Among the features characteristic of the modern mentality, the tendency to bring everything down to an exclusively quantitative point of view will be taken from now on as the central theme of this study. This tendency is most marked in the ‘scientific’ conceptions of recent centuries; but it is almost as conspicuous in other domains, notably in that of social organization — so much so that, with one reservation the nature and necessity of which will appear hereafter, our period could almost be defined as being essentially and primarily the ‘reign of quantity’. This characteristic is chosen in preference to any other, not solely nor even principally because it is one of the most evident and least contestable, but above all because of its truly fundamental nature, for reduction to the quantitative is strictly in conformity with the conditions of the cyclic phase at which humanity has now arrived; and also because it is the particular tendency in question that leads logically to the lowest point of the ‘descent’ that proceeds continuously and with ever-increasing speed from the beginning to the end of a Manvantara, that is to say throughout the whole course of the manifestation of a humanity such as ours. This ‘descent’, as has often been pointed out on previous occasions, is but a gradual movement away from the principle, which is necessarily inherent in any process of manifestation; in our world, by reason of the special conditions of existence to which it is subject, the lowest point takes on the aspect of pure quantity, deprived of every qualitative distinction; it goes without saying that this point represents strictly speaking a limit, and that is why it is not legitimate to speak otherwise than of a ‘tendency’, for, during the actual course of the cycle, the limit can never be reached since it is as it were outside and beneath any existence, either realized or even realizable.
We come now to a matter of particular importance which must be established from the outset, both in order to avoid possible misconceptions and in order to dispose in advance of a possible source of delusion, namely the fact that, by virtue of the law of analogy, the lowest point is as it were the obscure reflection or the inverted image of the highest point, from which follows the consequence, paradoxical only in appearance, that the most complete absence of all principle implies a sort of ‘counterfeit’ of the principle itself, something that has been expressed in a ‘theological’ form in the words ‘satan is the ape of God.’ A proper appreciation of this fact can help greatly toward the understanding of some of the darkest enigmas of the modern world, enigmas which that world itself denies because though it carries them in itself it is incapable of perceiving them, and because this denial is an indispensable condition for the maintenance of the special mentality whereby it exists. If our contemporaries as a whole could see what it is that is guiding them and where they are really going, the modern world would at once cease to exist as such, for the ‘rectification’ that has often been alluded to in the author’s other works could not fail to come about through that very circumstance; on the other hand, since this ‘rectification’ presupposes arrival at the point at which the ‘descent’ is completely accomplished, where ‘the wheel stops turning’ — at least for the instant marking the passage from one cycle to another — it is necessary to conclude that, until this point is actually attained, it is impossible that these things should be understood by men in general, but only by the small number of those who are destined to prepare, in one way or in another, the germs of the future cycle. It is scarcely necessary to say that everything that the author has set out in this book and elsewhere is intended to be addressed exclusively to these few, without any concern for the inevitable incomprehension of the others; it is true that these others are, and still must be for a certain time to come, an immense majority, but then it is precisely in the ‘reign of quantity’, and only then, that the opinion of the majority can claim to be taken into consideration at all.
However that may be, it is particularly desirable before going any further to apply the principle outlined above to a more limited sphere than that to which it has just been applied. It must serve to dispel any confusion between the point of view of traditional science and that of profane science, especially as certain outward similarities may appear to lend themselves to such confusion. These similarities often arise only from inverted correspondences; for whereas traditional science envisages essentially the higher of the corresponding terms and allows no more than a relative value to the lower term, and then only by virtue of its correspondence with the higher term, profane science on the other hand only takes account of the lower term, and being incapable of passing beyond the domain to which it is related, claims to reduce all reality to it. Thus, to take an example directly connected with the subject of this book, the Pythagorean numbers, envisaged as the principles of things, are by no means numbers as understood by the moderns, whether mathematicians or physicists, just as principial immutability is by no means the immobility of a stone, nor true unity the uniformity of beings denuded of all their qualities; nonetheless, because numbers are in question in both cases, the partisans of an exclusively quantitative science have not failed to reckon the Pythagoreans as among their ‘precursors’. So as not unduly to anticipate developments to follow, only this much need be said here, namely that this is but one more instance of the fact that the profane sciences of which the modern world is so proud are really and truly only the degenerate ‘residues’ of the ancient traditional sciences, just as quantity itself, to which they strive to reduce everything, is, when considered from their special point of view, no more than the ‘residue’ of an existence emptied of everything that constituted its essence; thus these pretended sciences, by leaving aside or even intentionally eliminating all that is truly essential, clearly prove themselves incapable of furnishing the explanation of anything whatsoever.
Just as the traditional science of numbers is quite a different thing from the profane arithmetic of the moderns, including all the algebraic or other extensions of which the latter is capable, so there is also a ‘sacred geometry’ no less profoundly different from the ‘academic’ science nowadays designated by the same name. There is no need to insist at length on this point, for those who have read the author’s earlier works, in particular The Symbolism of the Cross, will call to mind many references to the symbolical geometry in question, and they will have been able to see for themselves how far it lends itself to the representation of realities of a higher order, at least to the extent that those realities are capable of being represented in a form accessible to the senses; and besides, are not geometrical forms fundamentally and necessarily the very basis of all figured or ‘graphic’ symbolism, from that of the alphabetical and numerical characters of all languages to that of the most complex and apparently strange initiatic yantras? It is easy to understand that this kind of symbolism can give rise to an indefinite multiplicity of applications; and it should be equally clear that such a geometry, very far from being related only to pure quantity, is on the contrary essentially qualitative. The same can be said of the true science of numbers, for the principial numbers, though they must be referred to as numbers by analogy, are situated relatively to our world at the pole opposite to that at which are situated the numbers of common arithmetic; the latter are the only numbers the moderns know, and on them they turn all their attention, thus taking the shadow for the reality, like the prisoners in Plato’s cave.