system whose base is the horizontal spiral considered in one single position; this system has already been described. Here, the directions of the three axes of coordinates are given, but only the vertical one is in fact determined in position; one of the two horizontal axes will lie in the vertical plane just
mentioned, and the other will naturally be perpendicular to it ; but the horizontal plane that contains these two straight lines still remains undetermined. If we were to determine this plane, we should also thereby determine the centre of the space, that is, the origin of the system of coordinates to which that space is referred, since that point is none other than the intersection of the horizontal plane of coordinates with the vertical axis. All elements in the figure would then in fact be determined, and this would allow the tracing of the three-dimensional cross which measures the extension in its totality.
It should again be recalled that, in order to constitute the system representing the total being, we have had to consider, first a horizontal spiral and then a vertical cylindrical helix. If we consider in isolation any one turn of such a helix, and if we neglect the elementary difference of level between its two ends, we may regard it as a circle described in a horizontal plane ; each turn of the horizontal spiral can similarly be taken as a circumference, if the elementary variation of the radius between its two ends is neglected. Consequently, every circumference described in a horizontal plane and having as its centre the actual centre of the plane, that is to say its intersection with the vertical axis, can conversely, and with the same approximations, be envisaged as a turn belonging at once to a vertical helix and to a horizontal spiral [^1]; it follows that the curve we are representing as a circumference is strictly speaking neither closed nor plane.
Such a circumference will represent any one unspecified modality of an equally unspecified state of the being, envisaged along the vertical axis, which will project itself horizontally in a point, the centre of the circumference. If, however, it were to be envisaged along either of the two horizontal axes, it would project itself in a segment-symmetrical in respect of the vertical axis-of a horizontal straight line which, taken with the latter, forms a two-dimensional cross, this horizontal straight line being the tracing, on the
vertical plane of projection, of the plane in which the circumference in question is situated.
As regards the significance of the circumference and the central point, the latter being the tracing of the vertical axis on a horizontal plane, it should be pointed out that according to a quite general symbolism, the centre and the circumference represent the starting-point and the termination of any one mode of manifestation. [^3] They therefore respectively correspond to what, in the Universal Order, are " essence " and " substance " (Purusha and Prakriti in the Hindu doctrine), or again Being in itself and its possibility, and for any mode of manifestation they depict the more or less particular expression of these two principles regarded as complements, active and passive in their mutual relationship. This finally justifies what was said before about the relation between the different aspects of the symbolism of the cross, for it follows that in our geometrical representation the horizontal plane (which is deemed fixed quā plane of coordinates, though it may occupy any position, being determined in direction only) will play a passive part in respect of the vertical axis, which amounts to saying that the corresponding state of the being will be realized in its integral development under the active influence of the principle that is represented by the axis [^2]; this will become more intelligible in what follows, but it was important to point it out here and now.