The Reign of Quantity and The Signs of the Times Read online

  Before going further it should be noted here that the physicists’ ‘matter’ can in no case be anything but a materia secunda, since the physicists regard it as being endowed with properties, on the nature of which they are incidentally not entirely in agreement, so that their ‘matter’ is not potentiality and ‘indistinction’ and nothing else besides; moreover, as the physicists’ conceptions relate to the sensible world and do not go beyond it, they would not know what to do with the conception of a materia prima. Nonetheless, by a curious confusion, they talk all the time of ‘inert matter’, without noticing that if it were really inert it would have no properties and would not be manifested in any way, so that it could have no part in what their senses can perceive; nevertheless they persist in pronouncing everything that comes within range of their senses to be ‘matter’, whereas inertia can actually only be attributed correctly to materia prima, because it alone is synonymous with passivity or pure potentiality. To speak of the ‘properties of matter’ while asserting at the same time that ‘matter is inert’ is an insoluble contradiction; and, by a strange irony, modern ‘scientism’, which claims to eliminate all ‘mystery’, nonetheless appeals in its vain attempts at explanation only to the very thing that is most ‘mysterious’ in the popular sense of the word, that is to say most obscure and least intelligible!

  The question now arises, after setting aside the supposed ‘inertia of matter’ as being really no more than an absurdity, whether ‘matter’, endowed as it is with the more or less defined qualities that enable it to be manifested to our senses, is the same thing as the materia secunda of our world as understood by the scholastics. Doubt will at once arise as to the validity of any such assimilation, if it be noted that the materia secunda in question, if it is to play a part in relation to our world analogous to that played by materia prima or universal substance in relation to all manifestation, must in no way be manifested in this world itself, but can only serve as ‘support’ or ‘root’ to whatever is manifested therein, and that in consequence, sensible qualities cannot be inherent in it, but on the contrary must proceed from ‘forms’ implanted in it; and this again amounts to saying that anything that is quality must necessarily be referred to essence. Here a new confusion makes its appearance: modern physicists, in their efforts to reduce quality to quantity, have arrived by a sort of ‘logic of error’ to the point of confusing the two, and thence to the attribution of quality itself to their ‘matter’ as such; and they end by assigning all reality to ‘matter’, or at least all that they are capable of recognizing as reality: and it is this that constitutes ‘materialism’ properly so called.

  Nevertheless, the materia secunda of our world cannot be devoid of all determination, for if it were so it would be inseparable from the materia prima itself in its complete ‘indistinction’; neither can it be a sort of generalized materia secunda, for it must be determined in accordance with the special conditions of this world, in such a way that it can effectively play the part of substance in relation to this world in particular, and not in relation to anything else. The nature of this determination must then be specified, and this is what Saint Thomas Aquinas does when he defines this particular materia secunda as materia signata quantitate; quality is therefore not inherent in it and is not that which makes it what it is, even if quality is considered only in relation to the sensible order; its place is taken by quantity, which thus really is ex parte materiæ. Quantity is one of the very conditions of existence in the sensible or corporeal world; it is the condition that belongs most exclusively of all to that world; therefore, as might have been expected, the definition of the materia secunda in question cannot concern anything other than this world, but it must concern this world as a whole, for everything that exists in this world is necessarily subject to quantity. The definition given is therefore fully sufficient, and there is no need to attribute to materia secunda, as has been done to modern ‘matter’, properties that can in no way really belong to it. It can be said that quantity, regarded as constituting the substantial side of our world, is as it were its ‘basic’ or fundamental condition: but care must be taken not to go too far and attribute to it an importance of a higher order than is justifiable, and more particularly not to try to extract from it the explanation of this world. The foundation of a building must not be confused with its superstructure: while there is only a foundation there is still no building, although the foundation is indispensable to the building; in the same way, while there is only quantity there is still no sensible manifestation, although sensible manifestation has its very root in quantity. Quantity, considered by itself, is only a necessary ‘presupposition’, but it explains nothing; it is indeed a base, but nothing else, and it must not be forgotten that the base is by definition that which is situated at the lowest level, so that the reduction of quality to quantity is intrinsically nothing but a ‘reduction of the higher to the lower’, and some have very rightly attributed this very character to materialism: to claim to derive the ‘greater’ from the ‘lesser’ is indeed one of the most typical of modern aberrations.

  One further question presents itself: we meet with quantity under diverse modes, and in particular as discontinuous quantity, which is nothing but number,[6] and as continuous quantity, which is principally represented by spatial and temporal magnitudes; among all these modes, which is the one that can most accurately be called pure quantity? This question has its importance, all the more so because Descartes, whose place is at the starting-point of many specifically modern philosophical and scientific conceptions, tried to define matter in terms of extension, and to make his definition the principle of a quantitative physics, which though not yet quite ‘materialism’, was at least ‘mechanism’, and it might be tempting to draw the conclusion that extension, as being directly inherent in matter, represents the fundamental mode of quantity. On the other hand, Saint Thomas Aquinas, when he says that numerus stat ex parte materiae, seems rather to suggest that number constitutes the substantial basis of this world, and therefore that it is number that must properly be looked on as pure quantity; and the attribution of a ‘basic’ character to number is in perfect agreement with the fact that in the Pythagorean doctrine number is taken, by inverse analogy, as the symbol of the essential principles of things. It should be noted too that the ‘matter’ of Descartes is no longer the materia secunda of the scholastics; it is on the other hand an example, perhaps the earliest in point of date, of the modern physicists’ ‘matter’, although Descartes’ notion did not then include all that his successors were gradually to incorporate in it in order to arrive at the most recent theories of the ‘constitution of matter’. There is therefore reason to suspect that there may be some error or confusion in the Cartesian definition of matter, and that some element not of a purely quantitative order must have slipped into it at that stage, perhaps unsuspected by its originator: the nature of his error will be made clear in chapter 4, where we shall see that extension, although it is obviously quantitative in character, like everything else belonging to the sensible world, cannot be regarded as pure quantity. It may also be observed that the theories which go farthest in the direction of a reduction to the quantitative are generally ‘atomistic’ in one way or another, that is to say they introduce discontinuity into their notion of matter in such a way as to bring it into much closer relation to the nature of number than to that of extension; and the very fact that the material from which bodies are formed cannot in any case be conceived otherwise than as extended is never anything but a source of contradictions in all ‘atomism’. Another cause of confusion is the habit that has grown up of considering ‘body’ and ‘matter’ as nearly synonymous; actually, bodies are in no sense materia secunda, which is not met with anywhere in the manifested existences of this world, bodies only proceeding from it as from their substantial principle. But number, like materia secunda, is never perceived directly and in a pure state in the corporeal world, and it is number that must without doubt be considered pr
imarily as constituting the fundamental mode in the domain of quantity; the other modes of quantity are only derived from number, that is to say they are so to speak only quantity by virtue of their participation in number: and this is implicitly recognized whenever it is maintained, as in fact it always is, that everything quantitative must be expressible in terms of number. In these other modes, even when quantity is the predominant element, it always appears as more or less mixed with quality; thus it is that the conceptions of space and of time, despite the efforts of modern mathematicians, can never be exclusively quantitative, unless indeed it be accepted that they must be reduced to entirely empty notions, without contact with any kind of reality; and is not the science of today in actual fact made up to a large extent of such empty notions, purely ‘conventional’ in character and without the least effective significance? This last question must be more fully dealt with, especially so far as it concerns the nature of space, for this aspect of the question is very closely connected with the principles of geometrical symbolism, while at the same time it provides an excellent example of the degeneration that traditional conceptions must undergo in order to become profane conceptions; the procedure will be to examine first of all how the conception of ‘measure’, the very foundation of geometry, can be transposed, in a traditional sense, in such a way as to give it a significance quite other than that which modern scientists attach to it, for they only see in ‘measure’ a means for getting as near as they can to their topsy-turvy ‘ideal’, which seeks to bring about by degrees the reduction of all things to quantity.

  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:

  For everything that can be conceived or perceived (in the manifested world) Sanskrit has only the expression nāma-rūpa, the two terms of which correspond to the ‘intelligible’ and the ‘sensible’, considered as two complementary aspects referred respectively to the essence and to the substance of things.[8] It is true that the word mātra, which literally means ‘measure’, is the etymological equivalent of materia; but that which is thus ‘measured’ is not the physicists’ ‘matter’, it is the possibilities of manifestation inherent in the spirit (Ātmā).[9]

  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 thi
ngs 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.