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Temporal Curvature and Contraction

A Modern Analysis of Time

The account of the whole time series as the issue of a reductive sequence which divides being and reality into ever-smaller quantities implies that all kinds of entities must displace and replace one another the more frequently in proportion to the degree to which reality is reduced to smaller quantities. But beyond the aspect of displacement of one thing by another, or of the displacement of one state of a given being by another state, this is still too general to help us understand the mechanism by which time is concretely experienced. This is a matter of analysis which has received much attention in modern philosophy. When numbers and calculations have to be applied to time, the detailed dynamics of the temporal flux are of special importance. The cyclic form of time is, among other things, the condition upon which time can be quantifiable, as in the case of the cycles of hours, days, and months. Time’s observable workings and its cyclic principle can be connected by a theory of time which was put forward by J.M.E. McTaggart.1

This takes the form of an analysis of time into two distinct series which run in parallel, these being referred to as the A series and the B series. The A series answers to the common sense perception for which temporal events function in the three compartments of past, present, and future. McTaggart draws attention to the contradiction which appears in this conception owing to the fact that membership of any one of these three categories is always exclusive of the other two, that is, things in the past or in the future can never be present, and vice-versa, while at the same time every member of these three categories constantly transforms itself into a member of the other two. Thus everything in the past was once future, and then present; everything present was future and will be past; and everything future will be present and then past. This aspect of time was made the basis of arguments to prove that it is unreal, though without that implying the unreality of the temporal world, since it was believed that time could be sufficiently abstracted from its contents for this purpose. In Platonic terms, this relative unreality of time is included in that of the realm of sense perception as a whole, according to the principle that time and the cosmos came into being together. The aspect of time which is least real is that which is comprised in the A series.

Everything in the A series, and not merely the present, is however in constant flux, because the passage of time means that everything in the past is moving ever more deeply in to the past, while everything in the future is moving ever nearer the present. The contents of past and future are thus in constant change by virtue of their changing relationships to the present, and the A series cannot, of itself, determine what is to occupy a place in past, present or future. In other words, it depends on a standpoint outside itself whence a given event is seen to fall into one of the three categories. This contrasts with the B series which is essentially static by nature. It comprises all the events and contents of time in a series where every member is fixed in the relations of being ‘earlier than’ one thing and ‘later than’ another one. Thus Queen Victoria is always later than George IV and always earlier than Edward VII, while Gothic architecture is always later than Romanesque and earlier than the Classical revival.

However, the relations ‘earlier than’ and ‘later than’ clearly derive from the temporal relations of the A series, whence its derivative position, despite its fixity or immunity from change. Every part of the B series must occupy a position in the A series, ranging through future, present and past, so that the time we experience consists in the movement of these two series in relation to one another. In this way, the content of the B series would be manifest in the present of the A series like a train passing a window. But which one is still, and which one moves? Common sense would see the Bseries as still, and the A series moving over it from past through the present into the future, though it could be the opposite way round, with the B series moving the other way, from the future through the present and into the past. McTaggart observes this ambiguity, but does not draw the consequences from it which it is capable of yielding.

A and B Series and Cyclic Order

The first and most general point to emerge from the above relative motion is that time, to give the experience of change, must form a combination of static and dynamic elements. A time series which consisted of pure dynamism could not supply any kind of experience because every element in it would have become something else before it could be known. On the other hand, a purely static time would not be temporal at all. Only a mingling of the changing with the unchanging can constitute time, and this is consistent with the idea of time as a lower degree of reality and not an unreality. The static and the dynamic elements may be related by a ‘forward’ or a ‘backward’ movement between past and future, but this is by no means an exclusive choice. If both were equally real it would have important consequences for the nature of time. A two-way flow through the present would in fact break down the distinction between past and future which can appear all but invincible.

To begin again from the common sense position, the immediate past issues in the present, through which the future is brought into being. From this point of view, one can see the future being formed from what is past. However, it remains equally true that everything in the past was once in the future, and this means that the contents of the past which we see to be the generator of the future have all come to it out of that very future, by virtue of an equal and opposite flow toward the past. On this basis, the present time is the scene of two equal and opposite flows which build up the future out of the past and build up the past out of the future. The present could thus be compared to a window through which one observes two columns of troops marching past each other in opposite directions. The relevance of this to cyclic time could not be more direct. Given this relation between past and future, the recurrence of the past in some form or other is inevitable inasmuch as there is a preponderance of persons, objects, and events which have to exist in a similar way in both past and future, owing to the constant interchange between them.

If every transition from past to future and vice-versa involved only a new combination of pre-existing elements which belonged to past and future equally, the balance would be tilted too far in the direction of pure repetition despite the possibilities of new proportions and combinations. Natural processes are not the only ones involved in this, since there is always the question of new content entering the temporal flow from outside its own course, both by creation and human ingenuity. However, it is possible that the above conception of temporal flow could still give rise to identical recurrences if the A and B series were both of finite length and returned upon themselves. To return to the above comparison, if the two columns of troops were both arranged in circles, one inside the other, the individuals seen through the window to be passing one another will inevitably recur, and so similarly with time, if its extent was finite in this manner. Given that time is a two-way flow, therefore, it must be of indefinite length if the possibility of identical recurrence is to be ruled out.

An absolute beginning of time would imply that time could start from a point at which the past contained nothing, which must be impossible if the essence of its flow is twofold. If such a beginning were to be made to occur, the contents of a past time would have to be specially created for it, in accordance with what has been said before about mature creation. This, however, seems to mean only that there cannot be an absolute beginning of time at its own level. If a general pattern of repetition is just as inevitable as the continuation of change, a starting-point for it, if there was one, would have to be arbitrary. The process of time is more complex than this because the states of existence which belong to it become progressively further removed from the archetypal realities which are their Formal causes. Since being admits of many degrees, the existences so affected become increasingly subject to change and instability as they diminish in essence. This kind of change can be represented by movement along a spiral towards its centre, that is, with an ever shortening radius of curvature. If complete continuity was represented by a straight line, a curved path like this would represent an increasing imposition of discontinuity.

Cyclic Form and Cosmic Change

This conception of past and future adds to what has been argued earlier for the cyclic order, where it is the basis of calculation in any field, whether it be that of sunspots, ice ages, the courses of the fixed stars, or human activities in the rise and fall of stock markets and levels of trade in different goods. There is no need to make an exception of the time-scale of universal history in this regard. The truth of cyclic time can be tested by calculation of the lengths of universal eras, and even by the matching of some historical periods with periods defined by cyclic laws. Such calculations can enable us to estimate our own position in the universal era from its beginning to the present and from the present to its end. For this purpose we shall have to look further at the mathematical aspect of this subject, and explore it by means of the analogy between spatial and temporal structures.

The comparison already made between spatial and temporal cycles is still too limited inasmuch as the successive turns of the spirals are conceived as being of constant radius. While the theory is not dependent on its geometrical expressions, the latter are of value because spatial relations are more open to the imagination, and without them, many things said about cycles of time may seem not to be part of a coherent system.

Successive moments of time are separated from one another in two ways, one of which is a qualitative change which makes each one unique in some respect, and the other lies in the way in which each present moment lies outside past and future. These two aspects of time are represented by two properties of the spiral. Each point on the spirals is like a position on a curving path which is fenced on either side so that there is no view before or behind. At the same time, the radius of curvature changes as a point travels along it, and this corresponds to the change in the prevailing quality of the successive parts of time. If time really was the rectilinear process it is usually taken to be, there would be no barriers to obscure one’s knowledge of the past. There would be an intercommunication between different times which would contradict the essential nature of time, which is to distribute being and reality, which are small in relation to what is comprised in their Formal causes. Thus the Form is manifest in time as a series of different but obviously related instances of itself.

As the change in the radius of curvature of the spiral answers to a steady change in the qualitative composition of time, it follows that as each moment affords a representation of all other times from its own point of view, the quality of that moment will be imposed on all other times for the experience which resides in that moment. From the present period, all other periods assume the aspect which is imparted to them by the temporal quality of this present time, as though seen through a colored glass. Each age has its human point of view, but this point of view is founded on cosmic conditions. By this means, man’s perception of his past is controlled in a manner more fundamental than that achieved by fashion and prejudice. In this respect, each part of time could be said to contain all others (within the lifetime of a civilization, at least) in a way which is comparable to the way in which each consciousness contains a representation of the world from its own point of view.

In the early stages of a cycle, the rate at which time elapses is at a minimum, reflecting its proximity to the next-higher reality, aevum. This is represented in the ‘clock spring’ spiral by the relatively short lengths of the curve which are traversed in one revolution when one starts near its center. Relevant to this early stage are the superhuman ages attributed to the early Patriarchs in the Book of Genesis, and the shortening of human life during the Kali-Yuga referred to in the Bhagavata Purana. It is probably in connection with the latter text that Guénon states in The Reign of Quantitythat human life is now shorter than it has ever been in this world-cycle, this being not in relation to the other natural cycles, but in relation to absolute duration. This contradicts the modern perception that human life is now longer than ever, because this greater length of life, which is measured in time units such as years, is purely relative to the duration of other phenomena. From the principle that the cyclic process involves an ontological contraction, the amount of duration comprised in a year, or in one revolution of the earth about the sun, will grow progressively less, though in a way which is not directly detectable, since all other phenomena are affected similarly.

The property of the spiral mode of change implies that the passage of time must accelerate in proportion as the end of the cycle is approached. However, this cannot cause perceptible accelerations in the natural order, for all its impact on human life. This amounts to a much more universal relativity of time than that which results from the velocity of the observer, according to the Theory of Relativity. But the idea of universal contraction may seem to give rise to the scientific objection that, if duration really was contracting in this way, the earth and the other planets would be having to travel ever faster in their orbits around the sun, in order to cover the same distance in less time. This, if it happened, would cause their orbits to lose their approximately circular shape, and become ever more elliptical until they became like the orbits of comets. This, however, would be a mistaken inference because it rests on the assumption that the planets would be traveling faster subject to a time-flow which was the same for all times. No such thing is envisaged, of course, because that would contradict the basic hypothesis that the rate of time-flow is not constant.

Nevertheless, the contraction of duration is a major human issue, even though it cannot be studied by physical methods. While everyone is subject to it, the choice remains of either counteracting it or of forming part of it. Such a possibility depends on a radical division between the human state and the natural order, already referred to in connection with the microcosm. This idea excludes the common sense belief that the real world is solely a physical system in which persons are as so many passive components, along with plants, animals and physical objects.

While mankind has a world in common, each person’s perceived world is a unique personal reconstruction of that world, characterized by their scale of values and priorities. Thus the real world includes innumerable inner worlds. We need some understanding of this idea in order to understand the traditional idea of time. Because each person’s world is represented by an outgoing act of an inner state of being, there are two directions in which consciousness can be deployed by preference. The will holds the balance between two realms, those of physical process and of the unchanging, i.e., God and metaphysical reality. It is free to devote the best part of its energies to the one or the other. On the one hand, this means that one can identify the self either with the represented realities or with a reality which is present at first-hand, that is, without mediation.

On the other hand, the self may become identified with the external, that is, with the products of its world-representation, in which case its mode of being becomes almost wholly temporal. The latter choice means that the self becomes part of the flux of phenomena, not in a neutral way, but as a motor principle which adds its force to the temporal condition. Temporality is humanly generated. Such is the basis of the draining away of the self-aware level of mind, the only one which is specifically human.

While this self-aware or intellective consciousness needs time to develop, like anything else, it depends on the content of duration in a way that the external faculties do not. For example, a loss of duration in the time in which one can walk a given distance takes nothing from the nature of the action, because, like all physical action, it is made up of a series of discrete elements which can be more or less compressed or expanded without essential loss.2 Our physical and practical activities, being based on the natural order, can for this reason be accelerated in the same manner as nature as a whole. However, the truth-seeking activities of the mind are not capable of any such acceleration. This is because the grasp of truth depends on a causality which is of the mental, not the physical order. Any intrusion of the latter would invalidate it. In Scholastic terms, the soul’s independent being in relation to the body and nature means that it has an operatio absoluta which is exercised temporally, but not subject to natural forces. Thus the contraction of duration allows ever less scope for the maturation of the intellect, while there is no detriment to the natural life. In this way, the passage of time increasingly empties human life of spiritual content.

The modern prolongation of human life in comparison with the lives of other creatures or in relation to the cycles of nature need not mean very much, therefore. While the addition of years must make some difference, this will be more than offset by the reduction in the absolute duration they contain. An increase in the relative chronological length of human life is a compensating factor which helps to prevent its absolute reduction from being a human disaster. The great ages attributed by the traditions to our remote ancestors would thus be firstly a symbol of the superior temporal duration in which they lived, while at the same time this would also reflect the greatness of their being in the supernatural order.

Contraction and Internal Infinity

The ancient chronologies ascribe shorter periods of years to the latter parts of the world-cycle, such as where the Kali-Yuga amounts to only one-tenth of the complete cycle. This outward and visible reduction corresponds to an inner reduction in the ‘time value’ or duration in these years, in which case the Iron Age or Kali-Yuga would be the shortest age both extensively and intensively. The multiplication of time-units without corresponding temporal content suggests a natural phenomenon resembling inflation in the sphere of economics. If the content of time-units became vanishingly small at the end of the cycle, the effect could be to make the end theoretically unattainable, since an infinite number of them might be required actually to reach the limit.

This property of diminishing time can be illustrated by means of a mathematical model in which a certain enclosed space allows objects inside it to have their full size only at its center. As they move toward its periphery their dimensions contract according to a mathematical function of their distance from it, so that the units of length would reduce to zero if the boundary was actually reached. However, the boundary never can be reached in this system, because the successive steps taken toward it diminish until they become infinitesimal before it is reached, and therefore an infinite number of them would in fact be needed. An observer in such a world would be convinced he was in a realm of infinite space, although it would be obviously finite to any observer outside it. The properties of worlds where space is relative can also be applied to the time of a cosmic cycle, showing how an apparent temporal infinity could result from a law of contraction if it went to an extreme degree. Such a pattern of development would make each cycle more completely a world in itself than if it were merely a measured segment of uniform time. Its finite nature would be balanced by an internal infinity by which it is symbolically the total cosmos.

The variation in the amount of duration contained in the cycle’s measures of time has its effect on our attempts to rediscover and reconstruct the past, and to establish dates in remote ages. Inevitably the time-measures used to fix such dates will be those of the present era, with the result that very large numbers will often be involved, where periods of the geological and cosmological order are involved. There is in effect a ‘chronological hyper-inflation’ in modern attempts to explore the origins of the present world. Besides the telescoping of time’s measures, another aspect of the cycle is that of a continual and accelerating removal away from the cyclic origin where there was the greatest fullness of being. This change is represented by the ever-lengthening radius at which a point traversing a spiral is removed from the center. This change is felt in an increasing loss of continuity between past and present and a loss of participation in the truth of the original state, even as a race memory. The increase in the radius of curvature in the outer part of the spiral (undergoing a reduction in curvature), represents the loss of qualitative distinction between the different parts of the world as well as between its successive states. In the limit, where its outer curve approximates to a straight line, it would reconnect with its eternal origin, from a state which was the polar opposite of the beginning of the cycle.

The irreversibility of time is represented in the same model by the way in which each new increment along the curve is at a slightly longer radius than the last. The curvature or constant change in direction which separates the points on the spiral illustrates the way in which moments are separated from one another which would not be possible if the points were arranged in a straight line. The different degrees of expansion of the spiral also reflect the manifestation of the spatial world itself, starting from a center in which all its realities are present and concentrated in a point. Creation has an aspect of ejection and dispersion and progressive dilution, which runs its course till it ultimately rejoins its supernatural cause.

The inherent relativity of time, as it appears in the cyclic concept, is both natural and traditional, since the modern rectilinear view of time was only created to provide the simplest conditions for calculations which were applied to the solution of technical problems. In earlier civilizations, which depended on the motion of the sun for their practical measures of time, it appeared obvious that time did not pass uniformly. The varying lengths of shadows cast by sundials and obelisks showed the constantly-varying speeds at which the tips of the shadows moved, these being most rapid in the early morning and late afternoon, and slowest around midday. Thus the hours around midday were taken to be the longest, and for similar reasons it was thought that all the hours were proportionately shorter in winter, when the sun’s course was lower and shadows were therefore longer and so faster-moving. Even when water clocks were invented, the Egyptians ensured that they worked at varying speeds, or to varying measures, to match the times of the day and of the seasons as reckoned by the sun.

If Time Ceased to Pass

Although the point of view of this book is mainly cosmic and collective, some of the abstract conceptions in the above have consequences of the destiny of individual persons, which I think are important enough to justify some separate consideration. The study of temporal being by means of metaphysics and mathematics is objective inasmuch as these disciplines derive from a reality which is not in time at all. Their independence of natural conditions makes them true manifestations of the non-temporal principle in human consciousness which has already been indicated as the means whereby we can discriminate between the past, present, and future contents of the temporal A series. Does this mean we could also become conscious of a cessation of time, in a way which was not the same as a cessation of existence? The fact that the intellect is superior to time implies that our own true being may be independent even of this.

At the end of a world-cycle there must be a cessation of time, if only as a transition to the next time series. Whether it be the end of a world or the end of an individual life, the question remains: does our being depend on the continuation of time? Past, present, and future have each a meaning only in relation to the other two; take away one, and the other two have either no meaning or a very different one. Consequently, if there were a ‘last moment’ there would no longer be a future, or in other words, the future would cease to be future, and for the same reason the past would cease to be past at the same moment. The last present moment would merge with what had been the past, which would then form a supra-temporal present in which everything dispersed by the passage of time would be reintegrated. It is only because of the forward impetus of the Aseries of time that past times are lost to us, and if this condition ceases, either because of the ending of a particular time series or because of the mystical attainment of a state of being outside it, the conclusion will be a fullness of being.

The A series is time at its most deceptive. It constantly presents fragments of beings as though they were the whole beings, and this distortion greatly magnifies the destructive and devouring aspect of time. In reality the true being of all individual persons and things is extended along the Bseries, where all their successive parts or stages of development exist simultaneously and immutably. What is seen to perish with the passage of time consists therefore only of the last temporal prolongations of beings. One consequence of this is that the resurrection of the dead would not require any reconstruction or reanimation of dead bodies; instead, there is a universal permanence which is not simply static, but living. (For a detailed treatment of this subject, see Living Time by Maurice Nicoll.)

1. The Nature of Existence, chap. 33.

2. This can be proved by means of geometry, where radii are drawn across two concentric circles which represent space, where any points A1, A2, An, on the larger circle can be chosen and joined to the center C. These radii cut the smaller circle at points B1, B2, Bn. No matter how many such points on the larger circle are joined to the center in this way, we never find one for which there is no corresponding point on B1, B2, Bn. No matter how many such points on the larger circle are joined to the center in this way, we never find one for which there is no corresponding point on the smaller circle. However much larger the outer circle is made, therefore, there will be no point on it for which there is no corresponding point on the inner circle. Even if the inner circle is reduced until it approaches the central point C, this equality remains, showing that the center contains in potentia all the points on the circles around it; and that spatial figures (and by implication bodies) are expansions of the same origin.

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