Harmonisation of Spiritual Development

I searched for you constantly
But love always eluded
Continually appearing
In false disguises
Turning away from the world
To escape all illusion
I journeyed in darkness
Alone at night
Then weary and dispirited
Every feeling dead
With no hope of finding you
In grief I slept
When at last dawn broke
There was a faint movement
In the depths of my soul
And you had been sleeping
Quietly at rest there
In a most secret place
And now awakening
You poured through me
With sweet inspiration
And exquisite tenderness
Swelling my heart
With joy and love
And you showed me a world
Newly created
Everywhere filled
With a sensuous presence
The sky, the mountains
The forests, the lakes
Tapestries of richest colour
Sounds of sweetest music
So many glorious shades
Of light and beauty
Reality wonderfully reborn
In your radiant image
Now all things
Were clearly illumined
In a mysterious fire
Strangely visible
And matter like
Insubstantial shells dissolved
Transformed through love
Growing brightly in the flames
And when my heart
Uniting with your's
Softly melted
All creation was consumed
In eternal ecstasy
As the flames subsided
A great calm descended
Enfolding a night
So peaceful and serene
And having unveiled
Your great mysteries
You were now once more
Within me
Hidden yet present
Absorbed into my soul
There you fondly embraced me
In closest intimacy
And in the silence
Of the night
Nature gently stood still
Softly caressing the darkness
Now captivated by love


The transition from point to radial level is characterised by another decisive transformation. One experiences a profound void which signals the end of possessive attachment to all phenomena, both of a direct (conscious) and indirect (unconscious) nature.

Though this experience represents a pure process completely without structure, there does exist an indirect mathematical means for rationally translating it in what I refer to as the null structures. These correspond directly with transfinite notions in mathematics. In a right angled triangle, where opposite and adjacent sides are of equal distance on the real and imaginary axes, the hypotenuse or connecting diagonal line can be represented as transfinite (i.e. of zero finite length).

In like fashion in psychological terms, the pure experience by which the cognitive "real" structures and affective "imaginary" structures are equalised or harmonised can also be represented as transfinite. Since this relates directly to the will, we now have a mathematical means for translating this central activity of the personality.

Thus the three domains of real, imaginary and transfinite quantities in mathematical terms have a direct qualitative complement in psychological terms. The cognitive mode of reason can be represented by the "real" structures, the affective mode of sense by the "imaginary" structures and the volitional mode of will by the "transfinite" structures respectively.

In keeping with my geometrical terminology, I have called this level the radial level. Ray, radiant, radiate are closely associated words which convey something of its fundamental meaning.

The radial level involves the integration of the previous linear, circular and point levels.

In geometry, a radius involves a straight line drawn from a point at the centre to the edge or circumference of a circle. Thus the radius inevitably involves the notions of line, circle and point.

Thus in psycho-spiritual terms the radial level can be viewed as involving straight lines or rays of light issuing from the centre of the personality in a circular unbounded fashion. In Jungian terms it represents realisation of the self. Indeed Jung describes the self in very similar terms: "The self is not only the centre but also the whole circumference which embraces, both conscious and unconscious".

We have already seen how the diagonal lines, equidistant from real and imaginary axes in the complex plane, are null lines (i.e. of zero finite length) which can be used in physics to represent rays of light.

It is quite remarkable how equally in complementary psycho-spiritual terms the diagonal structures (i.e. the pure activity of will) which unite and harmonise the "real" and "imaginary" structures of reason and emotion can also be understood as representing rays of light.

The spiritually integrated person with joy literally radiates light from the centre of personality. Not surprisingly the defining characteristic of this level is that of radiant bliss.

The radial level therefore represents a considerable victory of the personality, where all previous levels of experience are dynamically integrated in a vital and harmonious fashion. Each level, linear, circular and point is now equal, maintaining in relative terms its separate identity, while at the same interpenetrating and uniting with the other levels. Thus, because of the removal of possessive identification, each former level is seen as radiating an important though partial aspect of the overall spectrum of truth.

The radial level is well recognised in all the great mystical traditions. In Eastern mysticism it is sometimes referred to as non-dual reality. In Christian spirituality it is referred to variously as "Spiritual Marriage", "Unitive Life", "Superessential Life", and "Divinisation" . Here there is strong emphasis on this extra spiritual dimension of an intense ever present relationship with a God experienced as both the source and goal of everything in creation.

However, it is equally important to express the other pole. This is the totally ordinary nature of this level, where one becomes fully oneself and thereby truly human with no further need for false pretensions or wearing masks. Thus at one extreme, the radial level includes highly charismatic figures, who living with total commitment to their inner vision become major agents for transformation in society. It also includes however other spiritualised people who from a worldly perspective, attract little attention and remain largely unnoticed.

The radial level is sometimes represented as a final state of total fulfilment where no further psychological transformation is required. This is very mistaken, as in fact a considerable degree of further growth unfolds during this level.

Likewise, in dynamic personality terms, perfection is relative always entailing the complementary pole of imperfection. Thus coming to true knowledge of God's perfection entails corresponding awareness of the imperfection of self.

This is a vital point. From a correct religious perspective one does not attain final perfection on reaching the radial level. Rather through greater awareness of God's perfection, one comes to more fully accept one's imperfections which now in the light of this pure wisdom are more clearly understood than ever.

Ongoing progress through the radial level can take many forms. For convenience, I will deal with two major sub-levels.

The first is the more passive and - in relative terms - more contemplative - where one operating from a refined and integrated spiritual vision, slowly adapts once more to the world.

The second is more dynamic and active, where with a total desire to serve, one becomes deeply immersed in the market place of the world as a mediator of a divine healing presence.

Though the other levels - linear, circular and point have their own specific contribution to make to the spectrum of understanding, they ultimately represent a limited and distorted view of reality. The radial level approximates most closely to a truly integrated vision in spiritual, cognitive and affective terms. The world-view of this level serves therefore as the correct reference point for evaluating the more limited insights of the other levels.

I will be attempting to translate the key feature of the radial level in rational terms, using an approach which is inherently psycho-mathematical.

In other words, at the most abstract level of understanding, the basic structure of both psychological and physical reality - which ultimately are indivisible - is mathematical. As this involves the expression of what is truly dynamic, in static terms, it inevitably involves a form of reductionism.

The linear rational approach may implicitly recognise the role of intuition in understanding. Explicitly however - in formal translations - it reduces it to reason. In this sense it represents a gross and distorted form of reductionism.

The transrational approach - by contrast - sees all understanding as a dynamic interaction involving both reason and intuition, and explicitly preserves this dual aspect in formal translations. It thus represents by contrast a subtle and balanced form of reductionism.

Key Characteristics

I will attempt to outline the key features of the radial level. More detailed elaboration will follow later.

Experience involves the harmonious interplay of both a finite and transfinite aspect. Phenomena momentarily come into existence (finite) only to quickly go out of existence to reveal their underlying eternal essence (transfinite). Thus reality becomes a dynamic pulsating display reiterated in a continually renewed present moment.

Whereas the transfinite aspect - which is directly spiritual - is simple, the finite aspect - which involves the phenomena of physical reality - is (in mathematical terms) complex.

The simple spiritual aspect, manifests itself in two complementary ways. This brings with it the experience of reality as existing - not in space and time - but rather in the present moment.

These two aspects of the transfinite are the transcendent and immanent respectively.

The transcendent involves the eternal present in a holistic spiritual view of the spirit which pervades all creation (and nothing in particular). This helps to preserve a universal dimension to experience and the spirit of detachment so necessary to prevent excessive identification with specific responsibilites.

The immanent involves the complementary immediate present in a direct illumination by the spirit of specific phenomenona in nature. The unique nature of each object is revealed in spiritual light. This in turn tends to preserve the sense of the importance of each facet of creation (regardless of how minute) and facilitates intimate involvement in worldly affairs.

Both aspects of the transfinite contain a direct intuitive ability. The complementary poles of spiritual experience can be represented by light and darkness respectively. The former pole - which is the external manifestation of light - tends to be associated with immediate immanent experience. The latter pole - which is the internal manifestation of the light (or light unseen) - tends to be associated with transcendent eternal experience. Ultimately in the most mature and developed experience these two poles of the spirit themselves become identical in the direct experience of mystical ecstasy (the dazzling darkness).

However throughout most of the radial level, these spiritual poles are still separated to some degree. This is because one has not yet learned to fully integrate finite and transfinite experience. For some considerable time, contemplation and activity are not properly co-ordinated. One tends to have an intense and private contemplative life which in some measure is unrelated to one's involvement in daily responsibilities.

Indeed the key task of the radial level is to integrate these two poles so that commitment to the world ultimately represents a direct expression of one's spiritual life.

Finite experience of reality tends - in mathematical terms - to be "complex". Thus there is an continual dynamic interaction with both a "real" and " imaginary" aspect to all experience.

These "real" and " imaginary" aspects relate directly to the two complementary modes of experience and are purely relative.

If we define cognitive (rational) understanding as "real", then - in relative terms - affective (sense) understanding is "imaginary". What this entails is that experience involves a dynamic interaction of conscious and unconscious. Thus to bring the cognitive mode to consciousness and become "real", the affective mode is thereby momentarily rendered unconscious and "imaginary".

In like manner to bring the affective mode to consciousness again becoming "real", the cognitive mode must momentarily be screened out and rendered unconscious and "imaginary".

Thus both the cognitive and affective modes have "real" and "imaginary" aspects.

Both "real" and "imaginary" modes also have two polar directions. The positive direction relates to objective experience of phenomena; the negative relates to the subjective experience of the same phenomena.

The manifestation in experience of these "complex" aspects is itself as a direct result of finite and transfinite (spiritual) interaction.

When - as in conventional experience - the interaction of conscious and unconscious is somewhat rigid there is a continual confusion in experience. One tends to identify with the merely conscious aspects of experience which one identifies as "real".

Thus, when one has cognitive or rational experience of the world one interprets it as "real" experience. Equally when one has affective or sense experience of the world equally it is interpreted as "real". Then a basic confusion arises - particularly evident in science - whereby both modes - though qualitatively different are considered to be in direct correspondence.

Science prides itself on its rational approach and its ability to understand physical reality. However the data regarding physical reality comes through the senses (affective mode). The theories and hypotheses used to model reality come through reason (cognitive mode). In effect in science the affective mode is reduced to the cognitive so that the data of physical reality are believed to correspond to (appropriate) mental constructs in a "real" world.

Now, this comforting view breaks down at the sub-atomic level of quantum physics. Here the data increasingly manifest themselves as "imaginary" in relation to "real" rational understanding. In other words as we reach the fundamental ground of reality, its own implicate nature progressively manifests itself. Explicate phenomenal reality is increasingly the expression of this implicate (hidden) ground. This precisely mirrors the dynamic nature of understanding itself with an explicit (conscious) and an implicit (unconscious) dimension.

As well as the two modes giving both "real" and " imaginary" aspects, the two directions (i.e. objective and subjective) give a "positive" and "negative" aspect. We already examined this extensively at the circular level.

Thus with the start of the radial level we have a four dimensional understanding of finite reality. One now explicitly understands reality in its "real" and "imaginary" aspects with both "positive" and "negative" directions. The exact mathematical complement of this is the provided by the four roots of unity giving both real and imaginary solutions in positive and negative form.

Jung was convinced of the deep psychological of the number "4" as a symbol of integration. We can see the precise significance of this in the discovery of the truly "complex" nature of the radial level in mathematical terms.

Indeed, there is a direct correspondence as between the mathematical roots of unity and each of the major levels of psychological development.

The linear level is characterised by (solely) positive "real" understanding of a conscious kind.

This corresponds to the one root of unity which is + 1.

The circular level is characterised by experience of the complementarity of opposites. Though in dynamic terms experience is highly intuitive, when translated in reduced "real" conscious terms it exhibits both a positive and negative direction.

This corresponds to the two roots of unity which are + 1 and - 1 respectively.

The point level is characterised by the arrival at one pole of spiritual contemplative union (i.e. transcendent). It also involves projections from the unconscious which both a "real" and archetypal "imaginary" significance (with external and internal significance). These projections create throughout the point level a (confused) form of complex experience.

This level corresponds to the three roots of unity + 1, (- 1 + (-31/2))/2 and (- 1 - (-31/2))/2.

The radial level involves full differentiation of the two directions of experience (i.e. "positive" and "negative"), and the two modes of experience (i.e. "real" and "imaginary").

This corresponds directly to the four roots of unity + 1, - 1, + i and - i.

The physical world that we inhabit of three dimensions of space and one of time is one of broken symmetry.

The fundamental four dimensional structure of reality is simply obtained by extracting the four roots of unity.

We can say that the reduced one dimensional translation of supersymmetry yields two real and two imaginary dimensions of space.

However, in dynamic terms real space is imaginary time, and imaginary space is real time, so alternatively we can say that supersymmetry comprises two imaginary and two real dimensions of time.

These real and imaginary dimensions have positive and negative directions. The negative direction simply represents phenomena. The positive direction of phenomena in turn represents the negative direction of dimensions.

We thus have a simple means of translating material phenomena into dimensions (and dimensions into phenomena). We also have the means of translating space into time and time into space.

This highlights the truly relative nature of reality. Phenomena and dimensions interact in dynamic fashion. Phenomena are posited (i.e. come into existence) through the negation of dimensions. Dimensions are in turn posited through the negation of matter. In supersymmetry these coexist in mutual identity in the void of transfinite physical existence (i.e. the quantum vacuum). This represents the origin of the cosmos. Finite reality then involves the breaking of this supersymmetry in a dynamic phenomenal and dimensional creation.

The goal of evolution is to achieve supersymmetry again in a void of phenomenal reality, which now represents full spiritual union. This occurs especially in peak moments of mystical ecstasy, where cosmic evolution briefly realises its eternal destiny.

This is just one example of the remarkable complementary structure as between mathematical and psychological realities, which initially might be considered entirely separate.

Another important psycho-mathematical connection - this time in the transfinite domain - can now be stated.

The fundamental numerical symbols are 0 and 1. Indeed these are sufficient to construct the highly important and fully functional binary number system.

Indeed any phenomenon that exists does so as a definable unit (i.e. 1). This distinguishes it from non-existence (i.e. 0).

In dynamic terms existence and non-existence are intimately related. Each physical phenomenon can only be given meaning in the context of holistic spiritual intuition (which is nothing in phenomenal terms). A unit physically (1) is nothing in spiritual terms (0).

Likewise spiritual unity is nothing in physical material terms.

Thus unity and nothingness have both a horizontal (physical) and vertical (spiritual) significance which in dynamic terms are complementarity.

This is paralleled mathematically. 10 = 1; 01 = 0.

Reality can indeed be described as a dynamic computer system, comprising a binary system of on-off states with both horizontal and vertical aspects. What is on horizontally is simultaneously off vertically. What is on vertically is simultaneously off horizontally.

Before life begins there is total confusion by which no means exist for differentiating existence from non-existence.

With mystical union there is both full differentiation and corresponding integration of both aspects. Thus there is the experience of a plenum-void. What is experienced as nothing in phenomenal terms is yet experienced as full of spiritual meaning. "1" (the linear level) and "0" (the circular level) are now finally harmonised.

Let us now look in more detail at the changes that take place at the radial level.

Once again, for convenience we will identify the three sub levels of spiritual, intellectual and emotional development, though it is important to remember that now more than ever, these are highly interrelated at this stage.

We have seen earlier that the circular level is concerned with healing directional split (i.e. positive and negative) in the personality. In other words object and subject - which initially are understood as separate - are ultimately on completion of this level experienced as identical.

The point level is concerned in turn with healing modal split (i.e. real and imaginary) in the personality. Again initially reason and emotion - which initially are understood as separate - are experienced as identical on completion of the level.

The radial level is essentially concerned with healing process split (i.e. finite and infinite) in the personality. Again conscious and unconscious are initially separated to some degree. The task - which can never be fully achieved in this life - is to so integrate these two processes so that they are experienced as identical. In peak moments of mystical ecstasy this goal is momentarily achieved. Here, all distinctions as between finite reality (the world) and infinite reality (the spirit) disappear in the pure experience of love. As at any level, the quality of experience can vary greatly. Where a high level of integration is achieved, valuable experiences of ecstatic union would tend to be more frequent, though these are not a continual characteristic of this admittedly most advanced level.

Indeed, this is made clear in the mystical literature with the distinction as between actual or transforming union (mystical ecstasy) and habitual union (the more frequent non ecstatic state of union with the Divine).


Perhaps the key defining characteristic of experience at the radial level is a permanent and seemingly effortless union with the Absolute. One has by now has largely lost one's former ego identity to assume a new cosmic or universal personality. In Jungian terms - as we have seen - this is the realisation of the self. One no longer distinguishes as between human and divine aspects. A Christian thus would now readily identify with the words of St. Paul

"I live not I, but Christ lives within me"

Indeed there is a strange irony in the whole Christian message. Theology explains the unique nature of Christ as both God and Man thereby incorporating the divine personality in human form.

Paradoxically, this conventional perspective (i.e. of Christ's unique divinity), creates the image of One Who is essentially different from the rest of humanity.

However any worthwhile friendship depends on an essential equality of being. If I relate to another person as an inferior or superior this thereby reduces and debases the relationship. Therefore I can relate properly to Christ as a friend only on equal terms.

The real mystical truth - which is more readily appreciated in Eastern religion - is altogether more simple and more beautiful.

Every personality is both human and divine. We are all equal in this basic sense. However this is a truth which can only be experientially - and not factually - realised after a lengthy process leading to spiritual enlightenment.

Thus the theological definitions of the nature of Christ essentially amount to an attempt to grapple with the mystical personality, characteristic of the radial level. Such theology therefore is universal and applies equally to the authentic cosmic based personality (i.e. the true self) of every individual. Western theological understanding still labours greatly under rigid categories of thought more appropriate to the linear level. Thus the attempt to translate intuitively rich mystical experience in such reduced terms creates much distortion and confusion. Furthermore the teaching of all the major religions over time tends to become identified with such formulations. As the life and death of Christ so graphically illustrates the greatest threat to established religion therefore comes from authentic enlightenment. It is easier to pose as inferiors in relation to a Supreme Being. Thus, when someone like Christ - who himself finding the truth - calls upon us to realise the awesome truth that of our equality to God, it is far too revolutionary and threatening. Indeed in the major Western religions we are not able to fully accept union with God. For one in union with God essentially is God. Separation of human and divine personalities is no longer possible.

This cannot be grasped through intellectual formulation but rather through direct experience. It is the simple truth of the radial level.

However - especially in the earlier phases - there is a split as between the two processes of understanding. In spiritual terms experience is manifested under two complementary aspects. Direct experience of the infinite is in transcendent, while direct experience of finite phenomena is in immanent terms. However there remains some division as between these two aspects.

The transcendent aspect is highly holistic. As daylight imperceptibly breaks, a marvellous enhanced general outline of the created world slowly becomes visible. In many ways this resembles the earlier spiritual phase of the point level (i.e. Spiritual Espousal). However it is now an altogether more satisfying and complete experience.

During the earlier phase light was experienced in a one way direction as if coming from behind. Now the light - as an unbounded sphere - seems to surround one on all sides. One becomes slowly enveloped in the light.

Also, during the earlier phase, there is considerable interference in the form of projections from the "lower self". This leads progressively then to withdrawal symptoms creating a more transcendent form of spiritual experience ultimately disappearing altogether in the void.

On this occasion, by contrast there is very little "lower level" interference, as projected or involuntary phenomena are gradually eliminated from experience during the point level.

Consequently the sharp withdrawal symptoms of the previous phase are no longer experienced. At one moment the light is revealed externally. Then this light fades to darkness as an unseen inner light. However this transition in now entirely voluntary operating under the control of will.

This aspect could be looked on as the diagonal top down approach to spiritual experience. It emerges from the void as if from the edge of an unbounded sphere in a highly generalised and transcendent impersonal form of awareness. Initially it is very passive and contemplative with very little phenomenal content involved. However because of this integration of the "higher" with the "lower" self spiritual experience becomes progressively more identified with the world, though this can take some considerable time.

Also, as experience becomes more phenomenally based and related to the finite world, it also becomes more personalised and active and immanent in quality.

This parallels the very way in natural terms through which daylight emerges.

As the dawn breaks, visibility and temperature are still low. Also with most people still asleep there is still very little hustle and bustle about. As nature still rests there is a great air of peace and tranquillity in what can be the most beautiful time of the day. Likewise for someone of a natural reflective bent, this can be the most satisfying period of the radial level.

As mystical experience often depends on a deeply introvert capacity, there is a tendency to sometimes limit the radial level to this purely contemplative form of experience.

For example, anyone reading St. John of the Cross on the highest levels of spiritual transformation will recognise this strong other worldly dimension. It comes across as an experience almost divorced from normal secular affairs and as such represents the contemplative extreme. However, the most complete form of personality integration usually entails a far greater dynamic being maintained as between contemplative detachment and mature worldly involvement. Indeed this is a key task for someone at the radial level, in the light of their own personality and circumstances, is to find the correct balance.

In spiritual terms, one now lives simply in a present moment continually repeated. This transcendent aspect - detached from phenomena - reveals an eternal present (relating to everything in general and nothing in particular). Because of a permanent unity of the personality with absolute reality, the supernatural has become truly natural; the extraordinary has now become truly ordinary.

The complementary aspect of spirituality, that is simultaneously experienced is by contrast highly immanent and specific. This is revealed through finite phenomena which acquire a special uniqueness and intimacy through spiritual illumination.

Thus the "grains of sand" in the immediate - and apparently trivial - circumstances of everyday life now are filled with an unexpected meaning. As mediators of the divine light they impart an infinite dimension of universal significance.

This aspect is not really replicated at earlier levels. As we have seen, at the point level the attempt to achieve such intimacy is continually disturbed through identification with projected fantasies. It is only with the release of such repressed material that inner calm can be restored with "one's house fully stilled".

Indeed this immanent aspect represents the very human aspect of mystical experience. Having fully appropriated one's shadow, one is at last free to freely accept oneself and thereby - perhaps for the first time - experience unconditional love.

Whereas the transcendent aspect relates to a surrounding light, this aspect relates to the emergence of light - and corresponding joy - directly from the centre of personality which radiates outwardly in an unbounded fashion. One thereby discovers that one is loved in a uniquely personal and intimate fashion.

This immanent aspect represents the diagonal bottom up approach to experience. This is the honeymoon period of Spiritual Marriage where one in a passive manner initially enjoys the uniqueness of specific phenomena in the garden of one's immediate experience. Gradually, in the security of this divine love one's concern widens outwards to embrace the concerns of others in a more active manner.

The immanent aspect thus involves experience of a continual immediate present (i.e. the experience of each moment in particular and nothing in general). Through this aspect the natural becomes truly supernatural; the ordinary becomes truly extraordinary.

Of course these two aspects are themselves fully complementary. On the one hand - from the transcendent pole - the spiritual infinite is gradually brought down and integrated with finite physical reality. From the opposite immanent pole the finite world is gradually raised up to be incorporated with spiritual reality.

However this is not achieved all at once. For some considerable time there may be a gap as between the two poles. Thus transcendent experience may remain unduly holistic and impersonal, whereas immanent experience may by contrast remain unduly localised and specific. In other words the pure interaction of finite and infinite realms through conscious and unconscious processes can remain somewhat limited. This interaction above all requires an approach without ego to operate effectively. True dynamism of experience is thus only possible when a highly selfless approach - free of either voluntary or involuntary identification with phenomena - has become habitual.


It is important to remember that there is a high level of interaction as between spiritual and intellectual understanding during the radial level. Thus, finite phenomena are always experienced against a backdrop of spiritually infinite intuition. It is the maintenance of harmony as between finite and infinite aspects (i.e. reason and intuition) that is now the key.

The spiritual aspect provides experience of what I have referred to as the null or transfinite structures. These are purely simple and involve the complete fusion of the two polar directions of experience (i.e. objective and subjective) and the polar modes of experience (i.e. cognitive and affective). In more mathematical terms this involves the fusion of both positive and negative and real and imaginary aspects of experience. In other words in this pure transfinite (i.e. intuitive) experience such polarised distinctions are no longer possible.

Holistic Aspect

The intellectual aspect provides the complementary knowledge of finite structures.

Again this has two closely related aspects. The first which initially is highly general and intuitive is very much a top down approach providing an overall outline of the subtle interpenetration of phenomena. This represents the culmination of the psycho-mathematical understanding of the point level where intuitive (transpersonal) psychological and rational mathematical relationships are understood in fully complementary fashion. In mathematical terms these are complex. Whereas the null structures involve the mature integration of positive and negative directions and real and imaginary modes, these complex structures involve - from a holistic perspective - their mature differentiation. Thus in relation to all phenomena of experience there is now a clear and explicit distinction as between objective and subjective aspects (i.e. positive and negative) and cognitive and affective modes (i.e. real and imaginary). When combined with the corresponding null structures, this understanding of phenomena is eight dimensional (i.e. complementing the eight roots of unity) and extremely subtle.

As we have seen conventional scientific linear understanding of phenomena is highly reduced and distorted being strictly one dimensional. The spiritual transfinite process is reduced to the finite. The affective mode of the senses is reduced to the cognitive mode of reason. Finally the subjective internal direction is reduced to the objective external direction.

Thus scientific understanding - in mathematical terms - can be characterised as a finite real positive approach. However the intellectual understanding appropriate to the radial level involves understanding which is dynamically transfinite as well as finite, imaginary as well as real and finally negative as well as positive.

Let me now illustrate this approach with reference to the understanding of number. I have demonstrated some of these ingredients already at earlier stages of development. However because this interpretation is so central to clarification of the dynamics of this level some repetition is necessary.

If we take for example the number "2", understanding involves a dynamic interaction as between the particular perception of the number "2" and the general concept of "number".

Now the understanding of the number perception involves the interaction of both mind and matter and has both a positive and negative direction.

The positive direction involves the creation in experience of the particular number "2".

The negative direction involves the exclusion of all other numbers. In other words in dynamic terms we can only posit - to highlight a specific phenomenon (belonging to a class) - by simultaneously negating or eliminating all other such phenomena. Thus dynamic perception is open ended where the process of determination of phenomena is strictly relative, inevitably involving lack of determinacy of other phenomena. Thus in this case, the actual perception of the number "2", which is finitely determined, is made possible through the screening out of all other actual number phenomena which - in this context - remain finitely indeterminate.

Thus in the very perception of phenomena we see a psychological uncertainty principle here at work.

The understanding of the number concept in turn involves the interaction of both mind and matter again giving a positive and negative direction.

The positive direction involves the creation in experience of the general concept of number.

The negative direction involves the exclusion of any particular number. Thus dynamically the direct formation of any concept such as "number" involves the negation of any particular number perception. In this case therefore, the negation of the positive number perception "2", is the very means through which one is enabled to form the general concept of "number". The negation of this general concept - applying to all fintely indeterminate numbers - is as we have seen the means in turn of positing the number perception "2".

So far therefore we have demonstrated - using the number "2" - the dynamic directional interaction which applies to all perceptions and concepts in experience. This understanding - which emerges at the circular level - is indeed circular, for formation of perceptions inevitable involves (given) concepts, whereas likewise formation of concepts involves (given) perceptions.

Thus if there is initially a lack of balance in terms of development of both perceptions and concepts this will tend to be accentuated in subsequent experience. For example the pure theorist in a given field will typically be very strong on conceptual and relatively weak on perceptual development. There is thus a grave danger that further conceptual development would feed off this weak perceptual base reducing response to the environment and set severe limits to the dynamics of development.

Now the next stage of subtle interpretation of numbers involves a precise understanding of the relationship between the general number concept and particular number perceptions. On this, there is an immense amount of confusion in conventional mathematics.

Whereas the specific number perception of two represented by the symbol "2" refers to an actual number which is finite, the general concept of number does not refer to any actual number as such but rather the potential for number existence. Now indirectly a concept can be given - as we continually do in experience - an actual existence, but essentially its meaning transcends the finite and relates to the potential and not the actual domain.

As we have seen whereas the creation of an actual phenomenon involves merely the one dimensional positing of a phenomenon, the creation of the concept involves the corresponding negation of such a phenomenon giving a fusion of positive and negative poles. Thus - strictly speaking - the understanding of the concept involves switching the direction of actual understanding of perception yielding a two dimensional understanding. However to express this concept in understanding (which is two dimensional) in reduced one dimensional terms we must once again switch the direction and extract the square root.

This is precisely what in mathematical terms defines an imaginary number.

So now we can see that if the actual perception of the number "2" is real, then the corresponding understanding of the actual concept of number is imaginary.

Indeed generalising this finding, all actual concepts in experience are imaginary in relation to corresponding perceptions (which are defined as real). Of course this again is purely relative. If we define the actual concepts initially as real, then the corresponding perceptions are now imaginary.

All perceptions and concepts in experience therefore have both real and imaginary aspects. Strictly speaking we live in a complex (i.e. both real and imaginary) rather than a real world. What this means is that interaction of perceptions and concepts in experience necessarily involves both the affective mode of response through the senses and the cognitive mode of control through reason respectively. Conventionally - especially in scientific understanding - we simply reduce the affective to the cognitive mode and define the "real" world in terms of cognitive constructs.

Now this subtle understanding of the real and imaginary aspects of phenomena comes with the point level. However there is still a certain amount of reductionism involved. There is still an undue anxiety to reduce the purely infinite to finite categories of thought. Thus one gets around the inherent difficulty of the potential aspect of concepts by defining them in indirect actual terms.

However with the onset of the radial level and the complete detachment from egoic identification with phenomena, one is now ready to explicitly recognise the infinite or - in more correct mathematical terms - the transfinite as well as the finite aspect of phenomena.

What this relates to is the direct spiritual intuition or insight which is so important for the implicit recognition of all phenomena. This is something that is largely taken for granted in normal understanding.

For example a "rational" proof in mathematics concentrates on merely explicit recognition. However each step in a chain of reasoning to be followed, requires equally an implicit form of recognition which comes directly from intuition. It is only with this mental illumination that the coin can drop as it were and logical demonstrations be understood. Indeed if anything this direct intuitive understanding - even in mathematics - is more important than reason. However it is not formally recognised.

Indeed lack of this intuitive insight sets severe limitations to mathematical procedures whereby one - especially in terms of abstract analysis - can quickly lose the intuitive insight to follow the rational demonstrations.

Now let us look more closely now at this direct intuitive or transfinite aspect in the understanding of number.

As we have seen we create in experience our actual (finite) perception of the number "2" through positing the phenomenon. To move to the corresponding number concept we must negate this number perception. There is then in experience a decisive fusing of positive and negative directions of perception which in fact is the creation of psychic energy or intuitive insight which is the direct apprehension of the infinite or potential realm. This intuitive insight is what enables the switch from number perception to concept to take place. However as we have seen this concept quickly collapses as it were to finite form where the potential aspect is lost. In other words the intuitive understanding quickly gives way to the rational understanding of concept as the set of all actual number perceptions.

Again in the switch from the concept of number to the particular number perception of "2", there is the negation of the positive (actual) number concept which again leads to a direct fusion of energy providing that implicit insight so necessary to successfully make the switch to recognition of the number "2". In other words before we can recognise "2" as a specific number we must be able to intuit that it is related to the number concept which is potentially infinite. Just as intuition enabled Blake to see a world in a grain of sand, the same intuition enables one now to see the world of number (i.e. the concept of number) in the number "2".

Being more precise the positive transcendent aspect of spiritual experience is involved in terms of appreciating the infinite domain of concepts. The negative transcendent aspect is involved in switching from the intuitively implicit potential concept to the rationally explicit actual concept.

The positive immanent aspect of spiritual experience is involved in terms of appreciating the infinite domain of perceptions. The negative immanent aspect is involved in switching from the intuitively implicit potential perception to the sensibly explicit actual perception.

Thus corresponding to the four complex aspects of rational finite experience, we have the four simple aspects of transfinite intuitive experience.

The simple spiritual aspect does not directly manifest itself in phenomenal form but is essential as a lubricant of the whole dynamic process of understanding. When this intuitive aspect is not appreciated - as in conventional understanding - though remaining essential, it tends to dry up and sets severe limitations to the nature of experience. Understanding then tends to become rigid and literally unenlightened.

It is only now at this stage of the radial level that true integration of experience is possible. Because one has fully disidentified with attachment to any phenomena (conscious or unconscious) one is now able to maintain a harmonious and increasingly dynamic interaction in terms of the direction, mode and process of understanding.

Thus the external positive direction (objective) of understanding is balanced by the internal negative direction (subjective). The cognitive real mode (rational) is balanced by the affective imaginary mode (emotional). Finally the finite conscious process (phenomenal) is balanced by the transfinite unconscious process (spiritual).

Now this translation of the radial level involves a subtle form of reductionism. I am conveying the nature of experience in a scientific - indeed mathematical - fashion i.e. in a positive real finite fashion. Therefore the other direction, mode and process involved must be translated in appropriate fashion. This - as we have seen - involves subjective experience being translated as negative, affective experience as imaginary and unconscious experience as transfinite. To fail to make these appropriate translations involves therefore a gross form of reductionism.

Specific Aspect

Whereas the above aspect of intellectual experience is a diagonal top down approach and highly holistic and intuitive based on the complementarity of opposite poles, there is a complementary aspect which now emerges which by contrast is highly specific and rational.

This involves the differentiation of phenomena in terms of one's immediate experience. It is closely associated with the corresponding immanent phase of spiritual development.

For so long the key emphasis in experience is on the erosion of phenomena. This is necessary so as to eliminate excessive ego identification with them. Now with the radial level, this purgation is largely complete, so that one now is free once more to differentiate phenomena once more in experience.

Thus when one objectively posits a specific phenomenon in experience, one avoids undue attachment through simultaneous negation. This causes a switch from the external object to the internal self. One then posits the phenomenal self again avoiding undue attachment by simultaneously negating the self, thereby causing a switch back to the external phenomenon. Now this cancelling out process can never be perfectly attained (though peak moments of ecstasy would closely approximate). The mere awareness of phenomena necessarily entails some imbalance in the experience. However with a highly refined personality, considerable dynamism in the relationship between self and the world becomes possible. Phenomena then become highly transparent and luminous, serving as temporary mediators of an unseen ultimate meaning. Where these poles are unbalanced - typically with the positive too strong, one becomes trapped through attachment to phenomena. They then become dull and rigid considerably slowing down dynamic interaction with the self.

Likewise modal balance is now possible. If the cognitive mole is too developed experience will become detached and impersonal. If the affective is too developed experience will become over personal and involved. In either case undue ego identification with phenomena will result. However with equal development of cognitive and affective modes again smooth dynamic switching is possible, avoiding this problem.

Finally process balance is also possible. Typically the conscious process is - relatively speaking - too developed in experience. This leads to overidentification with finite phenomena. Occasionally - as with mystic contemplatives - the other spiritual intuitive unconscious process is too developed leading to an unduly otherworldly attitude.

Again the golden mean of equal balance is to be aimed at. This enables mature involvement with worldly affairs while simultaneously remaining firmly focused on the Absolute.

However because of such prolonged phenomenal starvation - during circular and point levels - it may take some time to get fully rooted in the world once more. One's specific finite activities may be restricted for some time to private affairs, while simultaneously at a global level adopting a highly general and universal approach. It is therefore important on the one hand to incorporate one's universal intuitive vision in a practical manner with everyday activity, while at the same time learning to extend these activities outwards in a more selfless concern for others.

I have stated before that the top down intuitive approach involves a circular form of logic where opposites are complementary. The bottom up rational approach involves a linear form of logic where opposites are separated.

Indeed we have here two complementary systems of binary logic. In the former circular system each on state vertically represents an off state horizontally; each off state vertically represents an on state horizontally. In the latter linear system each on state - either horizontally or vertically - excludes an off state.

Intellectually, reality can now be viewed as a complex computer system involving both circular (intuitive) and linear (rational) binary states. Conventionally however, computer logic is based solely on the "real" binary system and is limited to merely rationally programmed deductive connections. A more advanced computer logic is "complex" being based on both the "real" (linear) and "imaginary" (circular) systems of logic. As we have seen the radial level explicitly involves both binary systems.

Computers - based on the linear binary system - which can be viewed as an extension of the rational self, can now be connected world-wide serving as a global means of information. However computers - based on the circular system - which can in complementary terms be viewed as an intensification of the intuitive self - can also be connected world-wide serving as a global means of transformation. This simply represents the human mind intuitively or spiritually in communication with other minds. Indeed some of the great mystics provide striking examples of this form of communication, dramatically altering the lives of others even at a great distance. However in the present rational culture pervading much of the world such paranormal powers are widely ignored and underdeveloped. However we are rapidly reaching a point where there is a great need for a considerable advance in transforming rather than merely informing processes of communication. This is the noosphere of de Chardin which - because of the explosion of merely horizontal forms of technologically generated information - is now in great need of significant development.


The emotional aspects are very closely associated with both intellectual and spiritual developments. The overriding concern throughout is to see all these aspects as manifestations of a common unity. This in turn helps to reduce any danger of undue attachment to the various phenomena spontaneously emerging in experience. However there still remains with emotion - as with the other aspects - a certain divide as between the holistic and more personal forms of experience.

The radial level involves a marriage of both masculine and feminine principles in the personality.

So much sexual discrimination in society arises from rigid sexual stereotyping. The acceptance of true sexual equality however, primarily relates to the transformation within, whereby one at first recognises, and indeed eventually marries the other sex in one's own personality. As we have seen - when dealing with erotic fantasies at the point level - there are all sorts of subtle barriers operating in society against this transformation. In particular many of the cherished assumptions of patriarchal society, which are deeply embedded in institutional religion, can - following this transformation - be clearly seen as deeply discriminatory and without foundation.

The very word we most commonly use to refer to ultimate being, power or spirit i.e. God is itself a masculine word. Certainly in the great religions of the West there is an entirely inadequate recognition of the feminine aspect of the divinity. Even though it may be conceded that the divine is without sex and equally male and female, in practice "God" is invariably referred to as "He".

I have already commented on the intriguing way in which Western male mystics - in union, assume a feminine spiritual identity in order to preserve this orthodoxy. However for a heterosexual male this is artificial and unconvincing and not in keeping with true psychosexual dynamics.

As cultural attitudes - even for those without spiritual convictions - are deeply influenced by religious thinking, sexual equality in society must be underpinned by sexual equality in theological terms. If we are accustomed - as in Western society - to view the Supreme Being invariably as male, then men will inevitably assume the role as the dominant sex in society. Sexual discrimination is therefore inherent in our basic theological thinking. In turn this helps to powerfully reinforce - with unwarranted moral justification - attitudes at all levels of society which discriminate against women.

Thus for a man, Spiritual Marriage represents the culmination of a lengthy process whereby archetypal projections of the feminine are gradually appropriated and assimilated internally. Ultimately the perfect feminine archetype is understood as the image of one's own unconscious. When this happens there takes place an internal marriage which represents - in affective terms - the psychological union of conscious and unconscious. However initially this marriage is experienced as a void where all external projections of erotic desire cease.

When the plenum-void of the radial life unfolds this marriage expresses itself in a new and exciting form. Once more there are two aspects - initially separate - one of which is holistic and the other specific.

Once again we have a problem with language. Words in normal usage tend to convey polarised meanings. The spiritual for example, is generally understood in opposition to the physical. Thus the spiritual marriage of the mystic is often considered in opposition to the conventional notion of physical marriage. This is unfortunate and also leads to a deep misunderstanding of the great value of an authentic celibate lifestyle. Marriage for the mystic has complementary physical and spiritual aspects which become progressively interrelated, eventually becoming indistinguishable.

Thus the typical sexual abstinence of the mystic should not be viewed in solely negative terms. The real reason why many mystics refrain from sexual intercourse is to ultimately facilitate a more complete level of sexual fulfilment. In the conventional manner of sexual intercourse, physical fulfilment - though often an intense and even ecstatic experience - can remain unduly localised and instinctive. There inevitably is an attempt to seek fulfilment too narrowly through exclusive identification with another person. Paradoxically, this can limit the ability to receive sexual fulfilment in a powerfully meaningful yet non specific manner.

Properly understood everything in nature is charged with a personal - indeed a sexual - energy. However, remaining fully open to nature in this wider sense involves remaining free of a more exclusive sexual identification. Now admittedly this is no easy task and demands considerable sacrifice. However for someone with a genuine mystical vocation, it is a price that may be willingly paid. Somehow one knows, that to settle for an exclusive relationship with another person, would inevitably feed the ego in ways that would cause great conflict in terms of one's prime vocation. In a sense therefore the choice to remain celibate is an automatic consequence of this overriding key commitment.

The authentic spiritual vocation for transcendence does not directly relate to whether one has - in conventional terms - a religious vocation. Many who choose religious life are not in fact genuine celibates and it is sad to see them bound by an imposed vow. Also some, living in the world with a deep need for authentic transcendence, discover in the process a desire to remain celibate. The decision not to marry (in the conventional sense) is not taken at any stage as an absolute decision. Rather it gradually emerges as a free and appropriate response to one's situation, continually renewed as one's commitment becomes clearer.

To sum up therefore, in affective terms the radial level involves the integration of both the spiritual and physical aspects of sexuality. Perhaps the term "Cosmic Marriage" designed to include both complementary aspects would be more appropriate

The holistic aspect initially is highly transcendent where emotion remains - initially at any rate - somewhat detached representing the spiritual pole.. In many ways it represents the fulfilment of that earlier erotic development of the Spiritual Betrothal phase. Because of freedom from specific sense phenomena one is able to relate affectively to reality in a global universal manner. The spirit like the morning sun slowly emerges over the horizon. For the moment one is content to be bathed in its light and beauty, experiencing an austere joy. This holy experience fills one with a desire for purity of intention in one's affective desires so that they always will be governed by the divine spirit. It also sets the basis for the rekindling of precious friendship - with both sexes - unsullied by emotional manipulation or possessive desire.

In religious terms this phase represents the mature spiritual emergence of a feminine archetype of God, symbolised in Catholic Theology by the Virgin Mary.

Indeed what I am trying to describe is remarkably captured in the first lines of the Magnificat (describing Mary).

"Who is she that comes forth
As the morning rising
Fair as the Moon
Bright as the Sun"

Though one starts with a purely intuitive archetypal experience - indeed mature spiritual fantasy - gradually the incarnational aspect grows in a holistic sense awareness of the world.

In other words, affective experience - though still highly generalised - gradually assumes a warmer more immanent focus. Again all the earlier archetypal development surrounding the Great Mother now comes to fruition. Psychologically - deep in the unconscious - one has become one with an idealised perfect mother. In simple terms one has acquired a deep sense of peace and fulfilment free of (undue) anxiety of separation and loss.

Now, this union attained in the unconscious is freely projected in holistic form out into the World. One now sees the World - Mother Earth - as an extension of one's body from which all life emerges. The creative products of all this life are in a cosmic sense one's own children and of intimate personal concern.

This ecological awareness of reality is a deeply feminine one and sharply conflicts with that promoted though (impersonal) science. In many ways, economic and social development in the World - which is so fragmented and unbalanced - runs counter to this personal from of feminine awareness. The need to help in some way to heal this fundamental split may therefore now lead to a growing desire for active involvement.

Again we see this top down approach at work, where affective awareness - initially highly transcendent and spiritual in focus - gradually becomes more immanent and physical through growing contact with the World.

We also have simultaneously the complementary aspect at work in a deeply immanent experience at the centre of personality.

This immanent experience really involves the culmination of a refined physical form of sexual fulfilment.

Again - as we saw at the point level - substructure activity culminates with a complete merging of masculine and feminine personas (animus and anima) in the psyche. In unconscious terms there is literally - as I was at pains to emphasise - a direct merging of masculine and feminine bodies. Thus a man for example succeeds in fully uniting his "real" (conscious) masculine body with his "imaginary" (unconscious) feminine body. In other words by disidentifying with any rigid notion of being male, he uncovers fully his - formerly hidden - female body in the unconscious. Now as this female body is "imaginary" it can only be indirectly appropriated though projected fantasy. When this nears completion, fantasy ceases and there is an unconscious union of bodies which takes place in a void of phenomenal experience. This is a secret marriage which takes place in the depths of personality.

Now with the dawning of the radial level, this union starts to freely express itself externally. What it entails is an incredible form of personal intimacy. This unified body warmed by the heat of this emerging spirit completely melts as it were in a rapturous feeling of complete physical fulfilment. The embryo that lay in its (undifferentiated) prepersonal state in blissful union with the mother now attains full (differentiated) transpersonal union in this mature state of bliss which is as much physical as spiritual.

The accurate explanation of this aspect of union is problematic from a religious perspective. It is the immanent and feminine aspect of the divine in what represents union with the archetypal natural mother. One has resolved the Oedipus complex by marrying - in psychological terms - the (archetypal) mother.

Unfortunately this physical aspect of the feminine archetype is almost entirely missing in the theology of the Christian religions.

Mary, though especially important in Catholicism serves essentially as the (indirect) spiritual aspect of this archetype. Just as she is portrayed theologically as the obedient servant of God, her femininity is portrayed so as to be in conformity with the transcendent pole of spirituality. This is a masculine and somewhat impersonal otherwordly approach. Thus theologically everything is done to detach Mary from the World. She remains a virgin while giving birth. She is conceived without original sin (Immaculate Conception). She is transported directly to Heaven (Assumption) thus avoiding mortal decay.

The best biblical symbol of the complementary physical aspect is that of Eve in the Garden of Eden. However Eve is commonly portrayed as the fallen woman in striking contrast to Mary who redeems womanhood. The subtext of all of this is unfortunate. As Mary was obedient to her God, women in society - especially religious - are expected to show the same obedience to the wishes of their male masters. The directly feminine and immanent aspect of God has been therefore largely screened out of formal religion in the West, though informally of course it always remains.

A considerable mind-body split is evident in the spiritual literature, even in the attempted portrayal of authentic mystical development. The importance of the unconscious - of erotic fantasy and generally of legitimate physical desires - is rarely ever formally discussed. In psycho-mathematical terms, writers largely focus on "real" (transcendental) development based on overcoming the body, to the exclusion of "imaginary" (immanent) development based on full acceptance of the body.

The act of physical intercourse as an expression of love involves the desire to end physical separation through being united with another body. However though a high level of union may be experienced during intercourse, paradoxically the feeling of physical separation can be increased once the intensity of the act has passed.

Sexual intercourse in itself can be too specific and localised an experience to convey any permanent sense of union. In other words it often is too narrowly physical in focus. Spiritual and physical realms in truth are fully complementary. Therefore the highest level of physical experience requires equal and co-ordinated development of the spiritual. This is necessary so as to avoid confusing meaning with what is merely pleasurable to the ego. Likewise the highest level of the spiritual can only be attained in the context of balanced physical development so as to prevent repression and undue identification of meaning with specific religious experience.

Because of this mutual development of both aspects at the radial level, a more permanent and fulfilling answer to one's sexual longings is possible. Without undue possessive desire, one can freely enjoy many relationships. By avoiding (exclusive) attachment to any one relationship one is thereby made more free to enjoy many relationships without distinction.

One thus surrenders a limited freedom to embrace a far richer and more complete freedom.

Whereas this joyful experience of personal love is truly fulfilling and life enhancing and indeed is the honeymoon period of the radial level, one must soon return to the world with an enhanced sense of cosmic commitment. This is where the holistic affective pole is so important. The union which one has achieved with the (archetypal) natural mother in the unconscious is now replicated by a union with the same mother reflected in nature (i.e. mother nature). This is again the personalised affective response to creation so necessary to counteract the more common impersonal cognitive approach promoted through the scientific world-view.


It might be instructive at this stage to once more highlight the important role of fantasy in terms of affective perception.

As we have seen, the point level involved a highly specialised development of fantasy, largely divorced from conscious life. Now there is the emergence of a pure and mature form of fantasy which one progressively interrelates with actual life.

Let me try and illustrate its role by closely examining affective perception in the experience of my favourite flower which is the rose.

Affective experience involves a response pattern to reality conveyed through the senses. Thus the perception of the rose in the first instance involves a direct and immediate response in the experience of a special unique quality. Thus I become conscious - not of just any rose - but rather this particular rose which now engages my attention. Indeed without this unique and personal response, I would not be able to experience the rose or indeed any object. Not surprisingly when this quality of unique response is missing from experience objects lose their vitality and appear as "dead". This is what happens with the scientific world-view - which based on the complementary impersonal cognitive approach - views nature as inanimate.

Now the unique quality of response - which is the direct basis of affective understanding - comes from the unconscious. In the moment of perception, there is a implicit recognition of the immediate object as a mirror of a universal light and truth in which we all share. In other words with affective perception there is always an intuitive flash - however brief, where we personally unite with the object in the revealing of mystery. In other words in the recognition of the object as unique, there is the complementary discovery something of our own uniqueness. Put another way, finite and infinite realms join in this unique moment of intimate connection.

In early infancy this responsive approach is very much alive but in an immature and undifferentiated manner. The whole (of the archetypal unconscious) is directly confused with the part (in the discriminating conscious). Thus union is sought through a mergence with matter rather than spirit. Indeed this is the essence of the primitive instinctive response. In the dynamic act of perceiving an object there is an implicit recognition of an unique quality which one then mistakenly identifies as belonging to the object in itself. In attempting then to merge with it, one unwittingly surrenders one's freedom in making oneself the slave of that object. In varying degrees this confused response lies at the root of all egocentred desire which leads - quite literally - to the adoration of false Gods.

The linear level - as we have seen - involves the specialisation of the conscious mind.

Whereas this greatly facilitates cognitive understanding, it can do great damage to genuine affective response. Because of the inherent complementarity of conscious and unconscious, each (forward) stage of conscious development is inevitably accompanied by a (backward) stage - through repression - of the unconscious. Progress is then measured - as exemplified by the scientific paradigm - by the extent to which the unconscious can be successfully eliminated from formal understanding.

Once again the affective experience of the rose - as indeed with all objects - is this unique quality of response where in some measure the (infinite) whole is seen in the (finite) part. Through this, the rose for a brief moment mediates a cosmic meaning. This is an enhanced type of artistic perception.

However the cognitive experience of the rose - developed in opposition to affective understanding - leads to seeing the rose, though the experience may be highly refined and spiritualised, as simply an impersonal part of a larger whole. Here the rose is identified by its common membership of the conceptual class of "rose". From this perspective of a universal class, a particular rose has no unique significance. The ability to classify it in common with other roses is what is significant. This is the (rational) scientific perception.

The problem is that when the scientific world-view dominates, affective perception inevitably fades becoming almost entirely lost. Objects in losing their special uniqueness become insignificant fragments without ultimate meaning. In experiencing the world in such impersonal terms, not surprisingly, we become steadily depersonalised and alienated as a result.

Paradoxically this state of affairs increases the need and desire for affective response, but because the unconscious has by now been cut off from "reality" it tends to assert itself in a blind instinctive manner. This invites a "quick fix" route to happiness which can then often lead to various forms of addiction e.g. sex, power, money, drink, drugs, etc. which only increase the alienation and unhappiness.

So we live in a culture where unfortunately the two modes of affective and cognitive experience are largely divorced from each other. This in turn is due to overspecialisation of the conscious process with consequent underdevelopment of the unconscious.

Properly rehabilitating affective response is no by no means easy. Firstly the conscious process must be gradually screened out of awareness. As we have seen this is the task of the circular level. This then leaves the unconscious free to properly develop, which takes place during the point level. Now with the emergence of the radial level, true affective response can be properly restored.

Thus in experiencing an object such as the rose one incorporates (unconscious) fantasy with (conscious) fact. Thus through the former perception one sees the rose in its own unique fashion as a holistic archetypal expression of what is ultimately infinite and mysterious. We have here the harmony of two aspects. There is the immediate and instinctive physical response in a subsensory or intrasensory awareness; also there is the universal spiritual response in a supersensory or extrasensory awareness. Considerable attention during the point level was devoted to the purification of these complementary poles. Both now approach perfect balance. This is pure fantasy transformed through removal of ego attachment.

It involves the affective imagination in what is literally - from a mathematical perspective - the "imaginary" component of "complex" experience.

Through the latter perception one sees the rose as a common object i.e. related to other members of the class "rose". This is the rose experienced in its specific and finite partial state as a fragment of overall reality.

This involves cognitive reason in what is - again from the mathematical perspective - the "real" component of "complex" experience.

Indeed the conventional use of the word "real" here is unfortunate. Cognitive perception involves in truth experience of the "ideal". In other words, by its very nature phenomena are made to conform to an idea or concept which represents an ideal class to which the phenomena belong. Thus properly speaking a hard headed scientist is not so much a realist but rather an idealist (i.e. in seeking to make data conform to ideal conceptual classes). Likewise "real" numbers would more accurately be referred to as "ideal" numbers.

Reality, which is inherently dynamic, therefore is best understood in finite phenomenal terms as the "complex" relationship between the "imaginary" (i.e. the unconscious affective mode) and the "ideal" (i.e. the conscious cognitive mode). And the harmonious balance of these two modes comes from the central and spiritual activity of will which is purely "simple" and infinite.

In practice reality is reduced in distorted terms to the "ideal" cognitive mode of merely conscious understanding. This leads to the splitting off of the "imaginary" in an undifferentiated manner often remaining blind and merely instinctive. Thus spiritual capacity which develops so as to harmonise these modes cannot properly develop and remains greatly frustrated.

Mathematical Connections

There is a remarkable psycho-mathematical connection to each of the major transitions of development. These are the transitions from linear to circular, circular to point and point to radial levels respectively.

When we halve the full circular angle of 3600 we obtain a straight line. It denotes the x axis of the complex plane, in both positive and negative directions. Mathematically, these polar directions can be obtained by halving the 1st dimension i.e. extracting the square root of a number. Thus for example 11/2 is +1 and -1.

In complementary manner we double the angle of perception - as it were - of the linear level by moving to the circular level. As we have seen we thereby move from one dimensional conscious to two dimensional unconscious understanding. Here we formulate "real" structures with complementary opposite poles (i.e. positive and negative directions).

When we further (mathematically) halve the 1800 straight line we get a right angle giving an intersection at a point of vertical (y axis) and horizontal (x axis) lines. This mathematically can be obtained by extracting the 4th root of a number. It represents the complex number axes (i.e. real and imaginary in both positive and negative directions). Thus again the 11/4 = +1 and -1 (real directions) and +i and -i (imaginary directions).

In like fashion we again in complementary psychological terms double the angle of perception by moving into the point level. We move ultimately from two to four dimensions with the differentiation of both "real" and "imaginary" structures in positive and negative directions. As we have seen this is the precise mathematical translation of the supersymmetry of the void which culminates at the point level.

Finally, when we now halve the 900 right angles, we get - in addition to horizontal and vertical - diagonal lines which intersect the x and y axes. These can be obtained by extracting the eight root of a number. Because any point on these lines is - by definition - an equal distance from both axes (real and imaginary), using the Pythagorean Theorem these diagonal lines are of zero finite length. They are in fact transfinite, representing null lines which are rays of physical light. Thus once more 11/8 is +1 and -1 ( horizontal real directions), +i and -i ( vertical imaginary directions) 1/21/2(1+ i), 1/21/2(1- i), 1/21/2( -1 + i), and 1/21/2( -1 - i) respectively (diagonal complex directions).

Again in complementary psychological fashion, we again double the angle of perception by moving into the radial level. We now move from four to eight dimensions, with the differentiation of simple or transfinite structures in addition to the "complex" structures already formed. These simple structures are the means of equalising or harmonising "real" (cognitive) and "imaginary" (affective) modes of understanding in pure transfinite understanding. Again these are in psychological terms null lines, this time representing rays of spiritual light. This is the mathematical translation of the plenum-void supersymmetry of the radial level with "simple" diagonal lines (i.e. spiritual volitional mode) and "complex" horizontal and vertical lines (i.e. cognitive and affective modes).

So there is a precise and remarkable correspondence here as between fundamental psychological and mathematical experience.

Spiritual, intellectual and emotional aspects of experience - though progressive harmonisation - increasingly interpenetrate each other at the radial level.

The spiritual aspect of the radial level is "simple" and represents the diagonal lines or rays of light. It manifest itself in complementary transcendent (holistic) and immanent (specific) forms. The positive direction involves the infinite in divine illumination. The negative direction involves the ability to switch smoothly back to finite phenomena in experience.

The intellectual aspect is closely associated with the spiritual, which is mediated through it. The most subtle translation of reality now involves an eight dimensional approach where all phenomena have a positive and negative aspect (in terms of direction), a real and imaginary aspect (in terms of mode) and finally - both direction and mode - having a finite and transfinite aspect (in terms of process). As an illustration, I have attempted to outline this very intricate eight dimensional interaction in terms of the correct understanding of number.

Thus when one reflects on the linear mathematical interpretation which is solely one dimensional, one realises the extent to which conventional understanding is so reductionist.


The radial level does not so much represent a final state of psychological attainment but rather the beginning of a new life based on true integration of the personality. Essentially it involves the replacement of an ego based with a more selfless cosmic centred personality. Within it, all previous levels, linear, circular and point reach their true fulfilment, maintaining - in relative terms - a certain unique independence, while simultaneously coming progressively into dynamic interaction with each other.

Having already successfully harmonised the two directions (i.e. objective and subjective) and the two modes (i.e. cognitive and affective) of experience, the key remaining concern of the radial level is the direct harmonisation of the two basic processes (i.e. conscious and unconscious). This involves the ability to maintain a dual perspective on life where finite physical phenomena are seen continually as mediators of a spiritual light which is infinite.

The affective aspect of experience is now properly developed. This involves the incorporation of maturely developed fantasy in all experience where finite symbols continually mediate both their ultimate (subsensory) physical origin and (supersensory) spiritual destiny in a unique response which is infinite.

The key task of this passive stage of the radial level is to maintain a selfless involvement with all phenomena. With growing security and inner confidence, one can thus involve oneself increasingly with worldly affairs without losing spiritual focus.

Having finally transformed the self, one now increasingly concentrates on actively transforming the world. This is the latter part of the radial level.