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
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
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
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.