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INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
An independent forum for a critical discussion of the integral philosophy of Ken Wilber
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Publication dates of essays (month/year) can be found under "Essays".
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.
THE DYNAMICS OF DEVELOPMENTA True Integral ApproachPeter CollinsIntroduction
Quite simply, as Ken Wilber continually reduces integration to differentiation in development, his approach is very distorted from a dynamic perspective.
The purpose of this article is to identify the very important "integral fallacy". This is the use of an analytic, rather than a true synthetic method, to translate integration. Visionlogic as used by Ken Wilber represents a sophisticated analytic method, and is not appropriate therefore for genuine integral synthesis. The article is divided into two main parts. The first addresses key imbalances in Ken's work (that arise directly from his method of translation). The second proposes a Spectrum of Translation Methods (eight in all). Three are designed for analysis, three for synthesis and two for both analysis and synthesis. The conclusion is that a comprehensive approach to development requires employing the full range of translation methods. There is a fundamental problem with Ken Wilber's overall approach to development. It is surprisingly lacking in dynamism through being based on a limited form of rational translation. This leads to a basic misinterpretation of the nature of interactive processes [1]. In particular it fails to properly distinguish the nature of integration in development from that of differentiation. Basically, I would consider that Ken's overall model presents a superb multidifferential rather than a true integral approach [2]. Linear and Circular Understanding Before we can get to the root of his translation problem we need to carefully distinguish two types of logical understanding [3]. LinearThis is the logic of form, and is based on the clear separation of polar opposites (e.g. subject and object) in experience. Analytic science typically uses this logic viewing the (objective) world as distinct from the (subjective) observer. Relationships are formulated in either/or terms leading to onedirectional sequential interpretation. In terms of this logic, the atom for example, is contained in the molecule (but the molecule is not contained in the atom). CircularThis is formless logic and leads to a dynamic relative type of understanding, where polar opposites are complementary (and ultimately identical) in experience. It views logical connections bidirectionally in both/and terms leading to paradoxical simultaneous interpretation. Thus, in a circular relative sense, the atom is contained in the molecule and the molecule is contained in the atom [4]. The very purpose of this logic is to erode exclusive identification with the polarized distinctions of the linear method. This then serves as preparation for a qualitative transformation through intuitive insight (where paradoxical meaning can be directly apprehended in spiritual fashion) [5]. In terms of adequate rational translation, all transformation processes (e.g. human development) require the use of both linear and circular logic. The key point is that whereas linear logic is directly suitable for translation of the differentiation of experience, circular logic is required for corresponding integration. This can be briefly explained as follows. When one becomes aware of a phenomenal object such as an atom, opposite poles (which are ultimately identical) become separated. Thus the (objective) atom is given a meaning independent of the (subjective) self. When the world is viewed independent of self, phenomena can be connected in a onedirectional sequential manner. Development then appears to unfold from the atom to the molecule (but not vice versa). Differentiation is always based on this separation of opposite poles in experience e.g. object and subject, quantitative and qualitative, form and emptiness. This leads to an asymmetrical interpretation of development. However integration involves a reverse process whereby opposite poles (which have been differentiated) are once again united. So awareness now moves back from the atom to the observing self. This leads to a dynamic negation of both poles (as separate) and a corresponding bidirectional fusion in an intuitive recognition of their common identity. Through this recognition, the atom is simultaneously seen as related to self (and self to the atom), in the nondual present moment [6]. So integration is always based on the complementarity (and ultimate) identity of opposite poles in experience. This leads to an appreciation of the underlying symmetrical [7] nature of all relationships [8]. Linear (onedirectional) logic is suitable for the sequential differentiation of phenomenal relationships. However circular (bidirectional) logic  based on the complementary of polar opposites  is required for their simultaneous integration [9]. As Ken Wilber's holarchical model of development typically employs a onedirectional logic, in effect, he reduces the process of integration to that of differentiation. This creates a persistent lack of balance in his work leading to a great number of halftruths and inconsistencies. Illustration: two drivers I will distinguish the important difference as between linear and circular understanding with a simple illustration. Imagine two drivers (Bill and Tom) heading in opposite directions along a motorway. In absolute terms they both move forward in a positive manner. However, in relative terms, they move in both positive and negative directions (with respect to each other). So as Bill moves forward (relative to Tom) then Tom thereby moves backward (relative to Bill). Likewise as Tom moves forward (relative to Bill) then Bill moves backward (relative to Tom). So in (absolute) linear terms, movement takes place for each driver sequentially in a positive direction. However in (relative) circular terms, movement takes place for the two drivers simultaneously in both positive and negative directions. Relevance for developmentNow this simple illustration is directly relevant for the understanding of dynamic interaction. Viewed in linear terms, development appears to unfold holarchically in a series of welldefined stages [10]. However from a dynamic perspective, development involves the interaction of opposite polarities (which can be understood in a way similar to our two drivers). The simplest kind of polarity is horizontal and operates within a given level of development i.e. exterior and interior. Every stage of development has exterior and interior aspects, which dynamically interact. The world is experienced in relation to the self and the self likewise in relation to the world. When we separate these polarities, once again development appears to unfold in holarchical fashion. Movement with respect to the exterior aspect of stages unfolds sequentially in a forward direction. Understanding of the world therefore progresses through a series of stages. In like fashion, the interior aspect of development unfolds sequentially in a forward manner. So selfunderstanding also progresses through a series of stages. However when we consider these aspects dynamically in relation to each other, absolute notions of movement are no longer appropriate. Thus if development of the exterior aspect moves forward, then the interior (relatively) moves backward in the opposite negative direction. Likewise when we switch our frame of reference so that the interior direction of stages is now defined as positive, then exterior movement (relatively) is negative. Thus from a dynamic perspective, understanding of the world and self takes place in opposite directions. Once again, the (linear) analytic approach separates poles and treats movement in an unambiguous onedirectional fashion. This is suitable for the differentiation of separate aspects of experience. However, the (circular) synthetic approach integrates these poles by treating movement in a simultaneous bidirectional manner. Its rationale is thus very different from the analytic. The key difficulties with Ken Wilber's approach stem from attempting to use a sophisticated analytic rather than a true synthetic approach to translate the overall nature of development. Holism and Partism Because of a failure to recognize the limitations of linear (onedirectional) understanding, Wilber's approach is very unbalanced from a dynamic perspective. His holarchical model explains development in an asymmetric fashion and is not consistent with integral appreciation. In particular it very much misrepresents the proper relationship as between transcendence and immanence (the two polar aspects of Spirit). In (circular) integral terms, a bidirectional symmetry exists as between whole and part (and part and whole). The whole is related to the part; the part is related to the whole. However holism  which is the basis for the holarchical approach  gives a onedirectional asymmetrical interpretation of this relationship. Starting with the notion of a holon (as a whole/part), development is portrayed as the process by which at each stage, "lower" wholes are transcended and included as parts of a "higher" whole. In this view "lower" atoms are transcended and included in the "higher" molecule. The movement here is onedirectional (from atoms to molecules). So the holarchical model places the emphasis on transcendence and the progressive evolution of more complex wholes. It is unbalanced as it gives primacy to the whole over the part. However in dynamic relative terms, development equally incorporates immanence (as well as transcendence), where the emphasis is now on the progressive evolution of more unique parts. So from this alternative (reverse) perspective, development is based on partism. At each stage, the "higher" part is made immanent and included as the whole of the "lower" part. (The holon is here a part/whole). So in this way, the "higher" molecule is made immanent and included in the "lower" atoms. When Blake saw "a whole world in a grain of sand" he was speaking from an advanced immanent stage of development, where a very "high" whole is qualitatively contained within a very "low" part. In the dynamics of development we have the simultaneous interaction of two opposite holarchical directions of whole/parts and part/wholes, so that "higher" and "lower" ultimately have a purely relative meaning. Indeed this provides an important clue as to the nature of these two holarchies. When one approaches development  in this context  from the (cognitive) scientific perspective, the whole includes the parts (in quantitative terms). In this sense, the atoms are (quantitatively) included in the molecule and given a collective impersonal identity. However from the corresponding (affective) aesthetic perspective, the position is (relatively) reversed whereby the part includes the whole (in qualitative terms). So here the molecule is qualitatively included in each atom leading to a unique personal identity. The very recognition of any phenomenon requires both (personal) affective and (impersonal) cognitive interpretation. The unique aspect is conveyed through the affective senses, whereas (relatively) the collective is conveyed through cognitive reason. So to identify a molecule, one must be able to recognize both its individual uniqueness and its collective relationship to other molecules. Analytic interpretation, by its very nature, reduces affective to cognitive translation [11]. Scientific and aesthetic understanding however relate to two distinct holarchies which cannot be successfully reduced in terms of each other. Transcendence often reflects the cognitive, and immanence the affective aspects of spiritual understanding respectively [12]. However, because  by definition  the transcendent holarchical model is asymmetrical, immanence cannot be incorporated within it in a balanced manner. In this model, immanence is explained in topdown fashion as the envelopment of the "lower" by the "higher". The "higher" molecule  as it were – permeates the "lower" atoms. So immanence in effect is explained as a function of transcendence (which is very mistaken). However true immanence is (relatively) about the reaching up of the "lower" to envelop the "higher" which is crucially different. In this context the correct immanent view is that the atoms permeate the molecule (so that the molecule is qualitatively reflected through the atoms). This distinction has practical consequences for authentic spiritual growth. Frequently, "higher" transpersonal development operates initially under the refined control of the (cognitive) mental self [13]. This leads to a transcendent emphasis on the Ascent where one attempts to integrate the "lower" emotions and body through the "higher" spiritualized personality. This inevitably causes a degree of instinctive repression and can set severe blocks to further progress. For development to continue successfully, one later needs to descend and deal with the (affective) emotions and physical body in terms of their own modes of expression [14]. In other words, one is required to switch from a transcendent to an immanent focus and then to embrace reality equally from that "lower" context. So whereas the transcendent aspect of envelopment has a topdown, the immanent has  relatively  a bottomup direction. Holism and partism (taken separately) are asymmetrical models. They cannot adequately give an integrated view of development, as they in fact represent very different holarchies. Holism can only incorporate immanence by reducing it to transcendence; partism in turn can only incorporate transcendence by reducing it to immanence. The starting basis for a true integral approach is the realization that every dynamic relationship has equally valid opposite interpretations (in linear terms). So once again we have identified two opposite holarchical models: holism based on the transcendence of the "lower" in the "higher", and partism based on the immanence of the "higher" in the "lower". Both of these models give rise to a onedirectional asymmetric interpretation of development (taken separately). However, because they are mirror images of each other, when combined and translated in dynamic relative fashion, bidirectional symmetry results. I will now briefly illustrate this very important point. In a footnote on P. 90 of "One Taste", Ken gives a brief summary of holism. "A holon is a whole that is also a part of other wholes. The universe is basically composed of holons; a whole atom is part of a molecule, the whole molecule is part of a cell, the whole cell is part of an organism, the whole organism is part of an ecosystem, and so on. Holons are organized holarchically, with each higher holon transcending but including its juniors; organisms contain cells which contain molecules which contain atoms – but not vice versa, hence the hierarchy (or holoarchy). The Great Chain is also a holarchy composed of holons; spirit transcends but includes soul, which transcends but includes mind, which transcends but includes body. Each senior holon enfolds, envelops and embraces its juniors, and this is the very nature of whole/parts, holons and holarchy; nests of increasing wholeness and embrace". This has a vertical mirror image interpretation as partism. "A holon (or onhol) is a part that is also a whole of (i.e. qualitatively includes) other parts. The universe is basically composed of holons; a part atom is also the whole of a molecule (i.e. qualitatively includes the molecule), the part molecule is whole of a cell, the part cell is whole of an organism, the part organism is whole of an ecosystem, and so on. Holons are organized partarchically, with each lower holon making immanent but including its seniors; atoms (qualitatively) contain molecules which contain cells which contain organisms – but not vice versa (in this relative qualitative sense), hence the partarchy. The Great Chain is also a partarchy composed of holons; spirit is made immanent but included in soul, which is made immanent but included in mind, which is made immanent but included in body. Each junior holon enfolds, envelops and embraces its seniors, and this is the very nature of part/wholes, holons and partarchy; nests of increasing (unique) partness and embrace". The irony is that in the very section where Ken lists this summary of holarchy, he describes in very poetic fashion the (reverse) immanent partarchy (without commenting on the important difference). "Think of the most beautiful person you have ever seen. Think of the exact moment you looked into his or her eyes, and for a fleeting moment you were paralyzed: you couldn't take your eyes off that vision. You stared, frozen in time, caught in that beauty. Now imagine that identical beauty radiating from every single thing in the entire universe, every animal, every cloud, every person, every mountain, every stream – even the garbage streams and broken dreams – every single one of them radiating that beauty". So here, the (whole) experience of beauty is made immanent and (qualitatively) included in "every single thing in the entire universe". Ken attempts to interpret the second in terms of the first holarchy, thereby reducing affective to cognitive translation. The crucial step in moving from a differentiated (asymmetrical) to an integrated (symmetrical) approach, is the clear recognition that all asymmetrical models have mirror image alternatives (where the direction of movement is reversed). Though both holism and partism are asymmetrical models (in isolation), when combined in integral terms they are dynamically symmetrical. So when we translate the nature of a holon in integral (symmetrical) terms we switch from an either/or to a both/and logic. Thus a holon is both a whole that is also (quantitatively) a part of other wholes and (relatively) also a part that is (qualitatively) a whole of other parts. An asymmetrical model by definition is unbalanced, and always entails coming down in favor of one side of a polarity (when the opposite is equally valid). Ultimately perfect integration is realized, with the spiritual intuitive experience of the pure relativity of all polarized statements. Circular bidirectional understanding serves as a vital  though indirect  tool in the gradual erosion of attachment to (reduced) linear interpretations of reality. One important purpose of a true integral approach is ultimately  through refined paradoxical translation  to fully demonstrate the onesidedness and inconsistency of all asymmetrical models. As this dynamic bidirectional appreciation is greatly missing from Ken Wilber's approach, it does not qualify as a true integral interpretation. Evolution and Involution This lack of dynamic understanding is also evident in his misleading identification of development with evolutionary progress. Once again, he very much misrepresents the true nature of evolution portraying it in unduly linear fashion. However in dynamic (circular) terms, evolution and involution are necessarily relative. When one become conscious of the (exterior) phenomenal world, awareness moves out from the self in a positive direction. However awareness of the (interior) self, entails the reverse movement in a negative fashion. Therefore relative to each other, evolution of the (exterior) world and (interior) self take place in opposite directions. So if the world moves forward and evolves (with respect to the self), then the self necessarily moves backward and involves (with respect to the world). Equally if the self evolves (with respect to the world), then the world (relatively) involves (with respect to the self). So if we identify evolution with the differentiation of "higher" level structures, then involution  relatively  relates to their corresponding integration [15]. Ken Wilber's failure to properly incorporate involution inside the process of development is largely dictated by an inadequate analytic translation and has important practical consequences. Just as all holarchies have (vertical) mirror image alternatives, equally they have mirror image alternatives (in horizontal terms). Ken's model is expressed in terms of transcendence and inclusion of the lower in the higher stage. He identifies this with evolution. However the holarchical model can be equally expressed in terms of transcendence and exclusion of the "lower" in the "higher", which (relatively) can be identified with involution. He places an unbalanced emphasis on evolution in historical terms as synonymous with "progress". For example on P. 63 of "The Eye of Spirit" he says; "But here is my point: we might say that the idea of evolution as returntoSpirit is part of the perennial philosophy, but the idea itself, in any adequate form is no more than a few hundred years old. It might be "ancient" as timeless, but is certainly not ancient as "old". However this view of evolution is based on a merely linear notion of time and from an integral perspective is very confused. Once again progress for the world and progress for the self, move (relatively) in opposite directions. So when we concentrate on progress in exterior terms (as with modern science and technology), inner selfdevelopment tends to lag behind. Indeed we may well have reached the point where society now needs to change direction and (relatively) involve to foster this neglected interior growth. This is also replicated in personal development. For example, the midlife crisis typically arises from an unbalanced emphasis on (exterior) progress as defined in worldly terms. It can then lead to corresponding neglect of (interior) selfdevelopment. So this important psychological crisis signals the need to switch emphasis from identification of progress as evolution (in relation to the world) to corresponding involution (in relation to the self). Correctly understood in dynamic terms, both evolution and involution are purely relative expressions of the nondual present moment. Time moves relatively both forward and backward in circular fashion from this central point. RegressionA very similar type of confusion relates to Ken's treatment of regression. The problem again arises due to an unduly linear interpretation. However, from a dynamic perspective, regression is vital in terms of balanced spiritual growth (where it has a circular meaning). Once again, Spirit always exists in the nondual present moment. As phenomenal notions of progress require a moving forward in time (away from this spiritual center), corresponding regression is continually needed in order to return (to the center). Indeed in a direct sense, this is the very means by which integration  as opposed to differentiation  takes place in experience. So in relative terms, there is always a moving forward and a moving backward from this nondual present center. So if we identify moving forward as progression  then relatively  the movement backward is regression. This necessary dialectic is well brought out in Christian mysticism. When the disciple confuses phenomenal progression with Spirit, attachment to secondary symbols necessarily takes place. So a corresponding (phenomenal) regression called purgation is required to undo this attachment, and return once more to one's deepest center. Regression in this circular fashion is vital in terms of integration and balanced spiritual development. Indeed  in a direct sense  the process of integration is inseparable from such regression. Likewise this regression necessarily takes place not only within but also between levels. The growing intensity of the spiritual light is necessary to reveal the deeply repressed shadow material from earlier "prepersonal" stages, thus enabling it to be gradually dissolved (in the light). Once again in dynamic terms, there is complementarity as between "higher" and "lower" stages. In the absence of the radiance of "higher" spiritual awareness, it would not be possible to properly access and heal the shadow of early development [16]. Indeed it is untenable to believe  as Ken appears to do  that regression is needed solely in service of the ego. Put another way, in mature spiritual terms, pre and trans are vertically complementary and inseparable from the very process of integration. Therefore, the deeprooted healing of the prepersonal shadow can only fully take place through transpersonal development. So Ken Wilber's failure to properly distinguish mature spiritual from pathological notions of regression, reflects the lack in his work of circular  as opposed to merely linear  notions of movement. The Four Quadrants The linear (onedirectional) approach is also very evident in Ken's treatment of the four quadrants [17]. In attempting to define each quadrant in unambiguous terms he himself uses a surprisingly reduced philosophical perspective. Indeed this is a fundamental problem with his general style. So often he attempts to analyze reality as if it were somehow independent of the interpreting mind. For example in describing his RightHand quadrants he says in "The Marriage of Sense and Soul", P. 117; "All RightHand events – all sensorimotor objects and empirical processes and ITs – can be seen with the mononological gaze, with they eye of flesh. You simply look at the rock, the town, the clouds, the mountains, the railroad tracks, the airplane, the flower, the car, the tree. All these RightHand objects and "ITs" can be seen by the senses or their extensions (microscopes to telescopes). They all have simple location, you can actually point to most of them". This is a very emphatic statement of the "myth of the given". However this description of RightHand events is untenable from an experiential perspective. Objects do not just exist "out there" but always in relationship to the observer. Thus in seeing a rock a bidirectional interaction is involved, where the rock is in relation to self (and the self in relation to the rock). The actual perception of the (individual) rock has both exterior and interior aspects (which mutually interact). Thus identifying the object solely with the RightHand is very onesided. Likewise the (individual) perception of "a rock" has no meaning in the absence of the corresponding (collective) concept of "rock". Thus Upper and Lower quadrants are likewise necessarily involved in the experience. So in dynamic terms all four quadrants are involved in the recognition of an object. We could equally start with Ken's other rigidly defined quadrants and likewise show that in dynamic terms all four quadrants are involved. There is in fact a basic confusion with his approach. He starts with the valid insight that every holon has exterior and interior aspects (in horizontal terms), and individual and collective aspects (in vertical terms). So by definition a holon belongs to all four quadrants. However he then attempts to compartmentalize these same holons in terms of (horizontal) RightHand and LeftHand, and (vertical) Upper and Lower quadrants. A rock for example is clearly a holon that dynamically belongs to all quadrants. So it makes little sense to attempt to identify this holon in static terms with just one quadrant i.e. the UpperRight. A true integral approach requires much greater subtlety. First of all, we accept that a holon does indeed belong to all four quadrants. Therefore in reduced linear terms, we can only identify locations by arbitrarily fixing our frame of reference. We can then consistently define quadrant locations (in this relative sense). By switching our frame of reference, we can give four equally valid quadrant explanations for any experiential event. These explanations are paradoxical in terms of each other. However, they provide the very basis for an integrated approach. In other words, through balanced paradox, we move from an either/or logic (where quadrants are differentiated) to a both/and logic (where they are integrated). Thus when we differentiate the quadrants in horizontal terms, an event is either RightHand or LeftHand. Depending on how we fix our frame of reference, we can give two equally valid asymmetrical interpretations of the event. However when we integrate these same quadrants (simultaneously using both frames of reference), the event is understood as both RightHand and LeftHand. In a direct sense, these complementary opposites are reconciled through intuitive awareness. However bidirectional paradoxical translation itself greatly facilitates this intuitive recognition. Ken clearly does not provide an integral interpretation of the quadrants. Also, insofar as he differentiates the quadrants he does so in a rigid absolute  rather than a balanced relative  manner. Not surprisingly this leads to a considerable amount of inconsistency. For example perception is associated with the Right and interpretation with the Left. However this makes little sense from a dynamic perspective (where such distinctions have a merely relative significance). Indeed the "myth of the given" arises directly from the attempt to give perceptions meaning without the need for corresponding (conceptual) interpretation. He then identifies his RightHand quadrants in "it" terms as the home of (empirical) science. However as in dynamic terms, scientific perceptions are meaningless in the absence of corresponding conceptual interpretation, we could equally identify the quadrants in "it" terms as (theoretical) science. As Ken places mental concepts in his LeftHand quadrants, then the theoretical aspect of science would be LeftHand, and the empirical, RightHand respectively. Likewise he identifies a value such as compassion with the LeftHand quadrant. However again in dynamic terms, an (interior) value has no meaning in the absence of an (exterior) objective context. Thus the sight of a suffering child might well be associated with compassion. However in reduced linear terms this has two equally valid interpretations. We could say that the sight of the child (exterior) causes the compassion; equally we could say that compassion (interior) causes one to notice the child. In other words, in dynamic terms the value cannot be exclusively identified with either quadrant. There are other obvious inconsistencies. Ken tries to identify the RightHand quadrants with "it" and the LeftHand with "I" and "We". As he considers Mathematics to relate to the interior aspect this would be placed in his LeftHand quadrants. However mathematics is considered a supreme expression of "it" understanding (though he identifies the LeftHand as "I" and "We") [18]. Likewise his attempts to identify morality with "We" makes little sense. Morality has certainly a (collective) "We" aspect. However it equally has an individual "I" aspect (as with existential morality). Morality also has an important "it" aspect. The programmatic approach of the institutionalized churches to moral behavior is based on a strong belief in "objective" morality. He also identifies beauty with "I" which is very onesided. There is a strong cultural "We" component to our notions of beauty. Indeed modern marketing and advertising have conditioned aesthetic perspectives to an unhealthy extent. Beauty clearly also has an "it" aspect where it is identified directly with (exterior) object symbols. Once again, by definition a holon includes all four quadrants. So as science, mathematics, morality, and beauty are holons, it makes no sense to try and exclusively identify them with just one quadrant. However it requires a dynamic relative treatment to preserve this balance. Ken then represents the disaster of modernity as the collapse of the Left to the Right. However if we associate the rapid growth of Mathematics with modernity (which he identifies with the Left), this position is not strictly tenable (even in his terms). The real problem is that he fails to distinguish true interactive from (merely) absolute notions of the quadrants. So properly speaking, the disaster of modernity represents the collapse of dynamic notions of Left and Right to (merely) reduced static interpretations (which can be identified with either Left or Right). Indeed in this respect, Ken's attempt to use an analytic approach, as a means of translating integration, is itself a reflection of the true problem of modernity [19]. Thus because of a lack of a dynamic approach, he continually comes down in favor of one side of a polarity (when the other is equally valid). From an integral perspective, his rather compartmentalized treatment of the quadrants is very confused, as he reduces dynamic interactions to rigid static interpretation. It must also be remembered that Ken's four quadrant approach deals solely with horizontal and vertical polarities (in an absolute fixed manner). A more comprehensive approach would also require the inclusion of diagonal polarities leading to an eight sectoral approach. These would then be interpreted in accordance with both the (linear) logic of form and the (circular) logic of emptiness. I would have further reservations regarding Ken's treatment that arise from his lack of diagonal polarities. For example, he would identify physiological reactions in the brain as the (exterior) aspect of (interior) thought processes. He is thus treating these as horizontal polarities in the same manner as sensorimotor objects (though they are quite different). However I would see them more accurately described in terms of diagonal polarities (where physical and psychological aspects directly coincide). Thus one can look at an object but not at the physiological aspect of one's own thought process. Spectrum of Consciousness Ken Wilber has introduced the invaluable notion of a Spectrum of Consciousness that extends the range of possible stages of development beyond those recognized in Western psychology. However, there are obvious problems with his approach. His holarchical model, which is very analytical, is not properly suited for integral interpretation. Synthetic (circular) logic is required to properly unravel twoway dynamic interactions. This lack of dynamic interpretation calls into question many of his key assumptions. Development for Ken entails a process of transcendence and inclusion, whereby at each stage, the "lower" is incorporated into the "higher". Though he accepts that dissociation can occur, he tends to interpret this as an aberration rather than an inevitable consequence of development. Therefore when development goes "right", no unfinished business is left over from earlier stages, and the "higher" Ascent can continue (without the need for regression). However this is all too neat and tidy and simply not tenable from a dynamic perspective. As opposite polarities are complementary, inclusion of one pole in a "higher" stage necessarily entails exclusion of the other pole (in a relative sense). Let me briefly illustrate this point with reference to cognitive unfolding, and the movement from concrete operational (conop) to formal operational understanding (formop) [20]. By definition, this has two horizontal aspects (i.e. exterior and interior) which dynamically interact in development. Thus when we focus on the exterior we can only transcend and include conop in formop by dynamically excluding the interior aspect. Likewise we can only transcend and include the interior aspect of conop in formop, by dynamically excluding the exterior. Therefore a degree of dissociation is inevitable at each stage of development. Differentiation is based on the separation of polarities. Whenever we differentiate one aspect of experience, repression of the unrecognized opposite aspect necessarily takes place. Though some integration (implicitly) occurs consistent with the level of development, some dissociation is unavoidable. We can of course distinguish as between "normal" and pathological dissociation. Normal enables one to function in a manner defined by cultural expectations of satisfactory development. Pathological would point to a severe malfunctioning in terms of such expectations. However, as we live in a highly differentiated society, "normality" in this context can be consistent with a significant level of dissociation. As differentiation of structures becomes more pronounced, dissociation is thereby likely to increase, considerably reducing dynamic interaction in experience. The key assumption of analytic science  that (objective) reality can be interpreted independent of the (subjective) mind  represents in extreme form the dissociated worldview. Here, dynamic interaction between opposite polarities is frozen completely out of formal understanding. Authentic spiritual development by contrast requires a great deal of experiential interaction. This indeed partially explains why so few, in our specialized rational society, proceed to the "higher" stages of development. Proper differentiation of structures is the vital first task of development. However in dynamic terms, this inevitably involves a degree of dissociation. Integration that is achieved in earlier development is necessarily subordinate to the prior task of differentiation. One important implication if this is that true integration cannot therefore be achieved at the centaur stage. At best a reduced form (accommodated to cultural norms) is possible. Quite simply, if full mind and body integration could be achieved at the centaur, there would be no need for transpersonal development.
So the "higher" stages of development are defined in a direct sense by the movement from specialized differentiation of structures towards true integration. With the gradual strengthening of spiritual awareness, unrecognized dissociated elements can thereby be properly accessed and healed (which would not be possible at earlier stages). So once again in a dynamic sense, vertical complementarity operates. Ken's way of dealing with dynamic negation relating to transcendence and exclusion is somewhat artificial and unconvincing. He attempts to make a distinction as between basic (or enduring) and transitional structures. However these basic structures continually change throughout development. Ken would identify conop for example as a basic cognitive structure. However it undergoes modification and refinement during the subsequent stages of development. Much of what Ken says in support of his position is inaccurate. He states on P. 141 of "The Eye of Spirit": "Once images emerge for example, the individual has full and constant access to the capacity to form images". This simply is not so. The "Dark Night of the Soul" which represents a vital stage in the mystical journey is associated with the deep (temporary) deprivation of image forming capacity. He then says "And images themselves will be an indispensable ingredient in the higher symbolic, conceptual, and formal thought." Again this is not strictly so. Indeed the very essence of conceptual thought is the ability to operate without concrete images. One could perhaps say that formop involves the use of abstract images but these clearly are qualitatively different from concrete. So rather than the concrete images of conop being included in formop, they are in fact excluded. Of course one may later combine conop and formop understanding giving access to both concrete and abstract images. However this represents the dynamic interaction of both stages (and should not be confused with the unfolding of formop from conop). So conop is really a basic structure that is always in transition (and can vary considerably over the course of development). Ken then gives moral development as an example of a transitional structure. However this is not really tenable. It is quite true that as development unfolds one's moral perspective changes. However earlier perspectives are not discarded. Rather they are maintained in a more refined manner consistent with one's ongoing development. Moral structures may indeed be inherently more dynamic than cognitive (involving greater polar interaction), but otherwise are structurally quite similar. I would see Ken's distinction as between basic and transitional structures as an unsatisfactory way of attempting to deal with the dynamics of development. He sidelines these dynamics into his transitional structures so that he can hold on to his root assumptions regarding transcendence and inclusion (in relation to basic structures). However despite all his carefully made distinctions as between both types, Ken fails to clearly demonstrate that there is any fundamental difference between them. So in dynamic terms the inclusion of "lower" in consecutive "higher stages is always a partial affair. Whenever we differentiate, some dissociation is inevitable. Therefore unfinished business from earlier development necessarily remains, requiring subsequent integration  often  at a much later stage. Indeed the very lack of full integration at a given stage is dynamically necessary to create the desire for deeper integration at a "higher" stage. We also have very important dynamic interaction in terms of the vertical polarities at each stage of development. This means in effect that transcendence dynamically excludes immanence and immanence excludes transcendence. This relates to the very important interaction as between cognitive and affective structures. So if we transcend in cognitive, then (relatively) we make immanent in affective terms. Transcendence in a new cognitive structure such as formop again requires  to a degree  repression of "lower" affective understanding. Typically, the focus on transcendence in development reflects a view that places undue emphasis on the cognitive aspect. And this invariably leads to repression of emotional affective experience. Ken makes a revealing comment on P.142 of "The Eye of Spirit" "Since I first published an article on these two different types of development ("Ontogenetic Development: Two Fundamental Patterns", 1981), I have stressed the extraordinary importance of this distinction, simply because the entire notion of "transcendence" depends upon it". Precisely! He has been forced to make an artificial distinction as between basic and transitional structures in the attempt to prop up a transcendent model of development that is itself untenable. Properly understood in dynamic terms, development in relation to any basis structure (such as conop) involves both inclusion and exclusion and also both transcendence and immanence. Therefore an attempted explanation solely in terms of "transcendence and inclusion" is clearly unbalanced. Ken attempts to extend his notion of holarchical development  which is based on a very linear translation  to all stages [21]. This is especially unsuitable for the treatment of "higher" spiritual development. There is in fact a marked discontinuity in the way he treats "conventional" and "contemplative" stages. He moves very quickly from a strongly analytic to a spiritual intuitive approach without establishing any proper interface as between the two modes of understanding [22]. Despite his great wealth of knowledge of spiritual traditions, his outline of transpersonal development is surprisingly sketchy. Most significantly, he provides no coherent explanation of the important subtle rational structures that unfold with the "higher" stages. This is a striking omission as these very structures form the appropriate basis for a true integral translation of reality. Indeed there is a very important confusion inherent in his treatment. He tends to identify the visionlogic of the centaur as the "highest" form of reason available [23]. However he never clearly distinguishes as between onedirectional and bidirectional reason (which are very different). Though he uses words that appear dynamic e.g. nonlinear, synthetic, dialectic, his actual use of visionlogic is surprisingly linear. Circular (bidirectional) reason is substantially different from Ken Wilber's visionlogic. It properly unfolds with the "higher" spiritual stages and leads to a very different approach to the interpretation of reality. Indeed there are several different degrees of this reason and their precise clarification is vital for an integral translation.
DYNAMIC MODEL OF SPECTRUM A key feature of this dynamic model of the Spectrum is that it is specifically constructed to allow for both linear and circular interpretation. It deals with the (linear) separation and differentiation of structures in development. However, equally the (circular) complementarity and integration of these same structures is also recognized. The (linear) logic of form is directly suited for translating the differentiation of structures. However the (circular) logic of emptiness is correspondingly suited for translation of their integration. It also distinguishes three fundamental polarities crucial to all development. Horizontal polarity exists at each level. This relates to the exterior/interior (and interior/exterior) aspects of development. Vertical polarity exists between levels. This relates to the whole/part (and part/whole) aspects of development. Finally diagonal polarity exists simultaneously both within and between levels. This relates to the fundamental actual/potential (and potential/actual) aspects of development [24]. The differentiation of holons is translated (directly) by the (linear) logic of form; their corresponding integration is (directly) translated by the (circular) logic of emptiness. (Ken's four quadrant approach distinguishes the horizontal and vertical aspects of holons. However his analytic method of translation is only properly suited for differentiating the quadrants in absolute fashion). By combining the two logical systems and the three fundamental sets of polarities we can construct a truly comprehensive map of development, that precisely encodes in (qualitative) binary terms the unique logical structure of every level (and stage) [25]. Another key feature is that the dynamic model represents a double Spectrum, which can be equally read as levels of psychological or physical reality. So from the psychological perspective, it represents a Spectrum of Consciousness. However equally from the physical perspective it represents a Spectrum of Nature. This leads to the very important insight that there are many different levels of science, with interpretation based on complementary psychological understanding of corresponding levels. I will briefly outline here the major levels (and transitions between levels). All levels have a unique binary coding, representing the interaction of linear and circular logic (with respect to the three sets of polarities). I demonstrate later the nature of the coding for each level. The Spectrum approximates to a linear mapping in the very middle (L0,H0). So strictly speaking the holarchical model would only apply for this level (and then in a very qualified sense). As we move away from the middle in both "lower" and "higher" directions, it becomes increasingly curved. Alternative models would therefore better apply for each of the other levels (and Radial Reality).
We start with three "lower" levels L3 (Lower 3) This is the "lower" null level and equates with the archaic stage [26]. It can be expressed as confused bidirectional understanding in relation to diagonal, vertical and horizontal polarities. It starts from a state of total confusion where unity is inseparable from nothingness (i.e. where neither differentiation nor integration has yet taken place in experience). In other words actual is confused with potential and potential with actual (diagonal) Whole is confused with part and part with whole (vertical). Object is confused with subject and subject with object (horizontal). So initial psychological development for the young infant entails both/and logic (that has not yet been disentangled). Because opposite polarities have not yet been sufficiently differentiated, integration cannot meaningfully take place. Indeed, using terminology from physics, spacetime for the young infant is extremely curved. Thus it is very mistaken to use (linear) either/or logic to translate the earliest stages of development. Transition from L3 to L2 This relates to stable (linear) differentiation of the diagonal polarity. So (finite) form is separated from (infinite) emptiness. Form has a bidirectional interpretation as a physical body (in relation to a physical world). So we have here the first important differentiation of the bodyself. L2 (Lower 2) This is the "lower" point level and equates with the magic stage. It involves ongoing linear differentiation of diagonal with the confused integration of vertical and horizontal polarities. So spacetime remains very curved (though not so much as at the previous level). Though some either/or logic is implicit in the infant's behavior, (undifferentiated) both/and understanding still predominates. There is still considerable confusion of the self with the world, where through primitive wish fulfillment, (personal) desire directly adheres to (impersonal) phenomena. Transition from L2 to L1 This relates to the (linear) differentiation of vertical polarities. So whole is now separated from part. This leads to the second major differentiation of the emotional self (where individual identity is now distinguished from the collective environment). L1 (Lower 1) This is the "lower" circular level and equates with the mythic stage. It involves ongoing differentiation of diagonal and vertical with the confused integration of horizontal polarities. Spacetime is now considerably less curved with either/or understanding predominating in experience. The use of language, images and concepts leads to the rapid development of phenomenal awareness. However the confusion of objective with subjective meaning is still evident in a mythical interpretation of spiritual realities. Transition from L1 to L0 This relates to the linear differentiation of the remaining horizontal polarities. It leads to the third major differentiation of a distinct mental self.
L0, H0 (Lower 0, Higher 0) This is the middle linear level and equates with Ken's rule/role, formal reflexive and visionlogic stages. There is now ongoing differentiation in relation to all three polarities. Spacetime becomes fully linear. (Circular both/and logic – in the explicit formal sense – does not apply). Analytic scientific translation is based on the understanding of this level. (Visionlogic represents the most sophisticated use of this understanding).
So starting from a situation of totally confused complementarity, the lower levels entail the movement to (linear) differentiated understanding. This culminates in the middle level of L0,H0. The "higher" levels entail the gradual movement from linear to (circular) integrated understanding.
Transition from H0 to H1 This represents the explicit unfolding of mirror understanding and the integration of horizontal polarities. All dualistic explanations now have mirror image equivalents. H1 (Higher 1) This is the "higher" circular level and corresponds to both the psychic and subtle realms [27]. It entails (circular) integrated understanding of the horizontal polarities (subject and object) with (linear) differentiation in relation to remaining vertical and diagonal polarities. Spacetime now starts to become curved (in a mature fashion). This is the means of integrating the mental self into personality. H1 is complementary in vertical terms with L1. So the mature understanding of H1 interprets the confused counterpart of L1. Transition from H1 to H2 This involves the explicit unfolding of virtual understanding and the integration of vertical polarities. (The virtual is the unconscious aspect  indirectly expressed  of all conscious phenomena). H2 (Higher 2) This is the "higher" point level and corresponds to the causal realm. It entails (circular) integration of both horizontal and vertical with (linear) differentiation of remaining diagonal polarities. Spacetime now becomes increasingly curved. This is the means of properly integrating the emotional self into personality. H2 is complementary in vertical terms with L2. So the (mature) understanding of H2 interprets the confused counterpart of L2. Transition from H2 to H3 It involves the unfolding of complex understanding and the integration of the diagonal directions. (Complex understanding relates to the simultaneous integration of both horizontal and vertical polarities). H3 (Higher 3) This is the "higher" null level and corresponds to pure nondual reality. It entails (circular) integration with relation to all three polarities (horizontal, vertical and diagonal). Because we are now approaching total curvature of spacetime the very notion of a level (which is a linear distinction) ultimately breaks down. So the culmination of H3 is strictly without level. This is the means of properly integrating the physical bodyself into personality. So the bodyself which is first to be differentiated in development is the last to be truly integrated. H3 is complementary and ultimately identical with L3. So with the culmination of nondual reality, "higher" and "lower" can be now seen as purely relative terms.
So the "higher" levels lead to the gradual specialized development of integrated understanding, and a spiritually refined permanent awareness of reality. It is only when both differentiation and integration in development have reached an appropriate level of specialization, that they themselves can be combined without undue confusion [28]. I refer to this comprehensive unfolding of experience as "Radial Reality". So Radial Reality involves the increasingly dynamic interpenetration of form with emptiness (and emptiness with form). Overall, this model is designed to reflect linear and circular aspects of development. This is essential to translate both the processes of differentiation and integration respectively (without undue reductionism). So from one perspective, we can look at development in linear terms. It progresses from L3  L2  L1 L0,H0  H1 H2  H3 culminating in Radial Reality.. From a circular perspective we have complementarity within each level. In relative terms reality has (exterior) physical and (interior) psychological aspects which dynamically interact. Next, we have vertical complementarity between levels. L1 is complementary with H1, L2 with H2 and H3 with L3. Strictly H3 and L3 represent no levels (diagonal complementarity). Finally, with Radial Reality the remaining level L0,H0 can interpenetrate with other levels. Once again a distinctive binary logical code (representing a unique configuration of linear and circular understanding) applies to each level. Conventional scientific translation is based on the logical code of the middle level L0,H0. Now if we attempt to translate other levels in terms of L0,H0 we basically misinterpret development. This applies to both "higher" and "lower" levels. The correct translation approach for a "lower" level is the corresponding understanding of the "higher". Thus to properly translate L2 (the magic), we need the understanding of H2 (the causal).
SPECTRUM OF TRANSLATION METHODS Each level (and even sublevel) can give rise to a unique method of translation. Thus we can generate a varied Spectrum of Translation Methods for the comprehensive interpretation of reality. Once again it is not possible to adequately translate from the perspective of visionlogic (which represents the translation method of the highest sublevel of L0,H0). Comprehensive interpretation requires the full range of translation methods. I will now outline these methods confining myself to mature translations. In each case, I will briefly indicate the precise application of the different methods with reference to the four quadrants. We have eight methods in all. The first group of "Differential Methods" relates to analytic translations (suitable for differentiation). The second group of "Integral Methods" relates to synthetic translations (suitable for integration). The final group of "Radial Methods" involves the mature combination of both analytic and synthetic translations (suitable for both differentiation and integration). DIFFERENTIAL METHODS These are directly based on the logic of form and are onedirectional (i.e. deal with development asymmetrically in a sequential fashion). 1) Analytic 1 This is based on the conop and formop understanding of L0,H0 and represents the conventional scientific approach. It leads to a marked tendency either to reduce understanding to the perspective of just one quadrant, or alternatively to confuse quadrants (due to lack of sufficient differentiation). 2) Analytic 2 This is based on the visionlogic of L0,H0. It essentially is a flexible intuitive based approach. Because it is so useful for the networking of ideas it has the appearance of a true synthetic method. However properly understood, it represents a refined multianalytic  rather than a true synthetic  approach and is therefore not suited for proper integral translation. Ken Wilber excels in the specialized use of visionlogic. In his later work he differentiates the quadrants (in absolute fashion). However he then tends to equate integral translation with this (differentiated) approach which is very misleading. By unambiguously fixing their location, Ken gives a very compartmentalized view that is not tenable in dynamic terms. Successful integral translation requires going considerably beyond visionlogic. However I would fully support Ken in his criticism of the more limited one quadrant analytic approach (which typifies most scientific disciplines). In terms of my frame of reference he is clearly using an analytic 2 method. 3) Analytic 3 This is based on the understanding that bridges H0 and H1 and represents the start of true relative appreciation. With analytic 2 we try to unambiguously fix the location of quadrants. Thus for example, in Ken's approach a molecule would be placed in the UpperRight quadrant. However in dynamic terms this makes little sense as by definition the molecule  which is a holon  involves the interaction of all four quadrants. The quadrants are complementary in both horizontal and vertical terms. So we are dealing in fact with different types of holarchies in each quadrant, where development unfolds  relatively  in opposite directions. To translate these in dualistic terms, we must arbitrarily fix our frame of reference with respect to one quadrant and define the kind of holarchy that applies. So if for example we fix the UpperRight quadrant by defining the holarchy applicable there in terms of transcendence and inclusion, the opposite UpperLeft holarchy entails transcendence and exclusion. The LowerRight then entails immanence and inclusion and the LowerLeft immanence and exclusion respectively [29]. Development that is defined in terms of just one kind of holarchy is very unbalanced. Because Ken emphasizes inclusion (rather than exclusion) he tends to identify development as the progressive evolution of stages. However from the equally valid complementary perspective, it also requires progressive involution in the undoing of previous structures (which represents the very process of integration). So whereas Ken describes a holarchy of transcendence and inclusion, St. John of the Cross, by contrast describes a holarchy of transcendence and exclusion. The former relates directly to the differentiation of structures, the latter – relatively  to their corresponding integration. Likewise Ken tends to identify successful development with transcendence, where the "lower" is included in the higher"; however again from the equally important complementary aspect, successful development is (relatively) identified with immanence (where the "higher" is included in the "lower") [30]. The very point therefore of the analytic 3 approach is to create balanced paradox in terms of all dualistic explanations. One cannot from this perspective represent development within just one asymmetric model (however sophisticated). An analytic 3 method would present development in terms of complementary asymmetric models (in horizontal, vertical and diagonal terms). The sequence of development would then be traced out in onedirectional fashion (within each holarchy). So the potential range of analytic inquiry would be greatly extended. However because these holarchies are mirror images of each other, dynamic symmetry exists in terms of the relationship of models. So a crucial balance can thereby be preserved. Subsequent synthetic methods deal with the dynamic unfolding of these symmetrical relationships. The analytic 3 method is extremely important as it provides the essential bridge as between differential and integral translation. INTEGRAL METHODS These are directly based on the logic of emptiness, and are bidirectional (dealing with relationships symmetrically in a simultaneous fashion). 4) Synthetic 1 This is based on appreciation of the dynamic interaction of development (in horizontal terms). It is also the basis for interpreting the confused understanding of L1. In the analytic 2 translation such dynamic appreciation does not yet apply. Exterior and interior aspects are fixed. Ken identifies the exterior with the RightHand and the interior with the LeftHand quadrants respectively. But in dynamic terms, both aspects are mutually interdependent. So in this sense the (absolute) fixing of quadrant positions is not justified. So now, every holon is seen in bidirectional terms. Like the relative movement of our two drivers, exterior and interior aspects keep switching location and thus have a merely relative identity. Direct appreciation of this dynamic interaction is intuitive. However paradoxical understanding is vital in dualistic terms, so as to prepare the mind for the necessary qualitative transformation to intuitive insight. Likewise intuition greatly facilitates appreciation of paradox in (reduced) dualistic terms. So intuition and rational paradox mutually enhance each other in the appreciation of bidirectional understanding. So the ultimate purpose of the synthetic 1 translation is the erosion of all rigid identification with (polarized) exterior and interior notions, until both aspects become inseparable from spiritual intuition. A remarkable new type of refined scientific understanding results from the application of the integral methods of translation. It is inherently dynamic and subtle in nature; also it has a qualitative (holistic) rather than a quantitative (analytic) focus, and always has complementary applications to both physical and psychological reality. I refer to this integral science as Holoscience. Every discipline such as Physics, Economics, Philosophy, Psychology etc. can be given an integral scientific translation (based on bidirectional appreciation). Besides opening up the possibility for fascinating new perspectives and connections within these distinct fields, it also greatly facilitates their integration with each other. Most importantly, Mathematics can be given a dynamic synthetic translation with direct implications for an integral scientific appreciation of reality. Brief Illustration of Holistic MathematicsBecause of its great significance, I will illustrate briefly this integral approach to Mathematics (which I refer to as Holistic Mathematics). 1 and 0 are the most important numbers in Mathematics (where they are understood analytically in quantitative terms). A comprehensive number system can be built using these two digits. Significantly, the digital revolution  with the potential to encode all information processes  is based on the binary numbers. However 1 and 0 have a deeper qualitative meaning as "oneness" and "nothingness" (form and emptiness). When these two digits are used in a synthetic sense to represent the (linear) logic of form and the (circular) logic of emptiness, they have the power to encode all transformation processes [31]. I am representing this qualitative use of the binary system in this article. Development is a transformation process, and each level can be encoded in terms of a unique configuration of the digits (i.e. logical systems) that apply at each level of the Spectrum. The methods of translation in turn are derived directly from these logical codes. Then, through application of these translation methods, fascinating new metaparadigms arise providing the basis for a truly multilayered scientific appreciation of reality [32]. Every mathematical symbol has an alternative synthetic translation (with complementary applications in physical and psychological terms). So there is enormous scope for a new integral appreciation of reality to unfold (based on synthetic rather than analytic principles). In the deepest sense, the fundamental structures of reality  which are inherent to all understanding  are mathematical (in this synthetic sense). Integral mathematics forms the appropriate basis in turn for the integral understanding of all the other sciences. I strongly believe that the integral scientific approach to reality should be based on the synthetic application of mathematical symbols. So integral translation starts with the synthetic 1, and becomes more refined with the synthetic 2 and synthetic 3 methods. 5) Synthetic 2 This is based on the understanding of H2. (It is also the appropriate method for interpreting the confused counterpart of L2). It involves bidirectional understanding in terms of both horizontal and vertical polarities. All four quadrants are now understood in dynamic relation fashion. So the location of the four quadrants is gradually eroded in intuitive awareness. Conventional notions of scientific "reality" are based formally on mere conscious interpretation. A synthetic 2 translation provides a means of formally incorporating the unconscious into scientific understanding. This requires moving however from a mathematical "real" to a "complex" interpretation of the world. So once again, just as in quantitative terms we have complex numbers (with real and imaginary parts), now in synthetic qualitative terms, "reality" itself is understood as complex (with real and imaginary aspects). This gives a precise integral mathematical way for defining the nature of the quadrants (in dynamic terms) [33]. Another important development here is the recognition that interpretation of the "lower" is based on the understanding of the "higher". Likewise the relationships of the "lower" call out for the interpretation of the "higher". This has great relevance for Physics. Below the macro at the subatomic level, the findings of physics are paradoxical in terms of the conventional paradigm, and require a synthetic logic for their full interpretation. So it is the "higher" transrational understanding which interprets the "lower" quantum reality. Likewise the findings of the "lower" quantum level lead to the need for the "higher" transrational understanding. This illustrates the important vertical complementarity of pre and trans that dynamically exists as between the physical and psychological domains. Indeed when we go even lower on the physical level to the minute scale relating to superstrings, we need a correspondingly "higher" level of transrational understanding to make intuitive sense of its findings [34]. Ken Wilber consistently misinterprets this important complementarity between "lower" physical nature and "higher" psychological understanding. (This in turn reflects his unduly rigid formulation of the pre/trans fallacy) [35]. For example in SES, in a note on P. 716 in the context of a strong attack on Fred Alan Wolf we have this statement: "A true humanistic psychology is based upon processes of intersubjective understanding and recognition about which quantum mechanics has not a single thing to say, not even vaguely, not even remotely. But by all means let us base our humanism on this power driven monologue with rocks". Then in "The Marriage of Sense and Soul", where he includes Quantum Mechanics as one of the "new paradigms in science" he states on P. 39. "But they are all without exception monological to the core. And thus, as important as they are in their own right, they have little to offer us in terms of actually integrating monological with dialogical and translogical  that is integrating science and spirituality". So he has now switched from a position where quantum mechanics has absolutely nothing to say (in terms of integrating science with spirituality) to a position where, though it has "little to offer" apparently has something  however small  to contribute. Unfortunately, Ken does not clarify what he means in this context, which in any case is inconsistent with the viewpoint that Quantum Mechanics is monological to the core. However when we get towards the end of "The Marriage and Sense and Soul" a further  and rather dramatic  shift in position takes place. This is a relevant quote from P. 196; "For objective empirical science is no longer relegated to the bottom rung of the hierarchy (which the traditional approach gave it and which contemporary epistemological pluralism still gives it); rather, empirical science is accessing the exterior modes of all the higher levels as well. This moves empirical science off the bottom level of the Great Chain and places it on the exterior side of each level of the Great Chain. (You can see this in Figure 51). Thus objective empirical science does not give us the whole story, but neither does it have nothing to say about the higher domains, which is the untenable stance of both traditional epistemological pluralism (and the crushing error that contributed to the collapse of the Great Chain of Being)." Taken together, these three statements present a very confused position. Again the main problem however is that Ken provides no true notion of integral science. This would require that the important complementary relationship between physical and psychological aspects of reality, be both recognized and applied (in horizontal, vertical and diagonal terms). What we are finally offered is a merely analytical  and very reduced view  of "a science of the higher levels" e.g. brainwave research in relation to meditation. 6) Synthetic 3 This is based on the understanding of H3 and the dynamic appreciation of development (in horizontal, vertical and diagonal terms). It is also the basis for interpretation of the extremely confused understanding of L3. This requires going beyond the four quadrants to the appreciation of the crucially important diagonal polarities. The diagonal polarities can be defined as the simultaneous coordination of opposites both within levels and between levels. However this means that the very distinction as between horizontal and vertical directions now breaks down. So strictly the culmination of H3 is without level. Diagonal complementarity, in this context, implies that H3 is now identical with the "lowest" level L3, which is the pure experience of nondual reality. Needless to say, Ken's attempt to "arrive" at nonduality using an analytic translation is somewhat unconvincing. At one moment he is vigorously defending his arbitrary asymmetrical notions of development, and then the next waxing poetic about the nondual nature of reality (where everything is now symmetrical). However he never shows how to consistently move from the asymmetrical analytic interpretation to the symmetric nondual experience. (This is the very purpose of a synthetic translation!) Once again it simply reflects the lack of a genuine integral approach. A remarkable "double" translation can be provided for these diagonal polarities (using the integral mathematical approach)[ 36]. This allows for both an intuitive and (indirect) rational understanding, which in an incredible manner, demonstrates the marriage of form and emptiness. So, nondual reality is not just a passive intuitive awareness of reality. Rather it relates to the extremely dynamic interaction of both conscious and unconscious, where phenomena are erased from memory as soon as they arise. However it is the exceptionally refined switching between the phenomenal poles of experience that sustains the intuitive awareness. So strictly speaking, nondual reality is not empty of phenomena but rather empty of rigid attachment to phenomena. In the appropriate context, where one is not attached to phenomenal translation, the synthetic mathematical translation of H3 provides an integral "Theory of Everything". The ultimate nature of reality can be explained in terms of three paradoxical sets of symmetries (relating to the complementarity of horizontal, vertical and diagonal polarities). Furthermore these can be given a fully coherent formulation in synthetic mathematical terms [37]. As well as demonstrating that the very structure of reality is mathematical (in this refined synthetic sense), it provides the vital key for translating the fundamental nature of both physical and psychological aspects (which in nondual terms are equal). Also it provides the means to show how both sets of explanations are fully complementary. Ultimately in terms of the integral "Theory of Everything", physical and psychological are identical. In the world of phenomenal reality both aspects are always separated to some degree. By allowing for the separation as well as complementarity of polarities, we can extend this "Theory of Everything" to precisely translate every level, sublevel and stage on the Spectrum (with both physical and psychological interpretations). So  as I have already stated  each level can be encoded as a unique configuration of the qualitative binary system (i.e. the interplay of the logic of form and the logic of emptiness). So as a transformation process, reality at all levels can be encoded in terms of the integral counterpart of the binary system. This in turn demonstrates just one extremely fruitful application of a synthetic mathematical approach. Rightly seen, the very purpose of an integral translation of reality is to ultimately lead to the dissolution of its own symbolic representations in the experience of pure mystery. From this mystery the symbols emerge and into this mystery they once again dissolve. However when appropriately used, they can be invaluable for both facilitating and (indirectly) clarifying the awareness of mystery. The translations of analytic science are not directly consistent with the contemplative experience. Indeed, the very basis for this scientific approach is that the world exists independently of the self, whereas in contemplative terms it is precisely the reverse. So when unchecked, analytic science itself can lead to patterns of understanding that pose a considerable barrier to authentic spiritual development. The keen realization of this deep problem has filled me for the past 30 years with the desire to create a "new" integral science, that would be directly consistent with contemplation and in turn facilitate growth in that experience. In other words with a true integral approach, science itself becomes naturally transformed into a unique form of spiritual meditation. RADIAL METHODS These are based on the mature interaction of both the (linear) logic of form and the (circular) logic of emptiness. 7) Radial 1 As we have seen linear logic is onedirectional and circular logic bidirectional respectively. Though Radial 1 now combines both types of logic, it does so in a somewhat onedirectional manner. In other words, one can analyze and also synthesize reality in a mature fashion but not yet combine both modes in a fully simultaneous manner. Radial 1 represents experience that is both differentiated and integrated (dual and nondual). This leads to a new creative vision of science that formally combines both analytic and synthetic understanding [38]. (In terms of the four quadrants one can now successfully combine the analytic compartmentalized treatment of each quadrant with the synthetic integrated appreciation of the interaction of all quadrants. However this understanding would still not be fully spontaneous). With Radial Reality, analytic understanding acts as a catalyst for transforming (synthetic) insight. Likewise, this transforming insight in turn greatly facilitates new analytic discovery. So information about reality and transformation of reality now go hand and hand. From a radial perspective, a proposition is not understood until one (a) can provide an analytic interpretation (b) also provide a synthetic interpretation (c) establish correspondence as between both analytic and synthetic aspects [39]. This will open up incredibly rich possibilities through an enlarged Spectrum of scientific inquiry. Some could specialize in the analytic, others in the synthetic, and perhaps some in establishing correspondence between both aspects. At any given time, some propositions would have analytic but lack synthetic interpretations; others perhaps would have a synthetic but not an analytic rationale; yet others could have both analytic and synthetic appreciation (but lack satisfactory correspondence between them). Looking at reality in this new way would not alone be full consistent with overall integration of experience, but greatly enhance the possibilities for analytic inquiry. "Unsolved" problems would yield up unexpected solutions, and the possibility for exciting  and yet unknown fields  would emerge. We are well aware nowadays of the digital revolution. This merely represents the quantitative use of the binary numbers (suited for the encoding of information). However as I have already mentioned, the synthetic approach gives rise to a corresponding qualitative interpretation of these same digits (suited for the encoding of all transformation processes). So the digital revolution in radial terms would combine both quantitative and qualitative binary aspects (representing both information and transformation), in a comprehensive double binary system. 8) Radial 2 Not alone would Radial 2 allow for the combined use of the (linear) logic of form and the (circular) logic of emptiness, but it would also enable both the onedirectional and bidirectional use of both systems. Thus depending on the context, one could sequentially separate both approaches. For example to deal with a practical matter, the logic of form would be directly appropriate; in terms of contemplation, the logic of emptiness would be more relevant. Likewise other situations would call for the combined interaction of both systems e.g. involvement in new uncharted areas. In relation to quadrants, one could here analyze or synthesize relationships in sequence, or analyze and synthesize simultaneously (depending on the requirement). The key defining characteristic of Radial 2 interpretation is a permanent absorption in divine reality. One's ego (which still survives in refined manner) is now effectively used as a mediator of the entire world process (representing an enhanced cosmic identity). With freedom from selfish attachment, little friction remains to the simple spontaneous working of Spirit. The logic of form and the logic of emptiness now interpenetrate as to be inseparable [40]. The Pre/Trans Fallacy The pre/trans fallacy, is probably the best known of all Wilberian concepts. A clear distinction is made as between prepersonal and transpersonal stages of development. So the pre/trans fallacy consists in either elevating pre to trans or reducing trans to pre. Now clearly there is an important sense in which Ken's interpretation is valid. However its truth is contained within the application of just one system (i.e. the linear either/or logic of form). However when one looks at the pre/trans fallacy from the alternative system (i.e. the circular both/and logic of emptiness), Ken's interpretation makes little sense. So in the (linear) logic of form, pre is absolutely distinct from trans. Therefore, experience is either pre or trans. However in the (circular) logic of emptiness, pre and trans are complementary with a merely relative distinction. So here, experience is both pre and trans. When development commences, as opposite polarities have not yet been differentiated, pre cannot be meaningfully separated from trans (or trans from pre). In a dynamic sense therefore, the infant does not so much operate in terms of a given level (as linearly defined), but rather has extremely confused access to all levels of the Spectrum. So the linear way of describing such development (i.e. as the first prepersonal stage) is not strictly accurate. As differentiation proceeds, this confused dynamic access is gradually reduced and development does indeed become more rooted in specific stages. When structures have been fully differentiated, the linear description becomes especially appropriate. We then have personal development confined to the middle band of the Spectrum (which is neither pre nor trans). However this arrival at the personal level is a twoedged sword. It does indeed represent success in terms of the specialized differentiation of structures. However equally, access to the other levels of the Spectrum is thereby greatly reduced. So the very process of differentiation tends to reduce the dynamics of interaction (through inevitable dissociation). This again explains why development so often plateaus at the personal stages with very few proceeding to "higher" levels. With the unfolding of authentic spiritual growth, experience once more becomes dynamic and interactive with access to all levels of the Spectrum gradually restored (this time in integrated fashion). So nondual reality therefore is not so much a level as it embraces all levels. Thus there is an important sense in which pre and trans are separate, and equally an important sense in which both are complementary, and it is vital to maintain both meanings in translation. In a direct sense, the differentiation of structures leads to the separation of pre and trans in experience (starting from an initial confused identity). However the integration of structures leads to their complementary interpretation. So when we use a linear definition of stages it is appropriate to clearly separate pre and trans. A stage therefore is either pre or trans. However, when we use a circular definition, pre and trans are always to some degree complementary. So a stage is now both pre and trans. Towards the very beginning and the completion of development the circular interpretation is appropriate. During the middle stages the linear appreciation is more applicable (as the emphasis is on differentiation in development). When seen in this light, Ken's interpretation of the pre/trans fallacy is especially unsuited for an integral translation. Even from his own frame of reference, his position seems hard to sustain. For example, he recognizes many different "lines of development" which can unfold in a relatively independent fashion. One could – in Ken's terms – be at a transpersonal stage in relation to one line (say, spiritual) and yet be at a prepersonal stage in relation to another (such as affective). At any given time, one's overall experience could thus combine both pre and trans elements. As some interaction of different lines necessarily takes place, then the pre elements of the "lowly" would interpenetrate to a degree with the trans elements of the more "highly" developed lines; likewise the trans elements of the "higher" would interpenetrate with the pre elements of the "lower" lines. So genuine spiritual (trans) experience would then be mediated through the (pre) symbols of a "lower" line; likewise these (pre) symbols would be expressed through the "higher" (trans) understanding; so the pre/trans fallacy would not then be tenable in its strict form. Also Ken has made so many other modifications, that his original distinction is not really viable. In "The Eye of Spirit" P. 182 he says: "In Wilber11, I maintain that any and all transpersonal experiences of infancy are not due to preegoic frontal structures but This represents one more example of the key problem with Ken's overall approach. Again it is multidifferential rather than truly integral in orientation. Over the years, he has made considerable modifications to his original model in a compartmentalized  and sometimes convoluted  fashion. However, when one begins to test the dynamic implications of these many modifications for the original core assumptions, the model becomes increasingly untenable [41]. This points to the need for a genuine integral approach (rather than further ad hoc adjustments to a mechanical type model). Otherwise we could have many sterile debates with Ken repeatedly accusing his critics of lack of familiarity with his overall approach. The real problem is that the dynamic implications of the modifications to the original model are inconsistent with its core assumptions. The truth is that pre and trans are necessarily interlinked in the dynamics of development. Actual experience of pre and trans can vary greatly from very confused to deeply integrated understanding. However rigid insistence on their clear separation is inconsistent with experiential dynamics and can in fact greatly hinder accurate recognition of these same dynamics [42]. Therefore the extension by Ken of his pre/trans fallacy beyond its valid range of interpretation, has had unfortunate consequences. It has led to an undue emphasis on the process of differentiation rather than integration in development. Also, because of its rigid formulation it has led to a somewhat closed approach in dialogue with critics [43]. Each major stage of development has its own unique manner of rational interpretation [44]. Considerable distortion arises from attempting to translate reality solely in terms of the understanding of just one stage. So, Wilber's particular interpretation of the pre/trans fallacy is based on the translation of the centaur (and is only appropriate for that stage). Very different translations for example are consistent with each of the integral approaches [45]. ConclusionIn conclusion, the lack of true dynamic translation is the major deficiency in Ken Wilber's work. He uses the linear (onedirectional) method of visionlogic based on the centaur stage. Properly understood however, this is a multidifferential approach suited to the understanding of asymmetrical phenomenal relationships [46]. However he fails to recognize the equal value of circular (bidirectional) understanding, based on the intellectual aspect of the "higher" spiritual stages. This provides the basis for a true integral approach geared to appreciation of the underlying symmetrical nature of reality. A comprehensive approach requires the full Spectrum of Translation Methods (requiring considerably more than visionlogic). Quite simply, as Ken Wilber continually reduces integration to differentiation in development, his approach is very distorted from a dynamic perspective.
NOTES1. I have developed Holistic Mathematics (Holomatics) as an appropriate scientific basis for a true integral approach to reality. This is applicable to all scientific disciplines e.g. Physics and Economics. It is based on the key insight that every mathematical symbol can be given an alternative dynamic interpretation based on bidirectional circular logic. So mathematics really has two aspects 1) a quantitative interpretation suited for scientific analysis and 2) a qualitative interpretation (Holistic Mathematics) suited for scientific synthesis. A true integral approach requires this latter qualitative interpretation. Grasping this point has the potential to open up enormous vistas of understanding. Development  in dynamic terms  is of course a transformation process. Thus, I see the use of the qualitative binary system incorporating the (linear) logic of form and the (circular) logic of emptiness as the true basis for a dynamic approach to development. I would classify scientific approaches in three main categories: (i) Analytical Science based on linear (onedirectional) understanding, which is suitable as a differential approach. (ii) Holistic Science (Holoscience) based on circular (bidirectional) understanding, which is suitable as an integral approach. (iii) Radial Science based on the two forms of understanding and suitable for the incorporation of both aspects (differential and integral). In Holistic Mathematical terms, Ken Wilber mainly attempts to translate development using what is essentially a qualitative unitary system (based on linear logic). A comprehensive approach would require a qualitative binary system based on the use at each stage of development of both the logic of form and the logic of emptiness (i.e. linear and circular logic). 2. Here is one relevant quote from "The Marriage of Sense and Soul" P. 141: "If a genuine integration of science and religion is to be a reality, then it will have to include an integration of the Big three (of art, moral and science), not by deforming any of them to fit some sort of pet scheme, but by taking each of them more or less exactly as they are. There is no need to force science to fit some sort of "new paradigm" that will then supposedly be compatible with spirituality. The very attempt is a massive category error, a profound confusion about the nature and role of monological science, dialogical philosophy and translogical spirituality, These are to be integrated as we find them, not as we deform them in a monological leveling that erases the very differences that are supposed to be integrated in the first place". This quote is revealing on two counts. First it clearly indicates that Ken confuses integration with a multidifferentiated approach. If we leave the Big Three "more or less exactly as they are" they remain differentiated (not integrated). Also, Ken persists in seeing science in terms of the reduced analytic approach i.e. monological science. However, true integral science is of a qualitatively different synthetic order (and is directly consistent with "higher" spiritual understanding). However Ken displays no appreciation of such integral science. 3. Ken Wilber does refer in Sex, Ecology, Spirituality to the dialectic of form (linear logic) and the dialectic of emptiness (circular logic). However typically he uses circular (bidirectional) statements when describing the nature of nondual reality. Though he refers in "The Eye of Spirit" (Introduction) to "the circle of understanding" his actual interpretation of development throughout the book is very linear. My key point is that one cannot properly approach the "circle of understanding" through linear translation. In dynamic terms it is necessary to show the precise interrelationship of both linear and circular logic at all stages of development. So there is a fundamental problem with Wilber's work, whereby he in effect largely collapses the translation of development to the dialectic of form. 4. In dynamic terms, circular (bidirectional) reason and intuition are very much interdependent. In order to erode rigid rational attachment to dualistic understanding, we must first appreciate the limitations of such understanding through equal recognition of the opposite (excluded) pole. This creates paradox in terms of all dualistic statements and prepares the mind for a qualitative transformation in intuitive awareness (where such paradox is reconciled). This intuitive awareness in turn increases the facility to recognize paradox once again at the (reduced) linear level of understanding. So in dynamic terms bidirectional understanding serves as the essential bridge between dualistic reason and intuitive awareness. In its mature form, this refined reason unfolds with the "higher" spiritual stages of development. 5. This is based on the complementarity of opposites which is very much missing from Ken Wilber's work. (In the comprehensive Index to "Sex, Ecology, Spirituality" neither the terms "complementarity" nor "complementary opposites" are listed). 6. The clear implication here is that time for the interior aspect of reality moves in opposite direction from the exterior (and the exterior in opposite direction from the interior). This is an extremely important point, and is not properly appreciated in science. The belief that the arrow of time moves irreversibly forward literally means that time is onedimensional (i.e. linear). So a linear approach is based on the assumption of forward moving time and thereby treats relationships in sequential fashion. In this sense, Ken Wilber's translation of development is very linear. However in a dynamic relative sense, if time has a positive direction (i.e. moves forward) for the exterior aspect of holons, then it has a negative direction (i.e. moves backward) for the interior (and vice versa). It is the very fusion of these two opposite directions of time that leads to the nondual experience of reality (in the present moment). 7. The key to moving to symmetrical (bidirectional) understanding, is the recognition that every asymmetrical (onedirectional) interpretation has a mirror image explanation (that is equally valid). Thus, though the original interpretation and its mirror equivalent are both asymmetric (when treated sequentially), when understood simultaneously they are symmetric. 8. Once again, reason and intuition operate in a dynamic complementary fashion. The appreciation of paradox at the rational level prepares one for a qualitative transformation in intuitive insight (where opposite polarities are directly reconciled). Intuition in turn facilitates a keener appreciation of paradox (at a reduced rational level). 9. Bidirectional reason has a fundamental interpretation in Holistic Mathematics as the dynamic understanding of addition and subtraction. Conscious understanding literally involves the positing of phenomena. To make understanding unconscious again, this onesided polarized understanding must be negated. So in dynamic terms, the continual interaction of conscious and unconscious involves a process of positing and negating (i.e. the dynamic equivalent of the mathematical operations of addition and subtraction). 10. The way reality appears reflects the philosophical lens we use to view this reality. So if we use a linear viewing lens, reality will tend to conform to this perspective. However when one looks at reality in a nonlinear fashion, holarchy no longer appears an appropriate model. Because each level of the Spectrum is associated with a different viewing lens, we need different models of development to reflect this understanding 11. Affective sense is necessary for the very perception of phenomena (so that they can attract our attention through their unique quality). However, as in formal terms analytical science is viewed in rational cognitive terms, its translations inevitably reduce affective to cognitive interpretation. Thus the extreme application of scientific method, leads to a considerable deadening in our very ability to respond to phenomena (and consequent loss of appreciation of their individual uniqueness). 12. It would be mistaken to equate transcendence (solely) with the cognitive aspect and immanence with the affective aspect respectively. Transcendence and immanence should be understood in relative fashion. So if we fix our frame of reference by identifying transcendence with the cognitive, then (relatively) we should then identify immanence with the affective aspect. However we are fully entitled to switch our frame of reference thus reversing our interpretation. So both cognitive and affective have transcendent and immanent aspects. Science itself (as a cognitive expression of meaning) has transcendent and immanent aspects. These are closely related in turn to the deductive and inductive approaches. The deductive is associated with the "higher" theoretical and the inductive with the "lower" empirical approach respectively. Thus in science, we can use theories to deduce relationship between facts (transcendent) or use relationships between facts to induce "new" theories (immanence). Ken Wilber's description of how he arrived at his four quadrants is a good example of the immanent approach i.e. he induced the "higher" theoretical explanation from a wealth of "lower" data. However it is at variance with his holarchical model of "transcendence and inclusion". Ken's account of his four quadrants (as a general theoretical construct) is in fact a good example of cognitive "immanence and inclusion". 13. The reason why spiritual development so often starts with an intellectual focus is due to the predominant emphasis on specialized mental ability in our society. It is thus natural that one would initially – at any rate – try to apply that strength to advancing in spiritual development. 14. Basically the affective aspect – in direct terms  relates to an ability to respond to one's environment whereas the cognitive relates to the ability to control. Properly speaking, the body would not be defined in terms of either (conscious) response or control, but rather a more primitive ability that instinctively combines both. Clearly one cannot properly incorporate emotions within an approach that is based on refined rational control of development. So if we define transcendence in terms of the intellectual approach, then immanence cannot be subsumed within it. The bodyself is generally the most difficult to properly integrate into personality. As its differentiation in early infancy precedes all distinct conscious activity (either affective or cognitive), likewise its proper integration in later life requires letting go of all conscious awareness. 15. The Ascent of Ken Wilber is very different for example from that of St. John of the Cross ("The Ascent of Mount Carmel"). Whereas Wilber in effect is dealing with evolution as the differentiation of "higher" level conscious structures, St. John  relatively in his Ascent  focuses on involution and the dynamic process by which they are integrated (through deep spiritual immersion in the unconscious). 16. When one looks at development from a dynamic perspective, dissociation in the early stages is inevitable as the normal process. What is often forgotten is that development involves opposite polarities (in horizontal, vertical and diagonal terms). So the very differentiation of one polarity in experience  by definition  requires a failure to recognize the equal importance of the opposite polarity. So it is thereby repressed and this leads to dissociation. 17. I would judge Ken Wilber's attempt to outline the fundamental structure of holons a partial success. In fairness he does identify the important horizontal (exterior and interior) and vertical (individual and collective) poles. However a full model requires the identification of diagonal polarities (which relate to the fundamental dichotomy as between finite and infinite poles i.e. form and emptiness). This inclusion of diagonal polarities then leads to a more comprehensive eight sectoral approach. However the major weakness of Wilber's holonic model is that he interprets the relationships as between opposite poles solely in terms of linear (onedirectional) logic. In other words he merely shows how to differentiate the quadrants (in fixed absolute fashion). A full treatment requires the interpretation of holons equally in terms of circular (bidirectional) logic (where opposite poles acquire a purely relative meaning). This is necessary as a means of properly integrating the quadrants. A profound mathematical explanation can be provided for the interpretation of holons. It is based on the holistic qualitative interpretation of the eight roots of unity (which geometrically has an important mandalic representation). It has such universal value as an integral model of the fundamental structures of reality that I refer to it as a "A Theory of Everything" 18. Mathematics is a holon and therefore has both interior and exterior aspects. What underlines mathematical activity is the assumption of double correspondence i.e. that the RightHand quadrant corresponds with the Left and that the Left corresponds with the Right. So even though mathematical constructs are of an interior nature, one accepts their direct correspondence with exterior interpretations of reality. So in this sense Mathematics is "objective". Likewise mathematicians would also accept that when we start with exterior data, corresponding interior representations directly correspond with this data. So in (conventional) Mathematics, dynamic interaction of both exterior and interior aspects is ignored  in formal terms  to an extreme degree. When the dynamic interaction between poles is properly recognized (as with "Holistic Mathematics"), mathematics itself become transformed, and its symbols acquire a powerful integral capacity.
19. Analytic science is also based on the double correspondence model (though not to the same extent as Mathematics). Certainly in the Newtonian worldview, direct correspondence is assumed as between scientific formulations and nature. Therefore a theoretical scientist will expect a "good" model of reality to subsequently explain the empirical data. Likewise a research scientist will try to derive "good" theoretical explanations directly from a knowledge of the data. However, such science is based on the (unjustified) formal exclusion of experiential interaction as between exterior and interior poles. Once again when we explicitly allow for this interaction through using bidirectional synthetic logic, the very nature of science is transformed and acquires a powerful integral capacity. This "new" qualitative science, I refer to as "Holoscience". 20. Ken would refer to this as the unfolding of the cognitive "line of development". However I have deep reservations regarding his "lines of development". Firstly, the very concept is  by definition  linear. Ken tries to view these "lines" as quasiindependent. However from a dynamic perspective this is untenable. Especially in the "higher" stages where dynamic interaction greatly increases, linear assumptions largely break down. Cognitive development itself can unfold with respect to the four quadrants. So it is necessary in a credible model firstly to have some way of dealing with this dynamic interaction (specific to the cognitive "line"). But I cannot see that Ken presents any explanation. Also the cognitive "line" clearly interacts with other "lines". For example we might justifiably ask its precise relationship to say, affective and moral "lines". However once again Ken does not get to grips with these important dynamic issues. In fact he has far too many lines (which are really composites of more fundamental interactions). Let me give an analogy. Color printing can operate on the basis of just three basic colors (from which an unending variety of "composite" colors can be derived). Likewise it is the same with development. So we need to identify the primary elements and then base dynamic understanding on these elements. (I do this with three sets of polarities – which are versatile enough to allow for all possible interactions in development). I consider that Ken's model avoids the implications of dynamic interaction. He makes many tightly defined modifications and refinements that are compartmentalized neatly into "Wilberian" boxes. However this approach – though admirable in detail  is much too mechanical, and invalid from an integral perspective. Initially he started with a simple holarchical stage model based on transcendence and inclusion. But now that has been considerably widened to include basic (enduring) and transitional structures and a self system (mediating between them), permanent and temporary states, differing lines of development and four quadrants applying to all the lines of development. However now at Wilber IV, his holarchical model has very much an ad hoc quality. The dynamic implications of all these later refinements for the original root assumptions are still largely untested. 21. The holarchical model  as it is unduly linear  is of limited value as an overall explanation. At best one can say that this is how development might look when viewed from the perspective of just one stage (i.e. visionlogic). However it makes little sense to interpret other stages exclusively in terms of visionlogic. Indeed a different representation would be appropriate at each stage. Thus as the psychic and subtle realms involve the growing fusion of linear and circular modes of understanding, a cyclical or spiral model would be more appropriate. The causal realm signals the arrival at a point center or singularity. However it also involves shortlived projections of an extreme relative nature that are both "higher" spiritually and "lower" physically. So a point model involving "virtual" circles above and below the point (in the figure of an 8) would be now appropriate. Nondual reality could perhaps be represented by diagonal "null" lines, which have a magnitude of zero. The most complete development would be best represented by a mandalic type approach that I refer to as the radial model. This involves a circle with horizontal, vertical and diagonal lines drawn from the midpoint to the circumference (which in holistic terms would be an unbounded circumference). So here we combine the important notions of point, horizontal vertical and null lines (in both directions) and circular circumference. So the radial model which is based on absolute Spirit (at the center) and at the unbounded circumference has relative expressions in both (absolute) linear and (relative) circular terms. Interestingly the "lower" stages would be complementary to the corresponding "higher" (where they represent a confused understanding). This would strongly suggest that the holarchical model equally is not appropriate for these "lower" stages 22. This raises another extremely important point that has been greatly ignored. We need to distinguish two types of basic structures. Differential structures relate to conscious, whereas integral structures relate (directly) to unconscious understanding respectively. The emphasis in development during the early prepersonal stages is on differentiation of conscious structures. This culminates with "middle" personal development. Such integration that takes place during this time is merely implicit (and not identifiable in terms of formal structures). So identified structures of development are therefore synonymous here with differentiated structures. When we move into transpersonal development the emphasis in on integral structures (based on the alternative logical system of emptiness). It is entirely inappropriate to try and extend the "transcend and include" model (based on differentiation) to these new integral structures. The simple fact is that former linear are not included in the new empty structures. Rather they are excluded. This is wellemphasized in Christian mysticism where the unfolding of "higher" integration is preceded by dynamic negation of former understanding (i.e. purgation). So transpersonal development can be temporarily associated with marked erosion of linear ability. Thus if we identify differential structures with holarchical inclusion, then the integral relate – by contrast – to holarchical exclusion. These integral structures are inherently dynamic in nature. Though directly based on intuition, they have indirectly a phenomenal form (that is dynamically inseparable from this intuition). There is also a marked contrast as between holarchical models based on transcendence and immanence respectively. This relates to the very important distinction as between cognitive and affective aspects of understanding. This means for example that a "transcendence" model of the cognitive is inapplicable as an interpretation of the corresponding affective line. Here  in relative terms – we require an "immanence and inclusion" model. And again as we can have differentiated and integrated structures, we need both "immanence and inclusion" and "immanence and exclusion" models. These findings simply result from the application of the dynamic four quadrant model (where a different holarchy – relatively – exists in each quadrant). A full account of development however requires the inclusion also of diagonal polarities (leading to an eight sectoral approach). Diagonal polarities can be described as the simultaneous interaction of horizontal and vertical aspects. They are especially relevant in the context of integration of the bodyself with the rest of experience. This requires a perspective that is both transcendent and immanent simultaneously. So the body cannot be integrated fully into experience without the attainment of pure nondual reality. Paradoxically, before one can be fully with body (physically) one must learn to be fully without body (transcendence); equally before one can be fully without body (spiritually) one must learn to be fully with body (immanence). The overall implication of this, is that different configurations of holarchy apply at each level of the Spectrum. Indeed the only level where the "transcend and include" model approximates to an accurate description of development would be at the middle (linear) level of the Spectrum (and only then in a very qualified sense). H1 (subtle realms) requires both inclusion and exclusion models; H2 (causal realm) requires both inclusion and exclusion and transcendent and immanent models; H3 (nondual reality) requires all models simultaneously; the "lower" levels require confused versions of the corresponding "higher" holarchies. 23. The visionlogic that Ken uses, simply represents the highest sublevel of the middle level of the Spectrum (L0,H0). Here, synthesis is attempted between opposite polarities, which maintain their identity (in absolute terms). So though this visionlogic is intuitively based, very flexible and versatile in its application, it still represents a onedirectional form of understanding. Close examination of the key issues in Ken's work clearly confirms this view. However this understanding is properly suited for differentiation (not for integration). The "higher" levels lead to a bidirectional form of understanding. At H1 (subtle realm) we have the unfolding of concrete, formal and visionlogic sublevels. This is associated with bidirectional understanding in relation to horizontal (exterior/interior) polarities. So opposite polarities now have a purely relative identity (which can be reversed depending on the frame of reference). With concrete understanding one can apply it at a practical sense level. With formal understanding one can apply it a deeper formal level. (Hegelian philosophy uses a translation based on the formal sublevel of H1). With visionlogic one can relate both concrete and formal understanding in a very intuitive manner. However the visionlogic of H1 is very different from the visionlogic of H0. At H1, though bidirectional circular understanding is used in relation to horizontal polarities, linear appreciation still dominates in relation to vertical and diagonal polarities. This leads to a linear confusion (which is evident in Hegel's work). Though he distinguishes complementarity (horizontally) within stages of development, he does not recognize this equal complementarity (vertically) between stages. So Hegel sees history in somewhat linear vertical terms as a progressive evolution of Spirit (which is inconsistent with a nondual interpretation). Ken Wilber follows Hegel in this linear confusion of development with progressive evolution. However, Ken does not use reason in the dynamic bidirectional manner of Hegel. At H2, bidirectional understanding now operates in relation to both horizontal and vertical polarities. Again this unfolds through concrete, formal and visionlogic sublevels. Linear understanding still remains here in relation to diagonal polarities. What this means in effect, is that one is not yet capable of fully equating (phenomenal) form with spiritual emptiness. A degree of attachment to phenomenal symbols remains. At H3, bidirectional understanding operates in relation to all three sets of polarities (horizontal, vertical and diagonal), culminating in pure nondual awareness where form is inseparable from emptiness. Here, there is no separation of sublevels. So the visionlogic of H3 is pure nondual awareness. It has a paradoxical translation in terms of three fundamental symmetries, and constitutes a "Theory of Everything". Radial Reality leads to the restoration of phenomenal form, which interpenetrates in a very refined manner with nondual awareness. So we could identify a Radial visionlogic which combines bidirectional and unidirectional interpretation. 24. These polarities could also be expressed as finite/infinite (and infinite/finite) or manifest/unmanifest (and unmanifest/manifest). The very point about diagonal polarities, is that one simultaneously switches as between horizontal and vertical aspects so that these directions themselves lose their meaning. When experience has reached this degree of dynamic interactivity, it has become extremely spiritualized with form giving away quickly to emptiness, and emptiness giving rise fleetingly to form.
25. I define my full model in terms of bands, levels, and transitions between levels, sublevels, directions, stages, phases and personality characteristics. There are three bands. The "lower" equates with "prepersonal" development, the middle with personal and the "higher" with "transpersonal" development. These bands can be given a linear interpretation where they are distinct or a circular interpretation where "higher" and "lower" are complementary. Full development ultimately culminates in Radial Reality. There are seven major levels (within the bands), three lower (L3, L2 and L1) a middle (L0,H0) and three higher (H1, H2 and H3). Again these levels can be taken in a linear fashion or circular (where L3 is complementary with H3, L2 with H2 and L1 with H1). Radial Reality combines the relative differentiation of each level with the integration of all levels. There are six transitions bridging levels where an important transformation takes place enabling successful movement to the next level. There are three sublevels (within each level) which I refer to as concrete, formal and visionlogic respectively. (These are closely related to the division of polarities in terms of horizontal, vertical and diagonal). The visionlogic stage represents a dynamic fusion of the concrete and formal sublevels. Directions represent the integration of polarities (within the sublevels of a given level). With (L0,H0) only one direction is integrated. Integration is here reduced to differentiation. (As Ken's visionlogic belongs to this level, it cannot therefore operate as a true integral method of translation). With H1 the horizontal polarities (objective and subjective) are integrated. At L1 they are integrated in confused fashion (as they are not yet properly differentiated). With H2 the vertical polarities (whole and part) are also integrated. At L2 they are integrated in confused fashion. With H3 the diagonal polarities (form and emptiness) are in addition integrated. At L3 all three sets are integrated in confused fashion. The division of sublevels, by directions, defines a stage of development, which is investigated with respect to affective, cognitive and spiritual aspects. (All "lines" are composites of the "Big Three"). Phases are used descriptive devices to express the dynamic unfolding of different stages. Another important distinction would be in relation to personality types, which can significantly influence the manner and type of development that unfolds. So if take H1 as an example (the subtle realm), this would be subdivided into three further levels. (The concrete sublevel would correspond to the psychic realm). Each sublevel would then have two directions (exterior and interior). We would then study the unfolding of affective, cognitive and spiritual development with respect to both exterior and interior stages (at each sublevel). We could portray the dynamic cyclical nature of each stage through a description of phases of development. Finally we could then perhaps contrast the nature of likely development at H1 for different personality types. (I have used Holistic Mathematics to derive a very coherent explanation for the likely influence of a particular personality type on development). What is remarkable is that all of this development – even at the detailed level of breakdown – can be precisely encoded in qualitative binary form. I am not at all suggesting that actual development is so neatly defined as this outline. My purpose is basically to identify the precise nature of structures that unfold at all stages of development. Though the mystical traditions offer comprehensive accounts of "higher" development, many of the structures involved (esp. intellectual) at each stage have never  to be mind  been properly identified. 26. My descriptions of levels are based on welldefined geometrical notions. The linear level is literally onedimensional. In geometrical terms, it is represented by a straight line drawn positively in one direction. This corresponds mathematically to the one root of unity (i.e. unity). The linear level therefore is onedirectional. The circular level is literally twodimensional. In geometrical terms, it is a circle drawn through two points (the line between which represents the diameter of the circle). The lines drawn from the center of the circle have both positive and negative directions. They correspond mathematically to the two roots of unity. The circular level is therefore bidirectional in horizontal terms. The point level is literally fourdimensional. In geometrical terms it is represented by the point at the center of the circle (representing the intersection of both horizontal and vertical lines). Mathematically, the horizontal lines are real and the vertical lines are imaginary (with positive and negative directions) and correspond to the four roots of unity. The point level is therefore bidirectional in horizontal and vertical terms. The null level is literally eightdimensional. In geometrical terms, it is represented by null lines  as well as horizontal and vertical  that emanate as diagonal lines from the center. These null lines have a magnitude of zero (with a location nowhere and everywhere). They can also be represented as complex lines (with equal real and imaginary aspects). Mathematically this level corresponds to the eight roots of unity. The null level is therefore bidirectional in horizontal, vertical and diagonal terms. Radial Reality combines all levels. So we have (finite) horizontal and vertical lines (emanating from the center), the circle (as unbounded circumference), the point (at center of the circle) and null lines (that are empty in magnitude), emanating diagonally from the center. (I use the term "Radial" for two reasons. First of all the lines horizontal, vertical and diagonal are radii moving from a central point to the unbounded circumference. Secondly radial also suggest "rays" of light. So the radial lines are equally rays of light). What is truly remarkable is that the entire Spectrum can be precisely expressed in mathematical terms  literally  as a reduced expression of oneness.
27. The psychic realm would equate with the concrete sublevel of H1.
28. The very word "integral" gives rise to much confusion. In popular terms it is used in a manner where it is not clearly distinguished from differentiation (and reflects the nature of our differentiated culture). So if someone leads an integrated lifestyle, this would mean that a coherent balance is maintained (integration) as between various activities (differentiation). So in this popular sense the word integration is combined with differentiation and not really distinct. Unfortunately, this can too easily lead to a reduced notion of integration where the whole is seen largely as the sum of its differentiated parts. In terms of intellectual translation an enormous "integral fallacy" prevails, whereby analytic methods are universally used in the attempt to synthesize reality. The problem is so common that it is not even noticed. I think it is extremely important to clearly distinguish (onedirectional) analytic from (bidirectional) synthetic understanding. Whereas the former is (directly) suited for differentiation of reality, the latter is (directly) suited for corresponding integration. So we have three main layers of translation:
29. The four relative definitions of holarchies are as follows:
Thus in dynamic terms each quadrant can be seen as the interaction of four asymmetrical interpretations (which are paradoxical both horizontally and vertical in terms of each other). It is this very appreciation of dynamic symmetry that leads directly to nondual experience. 30. Again the bodyself is first to be differentiated in development. However it is generally the last to be properly integrated with personality. As differentiation is identified with the "lowest" level L3, it requires the complementary "highest" level H3 for integration. 31. The symbols we use to represent the binary digits are the straightline (1) and  with slight modification  the circle (0). So the synthetic origin of these numbers is inherent in the very symbols used for their representation.
32. A metaparadigm in scientific terms relates to a unique method of rational translation so that the very nature of scientific inquiry fundamentally changes. A paradigm relates to a unique application of an existing translation. So for example, Euclidean Geometry (within mathematics) represents a paradigm (which is a special application of the analytic 1 method). NonEuclidean Geometry represents a different paradigm (using an alternative application of this analytic method). However both these paradigms occur within a given metaparadigm (i.e. the analytic 1 method). I am strongly suggesting that the time has come for significant metaparadigm expansion in science (which will greatly extend appreciation of the very nature of valid scientific inquiry)
33. Once again we must arbitrarily fix our frame of reference. So if the UR quadrant (representing transcendence and inclusion) is real and positive, then the UL (representing transcendence and exclusion) is real and negative. Then the LR (representing immanence and inclusion) is imaginary and positive, and the LL (representing immanence and exclusion) is imaginary and negative. So just as the four roots of a number, yield real and imaginary results with positive and negative values, likewise the four quadrants are real and imaginary and positive and negative (with respect to each other). Putting it in holistic mathematical terms the analytic 2 translation attempts to view all quadrants in positive real manner. However a synthetic 2 translation shows that in dynamic terms, movement in quadrants is real and imaginary (and positive and negative) with respect to each other. So time has now four directions so that movement takes place in positive and negative directions in both real and imaginary time. Conscious phenomena operate in real time; Unconscious phenomena (indirectly expressed in conscious form) operate in imaginary time. The experiential appreciation of these paradoxical relationships is through direct spiritual intuitive awareness.
34. Personality Types (esp. MBTI) can be given a simple holistic mathematical basis (as differing configurations of the four quadrants). One way of understanding each type is as a unique permutation of the four dimensions of spacetime. In this sense each personality relates to a specific "dimension" (i.e. unique configuration of the four dimensions). Integration requires combining the facets of different personality types i.e. all the "dimensions" of spacetime. One of the problems that has greatly puzzled physicists is the fact that the number of dimensions required for consistent theories in Superstring Theories (which unite Relativity and Quantum Mechanics) is greater than 4. Earlier theories were based on 26 and 10 dimensions respectively. The most recent is based on 11 dimensions. (In each case the relevant numbers used in physics are 24, 8 and 9 respectively with two added dimensions). However this becomes easier to understand when we look on "dimensions" in Superstring Theories as unique configurations of the original four dimensions. Interestingly, the corresponding numbers in physics equate with the main personality theories i.e. the original Jungian Model, the Myers Briggs  extended to include eight "missing" personality types  and the Enneagram). This makes much greater sense when we realize that dimensions would not yet have properly separated at the level of reality relating to Superstrings. So the only way of appreciating a "dimension" would be as a configuration of the yet undifferentiated four dimensions. So the fundamental structures we use to organize "higher" psychological reality (Personality Types) have identical correspondents in "lower" physical reality. The dimensions in Superstring Theories represent therefore fundamental types of physical structures  complementary to Personalities as psychological structures  based on unique configurations of the four "original" dimensions of spacetime. Using vertical complementarity, we can thereby establish remarkable parallels as between two areas (Personality Types and Superstrings) which otherwise would be considered totally distinct. Also, this approach greatly illuminates the fundamental nature of both aspects. These results can be derived simply as an application of the synthetic "Theory of Everything" (with diagonal polarities not directly required). So Superstring Theory which is seen in physics as the TOE does not relate to the fundamental ground level L3 (but rather the next level L2). 35. One can of course give a reduced account of quantum mechanics by interpreting its findings through the understanding associated with (L0,H0). However to make intuitive sense of the paradoxical nature of quantum mechanical relationships, then one must use the understanding appropriate to H1 which complements the quantum level of L1 (in vertical terms). So when properly interpreted, quantum mechanics necessarily involves "higher" level understanding. Ken Wilber consistently overlooks this very important point (by solely recognizing the reduced linear interpretation). There is a huge irony in Ken's view of (narrow) science. He sees it as necessarily reductionist and monological because he himself can provide no alternative interpretation (other than the reductionist and monological). This clearly indicates the need for a true integral approach. 36. The diagonal lines represent the hypotenuse of a rightangled triangle, where the other two sides represent the horizontal and vertical axes respectively, (which are radii of the circle). Now we define the horizontal axis as real and the vertical axis as imaginary. The diagonal lines can then be defined in terms of complex coordinates (where real and imaginary aspects are equal). However when we use Pythagorean Theorem to find the magnitude of these diagonal lines the answer = 0. They therefore are null lines. So these diagonal lines can be given a double synthetic interpretation;
37. The three sets of relationships relate to the three polarities. In horizontal terms we have "real" polarities that are positive and negative with respect to each other. This means in effect, that in synthetic mathematical terms, the interior and exterior aspects of phenomena are, dynamically, positive and negative (with respect to each other). This applies equally in both physical and psychological terms. In vertical terms we have "imaginary" polarities that are positive and negative with respect to each other. This relates to the indirect conscious phenomena (that emanate from the unconscious). These describe in synthetic mathematical terms the dynamic relationship between whole and part (and are opposites in imaginary terms). Real objects are whole/parts (or part/wholes). Likewise when we combine (multiply) two imaginary numbers (of opposite sign) we get a (positive) real number. Again this applies in both physical and psychological terms. The relationship between horizontal and vertical polarities describes the basic interaction as between perceptions and concepts (psychological) and objects and dimensions (physical). In diagonal terms we have "complex" polarities that are positive and negative with respect to each other. These diagonal polarities have a double mathematical interpretation as
They provide a synthetic mathematical way off describing the aspects of Spirit (as immanence and transcendence) and remarkably also the nature of physical forces. So these three sets of polarities lead to a synthetic mathematical "Theory of Everything" (the full understanding of which is inseparable from pure contemplation). The current search for a TOE in physics is very flawed. Firstly, it is conceived in analytic rather than synthetic terms. Secondly, it is not dealing with the fundamental ground of reality (L3) but rather L2. Thirdly, it does not attempt to integrate psychological with physical aspects of reality (which is required in a true integral TOE). 38. In holistic mathematical terms, this would be referred to as complex science (with real and imaginary components). The real aspect corresponds to the analytic aspect. So conventional science studies the "real" world. The imaginary aspect corresponds to synthetic or integral science (which is not formally included in the conventional approach). 39. Integral mathematics and indeed integral science would have both transcendent and immanent aspects. I do have some reservations regarding the choice of terminology of "Holistic Mathematics" to indicate the integral approach. The difficulty is that integral is employed in a precisely defined (more limited fashion) in conventional mathematics. So the use of the same term could be confusing. Also the integral approach that I would use bears little comparison to its current meaning in "Integral Studies". "Holistic Mathematics" does place the emphasis on the "whole" suggesting perhaps a more transcendent bias. And in an overall theoretical model of reality this emphasis is justifiable (provided we remain aware of the context). 40. We could perhaps appreciate the relationship between dual and nondual reality in terms of the fire analogy. For the fire to burn we need material (e.g. wood). This corresponds to dual reality. The fire then gives rise to energy and flames (corresponding to nondual reality). Both are vitally necessary if the fire is to continue to burn. (So we need dual and nondual reality). However when the fire is greatly ablaze it becomes ever more difficult to separate the material from the flames. This state of the fire would approximate to Radial Reality.
41. In relation to 1), I have grave reservations regarding Ken's attempt to give his interpretation of "The Tibetan Book of the Dead" a central role in a developmental model. The model should be much more generally based with the capacity to communicate across religious boundaries, and not rely on a specific esoteric tradition that requires acceptance of reincarnation. Ken's approach would not be very meaningful for example for someone rooted in Christianity! Also, though I am no expert in the "Tibetan book of the Dead", I would take it in a somewhat metaphorical sense (which needs very careful decoding for translation to a Western type model). Once again I would accuse Ken of using a very linear form of decoding in presenting his explanation. It is indeed possible to give it a more dynamic treatment (which would be consistent with my own approach). However a proper dynamic model does not require Bardo Realms (so I would see no need to use them). To be quite honest I see Ken's reliance on Bardo Realms as somewhat convoluted, and dictated by the need to compensate for the lack of true dynamic appreciation within his mechanical model. Indeed translating in Western terms the psychic/soul drop would refer to the role of the unconscious. So at all stages, we have the dynamic interaction of consciously differentiated structures with the unconscious (and the unconscious with these structures). Seen in this light the unconscious is an integral aspect of all development, and the purpose of a dynamic approach is to meaningfully translate its interactions with differentiating consciousness. Needless to say I would find Ken's attempt to explain transpersonal awareness in early infancy, as "trailing clouds of glory" from preconception involutionary realms as unacceptable. This would require first of all the acceptance of these involutionary realms, and also the assumption that there is necessarily some dynamic link as between these involutionary realms and (conscious) evolutionary development. However Ken does not provide a satisfactory explanation of this link. So I would see "trailing clouds of glory" as an unsatisfactory way of dealing with the fact that conscious and unconscious are necessarily closely linked in early development. Therefore trans awareness can easily leak  as it were  into prepersonal development (because in unconscious terms pre is inseparable from trans). With the gradual differentiation of structures pre and trans become slowly separated so that trans elements are less likely to leak into pre understanding. Ken's explanation of 2) amounts to an admission that the infant does indeed have access to all stages of the Spectrum (every 24 hours). So if the infant can access psychic, subtle and causal domains, this necessarily means some degree of access to transegoic structures. So therefore 2) amounts from a dynamic perspective, to an acceptance that prepersonal and transpersonal structures are necessarily linked. This provides a very simple and coherent explanation therefore for the existence of transpersonal awareness in infancy. Now the microgenetic involutional cycle relates to the fact that dual and nondual awareness are related from moment to moment. In terms of the nondual component of experience, the separation of polar opposites has no meaning. So therefore in the present nondual moment, involution and evolution coincide; equally of course pre and trans coincide. So pre and trans coincide and then separate in the microgenetic involutional cycle. Therefore, we should logically maintain the complementarity as well as the separation of preegoic and transegoic structures. In relation to 3) Ken also tries to explain temporary peak experiences in the same manner as "trailing clouds of glory" (as a leakage from preconception involutionary realms). However these "peak" experiences are possible at any stage. So we could  and indeed do  have "peak" experiences of the transpersonal at any of the prepersonal and personal stages. (Indeed the reason why this is still possible at the personal stages is because some pre elements  which are dynamically related to trans  in practice always remain at the personal stages of development). However Ken's "trailing clouds of glory" explanation maintains that these fade out quickly. However this is clearly not the case. Indeed these temporary "peak" experiences of the transpersonal in early development may be exceptionally important. Temporary states of great lucidity are possible (especially in those with latent mystical tendencies) which can serve as lifedefining moments. So once we accept that pre and trans necessarily interact in dynamic terms, we can provide a simple coherent explanation that covers all possibilities (without the need for unnecessary convolution). Clearly in the earlier stages (where differentiation has not properly occurred) pre and trans  though dynamically linked  are greatly confused. In the more advanced spiritual stages, pre and trans are again dynamically linked (this time in a more mature integrated fashion). However it is always a matter of degree; just as "prepersonal" stages of development can be associated with temporary "higher" trans states, likewise "transpersonal" stages of development can be likewise associated with temporary "lower" pre states.
42. I will now briefly go through the eight translation methods and reflect the various interpretations of pre and trans that apply. In an Analytic 1, pre and trans are separated (without reference to quadrants). In an Analytic 2, pre and trans are again separated with respect to each of the four quadrants. (Ken Wilber's interpretation of the pre/trans fallacy would only apply to these two methods). In an Analytic 3 again pre and trans are separated (with two opposite asymmetrical interpretations). In Ken's approach, development goes unambiguously from prepersonal to personal to transpersonal. However we can equally give an interpretation where the direction is reversed moving from transpersonal to personal to prepersonal. This would entail that in early development one has access to transpersonal experience in a very immature confused fashion; likewise it is only with mature development that one can properly access and heal the shadow of early (prepersonal) stages. So the two asymmetrical interpretations arise from a realization of the complementary nature of pre and trans. Ken's interpretation does not extend to analytic 3. In terms of synthetic methods, pre and trans are complementary. In the Synthetic 1 they are complementary in relation to horizontal polarities. In Synthetic 2 they are complementary in relation to horizontal and vertical polarities. In Synthetic 3 they are complementary in relation to horizontal, vertical and diagonal polarities. Thus with pure nondual awareness pre and trans are fully complementary (and indeed identical). The Radial Methods combine both analytic and synthetic interpretations. With Radial 1 both analytic and synthetic apply (though not in simultaneous manner). With Radial 2 any remaining division between analytic and synthetic is dissolved.
43. Rather than attempting to engage in open discussion Ken often defends himself against criticism by accusing his opponents of the pre/trans fallacy. I would consider that the Jungian approach is inherently more dynamic that Ken's (and better reflects the integral perspective). However as Ken accuses Jung of the pre/trans fallacy, he can be somewhat dismissive of valid Jungian insights. Ken excels in the precise differentiation of different concepts of development and I would accept that there is a lack of the same precision with many Jungian ideas. Therefore Ken's perspective has been of great assistance in challenging his opponents to give greater clarity to their criticism. However differentiation is not integration, and Ken's very detailed  but somewhat mechanical  model of development does not equate with a coherent integral approach. So once again in the very formulation of the pre/trans fallacy, Ken has come down sharply in favor of one side of a polarity.
44. The logical structure of the three "lower" levels (LL3, LL2 and LL1) is complementary with the corresponding "higher" levels (HL3, HL2 and HL1) respectively. It represents confused integral understanding (i.e. where proper differentiation of structures has not yet taken place).
45. Unfortunately the pre/trans fallacy has become something of a Wilberian dogma. I think that it would be greatly helpful in terms of opening up dialogue if it could be accepted that Wilber's interpretation is purely stage specific i.e. relating to the centaur and even within that stage not the only valid interpretation. Again his approach suffers greatly in that it lacks any real dynamism. There is a very important sense in which pre and trans are fully complementary terms (but this is greatly missing from his interpretation). Indeed on a more general level, Ken Wilber's overall translation of reality is very much stage specific (relating to the visionlogic of the centaur). Acceptance of this point would provide a valuable perspective from which to judge both the strengths and limitations of his approach.
46. Ken is not the only one of course using a onedirectional approach. It is in fact the norm in terms of present translation. It also has to be said that Ken uses visionlogic (i.e. of H0) with a greater level of precision than perhaps any writer. However this very strength, from another perspective can be a weakness. Because others often tend to use a "looser" style, meanings that are really applicable to the synthetic viewpoint can be more easily accommodated with their overall approach. They thereby can perhaps better capture the dynamics of experience (though in a manner less well defined than Ken's). I believe that there is now a great need at present to precisely clarify the nature of the various methods of translation. A comprehensive approach requires all. REFERENCESWilber, K. 1980. The Atman Project: A transpersonal view of human development, Wheaton I11. : Quest books —1995. Sex, Ecology, Spirituality: The spirit of evolution. Boston: Shambhala —1997. The Eye of Spirit: An Integral Vision for a world Gone Slightly Mad: Shambhala —1998. The Marriage of Sense and Soul: Integrating Science and Religion : Random House —1999. One Taste – The Journals of Ken Wilber: Shambhala Rothberg, D & S. Kelly. 1998. Ken Wilber in Dialogue: Conversations with Leading Transpersonal Thinkers: Quest Books Kavanaugh, K, Rodriguez, O. 1979. The Ascent of Mount Carmel in the collected works of St. John of the Cross, ICS Publications Underhill, E. 1993. Mysticism: The Nature and Development of Spiritual Consciousness: Oneworld Publications Ltd; Collins, P. 1997. The Science of Integration at website on Holistic Mathematics © 1999 Peter Collins
