Thursday, November 7, 2013

A Question of Balance

As we have seen, with the commencement of this stage (Band 3, Level 2), the real (conscious) polarities (external and internal) have already been substantially integrated in a nondual manner.

This therefore leaves the unconscious free to powerfully project itself into experience in an imaginary manner.

By its very nature, this requires that symbols serve a dual purpose. From one perspective, they are interpreted in a localised real manner. However at a deeper level, they now radiate a universal meaning in an archetypal fashion.

Now a degree of confusion is always initially present, where any undue attachment to the symbols in question, reduces their pure archetypal meaning (of an imaginary nature).

So in contrast to earlier real attachments (i.e. to symbols understood in a directly conscious manner) we now have the more refined imaginary attachments (i.e. to symbols that are understood in an indirect conscious manner as archetypes of a universal spiritual meaning).


Now the very nature of this level is that experience takes on profound vertical type characteristics, with rapid switching as between "higher" and "lower" stages increasingly taking place.

So in fact a two-way form of integration begins to unfold in experience. Thus from the "higher" transcendent perspective, one attempts to integrate in a top-down manner, "lower" stages; then in a reverse immanent manner, one attempts to integrate "higher" stages from the perspective of the "lower" in a bottom-up fashion.

However, because up to this point the transcendent aspect will have been especially dominant, a certain imbalance is likely to be initially present, where one places too much emphasis on the value of the "higher" stages (typically understood as spiritual) and corresponding too little emphasis on the value of the more instinctive "lower" stages (understood as physical).

Certainly, this was true in my own case, reflecting what I now see as a corresponding imbalance in the traditional Catholic emphasis on a mistaken hierarchy. Here the physical body (and its instinctive sense promptings) are placed on the lowest rung with reason and the intellect higher and then spirit (i.e. transcendent spirit) on the highest rung of the hierarchy. Thus from this perspective, the role of the aspiring contemplative is to use reason to discipline the lower senses before ultimately letting it go in the pure experience of the spirit.

However from the immanent perspective this hierarchy works in reverse. Thus, it is imperative here in terms of integration to allow the primitive impulses of the unconscious to speak for themselves, by gradually letting go of the censoring influence of reason. Then finally with full freedom allowed for such emotional expression, the involuntary nature of unconscious projection ceases, with spirit becoming fully immanent as the source of all one's experience.


However as I say, to someone trained from an early age (indeed indoctrinated) this change in emphasis from transcendent to immanent does not come easily.

So what typically happens is that one notices a recurring pattern in one's experience.

At one moment one seems to be flying high with a universal meaning attaching to one's spiritual revelations. However, inevitably a degree of attachment then builds up with respect to such activity.

This then sends out the mistaken message to the unconscious, that such spiritual consolations are more worthy of the disciple than exposure to primitive impulses (such as intimate erotic fantasies).

Therefore the "lower" unconscious attempts to compensate for this imbalance by sending - what in the spiritual literature is referred to as - "temptation" i.e. where one is subtly invited to participate in the physical experience that formerly one unwittingly repressed.

Quite simply, as long as this imbalance exists i.e. of the transcendent dominating the immanent direction, then "lower" level projections, when they occur, will always necessarily contain an involuntary element.


Now of course one cannot hope to correct this imbalance by adopting a permissive "anything goes" attitude in respect to the physical unconscious. Rather the task is to slowly let go of the censoring activity of super ego control, so as to gradually allow ever deeper primitive impulses to surface.

And when one learns to listen to these properly in an affective manner (properly understanding their nature) their involuntary nature ceases.

So the battleground - as it were - of this level relates to the slow unravelling of imaginary attachments.

And once again, certainly in my own experience, we have here both "higher" attachment to archetypal spiritual symbols (reflecting an unduly transcendent emphasis) and then corresponding "lower" attachment to primitive physical impulses (reflecting a lack in the corresponding immanent emphasis).

Thus both of these are fully complementary. Therefore success in erasing the "higher" attachment, makes it correspondingly easier to gradually erode the involuntary nature of primitive instinctive attachment.

However it is a long journey. So we will initially look at the nature of this new refined "higher" imaginary (in both affective and cognitive terms) before switching to corresponding "lower" imaginary activity.

Sunday, October 27, 2013

Transcendence and Immanence

As we have seen, level 2 (Band 3) is geared to the unfolding of the imaginary polarities relating to the true relationship (without reductionism) as between whole and part.

Once again, it comes in two complementary forms. From the transcendent perspective, the collective whole (as quantitative) uniquely mediates the universal spirit (as qualitative).

From the complementary immanent perspective, each individual part (as quantitative) again uniquely mediates the universal spirit (as qualitative).

Thus from these two related perspectives, the spirit is mediated both through (collective) whole and (individual) part phenomena. In this way, through both quantitative aspects being related to spirit in a complementary fashion, whole/part reductionism is thereby avoided.

Whole/part reductionism - as we have seen - consists of interpreting both wholes and parts with respect merely to their quantitative characteristics (with the whole in any context interpreted as the sum of its parts).

However when we properly allow for both quantitative and qualitative interaction, ultimately both wholes and parts can serve as symbols (or archetypes) of a universal spiritual meaning.

Thus imaginary understanding, in the holistic mathematical context  in which define the term, relates to the appreciation of both whole and part symbols as mediating this spiritual meaning.


Now the transcendent aspect of the contemplative journey represents the desire to ultimately go beyond all form in the appreciation of pure spiritual awareness. When attachment to phenomena arises, a reduction of spiritual to material meaning thereby takes place.

So what happens with authentic transcendent spirituality is that experience of phenomena becomes increasingly more general, enabling them to serve as collective universal archetypes.

With sufficient development in this direction, such phenomena can become so refined that they no longer even appear to arise in experience with pure contemplative awareness remaining.

So spirit is seen here as ultimately beyond all form.

However as I have stated in previous blogs there are obvious shortcomings with this approach, in that the attempt to continually negate attachment can culminate in significant (unconscious) repression.


So the immanent aspect is based on letting the unconscious aspect speak for itself, by gradually allowing it to freely emit projections into consciousness.  In this way the spirit can be seen ultimately as deeply inherent with respect to all form

When the involuntary element of projection is gradually removed, the unconscious is then enabled to more freely express itself (without undue "higher" level attempts at control).

Thus the (masculine) transcendent direction of spirituality represents a refined attempt (guided by growing spiritual awareness) at cognitive control of development.

By contrast the (feminine) immanent direction represents the corresponding refined attempt (also guided by growing spiritual awareness) at affective response with respect to development.

Thus ultimately true success with respect to consolidating authentic spiritual awareness, requires the balanced interaction of both transcendent and immanent aspects i.e. the balanced interaction of both cognitive and affective functions through (masculine) control and (feminine)  response.


In our culture with the dominance of the masculine principle, undue attention is placed on the transcendent aspect of spirituality, which leads in important respects to a crucial imbalance.

For example in Christian contemplative writing, I have yet to say a proper account of the important role of unconscious fantasy in spiritual development. Too often, because of an unduly transcendent emphasis, an unhealthy stance is adopted, with fantasy treated merely as "temptation" and thereby something to be controlled (and inevitably repressed through the "higher" conscious).

As we have seen Level 1 (Band 3) is concerned the attempted integration of the real (horizontal) polarities in positive and negative terms. Real in this context relates to the conscious polarities that are external and internal with respect to each other. And remember this occurs through dynamic negation of attachment with respect to customary dualistic understanding associated with each pole!

By the time Level 2 (Band 3) begins to unfold, substantial 2-dimensional integration with respect to these polarities (in the personal and impersonal aspects of understanding) will have taken place.

Now the imaginary notion (which entails in analytic terms the square root of  − 1, essentially relates to the attempt now to convey such 2-dimensional appreciation through conscious symbols of a linear (1-dimensional) nature.

If we initially identify the positive vertical pole with transcendence, then + i relates to the means by which generalised conscious symbols mediate a universal spiritual meaning.

The negative pole in this context − i then relates to the negation of undue attachment to such symbols.

However we can change  the frame of reference to identify with the immanent direction.  + i now relates to the means by which individual symbols (emitted from the unconscious) can likewise mediate a universal spiritual meaning.

The negative pole − i now relates to the negation of undue attachment to such symbols.

However it is important to grasp that the process of negation is quite distinct in both cases.
In the former case this is achieved through a refined form of cognitive control; in the latter it is achieved through a corresponding refined  form of affective response!

Thus equal emphasis must be placed on both reason and emotion in this regard.

We will deal with this imaginary understanding with respect to both the transcendent and immanent directions of understanding in future blog entries.

Friday, October 25, 2013

4-Dimensional Reality

In holistic mathematical terms, the structures of Level 2 (Band 3) can be characterized as of a 4-dimensional nature from a qualitative perspective.

Now we all accept in conventional scientific terms the quantitative importance of 4 dimensions (with our macro world seemingly structured in this manner).

However an equal (though largely unrecognised) importance attaches to 4 dimensions from a qualitative perspective (with again everyday reality seemingly structured in this fashion).

These the 4 qualitative dimensions correspond indirectly (in a reduced quantitative manner) with the four roots of 1 i.e. + 1,  − 1, + i and − i respectively.

Now we have already dealt with the significance of the the two real (horizontal) roots in the context of 2-dimensional interpretation.  Again, in dynamic relative terms, these refer to the interaction of external (objective) and internal (subjective) polarities (which necessary underlie all experience).

As we have seen, these horizontal polarities are integrated with each other (to a substantial degree) during Level 1 (Band 3).

So now the focus in development largely switches at level 2 to the corresponding integration of these vertical (i.e. imaginary) polarities.

I have frequently stated that in holistic  mathematical terms, the imaginary notion i, represents the indirect linear rational expression of meaning that is properly of a qualitative holistic nature. Put another way it is the indirect conscious expression of unconscious meaning.

In experience therefore, the unconscious can only indirectly express itself through projections that are attached to conscious symbols. So correct interpretation requires seeing seeing such symbols as but the indirect expression of a more universal holistic meaning.


Actually, all of this relates to the fundamental relationship between wholes and parts in experience.
Properly understood, in dynamic interactive terms, the relationship as between whole and part (and part and whole) is quantitative as to qualitative (and qualitative as to quantitative) respectively.

However in 1-dimensional terms (which defines Conventional Mathematics).a merely reduced quantitative interpretation is given, whereby in any context the whole is understood as merely the sum of its quantitative parts (both of which are interpreted in a real conscious fashion).

Now this equates in psychological terms with a merely rational interpretation of relationships.

But again actual experience is dynamically interactive in nature entailing both rational (quantitative) and intuitive (qualitative) elements.

Therefore, from a proper dynamic perspective, the collection of parts (in a quantitative manner) reflect the whole (which is understood in a - relatively - qualitative manner).

Likewise each part (in an individual quantitative manner) reflects the whole (again understood - relatively - in a qualitative manner).

From a Jungian psychological perspective these would both reflect symbols that are understood as mediating archetypes of a universal nature.

Thus in the former case, generalised symbols would be serving as archetypes; in the later case it would be individual  symbols of a local nature that would reflect these archetypes.

It is here where the spiritual contemplative traditions can provide additional assistance.

When the collective whole becomes the reflection of universal meaning, this is referred to as the transcendent aspect of spirituality;  then when  individual localised part symbols serve as the reflection of universal meaning this is now referred to in a complementary manner as the corresponding immanent aspect of spirituality.

So the transcendent (whole) and immanent (part) aspects of spirituality are once again truly complementary.

Therefore from this perspective, when collective symbols serve as the mediator of spiritual (unconscious) meaning we can  refer to them as imaginary (in a positive manner).

Then when one attempts in reverse fashion to switch to corresponding appreciation of individual symbols likewise serving as mediators of spiritual meaning we must first negate the earlier imaginary understanding.

In this way we can see that the transcendent and immanent appreciation of the qualitative nature of phenomenal symbols in mathematical terms correspond with the two imaginary roots (of the 4 roots of 1) as + i and − i  respectively.


The main practical problem that is now experienced however is that up to this point an unduly transcendent emphasis will have characterised spiritual development.

This means in effect that whereas one may find it relatively easy to see "higher" collective universal phenomena as serving as appropriate "imaginary" archetypes of spirit, it may for a long time be much more difficult to accept "lower" instinctive phenomena (such as erotic fantasies) as likewise serving as appropriate symbols of spiritual meaning.

In other words in most religious traditions, an undue emphasis is placed on the "higher" transcendent aspect of spirituality. This then can lead to considerable problems in fully accepting the "lower" physical aspect of human experience. However, until this is properly achieved, the immanent aspect cannot be properly integrated with the corresponding transcendent aspect of spirituality.

Put another way in vertical terms two types of psychological integration are required (that are ultimately fully complementary).

Thus from the transcendent aspect the emphasis is on top-down integration i.e. where one attempts to integrate the  understanding of "lower" from the perspective of the "higher" levels..

However for proper balance an equal emphasis must be placed on bottom-up integration, where one attempts in reverse fashion to integrate all "higher" levels from the perspective of the "lower" levels .

Indeed this distinction is crucially important for true appreciation of the nature of the Zeta 1 and Zeta 2 zeros respectively (in the context of the Riemann Hypothesis).

In fact, quite remarkably, the true nature of these zeros relates to the manner in which both top-down and bottom-up integration (of a holistic unconscious nature) is attained throughout development.

Thursday, October 24, 2013

A New Dawn

After about 5 years of "imaginary" activity (i.e. where conscious phenomena largely served as projections of unconscious meaning) I felt the growing inclination to drop many of my daily involvements through a new immersion in spiritual contemplation.

So in holistic mathematical terms, there was firstly the positing of "imaginary" activity leading to the old problem of growing possessive attachment to phenomena. This was then followed by a period of gradual withdrawal and detachment constituting the corresponding negation of such phenomena. However as the deeper roots of such attachment lie deep within the unconscious, there are strong limitations to the degree of possible success with mere active negation.


So as before there was now a return to the more passive stages of spiritual contemplative illumination.

It was around this time in the early 80's that once again I began to experience a strong resonance with the writings of St. John of the Cross.

Though whereas previously in was the "Ascent of Mount Carmel" and "The Dark Night" treatise that chiefly exercised my attention on this occasion it was "The Spiritual Canticle" to which I turned.

Now in many ways the approach of  "The Spiritual Canticle" is very different from the "The Dark Night"

Both are similar to the extent that are constructed in the form of opening poetic verse that is then followed by commentary and the more detailed explanations of the author.

However " The Dark Night" poem though utterly beautiful in its own right is very different in tone and much shorter at 8 stanzas from the substantial commentary that follows (which at best bears only a very tenuous connection with the poetic verse preceding).

In the case of "The Spiritual Canticle" the opening poem is  much longer (running to 40 stanzas). In this case the commentary directly elaborates on each stanza. However the commentary here is much less intellectually structured than with "The Dark Night". It seems obvious to me that St. John wanted to give freer affective expression to archetypal fantasies springing from the unconscious.

However this raises a considerable problem that I have already mentioned in that a certain discontinuity thereby exists with respect to spiritual development as portrayed in both "The Dark Night" and "The Spiritual Canticle".

In other words whereas St. John provides a satisfying intellectual account of the spiritual stages up to and including "The Dark Night", I do not consider that this is true with respect to his treatment of further on-going development.

One of the difficulties here is that he was not accustomed to the modern distinction as between the conscious and unconscious aspects of the psyche (though such divisions are indeed implied).

For example St. John would maintain that earliest contemplative life would centre around the life of the senses (followed later by intellect and will). So we have initially the illumination of the senses (both actively and passively) with the corresponding purgation of the senses (again actively and passively).

However it is very necessary in this context to properly distinguish the conscious nature of such activity from its unconscious counterpart.

Thus though the transcendent aspect is indeed vital with respect to the satisfactory cleansing of the (conscious) sense activity, the immanent aspect by contrast is necessary with respect to corresponding cleansing of (unconscious) sense activity (such as with erotic fantasies).

Therefore though the immanent aspect is indeed implied with respect to development succeeding "The Dark Night", St. John never successfully reconciles this with his earlier intellectual account.

In other words a decisive change in direction from transcendent to immanent is required to successfully negotiate "The Dark Night" crisis (which is never made clear by St. John).

However if we accept that much of what I am saying is indeed indirectly implied in his writing, then we can remain in substantial agreement with respect to the new spiritual illumination that now occurs.


It is in stanzas 14 and 15 that this new phase of illumination is depicted in a spiritual manner with the beautiful lines

"My Beloved is the mountains,
And Lonely Wooded valleys,
Strange islands,
And resounding rivers,
The whistling of love-stirring breezes

The tranquil night
 At the time of the rising dawn,
Silent music,
Sounding solitude,
The supper that refreshes and deepens love"


It has to be remembered that the earlier Level 1 (Band 3) which culminates in "The Dark Night" is geared to the successful harmonisation of both the external (impersonal) and internal (personal) aspects of experience.

So when illumination is eventually restored at this new level (level 2) it combines in a very passive peaceful manner, substantial nondual intuitive integration of both of these aspects.

Thus every symbol now directly mediates both twin personal and impersonal aspects.

So we are accustomed to look at the world from a scientific perspective in impersonal terms (with respect to its mere quantitative nature). We then are more accustomed to see the world in more personal qualitative terms from an artistic perspective.  However a considerable split remains in our culture as between both the scientific and artistic worldviews.

So one way at looking at this new stage of illumination is that it automatically combines both scientific and artistic appreciation in the same undivided experience.

Thus the spiritual illumination that unfolds is of a much more refined nature (where it is considerably less influenced by the distractions of everyday phenomenal activities).

Indeed it represents just like the dawn itself (before light properly appears) a dim form of contemplation where universal holistic appreciation of relationships remains very pronounced.

Alternatively it can be closely linked to the pale light of the moon which on a clear peaceful night can convey a wonderful sense of deep intimacy.

Now whereas illumination and purgation are dramatically contrasted at the previous level, this is not the case here. One indeed alternates as between illumination and its withdrawal (which St. John likens to a cold north wind). However to a considerable extent one can now integrate both aspects with equanimity. So one just accepts now as an inevitable part of experience that consolations of any kind are inevitably followed by periods of desolation (so as to prevent the undue attachment to the phenomenal means by which spiritual illumination is mediated).

The attention here in fact switches in a more vertical direction.

Whereas before one attempted to integrate polarities (external and internal) within a given level, the attention now starts to seriously focus on the integration of complementary "higher" and "lower" stages of development.

Wednesday, October 9, 2013

Return to Contemplation

I have been at pains to emphasise with specific emphasis on 3, that the odd numbered dimensions represent a certain dislocation with respect to customary contemplative experience.

Clearly there is both an active and passive dimension to experience. So from a balanced perspective, activity should be plentifully fueled from a spiritual well residing in the unconscious. However equally passivity (in the form of direct contemplation) should be periodically offset through activity. This to an extent then causes a temporary disequilibrium with respect to experience, which is resolved through further contemplation.

Thus properly understood, activity and contemplation are dynamically necessary for each other.

Of course the precise balance that is appropriate will vary considerably from individual to individual.

Some are naturally of a more active nature; others will always be more gifted in a contemplative direction. However it very much part of the successful art of  living to find the balance that is most appropriate for one's own personal circumstances.

This again was one of the significant lacks that I came to recognise in St. John of the Cross's writing where there is very little attempt made in his formal account to address this key important issue.

As I have stated before, though - in the context of the monastic reforms of his order - at one level he did lead an active life, one always gets the impression that it was as a somewhat reluctant participator. This in turn led perhaps  to an unduly negative reaction to the world and its failings which in the end led to a degree of conflict in his dealings with the Order which was perhaps avoidable.

A Christian mystic - though not as intellectually gifted as St. John - that I have been greatly attracted to, is the Flemish writer Ruysbroek.

Perhaps due to the fact that he spent many years in active ministry before fully engaging with the contemplative life, there is a healthier balance in his writings especially with respect to the manner in which activity and contemplations mutually serve each other. There is also a surprisingly modern feel to his writings with a great appreciation of the truly dynamic interactive nature of all experience.

However though some his descriptions are truly beautiful (blending cognitive and affective type experience), I would not want to exaggerate his importance as his writings are quite brief and only deal with the various issues in a somewhat general manner.


In my own case I mentioned how I had gradually become aware of a new significant form of attachment of an imaginary - rather than real - active nature.

In other words the attachments that were being increasingly exercised related largely to unconscious projections that became attached to my various activities.

In a general way, whether with respect to social and personal relationships, or the more impersonal work related and intellectual type pursuits, a growing problem arose from the underlying desire for some manifest form of recognition.

In one way this was not surprising as a very lengthy period of deprivation had taken place (during the "dark night") which by its very nature represented  a complete starvation with respect to such recognition.

So now having in a sense been released to a new freedom, such  desires, which in many ways had been repressed during the "dark night" captivity, were slowly reactivated.

However the difficult lesson that I now began to learn was that though outwardly now adapting more successfully to the world, true recognition was never going to be come from such pursuits.

So gradually I began to draw back again from my many outward involvements (and my misguided sense, provided through them, of possible worldly recognition and fulfilment).

In many ways the gradual relinquishing of such hopes represented another form of "active night" which on this occasion was imaginary - rather than real - in nature, relating to the deeper unconscious desire for meaning (indirectly expressed through conscious phenomena).

And after a period of time adjusting, a new phase of contemplative experience was to unfold.

Though this was much less dramatic than before, it was extremely important in terms of the proper clarification of exciting new states and structures that mysteriously began to re-emerge in experience.  

Thursday, October 3, 2013

3-Dimensional Reality

I have mentioned before the nature of 2-dimensional interpretation which in holistic mathematical terms defines the various structures (cognitive and affective) that unfold during Band 3 (Level 1).

Again this means that external and internal aspects of understanding are seen increasingly as complementary (and ultimately identical with each other).

Firstly we have the unfolding of the supersensory structures i.e. where 2-dimensional understanding is posited with respect to the more superficial concrete structures.

Then we have the corresponding negation of such structures (where rigid phenomenal attachment is eroded) leading to a purer nondual contemplative experience.

Then we have the unfolding of the suprarational structures  where 2-dimensional understanding is now posited with respect to the deeper formal structures.

Finally we have the "dark night of the soul" which represents the negation of rigid attachment to 2-dimensional structures at both the conceptual formal and empirical sense levels, culminating in  much purer (internal) intuitive  type experience.


Now in the Functional Equation of the Riemann Zeta Function a direct connection is made as between 
ζ(s) and ζ(1 – s). This means that when s (as dimensional number) is – 2, 1 – s = 3.

It is fascinating that psychological experience follows a similar dynamic pattern with the "dark night" representing dimensional experience holistically conforming to – 2, now slowly gives way to a new type of experience (that represents the holistic expression of s = 3).

In other words the transition period, that I was referring to in the last two entries, is now followed by - what in fact conforms to - the holistic mathematical interpretation of 3-dimensional experience.

Now remember we are referring to dimensions in their qualitative holistic sense and not in the reduced quantitative manner that is employed in conventional scientific terms!

The holistic nature of the 3 dimensions is indirectly expressed by the 3 roots of 1.

So these 3 roots are 1,   – 1/2 + .866i and – 1/2 - .866i.

Now the odd numbered roots are distinctly different from their even numbered counterparts. With the even there is always a direct complementarity of opposites in evidence i.e. where half of the roots are exactly counterbalanced by their negative expressions!

However with odd numbered roots such symmetry is not in evidence. One of the roots i.e. 1 always stands alone to an extent, with the remaining roots forming pairs that are complex conjugates of each other.


So we can see this in the case of the 3 roots in question.

The first root is 1 which stands separately. Then the other two form a pair (with the same real part in each case and the imaginary aspect alternating as between positive and negative).

Now linear activity is defined by the 1st dimension. So therefore with odd-dimensional understanding a linear (analytic) aspect is always involved.

As I stated in my own case ,this was very helpful in enabling me to readapt to the customary activities and relationships consistent with normal living.

However actual experience is never of a merely conscious (i.e. linear) nature. The unconscious is also necessarily involved in the form of projections that indirectly draw attention to the holistic nature of our desires.

Thus though we may focus on the conscious aspect e.g. in buying a new car, indirectly the very desire to purchase this item reflects a deeper holistic desire for fulfilment. So in some ways acquiring the car is therefore seen as fulfilling that purpose.

Now when our activities are conducted largely at the conscious level, we literally become blind to associated holistic (unconscious) elements.

And as we have see our conventional mathematical and scientific notions are formally interpreted in a merely real (i.e. conscious) manner.

However it is important to recognise that even here, every mathematical symbol, strictly speaking, represents an interaction as between both real (conscious) and imaginary (unconscious) aspects.

In this regard, all experience is complex (in a precise holistic mathematical sense). Thus the very pursuit of mathematical truth reflects a deeper unconscious quest for holistic meaning (which mathematical activity is seen to provide in some measure).


However the very nature of linear type activity (coming out of the "dark night") is that the direct conscious aspect has already become significantly eroded.

This therefore implies that the projections coming from the unconscious are much harder to ignore and in fact quickly become the most dominant aspect of experience.

So it is in the very nature of experience that the drive for integration (represented by even numbered stages) is directly followed by a new period of more refined differentiated activity (represented by the odd numbered stages).

Now until perfection is reached - which of course can only be imperfectly approximated in human terms -  there will always be some imbalance present in this activity (i.e. where involuntary attachments arise).

If we were to be fully free of involuntary attachment, this would require that as soon as a projection arises, that it would be immediately negated. In this way projections would - like virtual particles - keep dissolving as soon as they arise in consciousness.

If this ideal was achieved with respect to the 2nd and 3rd roots of 1, i.e. – 1/2 + .866i and – 1/2 - .866i, then imaginary aspect would be immediately eroded leaving just the real part of  – 1/2 in each case.

Thus when combined the sum of the real parts would be – 1, which would exactly balance with + 1.

However, in practice a considerable amount of temporary difficulties are likely to be  experienced in dealing successfully with projections.

Furthermore the transcendent stance that characterised the previous stages will not be effective in coming to terms with them!

Ultimately such projections reflect a limitation in properly listening to the nature of unconscious desires (through repression). This then leads to their involuntary projection (where they become rigidly identified with conscious symbols).

In fact at a deeper level when we obtain prime numbered roots (such as 3) this number will be contained in some form in the resulting root expression.

So for example .866 (which occurs in each root of the conjugate pairing) is the value of √3/2.

What is truly remarkable is that the qualitative notion of prime numbers is very closely related to - what we might refer to as -"primitive" i.e. prime instincts.

Therefore the very mastery of such primitive impulses (emanating from the unconscious as projections) requires on-going development through the various prime numbered dimensions.

However having said this, the early prime numbers such as 2 and 3 are the most important serving as a template for all further primes.

Thus we can see that the very task of understanding the qualitative nature of prime numbered dimensions is the very means of coming to terms with primitive (involuntary) impulses emanating from the unconscious.

Wednesday, October 2, 2013

When Reality is Imaginary

I explained in the last entry this transition period, following the "dark night" (i.e. passive night of spirit).

Now of course everyone is unique, so I would never consider offering my own particular experience as a template for others.

However my key point is that despite all the variations of individual experience, that universal features can indeed be identified with respect to human - indeed all - development (and its many stages).

Furthermore - and most importantly for our purposes - these possess a coherent holistic mathematical structure.

So in my own case my earliest realisation of the neglected qualitative aspect of mathematical understanding came from this attempted scientific mapping of human development.

Going back to my personal story, though this transitional period enabled me to readapt again to the world, with the consequent lifting of accumulated depression, I began to realise that this was no "normal" reality that I was now experiencing.

So the very problems of disillusionment with temporal phenomena and the consequent search for a deeper meaning began to surface once more in a very keen manner.


So briefly what had happened was this.

During the "dark night" a very significant erosion of conscious experience had indeed taken place both with respect to the concrete phenomena of everyday life and also the deeper conceptual structures underlying customary experience.

So having peeled away the conscious layers of experience so extensively, this now enabled the unconscious to project (without much resistance) into what remained of conscious life.

Initially this was perceived as of a very beneficial nature.

As I stated my own interpretation of the pathological element of repression accompanying the "dark night" is that it directly arose due to the continual (unintended) repression of "lower" primitive instincts through the ardent pursuit of a transcendent spiritual goal.

So therefore with the switch in direction in an immanent following the "dark night" crisis, the unconscious was now given a licence as it were to project these repressed desires into what remained of conscious experience.

And I the beginning, I thereby as I became slowly aware of all the natural instincts that has been suppressed I was able to take action to deal with the situations in the pursuit of necessary relationships and activities that had been placed on indefinite hold.

I remember at the time following my developing interest in physical black holes, I began to be fascinated with Stephen Hawking's views on black hole radiation, once again seeing a fascinating parallel with my emerging psychological experience.

Basically Hawking maintained that black holes in radiating could ultimately become transformed as energy. And I had already come to see (physical) gravity as representing a hidden internal source of such energy.

Hawking explained this radiation through the emission of virtual particles. Now virtual particles occur in matter/anti-matter pairs and tend to be extremely short-lived as they come into contact with each other. However Hawking postulated that it would be possible for the matter particle to be separated from the anti-matter particle thus escaping the event horizon of the black hole . So the radiation would occur from the emission of such virtual matter particles into the outside environment.

I began to look at the recovery - certainly my recovery - from the "dark night" in a complementary psychological fashion.

The word "virtual" has very close connections with the important notion of "imaginary" in holistic mathematical terms.

So the indirect expression of the unconscious takes place in an imaginary (i.e. virtual) fashion.

Now with conscious understanding opposite poles of experience (such as external and internal) are clearly separated.

However with unconscious understanding they are highly complementary (and ultimately identical).

So when the unconscious attempts to speak for itself as it were it does so in this imaginary fashion (where external and internal are closely connected).

However what typically happens is that in order to engage with conscious experience, these poles become separated. In this way the holistic (imaginary) unconscious projects itself involuntarily into experience (whereby it becomes misleadingly identified with specific conscious phenomena).


In fact this is a huge issue, which I felt had not been properly addressed by St. John of the Cross (or indeed any of the contemplative spiritual writers of my knowledge).

In other words in speaking about attachments there really are two distinct types

So we have conscious attachments both of an active (linear) and passive (circular) kind.

Now the transcendent aspect of spiritually (i.e. the "higher" ascent) is properly geared to the overcoming of such conscious attachments.

However we also have unconscious attachments again both of an active (linear) and passive (circular) kind. This arises when the unconscious in expressing its own needs freely projects (in an involuntary manner) into consciousness.

The immanent aspect of spirituality (i.e. the "lower" descent) is properly geared to the erosion of such involuntary unconscious attachment.

So properly understood there is a "top down" transcendent and "bottom-up" immanent aspect to spirituality both of which are necessary for true integration.

Thus in a more nuanced approach to contemplative development, we typically emphasise the transcendent initially (as attachments will be then readily identifiable in conscious terms).

However having cleared away to a considerable extent rigid conscious experience, the emphasis should now switch in an immanent direction so as to come to terms with involuntary attachments (emanating directly from the unconscious).

In my own case as the unconscious initially started to project more freely, this served to reduce the rigid congestion of repressed instincts that had accumulated (thus reducing the element of pathological depression).

Also by projecting its needs on to conscious phenomena, this enabled me to become more active in addressing such needs.

As I say this was all very desirable in terms of readapting successfully to the world.

However eventually the negative aspect started to break through in that it was helping to create a whole new set of attachments (of an involuntary imaginary nature).

In other words I became gradually programmed to seeking satisfaction from very fleeting phenomena (which could not satisfy my deeper desire for meaning).


However in many ways this was a very valuable learning process.

So I began to gradually interpret my new adaption to the world in holistic mathematical terms as linear activity of an imaginary nature. This was in contrast to such activity before the spiritual journey commenced which represented linear activity of a real nature.

Friday, September 27, 2013

Adapting to the World

The decisive crisis of the "dark night" is not resolved until a basis switch in direction takes place in the personality.

Typically during the "dark night" one uses refined rational control (guided by a largely hidden type of spiritual  intuition) in one's attempt to negate attachment to conscious phenomena. This applies especially to the deeper conceptual structures that form the normal framework for ego existence.

As we have seen this is associated with the transcendent aspect of spirituality (which unconsciously is associated with a degree of repression of primitive impulses).

As remaining rational control is gradually eroded, the faint intuitive light associated with one's decisions fades completely and one is left alone in the dark with no sense of direction. Though existentially this provides the opportunity to truly act in faith, unfortunately it is associated with great potential danger.

One may now have reached a state of physical and emotional exhaustion with signs of pathological depression steadily growing. Also there is no means of adequately communicating the spiritual basis of  this problem. On the contrary anyone concerned with one's well-being, is likely to consider the very suggestion as confirmation of a pathological state and urge the return to "normal" living.

Also because one is now so ill-equipped to deal with the outside world, external "crosses" only conspire to make the situation worse.

All this may well lead to a crisis event representing yet another type of conversion.

Paradoxically, only in the very moment that one seemingly abandons faith itself, does the first faint sign of recovery takes place.
What this actually represents is the surrender of the unduly transcendent focus adopted (which for many years has prevented "lower" primitive impulses from enjoying any autonomy).

So the pathological element of depression that is experienced relates in large measure to the unhealthy repression of such instincts (all in the name of transcendent spiritual desire).

Therefore though one considers this the final defeat i.e. the letting go of transcendent faith, in fact it is the first step to an important new phase of rebalancing, where the immanent aspect can be gradually harmonised with the transcendent.

Putting it crudely the transcendent aspect represents spirit over nature; the immanent aspect in reverse represents nature over spirit. So only when one  can properly balance these two aspects can the divine spiritual be properly integrated with one's natural human identity.


It would not be correct to exaggerate the speed with which this adjustment can take place.

In my own case having reached my lowest point, it took some time before recognising that things had subtly changed.

Pathological depression still remained, though I was aware that a floor had been reached. And I took the fact that things were not continuing to get worse as the first positive sign of improvement.

Likewise I noticed that though still very dark, my mood had lightened to a degree. Most of all freed now of the unrelenting attempt to discipline all ego attachment, I gradually began to feel more relaxed and better able to focus on rebuilding a relationship with the world.

So I stated returning to many of the "normal" things that had been put on hold for so long. I was now able to drive a car, swim, and feel more confident in social situations.

Thus with a new job, the experience of dating girls (for the first time in my life) and a number of new outside activities it seemed that life had returned to normal at last.

Indeed for a while it seemed as if the lengthy "dark night" stage which had preceded this new life represented just some strange aberration which thankfully had now passed.

However this new situation did not last long. Though on one level I was managing OK, I realised that I was not really deriving any true fulfilment from my activities.

Also I noticed that I was becoming keenly sensitive to projections (both affective and cognitive) which were greatly disrupting the security of this new existence.

So when I look back now, this overall period, which lasted for nearly 5 years, represented a necessary interlude. So on the one hand it allowed me to recover from the severe stress that had accompanied the "dark night"; equally important it allowed me to successfully readapt to the world and its various demands and pleasures,

So once this adaptation had run its necessary course, it was time to embark on the next stage of the spiritual journey.

Thursday, September 26, 2013

Dark Night of the Soul (7)

We return here to providing a holistic mathematical perspective on the "dark night" stage.

As we have seen the first level of the 3rd band (of which the "dark night" is the final and most important stage) is defined in terms of 2-dimensional interpretation.

Thus starting with the dualistic phenomenal distinctions (that characterise the 1st dimension) one then attempts to approximate as close as possible growing nondual spiritual awareness through a process of dynamic negation of attachment to all conscious symbols.

So this dynamic negation of conscious phenomena constitutes the 2nd of these two dimensions.

So we posit conscious phenomena in a linear dualistic manner (+ 1). We then unconsciously negate such phenomena in a circular nondual manner ( – 1).

Such positing and negating in experience leads to an ever increasing dynamic interaction as between the external (objective) and internal (subjective) aspects of experience. In this way, ever more refined dual recognition (freed of rigid attachment) becomes increasingly compatible with growing nondual awareness.

Now, positive interpretation of 2-dimensional understanding relates to the rational interpretation of this complementarity of opposite poles in experience.

However this indirectly again leads to the making of dualistic distinctions (albeit of a paradoxical kind).

Thus to release the pure nondual intuitive awareness of what is implied by 2-dimensional interpretation, one must negate such indirect rational notions.
In other words without such negation, passive attachment would inevitably be associated with such understanding.

So again "the passive night of spirit" as St. of the Cross intends, relates to the negation of such attachment with respect to the deeper conceptual appreciation of this complementarity of opposites.

Thus in holistic mathematical terminology it relates directly to the negation of 2-dimensional understanding (more properly of rigid attachment to such understanding).


This in terms of the development of true holistic - as opposed to analytic - interpretation, the "dark night" represents the most crucially important stage, where truly deep intuitive awareness (that is unconscious in origin) is consolidated as a habitual aspect of experience.

Put another way, the truly integrated - as opposed to differentiated - interpretation of reality, depends on the substantial development of such intuitive awareness.

Therefore in future, the proper development of integral - as opposed to analytic - science will be greatly dependent on authentic experience of this "dark night" stage.

A great tragedy in our culture is the total lack yet of any proper notion of the nature of integral science (and its great potential importance). And of course at an even deeper level, this reflects the corresponding lack of any notion of the nature of integral mathematics (on which the scientific notions are based). And because of the possible confusion used by integral which has a specialised analytic meaning in conventional mathematical terms, I customarily use the term holistic mathematics in this context!   


My initial interest in the Riemann Hypothesis derived directly from a holistic mathematical interpretation of the "dark night".

Now with respect to the Riemann Zeta Function, the first of the trivial zeros relates to the Function that is expressed in terms of the dimensional value (i.e. power)  – 2.

Now again this Zeta Function is defined as the infinite series,

ζ (s)  =   1–s  + 2–s  + 3–s  + 4–s  +……..,

Therefore when s = – 2,

ζ (– 2) = 1+ 22   + 3+ 42  +……..,

Thus in conventional linear terms,

ζ (– 2) = 1 + 4 + 9 + 16 + .........  which clearly is divergent


However according to the Riemann Zeta Function,

ζ (– 2) = 0.

Therefore, my initial attention was devoted to giving a satisfactory explanation of this seemingly nonsensical result.

Interestingly St. John in speaking of the "dark night" process refers to its purpose as "nada".

Now "nada"when translated means "nothing".

In my primary school years in Ireland the mathematical symbol 0 (i.e. zero) was customarily referred to as "nothing".

So as I reflected I began to realise that negative dimensional values of the Riemann Zeta Function were properly defined in a qualitative - rather than standard quantitative - manner.


This is a huge unrecognised issue in Conventional Mathematics!
Here, numerical values are defined in reduced terms with respect to their merely quantitative values.

This correlates in turn with a solely rational (dualistic) interpretation.

However properly understood in dynamic terms all mathematical understanding reflects the interaction of rational (quantitative) and intuitive (qualitative) aspects.

So a purely qualitative understanding of number (reflecting merely intuition) would be thereby nondual (with no quantitative value).

Put another way the first trivial zero (where s = – 2) corresponds to a Type 2 (holistic) rather than Type 1 (analytic) interpretation.
Quantitative values reflect 1-dimensional interpretation (where the external objective notion of number is separated in absolute terms from its internal counterpart).

However qualitative 2-dimensional interpretation reflects the complementarity of both external and internal aspects.

And as we have seen negative 2-dimensional interpretation reflects the negation of any (dualistic) rational element, thereby obtaining a purely intuitive nondual appreciation (which is nothing in quantitative terms).


Thus, true appreciation of the nature of the most simple of the trivial zeros provides the key to the realisation that the Riemann Zeta Function requires both Type 1 (conventional) and Type 2 (holistic) mathematical appreciation for meaningful interpretation.

The deeper implication again of all of this is that once we properly get to grips with the cognitive understanding that unfolds with "higher" level development (starting with Band 3) that the very nature of Mathematics and Science profoundly changes.


Though I have been saying this now for decades, little or no recognition yet exists out there of its great potential significance . Unfortunately this will remain the case until we begin to properly recognise the existence of these many higher bands on the psychological spectrum.