"There appeared to be a conflation here", I thought. Collins says in footnote 4 (p. 27/42) that one needs a Zen-like paradox to recognize the limitations of rigid (dualistic) understanding; but equal recognition of opposite (excluded) poles on different levels does not mean that molecules are included in atoms!

This is simply a misinterpretation of my position. This is due to the use of a rigid dualistic manner of explaining a relationship to criticize a more subtle bi-directional interpretation.

Let us examine this more fully.

When we say that atoms are included in molecules (and molecules not included in atoms), we are using the asymmetric scientific way of viewing relationships, where the qualitative aspect of experience is reduced to the quantitative. So strictly Mike's statement is only true in this scientific sense, which ignores qualitative appreciation.

However when we properly allow for both quantitative and qualitative aspects, understanding becomes bi-directional and symmetrical.

Thus if the atom is quantitatively transcended and included in the molecule, thereby the molecule - relatively - is qualitatively included and made immanent in the atom.

This reflects the all-important difference as between cognitive (impersonal) and affective (personal) type awareness.

With scientific (cognitive) understanding, we typically define parts in the context of wholes. This is the transcendent perspective.

However with aesthetic (affective) understanding, this position is - relatively -reversed, so that we define wholes in the context of parts. Thus when we see a whole world in a grain of sand, this reflects the immanent aesthetic perspective.

Mike is simply trying to dismiss a more subtle bi-directional appreciation that recognizes both quantitative and qualitative aspects, with a reduced scientific interpretation (based merely on the quantitative aspect).

So there is no conflation here! Rather there is a clear recognition of the subtle dynamic of circular understanding where intuition and bi-directional rational interpretation mutually interpenetrate.

"If I had conveyed this to him, Collins rejoinder to this may have been that I had failed to fully realise his point about needing partarchy to balance the holarchy - to see the world in a grain of sand as well as the grain of sand in the world, the necessary reciprocity of immanence and transcendence. Ah, Peter, I feared you may have said:

The method employed I would gladly explain,

While I have it so clear in my head,

If I had but the time and you had but the brain -

But much yet remains to be said.

Lewis Carroll: The Hunting of the Snark

I would have retorted "there's a difference between paradox and imprecision; you don't have to destroy the sense of linear logic, you just have to see its limitations and inevitable partiality. One transcends and includes to get to these 'higher' spiritual stages, not transcends and confuses. Seeing the world in a grain of sand is not the same as confusing the grain of sand for the world! Similarly, the paradox of immanence/transcendence is neither expressed nor facilitated by saying that the molecule is in the atom. A better vocabulary is required."

And I would retort Mike that the imprecision is coming from giving a reduced interpretation of what I actually say. I fully recognize the role of linear logic in its appropriate place. At the level of analytic science, I of course accept the validity of asymmetric distinctions such as that the atom is in the molecule (but not vice-versa).

However the key point is that this kind of appreciation is not strictly applicable at the level of circular understanding. This establishes the bi-directional symmetry, in dynamic terms, of all relationships! Also, I would fundamentally disagree with the continual emphasis on transcendence and inclusion. This again reflects very much a Wilberian bias, which is unbalanced.

Development is not just about transcendence; it is equally about immanence. To properly understand this, we have to keep switching as between the cognitive and affective manner of interpreting relationships.

Also, when one sees a world in a grain of sand, there is no necessary confusion involved. It is clearly appreciated in this context that we are referring - not to a scientific - but to an immanent qualitative type appreciation (which lends itself directly to poetic expression).

The confusion would only arise if one identified it directly with scientific analytic appreciation. But quite clearly I am not doing this, though you seem to say otherwise!

So once again it is very misleading to imply - without qualification - that I say that the molecule is in the atom. This does not reflect my actual way of interpretation, which is much subtler (and fully consistent within its frame of reference).

What I would say Mike is that following Wilber you are not properly recognizing immanent as opposed to transcendent type awareness. This in turn arises from a failure to distinguish in translation, scientific (cognitive) from artistic (affective) type appreciation.

So once again to imply that I say the molecule is in the atom is very misleading. One does not criticize Blake for seeing "a whole world in a grain of sand" for we know he is referring to a qualitative immanent appreciation. Likewise insofar as I identify the molecule with the atom, it is in this refined immanent sense.

Indeed because of the key importance of this issue, I have suggested a precise holistic mathematical way of preserving both the quantitative and qualitative aspects of understanding.

When we identify the quantitative as "real" then in a dynamic mathematical sense, corresponding qualitative meaning is "imaginary".

Therefore in this subtle holistic mathematical interpretation, the atom is quantitatively included in the molecule in real terms, whereas the molecule is - relatively - qualitatively included in the atom in imaginary fashion. If however we start by identifying the qualitative aspect as real, then the quantitative is imaginary. In dynamic terms, real and imaginary are merely relative terms.

Thus to preserve both the quantitative and qualitative aspects of reality, we need to move to complex rather than real interpretations.

This point has fundamental implications for science. Present science with its undue "real" emphasis is very unbalanced and geared only for quantitative appreciation of nature. So to solve this problem, it needs to provide a mathematically complex interpretation of reality (with "real" and "imaginary" aspects).

"From the above quote, Wilber's position is that immanence is an involution of the Formless, and that insight can be more readily recognized through evolution, but never realized by evolution. Collins seems to be saying, "well, whether that's so or not, a complete model must account for that immanence at every stage, not just the process of transcendence." Again in that aspect, I believe that Wilber would agree."

Well, I would say to you in response that if Ken truly believes that immanence should be included at every stage, it certainly is not properly reflected in his holarchical model of development.

The very basis of this model is an emphasis on transcendence and inclusion. Earlier versions did not even mention immanence and recent ones only do so in a limited and misleading fashion.

For example in SES we get a merely top-down approach to immanence, where it is identified as the integration from above of the "lower" level. However, this simply reduces immanence to transcendence.

The corollary in development is to try and integrate the emotions from the perspective of "higher" rational understanding. Speaking from bitter experience this simply does not work.

We need to integrate from below as well as from above. So we need a bottom-up as well as a top-down emphasis. However this bi-directional appreciation of transcendence and immanence is very much missing from Ken's work.

"If my UR reading of Collins had been correct, then his abovementioned apparent conflation of the words 'bi-directional', 'formless', 'emptiness' and 'circular' would have been completely understandable, because his right hemispheric faculties are attempting to grasp the left hemispheric tools of words!"

Again I would strongly dispute that there is any conflation. The meanings I attribute to these terms are fully consistent with my inherently dynamic understanding, where bi-directional reason and spiritual intuition mutually interpenetrate.

"Although I didn't say so at the time, it was with this in mind that I suggested to Collins that visual, spatial shapes and patterns may be a more effective method of communication. Mandalas, such as the Star Key, may communicate his meanings better, because they were the main means of communication of the right hemisphere. Certainly, the visualising example of the two drivers driving away from each other considerably facilitated my understanding of what he is talking about. The closest approximations, however, would share the dimensions of our universe - three space, one time, and many emergent levels."

Of course I would accept the value of visual spatial shapes. My approach is very much based on a simple mandalic pattern (with well known mathematical properties).

I am no artist and my skills in web-design are primitive. However I do provide the key diagram with its mathematical properties at my site.

Now Mike was kind enough to share his own fascinating Star Key, which demonstrates many remarkable number relationships. However, I have good reasons for my choice of mandala (which I attribute with universal type properties).

I am not at all averse to giving practical analogies if they can be of assistance. However though these may indeed be suggestive of meaning, they lack the more general significance that comes from a deeper conceptual appreciation. So I suppose it takes all types. I have a particular love of being able to process meaning in condensed form. Specific illustrations - though more accessible - lack this universality.

Another key point is that the very notion of three dimensions of space and one of time is asymmetric and only consistent with the analytic interpretation of reality.

This view of dimensions is inappropriate in terms of the circular appreciation (which characterizes holistic qualitative type understanding).

One remarkable connection I have been able to make, is the clear realization that the circular interpretation of dimensions corresponds exactly with the mathematical notion. This I believe is a truly important finding that can bring much greater integration to the appreciation of our world.

"But my reading was not correct; Collins is not talking about that at all. I do not know whether Collins has made any reference to the brain's UR organisation (although Wilber has [SES 95ff, for example], but perhaps only to the vertical divides [reptilian - paleomammalian - neomammalian], not the horizontal/hemispheric)."

No! I do not make any reference. Though I find research in this area interesting in its own right, it does not relate directly to my concerns, which are based on a deeply experiential approach.

Unfortunately, a lot of research in relation to the brain itself reflects the analytic type of interpretation, which greatly reduces its more mysterious holistic capacities.

So, any simple breakdown of brain functions is bound to be unduly simplified and misleading.

"No, Collins' is saying something far more radical. He is saying that within every 1 (holon), there is a 0 (Wilber's Formless); Collins places as strong an emphasis upon immanence as Wilber does upon transcendence (when talking from within the Atman Project)! There is nowhere that immanence is not."

I would rather say Mike, that I place an equal emphasis on immanence and transcendence in development, as they are complementary aspects of Spirit. I do not see this complementarity adequately reflected in Ken's work and his treatment is decidedly asymmetrical (and therefore unbalanced).

"And Wilber says that, too! Wilber has not come to praise Caesar (the Atman Project), but to bury him."

Wilber may say so in certain statements. However when one examines his actual approach to development it appears otherwise. I think Mike that you are too willing to accept general non-specific statements, which - from my perspective - are often quite inconsistent with the actual nature of his approach.

"Despite these abstractions, I consider that they both do; that transcendence is required to see, and immanence, to do. That's why I'm bothering with them. And Collins is bothering Wilber because he considers that Wilber is not expressing this insight as accurately as Collins is."

Yes, quite emphatically, I do not consider that Wilber translates the relationship between immanence and transcendence correctly.

However this is simply a reflection of a far deeper problem of method. Putting it in general terms, Ken has no adequate intellectual means of explaining how linear gradually give way to purely circular notions.

So intellectually, Ken builds a decidedly linear (asymmetrical) model of development based on holarchy. Then in terms of nondual reality he is quite happy to wax poetic, giving a very different circular interpretation (based on symmetrical pairings of opposites).

However what is greatly missing is any consistent means of showing how development becomes increasingly curved at the "higher" - and indeed the "lower" - stages of development. This in turn leads to many important imbalances in his overall approach with the lack of emphasis on immanence being just one important example.

To use an analogy from Physics, Ken's approach essentially represents a Newtonian framework and cannot properly deal with the Einsteinian World of Relativity. (In actual fact the problems are even deeper that suggested by this analogy).

So just as I would not question Newtonian mechanics within its own frame of reference, I would not question Ken's. However once we move into the area of dynamic relativity in development, which especially characterizes the "higher" and "lower" stages, his method of translation is very much wanting.

"But still, my puzzlement with Collins was not resolved. Bi-directionality cannot apply to the nondual, emptiness, the formless; there is no direction towards it at all, not horizontal, vertical, or diagonal, nor anywhere within a 3-D matrix, because it is not within dimensionality! In our mathematical processes, we are apt to skip along from -2 to -1 to 0 to +1 to +2 without missing a beat: "oh yeah, zero - that's between -1 and +1, right? That's what you get when you add those two together, or any such pair of negative and positive numbers."

I would not fully accept this Mike. Quite honestly I feel that there is an undue emphasis on merely intuitive states in Eastern mysticism. I find more recognition of the important intermediary role of refined rational understanding in Christian mysticism (with which I am most familiar). I consider that this is more appropriate in terms of creating a proper bridge as between science and mysticism.

The very point about a dynamic approach is that we cannot properly separate rational and intuitive understanding (as they continually interpenetrate).

Nondual Reality, in dynamic terms, represents such a highly refined state of awareness that phenomenal representations are dissolved as soon as they arise leaving no trace in memory,

Now this could be misleadingly equated with intuition but more accurately it would relate to an extremely rapid switching of opposite poles with little remaining attachment to these poles.

So once again to separate Form and Formlessness is itself dualistic.

There is an aspect of experience that is without direction (dimension) and another with an extremely dynamic appreciation of direction.

Without direction would mean the fusion of both poles. So intuitive experience is without dimension as it represents the identity of opposite poles.

In dynamic sense, nothingness (0) represents the identity of opposite poles as pure spiritual awareness. So we represent these two poles of form as + 1 and –1, then 0 = 1 – 1 in dualistic terms.

However when we accept that dynamic logic is based on the inherent complementary of opposites, 1 – 1 in linear logic is 1 (in complementary logic) = 0.

So 0 as nothingness - which is indeed nothing in phenomenal terms - represents the pure creative potential for all form.

"Was Collins' criticism of Wilber equivalent to saying "Ken, you've failed! You haven't pointed out that inside every 1 there is a 0"? (PE?) But "0" is the signifier for nothing at all, not anything that can be described as "Formless" (a quality), "empty" (a quality), or "circular" (a shape or method). Holons do not have a quality of non-existence: holons have to exist before they can be called holons. So if one wants opposites, whether seen as complementary or not, is 0 the 'opposite' of 1, or of infinity? Or is 0 the opposite of nothing at all, otherwise implying as it does a dialectic, and therefore a holonic existence? Opposites are intra-holonic."

Again this has to be understood in dynamic terms. Reflection on the interactive nature of particle life will give greater meaning to my notions.

Physicists will readily admit that particles are literally born out of nothingness (the fundamental ground of matter). There is then a highly dynamic interaction with particles and anti-particles meeting and fusing in energy and being born as new particles. So Form gives way to Emptiness and Emptiness to Form.

In dynamic terms all holons do have a quality of non-existence i.e. they emerge from Emptiness and return to Emptiness.

So in your very attempt to dispute my point, you are giving a merely static definition of holons.

In static terms holons exist; in dynamic terms there is ceaseless holonic interaction as between existence and non-existence.

You ask if 0 is the opposite of 1.

Once again I precisely define three kinds of opposites.

Horizontal would be represented as two lines at a 180-degree angle i.e. the x-axis. Interior and exterior (within a given level) are positive and negative with respect to each other.

Vertical would be represented by two lines at a 90-degree angle i.e. the intersection of the x with the y-axis.

Thus cognitive and affective for example, are vertically opposite in this sense and in dynamic terms are real and imaginary with respect to each other.

Diagonal would be represented by lines at a 45-degree angle to both the x and the y-axis.

Quite literally - using the Pythagorean Theorem - these diagonal lines are 0 in magnitude (null lines). (See my charts and diagrams at "The Science of Integration" for a full explanation).

So emptiness (0) is diagonally opposite to form (1) in this precise qualitative mathematical sense. This is yet another example of where Holistic Mathematics gives a fully coherent and precise explanation.

"But", I thought, "Peter must know this. I get it! He must be speaking of the eternal Tao, the one that 'cannot be known' in the Tao te Ching, the 'eternal non-existence' from where we can view the whole picture, in contrast with the 'eternal existence' from which we clearly see its apparent distinctions. He's using 0 figuratively, to express Divine Immanence."

I am using 0 in a dynamic sense as Nothingness (which is synonymous with emptiness). For example St. John of the Cross uses the term nada (nothing) to refer to the state of pure Emptiness.

In other words 0 (Nothingness) - from a dynamic perspective - is empty of phenomenal form (and the creative potential for all form).

However this state of dynamic Emptiness refers not alone to the immanent aspect of Spirit, but equally to the transcendent.

I am particularly grateful to Mike for the next section. It clearly shows that not only has he taken the time to thoroughly study my material but has been able to present it in a way which is valuable.

Now it is necessary to put this model of development in perspective.

It represents the application of the holistic mathematical approach, where the all of the major number types e.g. prime, rational, irrational, imaginary are used in their dynamic holistic sense to precisely structure the various levels (and sub-levels) of the Spectrum.

Now at first sight this might seem somewhat strange. However properly understood, I would strongly contend that it offers the most scientific approach available.

It is all based on a very simple rationale.

Number is the most appropriate means we have in the static analytic realm, for ordering quantities. Indeed number is synonymous with order in this sense.

However, properly interpreted, in a dynamic holistic sense, number is the best means we have for ordering the qualitative structures of reality.

Therefore when the holistic interpretation of number types is used, it provides the most appropriate method for qualitative ordering of the various levels of the Spectrum.

So here is a vitally important use for number, which is all but unrecognized. Yet the connections between number types and levels of the Spectrum are so strong that they are indeed synonymous with each other.

Thus if another psychological level was to be discovered on the Spectrum, this would entail the complementary discovery of a new unique number type; likewise the discovery of a fundamental new number type would imply the existence of a corresponding (unspecified) level of the Spectrum.

Thus in a very real sense, the levels of the Spectrum (which equally represent consciousness and nature), are synonymous with number in its dynamic holistic interpretation.

I will remodel this Spectrum slightly, giving its holistic number interpretations.

Transition between L3 and L2 - differentiation of diagonal direction; separation of finite notions from a complex confused state

Transition between L2 and L1 - differentiation of vertical direction; separation of real and imaginary

Transition between L1 and L0 - differentiation of horizontal direction; separation of positive and negative

L0 H0 rational - concrete, formal and integrative (one positive direction)

Transition between H0 and H1 - integration of negative (with positive)

H1 Irrational (algebraic) - concrete, formal and integrative (two directions: positive and negative)

Transition between H1 and H2 - integration of imaginary (with real)

H2 Transcendental – concrete, formal and integrative (four directions: positive and negative, real and imaginary)

Transition between H2 and H3 - integration of real with complex notions

H3 Transfinite (eight directions: the four formal directions and four null directions)

Radial 1 (all previous qualitative number notions in both linear and circular senses)

Radial 2 (Simple interpenetration of dual and nondual)

There is one important qualification I would make.

Mike refers to this model as representing a progressive increase in wholeness.

However with H1, all structures have both positive and negative directions in development.

So in effect, interior and exterior aspects are - relatively - positive and negative with respect to each other. So development dynamically entails both progression and regression at H1.

Then at H2 structures have real and imaginary directions of development.

What this means is that development is seen in terms of the bi-directional emergence of both more collective wholes (transcendence) and also more unique parts (immanence). In this way, linear notions are seen through intellectual translation to become more circular (i.e. curved).

The fallacy about the holarchical approach is that it requires the emergence of wholes to be based on (given) parts. However, in dynamic terms, the uniqueness of the parts is itself only properly realized through development. So, at H2, there is a clear recognition of the need for both holarchy (where "lower" parts are transcended in "higher" wholes) and partarchy (where "higher" wholes are made immanent in "lower" parts). Both relationships are dynamically complementary in a bi-directional sense.

Mike then asks the interesting question.

But how far is it possible to extrapolate our personal experience to universals?

Personal experience is of course unique in so many ways. However there are basic structural features - the development of which can vary considerably with individuals - that are universal. And the very point of the holistic mathematical approach is its precise definition of the nature of these universal structures.

It is a little like a system of personality types. If we take the well-known Enneagram system, the nine types are universal in that they are applicable to all personalities. However individuals can vary considerably with the profile of one particular type best describing their personality.

So I would say that my account is fully authentic in the sense that it is based on personal development.

I would not of course consider the precise nature of this development as universally applicable.

However I would maintain that the structures which have been identified are indeed universal and present, to a varying extent, in all personalities.

It must be remembered that I am mainly interested in extracting - for the purpose of precise scientific translation - the structure of each level.

Though child development varies greatly, we can identify various stages with well-recognized features. Likewise, I would say that development at "higher" stages also varies greatly but yet reveals structures with a universal validity. These structures can be precisely identified in holistic mathematical terms.

"Collins has assuredly sought confirmations from the literature; presumably, it was in just such a context that he encountered Wilber in the first place, and is the context in which he seeks feedback on his model by putting up his homepage, and engaging in discussions on the KWF. "

I would distinguish my approach from Ken Wilber's in that it is very much an experiential approach, based intimately on clarification of my own development.

Of course this does not exclude research and I would be able to draw distinct similarities as between personal experience and other spiritual accounts. I could therefore write in the conventional language of spiritual mysticism (and show strong parallels with their typically defined stages of development).

However where I consider my approach radical, is in the precise scientific identification of "higher" level cognitive (and affective) structures. These have been greatly ignored in the traditional accounts.

And it is their very identification that prepares the way for radical new meta-paradigms of science (giving a unique perspective).

The meta-paradigm of conventional science is based on the understanding of just one level H0, and is limited to analytic inquiry!

However the meta-paradigms of the "higher" levels lend themselves directly to more dynamic bi-directional appreciation (and are the basis for integral science).

I would then identify a more comprehensive form of science - radial - that combines the (rigid) analytic and (dynamic) holistic approaches.

The great benefit of my approach is therefore in providing a coherent structured means for significantly enlarging on the framework of scientific enquiry.

I distinguish three degrees of scientific inquiry.

Analytic science is based on linear sequential understanding where relationships are traced in asymmetric fashion in one direction (at a time)

This has three forms:

Analytic 1 – this is based on conop and formop understanding and provides the basis for conventional science.

Analytic 2 – this is a multi-analytic approach based on the vision-logic of the centaur. Ken Wilber with his four-quadrant approach is attempting to enlarge the range and comprehensiveness of scientific analytic enquiry.

Analytic 3 – this is based on the transitional stages of transpersonal understanding. It leads to a more subtle analytic approach where it is understood that - in reduced linear terms - all dynamic relationship can be given equally valid opposite asymmetrical interpretations.

Thus in analytic terms, at this level, development would be traced through opposite pairings of asymmetrical relationships.

For example one could represent development in terms of holarchy as the (asymmetric) transcendence and inclusion of the "lower" parts in the "higher" whole. The other would see development as the (asymmetric) immanence and inclusion of the "higher" whole in the "lower" parts.

Ken Wilber's model does not reach an analytic 3 form; the vision-logic of the centaur is inappropriate for recognition of this understanding.

Holistic science is based on circular bi-directional understanding where relationships are traced in symmetric fashion in both polar directions (simultaneously). It is directly suited for qualitative integral understanding.

Again this has three forms.

Holistic 1 – this is based on the understanding of H1 (psychic and subtle realms) and involves bi-directional appreciation of horizontal polarities (interior/exterior).

This culminates in refined intuitive understanding where the division between poles ceases i.e. the horizontal polarities are integrated.

Holistic 2 – this is based on the understanding of H2 (causal) and involves bi-directional appreciation of horizontal and vertical polarities (whole/part)

This culminates in refined intuitive understanding where the division as between horizontal and vertical poles ceases (i.e. horizontal and vertical polarities are integrated).

Holistic 3 – this is based on the understanding of H3 (nondual) and involves bi-directional appreciation in relation to all three sets of polarities.

This culminates in the refined intuitive understanding where divisions as between horizontal vertical and diagonal polarities cease and integration thereby takes place.

Holistic science is very different from the analytic variety. It is based on the inherent structural complementarity of relationships in relation to both physical and psychological aspects.

Thus in principle every structure in physical science - when dynamically interpreted - has a corresponding structure in psychological terms. I have also illustrated this with reference to the nature of light in both its physical and psycho-spiritual manifestations!

The reverse is also true. Every structure in psychological terms has a correspondent in physical terms.

This complementarity can be then studied in relation to horizontal, vertical and diagonal levels.

Radial science combines both (static) analytic and (dynamic) holistic understanding. It is suited for the combined process of differentiating and integrating reality.

This involves some sequential separation as between (circular) holistic and (linear) analytic understanding

This approaches simultaneous interpenetration of circular and linear understanding in a truly simple form of understanding.

"Collins has assuredly sought confirmations from the literature; presumably, it was in just such a context that he encountered Wilber in the first place, and is the context in which he seeks feedback on his model by putting up his homepage, and engaging in discussions on the KWF."

Yes, I eagerly wish for open and constructive dialogue on the issues that arise with those who genuinely can contribute.

However research based confirmation - by definition - is not a suitable way for appraising a radical new approach. Apart from tentative suggestions, I have not come across anything in the literature that bears comparison to what I am attempting. So proper appraisal can only come from people who are genuinely willing to study these new ideas while remaining open to the manner in which they lead to a uniquely different interpretation of experience.

The detailed criticism of Ken's approach represents an indirect means of appraisal. The very fact that my approach can be so effectively used to diagnose problems with Ken's model (and provide coherent remedies) suggests the great potential power of the qualitative mathematical approach.

"As far as I know, Collins' model has not been empirically verified or refuted by statistically valid surveys in its own right (but Collins is a statistician, so maybe!). Yet Wilber tells us that "developmental psychologists tend to find that it is not very current on recent research" - a comment that Collins found unsupported and somewhat gratuitous, and disputes (Ref 3)".

As I have said what is first required is a willingness to genuinely appraise these new ideas. Mike has written a fascinating article which refers to String Theory. He knows that String Theory has not yet been empirically verified and yet it is creating an enormous buzz in the physical community.

This is largely due to the internal coherence and consistency of its ideas. At a more dynamic qualitative level of experience, I would maintain the same in terms of my own very different approach. However my model can be applied - and is being applied - to a wide range of issues with very fruitful results.

I thought Ken's remark was disingenuous. Firstly he gives no information as to these anonymous psychologists. For my part I wonder if they can have any real appreciation of what I am attempting.

Secondly, Ken's remark was in response to an article based on methodological criticism of his approach. So in this context such a remark was not relevant.

Once again a new approach must be considered within its own frame of reference if its value is to be assessed.

"However, it seems apparent to me that Collins' descriptions of the various levels and stages could not have been intended as all being necessarily only interpretable through Holistic Mathematics (HM). Otherwise, the only ones to have ever become enlightened would all have to have arrived there along a holistic mathematical path - the path that Collins has pioneered! Clearly, he is using HM as a translative medium that he finds allows more precision than the left hemisphere's linguistic tools do alone. If he were asserting that his HM method of translation should be regarded as the only path, his model would collapse into a pile of self-contradictions and should be kicked out the door. Reading his works, the thought occurred to me that some may even infer that, but I do not. He is simply using one mathematical vocabulary to describe the process of differentiation and integration required for the growth of complexity, another for a description of the emergent stages through life's path, and integrating them."

Of course the levels are not only interpretable through Holistic Mathematics. When I started writing "Transformation Voyage" I was not at first viewing development through a mathematical lens. It was only later that I saw qualitative mathematical categories as providing a wonderfully precise framework.

However, just as with ordinary science, I would see mathematical vocabulary to have a special value as a precise integral form of understanding.

So in this sense Holistic Mathematics is not just another language. It is ideally suited for qualitative scientific appreciation.

I would like to briefly illustrate the way that this mathematical translation can be used.

Remember that this Spectrum approach is dynamic including both linear and circular interpretations! The circular is based on the complementarity of psychological and physical aspects of reality, that operates between levels (horizontal) within levels (vertical) and both within and between levels (diagonal).

Let me illustrate briefly this understanding.

For example H2 in my model (which equates well the causal realm) is defined by the holistic qualitative interpretation of transcendental numbers.

Now there are several ways of demonstrating the qualitative meaning of transcendental numbers.

p is the best known transcendental number and the most important constant in mathematics. It is the quantitative measurement of the ratio of the circumference of a circle to its line diameter. So in quantitative terms, the value of the most significant transcendental number is based on the relationship between the line and circle.

The number p in its qualitative holistic sense serves as an archetype of the mathematical notion of the transcendental, which is always based on the dynamic relationship as between linear and circular type understanding.

So transcendental understanding is extremely subtle. In its cognitive expression it is neither based on linear (rational) or circular (intuitive) understanding separately, but rather on the interactive relationship between both.

What characterizes transcendental understanding from an intellectual perspective, is an extremely close relationship as between refined reason and intuition.

In quantitative terms, the point at the center is common to both the circle and line diameter. In like manner intuition and reason are reconciled through the spiritual center of being.

So the refined phenomenal understanding of the transcendental level of understanding is very much the expression of one's spiritual center.

A transcendental number in mathematical terms has both finite and infinite aspects. In other words, though a number like p has a finite value, it cannot be expressed in rational form so that its decimal sequence expands indefinitely.

Likewise transcendental understanding has a finite phenomenal aspect but also an infinite (intuitive) aspect inseparable from its phenomenal translations.

This very refined transcendental understanding is intrinsic to the very nature of Holistic Mathematics.

So mathematical symbols have both quantitative analytic (linear) and qualitative holistic (circular) interpretations. Holistic Mathematics enables a common basis to be established as between both sets of interpretations. I have been using this understanding to interpret lines and circles in both the analytic and holistic sense and then linking this interpretation to the notion of the transcendental in Mathematics.

So a basic principle is that Holistic Mathematics has complementary dynamic interpretations in both physical and psychological terms.

I am illustrating this fact in the very way that I construct my Spectrum. It is a holistic mathematical interpretation where all the structures can be equally applied to Psychology (as a Spectrum of Consciousness) and to Physical Reality (as a Spectrum of Nature).

Now vertical complementarity would suggest that the structures of H2 have close parallels with L2.

Thus L2 represents in confused form what emerges in more mature fashion at H2.

This would suggest that there are close relationships as between the transcendental and prime number interpretations in qualitative terms.

Fascinatingly this is also true in quantitative terms. The Prime Number Theorem relates the distribution of primes to a transcendental number i.e.

log _en.

Now prime numbers in qualitative terms have very close parallels with the level of reality we refer to as strings (or superstrings).

A prime number has no factors other than itself and 1. So a prime number is inherently one-dimensional (no factors). Strings are likewise characterized as one-dimensional.

Also when we combine prime numbers to get a composite number, a qualitative dimensional aspect arises. So prime numbers can relate to quantitative or qualitative phenomena but not to both.

The implication of this in dynamic terms is that strings are special "objects". Normally we understand phenomena with reference to a defined background of space and time. However we cannot do this with strings. The dimensions in a sense are embedded in the strings. It is the subsequent dynamic interaction of both aspects of the string (i.e. vibration) that generates particles in space and time.

Just as the interaction of prime numbers (i.e. multiplication) generates the natural numbers, the interaction of strings generates the natural phenomena (forces and particles)

So the string in its passive state, as it were, incorporates both phenomenal and dimensional meaning and its dynamic activity generates particles within a phenomenal background.

This also throws clues on one of the mysteries of strings, which requires a "higher" number of dimensions than the customary framework.

Our four dimensional notions are based on the clear separation of phenomena from their dimensional background.

However by definition as strings belong to what are qualitatively prime dimensions, this does not apply.

So the way of interpreting "dimensions" here, is as a configuration of existing (entangled) dimensions.

So the meaning of a "dimension" is different at the level of strings where it relates to a certain permutation of the original four dimensions.

We can equally look at a personality type as representing a "dimension". In this way, each personality type can be looked on as representing a unique configuration of the psychological experience of space and time. I have used diagonal complementarity to establish links between the meaning of a "dimension" with respect to both personality types and strings.

Another idea is that of mirror symmetries. However again this is easy to appreciate as strings actually have a dual identity as objects and dimensions. So if one theory is a description of strings (as objects), the mirror theory is a description of strings (as dimensions).

Also String Theory is based on a deep appreciation of the underlying symmetries of nature. Holistic Mathematics provides a more dynamic appreciation of this symmetry.

Now when we accept horizontal complementarity at the string level of L2, we have the fascinating insight that it has direct psychological aspects.

Thus the psychological behavior of L2 remarkably demonstrates similar features to strings.

Once again the notion of a prime number is paramount. In fact it has direct links with the word primitive.

So infant behavior at L2 is instinctive and primitive. Once again this is based on an inability to separate qualitative dimensions from quantitative objects. So the infant has not yet formed the perspective to place phenomena within a stable framework of space and time.

Primitive instinctive behavior involves the direct confusion of holistic (qualitative) desire with specific (quantitative) objects.

Indeed this is the basis of instinctive response at any level. It represents a great loss in perspective, where one identifies holistic desire with the object of attention so that both are confused in the process. Quite literally with primitive instinctive behavior, there is a loss of a qualitative dimensional perspective (with which to place objects).

An infant at L2 is living in a framework of objects and dimensions, where phenomena are not properly separated from holistic desire. Fulfillment is seen in terms of direct identification with objects.

Remarkably, one very creative way to get better insight into the nature of String Theory, is through structuring psychological experience in qualitative mathematical terms.

Because transcendental understanding is vertically complementary to prime, this means that the confusion that exists at the "lower" level is largely resolved at the corresponding "higher" level.

So H2 represents the significant freeing of confusion, which arises though identifying holistic desire with objects, leading to an extremely refined form of awareness.

Also it is very interesting that String Theory in its analytic form is largely mathematical. What I am saying, is that in dynamic qualitative terms, strings also ideally lend themselves to mathematical understanding (through the very subtle cognitive understanding that unfolds with H2). So the understanding of the "higher" level is the appropriate means to understand the "lower".

Just as conventional mathematical understanding represents a unique specialized expression of conop and especially formop understanding of H0, likewise holistic mathematical understanding, in its mature form, represents a unique specialized expression of the corresponding highly refined conop and formop stages of H2. So associated with each level of the Spectrum is a unique mathematical expression.

I have gone on here at some length. However my point is to show that this holistic mathematical approach opens up an entirely new way at looking at experience, both in its physical and psychological aspects. Science is still seen as an analytic expression of understanding. It needs to be balanced with its corresponding holistic expression and my approach is geared for this very task.

What is greatly missing with String Theory and its attempts to understand reality, is a proper dynamic holistic framework (which would put analytic findings in proper context). Scientists readily admit that they have little intuitive appreciation of its rationale.

Also I would consider that its standard representations are very inaccurate as they create a static representation of what is inherently so dynamic that it cannot be presented in conventional terms.

For example, strings are presented as open and closed loops. This clearly points to the interaction of circular and linear notions. Indeed just as the prime emerge from the binary numbers (1 and 0), strings emerge from the primary qualitative state where unity (1) is totally confused with nothingness (0). Thus, it is this binary phenomenal interaction in a highly dynamic - but still confused - state that gives rise to strings. However to picture them in static terms as identifiable loops is most misleading.

So there is a need to retranslate these rigid notions in more dynamic fashion.

Clearly, this qualitative mathematical appreciation is greatly missing from current understanding.