The Reign of Quantity and The Signs of the Times

20 From Sphere to Cube

Now that a few ‘illustrations’ have been given of what has been called the ‘solidification’ of the world, there remains the question of its representation in geometrical symbolism, wherein it can be figured as a gradual transition from sphere to cube. Indeed, to begin with, the sphere is intrinsically the primordial form, because it is the least ‘specified’ of all, similar to itself in every direction, in such a way that in any rotatory movement about its center, all its successive positions are strictly superimposable one on another.[54] The sphere, then, can be said to be the most universal form of all, containing in a certain sense all other forms, which will emerge from it by means of differentiations taking place in certain particular directions; and that is why the spherical form is, in all traditions, that of the ‘Egg of the World’, in other words, the form of that which represents the ‘global’ integrality, in their first and ‘embryonic’ state, of all the possibilities that will be developed in the course of a cycle of manifestation.[55] It is as well to note in addition that this first state, so far as our world is concerned, belongs properly to the domain of subtle manifestation, inasmuch as the latter necessarily precedes gross manifestation and is its immediate principle. This is why the form of the perfect sphere, or that of the circle corresponding to it in plane geometry (as a section of the sphere by a given directional plane) is in fact never realized in the corporeal world.[56]

On the other hand, the cube is opposed to the sphere as being the most ‘arrested’ form of all, if it can be so expressed; this means that it corresponds to a maximum of ‘specification’. The cube is also the form that is related to the earth as one of the elements, inasmuch as the earth is the ‘terminating and final element’ of manifestation in the corporeal state;[57] and consequently it corresponds also to the end of the cycle of manifestation, or to what has been called the ‘stopping-point’ of the cyclical movement. This form is thus in a sense above all that of the ‘solid’,[58] and it symbolizes ‘stability’ insofar as this implies the stoppage of all movement; and it is evident that the equilibrium of a cube resting on one of its faces is in fact more stable than that of any other body. It is important to note that this stability, coming at the end of the descending movement, is not and cannot be anything but an unqualified immobility, of which the nearest representation in the corporeal world is afforded by the minerals; and this immobility, if it could be entirely realized, would really be the inverted reflection at the lowest point of the principial immutability of the highest point. Immobility or stability thus understood, and represented by the cube, is therefore related to the substantial pole of manifestation, just as immutability, in which all possibilities are comprehended in the ‘global’ state represented by the sphere, is related to the essential pole;[59] and this is why the cube also symbolizes the idea of ‘base’ or ‘foundation’ which again corresponds to the substantial pole.[60] Attention must also be drawn to the fact that the faces of a cube can be considered as being oriented in opposite pairs corresponding to the three dimensions of space, in other words as parallel to the three planes determined by the axes forming the system of coordinates to which that space is related and which allows of its being ‘measured’, that is, of its being effectively realized in its integrality. It has been explained elsewhere that the three axes forming the three-dimensional cross must be looked upon as being traced through the center of a sphere that fills the whole of space by its indefinite expansion (the three planes determined by these axes also necessarily passing through the same center, which is the ‘origin’ of the whole system of coordinates), and this establishes the relation that exists between the two extreme forms, sphere and cube, a relation in which what was interior and central in the sphere is so to speak ‘turned inside out’ to become the surface or the exteriority of the cube.[61]

The cube also represents the earth in all the traditional meanings of that word, that is, not only the earth as a corporeal element in the sense in which it was mentioned above, but also as a principle of a much more universal order, the principle designated in the Far-Eastern tradition as Earth (Ti) in correlation with Heaven (Tien). Spherical or circular forms are related to Heaven, cubic or square forms to Earth; since these two complementary terms are the equivalents of Purusha and Prakriti in the Hindu doctrine, which means that they are simply another expression for essence and substance taken in their universal meaning, exactly the same conclusion as before is arrived at in this instance. It is also evident that, like the conceptions of essence and substance, the same symbolism is always susceptible of application at different levels, that is to say either to the principles of a particular state of existence, or to the integrality of universal manifestation. Not only are these two geometrical forms related to Heaven and to Earth, but so also are the instruments used to draw them, namely, the compass and the square, and this is so in the symbolism of the Far-Eastern tradition as well as in that of Western initiatic traditions;[62] and the different correspondences of these two forms give rise in different circumstances to multiple symbolical and ritual applications.[63]

Another case in which the relation of these same geometrical forms is in evidence is that of the symbolism of the ‘Terrestrial Paradise’ and of the ‘Heavenly Jerusalem’, to which reference has already been made elsewhere;[64] and this case is specially important from the point of view adopted in this book, since the symbolism in question is in fact concerned with the two extremities of the present cycle. Now the form of the ‘Terrestrial Paradise’, corresponding to the beginning of the cycle, is circular, whereas that of the ‘Heavenly Jerusalem’, corresponding to its end, is square;[65] and the circular boundary of the ‘Terrestrial Paradise’ is none other than the horizontal section of the ‘Egg of the World’, that is of the universal and primordial spherical form.[66] It could be said that this circle itself is finally changed into a square, since the two extremities must join, or rather (the cycle never being really closed, for that would imply an impossible repetition) they must correspond exactly; the presence of the same ‘Tree of Life’ in the center in each case shows clearly that it is only actually a question of two states of one and the same thing, the square here representing the accomplishment of the possibilities of the cycle, which were in a germinal condition in the circular ‘organic girdle’ of the beginning, and are subsequently fixed and stabilized in a state of definition so to speak, at least in relation to the particular cycle concerned. This final result can also be represented as a ‘crystallization’, again showing affinity with the cubic form (or the square in the plane section): it becomes a ‘city’ with a mineral symbolism, whereas at the beginning there was a ‘garden’ with a vegetable symbolism, vegetation representing the elaboration of the germs in the sphere of vital assimilation.[67] Reference was made above to the immobility of minerals as being an image of the final state toward which the ‘solidification’ of the world is tending: but it is as well to add that in considering the ‘Heavenly Jerusalem’ the mineral has been regarded as already being in a ‘transformed’ or ‘sublimated’ state, for it figures as precious stones in the description of that City; that is why the fixation is only final with respect to the present cycle, and beyond the ‘stopping-point’ the same ‘Heavenly Jerusalem’ must, by virtue of the causal linkage that admits of no actual discontinuity, become the ‘Terrestrial Paradise’ of the future cycle, the end of the one and the beginning of the other being actually one and the same moment viewed from two opposite sides.[68]

It is nonetheless true that, if consideration is confined to the present cycle, a moment finally arrives at which ‘the wheel stops turning’, and here, as always, the symbolism is perfectly coherent: for a wheel is circular in shape, and if it were to get out of shape in such a way as to end by being square, it is obvious that it could not do otherwise than stop. This is why the moment in question appears as an ‘end of time’; it is then, according to the Hindu tradition, that the ‘twelve suns’ will shine simultaneously, for time is in fact measured by the passage of the sun through the twelve signs of the zodiac, making the annual cycle, and when the rotation is stopped, the twelve corresponding aspects will so to speak be merged into one, thus returning into the essential and primordial unity of their common nature, since they do not differ except in their relation to universal manifestation, which will then be at an end.[69] Moreover, the changing of the circle into an equivalent square[70] is also what is known as the ‘squaring of the circle’; those who declare that this is an insoluble problem, though they be wholly unaware of its symbolical significance, are thus right in fact, since the ‘squaring’ understood in its true sense cannot be realized until the end of the cycle.[71]

A consequence of all this is that the solidification of the world appears to some extent to have a double meaning: considered in itself and from within the cycle, as being a consequence of a movement leading down toward quantity and ‘materiality’, it evidently has an ‘unfavorable’ significance, even a ‘sinister’ one, opposed to spirituality; but, in another aspect, it is nonetheless necessary in order to prepare, though it be in a manner that could be called ‘negative’, the ultimate fixation of the results of the cycle in the form of the ‘Heavenly Jerusalem’, where these results will at once become the germs of the possibilities of the future cycle. Nevertheless, it goes without saying that in the final fixation itself, and in order that it may indeed become a restoration of the ‘primordial state’, the immediate intervention of a transcendent principle is necessary, otherwise nothing could be saved and the ‘cosmos’ would simply evaporate into ‘chaos’. It is this intervention that produces the final ‘reversal’ already prefigured by the ‘transmutation’ of minerals in the ‘Heavenly Jerusalem’, and bringing about the reappearance of the ‘Terrestrial Paradise’ in the visible world, where there will thereafter be ‘a new heaven and a new earth’, since it will be the beginning of another Manvantara and of the existence of another humanity.