Holistic Mathematics and Spiritual Development

Q You specifically state that you intend Holistic Mathematics as a scientific integral approach to reality. Does this emphasis on science thereby imply that it is unduly impersonal and one-sided representing a distortion in terms of true integration?

PC This is a very good question which I would be happy to clarify.

As I have previously stated substantial personality integration with respect to H3 (the most developed of the integral levels) requires that considerable balance be maintained as between the primary modes i.e. cognitive, affective and volitional. This in turn implies therefore a similar degree of balance with respect to the key composite modes (i.e. the Big Three representing scientific, artistic and moral development).

Though Holistic Mathematics is necessarily an all-quadrant (or more comprehensively an all-sectoral) affair, it is certainly true that in the scientific context I define, it will be inevitably biased in its direct expression towards a more universal type appreciation of reality that is spiritually mediated through the cognitive aspect.

It has to be clearly appreciated however that the very nature of understanding at the "higher" integral is quite distinct from the middle analytic development.

Because the middle stages are largely geared to differentiated understanding, it is indeed quite possible to achieve very specialised development with respect to one aspect in relative isolation from others. So for example one could be a brilliant mathematician (in analytic terms) while remaining considerably stunted with respect to artistic and moral development.

However because - by its very nature - integration relates to the interdependence of key aspects of development, it becomes more difficult at the "higher" levels to specialise in any one aspect without due recognition of its dynamic complementary nature with others.

Therefore because the cognitive and affective aspects are complementary through relationship to the will, increasing balance as between these modes must necessarily be maintained at the "higher" spiritual levels.

In other words therefore though Holistic Mathematics in direct terms is necessarily biased towards a distinctive refined form of cognitive expression, its appropriate appreciation indirectly requires that substantial balance be maintained with the other primary modes (affective and volitional).

So scientific, artistic and moral development can indeed be largely separated at the middle stages of development. However at the "higher" spiritual levels they become increasingly interdependent and ultimately reconciled in pure nondual expression (as their common origin and goal).

When I was in dialogue regarding the nature of Holistic Mathematics, I encountered a great deal of unwitting confusion as to its true nature. Because mathematical symbols can be interpreted in a merely rational fashion, many believed that Holistic Mathematics represented an attempt to reduce spiritual experience to the level of merely analytic understanding.

However the true position is quite the opposite. Holistic Mathematics requires an especially refined interaction of advanced cognitive structures with pure spiritual awareness.

Indeed properly understood, such mathematical understanding entails an extremely disciplined form of meditation practice in many ways much more demanding than in the mystical traditions (where a looser softer form of imagery can apply). It entails a continual attempt to strip reality to its barest essential structures (which possess universal applicability) and therefore requires unusual clarity of vision for its proper comprehension. I firmly believe that - given appropriate appreciation - it represents the closest one can come in the phenomenal realm to pure spiritual contemplation.

Q Does this not create a problem in terms of growth at the radial levels? As you define them these levels would require a considerable interpenetration of both refined activity and contemplation.

However a high degree of specialisation in contemplation would surely limit the possibilities for a great deal of active involvement?

PC Yes! This would indeed be true in many cases. As I have stated, mystical attainment at the "higher" levels requires considerable attention to achieving appropriate balance as between the primary modes (affective, cognitive and volitional). However it is still certainly true that earlier development tends to be more unbalanced being largely driven by just one (or more usually two modes).

I would consider that volition is the most central mode.

Mystical attainment above all represents an intense desire of the will for spiritual union. However it does not operate in a vacuum and is necessarily associated with the other modes (initially in a somewhat unbalanced fashion).

We could say that the volitional desire - which literally is most essential - is to realise one's true being (which is purely spiritual) and this I believe chiefly defines all authentic mysticism.

The cognitive desire will be seen in terms of knowledge and the affective in terms of (devotional) love. Of course ultimately the realisation of these three drives culminates in Spirit.

However typically there will be some imbalance so that for example the intellectual type of mystic might tend to emphasise knowledge (over devotion) and the emotional type devotion (over knowledge).

If the volitional desire for ultimate meaning is especially strong with however one of the other modes somewhat dominant, then I believe mystical development (assuming that it unfolds successfully) is unlikely to develop substantially into the radial levels.

Therefore in the pursuit of more authentic spiritual awareness, one will have to spend considerable time learning to restrain one's naturally strong inclination while also growing sufficiently to fully accept one's weaker side.

So the naturally disposed intellectual mystic may therefore have to concentrate on refinement of the cognitive mode (though lengthy purgative trials) while also opening up the weaker shadow side (affective) to an unusually intense degree of unconscious exposure.

It is unlikely in such instances that sufficient progress can be achieved to enable substantial active development at the radial levels.

Thus insofar as radial development does take place here it will tend to be defined more in passive (i.e. contemplative) rather than active terms.

Where the volitional desire is less dominant but is however associated with greater natural balance with respect to cognitive and affective modes, radial development is likely to entail a considerable degree of creative active involvement (without perhaps the same degree of contemplative attainment).

So we can have radial development that is defined largely in terms of contemplation (with more limited active involvement) or alternatively activity (with more limited contemplative attainment). However because this still represents a certain lack of balance, full radial development will not be possible in either case (and will be largely confined to - what I term - the Radial 1 - or at most - Radial 2 level).

The most complete expression of spiritual development (Radial 3) - which in my own Christian tradition is generally associated with its greatest Saints - clearly entails a much greater interpenetration of contemplation with mature active involvement. This often reflects personalities that are especially gifted in various ways with respect to all three modes thus enabling them to overcome those final blocks that hinder development for other mystics.

Discussion on Holons

Q I want to talk a little more about your own approach, so as to help place your holistic mathematics in context. How do you fundamentally describe the nature of reality? Would you for example describe it as being made up of holons?

PC Because of its widespread acceptance in the integral field I often use the term "holons" to facilitate communication. However I do so with considerable reservations.

The very term (i.e. holons) suggests a form of "stuff" as fundamental building blocks of the more comprehensive Kosmos which can thereby encourage a somewhat fragmented interpretation.

The key problem as I see it is the lack of an appropriate dynamic understanding of "holons". In practice - as in the conventional treatment of the four quadrants - the integral aspect is generally reduced to merely differentiated understanding thereby losing any true interactive meaning.

So if we are to maintain the notion of holons, we must place them directly in a dynamic context through accepting that they necessarily entail a continual interaction as between the twin aspects of differentiation (independence) and integration (interdependence). Furthermore it must be understood that these two aspects are qualitatively distinct requiring therefore unique manners of interpretation.

Unfortunately the great paradox with "Integral Studies" as presently constituted, is that it lacks any appropriate intellectual means of integral interpretation. This to my mind has long been the key problem to be resolved. Unfortunately very few - as yet - appear to even recognise the issue.

So once again we must clearly distinguish as between differentiation (based on asymmetric analysis) and integration (based on paradoxical appreciation).

I then refer to their mutual interaction (where the qualitatively distinct nature of both aspects is preserved) as irradiation.

A comprehensive treatment of "holons" really requires three distinct approaches i.e. a linear (1) analytic approach suited for differentiation, a circular (0) holistic approach suited for integration and a binary (1 and 0) radial approach suited for mutual differentiation and integration.

In my own early work - in place of holons - I simply used "relationships" which better preserves - I believe - the dynamic nature of fundamental phenomenal interactions.

So - in whatever context - we approach reality, it can been seen to embody relationships, again involving the twin aspects of differentiation (that which is to be related) with integration (that which is related) mutually interacting in a dynamic fashion.

Q So you are saying that reality is fundamentally composed of relationships?

PC Well, ultimately reality is pure Spirit. What we call reality i.e. phenomenal space-time reality, strictly constitutes mere appearance which distorts the fundamental nature of ultimate reality (which is without dimension).

However in terms of appearance, I would say that phenomenal reality is composed of relationships.

Q Are relationships more fundamental than perspectives?

PC Yes, I would say that they are! A perspective already implies a relationship. However in a certain sense we can have a relationship without implying a perspective.

The very word perspective is derived from the Latin word "perspicere" which means "to look closely". So a perspective therefore involves a certain view which is necessarily limited in terms of overall (i.e. ultimate) reality. The obvious reason for this is that "to look at" implies "that which is looked at".

Therefore though "that which is looked at" is necessary for a perspective to arise its reverse relationship with the viewer, is not directly embodied in the revealed perspective. In other words relationships - in dynamic terms - are always two-way. However a perspective in this context implies a particular one-way view.

So in dynamic terms a perspective necessarily implies its opposite direction (i.e. what is not in perspective) which thereby causes a switch in the direction of the perspective.

And the more readily we can freely switch the direction of perspectives, the more integrated our overall awareness becomes. So ultimately when the seer and what is seen are one through becoming "seeing" we enter into the pure ultimate nondual awareness (which is without any distinct partial perspective).

However I certainly would not want to get hung up on any particular word. Therefore it does not really concern me as to whether one refers to the fundamental nature of phenomenal reality in terms of "relationships", "perspectives" or "processes". What is important however is to demonstrate a truly dynamic understanding through incorporating the necessary dual aspects of differentiation and integration, and then interpret both in an appropriate manner (preserving their qualitatively distinct natures).

Q What other reservations do you have with holons?

PC In the four quadrant approach, holons are defined in terms of twin aspects (which are horizontal and vertical with respect to each other).

So in horizontal terms i.e. Left-Hand and Right-Hand, all holons are defined as having interior and exterior aspects. Then vertically (Upper and Lower) they have individual and collective aspects.

However the individual and collective aspects relate directly to part and whole.

Therefore - what is referred to as - "a holon" is defined with respect to just one of its two chief defining parameters (i.e. vertical).

We could equally refer to a "holon" as an "in-out" implying therefore that every holon is an inside/outside (with every inside outside an other inside). For example to experience my interior self (as individual) I must place it outside your interior self (as a separate individual).

So the actual term "holon" is therefore arbitrarily biased (in terms of its vertical parameter).

A much more serious limitation however relates to the fact that four quadrants are not sufficient to model all the essential aspects of either relationships (or perspectives).

As well as the horizontal (interior and exterior) and vertical (individual and collective), we also require twin diagonal aspects in order to provide a comprehensive interpretation for reality. So a comprehensive model - as I define it - is eight-sectoral (rather than four-quadrant) and in the holistic mathematical approach is given a precise scientific interpretation.

Now these additional (opposite) aspects can be defined in various ways.

From the volitional perspective they represent form and emptiness (immanence and transcendence). So immanence and transcendence have both heterarchical (horizontal) and hierarchical (vertical) aspects which are best modelled in diagonal terms.However the diagonal aspects have equally important representations in affective and cognitive terms.

It is extremely important to properly differentiate these key primary modes of experience (with their composite artistic and scientific expressions respectively) and this cannot be properly achieved within a four-quadrant model. For example I believe that they are vital for appropriate interpretation of instinctive behaviour and as a means of distinguishing psychophysical interactions from either direct psychological or physical interpretations of reality. Also, as I have demonstrated in the previous discussion, they provide the basis for interpretation of the fundamental forces of reality.

Quite remarkably through the holistic mathematical interpretation of these diagonal aspects, we can demonstrate precisely the ultimate nature of the relationship between form and emptiness (though its actual intuitive comprehension of course remains truly mysterious).

In this context I would find a certain problem with Ken's reference to "sentient" holons (which is unduly limiting). Sentience relates to "feeling" and the affective aspect. However the other primary modes also necessarily apply to every holon. So - however primitive their manifestation - all holons possess volitional, cognitive and affective capacities. In the most general sense the volitional relates to evolutionary drive, and the cognitive and affective to both control and response patterns with respect to the environment.

Now for me "experiential" rather than "sentient" better incorporates the three primary modes applicable to all holons.

So I would prefer to say therefore that all holons - or rather all relationships - in dynamic terms are characterised by "experiential being". There is however a certain limited context (applying to one-directional differentiation) where it is quite valid to characterise holons as impersonal.

So we need to avoid making sweeping statements regarding holons which ignore the different ways in which interpretation can validly take place.

By far the most serious problem however is Ken's inability to provide a consistent interpretation of holons. This reflects in turn the lack of appropriate dynamic understanding with the consequent failure to properly distinguish integral from (merely) differentiated understanding.

Q I know you consider this point especially crucial and have dealt with it many times before. However could you briefly - in the context of the present discussion - explain it again?

PC As I have stated before differentiation - in any context - is based on the clear separation of polar opposites (with understanding always taking place with respect to just one arbitrary reference frame).

For example the two horizontal polarities (i.e. interior and exterior) constitute opposite poles which from an integral perspective are fully interdependent.

However to differentiate these poles (as separate) we must arbitrarily fix the reference frame with just one pole.

So for example to differentiate an "object" in experience, we fix the reference frame (solely) with the exterior pole, thereby yielding the understanding of its relatively "independent" existence (from the subjective observer).

Likewise to differentiate the (personal) self, we fix the reference frame (solely) with the interior pole, thereby yielding the relatively "independent" existence (from the object observed).

In this manner we are enabled to fix the direction of various poles in experience in an unambiguous asymmetrical manner.

So if we - as in popular convention - identify exterior meaning with the Right-Hand, then interior meaning will be unambiguously identified with the Left-Hand Quadrant.

Also as a direct consequence of this approach, relationships in development will appear to have an (unambiguous) asymmetrical direction.

Thus for example, if I state that the atom is contained in the molecule but the molecule is not contained in the atom, this is a clear example of what I refer to as one-directional (linear) differentiation. In other words the truth of such an asymmetrical statement can only be taken one-way (thereby excluding its opposite interpretation).

Such one-directional interpretation clearly characterises Ken Wilber’s attempts to differentiate the four quadrants. So for example interior and exterior are unambiguously identified with the Left-Hand and Right-Hand quadrants; likewise individual and collective are (unambiguously) identified with the Upper and Lower quadrants respectively.

However, because from an integral perspective all quadrants are necessarily interdependent, then clearly we cannot reconcile this with a one-directional linear approach (where the quadrants are viewed as relatively independent).

Put quite simply, one-directional differentiation is not consistent with a proper integral approach. In other words the appropriate manner for intellectually dealing with the (integral) interdependence of variables is quite distinct from that for (differentiated) independence.

However Ken Wilber does not demonstrate how the dynamic interactive nature of quadrants can be consistently interpreted. That is why I maintain - without any hint of exaggeration - that I would characterise his model in intellectual terms as representing a reduced integral approach to development (where the integral aspect is not properly distinguished from differentiated understanding).

Ken indeed frequently makes integral sounding statements regarding the quadrants e.g. that they simultaneously co-arise in experience and that holons necessarily entail all quadrants. However such integral statements are clearly inconsistent with his one-way differentiation of holons (which then inevitably leads to their misleading identification with specific quadrants).

Thus the key task - in integral terms - is to show how we can move from differentiated understanding (establishing the relative independence of quadrants) to properly integrated understanding (where quadrants are seen as relatively interdependent).

Nature of Bi-Directional Approach

Q. So this is where your bi-directional approach is relevant! I know you have already done so repeatedly. However can you explain once more what precisely you mean by a bi-directional approach?

PC Because of the great emphasis on differentiation in our culture, we tend to look on the notion of direction as unambiguous where for example Upper is clearly distinguished from Lower (and Lower from Upper).

However this simply reflects the fact that such understanding is based on the arbitrary fixing of independent polar reference frames.

However when we attempt to view such reference frames as interdependent, the very notion of direction (in any development context) becomes deeply problematic (with Upper and Lower now rendered paradoxical).

As Heraclitus said "the way up is the way down, the way down is the way up". However the dynamic meaning of this statement is rarely properly appreciated.

Because of its truly immense significance for development, I will once again attempt to illustrate with a simple example.

Imagine one is stranded in a desert and encounters a straight road. Now if one arbitrarily points one way and defines it as "up" then the opposite direction (on the road) will thereby be - relatively - "down".

So by fixing our reference pole (i.e. up) in this arbitrary manner one can establish an unambiguous asymmetric notion of direction.

However one could equally have pointed initially in the other direction designating this as "up" whereby the opposite direction would now be - relatively - "down". So once again by arbitrarily fixing the reference pole in this alternative manner one can again establish an unambiguous notion of direction.

Therefore we have two notions of direction which (within their own independent polar reference frames) are unambiguously asymmetric.

However when we attempt to relate such reference frames simultaneously (as interdependent) paradox results.

So what was "up" in terms of the first reference system is "down" in terms of the second; and what was "down" in terms of the first is "up" in terms of the second.

The deep relevance of this illustration is that all development is necessarily conditioned by opposite polarities (e.g. Upper and Lower) which keep switching in experience.

Therefore in terms of any pair of such opposites, we can always arbitrarily fix the polar reference frame for the differentiated interpretation of any event in two equally valid opposite ways.

Though each of these interpretations as independent gives an unambiguous asymmetrical notion of direction, when related to each other, such interpretations are rendered paradoxical (with direction having a merely arbitrary relative meaning).Thus the appropriate means of differentiation for consistent integration is bi-directional (i.e. where every event can be given two equally valid opposite linear interpretations).

However when considered as interdependent, understanding becomes paradoxical and circular (again in bi-directional fashion).

So - in intellectual terms - the integral aspect of understanding is appropriately interpreted in a circular paradoxical fashion whereas by contrast the differentiated is interpreted in a linear unambiguous manner.

Furthermore, true circular appreciation at an integral level must be supported by a bi-directional interpretation (in linear terms).

Q Can you now briefly illustrate this with respect to the notion of a holon?

PC From a dynamic (interdependent) perspective the relationship between whole and part (and part and whole) is circular. In other words the whole is necessarily related to the part; the part is necessarily related to the whole.

"Holon" however literally means whole/part and is defined in an arbitrary fashion through fixing the polar reference frame with the whole aspect.

Thus a holon is thereby defined as a (lower) whole which is also part of a (higher) whole. This thereby defines a consistent vertical direction for development towards ever more collective wholes (i.e. holarchy)

However by fixing our frame of reference with the opposite pole (i.e. part) we have an equally valid differentiated means of defining a holon (or rather an onhol).

So - from this perspective - an onhol is a part-whole whereby a (lower) part is also a whole (in the context) of a (higher) part. This equally defines a consistent vertical direction for development towards ever more unique parts (which we can term "partarchy").

We now have defined two equally valid asymmetrical directions of development, that are holarchical and partarchical within their independent frames of reference. This constitutes the bi-directional (linear) aspect of development (relating to differentiation).

However when we attempt to simultaneously relate both frames of reference as interdependent (befitting integration), the very notion of direction is rendered problematic (with a merely arbitrary relative meaning).

Thus what constitutes "forward" moment with respect to the holarchical direction of development is - relatively - "backward" from a partarchical perspective; likewise what is "forward" from a partarchical is thereby - relatively - "backward" from a holarchical perspective.

This constitutes the bi-directional (circular) aspect of development (relating to integration).

It is important to appreciate - though both aspects necessarily interact in experience in a dynamic composite manner - that the integral aspect of understanding is strictly nondual and spiritual. (Insofar as interdependence has been established therefore separate polarities have no meaning). So it is the clear appreciation of the paradox of dualistic referencing systems - at an intellectual level - that enables the transformation to nondual spiritual insight. Likewise the deepening of such contemplative awareness greatly facilitates the appreciation of paradox at the reduced phenomenal level.

So in the actual dynamics of experience therefore, holons (whole/parts) keep switching to onhols (part/wholes) and onhols (part/wholes) to holons (whole/parts).

Indeed this is another reason why I have reservations regarding the term "holons" (as it implies an unambiguous holarchical direction to development).

However when we attempt to arbitrarily fix the direction of development with its holarchical expression we fundamentally misrepresent the true dynamic nature of experience.

Correctly understood - from an integral perspective - development in a primary sense is neither holarchical nor partarchical. However in a secondary manner it can be given a relative phenomenal interpretation (which keeps shifting direction).

Thus the holarchical approach to development represents an arbitrary one-directional (linear) differentiated interpretation of the vertical aspect (where an opposite partarchical interpretation is equally valid).

Clearly therefore - in the context that I define it - the holarchical approach is not integral.

To move to integral appreciation, we must first interpret the differentiated aspect of development in bi-directional (linear) terms through recognising the equal validity of both holarchical and partarchical expressions.

Thus we obtain bi-directional (circular) appreciation enabling appropriate interpretation of the integral aspect through recognition of the dynamic complementarity of opposite poles. This in turn yields a paradoxical appreciation of both directions (i.e. the way "up" is the way "down" and the way "down" is the way "up").

What is represented here is consistent with an Integral 1 approach (that deals with the relationship between directly opposite poles). As we have seen, this requires Type 1 (linear) differentiation and also Type 1 (circular) integration, both understood in a bi-directional fashion. This in turn represents the refined cognitive understanding of H1 (the subtle realm).

This I feel is sufficient to deal with the integration of phenomena (represented in merely conscious terms).

A much more intricate form of integration i.e. the Integral 2 approach (incorporating Type 2 differentiation and Type 2 integration) is required to incorporate the unconscious with the conscious interpretation of phenomena. This entails a consistent interpretation of poles which are not directly opposite each other (i.e. horizontal and vertical and vertical and horizontal) and requires a very refined cognitive interpretation of the dynamics of H2 (the causal realm).

The most complex form of integration i.e. Integration 3 (with Type 3 differentiation and Type 3 integration) is required to incorporate both the conscious and unconscious directly with spiritual type appreciation. This in turn requires relating diagonal with both horizontal and vertical poles in a consistent manner using the extremely refined cognitive interpretation of the dynamics of H3 (nondual reality).

Integral 1 Approach and the Four Quadrants

Q Briefly how would you suggest that Integral 1 understanding can be used to achieve a more consistent approach to the four quadrants?

PC As I have stated, with one set of polarities two equally valid opposite differentiated interpretations can be given for any event.

So when we use two sets of polarities (as with the four quadrants) then four equally valid opposite differentiated interpretations result.

Each set of interpretations is based on an arbitrary fixing of the polar reference frame.

For example we might initially attempt to fix a scientific observation with - as conventionally defined - the UR quadrant.

However when we accept that every exterior event has an equally valid opposite interpretation, then we can also fix it with the UL quadrant.

Then with respect to the vertical polarities, every individual event has also a collective understanding. So this enables in turn both LR and LL interpretations of the event.

Therefore it is certainly true that when we arbitrarily fix our frame of reference (with respect to both horizontal and vertical polarities) that any differentiated event will appear to belong to one specific quadrant (yielding a distinctive perspective).

However through appreciating the bi-directional nature of differentiation, we recognise that the polar frame of reference can always shift to the opposite quadrant (yielding an equally valid distinctive perspective).

Therefore because we can shift the frame of reference with respect to both horizontal and vertical aspects, then four distinctive perspectives can be given for any one event.

In other words an event that initially was unambiguously identified with just one quadrant is now seen - through bi-directional differentiation - to have valid interpretations in each of the four quadrants.

We have already illustrated this with respect to the vertical polarities, where we showed that any event can be given both holarchical or partarchical interpretations (which are opposite with respect to each other). Thus an event that is defined in the Upper quadrants with respect to holarchical interpretation will thereby be - relatively - defined in the Lower quadrants (in a partarchical manner).

It is quite similar in heterarchical terms (where exterior and interior are - dynamically - opposite in direction to each other) so that in a bi-directional sense, events will shift as between horizontal quadrants (depending on which perspective is adopted).

In other words we have four distinct ways of referencing the quadrants.

However integration is distinct from differentiation. So again, integration entails the simultaneous attempt to reconcile opposite frames of reference (in both horizontal and vertical terms). This implies that all events move - relatively - "forward" and "backward" (and "backward" and "forward") with respect to each other in both horizontal and vertical directions.

This paradoxical notion of direction is alone consistent with the nondual spiritual appreciation of the event (which represents the integrated aspect of perspectives).

So we have both a differentiated and an integral appreciation of perspectives (which should not be confused with each other).

The differentiation of perspectives always relates to the attempt to arbitrarily fix events according to the reference frame of one quadrant.

As we have seen one-directional (linear) differentiation attempts to fix events absolutely (i.e. solely with one quadrant) and is inconsistent with the movement to integral appreciation.

Bi-directional (linear) differentiation fixes events relatively (with each of the four quadrants) giving rise in turn to the differentiation of primary (or primordial) perspectives.

Bi-directional (circular) integration comes from the simultaneous attempt to reconcile differentiated interpretations (which are opposite with respect to each other) always leading to a merely paradoxical notion of direction. This in turn is consistent with the integration of primary perspectives.

From an integral perspective we cannot unambiguously distinguish Right-Hand from Left-Hand or Upper from Lower. Neither can we unambiguously distinguish 1st person from 2

^{nd}person or 1st person from 3^{rd}person (or indeed 2^{nd}person from 3^{rd}person).Therefore perspectives based on these designations are again - clearly in the context that I define them - of a differentiated rather than a properly integral nature.

Perspective on Perspectives

Q Can you comment briefly on Ken Wilber's recent work on perspectives. Do you see this as a fundamental advance regarding the implications of quadrants? Also, how do you view his development of an integral mathematical approach to designate perspectives?

PC In fairness to Ken I do not wish to give a very detailed assessment at this stage (as proper assimilation of any new position takes time).

However I will make a few general comments which - in the context of my own approach - do appear valid.

Firstly I would see his perspectives approach - as in the designation of his event horizons or hori-zones - as an interesting modification of the somewhat limited four-quadrant model (where the locations are unambiguously fixed). We now seem to have in relation to the horizontal aspects, the beginning - though still in merely differentiated terms - of a more refined bi-directional treatment.

So Ken now recognises that all quadrants have both an inside and an outside. However this refinement cannot really be properly accommodated while attempting to maintain a static representation of the quadrants (i.e. where locations are fixed in unambiguous terms).

Saying that the four quadrants can be looked at from the inside and outside can equally be expressed by saying that they have interior and exterior aspects. This in turn implies that interior and exterior quadrants have both interior and exterior aspects (which starts to render such notions as paradoxical).

In other words it calls into question the very basis on which Ken attempts to define his quadrant locations.

Now of course this is what should be the case (i.e. paradox) from an integral perspective, but because of the lack of dynamic interpretation, Ken seems at present to be avoiding rather than embracing such implications.

I suggest that the logical next step for Ken is to recognise that each quadrant can

equally be looked at from an individual and collective perspective (indicating therefore that each quadrant location can in fact shift between all locations).With the inclusion of this vertical dimension, we would then have 16 primordial perspectives.

However I would suggest that the correct - and inherently more dynamic - manner of representing these perspectives is through proper recognition of the manner in which quadrant locations themselves dynamically shift in relation to each other in experience, giving four distinctive mappings of quadrant locations. So in this context the four quadrants yield 16 (i.e. 4 X 4 primary perspectives).

However in an eight-sector approach (which I believe is necessary to comprehensively model reality) we would generate 64 primordial perspectives (i.e. 8 X 8).

So I would see Ken's perspectives as representing - in a still somewhat static manner - the growing recognition that because quadrant locations can shift in experience (a greater number of primordial perspectives than quadrants exist).

However the appropriate differentiation of perspectives - though valuable - does not constitute integration.

Once again proper integration requires the (circular) complementary pairing of interpretations based on opposite poles (and I cannot see as yet this type of understanding reflected in Ken's approach).

In the Appendix where Ken introduces his Integral Mathematics he seems to be largely dealing with composite rather than primordial perspectives and once again in a manner which concentrates on their differentiated (rather than integral) aspect.

I do not greatly favour the language of 1

^{st}person, 2^{nd}person and 3^{rd}person perspectives for the simple reason that such common use of terminology does not adequately reflect the important complementary relationship between opposite quadrants (which is the basis for true integral understanding). It is important therefore in a dynamic sense to recognise that the personal aspect has no meaning in the absence of the impersonal; equally of course the impersonal has no meaning in the absence of the personal.Ken in his treatment of quadrant locations attempts to dualistically split personal and impersonal aspects through an arbitrary identification of the Left-Hand quadrants with the personal and the Right-Hand quadrants with the impersonal aspect respectively.

Of course the mirror image interpretation - which is equally valid - is in the recognition that all "objects" necessarily have a personal, and that all "subjects" likewise an impersonal aspect. Indeed the very dynamics through which we are enabled to switch between both aspects (i.e. personal and impersonal) in experience implicitly requires recognition of their complementary nature.

Now in his perspectives approach (at least this version in the Appendix, he seems to me to be over-emphasising the personal language of perspectives) which as I say, does not directly lend itself to complementary type appreciation (i.e. where personal and impersonal aspects are understood in dynamic balance). Now of course such complementarity is indirectly implied through correct interpretation of the personal language of perspectives. However it makes the integral task ultimately much more difficult.

Also - as is habit - Ken seems to me to already throwing out a variety of perspectives (on perspectives) which are not directly consistent with each other.

In any approach that is designed as integral this is a major shortcoming. There is a danger that we will get a profusion of many differentiated perspective systems (based on varying interpretations of the meanings implicit in ordinary language terminology) with no clear indication given as to how these can be properly integrated in experience.

As regards Ken's Integral Mathematics, admittedly he has valuable insights to offer regarding its all-quadrant nature. Again in his recognition that an equation can be given both an interior and an exterior meaning, seems another indication of bi-directional appreciation.

Ken's interpretation here is in fact consistent with the concrete expression of - what I refer to as - the Analytic 3 approach, which represents a "higher" stage than vision-logic (Analytic 2).

Indeed for me this represents the most interesting development in Ken's latest work in that it represents intellectual interpretation that in many respects has moved strictly beyond centaur vision-logic in concrete terms (though still not adequately reflecting dynamic paradoxical type appreciation).

However, if I am correct that Ken is growing into a new analytic stage of intellectual interpretation, this will inevitably create problems in terms of the consistency of his latest views with earlier work.

For example his present take on the nature of Mathematics is not properly consistent with his earlier identification of Mathematics in "The Marriage of Sense and Soul" with the interior quadrants!

More significantly, he will need I believe to reformulate his previous characterisation of the nature of science.

Ken attempted to portray science as "monological" being confined solely to the Right-Hand quadrants. However this never really made sense, even in terms of Ken's formulation of the quadrants!

(Individual) empirical data (exterior) can only be registered through corresponding (interior) perceptions. Likewise (collective) hypothetical constructs (exterior) can only be registered through (interior) concepts.Of course scientific constructs are often dictated by the needs of empirical research (so that the interior is thereby made dependent on the exterior aspect).

However equally the interior can dominate the exterior as with the formulation of new theories (as with present String Theory).So science therefore is necessarily an all-quadrant affair though it can be biased in terms of certain quadrants (depending on context).

However it is true that science largely operates from an impersonal primordial perspective (3rd person view of 3rd person reality) with respect to the quadrants and that in this sense it is indeed limited. So this would provide a much more accurate manner of defining its true nature.

Unfortunately Ken's differentiated approach on perspectives is not capable of dealing with the other serious limitation of conventional science i.e. that it is interpreted in merely static terms (where the interaction as between opposite quadrants is thereby effectively frozen).

For the most part such science accepts - in effect - the double correspondence view whereby (exterior) events are not changed through (interior) understanding and likewise (interior) interpretations remain unchanged through (exterior) application.

True integral appreciation therefore requires the interpretation of opposite quadrants to take place in dynamic terms whereby the nature of understanding is thereby changed through interpretation (and the nature of reality is altered through the application of mental constructs). This is likewise associated with a new integral perspective (i.e. overall perspective) whereby the role of science is understood in an entirely new light.So I am drawing attention to the need for clarfication of the vertical integral nature of perspectives (i.e. overall perspective) for each stage of development.

With respect to the notational system that Ken employs to encode perspectives (primordial and composite), though it is very interesting in its own right and will undoubtedly lead to valuable insights, I would see it very much as representing a language of differentiation (rather than integration).

The final difficulty I would see again with his treatment of perspectives at this stage is that it seems to be lacking any real vertical dimension (which is closely associated with a corresponding lack of direct focus on integral interpretation).

Now it is true that a certain integral appreciation (overall perspective) must already be in place before primary perspectives can even arise in experience.

I would also accept for example that all development - at whatever stage - is necessarily characterised by the interaction of primary perspectives. However the quality of this interaction changes for each stage and indeed in a sense thereby defines its very nature.For example at the earlier prepersonal stages, these perspectives in certain respects will not yet be properly distinguished from each other thereby operating in a somewhat confused manner.

Appropriate (i.e. one-directional) differentiation of distinct perspectives will then take place at the middle stages. However it is only with the unfolding of the "higher" spiritual levels, that the proper interdependence of perspectives (i.e. overall holistic perspective) can be established.

So I would maintain that true integration of primordial perspectives is the appropriate task of the "higher" levels of development and that an integral treatment must therefore deal convincingly with this issue.

Then the most advanced expression of development - which I refer to as radial reality - combines the mature (nondual) integration of perspectives with a very flexible multifaceted appreciation of the relative validity of distinct partial perspectives (that depend on context).

I would in fact divide the treatment of perspectives into three main areas.

"Analytic Studies" which would be largely devoted to the task of clearly distinguishing the major perspectives (primary and composite) involved in experience. This is the work that I see Ken so fruitfully engaged on at present.

"Integral Studies" would then be concerned with establishing the nature of the overall holistic perspective - defined by a characteristic manner of interpreting the interaction of distinct perspectives - that is appropriate in terms of the understanding of each stage of development.

For example a formulation that is viewed as effective in terms of the vision-logic interpretation of the centaur, would thereby be inappropriate in terms of the more refined bi-directional formulation that I believe is now emerging in Ken's views. In other words a change is taking place in Ken's overall holistic perspective on development (which will inevitably lead to a certain inconsistency with respect to previous positions).

Finally "Radial Studies" would be concerned with understanding of the flexible interplay of a variety of distinct perspectives within an overall holistic perspective that has become highly integrated.

Ultimately it is concerned with providing the most comprehensive - and consistent - understanding of the nature of dynamic interactions. This then becomes the means of seeing clearly into the strengths and limitations of the other approaches.

Much of my own work has been devoted to clarification of this vertical notion of perspectives with the recognition that associated with each major stage of development is a unique intellectual manner of interpreting reality (which we will deal with in much greater detail in future discussions).

Indeed I would consider the issue of vertical holistic perspectives central to the fruitful discussion of intellectual ideas and the future development of "Integral Studies".

Because of Ken Wilber's enormous influence there is a danger that his approach will be prematurely viewed as providing the appropriate overall perspective for future research in the field.

I can already see ample evidence of this in the manner the Integral Institute has been formulated and the way in which criticism is often misunderstood (both by Ken and his supporters) through an unwillingness to look outside a Wilberian perspective.

Because Ken's overall approach is indeed so remarkably comprehensive, many therefore equate this with integral.

However let us assume for the point of argument that my own fundamental criticism of his work is substantially correct i.e. that it unduly reflects the intellectual understanding of the centaur, whereas a true integral approach (that is consistent) requires the more refined bi-directional understanding associated with the "higher" levels.

Then in this case the Wilberian perspective would - by definition - not be adequate to properly "see" the nature of the criticism addressed. So clearly then we need to accept the need for new overall perspectives for fruitful discussion to even take place on such issues (with perhaps the eventual realisation that what seems most comprehensive may not necessarily be most integral).

I think that it would be much healthier at this stage to recognise that the future of "Integral Studies" would be better promoted through the encouragement of several distinctive perspectives especially those that attempt to adequately reflect the intellectual understanding of "higher" spiritual levels of the Spectrum. (I am providing one such approach based on a strong scientific type rationale. I would be delighted to see other attempts to deal with these levels using alternative approaches!) This would help to deal with very important issues that have not yet been addressed.

Q Coming back to holons I notice that you generally refer to their exterior and interior (and individual and collective) aspects as poles?

PC This is correct because I believe that in the context of my approach "poles" is a stronger term than aspects (and more suggestive of the relationships I see as important).

The use of the term "poles" immediately draws attention to the fact for example that interior and exterior aspects are indeed opposite.

Then I would emphasise the fact that there is a linear (asymmetric) manner of dealing with opposites (where they are treated as independent) and a circular paradoxical manner (where they are treated as complementary i.e. interdependent).

Furthermore the linear (asymmetric) approach is directly associated with differentiation, whereas the circular (paradoxical) approach is suited to integration.

Again I would see a considerable weakness in Ken's general approach to development, in that it is greatly lacking in this complementary type appreciation (which is characteristic of integration).

Even when he appears to be dealing with complementary relationships (as in the Chapter in SES "The Way up is the Way down", closer examination reveals a somewhat linear - and thereby misleading - interpretation.

So I would suggest that a first step towards a truly dynamic understanding would be to accept that all holons are conditioned by opposite polarities (with both linear and circular interpretations).

Q However you would rather refer to "holons" as "relationships"?

Yes! More correctly I would say that all relationships are conditioned by opposite polarities which can be given both a linear (differentiated) and circular (integrated) interpretation. This avoids confusing the implicit rules governing all relationships - which are mathematical in a dynamic holistic sense - with specific phenomena, thereby enabling a more consistent universal type understanding.

Furthermore I would see three (rather than two) fundamental polarity sets as necessary and sufficient for the phenomenal interpretation of relationships.

So using geometrical language (which has a firm holistic mathematical rationale) we have horizontal polarities i.e. exterior and interior (and interior and exterior), vertical polarities i.e. part and whole (and whole and part) and twin diagonal polarities i.e. transcendence and immanence (and immanence and transcendence). The diagonal polarities have an alternative explanation in terms of affective and cognitive (and cognitive and affective) poles. Therefore from a dynamic perspective all relationships are defined in an ontological manner (i.e. characterised by experiential being).

In my approach every stage is defined in terms of a unique configuration of the three fundamental polarities (with respect to both linear and circular interpretation).

Q Briefly how would you characterise your holistic digital binary system?

PC Perhaps the simplest way of expressing it is as the recognition that the interpretation of all development processes is characterised by both linear (1) and circular (0) aspects, the precise configuration of which can be uniquely characterised for each stage. 1 in this context represents "oneness" which is characteristic of the recognition of form. 0 - by contrast - means "nothingness" - i.e. in phenomenal terms - which is characteristic of spiritual emptiness.

Expressed in more detail we can say that all phenomenal reality is conditioned by the relationship between opposite poles, which can be characterised in - relatively - "real" (horizontal), "imaginary" (vertical) and "complex" (diagonal) terms.

Furthermore the relationship between these poles can be interpreted in (differentiated) linear terms as unambiguous form (1) or in (integral) bi-directional circular terms as paradoxical form (1 - 1) where equally, paradoxical form (1 - 1) is associated with spiritual emptiness (0).

1 (i.e. + 1) is here associated with the positing of form (i.e. in a unitary manner); - 1 is here associated with the dynamic negation of form.