It is evident that in order to carry the idea of measure beyond the limits of the corporeal world, it must be analogically transposed. The manifestation of the possibilities of the corporeal order takes place in space, so that space may be made use of to represent the whole domain of universal manifestation, which otherwise would not be ‘representable’; thus the idea of measure, when it is applied to this comprehensive domain, is an essential part of the spatial symbolism that is so frequently employed. Fundamentally then, measure is an ‘assignation’ or a ‘determination’ necessarily implied in all manifestation, in every order and under every mode; as a determination, it naturally conforms to the conditions of each state of existence, and it is even in a certain sense identified with those conditions themselves, it being truly quantitative only in our world since quantity, like space and time, is no more than one of the special conditions of corporeal existence. But there is in every world a determination that can be symbolized for us by the quantitative determination we know as measure, because it is the determination corresponding in other worlds to measure in our own, in accordance with the difference of conditions in each; and it can be said that through this determination these other worlds, together with all that they contain, are realized or ‘actualized’ as such, since it is inherent in the very process of manifestation. Coomaraswamy remarks that ‘the Platonic and Neoplatonic concept of “measure” (μέτρον) agrees with the Indian concept: the “non-measured” is that which has not yet been defined; the “measured” is the defined or finite content of the universe, that is, of the “ordered” universe; the “non-measurable” is the Infinite, which is the source both of the indefinite and of the finite, and remains unaffected by the definition of whatever is definable,’ that is to say by the realization of the possibilities of manifestation which it carries in itself.
It is clear from this that the idea of measure is intimately connected with that of ‘order’ (in Sanskrit rita), and ‘order’ is in turn related to the production of the manifested universe, the universe being, according to the etymological meaning of the Greek word κόσμος, a production of ‘order’ out of ‘chaos’, the latter being the indefinite in the Platonic sense, and the ‘cosmos’ the definite.[10] The production of ‘order’ is also assimilated in all traditions to an ‘illumination’ (the Fiat Lux of Genesis), the ‘chaos’ being symbolically identified with darkness: ‘chaos’ is the potentiality from which as starting-point manifestation will be ‘actualized’, that is to say, it is in effect the substantial side of the world, which is therefore described as the tenebrous pole of existence, whereas essence is the luminous pole since it is the influence of essence that illuminates the ‘chaos’ in order to extract from it the ‘cosmos’; all this is in agreement with the inter-relation of the different meanings implicit in the Sanskrit word srishti, which designates the production of manifestation, and contains simultaneously the ideas ‘expression’, ‘conception’, and ‘luminous radiation’.[11] The solar rays make apparent the things they illumine so that they become visible, the rays thus being said symbolically to ‘manifest’ them; and if a central point in space is considered, together with the radii emanating from it, it can also be said that these radii ‘realize’ space by causing it to pass from virtuality to actuality, and that their effective extension is at any instant the measure of the space realized. These radii correspond to the directions of space properly so called (these directions being often represented by the symbolism of ‘hair’, a similar symbolism being used in connection with the solar rays); space is defined and measured by the three-dimensional cross, and in the traditional symbolism of the ‘seven solar rays’, six of those rays arranged in two opposite pairs form the cross, while the ‘seventh ray’, the ray that passes through the ‘solar gate’, can only be represented graphically by the center itself. All this is perfectly coherent, and is linked together as rigorously as could be; and it may be added that, in the Hindu tradition, the ‘three steps’ of Vishnu, whose ‘solar’ character is well-known, measure the ‘three worlds’, which amounts to saying that they ‘effectuate’ the totality of universal manifestation. We know too that the three elements that constitute the sacred monosyllable Om are designated by the term mātra, showing that they also respectively represent the measure of the three worlds; and by the mediation of these mātras, the being realizes in itself the corresponding states or degrees of universal existence and so becomes itself the ‘measure of all things’.[12]
The Sanskrit word mātra has as its exact equivalent in Hebrew the word middah; and the middoth are assimilated in the Kabbalah to the divine attributes, by which God is said to have created the worlds, and this conception is also brought directly into relation with the symbolism of the central point and the directions of space.[13] In this connection the Biblical statement may be recalled, according to which God has ‘arranged all things by measure and number and weight’;[14] these three categories clearly represent diverse modes of quantity, but they are only literally applicable as such to the corporeal world and to nothing else, though by an appropriate transposition they may nevertheless also be taken as an expression of universal ‘order’. The same is also true of the Pythagorean numbers, but the mode of quantity that is primarily associated with measure, namely, extension, is the mode that is most often and most directly brought into relation with the process of manifestation itself, by virtue of a certain natural predominance of spatial symbolism in this connection, arising from the fact that space constitutes the ‘field’ (in the sense of the Sanskrit kshetra) within which corporeal manifestation is developed, corporeal manifestation being inevitably taken as the symbol of the whole of universal manifestation.
The idea of measure immediately evokes the idea of ‘geometry’, for not only is every measurement essentially ‘geometrical’ as we have already seen, but also geometry itself can be called the science of measurement; but it goes without saying that geometry understood primarily in a symbolic and initiatic sense is here in question, profane geometry being merely a degenerate vestige thereof, deprived of its original deep significance, which is entirely lost to modern mathematicians. Such is the essential foundation of all conceptions in which divine activity, conceived as producing and ordering the worlds, is assimilated to ‘geometry’, and consequently also to architecture, for the two are inseparable;[15] and it is known that these conceptions have been preserved and transmitted in uninterrupted succession from Pythagorism (which was itself only an ‘adaptation’ and not really ‘original’) down to what still remains of the Western initiatic organizations, however unconscious these organizations may now be of the nature of the conception in question. Related to this very point is Plato’s statement that ‘God geometrizes always’ (ἀεὶ ὁ Θεὸς γεωμέτρει), recourse to the neologism ‘geometrizes’ being inevitable in order to translate this exactly, as there is no authentic word to describe the activity of the geometrician; and the corresponding inscription said to have been put on the door of his school is: ‘Let none but a geometrician enter here,’ implying that his teaching, at least on its esoteric side, could only be truly and effectively understood through an ‘imitation’ of the divine activity itself. A sort of last echo of this in modern philosophy (modern as to its date, but really in reaction against specifically modern ideas) is found in this statement of Leibnitz: ‘while God calculates and practices His cogitation [that is to say, sets out his plans] the world is made’ (dum Deus calculat et cogitationem exercet, fit mundus), but, all these things had a far more precise significance for the men of old, for in the Greek tradition the ‘geometrician God’ was none other than the hyperborean Apollo, and thus we are brought back once more to the ‘solar’ symbolism, and at the same time to a fairly direct derivation from the primordial tradition; but that is another question, which could not be developed here without getting entirely off the subject; all that can be done now is to give, as opportunity occurs, a few glimpses of the traditional knowledge that is so completely forgotten by our contemporaries.[16]
10
The Sanskrit word
15
In Arabic, the word
16
Coomaraswamy has called attention to a curious symbolical drawing by William Blake representing the ‘Ancient of Days’, appearing in the solar orb, whence he points toward the outside a compass held in his hand, all of which might illustrate the following words from the