An Integral Theory of Everything (1)

Introduction
 
We live in an age that is increasingly dominated by digital technology
All data can be potentially encoded though use of the binary digits 1 and 0, which can be readily adapted for use in electronic circuits. This in turn enables the transfer of increasingly complex forms of information e.g. in computers, telecommunications and entertainment.
Number provides the best means for the quantitative ordering of information and is widely synonymous with this role. Indeed in this context the binary numbers 1 and 0 provide the most fundamental symbols and as we have seen with digital technology, they provide an extremely important example of the power of number to order information.
In conventional terms number is understood in static analytic terms.
So the binary digits are based on an either/or logic, which are defined in an unambiguous manner where they are clearly separated from each other.
However what is not yet properly appreciated is that all-mathematical notions such as number have dynamic holistic interpretations incorporating an alternative both/and logical system. 1
The implication of this alternative appreciation is enormous as it directly implies that mathematical symbols can also be used in a precise scientific manner to translate an integral vision of reality. 2
So just as science - as conventionally understood - requires the use of analytic interpretation provided by mathematical symbols, equally - from this perspective - integral science, representing a dynamic universal appreciation of reality, requires a corresponding holistic interpretation of these same symbols.
 
In this context let me immediately address one key application of this holistic interpretation.
We have just commented on how the (analytic) interpretation of the binary digits can be used to potentially encode all information processes.
Quite remarkably, the dynamic (holistic) interpretation of these same digits can be used in a corresponding manner to potentially encode all transformation processes.
 
Phenomenal existence in all its varied manifestations, human and natural, represents a dynamic transformation process. So for example, all key structures with respect to the Spectrum of Development - both psychological and physical - can be precisely encoded in a binary digital manner.
I firmly believe that such a translation - based on deep appreciation of the holistic interpretative power of mathematical symbols - is urgently needed to provide a scientific translation of development that is fully integral. Equally, it can greatly facilitate the opening up vast new areas of inquiry that would be virtually impossible to access by other means.
So the purpose of this series of articles is to explain some basic features of the holistic mathematical approach. We will then show how it leads to a dynamic "Theory of Everything", directly based on the binary system, that can be used in a wonderfully coherent - yet extremely detailed - fashion to precisely encode the fundamental structures underlying all stages of the Spectrum.
 
 
Numbers
In order to outline properly the nature of this holistic binary system, we will now introduce a series of related holistic mathematical concepts.
 
The binary digits
We start with the fundamental binary numbers 1 and 0.
Firstly, let us examine these numbers in analytic terms.
Implicit in the distinction of any (separate) form is this notion of oneness. (If I for example notice a house, I implicitly recognise it as a unit i.e. one object). 3
Likewise generalised notions of form imply the recognition of more holistic notions of oneness.
By contrast 0 in analytic terms implies the absence of form and the notion of nothingness (or emptiness). Thus, if for example a box is empty, there is nothing in it.
So in analytic terms 1 is directly identified with form and 0 with emptiness respectively. Furthermore these notions are clearly separate (i.e. mutually exclude each other).
However from a dynamic holistic perspective form (1) and emptiness (0) become increasingly interdependent (and ultimately identical).
Indeed the holistic use of these digits is deeply implicit in the understanding of the mystical traditions.
Western traditions tend to approach the ultimate mystical experience from the perspective of form. Thus the highest experience is typically identified as oneness i.e. the experience of union. (Here the separation inevitably attached to merely dualistic notions of form is finally eroded). Indeed in Christian mysticism the most advanced stage is commonly referred to as the unitive life (which is another expression of oneness). 4
In the Eastern esoteric traditions the ultimate experience is frequently approached through the corresponding notion of emptiness. Here the highest experience is often identified in terms of a creative void or spiritual emptiness that is absent of phenomena.
Of course ultimately, in balanced mystical terms, these two aspects are themselves identical and the most complete experience is identified as a plenum-void where the pure potential of emptiness continually gives way to a refined world of form.
"Form is not other that Void
Void is not other than Form"
Thus though the binary digits are completely separate in analytic terms, ultimately from a dynamic holistic perspective they are identical.
In dynamic terms, form and emptiness, in both their separate and complementary aspects, continually interact and provide the basis for all development processes.
A key task in integral terms is to show how experience moves from the dualistic identification of form (where it is separate from emptiness) to the nondual experience (where it is dynamically complementary with emptiness).
Alternatively we could say the task is to show how understanding moves from the appreciation of differentiated phenomena to the experience of their corresponding integration.
This requires showing that the binary digits, which are separate in analytic terms, are yet ultimately identical from a dynamic holistic perspective.
 
 
Operations
 
Addition and subtraction
To appreciate how the binary digital approach can be applied to this important task of moving from dual to nondual appreciation we now need to introduce the two most familiar operations in mathematics i.e. addition and subtraction.
Once again these operations can be given both analytic interpretations that are unambiguous and holistic interpretations that are paradoxical.
In mathematics from an analytic perspective, addition carries a positive sign whereas subtraction carries a negative sign.
Thus in analytic terms 1 is related to 0 through combining both its positive and negative signs. i.e. 1 - 1 = 0. (1 = + 1)
We have here a static transformation of 1 (through combining both signs) that leads to 0.
Alternatively we could say equally that 0 is related to 1 though reversing the direction of this transformation i.e. 0 = 1 - 1.
So to move in analytic terms from 1 to 0, or 0 to 1, we must negate what has been statically posited (i.e. 1).
 
Once again, we have exact matching dynamic holistic interpretations of these two mathematical operations, which are fully complementary.
Here the two operations relate to the fundamental manner through which phenomena are posited and negated in existence.
In psychological terms to posit is simply to make conscious thus enabling differentiation of phenomena. 5
However interaction with the unconscious requires corresponding negation. The implicit recognition of the other pole then enables a switch in experience to take place (to this opposite pole). So in terms of exterior and interior poles, recognition keeps switching from exterior to interior (and interior to exterior).
When complementary reference frames are not properly recognised, one thereby identifies with the merely positive pole so that considerable reductionism takes place. Phenomena obtain a rigid unambiguous identity (with the opposite pole becoming largely repressed in the unconscious). Limited dynamic negation can then take place greatly impeding balanced interaction in experience.
However when complementary poles are clearly recognised through growing spiritual awareness, a far greater degree of balanced negation is possible. Phenomena then reveal their inherent mystery and become increasingly transparent. This in turn facilitates a more dynamic flexible interaction between poles.
Ultimately the purest experience of spiritual emptiness results from complete dynamic negation of all phenomena as soon as they are posited.
Because phenomena are now successfully negated the moment they arise they do not even appear to be present in experience. This in turn leads to a total immersion in spiritual emptiness.
A beautifully simple explanation of these dynamics can be given in holistic mathematical terms, where we combine the two binary digits with the fundamental operations of positing and negating.
From one perspective
1 - 1 - 0
In dynamic holistic terms, when the positive direction of form (i.e. 1) is completely negated by its opposite (- 1), emptiness (i.e. 0) results.
So here in this simple relationship we have a proper dynamic balance maintained as between form and emptiness. Emptiness in this context cannot be conceived in the absence of form.
We could equally say from the opposite perspective that
0 = 1 - 1.
In other words a state of emptiness is the very basis for positing and negating form.
So in the highest mystical experience of reality, refined form continually gives way to emptiness and emptiness to refined form.
So when we say that form is not other than emptiness we are referring to a dynamic notion of oneness where the positing of form is fully balanced in experience by its corresponding negation.
Equally to say that emptiness is not other than form refers to the corresponding reality that emptiness (nothingness) represents the pure potential for the creation of a world of form (in both its positive and negative aspects).
However by definition the dual and nondual aspects necessarily interpenetrate at all levels of experience. So the nondual can only be experienced to the extent that the dual is negated. Likewise the very ability to creatively experience the dual world of form depends on the degree of nondual awareness already present.
Putting it in yet another way directly pertinent to my approach, differentiation in experience is always based on the positing of phenomena. Integration by contrast - at least implicitly - requires their corresponding negation.
Therefore when the negative direction is not properly emphasised in experience, integration cannot fully take place. A reduced experience of integration then results where it is unduly identified with differentiation. 6
Thus a proper integral approach must incorporate the negative (as well as the positive) direction of experience.
To appreciate more deeply the precise nature of this integral approach we will now introduce some fundamental geometrical notions.
 
 
Geometry
 
Line, circle and point
 
 

Once again we start with the analytic interpretation of symbols.
Above we have a circle with its diameter represented by a horizontal line. The radius of this circle (i.e. half the diameter is 1 unit).
Now when we examine this line we find that it has two directions.
So starting from the centre point (which is represented by the o (the origin which is 0), movement to the right is defined as positive. So the radius in a right direction is  + 1.
However movement in the opposite direction is thereby negative.
So the radius in a left direction is - 1.
However it is important to understand that the identification of sign is merely an arbitrary convention.
We could equally define movement of the line to the left as positive, in which case corresponding movement to the right would be negative.
The very symbol, which is used to represent one, is in fact a straight line. Likewise the symbol used to represent zero (nothing) is - with very minor modification - a circle.
There are intimate connections as between 1 and 0; likewise there are intimate connections as between the line (diameter) and the circle (circumference).
Just as numerically 0 is connected to 1 through combining the positive and negative signs of 1 (i.e. 0 = 1 - 1), likewise the circle (circumference) is connected to the line through combining both the positive and negative directions of the line (diameter).
So both directions of the line (drawn from the centre) are enclosed by the circumference of the circle. Likewise this bi-directional line defines the nature of the corresponding circular circumference.
 
Holistic Interpretation
Now once again there is an extremely important dynamic holistic interpretation of these same symbols - the proper appreciation of - which greatly clarifies the very nature of both differentiation and integration in development.
In relation to the notion of a line we have in holistic terms a linear approach to development.
In relation to the notion of a circle we have a corresponding circular approach.
Positive and negative equally define opposite poles of development.
Quite simply when we look at development asymmetrically (i.e. solely with respect to its positive direction) we thereby adopt a linear approach.
This always entails an arbitrary fixing of the frame of reference with just one pole (whereby it is treated as largely separate from its opposite pole).
This can be made much clearer through a simple illustration.
It has become customary to interpret development in holarchical terms.
For example we might say that the atom is transcended and included in a molecule which is transcended and included in a cell which in turn is transcended and included in an organism and so on in an ascending sequence of more collective wholes.
Now this represents - as I define it - the linear approach.
In dynamic terms our experience of the world entails the self in relation to the environment so that interior and exterior poles necessarily interact.
However with (linear) asymmetrical understanding there is always an attempt to define experience unambiguously with respect to one pole (as reference frame).
So in our example, the reference frame is fixed with the exterior pole and relationships then viewed as if somehow independent of the interacting mind.
Relationships here are defined with respect to the positive pole (in this case the exterior) and viewed as moving solely in one-direction leading to the typical asymmetric interpretation e.g. atoms are included in molecules; thereby molecules are not included in atoms.
Now I am not criticising such linear interpretation. It plays an extremely important role in understanding and is vitally necessary for the proper differentiation of experience.
Rather - with the help of fundamental holistic mathematical concepts - I am defining its true nature.
So (linear) asymmetric understanding always results from the attempt to understand in terms of just one arbitrarily fixed reference pole (though the opposite pole is equally valid).
However as we have seen with our circle, we could equally define understanding in terms of the other pole as reference frame (in this case the interior) leading to an opposite asymmetric interpretation of development which is equally valid.
By definition we cannot hope to reconcile these paradoxes within a linear approach which is necessarily partial. Therefore when we come to translate integration in experience (as opposed to differentiation) a very distinctive approach is required.
In simple terms proper integral translation requires a balanced circular approach (which fully recognises the true complementarily of opposite poles of development).
Now this is beautifully symbolised in the diagram of the line and circle.
So in holistic terms the circular approach includes two linear directions of interpretation that are always opposite in terms of each other.
In other words circular understanding results from linear understanding that is dynamically bi-directional.
It leads in turn to the deep realisation - trough clear recognition of the arbitrary fixing of polar reference frames - that all dualistic understanding can be rendered paradoxical.
Now the actual recognition of such paradox is nondual and arises through deepening spiritual awareness.
However form and emptiness are themselves dynamically complementary. Therefore the appreciation of paradox at a dualistic level acts as a catalyst towards its reconciliation through spiritual intuitive awareness. Equally the deepening of this awareness sharpens recognition of the inevitable paradox at a dualistic level. So bi-directional appreciation of form and spiritual intuition, increasingly interpenetrate mutually enhancing each other.
 
Duality and the number 2
After 1 and 0, 2 is the next most important number.
In mathematical terms it can be simply derived from 1 in this manner;
1 + 1 = 2.
Therefore whereas 0 derives from combining 1 with 1 using opposite signs (i.e. 1 - 1), 2 by contrast is derived from combining 1 with 1 using the same sign.
As before the holistic interpretation of 2 can be obtained in similar manner where now the interpretation of symbols carries a dynamic rather than a static meaning.
So in dynamic holistic terms 1 + 1 = 2.
What this in fact implies is that duality derives from combining opposite poles that are defined in a positive manner.
In other words duality results from the separation of opposite poles with both now recognised in terms of their merely positive (i.e. phenomenal conscious) aspect.
For example objective and subjective constitute opposite poles. Now from a nondual spiritual perspective there is a dynamic coincidence of opposites in union (which equally constitutes a creative void or emptiness).
However from a dualistic phenomenal perspective, objective and subjective poles are always - to a degree - separated so that literally these poles come into opposition with each other.
Thus a world of (objective) phenomenal form is now experienced in opposition to a (subjective) observing self and equally from the opposite perspective the (subjective) self is experienced in opposition to the (objective) world..
So duality always results from a splitting off or separation of opposite poles e.g. subjective and objective, whole and part, form and formlessness (which from a nondual spiritual perspective are ultimately identical).
In view of these fundamental holistic mathematical relationships, let us explore briefly the dynamics of how the self interacts with the world in terms of the horizontal i.e. exterior/interior poles.
The very interaction of both poles implicitly requires nondual awareness (where to a degree they are seen as identical). So in this awareness the opposite poles of form (1 - 1) cancel out in nondual spiritual awareness (0).
However the phenomenal identification of dualistic phenomena (exterior or interior) requires a degree of separation of both poles (as positive) so that they are experienced in opposition to one another. Here 1 + 1 = 2 (In other words the separation of both polar aspects of form leads to duality).
Now the switching in experience as between both poles results from the conflict as between the nondual awareness (where they are implicitly identical) and their dualistic separation in the experience of conscious phenomena.
If nondual awareness is largely undeveloped, little dynamism in this interaction will be possible.
Therefore phenomena will tend to become rigid and dense with subjective (interior) attitudes and objective (exterior) events mutually confirming each other in a non-creative fashion.
However where a very significant level of nondual awareness exists (as with the mystical stages of development), considerable dynamic interaction can take place. This then leads to very creative understanding that serves to highlight the paradox associated with dualistic understanding based on isolated poles. This in turn acts as a necessary catalyst for the reconciliation of such paradox through a transformation in nondual spiritual awareness. In this way transformed nondual awareness and (reduced) bi-directional paradoxical understanding mutually support and enhance each other.
 
 
Horizontal, Vertical and Diagonal Polarities
 
 

We can draw the (bi-directional) line diameter of the circle as a horizontal line.
However equally we can draw it as a vertical line (through the centre at right angles to the horizontal).
Finally we can draw it as two diagonal lines (though the centre at an equal distance from both horizontal and vertical).
These lines have immense significance in dynamic holistic terms relating to the most fundamental designation of polar opposites.
 
Horizontal Poles
The horizontal line can be used to represent polarities that condition experience within a given level of experience.
These relate to the important objective/subjective (and subjective/objective) polarities which can be referred to in various ways e.g. exterior/interior, external/internal, outer/inner etc. In holistic mathematical terms these polarities are positive and negative with respect to each other.
In other words - whatever the level of understanding - phenomenal experience necessarily entails exterior and interior (and interior and exterior) poles that are in dynamic relationship with each other.
It is important to appreciate that the relationship between poles can be interpreted in two ways
1) Differentiation: here opposite poles are relatively separated leading to (asymmetrical) dualistic understanding.
As we have seen in precise terms this means that both poles are understood in terms of their (merely) positive aspect (i.e. 1 + 1 = 2). Understanding is here linear and unambiguous in one-directional (asymmetric) terms.
2) Integration: here opposite poles are understood as relatively complementary (and ultimately identical) leading to bi-directional dualistic understanding. This is inherently paradoxical (in dual terms) and is reconciled through a dynamic transformation to nondual (spiritual) awareness (i.e. 1 - 1 = 0). So in dynamic terms understanding here is both linear and paradoxical - in bi-directional (symmetric) terms - and circular and nondual. So just as the bi-directional line diameter and the circular circumference are intimately related in analytic geometric terms, likewise bi-directional linear understanding and nondual circular understanding are intimately related in a holistic mathematical fashion. 7
In dynamic terms therefore - for all transformation processes in development - we have the ceaseless interaction of the two aspects of differentiation and integration.
Once again in the first case opposite poles separate in development (though of course never completely separate).
In the second case these opposite poles to a degree unite through recognition of their complementary nature (though again never completely).
So development is characterised by the relationship between opposite poles that is always to a degree dual (where they are separated) and nondual (where they are complementary) though the balance can vary greatly.
 
Vertical Poles
The vertical line can be used to represent poles that condition experience between various levels of experience.
These relate to the extremely important whole/part (and part/whole) polarities that can again be expressed in various ways e.g. individual/collective, particular/general, quantitative/qualitative etc. Once again in holistic mathematical terms these are positive and negative with respect to each other.
Strictly speaking whole/part transformations in development always entail changes in the level of development. Thus from the perspective of holism, evolution involves the movement of reality to more complex whole levels of (collective) organisation. Equally evolution here entails the movement from lower quantitative (physical) to higher (spiritual) structures. 8
As with the horizontal poles (within a given level), the relationship between vertical poles (between levels) can be given a (linear) differentiated interpretation and a (circular) integrated interpretation respectively.
 
The Four Quadrants

When we combine both horizontal and vertical lines through the mid-point of the circle we literally create four quadrants in geometrical terms.
In analytic terms the first important thing to observe is that these quadrants - by definition - combine both lines and circle.
Therefore in corresponding holistic terms the interpretation of the four quadrants combines both linear and circular notions.
Likewise - as we have seen - the signs of the lines in opposite quadrants are positive and negative with respect to each other respectively. By convention the sign of the horizontal line in the Right-Hand quadrants is positive and the Left-Hand negative; also the sign of the vertical lines in the Upper quadrants is positive and the Lower negative. (However we are equally entitled to fix the sign of the horizontal line in the Left-Hand quadrants as positive with the corresponding sign in the Right-Hand as negative; also we can fix the sign of the vertical line in the Lower quadrants as positive with the sign in the Upper Quadrants negative).
Though in dynamic terms the signs in each quadrant, horizontally and vertically, keep switching, in a rigid linear interpretation the positive direction is solely emphasised (in each of the four quadrants). Thus the direction of development appears similar for each quadrant (moving from lower to higher levels in each case). However this position is untenable from a proper dynamic perspective.
Again in dynamic holistic terms, linear understanding is positive and negative (i.e. complementary) with respect to opposite quadrants.
Thus though the direction of understanding - in horizontal and vertical terms - is unambiguous for each quadrant taken separately, when opposite quadrants are related to each other the directions are complementary and paradoxical
So once again the task of differentiating and integrating quadrants has to be clearly distinguished. When differentiating, the direction of movement (for each isolated quadrant) appears unambiguous; however when integrating the directions for opposite quadrants are complementary and paradoxical. 9
 
Diagonal Poles
The two diagonal lines can be used to represent poles that condition experience (simultaneously) both within and between the various levels of experience.
These relate to the most fundamental form/emptiness (and emptiness/form) polarities that can be also expressed in various ways i.e. actual/potential, finite/infinite, immanent/transcendent etc.
In holistic mathematical terms these are positive and negative with respect to each other. However as they combine both horizontal and vertical aspects (in balanced fashion) the sign designation is more complex.
Thus in the UR quadrant the designation is +, +, with the corresponding designation in the diagonally opposite LL quadrant  -, -.
Also in the UL quadrant the sign designation is -, +, with the corresponding designation in the diagonally opposite LR quadrant  +, -.
Of course the very implication of combining polarities both within and between levels simultaneously is that the very notion of a level loses any distinct meaning.
So as pure nondual awareness is approached in mystical terms, these fundamental diagonal polarities are the last to be successfully reconciled. 10
 
The Eight Sectors
For a comprehensive interpretation of development, reality must be defined in terms of horizontal polarities (within levels), vertical polarities (between levels) and diagonal polarities (simultaneously within and between levels). 11
A differentiated understanding of reality results from the relative separation of these poles yielding a (linear) asymmetrical interpretation.
However though such interpretations appear unambiguous within each sector considered in isolation, when related to each other, dynamic complementarity exists in horizontal, vertical and diagonal terms. 12
This in fact implies that we are dealing with eight different holarchies.
 
 
 
Basic Outline of the Theory of Everything
 
Already with the aid of some simple mathematical notions - interpreted in a dynamic holistic sense - we have a system that can fundamentally structure the nature of any development process.
So to recap we started with number and in particular the binary digits 1 and 0 which in holistic terms encode form and emptiness respectively.
Next we had the operations of addition and subtraction, which in dynamic holistic terms encode the means by which phenomena are posited (as conscious) and negated (as unconscious) respectively.
We then introduced the basic geometrical symbols of the line, circle and point and their dynamic equivalents in relation to both linear, circular and nondual understanding. We established their close relationship (in both analytic and holistic terms) to the binary digits and the operations of positing and negating. We also gave a compelling dynamic explanation of duality (i.e. the holistic meaning of "2")
 
For the moment the Theory of Everything can be summed up as follows. 13
All dynamic processes are conditioned by polarities that can be identified - in holistic mathematical terms – as positive and negative.
Differentiation entails the dualistic separation of poles (where both are treated as positive). This leads to an unambiguous linear appreciation of relationships.
Integration entails the nondual complementarity (and ultimate identity) of opposite poles (which are positive and negative with respect to each other).
This leads to a paradoxical circular appreciation of relationships.
There are three fundamental polarities, which operate in a horizontal, vertical and diagonal fashion.
The horizontal polarities operate within a given level (e.g. interior and interior).
The vertical polarities operate between levels (e.g. wholes and parts).
The diagonal polarities operate both within and between levels simultaneously (e.g. form and emptiness).
Remarkably, every process – physical and psychological - can be precisely encoded using these three polarities i.e. horizontal, vertical and diagonal with respect to both their linear and circular interpretations.
I will demonstrate later – in considerable detail – how this holistic mathematical encoding is applied to structuring the entire Spectrum of Development.
Indeed the Theory of Everything represents the holistic counterpart of the (analytic) binary digits that can potentially be used to encode all information processes.
In like manner this inherently dynamic interpretation of these same digits can be used to potentially encode all transformation processes.
However for a deeper appreciation of the nature of the Theory of Everything we need to introduce some further holistic mathematical notions.

 
 

                                     Notes
 

1. Nature of Holistic Mathematics

2. Reductionism and Holistic Mathematical Symbols

3. Holistic Mathematics and the dynamic interaction between perceptions and concepts

4. On One God

5. Complementarity of Physical and Psychological Processes

6. Mystical Purgation as Dynamic Negation

7. Holistic Mathematical Interpretation of a Point

8. Holism and Partism

9. Dynamic Nature of Four Quadrants

10. Integration of Body-Self

11. Levels of Development

12. Illustration of Dynamic Eight Sectoral Approach

13. Nature of TOEs

A Binary Digital TOE - Introduction

                                        A BINARY DIGITAL TOE

All mathematical symbols can be given a fully coherent alternative interpretation that complements the standard analytic understanding of conventional Mathematics.  This interpretation - which is inherently dynamic in nature - I refer to as Holistic Mathematics and provides the proper scientific basis for a truly integral appreciation of reality.
One important application of Holistic Mathematics relates to the binary system. Just as in conventional terms, the analytic interpretation of the binary digits provides the basis for the potential encoding of all information processes, equally the alternative holistic interpretation of these same digits provides the firm basis for the potential encoding of all transformation processes.

In the following Chapters, I outline the nature of this dynamic binary system and show how in can be applied in detail to the scientific translation of all the various stages in the Spectrum of Development.

                                                                  Part A

1. Integral Theory of Everything 1 

2. Integral Theory of Everything 2

3. Stages of Development

Holistic Mathematics - Conclusions

          Q. How would you describe your own approach?

PC  For convenience we can identify two distinct approaches in terms of the mapping of the mystical life.

The first is extensive and largely research based representing predominantly a synthesis of existing accounts and traditions. The second is more intensive and existential depending on intimate reflection on personal experience.

Both of these approaches are in fact complementary. Whereas I would classify Ken's work largely in terms of the first my own is mainly an example of the second. In the process of offering an authentic personal account of the spiritual life, the fundamental dynamic structure of reality - which is mathematical in a qualitative sense - was mysteriously revealed.

Because of the natural - yet marvellous - way that all the key insights of Holistic Mathematics occurred, I have a very deep level of conviction regarding their truth.


Q.  What is Holistic Mathematics?
 


PC  Holistic Mathematics is very different from what conventionally is understood as mathematics. By its very nature it does not obey strict disciplinary lines and involves - especially - the integration of psychology, physics, philosophy, mystical spirituality and mathematics. This integrative process itself becomes the means of highlighting the holistic (mathematical) structures common to all understanding.

Holistic Mathematics greatly enhances the scope of mathematical activity. Despite its great achievements standard (analytical) mathematics is limited by its merely horizontal perspective. In other words understanding takes place exclusively within the context of the rational (linear) paradigm.

Holistic mathematics provides the complementary vertical perspective (where understanding takes place within a range of differing paradigms). This greatly increases the power and scope of mathematics. For example - as I have demonstrated - all psychological understanding can be precisely translated in mathematical terms.

Despite its great neglect Holistic Mathematics - because it is inherently dynamic - provides a truly fundamental interpretation of mathematical symbols. Thus the absolute use of these same symbols - in conventional mathematics - is rooted in a more original and rich holistic meaning.


 

Q.  Using Holistic Mathematics can you throw light on the nature of number?

PC I believe number to be the most fundamental of all archetypes.

Of special relevance are the binary numbers 1 and 0.

Now these (quantitative) binary digits - which obey a logic of clear separation - are extremely important in standard mathematics. Indeed all other number types can be ultimately expressed in terms of the binary number system.

As we know this binary system is the very basis of our digital age. Even the most complex of information can be translated in terms of the two binary digits 1 and 0.

In this sense (all) information can be encoded in (quantitative) binary form.

Now both the binary digits 1 and 0 have - necessarily - a (reduced) static interpretation in information technology.

However these same symbols have a deeper (qualitative) holistic meaning and refer to the fundamental nature of unity (1) and nothingness (0) respectively.

This latter holistic interpretation ultimately relates to the archetypal state where the two holistic symbols (i.e. unity and nothingness) are identical and - in the most general sense - is the basis of all transformation processes (both physical and psychological).

In this sense (all) transformation can be encoded in (qualitative) binary form.

Unity in this holistic sense is related (psychologically) to (rational) consciousness and the recognition of (phenomenal) form.

Nothingness is correspondingly related to the (intuitive) unconscious and the absence of phenomenal form (through spiritual awareness).

Western religion - which is rooted in a rational culture - correspondingly sees ultimate form in terms of oneness. Thus, here there is one God and the "highest" spiritual experience is seen in terms of mystical union.

Eastern religion owes more to intuitively based spiritual experience and often interprets ultimate reality in terms of nothingness (i.e. a creative void free of all phenomenal form).

Of course these two interpretations are themselves complementary so that the fullest expression of "transformed" spiritual experience is in terms of a plenum-void (both unity and nothingness).

This is concisely expressed in the most famous of all Buddhist sutras

"Form is not other than void

Void is not other than form".


Thus the static (reduced) interpretation of the (quantitative) binary symbols (1and 0) - as used in conventional mathematics - is actually rooted in a more fundamental (qualitative) dynamic interpretation of these symbols.

Indeed the very symbols used to represent 1 and 0 are the (straight) line and circle. These same symbols have long been used to represent (conscious) reason and (unconscious) intuition respectively.

Conventional mathematics strives to give a merely (rational) quantitative interpretation of symbols (based on an either/or logic of separation).

Holistic mathematics is designed to restore the complementary (intuitive) qualitative interpretations of these same symbols (based on a both/and logic of complementarity).
 
A comprehensive approach to reality involves both (horizontal) information and (vertical) transformation processes. Thus - at its simplest - a proper translation of reality requires the use of a double binary system that incorporates the interaction of two different logical approaches.
 

I have been continually amazed at the sheer aptness of the key symbols used in (conventional) mathematics. Invariably their holistic qualitative origins are implicit in the symbols. However because this latter aspect is rarely emphasised, appreciation of Holistic Mathematics is practically non-existent.


Q.  What about other numbers and relationships?
 
 

PC  Yes, I have been able to use three basic notions of dynamic complementarity to derive the holistic interpretation of the main mathematical relationships (addition and subtraction; multiplication and division; powers and roots).

These operations - in dynamic terms - are inherent in the most fundamental of all archetypes (i.e. the binary archetype of unity-nothingness). Using the binary symbols (and their inherent complementarity) I have derived all the other number types in holistic qualitative terms.

Thus every (linear) number type has a quantitative interpretation (in horizontal terms) that is balanced by a corresponding (circular) number type with a qualitative interpretation (in vertical terms).

Numbers thus have two distinct roles. They can be used analytically in terms of quantitative order. Equally they can be used holistically in terms of qualitative order.

Perhaps the most remarkable finding of Holistic Mathematics - which constitutes a form of theorem - is that the (full) Spectrum of Consciousness is in fact the qualitative number system.


Q.  Can you list some of your main findings.
 
 

PC  Of key importance is the realisation of the existence of a coherent qualitative mathematical system (which complements the well known quantitative system). This qualitative system - which I call Holistic Mathematics - provides the truly scientific basis for the study of consciousness and integrated studies generally. Amazingly, despite its great potential, the holistic aspect of mathematics has never been coherently articulated and effectively ignored throughout the history of mathematics.

As already stated I believe that the identification of the full Spectrum of Consciousness as the qualitative number system is highly significant. As well as demonstrating that (all) dynamic relationships can be translated precisely in (holistic) mathematical terms, it also provides a uniquely coherent and detailed mapping of the various levels and stages of psychological development.

The discovery of Holistic Mathematics - which is inherently dynamic - alters fundamentally our appreciation of the very nature of mathematics.

What this entails is that in principle every mathematical relationship has a direct dynamic application to physical and psychological reality (both of which are complementary).

Holistic Mathematics provides a precise interpretation of the three fundamental types of complementarity which underlie all relationships. These are so important that they truly constitute "The Theory of Everything".


Q.   Briefly, what is "The Theory of Everything"?
 
 

PC  Reality - at its most fundamental - can be described in terms of three dynamic symmetries (complementary relationships). These symmetries - which have a precise mathematical rationale - are horizontal, vertical and diagonal respectively.

Horizontal symmetry refers to the fact that all levels of reality (physical and psychological) have both external and internal aspects (which are dynamically complementary). In psychological experience for example, objective (external) is always balanced by subjective (internal) experience.

In mathematical terms these complementary (horizontal) polarities are positive and negative with respect to each other (Positive and negative signs - which are so basic in conventional mathematics - are here understood in their original dynamic sense).

Vertical symmetry refers to the fact that all levels of reality have both quantitative and qualitative aspects (which again are dynamically complementary). Alternatively we can say that for all relationships parts are related to wholes (and wholes to parts). In psychological experience this relates to the fundamental relationship as between cognitive (mental) and affective (sense) experience.

In mathematical terms these complementary (vertical) polarities are real and imaginary with respect to each other. (Once again these terms are used in their original dynamic sense).

Finally diagonal symmetry refers to the fact that all levels of reality have both actual and potential aspects (again dynamically complementary). Alternatively we can say that for all relationships form is related to emptiness. In psychological experience this relates to the fundamental connection as between reason (actual) and intuition (potential).

In mathematical terms these complementary (diagonal) polarities are finite and infinite (or transfinite) with respect to each other (Again these terms are defined in terms of their true original meanings).

In the fundamental unity-void (which is both ground and goal of existence) we have perfect symmetry (i.e. in all three cases, complementary poles are identical).

In phenomenal reality, these symmetries - while remaining implicit in relationships -
are broken. Returning to that original state of existence, requires restoring the three vital symmetries.


Q.  Can you demonstrate - briefly again - how you apply these symmetries to the understanding of number?
 
 

PC  Basically the same approach applies to the (dynamic) understanding of all phenomena. However mathematical symbols - which are often viewed differently from other phenomena - provide a particularly interesting illustration.

We can start with a (particular) number perception or alternatively the (general) number concept.

If we start with a number perception (e.g. the number "3"), then - in dynamic terms - horizontal complementarity applies.

The number perception has a positive (external) direction i.e. the number "3" (in relation to the perceiving mind).

Likewise the number perception has a negative (internal) direction i.e. the perceiving mind (in relation to the number "3").

Thus understanding - which in dynamic terms is purely relative - involves the interaction of these two (horizontal) directions. The conventional absolute position - which ignores this interaction - is thus a reduced static interpretation.


Likewise, in relation to the number "3", vertical complementarity applies.

The particular number perception "3" has a real (quantitative) meaning (in relation to the corresponding concept). The general number concept has - in relative terms - an imaginary (qualitative) meaning (in relation to the corresponding quantitative perception). Thus understanding - again in dynamic terms - involves the interaction of these two (vertical) directions. To accurately portray this quantitative-qualitative relationship therefore involves defining reality mathematically in complex terms (with real and imaginary aspects).

Again the conventional static mathematical position reduces this complex relationship to a (merely) quantitative real interpretation.

Finally, in relation to the number "3", diagonal complementarity applies.

Again the rational understanding of the number "3" has a finite (actual) meaning (in relation to corresponding intuitive understanding).

Intuitive understanding of the number "3" has an infinite (potential) meaning (in relation to corresponding rational understanding).

Thus understanding - in dynamic terms - involves the interaction of these two diagonal directions. Once again the conventional understanding of number simply reduces this interaction to a merely finite interpretation.

Though I have demonstrated these three types of complementarity in relation to the dynamic understanding of number, they equally apply to understanding of all phenomena.

Thus with horizontal complementarity, positive (objective) and negative (subjective) poles are integrated; with vertical complementarity real (cognitive) and imaginary (affective) poles are integrated; with diagonal complementarity finite (rational) and infinite (intuitive) poles are integrated.


 

Q. How would you apply this complementarity to the understanding of evolution?

PC  I would adopt a strongly centrist approach here (which is the only one consistent with nondual reality).

Thus all evolution essentially begins and ends in the present moment.

Now the question then arises as to how to reconcile relative linear interpretations with this central ever present point of reality.

This is where the three fundamental complementarities once again apply.

The critical thing to remember is that evolution always involves the bi-directional relationship of matter and mind.

Again we can look on this in horizontal terms. Thus at any given level of reality we have a positive (external) and negative (internal) aspect.

What this ultimately means is that - at every level - nature and mind mutually reflect each other. In linear terms however we must necessarily separate these poles.

Conventional science is still largely based on an attempt to study nature (independent of mind). Psychology (esp. transpersonal) is by contrast often presented largely as the study of mind (independent of nature). Both positions of course are unbalanced. An extremely common problem - exemplified by Ken Wilber - is to try and combine both approaches in a linear fashion. Thus typically here we have an attempt to portray evolution as a progression from "lower" physical levels (nature) through intermediate biological levels (life) on to "higher" spiritual levels (mind). Thus in Ken's treatment the physiosphere (and biosphere) are "lower" in evolutionary terms than the noosphere (and theosphere).

This involves exactly the same confusion that is manifest in his pre-trans fallacy.

We cannot properly separate physiospere and noosphere for they are complementary. (Our very notions of the physiospere depend on the mental constructs of the noosphere). At all "lower" levels of evolution they exist in an undifferentiated confused manner. Here we have a highly confused physioshere-noosphere. (Mind literally is not able to properly reflect on its own nature).

At "higher" levels of evolution they exist in a differentiated refined fashion. Here we have a more mature integrated physioshere-noosphere. (Mind is now able to adequately reflect on nature).

Thus at each "higher" level of spiritual experience both mind and nature are equal and mutually reflect each other in a transformed manner. In other words horizontal complementarity exists.

We can also look at this bi-directional nature of matter and mind in vertical fashion.

Thus at differing levels of reality we have real (quantitative) and imaginary (qualitative) aspects. What this entails is that "lower" levels of physical reality (quantitative) and "higher" levels of psychological reality (qualitative) mutually reflect each other.

There is a particular problem here with Ken Wilber's holarchical approach (i.e. where "lower" level holons are transcended and included in "higher" level wholes).

This process in fact is bi-directional so that we have both a holarchy and partarchy which

are complementary (in vertical terms).

Thus we have two complementary processes

• where "lower" holons are transcended and included in "higher" (qualitative) wholes (holarchy) and

• where "higher" holons are prescended and excluded in "lower" (quantitative) parts (partarchy).
Just as the "higher" wholes depend on the "lower" parts, equally the "lower" parts depend on the "higher" wholes. (to maintain balance holism must be balanced by partism).

This entails that it is meaningless for example to talk of "lower" level quantitative holons (e.g. quarks and atoms) in the absence of complementary "higher" level qualitative holons (corresponding mental constructs).

Thus evolution can be viewed - in linear terms - as the qualitative movement from the "lowest" to the "highest" holons (holarchy); equally it can be viewed as the quantitative movement from the "highest" to the "lowest" holons (partarchy).

Now these two directions are complementary (in vertical terms). Thus correctly speaking "lower" (quantitative) and "higher" (qualitative) holons mutually reflect each other and are ultimately identical (in the present moment).

A correct approach to evolution involves great subtlety.

Thus at any given level we start with a (horizontal) linear approach. However we then recognise that it is always bi-directional. In other words we can have a separate external (physical) or internal (psychological) interpretation in rational linear terms.

However when integrated these approaches become complementary (in horizontal terms) and cancel out in an intuitive realisation of the (eternal) present moment.

In terms of differing levels we start with a (vertical) linear approach. However we again recognise that it is bi-directional. Thus we can have separate rational approaches relating to the qualitative evolutionary movement towards the ultimate whole (mind), or the quantitative evolutionary movement towards the ultimate part (matter).

However when integrated these approaches become complementary (in vertical terms) and cancel out in an intuitive realisation of the (immediate) present.

Diagonal complementarity starts from a clear intuitive realisation of both the eternal and immediate present (i.e. the fundamental void with both transcendent and immanent aspects).

This then gives way to a simple yet complex interactive understanding of evolution involving both rational (linear) and intuitive (complementary) understanding.

This is the kind of understanding that is compatible with the radial level (nondual reality).

Linear interpretations of evolution are now understood to have a strictly relative validity always emanating from and returning to an ever-present central moment.


Q.   What are your own intellectual plans for the future?
 
 

PC  There is considerable scope for expansion of my findings.

For example associated with each of the number types quantitatively understood, is a corresponding qualitative interpretation which constitutes a distinct paradigm for viewing reality.

The current scientific approach can be accurately classified - in qualitative terms - as the positive real rational paradigm (which in terms of all the possible paradigms available is very limited indeed). Now a major task still remaining is to adequately flesh out the precise nature, uses and limitations of all the other possible number paradigms. This will entail nothing less than a dramatic revolution in what we understand by science.

Personally I am especially interested in developing the most comprehensive of these paradigms (i.e. the "complex" rational paradigm).

This involves the mature integration of both "real" analytical and "imaginary" holistic aspects of understanding and has been alluded to in some of my postings.  

The application of Holistic Mathematics to differing disciplines leads to an entirely distinctive approach. Though they still remain very much integrated with each other it is valid to highlight differing facets. Thus we can have Holistic Physics (Holophysics), Holistic Psychology (Holopsychology), Holistic Philosophy (Holosophy), Holistic Biology (Holobiology), Holistic Economics (Holonomics) etc.  

I am particularly interested in applying my qualitative number spectrum to physics (and establishing full complementarity with Holistic Psychology). This approach I believe will lead to deep creative insight at both levels.

Also as a qualified economist, I intend in the future to use my methods to develop a satisfactory modern interpretation of economic reality.

In terms of the Forum, I may take a rest for a while.

However because it is so fundamental on returning I hope to demonstrate how the holistic mathematical interpretation of all the major number types is derived.


Q.  Any final thoughts?
 

PC  I have always felt it important to be true to my personal convictions. This work owes a great deal to that spirit.

I say again that mathematics can be reformulated in a radically different qualitative sense and that this provides the true scientific basis for the study of consciousness (and integrated studies).

Anyone who reflects on this for a moment will realise that it is a highly significant claim. With Holistic Mathematics I believe that I have already demonstrated its validity.

 

Personality Types and Superstrings

Q.  You have said that Jung dealt with psychological reality implicitly in holistic mathematical terms. Can you start by briefly outlining his treatment of personality types?
 
 

PC The Jungian system is based on four functions (thinking, feeling, sensation and intuition) and two attitudes (extroversion and introversion). Combining each of these four functions with the two attitudes, Jung came up with 8 personality types as follows:
 
 

Extrovert Thinking

Introvert Thinking

Extrovert Feeling

Introvert Feeling

Extrovert Sensation

Introvert Sensation

Extrovert Intuition

Introvert Intuition
 
 

Now the characteristics associated with each type have been well documented elsewhere so I will not deal with them here.
 
 

The Myers-Briggs personality type indicator - which builds on Jung’s analysis, distinguishes 16 different personalities types.

This system is based on the same four functions (sensing, thinking, feeling and intuition) and four attitudes (extroversion, introversion, perception and judgement).

One way of arriving at the 16 personality types is through permutating (i.e. arranging) functions (two at a time) one dominant and the other the auxiliary, each having either an extroverted or introverted attitude respectively.
 
 

Thus if we take sensing and thinking as the initial two functions we can obtain the following four personality types:
 
 

ISTJ (sensing dominant and introverted, thinking auxiliary and extroverted)

ISTP (thinking dominant and introverted, sensing auxiliary and extroverted)

ESTP (sensing dominant and extroverted, thinking auxiliary and introverted)

ESTJ (thinking dominant and extroverted, sensing auxiliary and introverted)
 
 

When we take sensing and feeling as the initial two types, we obtain the following four:
 
 

ISFJ (sensing dominant and introverted, feeling auxiliary and extroverted)

ISFP (feeling dominant and introverted, sensing auxiliary and extroverted)

ESFP (sensing dominant and extroverted, feeling auxiliary and introverted)

ESFJ (feeling dominant and extroverted, sensing auxiliary and introverted)
 
 

Combining intuition and feeling as the two types, the following four emerge
 
 

INFJ (intuition dominant and introverted, feeling auxiliary and extroverted)

INFP (feeling dominant and introverted, intuition auxiliary and extroverted)

ENFP (intuition dominant and extroverted, feeling auxiliary and introverted)

ENFJ (feeling dominant and extroverted, intuition auxiliary and introverted)
 
 

Finally, combining intuition and thinking, we have the following:
 
 

INTJ (intuition dominant and introverted, thinking auxiliary and extroverted)

INTP (thinking dominant and introverted, intuition auxiliary and extroverted)

ENTP (intuition dominant and extroverted, feeling auxiliary and introverted)

ENTJ (thinking dominant and extroverted, intuition auxiliary and introverted)
 
 

However when we combine from four (two at a time), six (rather than four) distinct arrangements are possible (i.e. 4C₂ = 6). Thus in terms of our functions we can also start with intuition and sensing or alternatively with thinking and feeling.

Thus combining these with the two attitudes (extroversion and introversion) we can generate eight additional personality types (two more groupings representing in each case four distinct personality types).

Therefore we should generate 24 - rather than 16 - distinct personality types.
 
 
 

Q.  So you are saying that there are eight missing personality types in the Myers-Briggs typology?
 
 

PC  Yes, this is clearly the case. The Myers-Briggs approach is based on the identification of polar opposites. Thus one is classified as either an extrovert or introvert (E or I); one is either sense orientated or intuitive (S or N); one is either a thinking or a feeling type (T or F); finally one uses perception or judgement in making decisions (P or J).

However - as we will see shortly the very essence of the eight "missing" types is the combination of these opposites in personality.
 
 
 
 

Q.  So tell us now about your revision of this system?
 
 

PC The Jungian system of types and preferences - though admittedly highly useful - is in some respects confusing. Whereas in normal language feeling relates to emotional-affective experience, Jung treats it as a rational evaluation function.

Also, intuition (which relates primarily to unconscious experience) can be explained as essentially resulting from the dynamic interaction of conscious functions.

Indeed the 24 personality types (including the 16 recognised in the Myers-Briggs personality type indicator) can actually be derived from just four aspects with two modes (i.e. functions) and two directions (i.e. attitudes).

The two modes are the cognitive (rational) and the affective (emotional) respectively. The two directions are the external (objective) and internal (subjective) respectively. Combining these two modes and two directions yields four functions.

The cognitive mode in an external direction is the thinking aspect. The corresponding mode in an internal direction is the judgement aspect (i.e. reason applied to subjective decisions).

The affective mode in an external direction is the perception aspect. The corresponding mode in an internal direction is the feeling aspect.

So we now have four aspects. Each permutation or arrangement of these four aspects (taking all four at a time) gives a distinct personality type.

In mathematics 4P₄ = 24, so 24 such permutations or configurations are possible thereby giving 24 personality types.
 
 
 

It would be very helpful in what follows to picture the four functions as the corners of a square.

The horizontal lines represent functions of same direction (and differing mode).

The vertical lines represent functions of differing direction (and same mode).

The diagonal lines represent functions both of differing direction and differing mode.
 
 
 

We can now use this diagram to derive three distinct groups (comprising in each case 8 personality types) giving 24 in all.
 
 

Each permutation (or arrangement) of aspects gives a distinct personality type. The first represents the dominant, the second the auxiliary, the third less developed and the final the inferior aspect.
 






Q.  What are the characteristics of the first group?
 
 

PC The first group is the horizontal and includes those personality types with the two principal aspects of same direction (and differing mode). Because unconscious intuition is based on the dynamic interaction of opposite directions, relatively little is generated by these types. They operate very much out of the conscious process. As they are thereby most firmly rooted in actual reality they can be mathematically termed the "real" types. These indeed correspond to the sense types in the Myers-Briggs typology. The following are the eight types (with corresponding Myers-Briggs designation).
 
 

 P+T+F-J- (ESFP)

P+T+J-F- (ESFJ)

T+P+F-J- (ESTP)

T+P+J-F- (ESTJ)

F-J-P+T+ (ISFP)

F-J-T+P+ (ISFJ)

J-F-P+T+ (ISTP)

J-F-T+P+ (ISTJ)
 
 

The dominant and auxiliary functions are of the same sign (Equally both the less developed and inferior functions are of opposite sign). When the dominant and auxiliary functions carry a positive sign we get extroverts; when negative we get introverts.

Again in terms of the Myers Briggs type indicator all of these personalities (by definition are S types).

If the dominant function (in my classification) is affective (F or P) then in terms of the 3rd letter (in Myers Briggs) we get F; if dominant function is cognitive (T or J) we get T (in Myers Briggs).

Finally if the third letter (in my classification) is affective (P or F), then the final letter in Myers-Briggs is P; otherwise (if T or J in my classification), it is J in Myers Briggs.
 
 
 

Q.  What about the second personality group?
 
 

PC The second group is the vertical which includes those personality types of differing direction (and same mode). When dominant and auxiliary aspects are well balanced much intuition can be generated through this fusion of opposites. As these tend to operate so much out of the unconscious they are more flexible and creative being interested in the potential for changing reality. They can be accurately described in mathematical terms as the "imaginary" types. These correspond to the intuitives (N) in the Myers-Briggs typology.

Again these are the corresponding eight types (with Myers-Briggs designation).
 
 

P+F-T+J- (ENFP)

P+F-J-T+ (ENFJ)

T+J-P+F- (ENTP)

T+J-F-P+ (ENTJ)

F-P+T+J- (INFP)

F-P+J-T+ (INFJ)

J-T+P+F- (INTP)

J-T+F-P+ (INTJ)
 
 

The dominant function here will decide the overall direction of experience. If the dominant function (on left) is positive, then we get an extrovert; if negative we get an introvert.

Because dominant and auxiliary are (by definition) of opposite signs we get intuitives (N in Myers Briggs) in all cases. If the second auxiliary function (on left) is cognitive (T or J), the third letter in Myers-Briggs is T; if auxiliary (on left) is affective (P or F) then third letter (in Myers Briggs) is T.

Finally if third letter (on left) is positive, then we get P for fourth letter (in Myers Briggs).

If third letter (on left) is negative the fourth letter (in Myers Briggs) is J.
 
 
 
 

Q.  Most intriguingly what are the characteristics of your "new" personality group?
 
 

PC The third (unrecognised) group is the diagonal which includes those personality types both of differing direction and differing mode. These find it particularly difficult to find a centre of being around either a (conscious) sense or (unconscious) intuitive based approach and are driven - in reaching integration towards the mid-point or centre of personality which connects both. As successful integration relates directly on this spiritual centre they can be referred to mathematically as the infinite or "transfinite" types orientated to the transparent or empty fundamental ground of what essentially is.

They can alternatively be described as the "complex" types reflecting the balancing of personality characteristics that are diagonally opposite (in both mode and direction).
 
 

From one perspective this personality group - with mature development - is the most simple of all, successfully balancing polar inclinations that exist with both the "real" and "imaginary" groups.
 
 

Thus they are primarily neither extroverts nor introverts as such but rather centroverts. Thus in place of the E/I classification in the Myers Briggs we now have C for all 8 types in this group.

Likewise they are neither sense nor intuitive orientated but rather mystical (i.e. spiritual in a direct experiential way) Thus we can replace the S/N classification in the Myers Briggs with M for the 8 types.

Again these types operate directly from neither feeling nor thinking as such but rather volition (i.e. the direct capacity of the will). Thus T/F can be replaced with V for the group.

Finally they neither display perception nor judgement but rather a more balanced attitude in what be called discernment. Thus P/J can be replaced here with D.

So in a fundamental manner all 8 types of this third diagonal group share the same personality type which represents the golden mean as between the opposing tendencies of the other groups. (CMVD).
 
 

However just as these types (from this primary integrated perspective) are "simple", equally from a secondary perspective they are "complex" combining - in the same personality - opposite characteristics.

We can list these eight types as follows (giving the corresponding Myers Briggs types).
 
 

P+J-T+F- ENFJ and ISTP

P+J-F-T+ ENFP and ISTJ

J-P+F-T+ INTP and ESFJ

J-P+T+F- INTJ and ESFP

T+F-P+J- ENTP and ISFJ

T+F-J-P₊ ENTJ and ISFP

F-T+J-P₊ INFJ and ESTP

F_-T₊P₊J- INFP and ESTJ
 
 

In a primary sense these are all centroverts. If first letter i.e. dominant aspect (on left) is positive, in terms of Myers Briggs we get a secondary extrovert (with strong shadow introvert personality characteristics); if first letter (on left) is negative then we get a secondary introvert (with strong shadow extrovert tendencies).

Again in a primary sense, all these types are (potentially) mystical. Because dominant and auxiliary functions are of opposite signs, in secondary terms they are all intuitives (N) with strong shadow sense (S) tendencies.

All - in a primary sense - are volitional (operate through the will). If the dominant function (on left) is cognitive (T or J), then in a secondary sense (in Myers Briggs) we will get T as our 3rd letter; if dominant function (on left) is affective (P or F), then on Myers Briggs we will get F as 3rd letter. Again in each case these are strongly counterbalanced by opposite shadow tendencies.

Finally in a primary sense all these types use discernment as a preference.

The third function (on left) if cognitive (T or J) in a secondary sense will lead to the choice of J as 4th letter (in Myers Briggs); if third function (on left) is affective (P or F), then in a secondary sense will we have P as final letter. Once more these are counterbalanced by opposite shadow tendencies.
 
 

When a high level of integration is achieved, well developed characteristics in the personality will also exist that literally shadow those presented at face value.

At low levels of integration, these opposite characteristics lead to considerable confusion and a lack of any coherent self identity. Putting it another way, such personalities are especially sensitive to their shadow selves. This is why the development of a strong spiritual centre is so vital for true integration to be achieved. It is to this group that the lines from Dryden especially apply.
 
 

"Great wits are to madness near allied

And thin partitions do their lines divide"
 
 
 

Q.  Can you know clarify the holistic mathematical rationale of your classification?
 
 

PC  There is a fundamental logic underlying my four aspects of understanding. They can be simply expressed as the four "complex" co-ordinates corresponding to the circle of unit radius (i.e. the cross within the circle with the horizontal line representing the "real" x axis and the vertical line representing the "imaginary" y axis). If we take the objective external direction of understanding as positive, then the subjective internal direction - in relative terms - is negative. Likewise if we take the cognitive (rational) mode as "real", then again - in relative terms - the affective (emotional) mode is "imaginary". This is the basis of so many mandalas which deeply symbolise integration of the psyche. We can now give a coherent mathematical reason as to why this in fact this is the case. The four aspects of understanding - from which all personality types are derived - can be simply obtained from obtaining the four roots of unity. In this sense all understanding is simply a reduced expression of unity.

This also helps to explain the limited nature of most of our actual experience of the world. Properly interpreted all four aspects are equally important and at the appropriate "high" level of understanding are fully unified. However each of our 24 personality types is built on a certain specialisation around two aspects only,

Thus the "real" group attempts to unify with dominant and auxiliary aspects of the same direction (and opposite mode).

The "imaginary" group attempts to unify with dominant and auxiliary aspects of the same mode (and different direction).

The "transfinite" group finally attempts to unify with dominant and auxiliary aspects of differing mode (and differing direction).

However true integration requires that all four aspects be properly differentiated and then combined in a dynamic harmonious fashion. In a direct sense this is the task of transpersonal spiritual development. It is to this we now turn.
 
 
 
 

Q.  You believe that one's personality type is especially relevant to the manner of transpersonal development. Can you briefly elaborate on this important point?
 
 

PC It would be helpful at the onset to outline the major "higher" levels of psychological development. For convenience we can list four i.e. the linear (gross realm), the circular (subtle realm) the point (causal realm) and the radial (non-dual reality).
 

In our Western culture, personality development rarely goes significantly beyond the rational linear level and is based on a high level of specialisation of the conscious mind.

The first "real"group are most firmly rooted in the conscious world. Integration for this type would normally not entail radical transpersonal development. They fit in too well with accepted conventions and are less prone to serious existential questioning.

Specialisation of the linear level is largely completed by early adulthood. Further growth would essentially entail achieving a more moderate and flexible approach to understanding and the cultivation of what might be termed "vision logic". Though this does not rule out authentic mystical experience, for the "real" group, the rational (linear) paradigm is likely to remain the predominant means of interpreting reality.
 

For the second vertical group the most fundamental feature is that strongly developed structures are of the same mode but of opposite direction. Thus someone, for example, with perception as the most developed structure, will tend to have the opposite affective structure of feeling as the main auxiliary. There is likely to be far more directional switching here, especially if both structures approach equal strength. This entails that that the (positive) conscious information of one structure, is continually negated through unconscious switching to the other. This in turn means - that if co-ordinated - far more spiritual fusion or energy is likely to be developed, thus rendering experience very intuitive in character.

Such types are likely to be less well adapted to the world. There is always an underlying conflict as between their own unconscious tendencies and the prevailing cultural paradigm. However, if resolved this tension can be very creative.

With their intuitive vision, they are not so much interested in actual reality but rather the creative potential for changing reality.

Integration for this group, requires going significantly beyond the linear level into the circular level. Otherwise, unconscious potential will never be properly realised, remaining untrained and unduly instinctive and immature.
 

The third - and least recognised - is the diagonal group.

The defining characteristic of this group is that the two main structures are both of opposite mode and opposite direction. Thus for example, someone with the cognitive structure of reason, strongly developed in an external direction, will have the affective structure of emotion, also well developed in an internal direction.

Whereas the first group can identify (directly) with the conscious process, and the second group (directly) with the unconscious process, this group can do neither. Not surprisingly there is likely to be a considerable identity crisis involved.

At one end of the spectrum, many with unresolved psychotic problems who have failed to achieve integration, belong to this group. At the other end some of the greatest mystics, who after a long painful struggle to achieve psychic harmony also belong to the same group. Resolution of the existential problem here is likely to be more demanding than with the other groups. In fact, the answer depends especially on authentic spiritual development. In other words it is the third essential process that is now especially relevant for integration.

If the first group is "real", relating to actual reality, and the second "imaginary", relating to potential reality, this group is aptly defined "complex" (i.e. both "real" and "imaginary") relating to essential reality. The paradox is that a high degree of true simplicity finally underlines integration of this inherently complex personality type. It primarily involves neither conscious or unconscious understanding as such, but rather that point (i.e. will), at the centre of being itself, which unites both.

For someone belonging to this group, therefore full integration is likely to involve moving beyond both linear and circular levels into the point level.
 
 

The key determinant of whether some will go on to the radial level - representing the most complete level of personality development - depends essentially on whether the two weaker aspects can be developed sufficiently to counterbalance the two strong aspects (dominant and auxiliary). This necessarily entails a lengthy period of intense exposure to the "shadow" side of one's personality.
 
 
 

Q.  Because integration for your vertical and diagonal groups involves "higher" levels of transpersonal development are you implying that these personalities are superior?
 
 

PC No, not all. I would be very opposed to any form of elitist categorisation on these lines.

Remember the classification of personality types is neutral as regards talent or intellectual ability. Most "successful" people will actually belong to the "real" group. For example leaders successfully running governments, businesses etc. generally belong to this group and can display a wide range of abilities. Indeed as this group finds a grounding easily in actual reality, they can often find their niche early in life subsequently developing in an extensive direction (with multiple interests).

Highly creative individuals will often belong to the "imaginary" group. However they can experience difficulties finding a satisfactory resolution as between the demands of society and their own inclinations. Too often they fail to get their act together and do not realise their abilities.

The truly mystical types belong to the "diagonal" group. Though possessing the potential for the highest level of integration, personalities of this type are most prone to their shadow selves (and psychological illness). Properly understood many of the great saints faced a stark dilemma in having to achieve a high level of spiritual integration to avoid falling into mental illness.
 
 
 

Q.  Indicate now how your classification of personality types can lead to a "new" psychological interpretation of dimensions?
 
 

PC There is a fascinating - if unappreciated connection - as between our profile of personality types and the dimensions of space and time.

To his great credit Jung was deeply conscious of this potential link with physical reality and saw his four functions as - in a fundamental sense - mirroring the four dimensions of space and time in physics. Unfortunately the conventional world-view of three dimensions of space and one of time is one of broken symmetry. Jung came very close to accurately expressing the true four-dimensional "complex" symmetry of space-time with his classification of two rational functions (thinking and feeling) and two irrational functions (sensation and intuition).

In my own mathematically "complex" reclassification, we have - in relative terms - two modes ("real" cognitive and "imaginary" affective) and two directions ("positive" external and "negative" internal). In this system the four functions are (in relative terms):

Real (positive) = thinking

Real (negative) = judgement

Imaginary (positive) = perception

Imaginary (negative) = feeling
 
 

Now, equally these four functions represent the "complex" symmetric aspects of space-time. In other words we have two dimensions of space (one positive, one negative) and two dimensions of time (one positive, one negative). Thus we can rewrite our scheme as follows:

Time (positive) = thinking

Time (negative) = judgement

Space (positive) = perception

Space (negative) = feeling
 
 

In other words we literally create space and time in experience through the interaction of all four aspects.
 
 

Now in pure symmetry time and space cancel out in the experience of the eternal and immediate present which can be represented by the binary structures as 1 and 0 (i.e. both fullness and void).

However in terms of broken symmetry each personality type experiences space and time differently. Thus each personality type represents a unique configuration of space-time.

In the original Jungian profile of personality we have eight distinct types.

This - combined with the implicit binary structures - leads to 8 + 2 = 10 such unique configurations.

In our modified version of the Myers-Briggs we have 24 personality types which when combined with the implicit binary structures gives 24 + 2 = 26 unique configurations.

Thus when we look on dimensions psychologically in this new way - as representing unique (reduced) configurations of the 4 complex poles of space-time, we ultimately obtain 10 or alternatively 26 dimensions of space-time.
 
 

What this simply means is that each personality type experiences space and time in a unique fashion. Thus a dimension in this sense refers not to space and time (as separately considered) but rather to a unique configuration (i.e. permutation) of all four aspects.
 
 
 

Q.  So full personality integration would require all 10 (or alternatively 26) "dimensions"?
 
 

PC  Yes, this is true. Of necessity everyone uses all to some degree. However usually one - or at most two aspects - tend to dominate. The other aspects remain inferior and misunderstood frequently breaking into consciousness through projection.
 

Now as I have already explained those personalities of the third "diagonal" group are particularily sensitive to the projected "shadow". Thus full development for this type requires differentiating all four aspects to a considerable degree. At the later stages of the point level this task approaches completion. So all dimensions are now considerably fused. The "real" conscious and "imaginary" shadow personalities now approach integration.
 

So the 26 ways of organising dimensional qualitative reality now equally represent 26 ways of organising phenomenal (quantitative) reality. As we have already seen objects and dimensions are "real" and "imaginary" with respect to each other.

Thus dimensions can be looked on as shadow (i.e. imaginary) objects. Likewise objects can be viewed as shadow dimensions. Thus reality (real) and its shadow (imaginary) now mutually reflect each other.

Thus saying that reality has a shadow counterpart is just another way of saying that reality is dynamically "complex" with "real" and "imaginary" aspects.
 
 
 

Q.  All of this has a bearing on Superstring Theory. Can you explain how this is so.
 
 

PC  Yes this represents an excellent example of what I term vertical complementarity (where "low level" physical reality is reflected in "high level" psychological reality).

So just as we have a "high-level" psychological understanding of space-time, we equally have a complementary "low-level" physical understanding relating to material reality.

Once again ultimately physical reality can be represented in symmetrical terms by the four "complex" poles of space-time. In original binary terms this represents pure nothingness or alternatively pure fullness (i.e. the potential for all actual existence).

Now in the material physical world of broken symmetry, these four poles can be permutated (four at a time) to give unique (reduced) configurations of space-time. Combining these configurations with the implicit binary dimensions, we can therefore represent the world as comprising 10 (or alternatively 26 unique dimensions).

This is intimately tied to the Theory of Superstrings which - in some respects - promises to provide the most satisfactory mathematical model of the fundamental nature of physical reality. One of the most puzzling features of this approach is that it requires moving away from conventional 4 dimensional space-time.

One of the earlier versions seemed to work successfully only in 26 (24 + 2) dimensions, whereas recent versions seem to work best in 10 (8+2). Though mathematically satisfying, such an approach seems highly non-intuitive (judged by conventional criteria).

However if we accept that such dimensions actually represent unique configurations of the original 4 (symmetric) poles of space-time then suddenly it all makes great sense.

The dimensions to which Superstring Theory apply can be simply expressed as differing configurations of the same four aspects of space-time (with each configuration representing a unique dimension). The standard explanation of "compactification" is unsatisfactory. This states that the "extra" dimensions are curled up in incredibly small regions of space and invisible in the conventional four dimensions. The true problem here is this rigid insistence on four dimensional space-time which so dominates physics. Simply redefining a "dimension" in more dynamic terms (as a unique configuration of the four polar aspects of space and time) solves this dilemma.
 

There are deep and remarkable connections as between the standard analytical approach and this holistic mathematical treatment of Superstrings. Modular functions are especially relevant in terms of the analytical approach. These functions describe a four dimensional hyperspace defined in the upper right quadrant of the complex plane (i.e. where space has two real and two imaginary dimensions). These modular functions possess remarkable symmetry features.
 

Now in holistical mathematical terms I define space in complementary qualitative

"complex" fashion with two "real" and two "imaginary" dimensions. (However because this is a dynamic approach, space here has both positive and negative directions). This - as I have so often stated - provides the appropriate way for understanding the dynamic symmetries of nature.

So here we have a good example of the comprehensive mathematical paradigm at work

where "real" quantitative and "imaginary" qualitative aspects complement each other.

The "real" aspect provides the quantitative analytical (rational) interpretation of space-time.

The "imaginary" aspect provides the corresponding qualitative holistic (intuitive) interpretation of the same space-time.

Physicists will readily admit that they have no real understanding of the dimensions of Superstring Theory. This is due to the lack of a coherent holistic element in mathematical understanding. However once we supply this missing element we can give a surprisingly simple yet intuitively satisfying explanation of what these "dimensions" actually mean.

More importantly - in my opinion - it demonstrates the power of the holistic mathematical notion of vertical complementarity. Through this the psychological world of "personality types" and the physical world of "particle types" are now seen to be intimately connected.
 
 
 

Q.  Can you develop these connections any further?
 

PC  Yes. As you will recall I defined my "personality types" in terms of three groups.

The first horizontal "real" group involve personalities of differing mode and same direction.

The corresponding "real" group on the particle side would be the fermions (e.g. matter particles such as protons, electrons etc.)

The second vertical "imaginary" group involves personalities of same mode and same direction.

The corresponding "imaginary" group on the particle side would be the bosons (e.g. radiation such as photons where opposite directions coincide).

The third diagonal "complex" group involves personalities of differing mode and differing direction.

The corresponding "complex" group on the particle side would be the superstrings (where bosons and fermions can no longer be identified separately).
 

The linear level is the domain of the horizontal personality type. Likewise the linear level is the domain of the horizontal particle type (i.e. fermions readily exist at this level).
 

The "higher" circular level is the domain of the vertical personality type. Likewise the "lower" circular level is the domain of the vertical particle type (i.e. bosonic activity is more evident at this lower level of reality).
 
 

The "higher" point level is the domain of the diagonal personality type. Likewise the "lower" point level is the domain of the diagonal particle type (i.e. superstrings).
 

Now at the "higher" psychological point level, objects and dimensions are highly differentiated with respect to each other. At the "lower" physical point level, objects and dimensions are highly undifferentiated i.e. confused. This state is what I refer to mathematically as prime structures.
 
 
 
 

Q.  Can you elaborate on this point ? What do you mean by prime structures?
 
 

PC Again this starts from the notion of a prime number in mathematics.

Now a prime number (e.g. 7) is one with no factors (other than itself and 1). A prime number is thus strictly a one dimensional number.

All other natural numbers (i.e. composite) are obtained from a unique combination of prime numbers. Thus 6 = 2X3 is two dimensional (i.e. has two factors). It therefore has both horizontal (quantitative) and vertical (dimensional) aspects

Prime numbers therefore are the basic building blocks of the number system.
 

Now we can look on phenomenal reality in dynamic complementary fashion.

Natural (i.e. composite) phenomena - starting with observable particles such as fermions and bosons) - are obtained from a unique combination of prime elements. These prime ingredients in fact are the superstrings.

Now just as a prime number involves the separation of quantitative and qualitative aspects and is one dimensional, a superstring - in complementary fashion - involves the confusion of quantitative and qualitative aspects and is one dimensional.

Thus at the level of the superstrings we cannot meaningfully separate particles from background dimensions. As the observation of particles is always in the context of a background of space and time, superstrings cannot be directly identified. In a true sense the dimensions are contained within the superstrings.
 

Now the standard interpretation of superstrings in many ways is quite similar. They are viewed as tiny one dimensional objects which vibrate with varying frequencies (i.e. interact with their dimensions) to produce the observable phenomena of nature.

However the interpretation is too linear.

Clearly a one dimensional object has no phenomenal meaning (in the conventional sense). Therefore diagrams explaining the splitting and joining of strings cannot be taken literally and are misleading. Also even though it is meaningless to try and isolate superstrings as in any way separate from dimensions this is what the standard approach seems to attempt.

This leads to an interesting problem. Superstring Theory predicts "two worlds" - the "real" world of particles and an identical "shadow" world where these are invisible.

When placed in a dynamic context this is easy to explain.

Because superstrings - dynamically - are equally prime "particles" and "prime" dimensions, in reduced static terms we can view them alternatively as particles (with dimensions fixed) or dimensions (with particles fixed). This latter interpretation refers to the "shadow" universe predicted by the theory.

However just as in psychological terms ones persona and shadow are complementary aspects of the same personality, likewise in physical terms the universe and its shadow are complementary aspects of the same reality.
 
 
 

Q.  To be consistent with your principles of horizontal complementarity, there should be a psychological counterpart in experience to this reality. Is this so?
 
 
 

PC  Yes this is one of the most remarkable applications of horizontal complementarity.

There is a fascinating connection as between the meaning of the word "prime" in holistic mathematics and "primitive" in psychology.

A prime structure can be defined as the confusion of the quantitative and qualitative aspects of reality. Equally this could be expressed as the confusion of the horizontal and vertical; the confusion of "real" and "imaginary"; the confusion of objects and dimensions; the confusion of parts and wholes.

In other words at this level these aspects have no clear separate identity.

Now this is what defines primitive infant behaviour. Here fleeting instinctive impulses are at one and the same time the expression of qualitative whole desire (unconscious) and quantitative part phenomena (conscious). However because of the high level of confusion, neither is clearly distinguishable. Thus neither the dimensions of space and time nor the phenomenal objects which they contain can achieve any permanence. However these primitive interactions gradually lead to the emergence of natural phenomena in space and time.
 

Thus in holistic mathematical terms the (psychological) instinctive behaviour of the early infant involves prime objects (confused with prime dimensions).

Remarkably this directly complements (in horizontal terms) the (physical) behaviour of superstrings where equally involves prime objects (confused with prime dimensions).

However it requires the "higher" understanding of the vertically complementary point level to properly interpret the nature of this "lower" level reality.
 
 

So just as we can interpret the fundamental ground of reality (physically and psychologically) in terms of qualitative binary numbers, equally we can interpret the next "lowest" level in terms of qualitative prime numbers. Ultimately all other levels of reality can be interpreted in terms of the appropriate qualitative numbers.

Thus the holistic structures of reality - physically and psychologically - at all levels can be precisely explained in terms of qualitative numbers.
 
 
 

Q.  Can you know briefly summarise your findings.
 
 

PC The original Jungian classification of personality types has eight distinctive types.

The Myers-Briggs revision has 16 types. However it can be easily shown that there are eight "missing" personality types. So the full system has 24 types.

This extended personality profile can be easily translated in holistic mathematical terms and classified as three distinct groups with "real", "imaginary" and "complex" types.

The personality group one belongs to, in general terms determines the subsequent manner of transpersonal development.
 

Each of the 24 personality types can be interpreted as representing a distinct arrangement of four polar co-ordinates representing space and time. Each configuration of space and time represents a unique dimension. When combined with the universal binary "dimensions" (1 and 0), this leads to 26 (24+2) or alternatively 10 (8+2) "dimensions".

This simply entails that each personality type experiences space and time in a different manner.
 

Using vertical complementarity, there is a fascinating connection here with the "lower" level physical reality of superstrings. In like manner dimensions represent unique permutations or configurations of the four 4 polar co-ordinates of space and time.leading to 26 (24+2) or alternatively - in more general terms - 10 (8+2) dimensions.

These configurations simply arise due to the fact that by definition the four aspects of space and time cannot yet be successfully separated. Thus a "dimension" necessarily involves a combination of all 4 types.
 

Thus psychologically at the "high-level" we have unique personality configurations (representing subjective experience of space-time). In complementary terms at the physical "low-level" we have unique particle configurations (representing the objective nature of space-time).

Superstring theory therefore represents these fundamental "objective" organisations of "broken" space-time. They closely mirror Jung’s theory of personality types representing - in experience - fundamental "subjective" organisations of the same broken space-time.
 

Holistic mathematics can also throw valuable light on other issues - such as "shadow" matter. It also precisely defines in qualitative number terms both the - highly interrelated - "objects" and "dimensions" - which superstrings represent - as prime numbers.