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Peter Collins is from Ireland. He retired recently from lecturing in Economics at the Dublin Institute of Technology. Over the past 50 years he has become increasingly convinced that a truly seismic shift in understanding with respect to Mathematics and its related sciences is now urgently required in our culture. In this context, these present articles convey a brief summary of some of his recent findings with respect to the utterly unexpected nature of the number system.

An Integral Mathematical Stage Model of Perspectives

Part One: Lower and Middle Levels

Peter Collins

In this model, each stage of development is given a unique integral mathematical configuration in terms of the holistic binary system (that thereby scientifically defines the fundamental structure of the stage). Though discussion is limited here to the 12 major levels, the approach can be extended in considerable detail to every stage of development. In this way all transformation processes are seen to be encoded in a dynamic binary digital manner. The nature of perspectives in turn is stage specific leading to a unique pattern of distinct (differentiated) perspectives and overall (integral) perspective in each case. These in turn can be scientifically interpreted through the holistic interpretation of the major number types.

Introduction

I introduced my basic model of development in "Clarifying Perspectives 4" consisting of four major Bands (with three Levels in each Band). 1 However what is unique about this model is that it is constructed more closely with respect to the inherent dynamic interactive nature of development with both linear (differentiated) and circular (integral) interpretations for each stage. 2 Indeed the explicit interaction as between linear and circular aspects constitutes the basic holistic binary nature of this approach. 3

However clarity as to the precise nature of each stage requires recognition of the three fundamental polarities of development (that I refer to as the eight-sector approach).

So once again all reality is conditioned by exterior and interior (and interior and exterior) polarities that operate horizontally (i.e. heterarchically) within a given level.

Likewise reality is conditioned by fundamental whole and part (and part and whole) polarities that operate vertically (i.e. hierarchically) between different levels. 4

Finally reality is conditioned by - what are truly the most fundamental of all polarities - form and emptiness (and emptiness and form) that operate diagonally (i.e. simultaneously horizontally and vertically) as between levels.

By the very nature of human development the diagonal polarities are first to emerge (initially in a greatly confused fashion). Equally the diagonal polarities are last to be successfully integrated (in a mature manner). So with successful integration, we have the marriage of the most instinctive psychophysical aspects of the body/mind where conscious and unconscious simultaneously interact (as form) and mature nondual experience of Spirit (as emptiness). 5

The differentiation of vertical polarities largely occurs after the diagonal with the horizontal occurring last. However integration at the higher levels reverses this process with reconciliation of the horizontal first, then followed by the vertical and finally the diagonal. 6

So to properly explain the basic nature of development (which can be extended in considerable detail for all stages) we need to distinguish these horizontal, vertical and diagonal poles, which can be given both linear (differentiated) and circular (integral) interpretation.

Remarkably the relationship between these three poles has a complete holistic mathematical explanation - literally as a reduced form of oneness - through the geometrical diagram representing the eight roots of unity.

Now just as these lines horizontal, vertical and diagonal lines have analytic interpretations as real (horizontal), imaginary (vertical) and both real and imaginary (diagonal) relationships, likewise these same lines have precise holistic mathematical interpretations (using the dynamic interactive meaning of the same notions). 7

I do not intend to go into great detail on the holistic mathematical aspects of development at this stage (which may seem unrelated to customary understanding). However I think it is important to recognise - at least in a general way - that the nature of all development is indeed inherently mathematical (though in a manner that cannot be identified with the conventional analytic appreciation of symbols). 8

And because it is mathematical (in a holistic manner) this prepares the way for a truly scientific appreciation of development, that has the capacity for opening up vast new fields of intellectual knowledge (that we can scarcely yet imagine). 9

The Bands and Levels of Development

It must be consistently remembered for appreciation of this approach that all stages can be given both a linear and circular interpretation. Though these necessarily interact in the dynamics of experience, for presentation purposes they must to a degree be abstracted from each other.

In this system there are four Bands. When viewed in a relatively independent manner these can be understood in linear (asymmetrical) terms as Lower (prepersonal), Middle (personal), Higher (transpersonal) and Radial (all personal). However when viewed from the corresponding relatively interdependent perspective, these Bands are continuous with each other through circular (complementary) connections (in horizontal, vertical and diagonal terms).

In other words horizontal complementarity exists (within each Band) as between the exterior and interior (and interior and exterior) aspects. 10 Vertical complementarity then exists as between "lower" and "higher" (and "higher" and "lower") Bands. Finally diagonal complementarity exists simultaneously within and between "lower" and "higher" (and "higher" and "lower") Bands. So for example the exterior aspect of a "higher" Band bears a diagonal complementary relationship with the interior aspect of the corresponding "lower" Band.

We will be dealing with the nature of complementarity more fully in relation to the various Levels (of the Bands).

However perhaps it might be instructive at this stage to illustrate in more detail the nature of vertical complementarity (with respect to the Bands).

Once again - in vertical terms - "lower" is complementary" with "higher" (and "higher" with "lower").

However the middle - which is neither "lower" nor "higher" - is ultimately complementary with what is both "lower" and "higher". So in the final stages of development i.e. Radial, "higher" and "lower" (and "lower" and "higher") stages - that have already been substantially integrated with each other - are then incorporated in mature fashion with the middle levels.

I will now put both these linear and circular features together to give an account of the nature of development from the radial perspective.

Earliest development is best considered as a state of confused integration (before differentiation of structures commences). This entails that "lowest" and "highest" Bands are still dynamically entangled with each other (in a largely undifferentiated manner). In other words earliest development is both prepersonal and transpersonal (in this undefined sense).

However with growing differentiation of structures the linear (discrete) elements gradually become more important. So we can thereby characterise early development as the gradual movement away from confused integral to properly differentiated notions.

Therefore by the Middle Band, development is best portrayed in linear (discrete) terms (where prepersonal and transpersonal notions have been largely separated from each other). 11 However the price that has to be paid is that the integral is thereby significantly reduced to such differentiated notions.

Thus the "higher" Band is now characterised by growing circular complementarity allowing ultimately for the successful mature integration of both "higher" and "lower" (and "lower" and "higher") Bands.

So the middle Band represents the specialisation of dual (differentiated) development and the "higher" (which in dynamic terms is truly the integration of "higher and "lower") nondual (integral) development. The radial Band then incorporates the mature differentiated activity of the middle with the successful integration of all other Bands.

The radial Band therefore represents the most mature expression of both the linear (differentiated) and circular (integral) aspects of experience.

One of the great advantages of this approach is that - because actual experience comprises both linear (differentiated) and circular (integral) aspects in a widely varying fashion - this allows for a great deal of possible dynamic configurations with respect to the precise manner in which development can unfold for each person. 12

However the delineation of Levels (within the Bands) allows for a much more detailed map of development.

Approaching this in linear terms, the lower Band has three Levels. Starting from the lowest these are L3 (Lower 3), L2 (Lower 2) and L1 (Lower1) respectively. Though my treatment would differ in important respects we can identify these quite closely with Ken Wilber's archaic, magic and mythic stages!

The middle Band has also three stages with dual classifications as M1 (Middle 1), M2 (Middle 2) and M3 (Middle 3) and Lower 0 (L0), Lower 0 as also Higher 0 (L0, H0) and Higher 0 (H0) respectively. (These relate to Ken's rule/role, formal reflexive and centaur stages respectively).

The higher Band consists of Higher 1 (H1), Higher 2 (H2) and Higher 3 (H3) which in more mathematical terms I refer to as circular, point and null levels. 13

Finally the radial Band consists of Radial 1 (R1), Radial 2 (R2) and Radial 3 (R3). These have no close correspondents in Ken's system where they are treated - somewhat misleadingly - as a continuation of nondual reality (where form and emptiness interpenetrate). 14

So from a linear perspective (full) development proceeds through the 12 levels from L3 - L2 - L1 - L0 - L0,H0, - H0 - H1 - H2 - H3 - R1 - R2 - R3.

However there are also very important circular connections - establishing interdependence - as between these levels (which again can be viewed in horizontal, vertical and diagonal terms).

Thus complementarity in horizontal terms exists as between the interior and exterior (and exterior and interior) aspects of each level. The appreciation of this has significant implications providing a means of establishing unexpected links as between physical and psychological reality.

For example we could attempt to understand the preliminary structures of L3 from a psychological (interior) perspective. However - by definition - these structures have a complementary application to physical reality. What this means in effect is that there are close structural relationships as between the world of strings (strictly pre-strings) and earliest psychological development. Put another way a complementary relationship here exists as between each stage (as self) and each stage (as reality).

Complementarity also exists vertically as between "lower" and "higher" and "higher" and "lower" levels, which is somewhat more intricate. Ignoring the radial levels for the moment each "lower" is complementary with its "higher" (and the higher" with the "lower") level.

So L3 (archaic) is complementary with H3 (nondual) and H3 with L3.
L2 (magic) is complementary with H2 (causal) and H2 with L2.
L1 (mythic) is complementary with H1 (psychic/subtle) and H1 with L1.
Finally L0 (rule/role) is complementary with H0 (centaur) and H0 with L0. 15

More strictly these relationships are all defined by Type 1 complementarity (which in the case of the middle level remains merely implicit).

However further complementarity exists within the Bands. So L2 and L1 (and H2 and H1) are complementary with each other through Type 2 Complementarity (which unfolds at H2 and L2). Finally these combined levels (L2 and L1 and H2 and H1) are complementary with L3 and H3 through Type 3 complementarity (which unfolds at H3 and L3).

We also have diagonal complementarity combining the other two types so that the exterior of a "higher" for example can be integrated with the interior of a "lower" level respectively. 16

In this way therefore we establish the full interdependence of all "lower" and "higher" (and "higher" with "lower") levels which defines nondual contemplative reality.

Finally, theses integrated "higher and "lower" levels can be combined with the middle levels (which are neither "higher" nor "lower" allowing for activity that is both fully differentiated yet also fully integrated.

At R1 we have diagonal separation of polarities, at R2 both vertical and diagonal and finally at R3 both separation of all three polarities allowing for fullest expression of differentiated activity (that is also fully integrated).

In brief, by combining both linear and circular aspects of development, we can provide an overall model more intimately reflecting the true dynamics of experience that is both extremely comprehensive and potentially highly versatile. And what is really remarkable is that all these relationships have a coherent holistic mathematical interpretation. So the nature of development through and through is mathematical (in this overall integral sense).

To provide additional clarity on this model, we will now look at the 12 levels in more detail (especially with respect to interpretation of the perspectives involved).

The Lower Levels

It is important to remember that in this radial approach each level has both a linear - discrete - interpretation (thereby distinguishing its relative independence) and also a circular - continuous - interpretation (likewise enabling its relative interdependence with all other stages).

So the overall interpretation of a stage - in any context - is inherently dynamic (combining in various ways both discrete and continuous aspects).

So in holistic mathematical terms the binary digital encoding of development relates directly to both the linear (1) and circular (0) aspects (that are applicable to all stages).

However equally, each stage of development is defined with respect to fundamental horizontal polarities i.e. interior and exterior (and exterior and interior) that operate heterarchically within the stage.

Secondly each stage is defined with respect to the equally fundamental vertical polarities i.e. whole and part (and part and whole) that operate hierarchically between stages.

Finally each stage is defined with respect to the most fundamental diagonal polarities i.e. form and emptiness (and emptiness and form) that operate in a simultaneous heterarchical and hierarchical manner (both within and between levels).

Once again these three sets of polarities can be given a fully coherent mathematical interpretation as the holistic understanding of the eight sectors of the circle of unit radius (where the circle is divided into eight equal sectors by its horizontal, vertical and two diagonal line diameters).

So using the conventional notation (now understood in a dynamic holistic manner), the horizontal polarities are defined in "real" (conscious) terms.

The vertical polarities are defined - relatively - in "imaginary" (unconscious) terms. Finally the diagonal polarities are defined in simultaneous ("real" and "imaginary") terms of form as both conscious and unconscious. However - remarkably - as these diagonal lines have a magnitude of zero (i.e. = 0) equally they can be given a coherent interpretation as relating to emptiness. So the mathematical nature of the diagonal lines of the circle (when given the appropriate integral interpretation) beautifully demonstrate in dynamic terms the ultimate relationship as between form and emptiness.

So life initially emerges with respect to its diagonal polarities from a state where form and emptiness are totally confused (i.e. before differentiation properly takes place). It then approximates its ultimate mature state - with respect to the diagonal polarities - when form and emptiness are truly reconciled (in an integral manner).

Thus the overall nature of development can be expressed in a fully coherent integral manner with respect to the 3 fundamental polarities with both linear and circular interpretations in each case.

And as all of these dynamic relationships have a precise holistic mathematical interpretation, we can perhaps realise that the very nature of development (with respect to all its basic structures) is indeed "mathematical" through and through.

Lower 3 (L3)

From a linear perspective this represents the first of the prepersonal levels of development (which can be identified as the "archaic" stage).

The very nature of earliest experience is that form (initially in a somewhat amorphous manner) is gradually differentiated from emptiness. However though this stage does gradually take on a discrete identification (through the initial differentiation of the bodyself) its overall nature is more accurately defined in a circular (continuous) manner where all stages - with the potential for later differentiation - still remain largely entangled with each other. Therefore from this perspective the "lowest" still remains most entangled with its complementary "highest" stage (and ultimately by extension, through the other forms of complementarity, to all stages).

So for example, from this dynamic perspective the "lowest" stage (which is most entangled with the "highest") represents the confused interaction of both pre and trans (and trans and pre) experience. In other words because form is not yet properly separated from emptiness (or emptiness from form) spiritual experience is directly identified with matter in a grossly reduced manner (where neither can maintain a stable identity).

However if development proceeds successfully through this 1st stage (understood as discrete) successful linear differentiation with respect to the diagonal polarities eventually takes place. In other words the culmination of the stage is marked by the successful differentiation of the bodyself. So the infant is now able to identify a stable form (i.e. the body) that is to a degree separated from its environment. However because very little differentiation with respect to the other polarities will have yet taken place, a confused integral perspective still predominates. In other words whole and part still remain greatly entangled (leading in turn to the hierarchical confusion of "higher" with "lower" levels). Even more so interior and exterior aspects will have as yet undergone very little differentiation thereby leading to the heterarchical confusion of the self with reality. So in holistic mathematical terms, L1 starts from the confused circular complementarity of all 3 sets of polarities (i.e. a confused state of overall integration) before proceeding to gradual linear differentiation with respect to diagonal polarities.

However the proper understanding of the confused dynamic interactive structure of this 1st level (L3) requires the corresponding mature interpretation of its complementary "higher" level (H3).

Another remarkable insight provided by this interactive approach is the realisation that the psychological structures of early infancy are necessarily mirrored in the earliest structures of physical reality. So as we probe more deeply into the nature of strings we are dealing with the same dynamic structures that unfold in early infancy. 17

Perspectives of Stage

Because of lack of sufficient differentiation, distinct perspectives do not emerge in a coherent manner at L3. Therefore considerable confusion again remains with respect to basic distinct perspectives (of a somewhat amorphous nature) and overall perspective (with respect to the relationship as between differentiated perspectives).

Perspectives here are limited to form and emptiness. However in bi-directional terms these keep switching. What this means in effect is that - due to lack of differentiation - form is immediately identified with emptiness (and emptiness with form). Therefore in earliest infancy phenomena achieve little stability and tend to disappear from memory (as soon as they arise). However by the end of the stage - through recognition of the bodyself as distinct from the environment - these basic perspectives are stabilised, though overall (integral) perspective remains greatly confused.

As we know, the analytic interpretation of number is synonymous with order in quantitative terms. Likewise the holistic interpretation of number is synonymous with order in a qualitative sense. 18 This means in effect that the holistic interpretation of the major number types can be used to precisely define the nature of perspectives associated with each stage. In this sense, each major stage has a holistic interpretation (as qualitative number type).

Now the most basic (and important) numbers are the two binary digits 1 and 0. In holistic terms these are inherent in form and emptiness as oneness (1) and nothingness (0) respectively.

So the holistic binary numbers - where oneness cannot be properly differentiated from nothingness - can best define the nature of perspectives for this opening stage. This would also suggest that with respect to the physical aspects of reality a more basic stage of matter than strings (i.e. a binary state of matter) could be identified. 19 However eventually this binary stage gives way to stable duality (i.e. the holistic interpretation of 2) with respect to the diagonal polarities. 20

Lower 2 (L2)

In discrete terms this represents the second of the prepersonal stages, which is referred to as the magical level. It deals with the more advanced development of sensorimotor experience, which in continuous terms is especially complementary with H2 (in a confused manner). By this stage a stable body self has been differentiated (relating to the linear separation of the diagonal polarities). This development is now further consolidated during this stage. However the process moves on to the gradual linear separation of vertical polarities.

The vertical polarities relate to whole and part aspects, which initially are very much confused with each other. This in turn relates to entanglement of the conscious and unconscious. So the unconscious dimension of experience relating to the potential for wish fulfilment is thereby directly projected into actual (conscious) experience leading to its characteristic magical nature. In orders words the infant sees "objects" in animistic terms as being imbued with magical properties as the means for fulfilling a primitive desire for spiritual meaning.

Thus from a psychological perspective the "imaginary" (unconscious) is still greatly confused with the "real" (conscious) aspect of experience. This likewise equates with the dimensional aspect (providing an overall perspective) being confused with objects, which is the very basis of primitive instinctive understanding. With such behaviour a continual collapsing of the overall dimensional context of experience takes place, so that it is directly identified in an immediate involuntary manner with the object phenomena thereby arising.

Therefore the overcoming of instinctive behaviour requires the gradual development of a stable dimensional background through the enfolding of the emotional self literally creating space and time as between objects that thereby arise.

By the end of L2 this second development will have been sufficiently consolidated allowing the stable distinction without undue confusion of the emotional (personal) self and the (impersonal) world.

So the differentiation of the emotional self is associated with the corresponding differentiation of the vertical polarities. Here from the psychological perspective, the "real" conscious is separated from the "imaginary" unconscious; from the complementary physical perspective, "imaginary" dimensions are separated from "real" objects.

However once again a significant price is paid for such progress in that the unconscious is thereby repressed with the integral aspect significantly reduced to the differentiated. Indeed this is the very means by which phenomena achieve a more rigid unambiguous identity. 21

In holistic mathematical terms, L2 is initially defined by the linear differentiation of diagonal polarities and the confused circular complementarity of both vertical and horizontal polarities. However by its conclusion the vertical polarities will also have achieved successful linear differentiation.

Perspectives of Stage

We have already used the holistic definition of the two most fundamental binary digits (1 and 0) and that of 2 (as duality) to explain the perspectives of the first stage in number terms.

Now greatly pertinent to this second stage (L2) is the holistic definition of prime numbers. 22 I indicated before in "Clarifying Perspectives 2" how the very notion of prime numbers holistically bears a close relationship in physical terms with the nature of the "primary" constituents of matter (i.e. strings) and in complementary manner primitive (instinctive) behaviour from a psychological perspective.

So the prime number notion in dynamic interactive terms relates to the situation where dimensions are so directly identified with object phenomena (that neither can be properly distinguished).

The very identification of stable phenomena (in physical and psychological terms) requires that they can be sufficiently separated from a background dimensional context of space and time. Put another way it requires that distinct perspectives can be sufficiently separated from an overall perspective (to allow their identification).

So therefore we can define prime space-time as a dimensional structure that precedes the stable identification of phenomena (where - by definition - it is still dynamically inseparable from distinct objects).

Therefore what are referred to as "strings" relate to a world defined by such holistic prime notions. Likewise primitive instinctive behaviour of the early L2 stage likewise relates to the same prime dimensional framework. Therefore properly understood, each stage of development (with complementary physical applications) is defined by a unique dimensional framework (that can be defined in a holistic number manner).

So in terms of perspectives we start L2 with the basic distinction of form (matter) and emptiness (spirit). Initially the additional perspectives with respect to whole and part are greatly confused with each other. However these are likewise eventually differentiated (in a stable unambiguous manner). So with the growing identification of these distinct perspectives (diagonal and vertical) an overall integral perspective (relating to their dynamic interaction) likewise emerges. However this overall perspective in part still remains confused (due to lack of separation of horizontal polarities); it is also somewhat reduced due to growing association with (mere) differentiated elements.

Lower 1 (L1)

In discrete terms this relates to the third of the prepersonal stages in what is referred to as the mythic level. In continuous terms however it is most closely associated with H1 (the psychic/subtle) with which it is directly complementary (in hierarchical terms). In other words it requires the mature understanding of H1 to properly interpret the confused dynamic interactivity of L1.

By this stage both diagonal and vertical polarities have been sufficiently differentiated allowing the distinction of form and emptiness and whole and part. Therefore the identification of phenomena - with an increasing degree of stability - can now take place against a background of space and time. Put another way, there is a growing capacity to distinguish (spiritual) states from (phenomenal) structures.

This also entails in physical terms that phenomenal identification (e.g. at the quantum level of sub-atomic particles) can now take place, which at higher levels of macro organisation attain a greater degree of stability.

Indeed we have here quite literally the unfolding of natural reality. So as the level of differentiation increases, the chaotic dynamic instability that characterises earlier interactions gradually gives away to more stable forms of an increasingly rigid nature.

However in psychological terms a degree of confusion still exists due to lack of sufficient differentiation with respect to the horizontal interior and exterior polarities. What this means in effect is that conscious and unconscious are still entangled to a degree, so that holistic (potential) meaning - pertaining ultimately to the universal spiritual nature of reality - is still confused with local (actual) phenomena. In other words such local phenomena can still resonate to a degree with archetypal mythic meanings. 23

This also entails that in mythic type societies - because of lack of sufficient differentiation of the (interior) self from (exterior) reality - one's role tends in society to be predefined through custom or tradition (that has perhaps remained unchanged for a considerable period of time). However as linear differentiation proceeds, the horizontal polarities are gradually separated through the differentiation of the mental self. In other words one is increasingly able to abstract the (interior) self from the (exterior) environment thereby offering increasing possibilities to act upon and thereby change that environment.

In holistic mathematical terms the initial structure of L1 is defined in terms of growing linear differentiation of polarities with respect to both diagonal and vertical aspects with continued confused integration with respect to remaining horizontal polarities. However by the end of the stage (with the differentiation of the mental self), the linear polarities also achieve a critical degree of differentiation. However because specialised development of the differentiated aspect has not yet taken place a degree of integral confusion will implicitly remain.

Perspectives of Stage

We have seen how the perspectives of the earlier stage (L2) were precisely defined in terms of the holistic interpretation of prime numbers. Now the perspectives of this stage are defined by the corresponding holistic interpretation of natural numbers.

In conventional analytic terms, all natural numbers are obtained from prime numbers (combining them one or more at a time). In this way most natural numbers represent the composite mix of several prime numbers. Now for example 3 which has no factors (other than itself and 1) is prime; However 6 = 2 X 3 and 12 = 2 X 2 X 3 are composite numbers. Likewise in holistic terms, as the prime constituents of matter (strings) are combined in a coherent manner, natural particles (of increasing greater stability) emerge. The fact is that the very ability to achieve this coherent mixing of prime particles requires a slowing down in the rate of dynamic interactivity, thereby enabling the more composite and identifiable rigid phenomena of nature to emerge.

So the predefining quality of nature is that we can literally identify holons (i.e. integral wholes) resembling the manner of identification of the natural numbers (which are integral wholes).

In nature generally, though distinct perspectives with respect to form and emptiness and whole and part can emerge, very little evolution generally takes place as with respect to the horizontal polarities (interior and exterior). Thus human evolution is somewhat unique in the manner in which the self conscious self can be differentiated from the impersonal environment, thereby enabling it to increasingly act upon and change this environment.

So with human development, distinct perspectives at this stage emerge in a developed manner with respect to both diagonal, vertical and horizontal polarities (comprising all the key native or indigenous perspectives). Though these are likewise necessarily present in the rest of nature they do not develop to the same degree. However due to the increasing emphasis on differentiation (of distinct perspectives) overall perspective - representing the dynamic configuration of these natural perspectives - is now significantly reduced to their distinct elements.

The Middle Levels

The middle levels represent the specialised linear differentiation of the three sets of polarities (horizontal, vertical and diagonal) leading to the maximum separation in experience of conscious from unconscious aspects. In formal terms the unconscious is then greatly reduced - especially in science - to merely "real" conscious interpretation.24

Lower 0 (L0)

This really represents the transition stage as between understanding that is still in part mythical (relating to remaining confusion as between conscious and unconscious) and specialised rational understanding (relating to the developed conscious).

L0 is also commonly referred to as concrete operational (conop) or rule/role (in Wilber's terms).

Though mythical appreciation still relates to one's general viewpoint of reality, increasingly at an empirical level, clear rational understanding can be applied enabling activities to be sub-divided and then rearranged in a coherent manner. In other words because the mental self has by now been sufficiently separated from its environment, one can thereby increasingly operate on and thereby control that environment (in a concrete manner). It also allows more independence in adopting a number of roles (reflecting differing views of the self) with respect to society.

In holistic mathematical terms, L0 is defined explicitly in terms of linear differentiation with respect to horizontal, vertical and diagonal polarities (at a concrete level) though implicitly unconscious mythical confusion still permeates more general (universal) understanding.

Perspectives of Stage

The holistic interpretation of rational numbers is especially relevant in terms of the number understanding of all the stages of the middle level. As we have seen the previous stage was identified with the natural numbers 0, 1, 2, 3, 4,……… However beyond this we have the set of all integers where these numbers can be given a negative (as well as positive) interpretation. This means in holistic terms that one learns in the latter phases of L1 to implicitly negate (as well as posit) concrete phenomena thus enabling clearer separation of the (interior) self from (exterior) reality.

However now something remarkable happens in psychological terms with a direct link to the mathematical notion of a rational number.

Though rational numbers include all the previous number types (already dealt with) they also include fractions.

For example 1/2 would be the simplest example of a fraction. Now whereas 2 would be written strictly as 2 (raised to the power of 1), 1/2 would be represented as 2 (raised to the power of -1). So the switch here from 2 to its reciprocal 1/2 entails a corresponding linear switch in dimension from positive to negative (i.e. + 1 to - 1).

Now whereas the concrete object phenomena of experience are represented directly by the number quantities as perceptions, the actual dimensions relate to their corresponding concepts.

Therefore in holistic terms the continual interaction in experience of perceptions and concepts (and concepts and perceptions) entails the corresponding interaction of object phenomena with dimensions and dimensions with object phenomena.

Therefore in holistic terms, the formation of the negative linear dimension (represented by the power of - 1) relates to the ability to implicitly negate in experience concepts (as well as perceptions). In this way the self is able to abstract itself from both object phenomena (represented by concrete perceptions) and their corresponding dimensions (represented by their concepts).

Through this ability to abstract (with respect to perceptions and their corresponding concepts) one is thereby enabled to operate rationally on the concrete world i.e. where wholes can be sub-divided into constituent parts and where these parts can again be synthesised once more into wholes. Therefore when understood appropriately in holistic terms, rational activity - which increasingly characterises the middle levels - has a fully coherent philosophical interpretation (in mathematical terms). 25

Thus rational activity from a psychological perspective bears a direct relationship to rational numbers in mathematical terms. Just as a rational number can be subdivided - without limit - into smaller constituent parts, likewise rational activity is based on the belief that reality can be analytically subdivided into ever-smaller constituent units. 26

The power of abstraction with consequent growth in rational ability likewise transforms the nature of perspectives so that they can be controlled and changed. This thereby enables increasingly complex higher order distinct perspectives to emerge. However the downside here is that due to specialisation with respect to the differentiated aspects, there is a corresponding reduction of the integral aspect of overall perspective to distinct perspectives. In other words overall perspective becomes more fragmented. However because at this stage rational ability is still somewhat superficial, higher order perspectives would be largely limited to local concrete type situations.

Lower 0, Higher 0 (L0, H0)

This stage is the true middle (of the middle) forming a direct bridge as between "lower" and "higher" levels. Thereby it alternates between the ceiling of the "lower" and the floor of the "higher" stages. It is a very important stage - especially with respect to customary intellectual understanding - and is commonly referred to as formal operational or formop (Piaget) or formal-reflexive (Wilber). 27

This represents - especially from the cognitive perspective - the specialisation of linear differentiated understanding thus enabling increasingly abstract interpretation of a universal nature to emerge.

Indeed such understanding is very evident in our conventional notions of science. When we look at the three fundamental sets of polarities we can see how such science is based firstly on the abstraction of form from emptiness. So conventional science - especially as for example in physics - tries to understand the phenomenal world of form (as if separate from Spirit). Secondly wholes (in the archetypal sense) are separated from parts. In other words whereas parts are quantitatively contained in wholes (in a reductive sense) wholes are not (qualitatively) contained in parts. Once again this reductive belief is associated with the typical fragmented worldview of conventional science. Finally the (interior) self is separated from the (exterior) world. This leads to the strong belief that the reality can be studied with respect to its behaviour (as if independent of self).

I cannot stress strongly enough that our conventional notions of science directly reflect the limited understanding of the middle stages of development (where linear differentiated notions are carried to extremes).

In other words the metaparadigm for such science is based on merely linear interpretation with respect to the three fundamental polarities.

However once we allow for differing basic assumptions with respect to these polarities, completely distinctive metaparadigms for science (applicable to all development) emerge.

And as each major level is uniquely defined in terms of the relationship of these fundamental polarities, this means that a unique scientific metaparadigm arises in each case.

Therefore - as we shall see at the "higher" levels - science is defined by increasing complementarity with respect to these polarities leading to a very distinctive integral vision. 28

So in holistic mathematical terms, L0, H0 is explicitly defined in terms of linear differentiation with respect to horizontal, vertical and diagonal polarities.

Perspectives of Stage

The perspectives of this level are marked by the increasing development of rational ability. Whereas in the earlier stage (L0) one was limited analytically with respect to concrete situations, here one can increasingly operate on the more universal dimensional aspects of reality (through general conceptual ability) thereby enabling more powerful potential control of reality. So whereas the previous stage was associated with the holistic counterpart of the concrete notion, this is now associated with the more general abstract notion of a rational number.

Now the word "potential" as we have seen related directly to the imaginary unconscious aspect of experience. However because of specialisation of conscious abilities, the unconscious is largely reduced to conscious interpretation. This means in effect that the ability to imagine new perspectives - thereby facilitating change in our present circumstances - is largely understood with respect to actual "real" situations (i.e. as amenable to conscious control). Thus though our modern age has indeed witnessed a dramatic change in our ability to quickly alter perspectives, it is largely confined to the merely conscious differentiated aspect and increasingly to a narrow range of impersonal type perspectives. So this stage is certainly characterised by the increasing capacity to form higher order distinct perspectives but in a somewhat unbalanced manner (where the impersonal aspect dominates). Likewise the great increase in fragmentation thereby brought about is associated with a considerable loss in genuine overall (integral) perspective.

Higher 0 (H0)

This stage - referred to as the centaur by Ken - represents the highest of the middle stages where it properly represents the ground floor as it were of the "higher" levels.

Now the understanding of the centaur i.e. vision-logic represents to a degree two Bands. In explicit cognitive terms, it still relies on the linear asymmetrical type interpretation (associated generally with the middle levels) though in a more multifaceted flexible manner. Because conop and formop can now be combined with respect to their developed expressions, increasingly creative analytic linkages (of both a deductive and inductive kind) can be made. However the spiritual contemplative awareness that is properly associated with the "higher" levels can be incorporated in various degrees with this cognitive understanding. Indeed it is this spiritual aspect that - in direct terms - provides the "vision" (imbuing the logic) that is characteristic of its nature.

Therefore in explicit intellectual terms, vision-logic represents the most advanced of the linear (asymmetrical) types of understanding associated with the middle levels. (These by their nature are geared for the differentiated appreciation of reality). However implicitly, vision-logic can equally - because of its spiritual aspect - impart something of the integral appreciation properly associated with the "higher" spiritual levels.

However let's be clear on this very important point! In terms of formal intellectual translation, vision-logic cannot provide an integral interpretation of development that is properly consistent.

Thus Ken Wilber's intellectual interpretation of development based - as it is - on vision-logic, does not provide a consistent integral translation of development.

From my very first posting on the original Ken Wilber Forum over 7 years ago, I have pointed to a crucial discontinuity that is characteristic of his writing.

In structural terms, Ken's interpretation of development is very much confined to the unambiguous asymmetrical type distinctions that are identified with the middle levels (though admittedly in an unmatched comprehensive manner). Also in terms of states, Ken clearly has a sincere commitment to emptiness in the attainment of pure nondual awareness (and undoubtedly is extremely knowledgeable of many of the Eastern mystical traditions).

However what I find greatly lacking in his writing is the dynamic interaction of spiritual states with phenomenal structures that necessarily leads to continual paradoxical transformation in their very nature.

Therefore at the "higher" levels, a very distinctive circular bi-directional treatment of relationships is required to do justice to such growing interactivity. Furthermore it is only through combining such circular paradoxical notions of development with previous linear constructs, that a consistent interpretation of development (that is properly integral) can be given.

It is certainly not enough to throw out occasional remarks about dual interpretations being ultimately paradoxical in the light of the nondual, without consistently showing how this applies to all - necessarily arbitrary - asymmetrical distinctions regarding development at the level of vision-logic. And this Ken Wilber does not do!

So quite frankly, I do not consider his interpretation of development as properly integral (and this has been my considered position now for many years). Of course I will readily concede - when looked at from the perspective of vision-logic - that his overall interpretation may indeed appear integral (assuming that many of his serious readers share the same broad perspective). In other words the inconsistencies implicit in vision-logic only become properly apparent from the overall intellectual perspective of a "higher" level!

Thus to test the assertion that I am raising i.e. that his vision-logic interpretations are fundamentally inconsistent when seen from a "higher" cognitive level, then it requires first a willingness to try and appreciate the perspective (from which the assertion is made).

Also I am not impressed with the manner in which Ken attempts to deal with criticism. By invariably complaining of misrepresentation - even by his most able and devoted followers - he thereby avoids properly addressing any issues raised.

I would also strongly disagree with his present stance on "relevant" criticism - now seemingly to be confined to "in-house" associates in regular communication with Ken - as his overall perspective is not likely to be seriously challenged in such circumstances.

In this respect the lack of dynamic interactivity - which generally characterises his intellectual interpretation - is again very much evident in his approach.

Ken seems to think that he is the only competent judge on whether someone is adequately representing his viewpoint. This would indeed be true if there was only one valid perspective that could be adopted on his work (i.e. Ken Wilber's).

However when one adopts a distinctive perspective from Ken's, then one will thereby see his approach in a new light (possibly revealing problems which Ken cannot yet see from his own viewpoint). So from a dynamic perspective it is quite conceivable that an outsider may see important aspects of one's approach more clearly (due to the distinctive perspective adopted). And of course this equally applies in reverse fashion. So proper mutual dialogue - especially in an integral context - should bring a new enhanced appreciation of both participants' perspectives.

Now Ken goes on and on about all the wonderful criticism he is receiving from his "in-house" critics. However as he is attempting to control the process on his terms (i.e. through the implicit acceptance of his overall perspective), I am more than a little sceptical. 29

For example he has as yet to address one key issue i.e. the appropriate intellectual nature of an integral interpretation of development. Again I firmly believe that this matter is truly fundamental for Integral Studies generally. So once more, though Ken Wilber admittedly excels in the demonstration of a certain type of vision-logic understanding, I would find it very inconsistent from my integral perspective.

In holistic mathematical terms, H0 is characterised in explicit terms by linear differentiation with respect to the three sets of polarities (horizontal, vertical and diagonal). Implicitly it is also characterised in varying degrees by the intuition appropriate to the "higher" spiritual stages. However the spiritual aspect is still significantly reduced to the structural level of form. In other words, despite increasing creativity and flexibility of understanding, structural relationships are still largely understood in unambiguous asymmetrical terms.

Perspectives of Stage

H0 is - somewhat misleadingly - viewed in terms of the integration of all previous stages. In fact it entails the significantly reduced integration of previous stages. (True integration requires the "higher" stages). However in holistic number terms we can appropriately view H0 in terms of the integration of all the previous number types (where they are viewed qualitatively in a merely rational manner). In quantitative terms, the binary digits are part of the rational number system. So are the prime numbers and the natural numbers and finally rational numbers (as fractions). So therefore in holistic terms, when we attempt integration through imposing the rational understanding of H0 on all previous levels, we obtain a reduced - merely linear -interpretation.

However H0 equally allows for increasingly more complex higher order distinct perspectives. Also - as we have seen with Ken Wilber - it allows for much greater reflection on the nature of these perspectives. However explicit demonstration still falls short of adequately interpreting their highly intricate nature. This is inevitably associated with considerable phenomenal identification with such perspectives. So once again, overall perspective (though perhaps implicitly spiritual) is significantly reduced to the structures of distinct perspectives (thereby breeding undue rigidity and selfish attachment).

Notes

1. As I use the term a stage is any sequence of development defined by a unique holistic structure. It can be broadly or narrowly defined. The Bands represent the broadest classification of stages in my approach followed by levels, transitions between levels, sub-levels, dimensions (or directions) modes (primary and secondary) which in turn are defined with respect to types (i.e. personality types) and phases. What is remarkable is that the holistic mathematical approach can be extended to interpret all these stages. However in this introduction we are confining ourselves to Bands and Levels.

2. I distinguish an open from a closed integral approach. In the closed version the emphasis is on the negation of form so as to attain the pure experience of emptiness. This typically results in contemplative type experience that is somewhat removed from the world. However in the open approach an equal balance is ultimately maintained as between form and emptiness (though a predominant emphasis on contemplative awareness may well initially characterise the "higher" spiritual stages). So in the open approach the final stages are radial where the mature balanced expression of the specialised aspects of development (both differentiated and integrated) takes place.

3. Once again it is no accident that the very symbols we use to represent one (1) and zero (0) are - with minor modifications - the line and circle respectively. Implicit in the very recognition of form is the holistic notion of oneness (1) through which form can be identified. Likewise implicit in emptiness is the holistic notion of nothingness (0).

4. The whole and part polarities of course relate to individual and collective (as used by Ken Wilber). However I personally prefer the whole and part terminology (which is a little stronger than individual and collective).

5. A considerable weakness of the four-quadrant model - even when understood in dynamic interactive terms - is that it cannot successfully deal with the nature of psychophysical interactions. Therefore the eight-sector approach, which can successfully accommodate such interactions through the inclusion of diagonal, is more comprehensive.

6. As the horizontal, vertical and diagonal polarities are ultimately interdependent, they necessarily overlap to a degree throughout development. Therefore their independent development is strictly of a relative nature.

7. I have referred to this in the past as "The Theory of Everything". A very quick summary of the mathematical relationships is contained in the given reference.

8. Holistic mathematics has a very different rationale from its analytic counterpart where (with from static axioms or assumptions) conclusions are logically deduced through the making of sequential asymmetrical connections as between relationships.

With holistic mathematics the purpose is to establish the underlying dynamic symmetry of all relationships through complementary type appreciation with respect to polarities. In this way the ultimate integration of all reality with respect to both its physical and psychological aspects can thereby be facilitated.

9. In formal terms conventional mathematics is understood solely with respect to "real" (conscious) understanding. In this sense it is literally lacking imagination (that relates to the unconscious aspect). Therefore as holistic mathematics relates directly to the "imaginary" unconscious aspect, it opens up immense creative possibilities that cannot be imagined from the analytic perspective. So analytic mathematics relates directly to the "real" (conscious) aspect; holistic mathematics relates to the "imaginary" (unconscious) aspect and radial mathematics relates to both the "real" (conscious) and "imaginary" (unconscious) aspects of understanding. However though holistic mathematics does indeed open up a truly integral scientific appreciation of development, it is not designed to replace other valid approaches which can perhaps better deal with alternative perspectives.

10. Put another way the interaction as between horizontal polarities (for the various stages) relates the corresponding interaction of stages of self with stages of reality. (Type 1 Complementarity). The interaction as between vertical polarities (with respect to "real" and "imaginary" aspects) relates to the interaction of states and structures between stages (Type 2 Complementarity). Finally the interaction within and between levels of diagonal polarities relates to the simultaneous psychophysical interaction of body and mind aspects (Type 3 Complementarity).

11. What is neither prepersonal nor transpersonal is thereby personal. So the middle levels are commonly referred to as the personal stages of development.

12. For example we could identify three general types of mystical experience of the radial levels.

Firstly we have - what is sometimes referred to as - active mysticism. This would be characterised by greater development with respect to the middle than the higher levels (though considerable authentic spiritual development would necessarily be involved). Secondly we have the more passive variety of contemplative mysticism which would entail relatively greater attention to the "higher" than the middle levels. Finally we have the most advanced type that is both active and contemplative to a marked extent entailing equal balance as between middle and "higher" levels.

13. This terminology of circular, point and null has been carefully chosen. When we draw a circle we can draw lines (through to the centre) to the outer circumference. In like manner when circular (i.e. bi-directional) understanding first emerges, it is necessarily conveyed in a somewhat linear format (inspired by Spirit at the centre of one's being). The circular here corresponds with the psychic/subtle stage. However as attachment to the dualistic linear element is eroded, the circle as it were continues to contract inwardly. Therefore when no (rigid) linear element remains we are left with the point (at the centre of both circle and lines). In like manner the point level represents this centre (as emptiness) in the arrival (inwardly) at pure spiritual awareness. So the point level corresponds with the causal stage. However because the emphasis so far has been on the erosion of form, there can be a subtle attachment remaining to this very process (of negation of form). So in the third of the "higher" stages this imbalance is addressed so that with no undue attachment to emptiness (over form) or (form over emptiness) proper balance can be maintained as between both aspects. So I refer to this as the null level which is based directly on the diagonal null lines of the circle (in the complex plane) which literally are of zero magnitude (though in pictorial representation they will have finite extent). This would correspond most closely with nondual reality (where emptiness = form and form = emptiness).

14. I use the term "radial" in two senses, which are intimately related. Firstly the radii or radial lines join the centre of the circle in a linear manner to the circumference (which is circular). And this can equally be read in reverse as the lines joining the circle to the centre. Thus radial is meant to dynamically combine Spirit (as essence) with both linear (differentiated) and circular (integrated) modes of understanding. Likewise the term is used to convey the notion of spiritual rays of light emanating in all directions from the centre to the outer circumference (and in reverse from the undefined circumference to the centre).

15. Remember that in dynamic terms that opposite stages ("lower" and "higher" and "higher" and "lower") are vertically complementary with each other. In early development a very confused relationship exists. So for example the newly born infant directly confuses L3 with H3 (and H3 with L3). However with later advanced spiritual development (assuming it takes place) these stages will again be experienced in a complementary manner (this time in mature fashion). So again H3 is complementary with L3 (and L3 with H3). However it requires the mature interaction of opposite levels (in both directions) to properly interpret the confused interactions (again in both directions).

16. I will just briefly give examples of the application of the three types of complementarity with respect to the philosophical interpretation of quantum mechanical relationships in physics.

Type 1 Complementarity would lead to the realisation that it requires the "higher" physical structures (of H1) where reality is understood in an enhanced spiritual fashion to interpret the "lower" physical structures (of L1) to which quantum relationships refer. Type 2 Complementarity would lead to the further realisation that the "higher" illumined state of H1 is likewise needed to satisfactorily understand the "lower" structure of L1 (Remember that states and structures are "real" and "imaginary" with respect to each other). Type 3 Complementarity would entail further that the (interior) mental constructs of H1 are needed to interpret the (exterior) sense phenomena of L1. (So here we are relating opposites in both heterarchical and hierarchical terms with respect to cognitive and affective modes!)

17. Of course the infant cannot establish the structural complementarity of the earliest psychological with the earliest physical structures because experience is necessarily confused at this stage. However it is possible - through the advanced development of the "higher" stages (strictly the advanced interaction of "higher" and "lower" and "lower" and "higher") - to interpret the structural heterarchical complementarity (physical and psychological) of the corresponding "lower" stages (strictly the confused interaction of "lower" and "higher" and "higher" and "lower").

18. Again strictly speaking the holistic notion of number is synonymous with the complementary dynamic relationship as between quantitative and qualitative notions of order. So the holistic notion applies to both the physical and psychological aspects of reality (which are complementary).

19. I would see some parallels here with respect to the work of Sir Roger Penrose on spinors (where matter is defined in terms of two fundamental states).

20. The holistic relationship as between form and emptiness (and emptiness and form) is encapsulated in the dynamic binary relationship 1 - 1 = 0. In other words when the identification of (posited) form is fully negated, nothingness (as spiritual emptiness) results.

Ken Wilber refers to the I-I relationship. However I would find this 1 - 1 relationship even more meaningful. Now duality simply results from viewing both aspects of form with respect to positing. Thus when we posit form and then (instead of negating) continue to posit it (as mere differentiation), then duality (as rigid opposite polarities of form) results.

21. This leads to a very important point regarding the reduced nature of conventional experience. Whereas the interaction as between (specific) objects and (general) dimensions necessarily entails the corresponding interaction of both conscious and unconscious, we interpret this interaction in a merely conscious manner. Thus both "objects" and "dimensions" are understood as "real". However the true relationship - incorporating both conscious and unconscious in a balanced manner - is that "objects" and "dimensions" are "real" and "imaginary" with respect to each other. In other words in any context, if one is "real" the other is "imaginary" and vice versa. However this understanding only properly unfolds at H2 (where both conscious and unconscious are properly differentiated from each other).

22. Now the original relationship as between form and emptiness is 1 - 1 = 0 (strictly 1 (raised to the power of 1) - 1 (raised to the power of 1) = 0. Now replace 1 in the first case with respect to both quantity and quality (dimension) by 2 (which is the root prime number). Then 2 (raised to the power of 2) - 1 = 3 (which is prime).

If we now raise 2 to this new power of 3 and subtract 1 we get 2 (raised to the power of 3) - 1 = 7 (which is also prime).

Repeat this process again and we have 2(raised to the power of 7) - 1 = 127 (which is again prime).

Do this once more and we have 2 (raised to the power of 127) - 1 = 170,141,183,460,469,231,731,687,303,715,884,105,727 (which is also prime). This number (with 39 digits) held the world record as the largest known prime number from 1876 to 1951. But look at how simply it can be derived!

So what I am saying here is that in holistic terms, the prime notion - with special reference to primitive forms (where objects cannot be clearly distinguished from dimensions) - is especially related to diagonal transformations of duality (corresponding to the differentiation of the diagonal polarities) which as we have seen leads to the first stable emergence of duality in experience. (In this sense a number raised to a power is diagonal as both the number quantity and dimensional quality are thereby inextricably linked).

Now procedures to generate primes (through any method) gradually break down. For example if we start with 2 and multiply it by other prime numbers and then subtract 1 we will tend to generate a lot of primes. So primes (with no factors) are closely related to the most composite numbers (with many factors) through subtraction of 1. For example 2 X 2 X 2 X 3 X 3 = 72 (which is very composite with 5 prime factors). However 72 -1 = 71 is a prime number! However ultimately all these processes break down so that we are left generating many natural numbers. Thus in creation, all prime processes (that cannot be directly identified) ultimately - through being related to each other - give way to natural observable phenomena. However just as the natural number system includes the primes, nature thereby includes - as well as observable composite phenomena - non-observable prime constituents (such as strings).

23. Indeed this has a firm basis in quantum mechanics where it is now widely accepted (though disputes remain) that sub-atomic particles can indeed effect each other (even at a great distance). So there is an archetypal universal order explaining the behaviour of individual particles.

24. The very word "reality" as used - especially in physics - corresponds to what can be known in conscious ("real") terms. It is therefore a very reduced notion as it ignores the vitally important interaction of conscious and unconscious in all experience.

25. Once we understand the manner by which perceptions and concepts interact in experience, it directly implies the existence of negative as well as positive dimensions. In other words whenever we posit concept phenomena in experience we thereby create positive dimensions. Likewise when we negate concepts we create negative dimensions (which cancel out those posited). This is why the spiritual person primarily lives in the present (where the positive creation of objects and dimensions is balanced by the negative). However though implicitly, negation (of perceptions and concepts) necessarily applies at the L0 stage, a reduced - merely positive - interpretation is given (leading to unambiguous notions with respect to objects and dimensions).

26. This was deeply important to the Pythagorean School, which attempted to combine holistic philosophical ideas with respect to mathematical activity with quantitative analytic behaviour.

Therefore there was a strong belief in the direct correspondence as between the rational qualitative order (i.e. as a scientific paradigm for studying reality) and the actual behaviour of rational numbers. So rational numbers in their unambiguous identity were believed to correspond with a qualitative viewpoint that scientific laws were equally unambiguous. Thus the discovery of irrational numbers as a result of their famed Pythagorean triangle (i.e. square root of 2) was a mortal blow to this whole belief system. What is required in therefore to restore the Pythagorean system at a new level is to establish a corresponding philosophic "irrational" paradigm that directly corresponds with the behaviour of irrational numbers. We will return to this later.

27. This level entails much more than cognitive development e.g. affective and moral. However it is certainly true that in our society because of the great emphasis on the cognitive understanding of this level that it does indeed influence the development of other modes also. Thus because the unconscious element is so much unrecognised with respect to cognition, it often tends to express itself in an involuntary manner with respect to affective understanding. Thus the more we consciously attempt to exercise cognitive control (with respect to reality) the more we lose affective control at a deeper unconscious level.

28. Integral science largely relates to the establishment of deep - and often unexpected - complementary relationships with respect to physical and psychological reality (in horizontal, vertical and diagonal terms). It is the realisation of these common underlying relationships with respect to all aspects of reality that directly facilitates the integral viewpoint.

I can find little emphasis on such integral science in Ken Wilber's writings. Indeed his science of the "higher levels" as for example in meditation research is based on the application of merely analytic type investigation to spiritual experience.

29. From what I can judge - though I sincerely hope that I am wrong on this - an "inside" critic who would dare to fundamentally challenge Ken's overall approach would quickly become an "outside" critic (accused of grossly misrepresenting his position) and thereby forfeit the privileges of being a member of the "insider" club. So whereas I do certainly accept that Ken is open to various criticisms that can enhance presentation within his existing overall perspective, I would see little evidence that he is truly open to fundamental criticism of this perspective.

Thus through a remarkable evolution in his thinking has indeed occurred over the years (from his Wilber 1 to Wilber 5 phase) I would see this as a logical progression of a developmental approach associated with the overall perspective of vision-logic.

However the question as to how suited such a vision-logic interpretation can be as an integral approach in the light of the intellectual approaches that unfold at "higher" levels is of a much more fundamental nature.

References

Collins, P (2003), Development: the Radial Approach