In my developmental approach, I outlined 3 distinct types of integration.

Integral 1 related to the dynamic two-way integration of the "horizontal" polarities in development i.e. external and internal. Thus at each stage, successful integration required that an appropriate balance be maintained as between out-in i.e. integration of the (internal) self with respect to the (external) world and in-out i.e. integration of the (external) world with respect to the (internal) self.

Integral 2 related to the corresponding dynamic two-way integration of the "vertical" polarities i.e. whole (collective) and part (individual). Thus between "higher and "lower" stages, successful further development required that an appropriate balance be maintained as between top-down i.e. integration of the - relatively - lower (part) with respect to the higher (whole) stages and bottom-up i.e. reverse integration of the higher (whole) from the lower (part) stages.

To assist recognition of such integration, I defined each of the 3 "lower" stages (Level 1) in a complementary manner with the corresponding 3 "higher" stages (Level 3) with the "lowest" directly complementary with the "highest". So, only through successfully unravelling the most primitive instinctive elements with respect to the "lowest", could pure spiritual awareness properly unfold at the corresponding "highest" level.

Integral 3 then represented the most refined and advanced form of integration that indicated the dynamic relationship as between the most fundamental polarities in development.

This related to the dynamic four-way integration of the "diagonal" polarities of form and emptiness. This in turn entailed the simultaneous two-way integration of the "horizontal" polarities (within each stage) and the "vertical" polarities (between stages).

Success in this regard then led to the dynamic approximation in experience of form and emptiness.

This was in turn beautifully illustrated in holistic mathematical terms through the four additional roots (of the 8 roots of unity).

As one can see, the four roots of 1, geometrically represented by the 4 equidistant points on the unit circle (connected by horizontal and vertical lines through the centre) divide the circle into four quadrants.

Then the additional 4 roots (of the 8 roots of 1) represented by the diagonal lines, bisect the 4 quadrants. Now if we concentrate for a moment on the triangle drawn in the UL quadrant, both the opposite (vertical) and adjacent (horizontal) sides are equal. Now, the hypotenuse (diagonal) represents the 3rd side of this triangle. And by the Pythagorean Theorem, the square on the hypotenuse = the sum of squares on the other two sides. However because the adjacent and opposite lines represent real and imaginary units respectively, this entails that the combined sum of squares of these two lines = 0.

Therefore the diagonal lines (representing the 4 additional) roots are - what are referred to as - null lines with magnitude = 0, while the co-ordinates of these lines (as the points where they meet the circumference of the circle) comprise equal real and imaginary components.

The holistic mathematical explanation of this is deeply revealing, as it implies in dynamic experiential terms, that the state of spiritual emptiness (i.e. nothingness) implies the highly dynamic refined experience of phenomena of form (that are equally both real and imaginary in nature).

This in turn implies the perfect balance of both conscious and unconscious of experience so that undue attachment does not arise with respect to either voluntary (conscious) or involuntary (unconscious) aspects.

Now the absolute experience of emptiness therefore can be ever more closely approached in a relative highly transparent phenomenal manner (without being capable of total realisation).

So we have here the holistic mathematical interpretation of the mystical notion of the plenum-void in the experiential equality of form and emptiness.

"Form is not other than Emptiness

Emptiness is not other than Form"

So the most advanced form of integration in development entails the simultaneous ability to seamlessly integrate bi-directionally within each stage as between external and internal polarities, while also seamlessly integrating bi-directionally whole and part polarities between stages . And when this is successfully attained, one approaches ever more closely the point where form itself (as phenomenal structure) is integrated with emptiness (as spiritual state).

So put another way, diagonal integration entails the balanced integration of both states and structures with respect to all stages of development.

## Monday, February 29, 2016

## Friday, February 26, 2016

### Integral Studies (4)

Just as I had found substantial imbalance with respect to horizontal same stage integration, due to the predominant emphasis of the internal psychological aspect throughout the spectrum, equally I found a similar imbalance with respect to vertical higher and lower stage integration.

This was due to the mistaken asymmetrical emphasis on development as the progressive movement to higher stages of a more collective holistic nature.

Indeed in this context, much use is made of the notion of a holon (i.e. literally a whole/part). A holon is then defined as a whole that is also part of another whole. So for example an atom would represent a holon where the (whole) atom is also part of a (whole) molecule.

However in dynamic interactive terms, we need to stress the two-way movement of wholes and parts. So therefore counterbalancing the holon (whole/part) where each whole is part of another whole is the onhol (part/whole) where each part is also whole in the context of other parts.

When one merely stresses reality as comprised of holons, the emphasis is then unambiguously on higher stages of development as representing increasing degrees of collective wholeness until eventually with pure nondual awareness, one reaches appreciation of the spiritual whole beyond all phenomenal representation.

This leads to an unbalanced - merely top-down - approach to development, where one seeks integration of all earlier stages from the latest to yet unfold.

However when one equally stresses onhols, the emphasis is also on lower (revisited) stages of development as representing progressive degrees of individual uniqueness, so that again with pure nondual awareness, one reaches awareness of spirit that is already prior to all phenomenal representation as parts.

So this latter emphasis enables a corresponding bottom-up approach to integration ,where one seeks integration of later from the more refined appreciation of earlier stages (that have been continually enhanced through constant revisitation).

So balanced integration (in vertical terms) should be both top-down and bottom-up in nature with an equal emphasis on both transcendence and inclusion (top-down) and immanence and inclusion (bottom-up).

In this way, development is akin to one who travels up and down a road.

When one puts the emphasis on the "up" direction - as in holonic development - one can identify in unambiguous terms both left and right turns. Likewise when puts emphasis on the "down" direction - as in "onholic" development - one can again unambiguously identify left and right turns.

However when one simultaneously tries to combine both "up" and "down" directions, all left and right distinctions are rendered paradoxical (for what is "left" from one reference frame is "right" from the other and what is "right" from one, is "left" from the other).

It is precisely similar with the dynamics of development, where all the carefully made asymmetrical distinctions that appear to be valid in terms of holonic development are rendered paradoxical when balanced with its counterpart onholic direction.

And this is the very means by which vertical integration takes place (i.e. through erosion - at least implicitly - of the dualistic distinctions that characterise the differentiated aspect of each stage)

Thus whereas differentiation in development corresponds to one-way linear type understanding, integration implies two-way circular appreciation.

Therefore my key criticism of the entire thrust of Integral Studies at the time, was this continued failure through intellectual interpretation, to properly distinguish the nature of differentiation in development from that of integration.

Thus when one intellectually attempts to define integration in a linear asymmetrical manner, its very nature is fundamentally misrepresented.

So from my perspective, what was referred to as "Integral Studies" more properly represented "Multidifferentiated Studies". So whereas this approach was indeed successful in identifying the many distinctive stages of development, it could not properly deal with the manner of their integration!

In this context I also found myself completely at odds with the so-called pre/trans fallacy (which in fact in itself represents a substantial fallacy with respect to the true dynamics of development).

The pre/trans fallacy essentially adopts a one-way hierarchical (i.e. holonic) approach to development, whereby a clear distinction is drawn as between pre (prepersonal) and trans (transpersonal) with trans unambiguously considered more advanced and more developed .

From this perspective, the earlier stages are defined as pre, the middle personal and then the higher more advanced stages as trans respectively.

However this linear asymmetrical approach does not allow for the two-way dynamics of higher with lower (and lower with higher) stages that properly characterise development.

Thus from a dynamic perspective, the earlier stages represent the confused interaction of both pre and trans. When unconscious confusion has been significantly removed, the personal (conscious) stages unfold (that are neither pre nor trans). Then when the unconscious is gradually restored in a mature fashion, we have the more advanced stages (that again are both pre and trans in integral terms). However, mature from a proper interactive perspective, implies the balanced two-way integration of both "higher" "lower" stages that are - relatively - pre and trans with respect to each other.

So, pre and trans properly equate with the immanent and transcendent aspects of spirituality respectively.

This dynamic interpretation then enables one to properly explain why both "peak" and "valley" experiences are common in development.

Thus it is certainly possible for someone who is customarily at - say the mythic - to have a temporary peak experience of the subtle level.

This is due to the fact that both confused and mature experiences of pre and trans are necessarily complementary.

Thus one whose customary experience of this relationship is confused, can in one's better moments enjoy a temporary exposure of a mature nature. Likewise someone whose customary experience is of a mature subtle nature, can in one's weaker moments lapse back temporarily to the more confused experience of the mythic level.

Another major weakness that I outlined - again arising from the linear asymmetrical type approach - was the failure to properly relate the dynamics of states and structures with respect to each stage.

For example at the subtle level a dream state - representing a distinctive form of spiritual intuition - typifies the experience. However refined cognitive and affective structures (of a circular paradoxical nature) likewise unfold and successful progress entails that a certain balance be maintained as between the states and structures, which are again dynamically complementary.

In holistic mathematical terms, I found that structures and states are real and imaginary with respect to each other. And these can occur in both an external and internal manner. So the proper incorporation of both states and structures entails the 4-dimensional complex holistic mathematical approach that I outlined in the last blog entry.

Incidentally mathematics and science - as conventionally defined - relate solely to the linear type structures of the middle levels of development . Though these levels necessarily entail the waking state, the interaction as between this state and associated cognitive structures is not considered.

However at all other levels a dynamic relationship characterises the interaction of states and structures, which cannot be ignored.

Another important application of vertical integration relates directly to quantum mechanics.

Quantum mechanics appears highly non-intuitive when viewed through the lens of understanding of the middle levels.

However lower sub-atomic levels of reality bear a complementary relationship with the understanding of this same reality that occurs at the "higher" level.

So for example the "observer problem" with respect to recognition of a particle, simply reflects the fact that both external and internal polarities are now required. And this form of dynamic understanding naturally unfolds at the first of the "higher" levels.

The wave/particle duality of particles then reflects the additional requirement that both real and imaginary aspects characterise all phenomenal interactions. And this form of understanding naturally unfolds at the second of the "higher" levels.

So in effect the very behaviour of matter in quantum mechanical terms is clearly pointing to the inadequacy of the conventional scientific paradigm (which solely represents the middle levels).

This was due to the mistaken asymmetrical emphasis on development as the progressive movement to higher stages of a more collective holistic nature.

Indeed in this context, much use is made of the notion of a holon (i.e. literally a whole/part). A holon is then defined as a whole that is also part of another whole. So for example an atom would represent a holon where the (whole) atom is also part of a (whole) molecule.

However in dynamic interactive terms, we need to stress the two-way movement of wholes and parts. So therefore counterbalancing the holon (whole/part) where each whole is part of another whole is the onhol (part/whole) where each part is also whole in the context of other parts.

When one merely stresses reality as comprised of holons, the emphasis is then unambiguously on higher stages of development as representing increasing degrees of collective wholeness until eventually with pure nondual awareness, one reaches appreciation of the spiritual whole beyond all phenomenal representation.

This leads to an unbalanced - merely top-down - approach to development, where one seeks integration of all earlier stages from the latest to yet unfold.

However when one equally stresses onhols, the emphasis is also on lower (revisited) stages of development as representing progressive degrees of individual uniqueness, so that again with pure nondual awareness, one reaches awareness of spirit that is already prior to all phenomenal representation as parts.

So this latter emphasis enables a corresponding bottom-up approach to integration ,where one seeks integration of later from the more refined appreciation of earlier stages (that have been continually enhanced through constant revisitation).

So balanced integration (in vertical terms) should be both top-down and bottom-up in nature with an equal emphasis on both transcendence and inclusion (top-down) and immanence and inclusion (bottom-up).

In this way, development is akin to one who travels up and down a road.

When one puts the emphasis on the "up" direction - as in holonic development - one can identify in unambiguous terms both left and right turns. Likewise when puts emphasis on the "down" direction - as in "onholic" development - one can again unambiguously identify left and right turns.

However when one simultaneously tries to combine both "up" and "down" directions, all left and right distinctions are rendered paradoxical (for what is "left" from one reference frame is "right" from the other and what is "right" from one, is "left" from the other).

It is precisely similar with the dynamics of development, where all the carefully made asymmetrical distinctions that appear to be valid in terms of holonic development are rendered paradoxical when balanced with its counterpart onholic direction.

And this is the very means by which vertical integration takes place (i.e. through erosion - at least implicitly - of the dualistic distinctions that characterise the differentiated aspect of each stage)

Thus whereas differentiation in development corresponds to one-way linear type understanding, integration implies two-way circular appreciation.

Therefore my key criticism of the entire thrust of Integral Studies at the time, was this continued failure through intellectual interpretation, to properly distinguish the nature of differentiation in development from that of integration.

Thus when one intellectually attempts to define integration in a linear asymmetrical manner, its very nature is fundamentally misrepresented.

So from my perspective, what was referred to as "Integral Studies" more properly represented "Multidifferentiated Studies". So whereas this approach was indeed successful in identifying the many distinctive stages of development, it could not properly deal with the manner of their integration!

In this context I also found myself completely at odds with the so-called pre/trans fallacy (which in fact in itself represents a substantial fallacy with respect to the true dynamics of development).

The pre/trans fallacy essentially adopts a one-way hierarchical (i.e. holonic) approach to development, whereby a clear distinction is drawn as between pre (prepersonal) and trans (transpersonal) with trans unambiguously considered more advanced and more developed .

From this perspective, the earlier stages are defined as pre, the middle personal and then the higher more advanced stages as trans respectively.

However this linear asymmetrical approach does not allow for the two-way dynamics of higher with lower (and lower with higher) stages that properly characterise development.

Thus from a dynamic perspective, the earlier stages represent the confused interaction of both pre and trans. When unconscious confusion has been significantly removed, the personal (conscious) stages unfold (that are neither pre nor trans). Then when the unconscious is gradually restored in a mature fashion, we have the more advanced stages (that again are both pre and trans in integral terms). However, mature from a proper interactive perspective, implies the balanced two-way integration of both "higher" "lower" stages that are - relatively - pre and trans with respect to each other.

So, pre and trans properly equate with the immanent and transcendent aspects of spirituality respectively.

This dynamic interpretation then enables one to properly explain why both "peak" and "valley" experiences are common in development.

Thus it is certainly possible for someone who is customarily at - say the mythic - to have a temporary peak experience of the subtle level.

This is due to the fact that both confused and mature experiences of pre and trans are necessarily complementary.

Thus one whose customary experience of this relationship is confused, can in one's better moments enjoy a temporary exposure of a mature nature. Likewise someone whose customary experience is of a mature subtle nature, can in one's weaker moments lapse back temporarily to the more confused experience of the mythic level.

Another major weakness that I outlined - again arising from the linear asymmetrical type approach - was the failure to properly relate the dynamics of states and structures with respect to each stage.

For example at the subtle level a dream state - representing a distinctive form of spiritual intuition - typifies the experience. However refined cognitive and affective structures (of a circular paradoxical nature) likewise unfold and successful progress entails that a certain balance be maintained as between the states and structures, which are again dynamically complementary.

In holistic mathematical terms, I found that structures and states are real and imaginary with respect to each other. And these can occur in both an external and internal manner. So the proper incorporation of both states and structures entails the 4-dimensional complex holistic mathematical approach that I outlined in the last blog entry.

Incidentally mathematics and science - as conventionally defined - relate solely to the linear type structures of the middle levels of development . Though these levels necessarily entail the waking state, the interaction as between this state and associated cognitive structures is not considered.

However at all other levels a dynamic relationship characterises the interaction of states and structures, which cannot be ignored.

Another important application of vertical integration relates directly to quantum mechanics.

Quantum mechanics appears highly non-intuitive when viewed through the lens of understanding of the middle levels.

However lower sub-atomic levels of reality bear a complementary relationship with the understanding of this same reality that occurs at the "higher" level.

So for example the "observer problem" with respect to recognition of a particle, simply reflects the fact that both external and internal polarities are now required. And this form of dynamic understanding naturally unfolds at the first of the "higher" levels.

The wave/particle duality of particles then reflects the additional requirement that both real and imaginary aspects characterise all phenomenal interactions. And this form of understanding naturally unfolds at the second of the "higher" levels.

So in effect the very behaviour of matter in quantum mechanical terms is clearly pointing to the inadequacy of the conventional scientific paradigm (which solely represents the middle levels).

## Wednesday, February 24, 2016

### Integral Studies (3)

Yesterday, I talked briefly about the 2-dimensional approach to interpretation based on the dynamic (bi-directional) complementarity of external and internal polarities.

This leads to the direct realisation that both the physical and psychological aspects of reality are likewise complementary. Therefore a new psychological stage of reality necessarily entails a corresponding new interpretation of physical - indeed ultimately of mathematical - reality.

So rather than just one accepted form of science (and mathematics) interpreted in a somewhat absolute fashion, properly speaking a whole range (or spectrum) of possible sciences exist (of a dynamic relative nature), which are intimately related to corresponding major stages of development.

It was a strong contention of mine that the unquestioned acceptance of present conventional mathematical and scientific interpretation itself acts as a major barrier against the possible emergence in development of the "higher" contemplative stages (with remarkably few in our culture experiencing them to any substantial degree).

In other words through conventional science - and especially conventional mathematics - we are trained to look at reality in an unquestioned dualistic fashion. And such dualistic thinking then tends to dominate our thinking on all issues!

The 2-dimensional approach is in turn associated with - what I refer to as - horizontal integration.

In other words at each stage, balanced development requires the two-way integration of both external and internal polarities, reflecting again both individual psychological growth and a new relationship with physical (and social) reality.

However to properly deal with the relationship as between wholes and parts, an even more refined 4-dimensional approach - in holistic mathematical terms - is required.

Now the 4 roots of 1 - serving as the indirect linear analytic interpretation of these dimensions - are

+ 1, – 1, + i and – i respectively. So we now have four polar reference frames, two of which are real and two of which are imaginary (with real and imaginary having positive and negative aspects respectively).

Real in a holistic context relates to actual understanding that is directly conscious in nature; however imaginary relates more properly to potential understanding that is directly expressive of the unconscious.

In truth, because understanding entails the interaction of both conscious and unconscious, this entails that we properly inhabit a complex world with all transformation in experience reflecting this interaction of real (actual) and imaginary (potential) aspects.

Again conventional science breeds the considerable illusion that we can deal with a "real" world in a merely conscious manner. It then breeds the further illusion that this world can then be investigated with respect to its - mere - external aspect. So once again this represents the linear (1-dimensional) rational approach.

However we have now moved on to a much more refined 4-dimensional interpretation in holistic mathematical terms, where the world is viewed in complex terms with real (conscious) and imaginary (unconscious) aspects, with both possessing positive (external) and negative (internal) directions.

From a phenomenal perspective, the unconscious is strictly ineffable. However indirectly it expresses itself through projections and symbols that signify a holistic - rather than analytic - meaning.

So there we have it! Whereas in holistic terms the "real" aspect relates to the analytic, the "imaginary" by contrast relates to the holistic aspect of meaning. And both aspects necessarily interact in all experience.

In conventional scientific interpretation - and in discourse generally - wholes and parts are given a merely reduced analytic interpretation (i.e. as "real" phenomena).

However the very transition from whole to part (and part to whole) recognition would not indeed be possible without the intervention of the unconscious (in "imaginary" terms).

Ultimately, the pure recognition of the relationship as between part and whole (and whole and part) is of a highly transparent spiritual nature where each part reflects in a unique manner spirit and where in reverse, the whole is seen to collectively reflect its parts (again in a spiritual manner). In this way spirit becomes fully immanent in each part while also fully transcending each whole.

Probably the single greatest and most damaging form of understanding in our culture is the gross manner in which whole/part reductionism dominates both mathematical and scientific interpretation.

So properly the relationship as between whole and part (and part and whole) in any context is as real to imaginary.

Therefore this relationship cannot be properly understood in a merely reduced analytic (i.e. real) manner but properly requires both analytic (real) and holistic (imaginary) aspects. And as we have seen both of these aspects are defined in both positive and negative directions (which are external and internal with respect to each other).

Such 4-dimensional appreciation was then to form the basis of a much more comprehensive form of integration which I will return to in the next blog entry.

This leads to the direct realisation that both the physical and psychological aspects of reality are likewise complementary. Therefore a new psychological stage of reality necessarily entails a corresponding new interpretation of physical - indeed ultimately of mathematical - reality.

So rather than just one accepted form of science (and mathematics) interpreted in a somewhat absolute fashion, properly speaking a whole range (or spectrum) of possible sciences exist (of a dynamic relative nature), which are intimately related to corresponding major stages of development.

It was a strong contention of mine that the unquestioned acceptance of present conventional mathematical and scientific interpretation itself acts as a major barrier against the possible emergence in development of the "higher" contemplative stages (with remarkably few in our culture experiencing them to any substantial degree).

In other words through conventional science - and especially conventional mathematics - we are trained to look at reality in an unquestioned dualistic fashion. And such dualistic thinking then tends to dominate our thinking on all issues!

The 2-dimensional approach is in turn associated with - what I refer to as - horizontal integration.

In other words at each stage, balanced development requires the two-way integration of both external and internal polarities, reflecting again both individual psychological growth and a new relationship with physical (and social) reality.

However to properly deal with the relationship as between wholes and parts, an even more refined 4-dimensional approach - in holistic mathematical terms - is required.

Now the 4 roots of 1 - serving as the indirect linear analytic interpretation of these dimensions - are

+ 1, – 1, + i and – i respectively. So we now have four polar reference frames, two of which are real and two of which are imaginary (with real and imaginary having positive and negative aspects respectively).

Real in a holistic context relates to actual understanding that is directly conscious in nature; however imaginary relates more properly to potential understanding that is directly expressive of the unconscious.

In truth, because understanding entails the interaction of both conscious and unconscious, this entails that we properly inhabit a complex world with all transformation in experience reflecting this interaction of real (actual) and imaginary (potential) aspects.

Again conventional science breeds the considerable illusion that we can deal with a "real" world in a merely conscious manner. It then breeds the further illusion that this world can then be investigated with respect to its - mere - external aspect. So once again this represents the linear (1-dimensional) rational approach.

However we have now moved on to a much more refined 4-dimensional interpretation in holistic mathematical terms, where the world is viewed in complex terms with real (conscious) and imaginary (unconscious) aspects, with both possessing positive (external) and negative (internal) directions.

From a phenomenal perspective, the unconscious is strictly ineffable. However indirectly it expresses itself through projections and symbols that signify a holistic - rather than analytic - meaning.

So there we have it! Whereas in holistic terms the "real" aspect relates to the analytic, the "imaginary" by contrast relates to the holistic aspect of meaning. And both aspects necessarily interact in all experience.

In conventional scientific interpretation - and in discourse generally - wholes and parts are given a merely reduced analytic interpretation (i.e. as "real" phenomena).

However the very transition from whole to part (and part to whole) recognition would not indeed be possible without the intervention of the unconscious (in "imaginary" terms).

Ultimately, the pure recognition of the relationship as between part and whole (and whole and part) is of a highly transparent spiritual nature where each part reflects in a unique manner spirit and where in reverse, the whole is seen to collectively reflect its parts (again in a spiritual manner). In this way spirit becomes fully immanent in each part while also fully transcending each whole.

Probably the single greatest and most damaging form of understanding in our culture is the gross manner in which whole/part reductionism dominates both mathematical and scientific interpretation.

So properly the relationship as between whole and part (and part and whole) in any context is as real to imaginary.

Therefore this relationship cannot be properly understood in a merely reduced analytic (i.e. real) manner but properly requires both analytic (real) and holistic (imaginary) aspects. And as we have seen both of these aspects are defined in both positive and negative directions (which are external and internal with respect to each other).

Such 4-dimensional appreciation was then to form the basis of a much more comprehensive form of integration which I will return to in the next blog entry.

### Integral Studies (2)

My consistent criticism of "Integral Studies" throughout my tenure on its various forums was that interpretation invariably consisted of the predominant use of the linear asymmetrical approach. This then led in many ways to a reduction of the holistic notion of integration to that of differentiation.

Not surprisingly, in turn it led to numerous inconsistencies from an overall (i.e. integral) perspective.

The importance of number can perhaps be grasped from the fact that in this context, "1" holistically encapsulates the general method of interpretation that characterises our conventional approach to science and indeed to a considerable extent general intellectual discussion.

In this holistic context "1" precisely relates to the manner in which the polar opposites, which fundamentally condition all phenomenal experience, are related.

Two of these polar parings are especially important. So firstly external always implies internal (and internal implies external). Secondly part always implies whole (and whole implies part).

Now in 1-dimensional terms a clear separation is made as between these polar opposites. So typically - as in the scientific perspective - the external world (as objective) is abstracted from the internal knower (as subjective). In other words the subjective aspect of experience is reduced in an objective manner.

Likewise, the parts are abstracted from the whole (with the whole effectively treated in quantitative fashion as merely the sum of its parts).

Therefore, in every relevant context, with respect to the polar opposites in experience, reality is interpreted in terms of just one isolated reference frame (that is treated in a somewhat absolute fashion).

What is truly remarkable - when properly grasped - that associated with every other number (≠ 1) is a unique manner for overall interpretation of reality.

Not surprisingly, in turn it led to numerous inconsistencies from an overall (i.e. integral) perspective.

The importance of number can perhaps be grasped from the fact that in this context, "1" holistically encapsulates the general method of interpretation that characterises our conventional approach to science and indeed to a considerable extent general intellectual discussion.

In this holistic context "1" precisely relates to the manner in which the polar opposites, which fundamentally condition all phenomenal experience, are related.

Two of these polar parings are especially important. So firstly external always implies internal (and internal implies external). Secondly part always implies whole (and whole implies part).

Now in 1-dimensional terms a clear separation is made as between these polar opposites. So typically - as in the scientific perspective - the external world (as objective) is abstracted from the internal knower (as subjective). In other words the subjective aspect of experience is reduced in an objective manner.

Likewise, the parts are abstracted from the whole (with the whole effectively treated in quantitative fashion as merely the sum of its parts).

Therefore, in every relevant context, with respect to the polar opposites in experience, reality is interpreted in terms of just one isolated reference frame (that is treated in a somewhat absolute fashion).

What is truly remarkable - when properly grasped - that associated with every other number (≠ 1) is a unique manner for overall interpretation of reality.

And whereas (default) 1-dimensional interpretation is absolute, all other interpretations are of a dynamic interactive nature.

So essentially in this context, the holistic notion of number relates to a unique manner in which the fundamental polarities of experience (external/internal and whole/part) are configured.

Of special importance in an integral context are the interpretations associated with "2" and "4" respectively.

In analytic terms, this notion of "twoness" is indirectly represented (in linear fashion) through the 2 roots of 1 which are + 1 and – 1 respectively. Now in analytic terms these roots (representing opposite poles) are clearly separated. However in a holistic manner they are viewed as dynamically complementary (and ultimately identical) with each other.

Thus, in actual experience, we keep switching as between positive and negative poles. So one moment we are aware of the external world (as positive) in relation to the self as negative. Then at the next moment we are aware of the internal self (as now positive) in relation to the world (as negative).

Then when this interaction becomes sufficiently smooth and dynamic, we increasingly realise in nondual fashion the true interdependence of both positive (+) and negative (–) poles.

And it is this qualitative notion of interdependence, which can only be rationally expressed in a (circular) paradoxical manner, that constitutes the basis of all true integration in development (physical and psychological).

However I was strongly aware of a series of imbalances that characterised the typical approach to the overall spectrum of development, which ultimately related to the unquestioned dominance of the linear (i.e. 1-dimensional) method of interpretation.

For example, the stages of human development - even when "higher" spiritual contemplative states were duly incorporated - invariably focussed on the internal (psychological) pole.

However my consistent argument was that associated with every stage of development in psychological terms was a complementary stage of physical reality.

One clear implication of this is that what is conventionally termed "science" in fact represents the interpretation that is associated with just one major stage (i.e. band) of development.

Expressed more accurately, such science represents the linear (1-dimensional) approach that is properly suited for the quantitative interpretation of the various "parts" of the system.

However beyond this are more refined stages (where intuition and reason interpenetrate in an increasingly dynamic manner).

So overall I was led to define 3 major types of science that were intimately related to corresponding bands of development.

So firstly we have analytic science (of a quantitative nature). Then we have holistic (or integral) that is directly of a qualitative nature. And finally we have - what I refer to as - radial science, which combines both quantitative and qualitative aspects in both a highly creative and productive manner.

While on these forums, I mainly concerned myself with the clarification of the nature of holistic science.

This is based on the realisation of a two-way complementary nature with respect to the fundamental poles (external and internal) that dynamically condition all phenomenal reality. Therefore from one perspective, a matching psychological phenomenon exists for every major physical interpretation Equally from the opposite perspective, a matching physical phenomenon exists for every psychological interpretation.

Initially I was led on this holistic scientific path when I realised that all the key notions with respect to Einstein's Special Theory of Relativity had compelling psychological equivalents. Thus the very manner of achieving a more integral understanding of this reality - which was now in truth seen as psycho physical - was in the marriage of both aspects.

Later from the opposite perspective, I was led to a much deeper appreciation of the nature of black holes through the realisation of marked similarities with the mystical phenomenon of "the dark night of the soul".

So the goal of holistic science is to assist one to move smoothly to a truly nondual contemplative appreciation of reality through the marriage of its complementary physical and psychological aspects.

## Tuesday, February 23, 2016

### Integral Studies (1)

During my time on the "Integral Studies" forums, I was employing a highly ambitious strategy, which however may not have been fully obvious to the general participant.

In particular I was attempting to promote an entirely new form of Mathematics - which I termed "Holistic Mathematics" - as the proper scientific basis for the study of dynamic interactive relationships of a qualitative nature.

So just as Conventional Mathematics is now the indispensable tool for the study of quantitative relationships within the analytic sciences, equally I saw Holistic Mathematics as the corresponding indispensable tool within the social sciences and especially with respect to clarifying the transformational stages relating to human development.

However the great problem that I faced was the initial complete lack of recognition in the very possibility of this alternative type of Mathematics.

So it was my hope that in the detailed discussion of various key topics in "Integral Studies" that I could better illustrate the modus operandi of this new approach.

I have mentioned before the importance of the binary system, where the two digits 1 and 0 can be potentially used as a means of encoding all information processes. Indeed the widespread use of this digital system with respect to computerisation and IT has dramatically revolutionised the nature of our world in the past few decades.

Now this digital system is based on the clear analytic separation of the two digits 1 and 0.

However I had long recognised a complementary binary system - again based on the two digits 1 and 0 - that also be potentially used as a means of encoding all transformation processes. And this system would be especially useful for clarifying the transformation process that we recognise as human development.

In this holistic binary system the two digits 1 and 0 are used in a dynamic complementary fashion (which ultimately are identical in an ineffable manner).

Now the straight line is 1-dimensional so 1 in this holistic sense relates to the linear rational form of understanding that so typifies the conventional scientific approach.

By contrast 0 - which closely mirrors the symbol of the circle - relates to a corresponding circular intuitive form of appreciation that typifies the contemplative spiritual approach to reality.

Strictly speaking of course pure intuitive understanding is nondual and not directly amenable in phenomenal terms. However indirectly in can be represented in a "circular" paradoxical fashion (with respect to linear understanding).

In my holistic approach the notions of linear (1) and circular (0) were directly linked to the corresponding developmental notions of differentiation and integration respectively.

In this way all human - and indeed natural - development could be validly seen as the expression of differentiation and integration entailing both linear (1) and circular (0) interpretation respectively.

So in my own dynamic model of development, I was anxious to represent each stage as necessarily representing a unique configuration with respect to both differentiated and integrated processes respectively (which could be precisely encoded in a holistic mathematical fashion).

Central to this approach was the importance of the holistic interpretation of number.

As we know, number provides the most efficient means with respect to the quantitative ordering of data. Indeed without the quantitative notion of number, it would be impossible for science to proceed!

However equally - though not at all well recognised - number likewise provides the most efficient means with respect to the qualitative ordering of data (such as the stages of human development). So in future I have no doubt that an entirely new holistic form of science will be recognised based on this complementary interpretation of number!

Before engaging on these forums, I had already completed "The Number Paradigms" placing it on a web-site.

This showed in outline form how all the major number types could be holistically linked to the various main stages of development. However without further clarification, what was written here was unlikely to make much impression.

Therefore I very much welcomed the opportunity to engage in detailed fashion with the most heated topics being discussed on the various integral forums as a means of demonstrating the potential importance of these new holistic mathematical insights.

In particular I was attempting to promote an entirely new form of Mathematics - which I termed "Holistic Mathematics" - as the proper scientific basis for the study of dynamic interactive relationships of a qualitative nature.

So just as Conventional Mathematics is now the indispensable tool for the study of quantitative relationships within the analytic sciences, equally I saw Holistic Mathematics as the corresponding indispensable tool within the social sciences and especially with respect to clarifying the transformational stages relating to human development.

However the great problem that I faced was the initial complete lack of recognition in the very possibility of this alternative type of Mathematics.

So it was my hope that in the detailed discussion of various key topics in "Integral Studies" that I could better illustrate the modus operandi of this new approach.

I have mentioned before the importance of the binary system, where the two digits 1 and 0 can be potentially used as a means of encoding all information processes. Indeed the widespread use of this digital system with respect to computerisation and IT has dramatically revolutionised the nature of our world in the past few decades.

Now this digital system is based on the clear analytic separation of the two digits 1 and 0.

However I had long recognised a complementary binary system - again based on the two digits 1 and 0 - that also be potentially used as a means of encoding all transformation processes. And this system would be especially useful for clarifying the transformation process that we recognise as human development.

In this holistic binary system the two digits 1 and 0 are used in a dynamic complementary fashion (which ultimately are identical in an ineffable manner).

Now the straight line is 1-dimensional so 1 in this holistic sense relates to the linear rational form of understanding that so typifies the conventional scientific approach.

By contrast 0 - which closely mirrors the symbol of the circle - relates to a corresponding circular intuitive form of appreciation that typifies the contemplative spiritual approach to reality.

Strictly speaking of course pure intuitive understanding is nondual and not directly amenable in phenomenal terms. However indirectly in can be represented in a "circular" paradoxical fashion (with respect to linear understanding).

In my holistic approach the notions of linear (1) and circular (0) were directly linked to the corresponding developmental notions of differentiation and integration respectively.

In this way all human - and indeed natural - development could be validly seen as the expression of differentiation and integration entailing both linear (1) and circular (0) interpretation respectively.

So in my own dynamic model of development, I was anxious to represent each stage as necessarily representing a unique configuration with respect to both differentiated and integrated processes respectively (which could be precisely encoded in a holistic mathematical fashion).

Central to this approach was the importance of the holistic interpretation of number.

As we know, number provides the most efficient means with respect to the quantitative ordering of data. Indeed without the quantitative notion of number, it would be impossible for science to proceed!

However equally - though not at all well recognised - number likewise provides the most efficient means with respect to the qualitative ordering of data (such as the stages of human development). So in future I have no doubt that an entirely new holistic form of science will be recognised based on this complementary interpretation of number!

Before engaging on these forums, I had already completed "The Number Paradigms" placing it on a web-site.

This showed in outline form how all the major number types could be holistically linked to the various main stages of development. However without further clarification, what was written here was unlikely to make much impression.

Therefore I very much welcomed the opportunity to engage in detailed fashion with the most heated topics being discussed on the various integral forums as a means of demonstrating the potential importance of these new holistic mathematical insights.

## Thursday, February 18, 2016

### Forum Participation

My first foray on the Internet was to place the two books that I had written "Transforming Voyage" and "The Number Paradigms" on a hastily constructed personal site. To the best of my recollection this took place in 1995.

For some time there was no reaction. Then one day I received a very thoughtful response from a UN official based in Australia who had discovered the site. This in turn led to a very fruitful correspondence - mainly on mathematical relationships of mutual interest - that lasted several years.

Around this time, there was a significant growth in web forums of various kinds where people with the same interests could post their contributions.

In this regard various sites devoted to "Integral Studies" caught my attention as they related very much to my own interests. However through my development of "Holistic Mathematics", I felt that I could offer a distinctive approach.

I hesitated for some time fearing that my ideas were too novel to gain traction. Eventually however, I decided to jump in head first, as it were with a very lengthy initial contribution, that sought to outline my overall position.

For over a week there was complete silence. And then, quite unexpectedly I received a highly intelligent detailed response from a woman (again living in Australia), which addressed point by point what I had written while posing further questions for answer.

I found it immensely gratifying that a stranger would give such consideration to my ideas and became immediately "hooked" as it were on this new form of communication.

So for the next 4 years or so - up to about 2000 - I became a regular contributor to a number of these forums.

In fact I became strongly conscious of the fact that I had become intensely involved in a new "virtual" community.

It seemed of deep symbolic significance that the first two major responses came from Australia. Now, geographically Australia is about as far as one get from Ireland (where I live). However that was the very point! This new virtual community of like-minded individuals had no geographical boundaries. So in this regard one could intimately share one's deepest intellectual thoughts far more readily with people in far distant lands than in one's own locality And through the magic of the Internet, one could immediately hope to communicate ideas to those of similar interests.

In may ways I look back at this time with great fondness. After a lengthy period of total intellectual isolation, I now found myself regularly expressing ideas to a highly intelligent and creative group of individuals who were ready to show appreciation for my efforts.

So ideas that had been locked up in a deeply compressed fashion inside for so long were now free to find expression through this new expansive medium, as contributions on so many topics seemed to effortlessly flow from my mind through the various lengthy posts that I was now submitting on a near daily basis to these forums.

Of course it was not all sweetness and light. I often experienced difficulty in "converting" participants to what I considered were my most important ideas. Also though I soon discovered that I had an "admiring" fan base among some members of the forum, equally - as perhaps was inevitable - there was growing opposition and resistance from other quarters.

Indeed ironically just as the first two favourable communications had come from Australia, equally my most vocal critic likewise happened to be an "outspoken" Aussie.

However in a strange way, I didn't really mind criticism. In fact I always welcomed the opportunity to answer it through detailed replies. Initially I felt that by showing a willingness to directly face criticism, that I could win over the "detractors"and thereby further promote my ideas. However I soon discovered that this was a vain expectation. The way I would see it now is that we all have different personalities and background experience that heavily influence the manner we approach issues. So it is often simply the case that one's ideas will resonate readily with one intelligent contributor while equally being found off-putting by an another equally intelligent contributor. So in the market of ideas, one is always likely to win some and lose some!

When I look back, I am amazed at how much writing I got through during these years.

During the day I was working in the local "real" world, lecturing to business students in the Dublin Institute of Technology. Then in the evenings - and small hours of the morning - I would be intensely engaged in this global "virtual" world, elaborating on those notions about which I felt most passionate.

And there was no intersection between the two worlds, for I never spoke about my integral interests at work (regarding which no one displayed the slightest interest).

And soon it was not just lengthy postings to the Forums that engaged my attention but a growing e-mail correspondence that both directly and indirectly flowed from the Forum contributions. And one of these in particular with one highly impressive female contributor then led to a very special shared relationship in both emotional and spiritual terms.

As I remember it now, there was a heady excitement regarding those days with my fellow participants on the Forums. I suppose we believed in our naivete that we were somehow changing the world for the better through our dedication to the "integral approach".

However as I was to discover once again soon afterwards, life is never so simple!

For some time there was no reaction. Then one day I received a very thoughtful response from a UN official based in Australia who had discovered the site. This in turn led to a very fruitful correspondence - mainly on mathematical relationships of mutual interest - that lasted several years.

Around this time, there was a significant growth in web forums of various kinds where people with the same interests could post their contributions.

In this regard various sites devoted to "Integral Studies" caught my attention as they related very much to my own interests. However through my development of "Holistic Mathematics", I felt that I could offer a distinctive approach.

I hesitated for some time fearing that my ideas were too novel to gain traction. Eventually however, I decided to jump in head first, as it were with a very lengthy initial contribution, that sought to outline my overall position.

For over a week there was complete silence. And then, quite unexpectedly I received a highly intelligent detailed response from a woman (again living in Australia), which addressed point by point what I had written while posing further questions for answer.

I found it immensely gratifying that a stranger would give such consideration to my ideas and became immediately "hooked" as it were on this new form of communication.

So for the next 4 years or so - up to about 2000 - I became a regular contributor to a number of these forums.

In fact I became strongly conscious of the fact that I had become intensely involved in a new "virtual" community.

It seemed of deep symbolic significance that the first two major responses came from Australia. Now, geographically Australia is about as far as one get from Ireland (where I live). However that was the very point! This new virtual community of like-minded individuals had no geographical boundaries. So in this regard one could intimately share one's deepest intellectual thoughts far more readily with people in far distant lands than in one's own locality And through the magic of the Internet, one could immediately hope to communicate ideas to those of similar interests.

In may ways I look back at this time with great fondness. After a lengthy period of total intellectual isolation, I now found myself regularly expressing ideas to a highly intelligent and creative group of individuals who were ready to show appreciation for my efforts.

So ideas that had been locked up in a deeply compressed fashion inside for so long were now free to find expression through this new expansive medium, as contributions on so many topics seemed to effortlessly flow from my mind through the various lengthy posts that I was now submitting on a near daily basis to these forums.

Of course it was not all sweetness and light. I often experienced difficulty in "converting" participants to what I considered were my most important ideas. Also though I soon discovered that I had an "admiring" fan base among some members of the forum, equally - as perhaps was inevitable - there was growing opposition and resistance from other quarters.

Indeed ironically just as the first two favourable communications had come from Australia, equally my most vocal critic likewise happened to be an "outspoken" Aussie.

However in a strange way, I didn't really mind criticism. In fact I always welcomed the opportunity to answer it through detailed replies. Initially I felt that by showing a willingness to directly face criticism, that I could win over the "detractors"and thereby further promote my ideas. However I soon discovered that this was a vain expectation. The way I would see it now is that we all have different personalities and background experience that heavily influence the manner we approach issues. So it is often simply the case that one's ideas will resonate readily with one intelligent contributor while equally being found off-putting by an another equally intelligent contributor. So in the market of ideas, one is always likely to win some and lose some!

When I look back, I am amazed at how much writing I got through during these years.

During the day I was working in the local "real" world, lecturing to business students in the Dublin Institute of Technology. Then in the evenings - and small hours of the morning - I would be intensely engaged in this global "virtual" world, elaborating on those notions about which I felt most passionate.

And there was no intersection between the two worlds, for I never spoke about my integral interests at work (regarding which no one displayed the slightest interest).

And soon it was not just lengthy postings to the Forums that engaged my attention but a growing e-mail correspondence that both directly and indirectly flowed from the Forum contributions. And one of these in particular with one highly impressive female contributor then led to a very special shared relationship in both emotional and spiritual terms.

As I remember it now, there was a heady excitement regarding those days with my fellow participants on the Forums. I suppose we believed in our naivete that we were somehow changing the world for the better through our dedication to the "integral approach".

However as I was to discover once again soon afterwards, life is never so simple!

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