7 ON THE PRODUCTION OF NUMBERS

'IN the beginning, before the origin of all things, was Unity,' say the loftiest of Western theogonies, which strive to reach Being beyond its ternary manifestation, not halting at the universal appearance of the Binary. But the theogonies of the East and Far East say: 'Before the beginning, before even the primordial Unity, was the Zero,' for they know that beyond Being there is Non-Being; that beyond the manifest there is the non-manifest, which is its principle; and that Non-Being is not nothingness, but on the contrary infinite Possibility, identical to the universal All, which is at the same time absolute Perfection and integral Truth.

According to the Kabbalah, the Absolute, in order to manifest itself, concentrates itself in an infinitely luminous point, leaving darkness around it. This light within the darkness, this point within limitless metaphysical extension, this nothing that is all in an all that is nothing, if one may so express it, is Being in the midst of Non-Being, active Perfection within passive Perfection. This luminous point is Unity, the affirmation of metaphysical Zero, here represented by unlimited extension; it is the image of infinite, universal Possibility. In order to serve as the center from which, like so many rays, the indefinite manifestations of Being will emanate, Unity once affirmed is united to Zero, which contains it in principle, that is, to the state of non-manifestation. Here the Decad already appears in potentiality, and it will be the perfect number, the complete development of the primordial Unity.

Total Possibility is at the same time universal Passivity, for it contains all particular possibilities, certain of which will be manifested, passing from potentiality to actuality under the action of Unity-Being. Each manifestation is a radius of the circumference that represents total manifestation; and this circumference, the points of which are indefinite in number, is again Zero in relation to its center, which is Unity. But the circle was not laid out in the Abyss of Non-Being, and it only marks the limit of manifestation, of the domain of Being within the heart of Non-Being; it is therefore Zero realized, and, through the totality of its manifestation following the indefinite circumference, Unity perfects its development into the Decad.

Moreover, with the affirmation of Unity even before all manifestation, if this Unity were opposed to Zero, which contains it in principle, the Binary would then appear within the Absolute itself, in the primary differentiation that leads to the distinction between Non-Being and Being. But in our study on the Demiurge we saw what this distinction is, and showed that Being, or active Perfection—Khien—is not really distinct from Non-Being, or passive Perfection—Khouen—that this distinction, which is the point of departure for all manifestation, exists only insofar as we create it ourselves, since we can only conceive of Non-Being through Being, the non-manifest through the manifest; thus the differentiation between the Absolute within Being and the Absolute within Non-Being only expresses the manner in which we represent things to ourselves, and nothing more.

Viewing things in this light, one might be tempted to speak of the Absolute as the common principle of Being and Non-Being, of the manifest and the non-manifest, although in reality it should be identified with Non-Being, since the latter is the principle of Being, which in turn is itself the first principle of all manifestation. Thus if one should wish to consider the Binary here, one would immediately find oneself in the presence of the Ternary; but in order for such to be a true Ternary, that is, already a manifestation, the Absolute would have to be primordial Unity, and we have seen that Unity represents only Being, the affirmation of the Absolute. It is this Unity-Being that will be manifested in the indefinite multiplicity of numbers, the entirety of which it contains in potentiality, and which emanate from it like sub-multiples of itself; and all of these numbers are included within the Decad, realized through the course of the cycle of the total manifestation of Being. It is therefore the production of this Decad, starting from the primordial Unity, that we must now consider.

In a previous study, we saw that all the numbers can be considered to emanate from Unity in pairs; these pairs of inverse or complementary numbers, which may be regarded as symbolizing the syzygies of the Eons of the Pleroma, exist within Unity in the undifferentiated or non-manifest state:

1 = 1/2 x 2 = 1/3 x 3 = 1/4 x 4 = 1/5 x 5 = ... = 0 x ∞

None of these groups, 1/n x n, is distinct from Unity, or from the other groups within Unity; they become so only when their constituent elements are considered separately; it is then that Duality is born, distinguishing one principle from the other, not in opposition, as is ordinarily—and wrongly—said, but as complementary principles; active and passive, positive and negative, masculine and feminine. But the two principles coexist within Unity, and their indivisible duality itself constitutes a secondary unity, a reflection of primordial Unity; thus, together with the Unity that contains them, the two complementary elements compose the Ternary, which is the first manifestation of Unity, for two, being the issue of one, cannot exist without three thereby existing as well:

1 + 2 = 3

And just as we can only conceive of Non-Being through Being, we can only conceive of Unity-Being through its ternary manifestation, the necessary and immediate consequence of the differentiation or polarization that our intellect creates within Unity. Whatever the aspect according to which this ternary manifestation is viewed, it is always an indissoluble Trinity, that is, a Tri-Unity, since the three terms are not really distinct, but are only the same Unity conceived as containing within itself the two poles through which it will produce all of manifestation.

This polarization is again found immediately within the Ternary itself, for if one considers its three terms to have an independent existence, one will thereby obtain the Senary number, implying a new ternary, which is the reflection of the first.

1 + 2 + 3 = 6

This second ternary has no real existence by itself; it is to the first what the Demiurge is to the emanative Logos, a tenebrous and inverted image, and in what follows we shall indeed see that the Senary is the number of Creation. For the moment let us content ourselves with saying that it is we who realize this number, as we distinguish the three terms of Tri-Unity, instead of envisaging principial Unity synthetically, independent of all distinction, that is, of all manifestation.

If the ternary is regarded as a manifestation of Unity, it will at the same time be necessary to consider Unity insofar as it is not manifested, and then Unity, joined to the Ternary, will produce the Quaternary, which can be represented here by the three vertices of a triangle, together with its center. One could also say that the Ternary, symbolized by a triangle of which the three vertices correspond to the first three numbers, necessarily presupposes the Quaternary, the first term of which, being unexpressed, would then be Zero, which indeed cannot be represented. Thus one could consider the first term within the Quaternary to be either Zero or primordial Unity. In the first instance, the second term will be Unity insofar as it is manifested, and the two others its double manifestation; in the second instance, on the contrary, these last two, the two complementary elements mentioned above, will logically have precedence over the fourth term (which is nothing other than their union), realizing between them an equilibrium in which principial Unity is reflected. Finally, if one considers the Ternary according to its lowest aspect, taking it to be formed from the two complementary elements and the equilibrating term, then the latter, as the union of the other two, will participate in both, such that one will be able to regard it as double; here again, the Ternary will immediately imply a Quaternary, which is its development.

Whatever manner in which one considers the Quaternary, one can say that it contains all numbers, for if its four terms are regarded as distinct, one will see that it contains the Decad:

1 + 2 + 3 + 4 = 10

This is why all the traditions say that one produced two, two produced three, three produced all numbers. The expansion of Unity in the Quaternary immediately realizes its total manifestation, which is the Decad.

The Quaternary is represented geometrically by the square, if the static state is considered, and by the cross, if the dynamic state is considered. When the cross turns about its center, it engenders the circle, which, together with its center, represents the Decad. This is what is called circling the square, and it is the geometric representation of the arithmetical fact set forth above; conversely, the Hermetic problem of squaring the circle will be represented by the division of the circle into four equal parts by means of two rectilinear diameters, and it will be expressed numerically by the preceding equation written in the opposite direction:

10 = 1 + 2 + 3 + 4

The Decad as formed by the set of the first four numbers, is what Pythagoras called the Tetraktys. In its entirety the symbol representing it had a ternary form, each of its exterior sides embracing four elements, and composed of ten elements in all. The figure is given, in a note, in the translation of the chapter on Pythagoras in the Philosophumena.

If the Ternary is the number that represents the first manifestation of principial Unity, then the Quaternity stands for its total expansion. This latter is symbolized by a cross of which the four branches are formed by two indefinite straight lines extending fully in each direction, and oriented along the four cardinal points of the indefinite, pleromatic circumference of Being, points the Kabbalah represents by the four letters of the Tetragrammaton, יהוה. The Quaternity is the number of the manifested Word, of Adam Kadmon, and one can say it is essentially the number of Emanation, for Emanation is the manifestation of the Word. From it, the other degrees of manifestation of Being are derived in logical succession, by the development of the numbers it contains within itself, the totality of which constitutes the Decad.

If the quaternary expansion of Unity is considered to be distinct from Unity itself, when it is added to Unity it produces the number five, and this again is symbolized by the cross with its four branches and center. Moreover, it will be the same for all new numbers whenever they are regarded as distinct from Unity, even if they cannot really be so, since they are only manifestations thereof; each of these numbers when added to primordial Unity, gives birth to the following number. Having pointed out this successive mode of production for numbers once and for all, we shall not return to it in what follows.

If the center of the cross is taken to be the starting-point for the four branches, it will represent the primordial Unity; if on the contrary it is only considered as their point of intersection, it will merely represent equilibrium, a reflection of Unity. This second point of view is marked Kabbalistically by the letter ש ['shin'], which, placed at the center of the Tetragrammaton, יהוה—the four letters of which represent the four branches of the cross—forms the pentagrammatic name יהשוה,^[1] the significance of which we shall not stress here, as we only wish to point it out in passing. The five letters of the Pentagram are placed at the five points of the Blazing Star, a figure of the Quinary, which symbolizes more particularly the Microcosm, or individual man. The reason for this is as follows: if the Quaternary is taken to be Emanation, or the total manifestation of the Word, then each emanated being, a sub-multiple of this Emanation, will be characterized by the number four; it will be an individual being to the measure in which it is distinguished from Unity, or from the emanating center, and we have just seen that this distinction between the Quaternary and Unity is precisely the genesis of the Quinary.

In our study on the Demiurge we said that the distinction that gives birth to individual existence is the point of departure for Creation; indeed, the latter exists to the measure in which the totality of individual beings, characterized by the number five, is considered to be distinct from Unity, which gives birth to the number six. As we have seen earlier, this number can be considered as formed from two ternaries, the one the inverted reflection of the other; this is represented by the two triangles in the Seal of Solomon, symbol of the Macrocosm, or the created World. Things are distinct from us to the degree that we distinguish between them; and it is precisely to this degree that they become external to us, as well as distinct from one another; from this point they appear clothed in forms, and this process of Formation, which is the immediate consequence of Creation, is characterized by the number that follows the Senary, namely the Septenary. We only need indicate the concordance of the preceding with the first chapter of Genesis: the six letters of the word בראשית, the six phases of Creation, and the formative role of the seven Elohim, representing the totality of natural forces, and symbolized by the seven planetary spheres, which latter could also be made to correspond to the first seven numbers, the lowest sphere, that of the Moon, being designated as the World of Formation. The Septenary, such as we have just considered it, can be represented either by the double triangle and its center, or by a seven-pointed star, around which are inscribed the signs of the seven planets; this is the symbol of the forces of nature, that is, of the Septenary in the dynamic state. If it were considered in the static state, it could be seen as formed by the reunion of a Ternary and a Quaternary, and it would then be represented by a square surmounted by a triangle. Much could be said on the meaning of all these geometric forms, but such considerations would take us too far afield from the subject of our present study. The process of Formation leads to what one can call material realization, which for us marks the limit of the manifestation of Being, which will then be characterized by the number eight. This number corresponds to the terrestrial World contained within the seven planetary spheres, and which he should be taken here as symbolizing the whole of the material World (each World is of course not to be understood as a place, but rather as a state or modality of being). The number eight also corresponds to an idea of equilibrium, because material realization is, as we have just said, a limitation, a halting point as it were with respect to the distinctions we create in things, the degree of these distinctions being a measure of what is symbolically designated as the depth of the fall. We have already said that the fall is nothing other than a means of expressing precisely this distinction that created individual existence, separating us from principal Unity. In its static state, the number eight is represented by two squares, one inscribed within the other in such a way that the vertices of the inner square intersect the sides of the outer. In its dynamic state it is symbolized by two crosses with the same center, oriented in such a way that the branches of one bisect the right angles formed by the branches of the other. If the number eight is added to Unity, it forms the number nine. For us this new number serves to limit the manifestation of Being, since it corresponds to material realization distinguished from Unity; it will therefore be represented by the circle, and will designate Multiplicity. We have said elsewhere that this circle, the points of which, indefinite in number, represent the formal manifestations of Being—we do not go further and say all manifestations, only the formal manifestations—can be regarded as Zero realized. Indeed, added to Unity the number nine forms the number ten, which also results from the union of Zero with the Unit, and which is represented by the circumference of the circle taken together with its center. On the other hand, the Novenary could also be envisaged as a triple Ternary; from this, the static point of view, it will be represented by three superimposed triangles, each the reflection of the one immediately above, such that the intermediate triangle is inverted. This figure is the symbol of the three Worlds and their relationships; this is why the Novenary is often considered the number of hierarchy. Finally, the Decad, corresponding to the circumference of the circle together with its center, is the total manifestation of Being, the complete development of Unity. It can therefore be regarded as nothing other than Unity realized within Multiplicity. Starting from it, the sequence of numbers begins again, forming a new cycle: 11 = 10 + 1; 12 = 10 + 2; ... 20 = 10 + 10 Then comes a third cycle, and so on indefinitely. Each of these cycles can be regarded as reproducing the first, but at another level, or, if one wishes, in another modality; they will therefore be symbolized by as many circles placed parallel one above another, in different planes; but since in reality there is no point of discontinuity between them, it is necessary that they be open circles, so that the end of each will at the same time be the beginning of the next. They will then not be circles, but the successive spirals of a helix traced on a cylinder, and these spirals will be indefinite in number, the cylinder itself being indefinite; and each spiral is projected as a circle onto a plane perpendicular to the axis of the cylinder, although in reality its point of departure and its point of arrival are not in the same plane. But we shall return to this subject in another study, when we come to the geometric representation of evolution.^[2]

We must now consider another mode of production for numbers, production by multiplication, and more particularly the multiplication of a number by itself, giving birth successively to various powers of the number. But here the geometric representation would lead us to considerations concerning the dimensions of space, which it is preferable to study separately; we would then have to consider in particular the successive powers of the Decad, which would lead us to consider the question of the limits of the indefinite in a new light, as well as the question of passage from the indefinite to the Infinite.

In the preceding remarks, we have simply wished to indicate how the production of numbers starting from Unity symbolizes the different phases of the manifestation of Being in logical succession starting from the principle, Being itself, taken as identical to Unity; and if Zero—preceding primordial Unity—is introduced, one can thus even ascend beyond Being to Non-Being, that is, even to the Absolute.