We now have reached the important section on "The Four Quadrants."

Ken refers to the fact that premodern religion and modern science have a defining hierarchy both of which are composed of enveloping nests of increasing embrace (development that is envelopment). And yet these hierarchies do not agree with each other.

In researching the problem, he did an extensive data search of several hundred hierarchies and noticed that without exception they fell into one of four major types.

This is what Ken refers to as the four quadrants (of which the classical hierarchy of traditional religion and the standard hierarchy of modern science are simply two).

In Ken's account the Upper-Right quadrant is the standard scientific account of the individual components of the universe: atoms, molecules, single cells and organisms of ever increasing complexity.

He views the Lower-Right quadrant again in scientific fashion, this time representing communities of holons. So the lower quadrant points to the collective forms of holons, galaxies, planets, Gaia system, ecological systems and the various forms of collective human organisations.

Ken defines is Upper-Left quadrant in terms of interior awareness moving from simplest prehension through sensations, perceptions, emotions, symbols, concepts culminating in vision-logic.

The Lower-Right quadrant represents the collective forms of this interior awareness as they unfold generally in the cultural community.e.g. physical-pleromatic, uoboric, typhonic, archaic, mythic rational and centauric.

Now what I find fascinating here is that Ken Wilber, using an entirely different approach from that of Holistic Mathematics, arrives at a schema that shows important similarities.

Thus Ken in effect is organising his quadrants in terms of the horizontal and vertical polarities of experience. Again horizontal polarities are represented by exterior-interior distinctions; the vertical polarities are represented by individual-collective distinctions.

However the limitation of his approach is that he essentially views these polarities in a very static manner.

Now the great value of the holistic mathematical method is that its formulations give rise to two complementary modes of interpretation.

Thus from one perspective one can view these polarities (horizontal and vertical) as separate. This is the approach that is suitable for differentiating the quadrants.

However from the equally valid alternative perspective we can view these polarities in dynamic terms as complementary. This is the approach that is directly suitable for integrating the quadrants. However there is no evidence at all of this alternative approach in Ken Wilber's thinking.

The holistic mathematical method is also more comprehensive in that it leads to a third kind of polarity (that is missing in Ken's account). In other words we need to include diagonal polarities (which represent the most fundamental distinction of all holons i.e. form and emptiness.

Furthermore a further feature of the holistic mathematical approach is that it contains within itself the very means of linking the two logical interpretations of the quadrants.

Thus a full treatment of the quadrants - which would then truly approximate to an underlying "Theory of Everything" requires that we introduce diagonal (as well as horizontal and vertical polarities).

It then requires that we interpret these polarities, which apply to all holons (at the three levels) in terms of two logical systems.

In the first (linear) systems opposites are viewed as clearly separate. This approach is suitable for a differentiated approach.

In the second (circular) system, opposites are viewed as complementary (and ultimately identical). This is the approach suitable for integration.

In the third comprehensive system opposites are viewed simultaneously in both differentiated and integrated fashion. This involves in fact the full working of the qualitative binary system which is the basis for translating all transformation processes.

So apart from the fact that Ken Wilber does not include (fundamental) diagonal polarities in his quadrant approach, the greatest limitation, is that he treats these quadrants in a merely static (absolute) fashion which invariably leads to a whole series of half-truths.

Now the method that is derived directly from holistic mathematical principles includes Ken Wilber's as a special limited case. However it goes considerably beyond this and is able to show precisely the relationship as between (partial) differentiated and (holistic) integrated understanding of reality.

Once again this integrated approach (and the relationship between it and the differentiated version) is entirely missing from Ken Wilber's analyis.

This is why I consistently maintain that Ken Wilber's work is not truly about integration (but rather differentiation of experience).

I have been illustrating already in my posts the precise nature of these half-truths.

However because the topic is so important let me return once again to it in a slightly different manner.

In speaking about the hierarchy of his Upper-Right quadrant on P. 67, Ken Wilber states the following:

"The hierarchy shows an asymmetrical increase in holistic capacity. "Asymmetrical" means "not equivalent": atoms contain neutrons, but neutrons do not contain atoms; molecules contain atoms but not vice versa. That "not vice versa" establishes an irreversible hierarchy of increasing wholeness, increasing holism, increasing unity and integration. This is why all such hierarchies are indeed higher-archies, containing successively higher or deeper wholes."

The essence of the differentiated perspective is that it is indeed based on an asymmetrical worldview. It is through asymmetry that we are able to differentiate phenomena in experience.

However the essence of the integrated perspective is one of symmetry (and Ken Wilber does not present this viewpoint).

Indeed the most important aspect of all is to provide the bridge as between the asymmetrical (differentiated) and symmetrical (integrated) worldviews which of course Ken does not provide. This requires a more subtle interpretation of hierarchical development.

When Ken for example says that atoms contain neurons, but neurons do not contain atoms, he is using the (conventional) common sense view of the relationship between wholes and parts (which is highly reductionist). In other words he is defining wholes in merely quantitative terms (as the sum of parts). In this sense a neutron is part of the total sum of parts (that comprises the atom). But once again this is a merely quantitative (reduced) explanation of the relationship between wholes and parts.

So the "irreversible hierarchy of increasing wholeness" that Ken is referring to is one which is based on a merely reduced quantitative notion of integration (which basically reduces the whole to the sum of its differentiated parts).

So in fact his notion of hierarchies is again very one-sided and unbalanced. Though parts and wholes are equally important aspects of experience Ken defines development solely in terms of a reduced notion of increasing wholeness (which is defined in merely quantitative terms). This in fact represents the transcendent view of development (where parts are contained in the whole).

However it would be equally valid to define development in terms of increasing "partness" (i.e. where one grows in realisation of the unique qualitative identity of each part). This indeed represents the immanent view of development (where the whole is qualitatively contained in each individual part).

So once again when Blake saw "a world in a grain of sand" he was describing the immanent view of development. Here the whole of creation is understood to be (qualitatively) contained in a single part.

However this complementary view of development is missing from Ken's approach.

The deeper problem with Ken's view of "scientific" hierarchy is that it perpetuates once again "the myth of the given". In other words he speaks of neutrons, atoms, molecules, cells as if they somehow have an existence (independent of mind). However this is entirely fallacious.

The very experience of a molecule (for example) is dynamic and bi-directional where interior and exterior (and exterior and interior) ceaselessly interact. Once again when we attempt to portray this dynamic experience in dualistic fashion two opposite interpretations are equally valid.

Thus we can attempt to portray development in holarchical evolutionary terms as a process of transcendence (where the parts are included in the whole).

However we can equally attempt to portary development in "partarchical" involutionary terms as a process of immanence (where the whole is included in each unique part).

And these interpretations are purely relative. We could equally apply immanence to the holarchical and transcendence to the "partarchical" interpretation. So in bi-directional terms any hierarchical model of development has a complementary mirror interpretation.

When we properly grasp this point we realise that fixing of quadrants is merely relative.

Thus if we locate our starting hierarchical model of scientific development, in the Upper Right-Hand quadrant, then the mirror interpretation will fall in the Left (and vice-versa).

Now this bi-directional understanding of quadrants forms the very bridge as between the differentiated (asymmetrical) and integrated (symmetrical) approaches.

Whereas it is true that any one-directional hierarchical model will be asymmetric, when we balance it bi-directionally with its mirror complement we get symmetry (in terms of these opposite interpretations).

Note that each of the holarchical models (the original and its mirror) are asymmetric in nature. However the relationship between both hierarchical models is symmetric and this is the starting basis for an integrated (as opposed to a merely differentiated understanding).

Thus if we try and view perception (as Ken does) as providing our scientific hierarchical model, then the (interior) interpretation provides the mirror model. As with an image reflected in a mirror movement in the mirror model takes place in the opposite direction.

However the image and its reflection (in the mirror) are symmetrical.

So fixing of quadrants is a purely relative affair. If the original is placed in the Right-Hand then its mirror goes in the Left-Hand quadrant. (However we could equally designate the mirror as the original with the previous original as the mirror).

Ken then places the outside of the collective in the Lower-Right quadrant. This represents - according to Ken - the scientific account of the unfolding of communities of holons.

However just as in dynamic terms we cannot have interior (without exterior) or exterior (without interior), likewise we cannot have individual without collective (or collective without individual) holons.

This in fact points to he all-important relationship as between wholes and parts (and parts and wholes). Again - because of the lack of a true dynamic approach Ken's treatment is one sided (i.e. one directional).

For example he defines a holon as a whole-part and represents development as an increase in holism. However equally a holon is a part-whole and development can be equally validly represented as an increase in partism.

So Ken Wilber portrays development in merely transcendent evolutionary terms whereas it can be equally represented in (relatively) involutionary immanent terms.

Now I would consider that the dynamic relationship as between whole and part (and part and whole) is the most important of all relationships. However because of the quantitative bias of Ken's treatment he fails to properly convey its true nature and effectively defines wholes in quantitative terms (as the sum of parts).

Perhaps the most important insight of all that I have derived from the holistic mathematics is the realisation that the relationship as between wholes and parts cannot be translated solely in scientific real "terms". We customarily think of a "real" world made up of "real" objects in "real" dimensions of space and time. However this results from the one-sided quantitative bias of modern science (based on solely conscious formulations).

If we are to properly translate the dynamic nature of reality (and the true relationship as between wholes and parts), then we must move over to mathematically "complex" notions (which combine both "real" and "imaginary" aspects).

Thus if in any dynamic context the part is represented as "real" then the corresponding whole - in relative terms is "imaginary". Equally of course if the whole is taken as "real", then the corresponding part is now "imaginary".

The implications of this insight are truly enormous. For example it means that if any perception is taken as "real" then its corresponding concept - in relative terms, is "imaginary". Thus if the perception of a molecule is "real" then the corresponding concept of molecule is "imaginary". So the implications of this insight (regarding the true mathematical relationship as between whole and part, and part and whole) redefines the way we look at reality in the most intimate fashion.

So in dynamic terms we live in a "complex" rather than "real" world.

In holistic mathematical terms horizontal (exterior-interior) polarities are - relatively - positive and negative with respect to each other.

In holistic mathematical terms vertical (individual-collective) polarities are - relatively - real and imaginary with respect to each other.

Thus a proper dynamic treatment of the four quadrants should be literally four-dimensional (with reduced translations that real an imaginary with positive and negative directions).

However Ken Wilber's approach is merely static and one-dimensional (where he attempts to treat directional movements in all quadrants in positive real terms).

Ken then tries to identify interior awareness unambiguously with the Left-Hand quadrants.

However again in dynamic terms this is not really tenable. Just as all exterior events necessarily have interior interpretations, all interior interpretations necessarily have exterior perceptions.

Once again Ken attempts to distinguish Right-Hand and Left-Hand by saying that Right-Hand events have simple location (which Left-Hand events do not). However again this is very one-sided and not strictly tenable.

He says on P. 73

"that you can point to a rock a planet a town a family an ecosystem - they all have simple location; but you cannot point to love, envy, pride, joy or compassion."

However this is very unbalanced. Notice here that Ken is contrasting particular notions (from the Right-Hand) with general notions from the Left-Hand.

However though one may well point to a particular rock (against the background of an assumed fixed conceptual interpretation), one cannot in fact point to the general concept of rock.

Likewise though one cannot point to the general concept of love, one can however point directly to a particular object of love (e.g. a family member).

So once we reverse Ken's selective choice of examples (by applying the general notion to Right-Hand and particular to Left-Hand quadrants) we now find that the Right-Hand does not have simple location (whereas the Left-Hand does).

There is another key difficulty with Ken's treatment of Left-Hand quadrants.

He never clearly distinguishes dynamic interactive notions from static non-interactive notions of awareness.

Thus the existential awareness of values such as love, justice, honour etc. has a dynamic interior component (arising from the interaction of both poles).

However the understanding of (conventional) mathematics - which would also belong in Ken's approach to the (interior) Left-Hand quadrants - does not carry a dynamic interactive interpretation (and is therefore lacking in existential meaning).

Also Ken does not distinguish clearly cognitive notions of interior awareness (such as ethical standards) from affective notions (e.g. emotional feelings).

Finally he does not really distinguish intentionality (as the basis of all authentic moral decisions) from merely cognitive and affective notions.

However I would strongly suggest that these distinctions cannot be consistently made in the absence of a true dynamic approach.

I would like to mention one other point. Ken has a habit of trying to justify his own positions by citing "expert" opinion.

Thus he cites the opinions of many prominent researchers who have located hierarchies in the four quadrants (similar to Ken's).

However inevitably these researchers in employing the same (quantitative) scientific paradigm, have been making the very same reductionist assumptions (as Ken).

My point is a very simple one. If we want to truly integrate experience, we cannot do so solely within the confines of the rational paradigm. As I have demonstrated any hierarchy that is drawn up using conventional science) can be shown to be very one-sided (with an equally valid mirror explanation that is overlooked).

So if Ken Wilber is really serious about defending the validity of his approach, I think it is time to answer these fundamental criticisms (which so far he has failed to address).

To be continued....