CHAPTER XXVI Incommensurability between the Total Being and the Individuality
It is now necessary to dwell on a point of the first importance. The traditional idea of the being, as set forth in this book, differs essentially and by its very principle from all the anthropomorphic and geocentric ideas which the western mentality finds so difficult to surmount. It might even be said to differ infinitely, and that would be no abuse of language such as occurs on most occasions when this word is used; on the contrary, it would be a more accurate expression than any other, and one better suited to the conception for which we use it, since this is truly unlimited. Pure metaphysic can in no wise admit anthropomorphism [^1]; if the latter sometimes seems to find its way into metaphysical expression, that is only a quite outward appearance, and indeed one that is to some degree inevitable, because any expression necessarily involves the use of human language. The apparent fault, then, is only a consequence of the imperfection necessarily inherent in all expression, owing to its very limitation; such a consequence is admitted only by way of an indulgence, as it were, or a provisional and accidental concession to the feebleness of the individual human understanding, and its inability to attain to that which transcends the domain of the individuality. Even before any outward expression takes place, this insufficiency already reveals itself in formal thought (which indeed is itself an expression if considered in relation to the formless order) : any idea that is thought of with intensity ends by adopting to some extent a human form, namely that of the thinker ; to use a striking simile of Shankaracharya, it might
be said that " thought flows into man as molten metal is poured into the founder's mould ". The very intensity of the thought [^2] makes it occupy the whole of the man, more or less as water fills a vessel to the brim; it then assumes the shape of that which contains and limits it, in other words it becomes anthropomorphic. Here again there is an imperfection from which the individual being, under the restricted and particularized conditions of his existence can hardly escape; indeed, in his individual capacity he cannot escape at all, though he is bound to strife towards doing so, for complete release from such limitation is obtained only in the extraindividual and supra-individual, that is, formless states, attained in the course of effective realization of the total being.
Now that this has been said in order to forestall any possible objection on the point, it is clear that there cannot be any common measure between the "Self", on the one hand, and any individual modification, or even the integrality of a state, on the other. The " Self ", conceived as the totalization of the being, integrates itself by the three dimensions of the cross, and is finally reintegrated into its primal Unity, realized in that very plenitude of expansion of which space in its entirety is but a symbol. An individual human modification is represented by only an infinitesimal element of that space; and even the integrality of a state, depicted by a plane (or at least by something regarded as a plane with the restrictions we have mentioned earlier), still implies only an infinitesimal element of three-dimensional space; the reason is that when this representation is situated in space (that is, amid the array of all the states of the being), its horizontal plane must be regarded as in fact moving by an infinitesimal quantity along the vertical axis [^3]. Since even this necessarily restricted and limited geometrical representation involves infinitesimal elements, it is
evident that between what is symbolized by the two terms that have just been compared, there is in actual reality and a fortiori an absolute incommensurability, not depending on any convention that is more or less arbitrary, as the choice of certain relative units must always be in ordinary quantitative measurements. Again, when the total being is in question, the indefinite is here taken as a symbol of the Infinite, in so far as it is permissible to say that the Infinite can be symbolized ; but naturally that in no wise amounts to confusing the two, as is not infrequently done by western mathematicians and philosophers. "If we can take the indefinite as an image of the Infinite, we cannot apply to the Infinite our reasonings about the indefinite; the symbolism descends and does not reascend." [^4]
This integration adds a dimension to the appropriate spatial representation. It is well known in fact that, starting from the line which is the first degree of indefinititude in extension, the single integral corresponds to the calculation of a surface, and the double integral to the calculation of a volume. Therefore, if a first integration has been required in order to pass from the line to the surface, which is measured by the twodimensional cross describing the indefinite circle which never closes (or the horizontal spiral envisaged simultaneously in all possible positions), then a second integration is required in order to pass from the surface to the volume, in which the threedimensional cross, by the irradiation of its centre throughout the directions of the space wherein it is situated, produces the indefinite spheroid, conceived as resulting from a vibratorymovement, or in other words the volume, open in all directions, that symbolizes the universal vortex of the "Way".