CHAPTER XIX Representation of the Continuity between the Different States of the Being
In this new representation, all that has been considered so far is one horizontal plane, that is, one single state of the being. It is now necessary to depict also the continuity between all the horizontal planes, which represent the indefinite multiplicity of all the states. This continuity is geometrically obtainable in a similar manner: instead of supposing the horizontal plane as fixed in three-dimensional space (a supposition which the fact of movement makes as incapable of material realization as is the tracing of a closed curve), we need only suppose that it changes its position imperceptibly, moving parallel to itself, that is, always remaining perpendicular to the vertical axis, in such a way as to meet this axis at all its points in succession, the passage from one point to another corresponding to the completion of one of the spiral turns that we have considered. The spiral movement will here be deemed isochronous, both in order to simplify the representation as much as possible, and also in order to express the equivalence of the multiple modalities of the being in each of its states, when regarded from the viewpoint of the Universal.
For further simplicity, we may provisionally consider each of the turns as a circumference, as we did in the case of the fixed horizontal plane. Here again, the circumference will not be closed, for when the radius that describes it comes round again and superimposes itself on its original position, it will no longer be in the same horizontal plane (deemed fixed, as being parallel to the direction of one of the planes of coordinates and marking a certain definite situation on the axis perpendicular to that direction); the elementary distance
that separates the two extremities of this circumference, or rather of the curve supposed to be a circumference, will then be measured, not now on a radius issuing from the pole, but on a line parallel to the vertical axis [^1]. These extreme points do not belong to the same horizontal plane, but to two superimposed horizontal planes; they are situated on either side of the horizontal plane considered in the course of its intermediary travel between these two positions (which corresponds to the development of the state represented by that plane), because they mark the continuity of each state of the being with the ones preceding it and immediately following it in the hierarchical scheme of the total being. If we consider the radii which contain the extremities of the modalities of all the states, their superimposition forms a vertical plane of which they are the horizontal straight lines, and this vertical plane is the locus of all the above-mentioned extreme points, which might be called the limiting-points for the different states, as they previously were, from a different standpoint, for the various modalities of each state. The curve that we provisionally regarded as a circumference is actually one turn, of infinitesimal altitude (the distance between two horizontal planes cut by the vertical axis at two consecutive points), of a helix described on a revolving cylinder whose axis is the vertical axis of our representation. Correspondence between the points on successive turns is here marked by their situation on one and the same generatrix of the cylinder, that is, on one and the same vertical line; the points that correspond to one another, throughout the multiplicity of the states of the being, seem to merge when we consider the totality of the three-dimensional space and view them in orthogonal projection on a base plane of the cylinder, that is, on a given horizontal plane.
To complete this representation it is now enough to envisage, simultaneously, on the one hand this helicoidal movement taking place on a vertical cylindrical system formed by an indefinite multitude of concentric circular cylinders (the radius varying by only an infinitesimal amount from one to
another), and on the other hand the spiral movement we considered earlier in each supposedly fixed horizontal plane. As a result of the combination of these two movements, the base plane of the system will be the horizontal spiral, equivalent to the aggregate of an indefinite multitude of non-closed concentric circumferences; but beyond that, in order to carry still further the analogy between the two- and three-dimensional extensions respectively, and also the better to symbolize the perfect mutual continuity of all the states of the being, we shall have to envisage the spiral, not in one position only, but in all positions it can occupy around its centre. We shall thus get an indefinite multitude of vertical systems such as the foregoing, having the same axis, and all interpenetrating one another when regarded as coexisting, because each of them equally comprises the totality of the points in one and the same three-dimensional space, in which they are all situated ; here again, this is only the same system considered simultaneously in all the indefinite multitude of positions that it can occupy while accomplishing a complete rotation about the vertical axis.
However, the analogy thus established is still not altogether sufficient ; but before proceeding further, it should be pointed out that all that has been said is equally applicable to the " macrocosmic " representation. In that case, the successive turns of the indefinite spiral traced in a horizontal plane, instead of representing the various modalities of one state of a being, would represent the multiple realms of a degree of universal Existence, while the vertical correspondence would be that of each degree of Existence, in each of the given possibilities it comprises, with all the other degrees. It should be added, to avoid mentioning the point again, that this concordance between the " macrocosmic " and the " microcosmic" representations will remain valid for the representations that follow.