A NOTEBOOK ON THINKING IN THE SIX TRIADIC FORMS

Anthony Blake

Part 3

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THE MONAD

The Monad

The unity of the monad is of a peculiar inclusive kind. That is to say, it is not defined by a boundary which divides the included from the excluded. If we need a provisional model, let it be something like a candle in a dark room, where its illumination decreases the further away one gets: There is some kind of gradation but no discontinuity. We should not attempt to interpret this model any further because we would fall into saying too much, too wrongly. The concept of a set is inadequate – ‘A Set is Many which allows itself to be thought of as One’ – because it suggests a start from some assembly of items and select from them according to a thought. In the true monad, any thought we might have of the unity is included with all the other content. Further, any item to do with the ordering or processing of the content is a part of the content. Nothing is prior to anything else, logically or otherwise. All of the content is equally given; equally gratuitous, or contingent. Thus, any judgments we might make are to be included in the content.

Thus, the principle by which we gather appropriate content is unknown. We do not know in advance, or through any general principle, what is relevant.

It is not that everything is equally relevant – which is to say that a monad is not the totality, the universe, the whole of wholes – but we have no way in which we can exclude anything. However, we do find that there is some measure for inclusion; a measure that has to do with the way in which the content, of itself finds affinity with itself. Relevance is disclosed through the assembly of content. As the content increases, so we find additions the more discerning. As the process continues, so we find some of the content fading away and other content growing stronger.

It is only through the assembly of content that anything becomes clear about the monad. It cannot be defined in advance; it is defined by the process of inclusion.

The monad has to begin with some content. It does not matter whether this is concrete or abstract; an attempt at definition or any exemplification; or even an association of words. As we continue in the process, something emerges. We may lightly touch on another model here: imagine the formation of a solar system and its early and vague beginnings in clouds of gas; after a certain degree of concentration is reached, we can recognize the rudiments of a solar system that will continue to define itself more and more determinately. The monad, then, is a self-correcting vagueness and there is no one principle by which coherence is developed.

The formal model for the monad is the empty set – which is the pure form of inclusion. The nature of the empty set is indication. We look for a closely allied notion; the way in which we can include empty sets within sets in various depths; as if the content could include the content in various ways. We use the word ‘content’ to cover: any item of content, the whole content, any part of the whole content and so on. We suppose that an ‘item’ of content is itself inclusive and without demarcation of boundary; therefore, there is no atomism at all, since everything includes yet other things (i.e is divisible). Every item then is an aspect of the monad and can be subject to the same process. The monad is a continuum: it is this that suggests the ’empty’ set.

There is no given near or far, or more or less. It is intrinsic to the process of the monad that everything is ‘equal’ in proximity to the centre: it is truly a sphere whose centre is everywhere. This is not mystical; it is simply a property of self-definition in which every item we allow serves as the centre. As the process goes on, certain items ‘melt away’ but never entirely disappear; for the monad includes ‘errors’ and ‘wrong turnings’.

If there is a law which applies to the monad it is that of mutual adjustment. However, if we think of this law then it becomes part of the content of the monad. We can have nothing that stands outside the monad or above it.

Hence, the character of the monad has been best dealt with by the Taoists. In thinking, the state of the monad corresponds to contemplation – particularly, ‘diffuse contemplation’.

In the tradition, it has been taken as axiomatic that ‘as one begins, so one continues’, a principle that is codified in the octave in the concept of the ‘sounding of the doh’.

A most important property of the process is the suspension of habitual judgment. In this respect, there are parallels with the epoche described by Husserl. Hence, the monad is thoroughly phenomenological; and we are divorcing ourselves entirely from the Monadology of Leibnitz (this is untrue, as we see later). What we are after, however, is no science of consciousness or any concern with consciousness per se. If we begin to think of consciousness, then this becomes merely another item of content. And, as an item of content, it must be treated as all other items. Our access to consciousness, we would have to say, is no more immediate than to any object we might consider. Such a distinction can only stem from the dyad. The concept of ‘epoch is allied to that of the empty set, since its sense is ‘bracketing’.

The act of epoche – which rests on the suspension and not elimination of judgment – is very powerful. It is the power of making a new beginning in the midst of the ever-present going-on of the familiar. It is the first freedom that we can have. It is the purest attention. It is attending upon rather than attending to. It is the condition for release of creativity. Our view of creativity is very much obscured by the mass of constructive effort that becomes involved. This effort is not the central core, which is more akin to patience and waiting (cf. Simone Weil ‘Waiting on God?). Whatever ingenuity, perspicacity or industry involved in assembling the content of the monad, the essence of it is in the singleness of the diffuse contemplation. The ever-present ‘danger’ concerns a degeneracy into sheer enumeration.

An important exemplification of the process of the monad is the technique of extensive expression, in which the theme or notion is given expression by a diversity of statements, usually a hundred. One of the important practical features of this technique is that it rapidly exhausts the capacity of the habitual judgment. After about five to ten statements the habitual representation breaks down. This is because the habitual representation aims at bringing the process to a close. The industry involved in the exercise far exceeds what can be automatically supplied. There are several stages in the process of the exercise at which the process itself – as a mechanism or procedure – breaks down. This succession of dissolutions is a reflection of the intrinsic properties of the monad; since, as we have said, ‘every item’ is determining the content of the whole according to its own nature. Therefore, every new item redefines the whole. However, since what is meant by an item is not itself determined, this can mean that a ‘group’ of items follows a certain ‘logic’ or ‘prejudice’ until it is added to by another group, which changes the rules’.

The dominant feeling, then, is one of dissolution. The ideal is the sphere whose boundary or surface is nowhere. Psychologists have wilfully neglected this aspect of thinking, judgment and creativity. Upon the monad rests any real attempt to re-examine any issue or fact. For example, if we take a simple object such as this table, then I can set myself to see it as a monad which will – or can – require me to assemble the content of this table in my experience or possible or conceptual experience. I would need to consider it as it is actually given: for example, in terms of the actual presentations it makes in my perception. This may at first sight appear as if we are indulging bringing into the picture of more and more of what is implied by everything else that is included. Of course, the notion of implication suggests that there are things ‘behind’ other things, at a different depth. Nevertheless, even when this is true, bringing such implications into the picture dissolves their special role. In the monad, there are no explanations of one thing by another. We do not find underlying motivations or laws. Everything that is included in the monad has the same weight of contribution to make. All we can be concerned with is that everything that is significant has been included – and this only to some degree of approximation which we are informed of by the content of the monad itself.

Such distinctions as that held between ‘nominalists’ and ‘realists’ cannot apply. Else, the distinction itself becomes part of the content of the monad – if it is significant.

It does not matter whether we argue that we determine what is significant or that the monad itself (its content) determines this. Such a distinction is not relevant unless it is part of the content of the monad.

FOR THE MONAD THERE ARE NO EXTRINSIC CONSIDERATIONS

We need also to realize that any content of the monad we might manage to represent through various media is not all the content that there is. The fleeting images, the feelings, the personal interactions, the dreams, etc. which proceed in us as we work on the monad are also part of the monad. Therefore, in the extreme, we come to the proposition: included in the monad is everything) including what we have failed to include ourselves. This we tend to indicate when we write:

THE MONAD IS ALL THIS, ETC.

The Monad as the True Beginning

It is quite false to suppose that we can start with an open mind. What is supposed to be the content of such a mind? It is the empty set! This is incapable of giving a start to anything. It is the zeroth system – the zerad, perhaps. It is outside our experience. When we make a beginning, we begin always with something and this is an integral part of the monad which itself begins with something and never with nothing. Our concern, then, must be with how we can make a true beginning – that is, not merely carry on from what we were doing anyway – that serves as an initiative but does not prejudice our future work. This is the whole intent of the monad. We have to start somewhere but we can do this in a way that does in habitual philosophy, concerning ourselves with the distinction and relation between perception and conception. But, let us think of an artist! A table painted by Picasso or Van Gogh is still a table as it is experienced; but it has been assembled out of the monad in a way which is not habitual. The painter goes back to see again from the beginning. He has attained the dissolution. His work is to dissolve the world as we know it – which means to dissolve away the chains of our habitual judgment. This can reach extremes as in Ouspensky’s ‘A man can go mad from one ashtray’.

As far as the monad is concerned, it is a matter of indifference whether the ‘object’ is known or unknown. We can consider assembling a monad of ‘what we do not know’. However, we must remember the like but, as we continue, what it is we are concerned with changes as its content is assembled.

The content may consist of hard facts, speculations, value-expression models, theories, rules, images, or anything whatsoever. There are no restrictions on media of expression. When a researcher scans the literature he is beginning a monad; in practice, he operates within the sphere of a monad which includes values, guesses personal feelings and the like which will never enter the sphere of his formal work. Someone may well decide to restrict himself to the public world of a topic and another man decide to follow his own subjective thread of meaning. But, these decisions must themselves be included in the content. Further, any restriction made on the process to confine it within certain bounds is to distort the monad. We may take Cromwell’s remark to the man painting his portrait: ‘Do it as it is, warts and all’ as a slogan for the monad. Now, we may well ask: how is it in practice possible for anyone to conduct a truly inclusive process? Will there not always be some form of restriction, stemming from our background, interests or even character? Our answer is that the monad is a process and it never comes to an end. Further, it has never really begun: since we can only ‘take up’ something which is already in hand. It is from this practical consideration that there stems the ajavata school of Hindu monism which claims there has been no creation and no birth. We emphasize again that

THE MONAD IS A PROCESS WITHOUT BEGINNING OR END

The beginning and end we experience stems from our thought: we say that we are beginning a monad and we say that we are finishing it – for the moment. What counts is the action of inclusion, the not tie us down to the limitations of our starting point. As we have seen, an important practical insight is that we can proceed by way of exhaustion of the habitual by demanding of ourselves more than habit can give- make possible. There is a quantitative dimension. Clearly, a suggestion that a definition, say, could serve as a monad is wrong. There would not be enough diversity.

Up until now, we have not made use of the traditional definition of the monad as:

UNITY IN DIVERSITY

What is the meaning of diversity and how may it serve us in the task of making a true beginning? Its meaning is that every item in a diverse content affords a distinctive perspective on the whole; it shifts the ground of relevance. This leads us to consider whether or not we have here some kind of criterion for judging the value of contributions to the monad? After all, in spite of our repeated emphasis on the all-inclusivity of the monad, we do not mean to suggest that we can include anything at all. So, we suggest that an item is making a contribution to the monad if it speaks to and of the whole content. But, this can only be the vaguest of guides, since, in the process of assembly, we have first to reach a critical complexity before the various items can be considered as a menge.

One of the definitions of a meng (it is usually spelt without the terminal ‘e’) is that of bringing living creatures together. Thus, when the monad begins to form, every one of its items can be considered as alive and autonomous; we have the beginnings of an ecology. But, to repeat, it is not until the monad becomes alive at a certain critical complexity that the items of its content assume their inherent power. Thus, as with an ecology, we cannot regard any one item as more important than another; while, at the same time, we can appreciate that the addition of an item changes the whole. It is this state of vitality and potency that characterize a true beginning. The monad then has a life of its own; it means what it is; it may even fail or flourish, evolve or decay.

We have spoken a great deal of ‘dissolution’ and the ‘suspension’ of judgment. What these terms address is our own conditioning par excellence. As we said, we do not make a fresh start through an open – and blank – mind. We have to find the beginning in the midst of what is already going on. We may well regard the discipline of the monad as a preparatory therapy. In some respects, psychoanalysis dimly echoes the process; but, in the monad of true beginning we are not seeking explanation:

We shall not cease from exploration
And the end of all exploring
Will be to arrive where we started
And know the place for the first time.
(Little Gidding T.S.Eliot)

The Monad and the Secret of Life

We have deliberately introduced into our discussion the phenomenon of life because we regard living wholes as the most persuasive images of the import of the systems (monad, dyad, triad, etc.) that we can have. It is also true that in spite of the efforts of such philosophical giants as Whitehead concerning the ‘philosophy of organism’ we have a very uneasy alliance between our conceptual world and the living world that we feel. The monad is important because it draws our attention to the un-bounded wholeness of living nature and enables us to contemplate the significance of ecologies, at least at the level of the living menge. We can appreciate the intrinsic significance of a Biosphere without having to resort to conceptual models of its mechanisms.

We speak of the ‘secret of life’ as that which makes the monad a true monad: a critical complexity. Recent considerations in physics and computing have provided a basis for calculating degrees of complexity and it may well be that life can be ‘measured’ in this way. Without, however, attempting to go into the state of current theory and practice, we can appreciate the point in qualitative terms. We do this anyway when we recognize living systems.

We do have the capacity to recognize life. Often, this amounts to a feeling. As a capacity, it is not based on being told that e.g. plants and cats are ‘alive’, but on an intrinsic recognition of complexity in menge form. It can extend beyond the obvious forms of life – plants and animals – to systems we produce ourselves, works of art and even to entities which are not ordinarily regarded as alive. In respect of the latter, we should mention the work of Fechner on the Earth as a living being, something which he felt directly. Our sense of life depends on the monad. We do not explain the complex whole on the basis of laws and we realize that any extant model of we have, such as that resting on genetics, is only provisional and incomplete. There is no aspect of a living complex that can be explained away; it can only be dissolved into some other aspect which in its turn, is being dissolved. There are no boundaries in life.

We have mentioned the affinity between our view of the monad and the tradition of Taoism. Chinese philosophy had a great influence Lo-on Leibnitz and, in spite of our earlier remarks, his Monadology must be seen as the first serious European attempt at a philosophy of organism. Joseph Needham (Science and Civilization in China, Vol. II) has drawn attention to the significance of Leibnitz as a philosopher who avoided the well-worn ways of both theological idealism and atomic materialism and as a bridge-builder, both between East and West and between the old and the new in Western thought, anticipating as he did the organic philosophies of Hegel and others until Whitehead. Needham refers to the study of Leibnitz made by Carr, in which the philosopher is described as proposing a view of the world not as a vast machine but as a vast living organism, ‘every part of which was also an organism’. His monads were organisms ‘participating as parts of higher organisms’.

Leibnitz himself said: ‘Every portion of matter may be conceived of as a garden full of plants or a pond full of fish; but every stem of a plant, every limb of an animal, and every drop of sap or blood is also such a garden or pond’. He also said that every constituent monad of the organism is somehow alive and cooperating in a harmony of wills (our italics) about which Needham comments: ‘…we are irresistibly reminded of that “harmony of wills” which we noted … as characteristic of the Chinese system of “correlative thinking” in which the whole universe in all its parts spontaneously cooperates without direction or mechanical impulsion.’

Leibnitz also said;’ There is neither absolute birth nor complete death in the precise meaning of the separation of soul and body. What we call births are developments and unfoldings, and what we call deaths are foldings and shrinkings.’

The model which Leibnitz offers for the way in which monads influence each other is that of two musical instruments which resonate even when separated from each other.

If we review these various ideas, then it becomes fairly obvious that our monad is a world of monads. Further, we should not regard the monads as either mechanically linked or as directed from ‘outside’ or ‘above’. There is no outside or above! Mechanism and theism are degenerate views. The monad is all-inclusive; and it is what life means.

Needham regards what we are dealing with as the monad (in our fullest sense) as exemplifying an ‘intuitive-associative’ system ‘which has its own causality and logic’. It is a system to be contrasted with the ‘subordinative’ thinking characteristic of European science ‘which laid such emphasis on external causation’. Further, Needham associates this system with magic. In ‘correlative thinking’, conceptions ‘are not subsumed under one another, but placed side by side in a pattern and things influence one another not by acts of mechanical causation, but by a kind of “inductance”‘. He quotes with approval from Tung Chung-Shu’s ‘Things of the Same Genus Energize Each Other’ (2nd c. B.C.) e.g.:

Thus it is that if (two) Chi are similar, they will coalesce; if notes correspond, they resonate.

Needham interpolates:’…everything in the universe is attuned to certain other things and changes as they change’. He also comments that things behave in a certain way because of their intrinsic natures and if they did not behave so, then they would turn into something other than themselves. The universe is a system at governed by a ‘mysterious resonance’. In an evocative passage, he writes:

It was an ordered harmony of wills, without an ordainer; it was like the spontaneous yet ordered, in the sense of patterned, movements of dancers in a country dance of figures, none of whom are bound by law to do what they do, nor yet pushed by others coming behind, but cooperate in a voluntary harmony of wills. (p.287)

We should add that Needham also discusses ‘correlative thinking’ in terms of number-mysticism – something germane to our whole enquiry. He quotes from Bergaigne:

Instead of the number depending on the actual (empirical) plurality of the objects perceived or pictured, it is, on the contrary, the objects whose plurality is defined by receiving it from a mystical number decided upon (as if in a prepared framework) before-hand.

We shall have to return to this question later on in our enquiry. For the moment, let us return to the organic thinking of the monad as we have proposed it and as we find discussed in Needham’s further comments on the Chinese system of ‘correlative thinking’. These comments extend to something which has been implicit all along in our own discourse: that one of the foremost models we have for the monad is the social system of democracy. Democracy is notoriously difficult to define; but its essence corresponds to the characteristics we have already noted; diversity, causation being from within the multitude of components, spontaneity, resonance; and the absence of ruling classes, external authority and the like.

Writing about the organic whole, Needham says:

…the universe itself is a vast organism, with now one and now another component taking the lead – spontaneous and uncreated it is, with all the parts of it cooperating in a mutual service which is perfect freedom, the larger and the smaller playing their parts according to their degree, ‘neither afore nor after other’.

Needham calls this the ‘democratic principle’ and he finds it in the workings of organisms. He exemplifies this by the ‘endocrine orchestra’ of mammals in which it is not easy to find which element is taking the lead at any given time.

It is time that we returned to Leibniz himself, before we attempt to elaborate further our assertion of the deep connection between the Monad and the ‘secret of life’. We will quote from the Monadology:

…every monad must be different from every other. For there are never in nature two beings, which are precisely alike, and in which it is not possible to find some differences which is internal or based on some intrinsic quality.

…every created thing, and consequently the created monad also, is subject to change, and indeed …this change is continual in each one.

…the natural changes of monads come from an internal principle…

…there must be a differentiation within that which changes

This differentiation must involve a plurality within the unity or the simple the simple must contain a large number of impressions and relations, although it has no parts.

The passing state, which involves and presents a plurality within the unity or simple substance, is nothing other than what is called perception …

…perception and that which depends on it cannot be explained mechanically that is to say by figures and motions.

(the) connection or adaptation of all created things with each, and of each with all the rest, means that each simple substance has relations which express all the others, and that consequently it is a perpetual living mirror of the universe.

…because of the infinite number of simple substances, it is as if there were as many different universes which are, however, but different perspective representations of a single universe from the different points of view of each monad.

And his is the means of obtaining as much variety as possible but with the greatest order possible; that is to say, it is the means of obtaining as much perfection as possible.

…everybody is sensitive to everything which is happening in the universe

…there is nothing waste, nothing sterile, nothing dead in the universe; no chaos, no confusions, save in appearance.

We should recall, at this point, that in our treatment of the monad we considered this true of our own thought or conceptions, as well as the universe; indeed, as true of anything we could consider ‘just as it is’ in all its diversity. We are not imagining everything as some kind of ‘animal’, that is, as some structure analogous to the living beings we know. We are concerning ourselves directly with life and the living, in whatever guise this appears. The sense of life is prior to knowledge of the plants and animals of this planet. It is the sense that Fechner had.

But, there are implications in the monad which are significant for our understanding of the organism forms we know, particularly for the theory of evolution. The point to be made is simple: the monad points out a way in which it is not necessary to look for antecedent causes. We will not find an explanation for evolution in terms of stages passing from one kind of existence to another: according to the monad, all such ‘stages’ must be present ‘from the beginning’; as time goes on, in the metamorphosis of the monads, one or another of the these ‘simple substances’ (to use the terminology of Leibnitz) becomes predominant. The reality is co-existence and synchronicity. There is no ‘magical’ production of living and even intelligent beings out of relatively inert chemicals; because they must have been ‘already there: This leads us to a new understanding of what is meant by ‘critical complexity’; most immediately, to bring into question what this complexity it ‘of’; that is to saw, the question of what monad we are considering.

We can think of the evolution of the cell: at some point, the complexity of a whole ecosphere was concentrated into a single entity (or type -‘simple substance’). It is now being recognized that the organization of the cell is not wholly directed from the DNA, since the genetic code needs to be read or interpreted and this involves the active role of the ‘heat-shock proteins’ for example (which determine the three-dimensional forms of crucial proteins). Nothing in the cell is wholly passive and determined by something else. The cell is a true monad. In Its evolutionary history, the cell has ‘learnt’ to contain bacteria, for example. Organisms develop through the synergy of various kinds of cell, already formed. Each ‘higher organisms’ encapsulates what has already existed in a more diffuse form.

We might well need to make a distinction between diffuse and concentrated monads. When a monad becomes concentrated in space and time, we have an organism. But, we can think of examples which Dim are not derived from the living order as we know it. Consider for a moment Aristotle’s ‘Poetics’ and the passages in which he deals with theatre. tiffs prime requirement for the dramatic work is ‘unity of time and place’. Yet, we also realize that, however ‘microscopic’ the scale of a given work may be, it may yet encapsulate the fate of nations or the whole meaning of life!

If there is a movement from the diffuse to the concentrated, then this transition will be something that we recognize, in the living world, as evolution. In the world of human culture, we will recognize this transition as art.

We can see that the condensation of the monad is recognizably creative; and we may understand creativity, now, as not making something out of nothing but making something definite out of something vague. What we might call ‘diffuse systems’ are turning out to be remarkably interesting; and we should recall our earlier reference to the birth of the solar system out of a diffuse but diverse content that had no clear boundaries. Astronomy recognizes the significance of the content of regions which far out-strip our technological capacity to create a vacuum. Extending the concept further, we have the vacuum-state of contemporary physics which, is, in fact, a veritable seething ‘sea’ of virtual particles: even where there is ‘nothing’ there is a monad which contains everything. In this sense, the vacuum is alive. This is not materialism, because we are averring that ‘in the beginning’ there never was ‘just’ matter.

We have greatly extended the scope of our argument and reached a limit in the prime stuff, hyle or ylem, which is the stuff of the monad. The mode of thinking we have been engaged in leads us to the point of view that all forms of reduction are ultimately false: the world presumed in physics, which is supposed to be the product of linear forces, is an abstraction. We would do far better to ‘regard the lilies of the field’ if we wish our thought to reflect reality.

Nations

It might at first sight be thought that nation states constitute the most rigid and artificial division of the human world that we can conceive of. However, consider this: nations are a condensation from the vagueness of pre-national existence; each is a complex whole with diverse content (think of Yugoslavia); and there are many kinds of nation (think of: the U.S.A., Armenia, Taiwan, Monaco, Lebanon, etc.). Often, the nation states are contrasted with the ‘peoples’ of the world, defined by language and culture and even race and religion. But, by the nature of human history, it would not have been possible for the ‘peoples’ to remain coherently concentrated each in its own locale. Diasporas are diffusions which contribute to the mange of humanity.

Every true whole must be a plurality.

This does not ignore the fact that the diversity within a nation leads to oppression and conflict, the violation of human rights and seemingly endless institutionalized dominance of one faction by another. Considered as a work of art, the nation state is an atrocity. But, we must consider whether this ‘atrocity’ is not part of the content! What we see evidenced in the nation state is the highest form of monadic intelligence of which mankind is capable. Nations come into being and are amalgamated, truncated or even eradicated altogether. There is a process; one which occupied the centre stage of the political history of the world over the last two thousand years. Further, the nation states have arisen out of the diversity which existed before, which ranged from the great empires of Persia, Greece and Rome – amongst others – to the smallest tribal unit. The nation state is unthinkable without written language and institutions of government based on law and consent.

To understand the nature of the nations, we would need to contemplate every one of them, first of all ‘diffusely’, allowing ourselves to be absorbed into their diversity, until there emerges, secondly, a single sense, a unified import. Then we would have the nations speaking ‘in one voice’ – the ‘one voice’ being the voice of the multitude, their pride and anguish together.

The example of the nations teaches us that the monad is explicated by the diversity of the monads which exemplify it. Peoples, wars, monarchs, democracies, socialism, organisations, languages, religions and so on are all in the nations as they exist together. Our diffuse contemplation dissolves away the rigid boundaries of the national frontiers and then allows these to reform, to condense with their brittle shells around them; but, it is in the process of diffusion and condensation that we have our understanding. We are enacting the very process by which the nation states themselves evolved and we can find ourselves with an intuitive sense of their future.

As an inner ‘line of work’ this process is one of assimilation, making as we say something tour own’; which means also that we allow ourselves to be absorbed into the something. We find the way of ceasing to be a mere observer; we live in the life that we have contemplated. Every part of ourselves – our senses, skills, memories, feelings, even our flesh and blood, our cells and hormones – participates. The true contemplation of the monad is the awakening of our own totality, diversity, plurality, unity. We are finding ourselves within ourselves; we enter into the living of our lives.

Assimilation and the Unity of Life

We have tried very hard to avoid making any statement that implies that it is out of the conceptual power of our minds or out of the unitive nature of our consciousness that the monad anises in its intensity. Consciousness does not ‘make’ unity, nor even ‘constitute’ it. Unity is entirely natural; and, we have been at pains to bring out how this natural unity is no opposite of diversity, plurality or the ‘many’. Unity in diversity is inevitable and is the only ‘given’. There are really no givens such as sense-impressions or, to take a very different example, archetypes; nor are there platonic ideal forms; nor even numbers. Always and in everything there is the diversity of the one. The apparent simplicity and clear-cut demarcation of ‘one’ is only evidence of an extreme in our apprehension of the monadic reality. As we have said, assimilation implies a taking into ourselves and making one with ourselves (what Gurdjieff called ‘transubstantiation for our being’); but, being is ubiquitous and we receive as much as we give. Assimilation is not a from or a too. It is the unification taking place in the diverse. There are not even two sides – for example, a subjective and an objective – there as many sides as there are monads within the monad, that is: as concentrations of life.

The unity of life is not some over-riding principle, or some elan vital. It is assimilation itself. There is no unity standing before or outside the course of events. There is no power of oneness which we have to suppose ‘engineers’ the integration of the plural into a whole. The very diversity of life itself is the unity of life.

EVERYTHING ISSUING FROM EVERYTHING AND AGAIN ENTERING INTO EVERYTHING

That is life, not some separate power hiding within the mechanisms and spirits of the overwhelming totality.

To assimilate means to live!

And the unity of life is feeling.

It is not in a conceptual unification, which must inevitably rest upon an abstraction. Feeling is concrete, not abstract. Feeling has within it the diverse, even the seemingly unordered. Feeling informs us of our unity with the world and with ourselves and with others. It is not possible to reduce feeling to something explicable by the conceptual apparatus. We speak of feeling and not emotion in the sense that Wordsworth implied when he spoke of the poetic art as ’emotion recollected in tranquillity’: the particular agitations of our emotions are allowed to die away and reveal the feeling that is the unity of life. The feeling is not a feeling about life: it is the unity in diversity of life. Feeling emerges from the vitality of our living body; it engages all that we contain as concentrations of all of the content of life.

Without feeling we are dead!

The world is full of death.

Choose life!

The Material Question

Throughout the history of both cosmogonic speculation and scientific enquiry there has been present some question about origins – the origin of the universe or the origin of life (even the origin of language for that matter). In recent times we have much discussion around how life arose on this planet from ‘inorganic matter’ and also around how the highly structured universe chat astronomy sees could have arisen out of the Big Bang. These questions correspond with the ancient ones in that both tend to regard the issue as one of explaining how complexity, life and intelligence could have arisen out of stages seemingly lacking in these. We wish to point out that, at the back of such questions and issues is the problem of understanding matter. Traditionally, or at least in the most widely known part of tradition, matter was regarded as having nothing in itself capable of differentiation, structure and movement. In Aristotle, for example, matter is pure inertia having a capacity only in its receiving of form. Bruno, in one of his dialogues (on ‘Cause’) says that from Aristotle came ‘the medieval notion of deprived matter’ which was also the ‘ecclesiastical notion of depraved sensual woman’ (from the commentary by J. Lindsay).

Bruno’s attack on the Aristotelian view of matter which, although avoiding the extremes of dualistic Gnosticism in which matter was regarded as ‘evil’, reduced it to a powerless inertia-is of great importance for our study of the monad. What had been done was a reduction.

The reality of phenomena pi had been cut into two parts such that one part was inactive and the other active (and also, ‘inferior’ and ‘superior’ respectively). This cut made it next to impossible to understand how the two parts could ever make one whole; it prohibited the approach of relatedness. There were alternative approaches. For example, Avicebron argued that the primal reality was will and in will ‘form’ (the ‘active’) and Matter (the ‘passive’) were united. In other words, he began from relatedness and the triad. As is fitting, he ascribed to matter its own kind of power or force; and, taking a minority view, asserted that even spiritual entities had also a materiality of a kind.

Once we understand that our view of matter is created by the acts we perform, our understanding of materiality can undergo a transformation. There is, for example, no such thing as an underlying substance which is used (analogously to clay) to fashion the things of the world. And, if there is such a thing as ‘form and matter’ then we should be able to divide form from matter by some act of our own; and, not just a mental act, either. What we have in scholastic tradition is literally ‘possession’ by a habit of abstraction, obscuring the elements of our actual experience, which are the phenomena of the world. It is not surprising that once thinkers had killed the living, they could consider matter as a corpse. In much the same way, physical science killed the living world and found itself with a matter from which it struggles to recreate a semblance of what everyone knows! If we adopt the outlook of the monad, we can begin to entertain the notion that there is no underlying substance, there is no matter as it is usual to suppose, and organized complexity is simply a matter of perspective. If we could see the universe in the correct perspective, we would see that it 2d.s alive! The ‘anthropic principle’ is a rudiment of this approach.

We are only able to find ‘inorganic’ matter because we have killed the organic. Matter must be vital and intelligent: we are aware of the world out of which we were made and, therefore, our awareness comes from what we see! However, the important principle is the following:

MATTER IS ITSELF DIVERSE

It is not possible to separate out matter on one side and contrast it with something else. Materiality belongs to the monad and it is plural. We have been deceived by the successes of atomism and the promise of the GUT’s. As we now know, there are no ‘atoms’ (indivisible) and we predict that the pursuit of a GUT will lead to the discovery of a pluralism of ‘forces’ never before suspected. The pursuit of unity must uncover diversity.

‘Countless Singulars’

We look for a universal law, we classify according to species and genus, we want to explain in terms of ‘underlying mechanisms’ or ‘overlying patterns’ and so on. In a word, we want to avoid the world as it is! The belief in laws, the work of classification, the attempt to explain are all worthy and meaningful; but the first thing is the monad and, for the most part, we neglect its wisdom in the pursuit of ‘superior’ insights. There is a reason for this, foremost amongst many others: it is that we can take the world as it is for granted; we can assume that it is easily and obviously at hand and is our common point of departure. This is not true. It is most unusual to return to the monad and make the new beginning; to look without making distinctions and generalizations and in the process of assimilation find the ever-fresh organic unity which plays in the diverse.

The phrase ‘countless singulars’ comes from Rilke and it is not surprising that we should turn to a poet for felicitous expression. It is pretty obvious that we use words like man (or woman!) and imagine that we know what we mean, that we can think about ‘man’ as such, believing that we will have coded into our brains somehow all that we can ever glean from our experience of men. By the time we are adult, we have been led to believe that we have all the basics sorted out; that we know what a ‘man’ is in general, or ‘democracy’ or even ‘God’. We have been led to believe that it is impossible to contemplate all at once the rich and changing diversity of experience of these things that proceeds in us: it would seem, to us, a plunging into chaos. Yet:

THE MONAD IS STARTING ALL OVER AGAIN.

It is all said perfectly by Rilke (‘Notebooks of Malte Lauris Brigge)

Is it possible that we say ‘women’, ‘children’, ‘boys’ not suspecting (despite all our culture, not suspecting) that these words have long since had no plural, but only countless singulars?

Is it possible that there are people who say ‘God’ and think that this is something they have in common… Is it possible to believe we could have a God without using him?

THE DYAD

The Dyad

Though it is easy to conceive of contradiction in its logical sense, it is quite another thing to appreciate this as a feature of the ‘real world’. How can we ever say that there are contradictions in the natural order? Surely this is something which we are imposing by virtue of the way or ways we choose to regard nature? This is one of the main issues surrounding the dyad which we have introduced here in the guise of contradiction, or mutual exclusion, as our starting point.

Mutual exclusion is certainly a property of the physical world. Two solid bodies cannot occupy the same place at the same time; two electrons cannot be in the same state; these are obvious examples. Mutual exclusion can be regarded as a degenerate form of the triad: there must be a point or surface of contact which is created by the exclusion force. This illustrates a central difficulty with the dyad; that it is almost inevitable that any expression we give of it must lead us to suppose a third term which is mutual to the two elements. We are caught in the form of our representation. We are required to have two elements and then also regard them as making one whole. How is it possible to conceive this oneness without entering the domain of the triad?

Our first suggestion is that, in some way, the dyad had two alternate states. In each of these states, one of the terms doubles as the whole. Therefore, we would speak of, alternately, each term ‘containing’ the other. These two forms amount to treating each of the terms, in turn, as absolute. The intrinsic dichotomy of the dyad is that between two poles of the absolute. It is a tension of explanation.

A commentary on Nicholas of Cusa includes the following; ‘Unity is not a number, but is the principle of number as the minimum and the end of number as the maximum’. In another commentary, we can read: ‘His doctrine amounts to this: the more abstract, simplex, united, the more actual; and also the more concrete, complex, separate, the more actual.’ In a word, the absolute (or actual) point implies two opposite directions. The abstract and the concrete; the absolute and the relative; the least and the most: these are examples in which each term can be taken as the whole, extinguishing the other. This is a peculiar sense of ‘mutual exclusion’. However, we have been reduced to purely conceptual manipulations. Where is the physical reality?

We must also remember that we have just ‘left’ the monad with its indeterminate diversity of inner relevance. And we are looking ‘towards’ the triad with its simple form of relatedness. The feeling this must give us is that the dyad should not be considered as simply a binary description, or a coupled pair of definitive terms. One means of approach is to think of every item in the content of the monad as entering a space wherein a tension emerges between the nature of the monad and the nature of the triad; the one strong in diversity and the other strong in unity. But, we need to be careful and explore various models.

For example, we may regard the ‘pull’ of the monad as towards dissolution and amorphousness; and the ‘pull’ of the triad as towards clarity and conservation – articulateness.

Somehow, we are dealing with states in the dyad. We want to argue that everything exists (or ‘is’) in two states at the same time. Ambiguity is built into the nature of reality. Without this, the totality would not be interesting, nor could it develop. It is not that there are two ‘things’ which make up the dyad; rather, everything is two-fold. The two-foldness seems to arise when we seek to ‘pin it down’; to fix, determine, define and limit the item. We draw nearer to what may prove to be the key characteristic of the dyad state; it is the question of limit.

This leads us to the Greeks and, in particular, Anaximander. However, we will begin with Heraclitus, renowned as he was for asserting the paradoxical identity of opposites. In his survey of the Pre-Socratics, Hussey explains that the fragments we have of the Greet thinker suggest two interpretations for the palintropos harmonie where he gives the examples of the bow and the lyre. In one interpretation, he is describing an alternation, and , in the other, a static tension (where the Greek word would then be palintonos). We may also consider the alternation interpretation as describing an oscillation. Here we have another kind of example of the alternate states of the dyad; or of the intrinsic two forms of the dyadic whole. The key fragments are:

They do not understand how what is at variance is in agreement with itself: a palintropos harmonie like that of the bow and the lyre (fr.51)

Conjunctions: wholes and not wholes, the converging the diverging, the consonant the dissonant, from all things one and from one all things. (fr.10)

God is day night, winter summer, war peace, surfeit famine; but he is modified (alloioutai), just as fire, when incense is added to it, takes its name from the particular scent of each different spice (fr.67)

‘I say merely either/or’ (Soren Kierkegaard, ‘The “Or”‘)

A life without compromise is very difficult; even more difficult is the confrontation with a choice that cannot be made on any grounds, i.e. on anything preceding, or on any system or principle; a purely naked choice. The ‘naked choice’ renders oneself naked and nothing; and, how is it possible for a ‘nothing’ to choose?

The form of the naked choice is between nothing and something, between the abyss and the familiar; rather than between good and evil, which are related. Nothing and something may sound like innocuous concepts, but the choice they entail is dangerous and irreversible. Very few of us reach this choice at its most intense; it is not something for the weak of heart, or for those who have made their lives a path of compromise. When we make a discussion of this choice, we do so at a distance, safely; we contemplate the possibility of the choice and not the choice itself. As far as we can, this should be remembered. For those who have never come to this, it will seem absurd: it will be imagined that there is always some kind of middle path, some way of combining the ‘best’ from ‘both sides’. But, in the Either/Or there is no middle ground and the choice of the one means the total loss of the other.

The most obvious parallel we have is that of the output in an electronic circuit which is either 1 or 0. It is very strange that this should be so, that the basis of our digitalization of information should have the same form as our most anguished moment. What is the ‘nothing’ we speak of? It is one with the sense that the ultimate reality, the truth, is not like anything we know; that it is without form, relies on no knowledge, builds on no prior experience, can be supported by no act of reason. In the realm of Christian theology and mysticism, it has been the ‘impossible faith’ or the faith in the impossible, as signified in particular by the faith that Jesus Christ was indeed God and suffered on our behalf, that God was made man. In non—theological mysticism, it is the unknown and therefore also the unconditioned, the unlimited; in contrast with the ‘known and the conditioned. And man himself is viewed as a duality in this way in the one nature unknown and in the other known. The something is all that we knows, (however much this might be) all we can work out and understand, the highest subtleties of reasoning, perception and discrimination. And in the something, we believe that everything there is can be related to and explained by what we have come to know and control; that it is of a piece with the familiar.

In this sense, God cannot be proved; for, anything that can be proved cannot be God. Any argument about the existence of God is absurd because it is an attempt to articulate the ineffable. In more formal language, the argument for God is of the kind:

a = b

Whereas, the affirmation of faith (there is no God but God) eschews all translations and is of the kind:

a = a

This introduction of more formal language leads us into more comfort-able areas. In particular, we can think of the two basic forms of explanation. In the one, of the kind a=b, explanation is extrinsic; while in the other, of the kind a=a, explanation is intrinsic. The former covers all attempts to explain something in terms of something else that is postulated. Thus, it includes the attempt to explain the world in terms of God; which, is tainted with absurdity because God alone is real. The latter includes all monistic assertions; including that in which the ‘All’ is considered as entirely material. This attempt, too, is tainted with the absurd, since it endeavours to consider e.g. consciousness as merely material; which is of the kind a=b.

In front of the ‘world’ – which we may consider in terms of the monadic whole we turn our attention upon – we have to ask: is this all there is? Is it what it appears to be? What is real? These questions – of the All, Appearance and Reality – are the absolute questions. Th have very practical implications. For example; at a certain moment in our lives we may contemplate the monad of our existence and ask: Is this all? We can be ready to cast everything into doubt. In varying degrees, such a moment comes to many people. Philosophy usually begins by confronting the world and asking: Is this mere appearance? Whether academic or ‘real life’, these moments of doubt bring us to a moment of choice, an either/or, no matter how well it is softened by compromise and vagueness. The absolute questions, the moment of doubt and choice belong to the dyad. They are what they are when there is no relatedness between the two terms: each has the power to extinguish the other. We say ‘extinguish’ even though any attempt to make anything of our choice is bound to lead us into contradiction and absurdity, arising from the two kinds of explanation (a=b and a=a). What has to be firmly grasped is that the choice is one of exclusion and exclusion and is the very nature of the dyad.

THE DYAD IS EXCLUSION

In this, the dyad destroys the unity of the monad. It is more powerful thing than was hinted at in the fragments of Heraclitus; the reason being that amongst the Greeks choice was never treated as an existential reality.

Codification of Choice

It is usual that we come across dyads in only a weak sense, somewhat distanced from their origin in the Absolute. The two ‘poles’ or terms can easily be regarded as alternatives and, in a sense, it is possible to ‘flip’ from one to the other; though it remains rare to be at the edge of the knife. An example of this comes from the mystical tradition which aims at an insight into God. From Dionysius stems the tradition of the via negativa and the via positiva. In the negative way, the choice is constantly to say ‘not this, not that’,i.e to deny that God has any relation with anything we know. In the positive way, the choice is to see God in everything , as the perfection of everything that we know. It is then fairly easy to think of following the two ways in a ‘balanced’ manner. However, they exclude each other and, at best, can only be undertaken in alternation. This is what we mean by a ‘codification’: in this, we ourselves are protected from the real choice and given a sense of neutrality. Interestingly enough, the world of electronics is more to the point. The binary states can act in switches and something is brought into operation of not according to whether the input is a 1 or a 0. In contrast to electronic circuits, however, the condition wherein ‘nothing happens’ is as powerful, in the human worlds as that in which something does happen. The blank state, the void, is something in human experience; it has an effect.

The idea that there can be a choice between Nothing and Something, that there is such an act with absolute significance, is itself subject to dyadic ambiguity: is such a choice real? Here we glimpse something important yet very elusive:

DYADS CODE DYADS

which means that every dyad is and is not translatable into another dyad. We return to the two-fold form of a=b and a=a. All codifications are of the kind a=b. Which, then, equally (a=a)

THERE IS ONLY ONE DYAD

The codification of choice is the avoidance of choice. It allows us to select between alternatives, which means that there is a ‘pseudo-choice’ that can be based on extraneous data. For example, in the case of the two-fold analysis of Dionysius, the alternatives appear in the framework of how we understand human psychology; whereas the central choice is the choice of God, the Absolute. Codification – or translation – brings into the side of the relative and away from the side of the absolute.

Codification leads to mechanism, to the computer, in which everything that happens has already been fixed. The complexity which this can reach should not obscure the reductionist simplicity from which it stems It is based on: if more than x, then 1; if less than x, then 0. That is, on a distinction. And, whereas distinction comes from intellect, choice comes from the will. Codification, translation (a=b) and distinction are all intellectual or cognitive. The simplest form involved in distinction consists of giving a ‘name’ to one side of the distinction and leaving the other un-named. This may be understood by the example of selecting out of field of data those items which are ‘relevant’, ‘important’, ‘true’, etc. in which we may disregard the remainder. This was made clear in the work of G. Spencer Brown is his ‘Laws of Form’. Brown replaced the Boolean algebra with one of his own devising: it can be interpreted as replacing the Boolean (and classical) true/false with just one term (usually, for technical convenience, ‘false’) leaving the other unspoken as what is not this term. This was an important step, since the form true/false leads us to think of ‘true’ and ‘false’ as not simply opposites of each other but as ‘somethings’ in their own right. As Browne was at pains to point out, the essential content is in the form of the distinction, not in what either side ‘is’.

If we follow this approach, then we have one term which is named or ‘noticed’ and we can think of this as ‘something’; what is then left is un-named and we may think of this as ‘nothing’. This is, of course, reflected in electronics where ‘something’ is 1 and ‘nothing’ is 0! 1 is then, not a number as in the sequence 1,2,3, etc but simply the name of ‘something’ in contrast with ‘nothing’. In this, we have the most perfect clarity; because the form is absolute. But, we should note that ‘half’ of the content is lost even though, in the form, ‘nothing’ is lost. If we make a distinction, we can only attend to one side. We should add: ‘at a time’ to the above.

Now, in the codification of the dyad – which is through making a dis-tinction and giving a name to one side – the term represented by 0, or the un-named, becomes unknown: therefore, the term ‘0’ represents our ignorance, or our unconsciousness. We gain the information afforded by codification at the cost of real choice. That is why we asserted that codification leads to mechanism.

The alternative is the anguish of choice, or the impossible: to choose to be without choice; for, once the choice is made, the alternative ceases. In the moment of choice, however, both alternatives are present – wholly present – which is an impossible state of affairs. Without choice, the state of affairs remains external ‘in code’. In this way, comes about the distinction between the ‘subjective’ and the ‘objective’, the ‘private’ and the ‘public’ in which either of the sides of the distinction become ‘projections’ of the other so that nothing ever can be understood. In the true moment of choice, there is no distinction but only exclusion: each side absolutely excludes the other. This is the ‘tearing apart’ of being which is pre—requisite for creative life.

‘Is it possible … that we have not yet seen, known, or said anything real and important?

Yes, it is possible’

(‘The Notebooks of Malte Laurids Brigge’ by Rainer Maria Rilke).

Whitehead, Relatedness and the Monad

Whitehead’s philosophy of organism was intended to cover the whole range of the sciences; a brave act in a time before the changes in physics away from the classical principles had brought it to the point of relying on relation as prior to eternal and separate existence. As Prigogine remarks; ‘ (in physics) for an interaction to be real, the “nature” of the related things must derive from these relations, while at the same time the relations must derive from the “nature” of the things.’ In Whitehead’s philosophy, relation is taken as fundamental but is not analyzed or articulated into ‘components’ – as we have been concerned with doing – remaining as an irreducible intuition. We believe that this was due to Whitehead’s over-riding concern with the categories of creativity and existence and, in particular, with his project of establishing in philosophy (and science) a basis for the concrete entity. He wrote:

the individual fact is a creature, and creativity is the ultimate behind all forms, inexplicable by forms, and conditioned by its creatures

It is with his ‘Category of the Ultimate’ that we may discover many coincidences with our own understanding. The quotation we have just given should be sufficient to underline the assertion that Whitehead was distancing himself from any conception of the world which supposed the ‘ultimate’ to be fixed, atomic and indifferent; for him, the ultimate was creative, relational and meaningful.

‘Creativity’, ‘many’, ‘one’ are the ultimate notions involved in the meaning of the synonymous terms ‘thing’, ‘being’, ‘entity’.

That is to say, we cannot regard ‘anything’ as simply ‘existing’ as a thing. It has come into existence, which is creativity. It comes into existence through the many. And, as he assent later, by its coming the many are made one, a kind of ‘one’ which renders this thing an ‘entity’.

The term ‘one’ does not stand for ‘the integral number one’ which is a complex special notion. It stands for the general idea underlying alike the indefinite article ‘a’ or ‘an’ and the definitive article ‘the’ and the demonstratives ‘this’ or ‘that’ and the relatives ‘which’ or ‘what’ or ‘how’. It stands for the singularity of an entity. The term ‘many’ presupposes the term ‘one’ and the term ‘one’ presupposes the term ‘many’.

It is interesting that Whitehead’s conception of the one and the many are not mathematical and that he explains what he means through the common use of words. He goes on to make use of a terminological distinction between the ‘disjunctive’ and the ‘conjunctive’: the former refers to the multiplicity of diversity while, in contrast, the latter refers to the unity in diversity.

‘Creativity’ … is that ultimate principle by which the many, which are the universe disjunctively, become the one actual occasion, which is the universe conjunctively. It lies in the nature of things that the many enter into complex unity.

For Whitehead, there were real changes in the universe – in contrast with Einstein, say, who regarded our experience of the passing of time as ultimately an illusion – and this meant that the coming into being – the becoming – of anything — was a change in everything.

‘creativity’ is the principle of novelty. An actual occasion is a novel entity diverse from any entity in the ‘many’ which it unifies. Thus ‘creativity’ introduces novelty into the content of the many which are the universe disjunctively.

He goes on to consider what it is he is asserting about the many and the one and about the disjunctive and the conjunctive; and takes as the critical notion that of ‘togetherness’.

‘together’ presupposes the notions ‘creativity’, ‘many’, lone ‘identity’ and ‘diversity’. The ultimate metaphysical principle is the advance from disjunction to conjunction, creating a novel entity other than the entities given in disjunction. The novel entity is at once the togetherness of the ‘many’ which it finds, and is also one among the disjunctive ‘many’ which it leaves… The many become one and are increased by one. In their natures, entities are disjunctively ‘many’ in process of passage into conjunctive unity. This category of the Ultimate replaces Aristotle’s category, of ‘primary substance’.

This passage may help the understanding of our concern to with the monad as ‘process’: as we add further content so the whole is both further unified and diversified; the monad is always a ‘one’ but the meaning of this changes with the addition of every ‘one’. Further, Whitehead’s replacement of the Aristotelian category of primary substance parallels our own attempt to do away with the scientific conception of underlying ‘matter’. He writes:

philosophy is explanatory of abstraction and not of concreteness.

Whitehead set himself towards the concrete, as we have done; and we discover that in his ‘Category of the Ultimate’ he has established – speaking, in our terms – the principle of the monad.

Now, in this respect, it would of course not be appropriate to enter into an analysis of relation; and, it may not even be possible. This, on two grounds. First, in the Ultimate we can consider only the essential content of organic unity; which, in Whitehead, takes ‘creativity’ as the universal of universals. Second, any attempt to analyse relation into a general form appears as an abstraction; and what we appear to be doing, is seeking some explanatory mechanism for what is given intuitively concerning the nature of reality. This strikes against the ultimate category of creativity which makes fundamental the novelty of every actual occasion.

Whitehead criticizes Newton for his systematization of the universe, one that required ‘a definite supernatural origin with (its) articulation’. He also says:

our notion of causation concerns the relations of states of things within the actual world and can only be illegitimately extended to a transcendent derivation.

The ‘relations of states within the actual world’ is an insistence on the creative actuality of the given; there are no separate ‘laws’ underlying the workings of the things we see, for what we see are things working together as they do. What is realistic and important is to see more and more about how things are working together, defining each other as they do so. Whitehead also says:

Every actual entity, in virtue of its novelty, transcends its universe, God included.

In his insistence upon the concrete diversity of the world, Whitehead has gone further than any other before him. He is a cosmic democrat, in that even the most fleeting occasion participates in its own special way in the becoming of the universe. But, he cannot leave the world of the monad; there is never a choice of ‘nothing’ over ‘something’; the opposites are ideals; the articulated system must be an abstraction that neglects creative becoming. We should remind ourselves, again:

Philosophy may not neglect the multifariousness of the world – the fairies dance and Christ is nailed to the cross

The world is one of contrasts and, Whitehead says: ‘What are ordinarily termed ‘relations’ are abstractions from contrasts’. He goes on (in ‘The Theory of Feelings’) to make this criticism:

A relation can be found in many contrasts; and when it is so found, it is said to relate the things contrasted.

… a relation will not do the work of a contrast. It fails to contrast.

… relations … are indiscretions of the absolute, springs of reality without self-consistency.

In the context of this argument of his, Whitehead speaks of a ‘multiple contrast’ which is not a ‘mere aggregation of dual contrasts’. Thus, he is saying that (aD a relation is unique to its relata, and (b) multiple contrasts form a unity which cannot be reduced to a single dual contrast, excepting in a misleading abstraction.

… the real synthesis of two component elements in the objective datum of a feeling must be infected with the individual particularities of each of the relata. Thus the synthesis in its completeness expresses the joint particularities of that pair of relata and can relate no others.

Thus, Whitehead does not deny relations – indeed, they are important in his philosophy – but relations arise out of the concrete complexity, the many in one and the one in many of creative becoming and cannot be considered ‘in their own right’ because they have nothing of their own. Have we been committing ‘indiscretions of the absolute’?

However, consider the following:

Prehensions (are) Concrete Facts of Relatedness

… every prehension consists of three factors: (a) the ‘subject’ which is prehending, namely, the actual entity in which that prehension is a concrete element; (b) the ‘datum’ which is prehended; (c) the ‘subjective form’ which is how that subject prehends that datum.

What he calls ‘positive prehensions’ are feelings.

a nexus is a set of actual entities in the unity of the relatedness constituted by their prehensions of each other.

Thus, there is an ‘eternal form’ of three factors which applies to every prehension; but this tells us nothing about the content of the prehension – the concrete fact of relatedness – itself. Whitehead’s three factors are almost banal, echoing the traditional subject, object and mode of contact between them.

We have the contrast between the universality of relatedness and the unique content of every relation. There is no universal relatedness which can inform us of the reality of things.

The Significance of Revelation

It was not for nothing that in the Christian tradition it was taken as axiomatic that the doctrine of the Trinity was a matter of revelation and could never have been arrived at through reason and the experience of the world. In a sense, the Trinity does everything: it is thus a complete explanation of reality when seen in this way. To see it in this way is, of course, a matter of choice. Interestingly enough, it is also a matter of our attitude towards revelation as such; i.e. whether we accept that information about reality can reach us in the form of a doctrine, without scientific work.

Our own approach, of setting off to look for what might be the characteristics of such a universal ‘law’ as the three-foldness of relatedness, is rather like acting. ‘as if’ we were in receipt of a revelation. Rather as the early Christian Fathers did, we struggle to make sense of our assumptions or starting points.

We have mentioned choice. This is going to prove the critical factor. There is little doubt in our mind, that Whitehead is thoroughly consistent and realistic in his exposition of the ‘nature of things’. There is no way in which we can generate out of the real diversity and interconnectedness of the world a ‘law of three’. There are only two laws: the ‘law of one’ and the ‘law of many’. We suspect that the terms ‘two’ and ‘three’ do not have the same kind of status as ‘one’ and ‘many’. Therefore, if we wish to realize our aim of finding ‘laws of understanding’, or ‘laws of laws of nature’ and the like, we have to assert something that has no rational foundation.

Bearing this in mind – and it has some radical implications – we can return to Whitehead and, in particular, to his doctrine of ‘creativity’. In our explorations, creativity has appeared with a ‘causative’ character. It has raised, for us, the whole question of what is active in a process. We have tended to dramatize the process of becoming in terms of a ‘push’ and a ‘resistance’ which, in its turn, leads us towards the notion of the third force (such as in the example of catalysis). Affirmation and denial go together, arise together; we tend to believe in a ‘higher nature’ by virtue of the feelings of resistance in our ‘lower nature’; a new idea has to struggle for its survival in a community, for there is always a tension between the new and the old; a variant in a species has to find a niche or create one, or it perishes. In contrast with Whitehead’s ‘Taoism’, our view of creativity has been linked with struggle.

Modern biology, in considering the path of evolution, tends to shy away from any view in which there really is a ‘higher’ superseding a ‘lower’ indeed, the criterion of survival, awards the laurel to such entities as the most primitive bacteria or the algae! Why do the biologists act in this way? Because, to admit the ‘higher’ is to admit everything they have tried to eradicate; that is, any supposed principle standing ‘outside’ or ‘above’ the natural order they study. To admit the ‘higher’ is to lay oneself open to the possibility that there are ‘higher causes’.

It is important for the biologists, then, to have a notion of ‘creativity which makes it all of a piece throughout the natural order. In respect of this, Whitehead has provided an inestimable service – though one only now beginning to be faintly realized, through the work of scientists such as Prigogine and scholars such as Needham. However, Whitehead speaks of God. How does he do this? Not, certainly, as some transcendent autocrat or superpower.

… the Galilean origin of Christianity … does not emphasize the ruling Caesar, or the ruthless moralist, or the unmoved mover. It dwells upon the tender elements in the world, which slowly and in quietness operate by love; and it finds purpose in the present immediacy of a kingdom not of this world. Love neither rules, nor is it unmoved; also it is a little oblivious as to morals.

And, yet, there is a structure to be found:

The universe includes a threefold creative act composed of (1) the one infinite conceptual realization, (ii) the multiple solidarity of free physical realizations in the temporal world, (iii) the ultimate unity of the multiplicity of actual fact with the primordial conceptual fact

… we conceive of the patience of God, tenderly saving the turmoil of the intermediate world by the completion of his own nature.

He does not create the world, he saves it; or, more accurately, he is the poet of the world, with tender patience leading it by his vision of truth, beauty and goodness.

God and the World are the contrasted opposites in terms of which Creativity achieves its supreme task of transforming disjoined multiplicity, with its diversities in opposition, into concrescent unity, with its diversities in contrast.

All the ‘opposites’ are elements in the nature of things, and are incorrigibly there. The concept of ‘God’ is the way in which we understand this incredible fact – that what cannot be, yet is.

What do we find here except a language which echoes our own? (And a sublime language, far superior to our own coarse expressions). Here is sameness – the one infinite conceptual realization – difference the multiple solidarity – and their unity. God ‘saves’ the world and does not ‘create’ it: thus, God is here the third force, the reconciler, And yet, also, it is Creativity which reconciles the contrasted opposites of God and the World. And, further, God enables what is ‘impossible’ (‘what cannot be’) to be. Again, in our own terminology, this is to regard God as the third force.

We find, then, that Whitehead – in his theology – is forced to consider the triad – not as such, but as the essentials of a threefold and irreducible harmony. What we do not find is the sequel (the chapter on ‘God and the World’ in Process and Reality is the last) in which the nature of God is to be found in every world. Perhaps, for Whitehead, this would be obvious and inconsequential, and one would not have, for example, to suppose that for every ‘world’ there was a ‘God’ making for ‘superior’ and ‘inferior’ Gods, but God would remain always ‘God’. He allows for ‘subtle gradations’ elsewhere; but even so, the principle would remain the same.

Most importantly, he makes no connection between the ‘triad of God’ – to use or impose our own terminology – and the world of concrete relations. This is just what we have attempted to do, making the ‘triad of God’ the pattern for all relations.

When the Christian theologians wrestled with the Trinity, they were seeking the salvation of reason. For them, reason was not sufficient in itself and it was necessary for revelation to be realized in its sphere of operations, else it was to be left without ultimate meaning. The project was – and is – to take the material of revelation and find its meaning in everything. It required two things (a) a claim to revelation, (b) the assertion of its immanent universality in every occasion.

These requirements are really choices, made under the threat of the absolute.

However, in common with Whitehead, they also entail an underlying sense of the unity in diversity of all things; that we cannot see something in one place and not find a meaning for this elsewhere. It is not restricted to a belief in the underlying rationality of the universe; because it puts into question what is rational, or what is order?

The fundamental choice is that of our ultimate categories, our most profound explanation for the nature of all things; taken in the understanding that these apply everywhere at all times and in all places and in the greatest and in the smallest. Beyond a certain point, the choice cannot be argued, only acted upon.

THE TRIAD IS ‘MADE POSSIBLE’ BY A CHOICE OF REVELATION

THIS CHOICE IS A DYAD

THE MONAD IS UNDISTURBED AGREEMENT

We may well suppose that the transition from monad to dyad is akin to the expulsion of Adam and Eve from the Garden of Eden. With the dyad, we partake of knowledge of good and evil – that is, we have choice – and the garden of the monad is forever closed to us.

Because we pass to the triad by way of a choice of revelation, we can never know whether or not we have ‘invented’ or ‘discovered’ what we find. We do not even know whether or not relatedness must involve three terms, or what this ultimately means. The other side to our choice of revelation is the realization of underlying uncertainty, of the essentially provisional nature of our conclusions.

The further we extend ourselves from the monad, the further we venture into the realm of creative uncertainty. With the Triad, we may be permitted to suppose that our labour serves to ‘save’ our understanding; and to learn how to surrender our conclusions almost in the same breath as we make their announcement. But, if we imagine going further still, we should have to consider whether or not we could ever cope with the accelerating flux of transformation. We have criticized any notion corresponding to that of the ‘infinite regress’, regarding this as a mere perversity of language when handled incorrectly. However, it hides a truth: the further we go from the monad, the deeper we are into ‘self-reflection’ – not of the same kind, endlessly repeated, but of different kinds and of kinds within kinds!

As we go further from the monad, at eh step we confront a choice and, sometimes, a multitude of choices. In front of all these we might well ask; How can I choose? There is no answer but in choosing. The dyad retains its power and anguish.

We might well imagine that, with the tetrad for example, we will enter a region of such supra-dynamic flux that it would prove almost impossible to say anything without gross error. The further we go, the higher the stakes.

However, here we introduce another factor. Let us turn the whole concept of the monad on its head! Let us imagine the real system of the monad in which every single term of the total diversity is recognized. Let us conceive of this as the ‘infinite system’. Let this be the truth. Then, as we go on, the truth comes to meet us!

From the Bible

The time in the garden of Eden is barely described (though Milton tried). How could it be? It corresponds to the ‘dream time’ of the aborigines. It is the world of the monad, attainable only in undisturbed contemplation; it is the Taoist harmony.

The Bible also passes rapidly over the moment of choice. It is called knowledge of good and evil which is a mere codification of the reality. We can hardly guess what it was that brought mankind to this moment – when he ceased to be ‘at one’ with all of nature and his path of special suffering and ‘sin’ arose before him.

The Old Testament is a document of conflict. Right at the beginning we have Cain and Abel. We have the doctrine of the ‘chosen people’ and Israel sets itself in opposition to all others.

In Deuteronomy we have the demand to choose: ‘I put before you this day blessing and cursing, life and death; choose life, therefore, that you and your deed might live.’

But, the New Testament is the document of salvation, of going beyond choice into the realm of will. This will is not the power of doing. This will is love. We are vouchsafed a glimpse of the ‘suffering god’. We are in the realm of the triad. All is relation. God and man are reconciled. Because of the ‘impossible’ fact that Jesus Christ is God, men were driven towards realizing the Trinity.

In this is the revelation that will is not doing but meaning. The Bible finishes with ‘Revelations’ symbolized in the four horsemen of the Apocalypse. The Apocalypse is not essentially a culmination of physical disaster: it signifies the end of previous understanding. We are in the era of the fourfold and struggle to find the revelation which will sustain us. It will be a doctrine beyond words. It will be made by the coming together of the four ‘winds’ from the four corners of the Earth. Nothing will ever be still again.

Complementarity

Quantum mechanics may prove to be the most important contribution science has made to human understanding of reality: because it has radically and irreversibly altered our conception of a ‘thing’. Nothing could have been more entrenched in human thought than that all the things of the world were akin to those we were able to see and touch; then, to discover ‘things’ which were ‘other’ to those of our familiar world produced a shock more profound than any of the previous destructions of ‘common sense’ such as the Copernican revolution, Darwinian evolution and even Relativity. To this day, our thought has not yet assimilated the import of quantum theory; controversy rages still with talk of alternative universes, or hidden variables and so on. The fundamental concept – for which Bohr was responsible – was that of complementarity. This supposes that the fundamental ‘units’ of the physical universe are capable of exhibiting two contrasting natures, according to the actions we perform to observe them. Thus, an electron for example can behave as a particle concentrated in a small location and capable of localized interaction with other entities; and it can also behave as a non-localized ‘wave–form’ distributed over space. Previously, these two behaviours were supposed to be the property of two quite distinct classes of entity, one a particle of ‘matter’ and the other a wave of ‘energy’. Complementarity asserts that we cannot have one without the other: every particle has wave-like characteristics and every wave-form has particle-like ones.

We have not introduced this concept into our earlier discussion of the dyad because we wanted, first of all, to establish the feeling of the dyad in terms of choice, the either/or. Complementarity seems to offer the possibility of having both sides together. However, this is only a conceptual possibility since any experiment must ‘choose? between the two natures: if we establish one behaviour, we lose the other. we cannot have both at once. Thus, complementarity is a ‘view from eternity’ and this must be remembered.

Complementarity has had a great influence amongst the ‘philosophical scientists’, just those whose writings and ideas are hardly ever brought into the forefront and, often, are not to be found in print. One important example is Pauli, who worked closely in his later life with Carl Jung on the concept of synchronicity as ‘complementary’ to ‘causality’ (or to statistics). A-causal synchronicity is the greatest challenge to the traditional world-view of physics and holds the greatest promise for understanding the ‘interaction which is not an interaction’ between the psychic and the physical reaps. Only a scientist of Pauli’s stature could not have been ridiculed for embarking on the study he made with Jung.

The simple understanding of causality is that of a ‘contact’ between contiguous entities of the same nature involving the exchange of energy. Synchronicity, on the other hand does not require ‘contact’ – though it does require some form of proximity – and does not entail an exchange of energy. Synchronicity generates meaning. Causality is without meaning because it is inevitable.

What we see here is a reflection at a deeper level of the contrast between the local and non-local forms which arose in quantum theory. There are even experiments in which it has been shown that two electrons, once related, maintain their relationship of states even when separated beyond the reach of light-signals (the ultimate channel of causality). It is supposed that there can be established some agreement, affinity or sympathy – to use anthropomorphic terms – between entities without physical interaction between them. Here we encounter elements of Taoism and the philosophy of organism.

It must be noted however, that all attempts to interpret this affinity or resonance at a distance in terms of some super-causality – e.g. through tachyons or hidden variables – have failed. In principle this must be so. The resonance excludes causality just as causality excludes resonance: there cannot be two different principles of connection at work in the same entities at the same time. Thus, an electron in resonance with another breaks its connection once brought into physical interaction with some other particle.

Pauli himself was responsible – in another sphere of quantum theory – for the famous exclusion principle named after him; in which two electrons cannot occupy the same state at the same time. It is this which makes chemical structures possible.

Complementarity does not resolve the dilemma facing us of having to deal with two quite contrasting ‘natures’ which have no common ground or ‘internal connection’ (waiting to be uncovered). With the two natures, we come to a stop: they cannot be combined together, since they exclude each other; it is an either/or. This is a far more disturbing state of affairs than that offered by the closely related concept of uncertainty in which previously independent parameters such as position and momentum can no longer be considered as such but calculated in combination. Of course, uncertainty does say: you can calculate position as accurately as you like but then the momentum becomes totally uncertain, or you can calculate momentum and lose precision in position. Either/or. Complementarity asserts that the two natures taken together under the law of mutual exclusion is the whole story. It is not an admission of ignorance. There is no ‘deeper structure’ to be found on the basis of which we can explain the ‘apparent’ dichotomy. Needless to say, such a state of affairs is extremely distressing – though not to all! It strikes at the traditional belief in the quest for a single underlying consistent order. A lot of scientists prefer not to think about it at all!

Amidst all the various schools of interpretation of quantum theory, Bohr’s ‘Copenhagen school’ holds fast to complementarity as itself a physical explanation: the universe is like this and the dichotomy is not a product of imperfections in us or in our instruments of knowledge. Complementarity is not a defect but the nature of things. With complementarity, then, we have a supremely clear example of a system (of the kind we have been exploring under the notions of monad, dyad and trail} which can be taken to describe physical reality and not just the ‘form of our understanding’ or the ‘laws of our judgment’. The broad characteristics of reactions to complementarity are easily predictable and we would like to draw attention to two types: in the first, there is a sense of ‘fullness’ in that the feeling is all is included; in the seco4d, there is a sense of ’emptiness’ in that the feeling that all is excluded,’ The latter reaction is based on the fact that each of the two sides exclude each other and ‘therefore’ both are excluded. The former reaction pays attention only to their togetherness, to their complementing roles, and says ‘both are true’ and ‘therefore’ included. These two types of reaction correspond to 1. and 0, in the binary codification. Thus, the same dyad of complementarity can be either totally accepted (1) or totally rejected (0).

It is under the supposition of state 1 that we can say that quantum theory has radically altered our view of physical reality in a way beyond anything before (or since). For, the assertion of complementarity is an assertion about the nature of reality never before countenanced in the history of thought. It is not the ‘unity of opposites’ of Nicholas of Cusa because the two sides cannot be made to coincide. Heraclitus? Hegel? Neither of these went far enough into exclusion. We have to remember that exclusion is more radical than negation; for the excluded is non-existent or ‘unreal’.

We can well appreciate how Einstein – probably in state 0 – came to hate such a view: it does mean an exclusion from the monadic paradise of physics, being driven into the wastelands of uncertainty. The expression:

THE DYAD IS EXCLUSIVE COMPLEMENTARY

is itself a contradiction: how can there be a complementation of mutually exclusive terms? Yet, this must be the formulation. We are not merely dividing the totality into two halves – which would be relational – nor are we allowing a rhythm or periodic oscillation between two states -which is also relational. In fact:

THE DYAD DENIES RELATION

The two ‘sides’ cannot combine, as probabilities can. Here we have the physical basis for the concept of distinction.

However, is it yet possible for there to be an inclusive complementarity? That is, can we have not only the exclusive function LOR but also the inclusive function AND? surely, this is the usual feeling of complementary that is, of a making up of a whole from two terms in tension with each other? For example, we have the traditional dyads of male and female, yin and yang. The whole tenor/these is inclusive: the male requires the female, the yang the yin. We cannot have ‘one without the other’.

What we will want to argue is that inclusive complementarity is, in fact, a feature of the tetrad. Male and female are not terms of a dyad but of a tetrad, where they have to be taken in a dual sense; the male necessarily; involves the female and vice versa, so that we say that a man has a woman inside him and a woman a man inside her. We know that, biologically, it is not a cut and dried choice which determines male and female; we do have ambiguous sexuality, trans-sexuality and contrast between physical and mental sexuality. This was made into a complete cosmological scheme by the transvestite Charlotte Bach and, interestingly enough, she treated sexuality as a tetrad.

In the Chinese schema, it is the combinations of yin and yan that are practical and interesting; and the overall concern is with balance; therefore, they are at least relational.

We want to argue that the absolute exclusion which characterizes the dyad as choice is necessary if we are to have the possibility of relatedness. Of course, what is related cannot be the mutually exclusive terms of the dyad. We, in the act of intervention, can only adjust – by virtue of a degree of freedom not accessible to them – the ‘product’ of two terms already in interaction. We move from the question of what really is to the meaning (or outcome) of interactions. The triad does not ‘resolve’ the either/or! Choice remains choice; but, what we may consider is the relation between choices, a matter of history and context which can be reduced, perhaps, to a minimum case which is the necessary connection between the ‘before’ and the ‘after’ of choice. With considerations of before and after we have such notions as ‘coming from’ and ‘resulting in’ and so on which easily suggest a connectivity of choices and a direction of change. In the act of choice, context is either all-included or all-excluded; there is no relation. But, choice does have a context; and it is this which gives it its meaning. This is the case in the experimental actions which include the existential choice of quantum complementarity.

TRANSITION TO THE TRIAD

Consequences of Making Symmetry in Representing the Act of Choice.

Once we allow context, we also allow a representation of choice such as we give below. In this picture, we have A as the prior undifferentiated ‘path’ meeting with the act of choice at A; where the ‘future paths’ bifurcate, giving the two exclusive options B and C. The ‘choice itself’ at X is shown in the picture as ‘two-in-one’, meaning that ‘at’ this point, the two are both immediately present. It is in the nature of the either/or that there is no explanation of this state: questions of whether it is possible, or how it might have come about, are not relevant.

From A we have an XOR function with respect to B and C. This, we shall write as:

A ( (B) (C) )

where the brackets stand for ‘exclusion’. We may now consider at least two types of symmetry which we might apply.

(1) Symmetry in ‘time’: that is, we might allow a meaning for the same process reversed in sequence (this would be equivalent to ‘advanced waves’ with respect to the usual ‘time-positive’ retarded waves of electromagnetism, both of which are permitted by the governing equations). For the reverse direction, we would write:

(B C) A

where the single brackets around B and C mean AND.

(2) Symmetry in ‘role’: that is, treating any of the three paths A, B or C as equally likely to play the role of the ‘initial pail If we adopt this symmetry, then we have four more expressions to add to the two above and the resulting total of six forms are:

A((B)(C))	(B C)A
B((C)(A))	(C A)B
C((A)(B))	(A B)C

The three forms of the left-hand column are based on exclusion, while those of the righthand are based on inclusion. It is easy to appreciate that, once we allow this kind of symmetry, the act of choice becomes ‘buried’ in the complex interaction of A, B and C. We can imagine impulses being reflected back from the ‘ends’ of A, B and C such that the whole process could be maintained, given very exact timing.

For example:

1. an impulse down C, activates an impulse up A
2. the A impulse reflects and synchronizes with an impulse down B
3. resulting in an impulse up C
4. an impulse down A combines with the impulse reflected in C
5. resulting in an impulse up B
6. which reflects and activates an impulse up C and so on. There is (a) use of both ‘inclusive’ and ‘exclusive’ forms (b) a periodic initiative in turn from A, B and C (other than ‘reflections’).

If we consider (ii) and (iii) in the above, we should note that each of the three ‘paths’ plays a different role:

• the impulse from B is ‘self-generated’
• the impulse from A is ‘reflected’
• the impulse ‘from’ C is ‘reversed by combination’ as ‘to’. Thus, we arrive at role-characteristics which are very close to those we have made implicit use of:
  • initiating
  • mediating
  • resulting

Now, we might also suppose that we can distinguish between A, B and C on the following lines: suppose that the whole process starts up from an impulse from one of these, then this would be the affirmative path; through the form of exclusion a second path is activated (‘chosen’) and this would be the receptive path; then the third path would be the reconciling in that it is necessary for the working of all the combinations and, especially significant, it is needed for the ‘regeneration’ of the first path, through the form of inclusion. We find it quite astonishing that in this simplistic representation, based on the irreducible context of choice and interpreted through the logical forms of XOR and AND, we have arrived at the structure of the Trinity! Thus:

the primal activation (first initiative) is the Father

the selected activation from the first (chosen) is the Son

the combination of the primal activation (repeated or sustained) with the reflection (self-reflection) of the selected activation makes the third activation by inclusion which is the Holy Ghost

It is fascinating to see that there are various alternatives for the treatment of the third term. For example, it could be a second selection from the first term; which was entertained in the theological arguments by those who claimed the holy Ghost was from the Father and not from the bother and Son together. However, we can appreciate how right the latter view is, since we have used self-activation (first term, the Father); selected (exclusive) activation (second term, the Son) already and have only the third possibility – that of inclusive combination (AND) – for an original act. We can almost say therefore, the holy Ghost comes from the Father and Son together!

We are now faced with having to ascribe to the paths a kind of memory. They need to remember the primal order of self-activated, selected and constituted. It is interesting that, in the efforts of Augustine to relate the Trinity to the workings of the highest functions in man, he ascribed memory to the Father, its reflection in intellect as the Son (image of the Father) and love (AND) to the Holy Ghost. Truly, the Trinity was and is the most remarkable of ideas and it is not lightly asserted that western thought, leading to science and radical innovation would not have been possible without it.

We may also consider that the begetting of Christ demanded a selection: this is the impossible drama of the Incarnation in a particular place and time. Then, all the rest, the ‘unselected’, the ‘non-localized totality’ of all-inclusiveness is reconstituted in the holy Ghost.

What we can see from these interpretations is that the triad appears to have an historical character and we may suppose that temporality in both senses of conservation and irreversibility apply to the articulation of the triadic forms.

The Mode of Temporality and the Mode of Temperance

We may say, in the light of the proceeding discussion, that the triad originates in the self-activation of an impulse which actualizes a path. The making of a path brings this impulse into an intersection with the contextual field; and, at the intersection, it selects (or, there is selected) a responsive agent, a reactive impulse. This response is incomplete; since there has been a selection. In co-operation, the first and the second impulse identify a third impulse which becomes active for them. In this agreement, the two initial impulses both fully participate; allowing the second impulse equal status with the first. This condition removes from the second impulse the bare relation of dependence. The third impulse is an attempt to realize the maximum meaning; that is, to take account of the whole context. The model here is of ‘triangulation’ in the sense that two independent sources can locate any other point in a plane. In the mode of temporality we have generation and dependence; whereas, in the mode of temperance we have equality and co-operation.

In the act of selection, we may regard the ‘chosen path’ as representing the ‘possible’; which means that the ‘unchosen path’ represents the ‘impossible’. The third impulse, then, comes out of the ‘impossible’ domain. This gives the characteristic of novelty which is required for the third force to be truly independent. The critical act is in the co-operation of the first and second impulses: this is improbable.

We suppose, then, that this improbability, some it has been realized, creates a self-creating system of three impulses which has its own holistic independence within the given context. This is the situation assumed in recent discussions concerning the emergence of higher orders of complexity in chemical and living contexts. For example, we might imagine a chemical intersection which, improbably, creates its own catalyst; which means, for example, that the original self-activation can be renewed (such a thing is exemplified in digestion).

In subjective relations, using the terminology sometimes used with respect to the Trinity, the One provokes the Other. This is a selection out of the field of human community in its specific contexts. Let us imagine the banal example of a man stirred in his sexuality (by his own chemistry!); he lights upon a woman to serve as a focus for his desires. However, she has her own stirrings. Up to a point, she has to live or act out her own stirrings with respect to that man; but she is not, thereby, reduced to reacting to him. She can offer her own impulse. This means that there is something else at work. We understand this easily in terms of e.g. the other men and women existing in the same context; but it is also internal to the two main characters. We say, that where they agree, something really happens (this is meaning). This requires another perspective, an angle of view which is not involved in the sexual tension of the moment. This may be on the part of an impartial friend (who will ‘impartial’ only in respect of the given relationship and not in general – i.e. the friend does not have to be a sage!). Or, it may be in terms of a ‘lesson’ which is learnt by the two characters, though in different ways. The idea of another ‘perspective’ implies a third character. This may seem an unwarranted invitation to irrational mysticism; however, what is meant is simply the ‘independent perspective’ relative to that of the protagonists. We might even suppose that there is a third character (in an eternal triangle’) personally involved who, nevertheless, provides another point of view which enables the two initial characters to realise what their encounter means.

In this sense, we have the One, the Other and the Third. The Third is humanity, which sounds like an abstraction until we realise that this ‘humanity’ can only reach the situation through a specific path. Interestingly enough, we can envisage that it is in the Third that learning accumulates. Maturity, then, is a matter of participation in the Third. Identification with either of the two initial roles does not develop understanding.

Our discussion may make itself more comprehensible if we think of the art of the novel. A novel will be based on relations between the One and the Other but, of course, the Third is really the novelist himself something of which modern novelists are well aware and have sometimes exploited (cf. John Fowles ‘The French Lieutenant’s Woman’)

We have to make some final remarks on temporality.

If we allow some process on the lines of the symmetry-making we have suggested then, in time, the initial distinctions between the terms given by their initial roles, fade away. What remains is a relation of three ‘materials’. One of Plato’s pupils, Xenocrates, postulated three ‘densities’ – pykna – which were the material aspects of the non-material ‘elements’ fire, air and water (rather on the lines of introducing the Higgs boson to account for the mass of particles). The doctrine of three densities is akin to that of the three kinds of substance – the intelligible, the heavenly and the sensible. The concept of the three realms or the three substances becomes divorced in time from the dynamical insight of the triad, the meeting of the impulses; as it obviously has been in the case of the gunas of a Hindu tradition. The gunas, the pykna, are statistical concepts reflecting the state of societies of triads; they do not enable us to understand anything of the working of the triad itself. In a sense, they describe the entropic triad, when what is most interesting has passed from sight.

Translation of XOR and AND into the Six Forms of the Triad

As yet, there is no exact parallel between the six expressions based or XOR and AND and the traditional six forms of the triad (123, 213, etc.)

We first establish that the expression of the type A((B)(C)) has two possible forms (i.e. the two possible selections):

A (B) O and A (O) B

This means that the three expressions of this type give six forms. Now, let us consider the other three expressions of the type (AB)C, deriving from the AND function. In order to produce a form of the type 123 we need to combine what we have deduced from XOR and AND. Thus, making the identities; A -1, B – 2 and C – 3, to produce the form 123 we need to combine:

A (B) C with (AB) O

says that the ‘unchosen’ path B plays a part in the realization of the path C. Thus, B represents a kind of ‘potential’ which influences the course of events which actualize in C.

123 can be represented as: (A B) C

Proceeding in this way, we can account for all six of the forms of the type 123, 213, etc.

A(B)G (AB)G

The new expressions suggest that the ‘middle term’ is ‘hidden’;

but:

What might have been and what has been

Point to one end, which is always present.
(T. S. Eliot ‘Burnt Norton’)

Let us be frank, however; this formulation offers a quite different interpretation of the six forms than the ones we used before. In this latest formulation, the middle term has its effect by absence; whereas, in the earlier, it had its effect through its positive response. Both of these are valid. We must remember that the terms we deal with are not things but rather subjective impulses. The Other who arises in relation to the One has an effect both as absence and as a reaction: the character of absence is, in reality, a measure of independence.

Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement. And do not call it fixity,
Where past and future are gathered. Neither movement from nor towards,
Neither ascent nor decline. Except for the point, the still point,
There would be no dance, and there is only the dance.
(T. S. Eliot ‘Burnt Norton’)

Eliot says that, at the heart of movement, change and dynamism, there is stillness. In our diagram introducing the XOR and AND functions, it would be represented by the point X. Is this nothing more than poetic image? We think it is a poetic image but not a ‘mere’ one. At the point X, the three impulses are coalesced as one (identity of substance in the Trinity). At the points A, B and C the impulses are disjoint. Between the ‘centre’ and the ‘periphery’ lies the realm of combination. Our discussion in this section treated of this in terms of XOR and AND. Now, this treatment suggests that – in respect of the forms 123 etc. which, as we have seen, have to be treated as themselves a kind of combination – we can recognize the relatively ‘open’ function OR at work. OR would mean, for example, that we could have A ‘produced’ by either B or C or both. There are, therefore, three possibilities. The either/or of B or C corresponds to ‘generation’ in the Trinity: this is the archetype of causality. The both/and of B and C corresponds to ‘spiration’ in the Trinity: this is the archetype of synchronicity.

If we imagine that B has ‘mental’ characteristics and C has ‘physical’ ones, then the relation B+C=A represents the meaning inherent in synchronistic occasions.

Interestingly enough, causality now appears as a matter of selection and exclusion. If we picture a primal state of relatedness then, when there is exclusion we have causal connection and when we have inclusion, we have synchronous connection.

The forms 123 etc. must, on this view, incorporate both causal and synchronistic connectivities. It is not surprising, therefore, that their interpretation is somewhat ambiguous. On the one hand, we have the ‘causal’ connectivities in which we can talk of one term being ‘produced’ by some combination of the others; and we also have the synchronous connectivities in which one term ‘is’ some combination of the others. There are ‘results’ and ‘meanings’.

We may, then, understand the 3-M equation of Matchett, in which we speak of the ‘making of meaning’, as asserting that meaning really is ‘made’ and also that it is the synchronous implication of the ‘coincidence’ of Media and Matter.

Cause and Relation

Our usual understanding of the world – our day-to-day unsophisticated thinking – tends to (a) distinguish mental from physical events, (b) consider physical events as occurring in a chain of causation such that antecedents determine or ‘make happen’ subsequent ones, (c) consider the proximity or coupling of mental with physical events to be a ‘parallelism’ or ‘correspondence’, (d) consider the arising of mental events not to be reducible to causation even from prior mental events. And, in our various studies of examples of the triad we have come across, however implicitly, a duality of connectivity where (a) physically certain elements produce or ‘make happen’ other elements, (b) mentally, certain elements ‘combine’ in a new perception. The former is of a causal nature and the latter of a synchronous nature.

The combination of causal and a-causal connectivity is exemplified most strongly in our account of will. We can regard the relation which we call ‘will’ to be one in which, if it is regarded from the perspective of actual movements, must be causal; but, if it is regarded from the perspective of the thought or ‘conception’ tends to be a-causal. The latter remark is justified if, for example, we consider the ‘incompatibility’ of the mental and physical for causal connection: thoughts cannot ‘make’ actual movements, not can actual movements ‘make’ thoughts (though there are those who would disagree with the latter). Recent studies of consciousness have shown that the experience of a desire to act occurs about half a second after a ‘readiness potential’ can be detected in the brain; the act itself, of course, occurs a little later. However, the experience of the desire is an interpretation and not merely a result. In other words, the experience is about a ‘model’ of the situation. It is in this sense that we argue that the thought is not simply a causal result. Also, to take an extreme interpretation, we might argue that the thought works ‘backwards in time’ to produce the readiness potential, using an analogy with the ‘advanced waves’ of electromagnetism. The connectivity involved in thought involves two or more levels, or types of process.

This is the domain of synchronicity: a-causal connectivity of levels. Will, in our view, supposes a complementarity of causal and a-causal. The step from the exclusivity of the dyad, the either/or (which may well characterize the ‘switching’ taking place at all levels) to the inclusivity of the triad, is the basis of becoming.

RELATEDNESS ARISES FROM THE INCLUSIVE COMPLEMENTARITY OF THE CAUSAL AND THE A-CAUSAL

In a relation, causality is modified by synchronicity and synchronicity is modified by causality; it is about behaviour in terms of a judgment and a judgment in terms of behaviour; it is the connection of the mental with the physical. In speaking thus, we are not attempting to define or explain relatedness but to further establish it as a fundamental category, out of which we abstract the causal and the a-causal.

The main characteristics of relatedness are creativity and meaning. That is why the 3-M equation is so powerful, since it bases itself on the very act of creation of meaning, or ‘logosynthesis’. Built into the equation is the requirement that the creation of meaning must involve both a material, tangible, knowable component and a non-material, unconditioned and unknowable component. Something must actually happen; but this must be ‘seen’ or ‘perceived’ from a numinous level for it to be meaningful. It is not only that this ‘perception’ is necessary as a simple ‘recognition’ of what has happened (or is happening) – like ‘someone’ being in the wood to hear the branch fall – but, more importantly, that it is necessary if the result is to be what it is. Here, we are clumsily appealing to the notion of synchronicity. Further, we are also asserting that this ‘perception’ is not confined to contingent personal, human, perception: it is a property of the relation.

In a work of art, what is presented (e.g. in a painting) is not simply an image (representational or non-representational) but also a way of looking. This is also the art of the photographer. The ‘way of looking’ is something in its own right and is not reducible to the ‘private’ or idiosyncratic perspective of the artist. Otherwise, it could not be communicated. Thus, in looking at a painting, we not only see it as a tangible artefact but also as a form of perception. The latter is, of course, what we mean by Media.

Thus, in Media we have the primacy of seeing over doing; whereas, in Matter, we have the primacy of doing over seeing. And most importantly, we recognize that seeing is a ‘higher form’ of doing! Seeing is not passive; but neither does it ‘do’ as ‘doing’ does.

CREATIVITY IS SEEING AND DOING AS ONE

Seeing ‘comes from’ Media, while doing ‘comes from’ Matter. In the exclusive bind of the either/or, either we see or we do. Thus, we can begin to grasp that the transition to the triad entails a transition in ourselves: the ‘ego’ which is realized in the dyad has to be dissolved into the ‘meaning’ which is realized in triad. It is crucial that it is realized that the ‘seeing’ entailed in the term Media is not my seeing but seeing of itself.

But, we might ask: how does seeing do anything? We answer: it does not do anything.

Then, we might ask: Then what difference does it make? We answer: without it there is no meaning.

But, we might ask: Is meaning then just a subjective property? We answer: Yes and No. It is not ‘just’, in that this ‘subjectivity’ (with which seeing is impugned) is related with the objective.

We might ask, again: But, what does this relation do with seeing? And we answer: Think of this – what I see I am doing affects what I am doing. And, we object: But, you have introduced yourself as an agent or principle: to explain yourself. We answer: this is not really ourself as an agent but as a meaning.

Again, we ask: Is it this meaning that enables seeing to have an effect? We answer: It is so. Seeing cannot have an effect ‘on’ doing without meaning.

But, we object: Surely, meaning is what agents such as yourself ‘make’; thus, you are making seeing have an effect, which is the same as doing. We answer: This is the most critical point: we do not regard ourself as anything apart from meaning.

THE ONE TRUE AGENT IS MEANING

We ask: What do you mean? We answer: he will respond to your question on meaning; first, by reference to our usual concepts. leaning is what is intended, what is the purpose. It is also the value or significance ‘built in’. it is kin to the will. it is synchronous within the causal. Second, an agent is not a cause, for causes die away in their effects. Meaning is.

We object: Either meaning acts causally or it does not. We answer: not so. The out of meaning is neither causal nor a-causal, or it is both. it is not in the dyad. Meaning is going from the dyad to the triad. To the agent which ‘makes itself’.

We ask: Explain what this ‘making itself’ amounts to. We reply: It amounts to this: that as the world makes the agent, so the. agent acts upon this making.

We ask: Does this mean that the agent has no effect on the world? We reply: No. The agent does not make the world. The world does not act upon the agent. Neither do anything to each other; they are related. Without the agent, the world would not be what it is.

We demand: But, you are saying that the agent cannot do anything to the world? We reply: As the agent determines what effect the world will have on it, so does the world with the agent. There are all kinds of ‘worlds’ or realms of material. The agent changes the meaning of the world. And thereby changes itself.

We insist: Tell us clearly whether you think the agent, as you call it, can cause things to happen. We answer: Senso stricto, no cause can be an entity; because, an entity would be connected with the world of its effect and therefore itself a patient of causation. It is not the entity qua entity that causes.

We press the point: are you not deviating the argument? You have shifted the ground in talking about entities. We answer: The agent is an entity, a being. This is an essential feature of the agent. In our sense of intrinsic, indwelling, meaning the agent has meaning because it is. Causality is an abstraction. It is a limiting case in which two entities are connected in a very local way. Synchronicity is also a limiting case in which the entities are both regarded from the whole context. In the causal case, we have a ‘flow’ in one direction. In the synchronous case, there is no ‘flow’.

We ask: What do you mean by flow? Especially, a flow between entities? We reply: ‘flow’ is used to indicate a one-way direction of something. Its nature is usually conceived of as more an impulse that transmits an impulse from one entity to another. Think of billiard balls.

We go on to ask: So, your ‘agent’ and something in the world can act as two billiard balls? We quickly reply: No. One entity can transmit an impulse to another only if they are of the same kind. There is no causation between the objects of the world and the agent. But, there is a relatedness.

We insist again: But, tell us, why you speak of the ‘agent’ when the agent cannot do anything to the world? We answer: The agent can ‘undo’ the world.

We ask: What does ‘un-do’ mean other than remain incapable of doing? Our reply is: The agent can change the effect of the world upon itself. This we said before. In synchronicity, this means that the world is changed.

We continue: Nothing in what you have said leads us to accept that anything in the real world can be changed by this agent. What you are suggesting, is simply a change in perception. We answer: Your ‘real world’ considered as somehow apart from perception is a world we cannot touch. It is a ‘residuum of abstraction’. It would be impossible to learn anything, about such a world. The real world we can live in, investigate through science, express through poetry changes under the gaze of the agent. Let us finish with a quotation from a favourite poet of ours, T.S. Eliot:

And the unseen eyebeam crossed, for the roses
Had the look of flowers that are looked at.

But, we protest: ‘Unseen eyebeam’ – what is this mysterious thing in your scheme of things? We answer with alacrity: This is Media! Or, rather, an intimation of Media. In the making of Meaning, it is Media that calls it forth. Media is the energy of seeing, let us say. It does not determine anything. It can be seen only through the ‘eye of meaning’. It contains the ‘programme of work’ for a ‘free agent’. Media makes Meaning effective. Freedom is neither gratuitous nor predetermined; but needs to be discovered in the heart of meaning. Freedom is never what it seems!

FREEDOM IS IDENTICAL WITH THE CREATION OF MEANING

Hence, Media is ‘beyond freedom’. Our questioning voice fades away, murmuring: Now we have talk of ‘beyond’. Undoubtedly, this will be claim ed as another part of relation; and, we have no doubt, we will be presented with the thesis that every entity of a characteristic state must have a ‘beyond’ for it to be at all! And, then, we say to ourselves: An interesting idea! Is it that nothing can come entirely from itself?

TIME AND RELATION

The Thought of the Thought

Let us assert: identity is not possible without a ‘beyond’ – or, an ‘Encompassing’, or an ‘horizon’ – just as we cannot have a here without implying a there. We want to assert this in a special way: no entity can be, as it is, distinguishable and distinctive unless the ‘rest’ lets it be. The whole of what ‘remains’ must ‘withdraw’ and ‘hide’. Ultimately, this means that God must hide in order to allow the creature existence. This withdrawal is a powerful act; and, it is given, rightly, a central place in the mysteries of Christianity. We hardly ever ask: why is it that, when there is the One, this unity is not overwhelming? How can the One enable this lesser one to be what it is without denying itself? The One must be capable of this extra-ordinary feat. This is the making of the Creator and the creature. We are used to seeing things ‘side by side’, not in their influence upon each other. We are not used to seeing things intensively connected, only extensively. Instead of the perspective of ‘side by side’, which we may regard as addition, we can adopt the perspective of ‘cumulatively together’, which we may regard as multiplication.

It must be no accident that we have these two operations in our most elementary mathematics: in addition, we have the external connection which we associate with space; while, in multiplication, we have the internal connection which we feel as time. Why do we associate the multiplicative with time? Because in time we have becoming, or the creation of existence; and this is not mere combination through external connectivity. In the multiplicative totality we have an important meaning of the One: the All in all. It is contrast with the privation of simple unity which is that of things as we survey them side by side.

Now, in the making of something, an entity, this multiplicative unity incorporates its inverse, or division. The identity of the entity comes from an act of division within the multiplicative unity. Every entity has a ‘place’ within the multiplicative One, in that it divides the total into two components. If we allow ourselves to introduce numbers, we do not assume we know what kind of numbers these are – though they are, presumably, transfinite – but we allow ourselves to multiply and divide them by each other. Thus, the entity divides the One into two parts, an alpha and an omega, which we will represent by the first letter A and the last letter Z. Then:

A x Z = 1 is the equation which identifies the entity

We may imagine a line drawn between the One (1) and the privation of additive connection (i), in which the entity is represented by a point on the line. We must note that, in additive connectivity, we never go beyond any one of the units. These units are the tokens of counting and are emptied of being. The One is the being of everything all together at once.

It is also possible to represent the entity as a ratio, as:

A/Z

which suggests that the entity implies all of A in its existence, while Z remains, as it were, beyond. By ‘allowing’ an entity to act in this way, to define a ratio, the One enables the entity to be what it is. But, we have to qualify our use of the word ‘time’. This is not the time along which we are fragmented by past and future: we have used the phrase ‘the being of everything all together at once’. This implies something like time and also utterly unlike time: the purely ‘internal’ or the eternal.

The representation of the entity in the ratio A/Z shows us that we can conceive of the entity as deriving from the multiplication A; though we also see that it is permitted through the multiplication Z. In the former, we have the basis of materialism and reductionism. In the latter, we have the basis of spiritualism and positive faith. Thus, for example: man has evolved from the animals (and these from the more primitive forms that came before and these, in their turn, from the chemistry of the surface of the Earth, etc.) while God has allowed him to possess a soul. Man ‘ascends’ from the dust and ‘descends’ from God. This is the ultimate synchronicity!

Simone Weil quotes Aristotle’s formula: ‘Thought is the thought of thought. This means thought in three ways: as a subject which thinks, as an object thought and as the thought which connects these. Simone Weil adds: ‘What God thinks is still a Being who thinks’. Thus, God is the thought that thinks (Z) the being that thinks (A). Every creature is an image of God and is thought by creatures nearer God than them.

In modern terms, concerning the workings of our thought and brain, where it is conceived that we have a multitude of ‘images’ (mental models) in which each thinks events, we may suppose that some of these images ‘think’ lesser ones, and so on. Our struggle is to realize that one image which thinks all the rest; which is to ‘know all that one knows all at once’ is a condition of unbearable multiplicative intensity. Unbearable, we might add, unless God thinks that one image for us.

What is above an entity (Z) and what is below it (A) cannot be put side by side. They touch only within the entity itself, in what it is. God is inescapable, even though He hides from us, so that we may live.

How is Friendship Possible?

Simone Weil, slightly rephrasing a Pythagorean saying, writes:

…friendship is an equality made of harmony

What is this equality? For Simone Weil, this is not the equality suggested by the plural, by the ‘we’. She says: ‘Nothing is more contrary to friendship than solidarity’ whether of social grouping, political or religious conviction, or even comradeship. And she says:

supernatural justice., supernatural friendship or love, are found to be implicit in all human relationships where, without there being an equality of force or need, there is a search for mutual consent. The desire for mutual consent is charity.

At another point, she even says: ‘If there is unilateral justice, it is one which is maimed.’ And, she says: ‘God is always mediator. Between himself and himself — which is the Trinity. Between himself and man — which is the Christ. And between man and man — ‘in the name of Christ’. This is very clear, insofar as we have explicitly stated (a) an inequality of the persons (b) finding unity in their mutual consent. The idea of equality which we have currently in the western world is a crudity which violates the essence of friendship. In a friendship, we have an enhancement of what the two people are. They do not meet by a reduction of themselves to some common property, even such a thing as a ‘common interest’. One may well be dominant, stronger and the other subservient, weaker. In fact, we should not imagine that there can be some ‘given’ balance of power in the relationship, which would be to reduce friendship to the equivalent of a mechanical system, such as we suppose at work in commerce (interestingly enough, we might say that the socialists want to regard themselves as agents of the ‘third force’ capable of intervening in the play of market forces to temper the strong and succour the weak!). Friendship is not negotiated or, the result of a bargain. For each side, there is both undeserved benefit and freely given sacrifice. Neither, in themselves, can see enough to realize their benefit or grasp the nature of the sacrifice they are free to make. In the example of giving which we discussed much earlier on, we came to understand that a harmony was possible only when the ‘recipient’ was also a donor; but, that this was not an exchange; that there were two quite different ‘currencies’ in operation which were beyond comparative measure. Thus, even a ‘slave’ can exalt his king!

Simone Weil makes friendship one of her ‘models’ of reality, that is, of God. In our scheme, when we spoke of ‘I’, ‘You’ and ‘He’ or of the One, the Other and the Third, we were speaking of this. To understand this reality, we need to face the ‘impossibility’ of friendship. There are no ‘skills’ of friendship. It cannot be learnt as courtesy, listening, honesty can, to a point, be learnt. Why? Because the act of friendship is always unique. It must arise out of the two who are friends with each other. But, each experiences his impotence in this regard. Each, without the other, cannot make the friendship. There cannot be a unilateral friendship, as Simone Weil points out. Yet how can the two coincide in their desire for friendship? When will each see and must see the value of it in different ways? To speak of God in this connection is not mystification. God is the most personal of persons since He, in hi, very own nature – that is, in the Trinity, – creates His own friendship of Persons. In Him is the power to create and to withdraw – which are really the same – that is, to be both active and passive. He can be the ‘common ratio’ between the two; He is friendship.

Whenever two people imagine that they alone can determine what their friendship means, they invite disaster. It is only God that can guarantee the authenticity of their friendship. The Other must always remain as an Other, representing a mystery, a truly immediate transcendence; a noumena. The One can never ‘have’ his friend, or ‘know’ his friend. However much they may be together, this will remain as being aside by side’, purely additive. Then, each has the friendship in his own ‘private way’. It is God that enables the two to multiply themselves together; to make a new creation, a new kind of entity.

This is far above the natural order of things, e.g. in sex. The man and the woman are side by side. Desire drives them towards multiplication in copulation. But, then, they separate again into two. If they procreate, then even this new creation comes to be side by side with them: multiplication then appears as it is sometimes taught to children; as repeated addition.

For the friends to ‘have’ their friendship, they must remember God. God alone is the friend. In Him, alone, can the friendship exist. The friendship cannot exist ‘besides’ the two friends. Thus, of course, there are not two people plus their friendship. The two are in friendship, an A and a Z forming the ratio of the spiritual entity.

This is also the spiritual, supernatural, marriage which is made in heaven. How, then, do we see Heaven? Rather as C. S. Lewis portrays it in his beautiful book ‘The Great Divorce’. It is a world of unbearable concreteness. The newly dead find that even the grass of this world cuts their feet! What does this picture mean, in our terms? It is the world of multiplicative unity. Just as there are few real friendships in the world because such friendship is felt to be, intuitively, unbearable; so, we hardly know of the multiplicative unity:

Go, go, go said the bird: human kind
Cannot bear very much reality.
T.S. Eliot ‘Burnt Norton’)

In his book on Hazard, J.G. Bennett makes this very clear. The true centre of friendship is too real for us to bear, if we allow any ‘sidedness’ to creep in. ‘Hazard’ is the name Bennett gives to the non-determined reality. It is the doorway to meaning.

In all our discourse about relationships, we should remember these words of Simone Weil:

‘We have in us and about us only relationships. In the semi-darkness in which we are plunged, all is relation for us, as in the light of reality all is in itself divine mediation. Relationship is divine mediation glimpsed through our darkness.’

However, we have this mystery:
This identity (i.e., of relationships with mediation) is what St. John expressed in giving to Christ the name of the relation, logos, and what the Pythagoreans expressed in saying: ‘All is number’.

We arrive at the alpha and the omega, the beginning and the end. God, the Mediator, the multiplicative unity, greater than which cannot be thought; and number, which we encounter in additive unity of enumeration, less than which cannot be thought. In this we have the coincidence of opposites of Nicholas of Cusa; but we find that they are not opposites at all. The concept of ONE embraces both the greatest and the least: it is the most simple and the most complex of concepts. And, thereby, we gain an intuition of how it is that mathematics can deal ‘of itself’ with the nature of things; for every number or kind of number is a sub-division of the whole, of God, in which everything is enacted. Because mathematics ‘says nothing’ – i.e., can be) treated merely as an arrangement of signs as the formalists claim – it can say everything.

This should go a long way towards explaining the seemingly absurd claim by the Pythagoreans that everything is made of number. There are no ‘underlying substances’. The only thing that is given is God in His transfinite multiplicative unity, such that any one thing can only be explained in terms of other things, in proportion. It is blindingly simple!

Human thought and the universe constitute the books of revelation par excellence, if the attention, lighted by love and faith, knows how to decipher them. The reading of them is a proof, and indeed the only certain proof. (Simone Weil — ‘The Pythagorean Doctrine’)

The Transfinite and the Six Forms

We have introduced into our discussion, though not in any way that can be claimed to be precise, the notions of an ‘ultimate 1’ (multiplicative unity) and ‘minimal 1’ (countable unity). We wish to explore some of the properties implicit in these two numbers and their associated terms, especially with regard to the operations of multiplication and addition. For our convenience (because the more ‘far out’ transfinite numbers are even more difficult to handle) we will replace the ultimate unity by the first transfinite number, w (little omega). Then, as this number stands for the transition from finite to transfinite numbers; so our usual unity 1 stands for the transition from nothing to something (for which idea we are indebted to Rudy Rucker).

w is first defined as lim(a), the last ordinal in counting which is greater than all the a’s. Using this principle, it is possible to see that w does not commute under the operations of addition and multiplication.

We wish to introduce further relations: those involving the two other mathematical operations which come next in the progression of increasing power, beginning with addition. These two operations are exponentiation and tetration. They are written, in this case as:

Tetration of w amounts to taking the following expression in the form of exponentiation:

and, therefore, works analogously with multiplication being taken as repeated addition. The number

forms a further ordinal, called ‘epsilon zero’.

We must consider some properties of w^w:

We can imagine even more powerful operations such as:

The prospect of an ever more powerful type of operation, no matter what power we have already reached, provides us with a taste of what the ultimate ‘infinity’, or ultimate unity, might mean. On the other hand, it is no more nor less than what is accessible to us in our own thinking: whatever we are thinking of, we can think at a deeper level of this and also the way we are thinking about it at the same time! As we have repeatedly said, this does not lead us into a meaningless ‘infinite regress’: because, at each stage, there has to be a new order to accommodate the previous stages.

So, contrary to the idea expressed in the phrase ‘that than which no greater can be thought’, this cannot itself be made a real thought without laying itself open to a ‘greater’! Theists have to give way to the ‘Godhead’ (Eckhart) and this, in its turn, to the ‘Void’ (and the Buddhists found themselves in dealing with different orders of the Void!

However, to return to our survey of the basic operations as applied to numbers of the type w and 1.

We wish to lay out the following pattern:

1. the progression from addition through multiplication to exponentiation is reflective of the progression in the forms from the third force being the final term, or ‘result’, through being the middle term, or ‘means’, to being the initiating term or ‘generator’.
2. the fact that these operations do not commute is a reflection of the binary nature of the forms given the previous sequence of three steps.
3. some possible implications of this arrangement can be made that are of some interest, though they cannot be justified in any mathematical way.

Thus, we start by taking (i) and (ii) to reflect 123 and 213, respectively, with these possible implications:

123 (ii) w + 1 = w + 1; creativity as generation

213 (i) 1 + w = w; creativity as unification

What we have is a reflection of Whitehead’s dictum: ‘The many become one and are increased by one’. The first part of this argument is (i) while the second is (ii). Of course, the ‘many’ is here represented only by 1; but 1 stands for ell that is separably countable. We must remember that w is not separably countable, being defined as a limit beyond which counting cannot reach.

We must note that we are adopting the equivalence:

w — affirmative (1)

1 — receptive (2)

and that we have no direct representation of the third force.

Now let us look at the forms in which we are supposing that the third force is ‘means’. These will correspond to 132 and 213

213 (iii) 2.w = w; the relation of unity, or identity

132 (iv) w.2 = w + w ; the relation of multiplicity, or interaction.

The ‘1’ now appears as ‘2’. In the formalism, this is to show the effect of the multiplication clearly. The first relation is ‘inward’ and the second ‘outward’. The ‘separable’ (2) enters into its identity in relation to the totality (w). This is the aspect of ‘above’ and ‘below’. In the second relation, the totality (w) enters into separability (2) which is the multiplication of effects (‘causation’ disperses into the many, though deriving from the higher One).

In the last pair of relations, we suppose that the third force acts as the ‘generator’ (this is a new term for us, meaning that the third term is in the ‘initial’ position which gives it properties of generation or origination).

312 (v) w.w^w = w^w ; the unity of all complexity; or order

321 (vi) w^w.w. = w^w+1 ; novelty out of complexity; freedom.

In these forms, we have a recurrence of the first two, since they depend on the relations: 1 + w = w and w + 1 = w + 1.

We now have to deal with the question of where the third term appears in these formulations. Straight away, we have to admit that it does not appear in any one definite place. It appears only in a ‘relational place’. In the first pair of formulations, it appears under the guise of counting. In the second, it appears under the guise of the multiplication itself. While, in the third, it appears in the form of exponentiation. We should note that we can take the formulation (vi) to anticipate the operation of tetration.

In this respect we can argue that the form of ‘freedom’ as we have described it, naturally suggests a movement towards a yet higher ‘ultimate order’: an evolution of God, we might say!

Now, what do we claim these informal excursions into formalism do for us? At the very least, they suggest a way of thinking that can bring into relation the finite and the infinite; and, not as simply in one way, but in several ways. We have, however, ramshackle it might be, a kind of calculus for Creator and creature and their relation. In some sense, this relation must be thinkable. We add: most importantly, it is not for nothing that mystics have laid claim to a ‘God beyond God’ who is beyond the relation of Creator to creature, such relation implying, as it certainly does (but in a very special way) a limitation on the Creator by the creature. We have to agree and say: Yes, for the Creator and the creature to be related, the creature must have an ‘effect’ on the Creator! There are ‘greater’ transfinite numbers than w (aleph one, for example) which cannot be manipulated in the way that w can.

We also have some kind of model for making sense of the descriptions which have been given the six forms (123, etc.). These have been indicated in our gloss, brief though it has been. We would like to draw attention to the following ‘readings’ of the forms and their correlations in the mathematics, which take things a little further:

123, 213: creativity, becoming; the source of change; the relation of the timeless with time

213, 132: the one and the many; unity in diversity; the domain of sets

312, 321: orders of complexity; the meaning of meaning; immanence and transcendence

In other words, we are groping after new fundamental categories. Or, we may turn this around and represent what we have in terms of the already formulated categories of Whitehead — since we have already referred to his work for an explication of the first two. In this case, we would argue that:

213, 132: refer to the category of Prehension (cf Whitehead)

312, 321: refers to the ‘category’ of God

We will adduce these statements:

The nexus of actual entities in the universe correlate to a concrescence, is termed the actual world’ correlate to that concrescence.

… a nexus is a set of actual entities in the unity of the relatedness constituted by their prehensions of each other, or – what is the same thing conversely expressed – constituted by their objectifications in each other.

… an actual entity by functioning in respect to itself plays diverse roles in self formation without losing its self-identity … ‘becoming’ is the transformation of incoherence into coherence

In the strict sense, God is not a category, but an entity. Whitehead writes:

…the perfected actuality passes back into the temporal world and qualifies this world so that each temporal actuality includes it as an immediate fact of relevant experience… the love in the world passes into the love in heaven, and the reality in heaven passes back into the world. In this sense, God is the great companion -the fellow-sufferer who understands.

Whitehead’s meaning of God is perfecting (in a thoroughly non-Platonic sense) which takes its cue, albeit unacknowledged, from the theologians’ account of the Holy Ghost.

In this respect, we might as well ourselves acknowledge that our first pair of forms correlates with the Father, the second with the Son and the third with the Holy Ghost.

Theological associations aside, and even philosophy aside, what we have brought our attention upon is the fundamental problem of clarity of thought. Where is this best to be found? In mathematics? In number? Or, in the unconscious? In DNA?

Whatever the field of discourse, we must surely face similar problems. A thought to be thought is a movement or is attended by a movement. Are we looking for clarity in the origin of this movement, or in its result, or in the movement itself? To take the latter, are we looking for something like the procedures of logic, the steps by which we move from premises to conclusions, no matter how obscure these premises are, or how bizarre the conclusion? For Descartes, the question was one of the starting points and of the procedure, or movement. But what was clear and self-evident to him has been distinguished into many components since and the ‘self-evidence’ of his is now regarded as part of his cultural prejudice. We have the conundrum that those things with which everyone will easily agree are just those things which are not understood! For example, we will agree that we are ‘alive’ but we have no clear and definite form of understanding what life is. Every attempt to bring out in full explication what this means can be doubted and found incomplete, dubious, or flawed.

The ‘Limits’ of Relatedness

We need to make it clear that one our motives for exploring the mathematical relations between w and 1 and the operations of + and x was to have in our formulations something that could not, as it were, be conceived of as a thing: namely, w. When we look towards w, we look beyond the limits of addition; i.e. beyond ordinal counting, correlative with the world of things. Indeed, both w and 1 are, in their own ways, limit cases. The advantage to us in this is that we do not need to look any further, to the ‘other side’ or to the ‘inside’ of the elements which we are considering in relation. In a sense, the terms are already themselves relational! The operations of + and x then, only spell out what is already inherent in them. Thus, the ‘other side’ or the ‘inside’ is already involved in the relationship we have.

What do we mean by ‘other side’? We are picturing to ourselves the terms as each a ‘something’ and, in making this picture, we have to imagine a ‘line’ between them, or several, which suggests that the line issuing from one term starts out from only ‘one side’ of it, leaving the ‘other side’ relatively unseen, or in shadow. Needless tc say this may all amount to only a comment on the misleading nature of pictures of a naive kind. We find that a spatial picture — and a picture is almost bound to be spatial — obscures relatedness, confuses the connectivity involved, introduces spurious elements. But, what kind of picture are we making? Surely, we must be thinking about something. If we do not have a picture and, further, if we are dealing with something (as we claim) which cannot be encapsulated within a mathematical formalism, but only illustrated or reflected in one, then what do we have? Of course, the mathematics formalism we have used to effect: it is something that enables us to represent something of what we are after without recourse to pictures This, in its turn, reflects the situation within mathematics, where pictures can be useful and suggestive but can never carry the burden of proof, which must rely on the abstract manipulation of symbols. Just as physicists have struggled to make unambiguous sense of a domain of nature and then found a branch of mathematics in which all that is essential can be said and brought into order (such as using matrices in quantum mechanics) so do we. However, we have not come any nearer to the possibility of calculation or even of deriving from the formalisms any conclusion which we did not already in some sense have. Perhaps we should qualify that statement and say: we cannot make predictions from the formalisms we use but we can, or possibly can, make new hypotheses which are in some sense testable from experience.

However, let us return to the question of making pictures. Anyone who sits down and draw a circle to represent one term and another circle to represent a second and then draws a line between them is not going to be able to make sense of relatedness by doing so. If te does this in the spirit of simply writing down, as Isaac and Gibson did, the bare fact of e.g. S (R) O, there is no problem. But, if he expects to find in his picture a model for the relation he is being deceived. We now wish to contradict ourselves! In one respect, something is shown which, if correctly read, brings to our attention the concern with which we began. It is this: what do we have to assume about the ‘rest’ of the term that is not involved in the relation? Or, do we have to assume that the whole of the term is totally involved in the relation? We can see, again, why it is we should be reluctant to deal in terms which are like objects; which, obviously, are involved in a multiplicity of relations if we are to make sense of the diversity and changeableness of things.

This is to raise the question of: what is the ‘limit’ to relatedness? Which is: where does the relation begin and end? White is again, a problem related to spatial representation, in that any hint of extension in the terms must lead us to suspect a partitioning in the terms.

The crude representation of two objects linked by a line that signifies the relation may reduce the objects to points; but then we have the line which boldly carries the very essence of extension. If, on the other hand, we represent the UWO objects as over-lapping circles; then we are left to consider what is happening in the parts which do not coincide.

What happens if we then conclude that any representation in spatial form, implying extension, is not permissible? From time to time in our discourse we have asserted that the terms cannot be things because things cannot relate: they simply exist ‘side by side’ and interact. Interaction, for example through physical forces, does not of itself amount to relatedness! What we have in interaction is what we can call the ‘physical side’ of relatedness; it lacks in the characteristics of purpose, value and meaning that are integral to the triad. This is claiming a great deal but we will leave this question for further exploration later on. For the moment, we can usefully concentrate on what might be meant by terms that are not extensive (and, we must add, as we shall see later: ‘with respect to each other’). First of all, taking extension in its simplistic spatial meaning, can we make sense of terms that are temporal? We would be reduced to thinking about, first of all, past, present and future. Contrary to Einstein, we would have to find a very powerful meaning for the term ‘present’ or ‘now’. On the other hand, we do have a starting point which allows us access in that the present must be where past and future meet; therefore, in some sense, the present enables past and future to ‘touch’. But, we do not know whether or this is merely a metaphor, some equivalent to our sketch of two things joined together. Let us remember that! This representation involves us in thinking that the past can act on the future and the future on the past. How could we ever justify such an idea?

What it does do for us is free us of considering ‘things’ while, at the same time, giving us a precise ‘locus’ in the present moment (presumably of some entity).

Now, in ordinary parlance, the past is incapable of acting on the future; even though we might suppose that the past goes a long way to ‘making’ the future. Similarly, there is no ordinary way of conceiving the future acting in any way; since it is supposed to be empty. Indeed, the extreme reduction leads us to a dyad in which the future is nothing as against the past which is something. The present, on the other hand, has no characteristics at all and is simply a ‘gate’ between past and future. We can say that the future ‘reflects’ the past or, even, ‘reshapes’ the past. Here, we are bringing in the power of perception (taken in its widest sense). Bringing perception in can lead us to bring in all kinds of thing and we must be careful. Certainly, now we can slip into talking about ‘somebody’ being present, we can talk of the past being ‘interpreted’ in terms of the future and the future ‘anticipated’ in terms of the past; where, of course, the term ‘future’ becomes somewhat ambiguous as both the actual future that comes to take place and the imagined future which might take place. If we restrain ourselves and consider the future only as future — what is not yet —then there certainly is a recurrent dynamism, but one depending on the experiencing subject we place in the centre of the ‘now’. To say what this dynamism is about without dragging in various psychological processes is extremely difficult.

However, let us note this: in thinking about this possible relatedness, we have no need to consider anything ‘passing’ from one term to another; nor the ‘extent’ of any of the terms, since what matters is only the contact of what makes contact. These are major advantages over any spatial picture. However, as we have suggested, we easily start to bring in all kinds of psychological factors, such as ‘consciousness’. And, what is the point of bringing anything in at all?

We find ourselves bringing other things in to explain ourselves, in the form of explaining the situation we are explaining! But, whatever we bring in, we have to relate it to what we are seeking to explain. The awesomeness of the endeavour begins to make itself felt! ‘Consciousness’ for example is no nearer us than ‘time’. This is part of the argument for apophatic theology, in that everything we can use in explanation is reducible to the same kind of thing, equally not-Truth. By the compounding of elements in explanations we do not make a single step of advance towards the source of all that needs explaining.

However, let us reckon our gains in dealing with time as an alternative to space in making a representation of relatedness. Besides those we have already mentioned – no ‘passing’ from one thing to another, no ‘extension’ in the terms – we have something that is immediately accessible to everybody and applies to everything. We could then say: think of time and the relation between (or, rather, in) past, present and future; what you make of this will be your understanding of relatedness. Thus, we would claim that temporality is a test case with subjectively universal implications. We would have communicated something about the triad without recourse to any definitions, formalisms or the like. We might adduce our own exposition of temporality but others would then be free to make use of them in their own way, agree and disagree, develop, add and so on.

It should not be surprising that we would take temporality as some kind of paradigm for our understanding of relatedness because we ourselves have tended to connect relatedness with dynamism or ‘change of some kind or other. Since time is the form of change, it fits very well.

We can see something further in the example of temporality, something crucial for our starting question of what are the limits of relatedness. This is that the ‘locus’ of temporality – the ‘now’ of the present moment, ‘specious’ or otherwise – provides a natural limit. We can say that the ‘extent’ or ‘range’ of the relation stems from the capacity of the present moment. If we go on to identify the present with our ‘third force’ then we arrive at a new understanding of what this term means. It is a meaning that we should be able to generalize. If we do not have something like this determining capacity of the third force, then the relation depends for its range on the three component terms, disjointly; which entails that we do have to take into account a plethora of relations ‘coming off the ends of’ the terms in their non-coincident ‘spaces’.

Besides space and time we have the option of a third kind of representation. de persist in using the term ‘representation’ even though, already with temporality, we cease to have anything we can draw on paper – which is usually assumed to be the characteristic feature of a representation – because we are ‘projecting’ still some even yet more primal notion of relatedness into various media to see what we can observe by doing so. This is, perhaps, the nearest we can get to experimental work. The third kind of representation concerns ‘orders of complexity’ (to cast it in contemporary jargon) such as we have touched upon in dealing with the ontological identity of entities in terms of the ratio A/Z and also with the relation of w to 1 through + and x.

When we considered the ‘nature’ of an entity as being defined by its ‘place’ in relation to an ‘above’ and a ‘below’ we did not, then, treat of the ‘above’ and the ‘below’ as different orders of complexity, but we might well have done. Roughly speaking, the degree of complexity of something is equated with the length of the minimum algorithm by which it may be produced, i.e. of the series of independent steps it involves. In a sense, it is straightforward to consider this series as multiplicative: the probability, for example, of the complex whole being produced by chance is the product of the separate probabilities of each step. In our representation of an entity, the factor A was the degree of complexity necessary to arrive at the entity; while Z was the degree of complexity needed to reach from that entity to the ultimate. We may take the example of man and picture each of the steps towards his formation as being steps in evolution, of which we have the signs in existing species and in the fossil records. But, beyond man, there are further reaches of complexity, in which man could represent only one component.

Now, the representation in terms of orders of complexity does not, at first glance, afford us any means of conceiving of an action of one order upon another. We may easily understand that they are related; but not so easily in what this consists. This problem comes to the fore when we consider what can be the effect of the ‘higher orders of complexity’ on an entity, or on the ‘lower orders’. If we have the outlook of a Neo-Darwinian and anti-vitalist, then there is no way in which the order of complexity ‘to come’ can influence the orders of complexity which are in existence. Much of the motive for this view comes from a rejection of the concept that there is a pre-ordained pattern which e.g., evolution follows. In much the same way, most people would reject any notion of the future ‘acting upon’ the past – or even upon the present. An exception would be Fred Hoyle who takes the idea of future acting upon the present quite seriously – just on account of his rejection of Darwinism.

We verge upon the area of a-causality once more. Again, the sphere of biology we have the attempts by Sir Alister Hardy to hypothesize telepathic communication between species, or of Sheldrake to invoke a morphogenetic field to account for the improbably rapid accumulation of information (learning) in the biosphere. Only Lovelock has gone some way in showing how a high order of connectivity can be effected through chemical adjustments of the environment. Then there is the realm of science fiction. Gregory Brentford’s novel ‘Timescape’ is based on the idea of a crisis-ridden present receiving tachyon messages from the future.

In general, the problem is posed in the form of: haw is it possible for information to reach the present from the future? Besides consideration of weird physical processes taking place faster than light, there have to be investigations of the status of the present. It is a matter of understanding where and how intervention is possible. According to our approach, this amounts to an investigation of the third force in the situation.

It is usual to consider that the future has many alternatives in connection with a single past. To allow for intervention, we have rather to suppose that the present has many alternatives; rather on the lines of the ‘alternative universes’ interpretation of quantum theory. The point of intervention is then a matter of adjustments between the various ‘presents’; for, it is through this that the future is decided (in the sense of the ‘future which turns into the past’). In this model, the future is manifold and the past, single. It is in the present that these two are unified. We say that the past is single because, once it is ‘that which has happened’ it is fixed. The future is manifold because experience seems to teach us that determinism extends only so far, even in simple mechanical systems, as has been explored by the recent studies of Chaotics. Chaos, which appears to be crucial to the increase in order of complexity which we observe, involves ‘sensitive regions’ where even the smallest of variations can make a radical difference. The sensitive regions have a fractal structure, and it is interesting to think of this concept applied to the present moment. Ultimately, we reach into the quantum levels; and the study of Chaotics includes insights into how information from the microscopic world emerges into the macroscopic. Part of the interpretation of quantum theory revolves around the different meanings of time that appear to hold in the two domains.

It is extremely significant that the possibilities for the emergence of higher orders of complexity revolve around the ‘fine detail’ of the present state of affairs. This corresponds closely to our conception of the third force. The intervention – which is what we are most concerned with – operates in the detail, not in the mass. In much the same way, the historian Toynbee in his study of history proposes that creative advance comes through small groups; and, it has often been pointed out that, when the dinosaurs became extinct, nobody would have credited the small mammals which then existed with the power to become the dominant life-form.

The manifoldness of the possible future has led many to suppose that the ‘agent’ of change (in terms of both ‘progress’ and ‘degeneration’) is chance. We have here a materialistic version of Bennett’s hazard. We have to ask: chance for what? The concept of chance is introduced — in a sense, quite validly – to signify ignorance. That is to say, there is no way in the present to discriminate between various alternatives or determine them in one way of the other (determination or actual intervention depending as it does – or so it seems – on having the relevant information). liow, this is part of the essence of the future. As in history, even though we may suppose general patterns, the recurrence of types of event, and so on, what actually comes to pass is always surprising. This means, again, that in the present we lack the information that the future brings. This is very important. It annihilates any theory that information is reaching the present from the future: either the information is in the future, in the sense that it does not yet exist; or it is also in the present, in which case the present loses its distinction from the future (and we have the Einsteinian view of the present being delusion as something in its own right).

The only way out of (a) wanting to preserve some sense of relatedness in temporality, which means that the present has a contributory power and (b) accepting that information does not travel from the future to the past, is to suppose that what is being transferred into the present from the future is not information. The ‘ignorance’ which appears in the guise of chance has, therefore, a positive character. The future is not nothing for the present, a kind of blank; nor is it an extension of the past, containing no more information than the past.

If we imagine some clairvoyant seeing the future, we have to say that the future thus seen can only be an extension of the past; and, this is not the interesting future, the future which is ‘more’, or which can be more. In fact, it is notorious that the information picked up by clairvoyants is perhaps, always of a kind which eludes application in a decisive way in the present. On the other hand, creative thought and creative action, always entail just that: effective intervention in the present to reveal a future of a higher order of complexity. Where does the new information generated in creativity come from except from the future?

We must make it clear that what we are doing is gradually shift the meaning of the ‘future’ from the simple sense of ‘what is happening tomorrow’ to something else, to the ‘future that counts as significantly different from the past’.

The Sense and Meaning of ‘Past’ and ‘Future’

We have reached the point at which we have to create a meaning for the future which will allow us to conceive of its action within the present in some form, without invoking any mechanisms for the transfer of information from the future to the present or past. We will begin with an extreme example, from the literature of spirituality in the East. There, in certain schools, it is supposed that we have led ‘many lives’ before this birth and face many more, unless we attain to ‘liberation from the cycle of birth and death’. It is also said, naturally, that a direct awareness is possible of our many lives in the past; and, even, that this is necessary in order to awaken us realistically to the prospect of an ending to our slavery to the wheel of life, that is to liberation. Let us consider that ‘many lives’ is the significant content of the past; then, ‘liberation’ is the significant content of the future. To repeat, the future containing yet more lives is the less significant future; since it would be only an extension of the past. However, now we come to the main problem: what is it that stands between this kind of past and this kind of future? This ‘something’ is critical: it is this that is capable of seeing the many lives and it is this which is capable of liberation. It becomes especially interesting when one considers that, of course, the state of liberation is of a ‘higher order’ but it is equivalent to an extinction of that which was born and died. Liberation, as detachment from life, appears to add no information; indeed, its prospect is regarded by most people in terms of utter privation or nothingness, imagined as pure ignorance (no sensations, emotions, thoughts, etc.) It is, in fact, highly probable (in the light of our own contentions) that liberation is intended as a higher order of complexity, but expressed in apophatic terms. The crucial element, however, is that, as far as the perspective of the past is concerned, this future of liberation is empty, or non—information.

Now, what of the present? The Buddhists, for example, do say that we have to learn or understand that the past — the cycle of lives — is something like a waste of time and is not going anywhere! This has to be realized now. In a sense, they also imply that this very realization is almost, but not quite, the realization of liberation itself. The renunciation of the past is keyed into the liberation of the future; but, in the sense that this liberation is not in simple future time, at some later date. In other words, again, the ‘future’ concerned is not of the meaning ‘what is happening tomorrow’ not least because, in this case, nothing is happening because happening has ceased.

The intellectual conundrums released by these views lead, naturally enough, to the view often expressed that we are ‘already liberated’ and have ‘only to realise this’. This ‘already’ is important. It does, of course, parallel the views of those who feel a resistance towards accepting ‘chance’ as the sole agent of evolution (in the context of ‘necessity’) who want to find a way of saying that the future is ‘already here’; an argument which has been steadily attacked since the rise of modern science. Any assertion of the kind that there is something operating in the present which is of the future has been invalidated; since, everything that can be pointed to and verified must, literally of necessity, belong to the past. Or, is simply an unknown which we might as well vindicate by the term chance.

The whole domain of spirituality in human community is bedevilled by tending to assert the existence of x things equivalent to the ‘hidden variables’ which are from time to time introduced into scientific thought. The problem being, that every time a hidden variable is made to become visible it ceases to play the role of the future, becomes a known; and, if it cannot be made visible, then it remains a mere fancy.

At this point, we may well be tempted to adopt the view that the category of the future is fundamental and represents the not—yet information without which the present loses all meaning. Imagine an artist in front of a canvas. At the beginning it is empty; while at the end of his work, it is full of content. In a sense, the empty canvas represents the future. It is not entirely a bland however: it is a canvas on which a painting is to be made by this artist; it is the canvas as looked at by the artist (‘an empty canvas is a wondrous thing’, Kandinsky once said). We might then suppose that when the painting is made, the future – our apparently blank unknown – has disappeared, having turned into the past. This is not so. Remember that the initial canvas in its blank state was, in fact the canvas as it was seen by the artist. how we have the painting as it can be seen by an audience. The painted canvas corresponds to the future of art. And, just as it not determined at the beginning just what the painting would be; so it is not determined just what the painting will mean in the cultural community. In both, there is hazard.

In presenting this example, we have presumed that the ‘future’ is so-to-say created by the ‘look’ of the artist or the audience. We cannot simply treat this as a ‘potential’ on analogy with the physical sciences, just because it is not determinate. However, we may well regard this future as arising from the context of the work. But, this is just to say that they arise from the present.

It is very important, now, to grasp that the empty canvas represents a higher order of complexity than the accomplished painting. This strange concept is intended to parallel what is meant by the transition from chaos to cosmos, in which creation takes place by -limiting the complexity inherent in chaos. Chaos, or emptiness, is simply that which we cannot accommodate in the present. Every artist knows the agony of feeling the gap, between the ultimate order of complexity he senses and that which he is able to realize, or ‘bring to pass’. That which he cannot bring to pass remains the unknown, the abyss; but is, nevertheless, a reality for him. In the individual man or woman, this chaos or emptiness is represented by the unconscious; but, only in the sense of the unconscious, which is of a higher order of complexity, the Jungian unconscious for example. In Jung, we have the ambiguous concept of the unconscious as being both chaotic and more highly ordered. Both notions axle necessary for the concept of higher order of complexity. No term such as ‘time’, the ‘unconscious’ or the like will serve us without qualification.

Before we go further, let us consider the past. The past is where everything happens as it has always happened. It is the realm of ‘necessity’ in contrast with that of ‘chance’. For the artist, it will be doing what he has already achieved (why do another pied of the same type and level except to make money!). No matter what the level of achievement, this is always the character of the past if it is extended. We see, again, that extension has to do with the ‘passive’ term.

The past is repetition while the future is novelty. The past does not add any information – or, rather, generate any information – while the future is that which does create new information – which may not be the same as ‘having’ more information than the past has. For the Buddhists, the cycle of births and deaths must continue until the lesson is learnt. Learning a lesson is a matter of generating new information, belonging to a higher order of complexity: it is adding another step to the algorithm, which we have represented in terms of multiplicative unity. Thus, another life does entail more information, but it remains side-by-side with the rest and does not ‘combine’ with it.

We may note, as an aside, that our use of + and x reflect the meaning of space and time, respectively. The ‘multiplication effect’ has to do with the proliferation of possible futures, a feature of higher order of complexity. In the multiplication of terms, every term has an effect on all the others. This is not the case for addition.

In this view of ours, we are supposing that the lesson can only be learnt given sufficient data; that it requires a sufficient complexity ‘brought into multiplicative unity’ to get the point. Which is to say that it is not possible arrive at some kind of vision of ‘it is all the same’ which has any power to transform the subject! Boredom is insufficient for realization! In boredom, there is no complexity, only sameness; hence, no relatedness, no dynamism, and no power to change.

The future, represented as ‘chaos’ – as we have explained it – is that which the present is unable to contain or bear. Hence the expression: ‘Being is what you can bear.’ The artist is, far more than he is a doing being, a being that endures suffering. He is called upon to accomplish the impossible, insofar as we measure possibility in terms of the past. Hence, the creative artist – and the creative man as such, for that matter – is one who accepts responsibility for the impossible, that is: becomes a vehicle of the future.

In none of this have we come any nearer to showing how it might be that the future ‘of itself’ acts upon the present or the past. And, we have begun to deal with the dynamism of temporality entirely in terms of the agent of the present. A simple analogy may begin to help, one taken from the work of Matchett. In this, the future – which is, of course, his Media – acts rather like a vacuum, pulling upon the present rather than pushing it. This presupposes an intelligible ‘space’ rather on the lines of the spiritual intelligence or substances of the scholastics. (Intelligences, substances and spaces are taken here as equivalent as they may be treated in this context). The only model proposed for the action of these intelligences or this kind of space involves the creation of images in the present which attract the interest of the present agent. This model was used, for example, in the film 2001. It extends into the realm of ideas, where it is supposed that ideas are limited and also capable of generating each other: the ‘ecology’ of ideas is where the past and future can meet. The value of this model is that it does not immediately claim that the future ‘does’ anything — it only ‘beckons’! We do, after all, have to explain how the future can communicate with the present.

Matchett’s model of a ‘pull’ from a ‘Vacuum’ absolves us from presupposing any extra—human intelligences lurking in the future, sending ideas into the present. But the difference is probably only one of temperament. Many people can accept the idea of some spiritual something exerting a pull on the present but far fewer can countenance the idea of a future kind of existence inhabited by denizens capable of taking individualized initiative. In correspondence with Heitler, we found him totally resistant to the idea of spiritual beings while fully accepting an abstract ‘spiritual principle’ at work in an ‘intelligent universe’.

The issue for us revolves around the mode of action of the future upon the present. There is a great attraction in using the model of communication, in that it enables us to understand a mode of action at work without having to understand its underlying mechanisms. Thus, we can treat of human communication on many levels without paying any attention to neurology, physiology or phonetics- However, we can hardly excuse ourselves in this way, since we are invoking the model per se of human communication in which the future is always excluded (in usual discourse, that is). The value of the model is tha it automatically suggests communication between persons. This, in spite of the fact that we would be even more hard put to conceive of the ‘person of the past’. In this respect, we would have to conceive of the present as a ‘catalyst’ capable of transforming its communication wits the future into a change in the past.

To explicate this relation with the future, it will be of some use to distinguish what we are calling ‘addition’ from ‘multiplication’. de take the elementary case of two elements (anything more complex works according to the same principles) which we designate as 1 and O. to give them each an identity. In the purely ‘additive’ state, we have only the choice: 1 or O. This follows such principles as: no two bodies can occupy the same space at the same time.

Now, in ‘multiplication’ we are considering, not the arithmetical product (which in this case 1 x 0 = 0!) but the combinations. These are measured by the arrangements we can make, first of all:

01

10

if we then combine these, we have a third:

11 which, of course, we have defined like this.

Hence we have, in our ‘multiplication’, three possible states:

01, 10, 11 which can, of course, be ‘read’ as 1, 2, 3

So, we have moved from a choice of two options to a choice of three. Also, note that they are not at all the same: we have not just added on another option. In this respect, note also that we are rejecting any move to add on free will to determinism. Also:

01 + 10 = 11 the basic trisdinction of arithmetic

Further, given this power of combination, we need not treat the three options as mutually exclusive. In fact, we can have them all together. Then, we have the further structure of six combinations:

01 + 10 = 11

10 + 01 = 11

01 = 11 – 10

10 = 11 – 01

11 = 01 + 10

11 = 10 + 01

These six forms say everything that can be said about the given combination, which is of 01 and 10. Of course, we have in arithmetic various ‘rules’ which render all these identical; but, in our context, this should be treated as an abstraction, a limiting case. We are more interested in the possibility that they can signify distinctly.

COMBINATIONS ALLOW US THE POSSIBILITY OF A LANGUAGE

If there is an influence from the future, then it will be something like a message expressed in this language! Interestingly enough, the code of DNA is itself ‘written’ in triplets.

Now, the ‘place’ for these combinations is not in space, nor can it be time. we postulate, therefore, a kind of time—space which has sometimes by other authors been given the name ‘eternity’. This is an unfortunate name, since it suggests something invariant and unchanging; whereas, the reality refers to an influence and a presence within the present moment in its dynamism. The ‘language’ we are referring to arises within the present as a possibility for the future with respect to the past.

We must remember, with respect to this ‘language’, that we are still prohibited from imagining that a message chm be sent from the future to the past. We do have, however, some kind of meaning for talking about what the present can bear: this refers to the range of combinations which can be entertained, or read off as implied in the content of the past influencing the present° Also, clearly, we are not claiming that the present agent becomes capable of something which it was not before capable of: in other words, we are not allowing miracles! The agent still has to do something, make some contribution to the past, add a component.

Our metaphor of a language can be extended in the following way: let the ‘past’ be the signs of the language, let the ‘present’ be its grammar, and let the ‘future’ be what is to be said (We should also allow that the ‘present’ be lexographical). Or, we can regard the past as providing a vocabulary allowing a compresence of possible statements, some of which may have meaning in respect of the future. Bence, it is supposed that ‘messages’ activated (by ‘chance’) in the present from the past can be novel and (by ‘chance’) turn out to relate positively to external circumstances arising in the future. Expressed in this fashion, we begin to have something which corresponds to the experience of people when they are engaged in creative work: they have a sense of what is going to turn out to be the new and powerful solution before it is proven or shown to be such. Creative work takes place in the medium of the past; but it has the feature of entertaining the meaning of ‘combinations’ which are not established in the past. There is always available in the present a redundancy of combinations (just as in writing a passage when there are ‘hovering around’ all kinds of ways of expressing or describing, some of which hardly correspond at all to previous text). It is a feature of creative work that there is a large variety of such combinations and there are systematic methods which involve exhaustively ‘going through’ each of these in an attempt to find new meanings.

The Action in the Present

There is a common error to be found amongst most ‘spiritually orientated’ cosmologies: that we can take for granted our experience of what seems to be the action of mind upon matter and generalize this to tell us about what is beyond man and below him. The truth is, we have no understanding of the action in the present moment which is subsumed under the action of mind. Our previous argument, leading to the proposition that communication with the future is translated in the present into a change in the past (even giving the terms ‘past’ and ‘future’ our own special meaning),we have to admit, falls into the same trap. We can make an argument that by ‘communication’ we did not just mean human communication – we would include the ‘communication’ of DNA to the chemistry of the cell, for example – but this does not give us the required degree of initiative and originality.

However, we can do one thing. That is, we can regard the change wrought in the nature of the past as itself a communication. What we mean is that what we can take for granted is altered: or, that ik is the ‘reading’ of the past that is altered. This is no mere anthropomorphism either. We have, in respect of DA-A, to introduce ‘readers’ of the code it embodies: otherwise, the genes would have no effect in the chemistry of the cells. A contemporary theory has it that the readers not only correct the bits of message they contact; they are also capable of generating missing parts and, even generating new items. (The latter gets us into novelty and evolution) If DNA represents the past, then we must have a way of ‘recalling’ the past or making the past operative in the present.

For the first time, we have model for how it is that we can reasonably talk of the past influencing the present that makes it a feature of the present as well as of the past. The effective past is selected by the – or in the – present! The biological model is essential in that it draws attention to an internal working which is from itself selective of the past. We are provided with a concrete meaning for the notion of ‘changing the past’ which, at first glance, is nonsensical. Wow, we understand that the ‘past’ we talk of is not the past in general but the past related to the given present; and we have found a positive meaning for this relation in the notion of reading. We have also found that this relation can ‘pass over’ into the generation of novelty – even if this is considered to take place ‘by mistake’! In our terms, this means that it can pass over into relation with the future.

However, the new meanings are related to the future (in its broad sense) that is, to other things which might happen. These other things may take place in the environment or in the semantic context. Thus, the possible meaning of the ‘redundant’ combinations depends on factors which are not in the given present moment. A mutation, for example, will take its meaning from the ecological context amongst other things. In this respect, the action in the present can be thought of along the lines of game theory: a move has to be made in the context of other moves taken independently. These other moves will be arising from the elsewhere as well as from the elsewhen. But, they will be moves which are coming into relation with the given move: that is, there is a game, a nexus of significant interaction.

In human affairs, this is crucial. For example, a man in front of a possibility of gaining something for himself may realize that what others do will affect what he can gain – there may be competition over resources or prizes – so he has to decide how he is going to anticipate what others will do. But, he may also see that he has to decide how others may anticipate what he himself will do. There have been some interesting experiments done concerning ‘rational game playing’ (cf. Hofstader) exploring the strategy of rational behaviour: if, for example, everyone will end up by getting very much less if they all try to be greedy, then the rational approach is to show restraint, because this gives a chance for rationality to be effective; thinking the worst of people and their motivations creates the worst. So, although the man cannot determine what others do, he can allow them to act in what is understood as a positive way. What he is doing is giving a meaning to certain combinations in his present moment belonging to a ‘higher motivation’, or to a ‘more intelligent response’; such meaning being conditional on what actually happens. However, the meaning he gives is not entirely conditional, in that he has acted according to a certain intent which remains inviolable.

This distinction between the conditional and the intrinsic meaning of ‘activated’ combinations is not usually applied in the domain of biological evolution; yet, it is implicit in those areas where we see amazing and beautiful things unrelated to survival. We would strongly assert that the beauty of nature is intrinsic meaning which does not arise out of conditional meaning. Thus, a man can be beautiful in an ethical sense even though relatively ‘ineffectual’ in life.

Now we can see that the ‘future’ is permeated with manifold meaning. It is the region in which the possible meanings being generated in various present moments combine in mutual relevance. The mode of combination is, perhaps, a step removed from that taking place in any present: it is of a different order of complexity. If we imagine for the sake of argument the combinations within the present to be represented by the transfinite number aleph-one, then the order of the future will be represented by aleph-two, an order of orders. We could also, for example, treat of the difference on the limes of the various ‘systems’ we are engaged in exploring. Up until now, we have mainly considered the triad with some reference to the monad and the dyad. If we take the order of the present to be the triad, then we would assign the order of the future to the tetrad. We must take into account that – just as we saw in the step from the dyadic order of the past to the triadic order of the present – the nature of the terms changes. We will not be dealing in the same currency in the future as we are dealing with ‘now’. It is this above all which makes the future the future and a real factor.

As far as the present Is concerned, the future may well appear as chaos, since it is uncertain and beyond the relations which are now. And, as we have suggested, ‘chaos’ represents a higher level of complexity which we cannot ‘yet’ handle in our ‘cosmos’. The higher order of complexity is capable of generating meaning without recourse to the vocabulary of the past. Hence, the future ‘speaks’ in another kind of language.

The future that we plan is a ‘fallen’ version of the future, as if it were collapsed back into the past. The ‘true’ future is totally unbearable and cannot be contained in any present. Or, we can say that for any given present, there is a ‘true’ future which is of the next order of complexity. After saying this, we might well regard the ‘Platonic Forms’ for example as being thoroughly misunderstood; for, in our scheme, they would have to be far from the quiet and invariant entities taey are usually described as. Similarly, the ‘spiritual entities’ – again, in our scheme of things – are seen to be represented as serene and ‘perfect’ only through wish-fulfilment: we tend to look to the future for a cessation of the struggle and anguish of the present. In fact, we may well regard the future as announcing our own present annihilation; further, the present may also be regarded as a barrier to the future. It is only by ‘resisting’ the future that the present can be. This is complementary to our earlier assertion that we are able to exist – like any entity – only because God hides Himself from us.

The Two Faces of Time

As we have discussed it, ‘time’ in its relatedness of past, present and future is far removed from the simple entropic time of classical physics. Our ‘time’ is more in line with recent thinking, in which increase in order of complexity is taken to be a real feature of the universal process. In terms of our scheme, we may well regard entropic time as mainly reflective of what we have called the ‘past’ whereas ‘complexity time’ can be seen as mainly reflective of what we have called the ‘future’. As has been pointed out on many occasions, entropic time does not prohibit the arising of higher orders of complexity within limited regions; but, only very recently has it been possible to provide a positive reason fur evolutionary processes.

The time we have been discussing is the time of meaning: the various ‘combinations’ are distinguishable by their meaning; even though, in entropic time, there is no such distinction (which leads to statistical laws). We have associated this meaning with ‘language’ by analogy; hence, we have to say that there must be some kind of syntax or grammar determining the form of ‘meaningful’ expressions (combinations). This syntax is a feature of the present; such that certain combinations can be read, but not others. However, this syntax is not invariant; and, whenever we have the effect of a new syntax, permitting new combinations to be ‘read’, we have what we wish to call a ‘message from the future’.

In the ‘future’ what is permitted and what is not permitted are both ‘present’ in combination. The future, then, has the power of changing the rules operating in the present in the sense that ‘previously’ unintelligible combinations become meaningful. To enable us to approach this concept, let us think of what has happened in the history of music. In the classical and romantic periods there remained a sense of what was ‘permitted’ – of what was to be accepted as ‘musical content’. With late romantic and early twentieth century music, the rules were changed. For many audiences, the ‘new music’ was not music at all but noise: they were not able to read it. The composers involved, such as Schoenberg, were in contact with the ‘future’ and they were reading music differently. In this way, a new order came into music. Schoenberg took it upon himself to develop an explicit syntax – known as the theory of composition in twelve tones or, later, ‘serial’ music. We can imagine, however, that at the source of the new music was an ‘experience’ in which the previously unintelligible became intelligible, though in a way which could not then be explained. The wide-scale rejection of the new music belongs to what we call the ‘resistance’ of the present to the future, which enables the present to ‘be’ something. It was a fear of ‘chaos’.

Thus, of what the present is indifferent belongs to entropic time; while of what the present is meaningful belongs to complex time. To provide a picture of what the future of complex time might be like, we can take the set of six forms in every possible combination. For example, if we allow them to combine again, three at a time, then there will be no less than 120 distinct forms. Allowing all possible combinations will produce more than a thousand. We note, however, that the ‘units’ brought into combination are the ‘forms’ generated within the present; just as these, in their turn, were generated within the present out of the ‘units’ of the past. The increase in number of possibilities has to be qualified by a conditional factor which has to do with capacity. The future that can be related to the present has to conform to the capacity of the present. In this sense we have a parallel with the requirement for ‘adequate variety’ for the power of adaptation to unforeseeable futures which is part of the theory of cybernetic systems. It is on these grounds that ecologists speak of a crisis in the state of the biosphere on account of the extinction of so many species on the planet.

The ‘critical capacity’ of the present, then, turns out to be something like the ‘monadic intensity’, the living organic diversity which is compresent now. We can then see that, quite naturally, creativity emerges more and more strongly as we have more and more diversity within the present. The influence of the future marks a transition from what is felt within the present to what is meaningful in an intelligible way. By ‘intelligible’ here we mean, of course, triadic or relational. What is only felt can remain only as a feeling and dissolve away as merely another component. The step to relation creates a ‘working model’ of time within the present and it is this which can carry the messages of the future.

We should also remember that the ‘future’ is a region in contact with many present moments. This, in two senses: the many signifies not only a plurality of ‘agents’ but also the plurality of present moments peculiar to one agent which are all related to a common future. If we picture the various present moments as one agent as not merging continuously into each other, then we can imagine a structure of them within the future; as they are, coupled with those of other agents, in higher complexity. What appears, therefore, to the agent (of the present moment) as his past, present and future may have alternative forms within the future (that is to say, in relation to the ‘future’ in its strong sense). It is this that can lend experiential support to the feeling of the future-influencing-the-past: one knows that the order of time which we have is not, in spite of the conditioning pressures of entropic time, the only one. Past and present will be redefined within the future.

Complex time is at least organic. We may picture, for example: the present ‘eating’ of the future and excreting the past. However, in the living realm, the ‘eater’ is usually on a higher level to that which is eaten; so, do we have to imagine that the future is eating the present?

In ordinary entropic time, it is more the past eating into the present that we think of: time as perpetual perishing, or the ‘dying’ of the present. Perhaps, after all, the two faces of time are not so different! The past and the future vie with each other to devour the present: they keep each other at bay to allow the present to be. Let us imagine an ecological model, with past, present and future represented as three levels of complexity; say, within a food-chain. Ecological systems incorporate both competition and co-operation. Given a context of limited resources, new elements have to compete with old. However, allowing for the redefinition of resources new elements need not be in competition; there can be synergies. In this respect, we hate a biological equivalent to rational game-playing. New species can emerge that enable the whole food-chain to utilize the total available energy (from the sun) more Efficiently (and, we would also say, more interestingly). The notion, then, of the future eating the is not one of bare predation at the expense of the present! What the present is ‘doing’ is to optimize the flow of ‘time’ from future to past. In this sense:

TIME IS OPPORTUNITY

Existentially, the future is an ‘advanced ecology’ while the past is the established one. These are not single-valued, in that, for every present moment (a species, let us say) there are many pasts and many futures. These, in their turn, relate to many versions of the present. On our own planet, the advanced ecology is sometimes labelled as ‘higher intelligence’ and it is also sometimes correlated with ‘latent powers’ of the human mind; the reason for this being an assumption that human beings are at the core of the ecological present moment of the Earth’s biosphere. It is interesting to speculate whether this present moment, in fact, is not exclusively centred in man. Such a notion is suggested in the work of Lovelock which supposes that all life on Earth makes up a self-governing entity, which he calls Gaia.

Relevance of the 3-M Equation

It is easy to see that, in our scheme, the future is the realm of Media while the past is the realm of Matter; and, of course, the present is the realm of Meaning. The practice of the ‘equation’ does entail, as we would suspect, a sensitization to higher orders of complexity through art, music and narrative taken in intensive combination, which is to encourage a contact with the future, or Media. The future is not the domain of selection, only of incorporation. Media works by inclusion, in contrast with Matter which works by exclusion. The future is enfolded within the present while the past is unfolded (to use the terms developed by David Bohm).

It is taken for granted that the realm of Media is, in reality, highly organized. It is not a blank, not the unconscious. It does not lack determination but transcends it. Thus, opposites are both true in the future, in a sense which fully conforms to their separate truth and in a sense which corresponds to another order of truth which can include the former.

The ‘utilisation’ of Media is through Meaning; that is, through the present. It is in the present that we can read the signs. In the realm of Meaning, we can pass through the ‘irrational’ to a higher rationality; we can pass from the gratuity of ‘chance’ to the imperative of creative advance.

In so doing, we find that we are ‘making our own future’ but at the behest of the future itself. There is always an element not of the present or past, an inexplicable connectivity, which can bring us closer to a higher order. In this respect, human experience is the forerunner of a future science, the science of active time. We are able to ‘detect’ the future, the realm of the higher order of complexity, in way which is outside of calculation and necessarily so – since calculation is based in the past. For the most part, this detection lies buried in our powers of thought and feeling. In one of earlier discussions of the 3-M equation, we made reference to faith and to conscience, just in order to suggest powers which are not to be understood in terms of concepts or emotions. Further, what are often referred to as ‘spiritual powers’ amount just to this power of detection of and response to the future. In this sense, suck powers are ‘organs of evolutionary advance’.

Back to the Future

We began our excursion into the nature of the relation of temporality by realizing the limitations inherent in any spatial representation of relatedness. It is difficult to keep to the discipline of non-spatial representation, especially if we involve ourselves in mathematical formalisms which lend themselves to such representation. Just think of the one of the most fundamental concepts, that of sets, and the point becomes obvious. In our treatment of the combinatorial possibilities inherent in the future, we distinguished combinations according to their sequences of terms as well as according to their content. We were, then, conceiving of the future as tin movement’ and not as a quasi-space, such as that we suggested as accompanying the present moment, a kind of ‘eternity’.

The idea of a past, present and future in movement is very important; not least, because it holds us back from spatial thinking, in which we bring ourselves to an impasse thinking of the duration of the present, for example, as an extension. Sequence is a crucial part of the higher order of complexity of the future and the future cannot be represented adequately as an arrangement of sets, for example. However, what the set model can do is to give us a picture of futures of different orders of inclusion. It is in this respect that ae can talk of greater or lesser present moments; since we suppose that the scope of the present is primarily defined in terms of the future with which it is related.

There is, in the concept of relation, something of absolute import for our understanding of time – and also, thereby, we would claim for time in reality. On various occasions, we have reached a point at which we simply imply that the real nature of relatedness lies yet beyond whatever form or description we have come to. Relatedness is the defining character of the present moment and the very same elusive quality of the present is shared with relatedness itself. .dut, we have also implied that the future is more than relatedness! If we attend to it in its own right, we come into an intersection of the possible with the impossible, constantly – if we may be allowed such a word in this context – adapting to itself. The future is not merely the higher complexity hinted at by the present; it is a working. This has to be grappled with, since we have set ourselves firmly against any notion of the future as a ‘timeless repository’ or as a blue-print for what might happen. The future is not of the nature of the genetic code, for example. It is not encoded. Its language is being generated ‘all the time’ within the present moment but its speech is creative In some measure, genius is an excursion into the future. There does not cease to be movement, but this kind of movement – whether in art or in life – appears as inexplicable to those who ‘lag behind’.

This conception does, up to a point, allow us to make a model for the way in which the future influences the present (and, therefore, as a consequence, the past): different present moments are differently related with respect to the future and are, at the ‘same time’ connected with each other. Thus, what is relatively inaccessible from the inside is relatively accessible from the outside. That is why communication (through space!) is an important feature of human creativity. This is evidenced – though never in an easily graspable way – in the arising of creative groups and in spiritual guidance. Thus, the real spiritual teacher communicates the future to his pupil. Obviously, this must lead to great difficulties in practice and that kind of relation is rarely effective. In the case of creative groups, no one can design these on purpose; they seem to arise of themselves at certain times. then they do arise, there is much evidence of a synchronous connection also; in which case, what we have is a manifestation of the future’s higher order working itself out in the manifold of mutually relevant present moments.

Past, present and future are what time means. The past is time as fixed, the present as time being worked out in a localized way and the future as time being created in a non-localized way. (Earlier on, we asserted that the triad creates time). All these are in relation with each other; which means, for example, that the past is not completely fixed nor the future completely open. The relevant past is constituted out of signals which are read in the present – as in the case of light from a supernova that exploded a thousand years or more ‘before’ and as in the case of the DNA which is being read in the biochemical activity of the cell. It is possible that there is a more ‘direct’ access to the past, one which is made possible only by meaning: such things have been described by Toynbee amongst others. The ‘meaning-link’ is an extreme case of reading. Science works in this way: we have to understand that the background radiation of the universe is relevant to its early history before we can accept this radiation as a ‘fossil’ of the Big-Bang.

In Pledge’s formalism of Bodies, Place and Time (BPT) he discussed the possibility of a ‘mental space’ in which the prohibited form of two bodies in the same place at the same time would be permitted. We, for our part, can propose a ‘mental time’ in which the same situation is allowed. The term ‘mental time’ is not desirable, but we will bear with it for the time being. We can see how, by altering our concept of ‘the same’ with respect to time, what is ‘impossible’ becomes ‘possible’. However, this time is the future in our scheme.

There is a scene in D.H. Lawrence’s ‘The Rainbow’ in which one of the characters tries to explain his vision in which: an angel is the union of a man and a woman. This is precisely illustrative of what we mean by the being in the same place at the same time in the future. Further, it brings out in a very strong fashion what the future implies. The ‘angel’ is clearly a higher order of complexity. So, we have a higher order being constituted out of a combination of two present moments, literally a fusion or ‘spiritual marriage’. It is also very important to realize that such a future is i different from the past or present.

Time is like this. It allows for a diversity of present moments which, at their own level of complexity, must remain mutually exclusive even though mutually relevant. It is only in the future that they can join together into a higher unity. Which means, in our scheme, in a higher multiplicative unity. The future is the focal point of hazard. It is the region of true friendship. It is where art is really created: the workshop and not the shop window. (cf Rumi)

The future relies upon the present to become especially itself, in order to be able to arrive at a higher order which includes it. But, when it does incorporate it, it is neither the same nor different from what it ‘was’. This logically impossible condition expresses something of the nature of the resistance of the present to the future. ‘When’ the future takes over, the present accelerates out of itself into a new relation; for the future is the field of temporal relations. What, in Jungian psychology, is called the ‘unconscious’ includes relations with the future. To ‘enter the future will appear as loss of consciousness, a threat. We find that the unconscious does not have the same kind of directiveness and discrimination which we feel in our present moment; and we make the false conclusion that this means that the unconscious is inferior to the conscious. Such a conclusion is often criticize& by spiritual authorities; but, it is immensely difficult to find an adequate model for the unconscious, one that can enable us to appreciate that it has an order ‘above’ our familiar level of discrimination. We also have the confusion between past and future, in that both appear to us only. indirectly. The future is the realm of the ‘black light’ and it is hard to trust in the workings-in-the-dark without falling back on the ‘light’ always available within our narrow circle: a point made in the Mulla Nasruddin joke of the man searching for his key, not where it was dropped, but under the lamp where he ‘could see’!

Attunement to what is not present is, however, possible. Jung says much the same thing through his own terminology. Matchett practices this with his students. According to our scheme, this practice most probably requires a grounding in the temporal relation; that is, in the experience of change. This will appear at first as destabilizing, in which memory and habit give way to becoming. We begin to admit the unconscious. We realize that we are within a field of becoming. Nothing stays still, even though nearly all our intellectual effort is directed towards keeping our attention on the invariant.

We have to take account of space. Usually, we consider there to be three dimensions of space to which we add one of time. However, in our scheme, we take the meaningful situation to be that in which we have the three aspects of time to which is added the one of space. The shift from the usual view to that of ourselves signifies a shift from emphasis on external processes to one on internal processes. Both views, as we may see, are contained within the tetrad; which, of course, first rises as a possibility for us in terms of a trinity to which a fourth must be added for completeness. This is not to say that such a construction corresponds very well to the authentic constitution of the tetrad.

We can portray both views on one figure, as an experiment. In this figure, the spatial dimensions have been translated into less usual attributes and they are given in brackets:

‘

Extension’ signifies the aspect of continuity; ‘distance’ that of separation; ‘inside/outside’ that of topology, the most relational of the three. ‘Inside/outside’ is most associated with the present moment – as a kind of ‘region’. ‘Distance’ is most associated with the past because of its character of separation. The future is absolutely without extension and therefore has no ‘distance’ from the present, neither can it be placed inside or outside the present. 4e called this an ‘experiment’. Let us continue this experiment: imagine that the axes implicit in the figure are rotated anti-clockwise through 45°. 4e can then read the figure as:

We can mentally rotate the original figure in the clockwise direction and very slightly change our terminology to give:

Which easily translates into Jung’s:

However, we must note that figures of this kind give not the least idea of the higher order of complexity implied by the tetrad e.g. in comparison with the triad. Yet, we have achieved something in rapidly moving between the 3 + view to the balance of opposites view. We can also offer a slight commentary on the figure just above, relating it back to our concern with space and time. Thus:

in sensation, space and time are combined

in thought, space is dominant

in feeling, time is dominant

in intuition, space is time

What is rather hard to grasp is that the ‘addition of a fourth term’ enables the other three terms to ‘move around’ and change places. This is really what the ‘space’ term in our first figure amounts to: it is a space of manoeuvre for the other terms and not the space of external perception. That is: it is, as it should be, a term which is intrinsically relevant to the nature of the others. It is not really to be ‘added’ but discovered. We can already begin to suspect that it is this term which is required if the different combinations of the other three which we have often discussed are to have distinguishable meaning. We should also note that the ‘space’ term is a reflection of the ‘future’ term. In other words, this ‘space’ is inherent in what we mean by the future; but, is only disclosed when we consider the other ‘functions’ involved (the past and future). Now, when we have ‘disclosed’ the fourth, the whole situation changes. In this respect, for example, we now have to say such things as: if the present is said to exist then the past and future must exist in some way also. .y saying this, we have been brought closer to something extraordinary: that, it would be far more accurate to have the term ‘space’ replaced by the term ‘existence’.

To nonchalantly toss away ‘space’ and replace it with ‘existence’ may appear unwarranted; but, what we are about is uncovering, something we did not have to do before or, at least, not in the same way. Here, we have ‘space’ as something and not as nothing; as bare unqualified existence, the vacuum—state perhaps. A little reflection can show that our idea of space does include that of existence, though not in a subservient way. We are on the way to removing ourselves from the simple vacuity of sets towards the fulsomeness of the real world. After ridding ourselves of spatial representation, we have not introduced space again as an integral part of our models. When we look around us at things, space is a condition but what we are looking at are the things: we look at something in a spatial relation with ourselves but do not abstract out of this space in itself.

Existence transcends the triad. It is this which leads people to regard the triad as ‘abstract’ in nature. It is also this which persuades people that the world may be treated of as number; a possibility if we remain within the context of relatedness alone. At first, existence appears as something ‘opaque’ — indeed, that word expresses something of its very character. We are unable to represent existence. This may lead us to conclude that it is entirely a mental construct — in contrast with our own argument that it underlies all representation.

We seem to come a choice: we may either go the way of saying that all we can come to ultimately are the forms of our perception (which may be all reducible to relations) or we may go the way of saying that what is ultimate is existence which is the only given. In our scheme, to exist means to ‘stand out’, to herald being.

In time, past, present and future share in existence and relate in that ‘medium’. Past existence, present existence and future existence differ from each other; but, everything exists; there are no bare abstractions or pure concepts; there could be no sustained relations without existence.

While the terms of the tetrad separately exist, the tetrad itself is, i.e. as ‘being is’. This means that the tetrad includes becoming. Thus

THE FUTURE IS A TETRAD WITHIN WHICH THE RELATIONS OF TIME PROCEED

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