The Reign of Quantity and The Signs of the Times

3 Measure and Manifestation

The use of the word ‘matter’, except where modern conceptions are being specially examined, will henceforth be avoided for preference; and it must be understood that the reason for this lies in the confusions to which it inevitably gives rise, since it is impossible to use the word without at once evoking, even in those who are aware of the different meaning attached to the word by the scholastics, the idea of that which modern physicists call ‘matter’, for this last acceptation is the only one that holds good in current language. The idea in question, as we have seen, is not met with in any traditional doctrine whether it be Eastern or Western; this indicates at least that, even to the extent that it might legitimately be admitted after clearing it of certain incongruous and even flatly contradictory elements, it contains nothing that is really essential and is related only to one highly particularized way of looking at things. At the same time, since the idea is very recent, it cannot be implicit in the word itself, which is far older, so that the original meaning of the word must be quite independent of its modern meaning. It must however be admitted that the true etymological derivation of this word is very difficult to determine — as if a more or less impenetrable obscurity must inevitably envelop everything that has to do with ‘matter’ — and it is scarcely possible in this connection to do more than distinguish certain conceptions associated with its root; this will be by no means without interest, although it is impossible to specify exactly which of the various conceptions is the closest to the primitive meaning of the word.

The connection that seems to have been noticed most often is that which relates materia to mater, and this fits in well with the idea of substance as the passive principle and as symbolically feminine; it can be said that Prakriti plays the ‘maternal’ part in relation to manifestation and Purusha the ‘paternal’; and the same is true at all the levels at which a correlation of essence and substance can be envisaged analogically.[7] On the other hand, it is also possible to relate this same word materia to the Latin verb metiri ‘to measure’ (and it will appear later that there is in Sanskrit a form still closer to it): ‘measure’ however implies determination, and determination cannot be applied to the absolute indetermination of universal substance or the materia prima, but must rather be related to some other more restricted notion, a point we propose to now examine more closely.

Ananda K. Coomaraswamy has said on this subject:

The idea of ‘measure’, brought in this way into direct relation with manifestation itself, is very important, and is moreover far from being peculiar to the Hindu tradition, which Coomaraswamy had particularly in view here. It can indeed truthfully be said that the idea is found in all the traditional doctrines in one form or another, and, while it is naturally impossible to attempt to enumerate all the relevant concordances that could be pointed out, enough can perhaps be said to justify this statement, and at the same time to clarify, as far as it is possible to do so, the symbolism of ‘measure’, which plays so important a part in certain initiatic forms.

Measure, understood in the literal sense, is principally concerned with the domain of continuous quantity, that is to say, it is concerned most directly with things that have a spatial character (for time, though no less continuous than space, can only be measured indirectly, by as it were attaching it to space through movement as intermediary, thus establishing a relation between the two). This amounts to saying that measure is specifically concerned either with extension itself, or with what is conventionally called the ‘matter of physics’, by reason of the character of extension that this last necessarily possesses: but this does not mean that the nature of matter can, as Descartes claimed, be reduced simply to extension and nothing more. In the first case, measure is correctly said to be ‘geometrical’; in the second case, it would more usually be called ‘physical’ in the ordinary sense of the word; but in reality the second case becomes merged in the first, for it is only by virtue of the fact that bodies are situated in extension and occupy a certain defined part of it that they are directly measurable, whereas their other properties are not susceptible of measurement, except to the degree that they can in some way be related to extension. We are at this point, as was foreseen, a long way from the materia prima, which in its absolute indistinction, can neither be measured in any way nor be used as a measure of anything else; but it is necessary to enquire whether the notion of measure be not more or less closely linked with whatever it is that constitutes the materia secunda of our world, and it turns out that a linkage exists through the fact that the materia secunda is signata quantitate. Indeed, if measure directly concerns extension and what is contained therein, it is only by the quantitative aspect of this extension that measure is made possible; but continuous quantity as such is, as explained, only a derived mode of quantity, that is to say it is only quantity by virtue of its participation in pure quantity, which in its turn is inherent in the materia secunda of the corporeal world; and besides, just because continuity is not pure quantity, measure always carries a certain degree of imperfection in its numerical expression, as the discontinuity of number makes a fully adequate application of number to the determination of continuous magnitudes impossible. Number is indeed the basis of all measurement, but, so long as number is considered by itself there can be no question of measurement, for measurement is the application of number to something else. An application of this kind is always possible within certain limits, but only after taking into account the ‘inadequacy’ just referred to, and this applies to everything subject to the quantitative condition, in other words, to everything belonging to the domain of corporeal manifestation. Only — and here the idea expressed by Coomaraswamy recurs — it must be most carefully noted that, despite certain prevalent misuses of ordinary language, quantity is never really that which is measured, it is on the contrary that by which things are measured; and furthermore, it can be said that the relation of measure to number corresponds, in an inversely analogical sense, to the relation of manifestation to its essential principle.

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]