Perhaps the most important single issue for the interpretation of reality is the proper clarification of the relationship as between whole and part (and part and whole).
There is immense confusion in science due to the reduced and unbalanced nature of existing translations.
The purpose of these two articles is to clarify the dynamic nature of the relationship and to suggest how Holistic Mathematics can be used to offer a coherent interpretation.
The implication of this new translation is truly fundamental and requires a decisive transformation in the scientific understanding of reality.
It also highlights the proper basis for a synthetic - as opposed to a merely analytic - approach to development. This in turn leads to a redefinition of the very meaning of Integral Studies.
Two Kinds of Perception
To understand this dynamic nature of holons we must distinguish clearly as between two types of perception which are based on the affective and cognitive aspects of understanding respectively. 1
In actual experience both of these are necessary for the recognition of phenomena to take place and lead to two opposite interpretations of the relationship as between whole and part (and part and whole).
However conventional scientific translation - which is based directly on the cognitive aspect – invariably, reduces this relationship, interpreting it misleadingly in one-directional terms. 2
In the experience of a phenomenal object such as a rose, two modes of perception are involved.
Affective understanding leads - in direct terms - to the artistic (aesthetic) perception of the rose.
Here we become aware of the unique (personal) nature of the object spontaneously presented through the senses. The whole is qualitatively contained in each part. In other words, the collective quality of "roseness" is fully contained in each individual rose (that enters perception).
When this affective perception is very refined it leads to an appreciation of the spiritual immanent nature of all objects (where the whole of creation is contained in each part). 3
Cognitive understanding by contrast leads - in direct terms - to the scientific (rational) perception of the rose. We now become aware of the common (impersonal) nature of the object through a process of mental control where it is defined in relation to its collective concept.
Each part is now quantitatively contained in the whole i.e. each individual rose is contained in the collective set of roses.
When this cognitive perception is very refined it leads to a corresponding appreciation of the spiritual transcendent nature of objects (where all parts are contained in the universal whole).
Thus in this context we have two complementary interpretations of the relationship between whole and part (and part and whole). 4However in conventional scientific translation, interpretation is reduced in terms of the cognitive aspect leading to fundamental imbalance.
Affective - the whole is (qualitatively) contained in each part. Cognitive - each part is (quantitatively) contained in the whole.
Thus in dynamic terms, every holon has both quantitative and qualitative aspects which ceaselessly interact. This vertical relationship as between "higher" whole and "lower" part is therefore always bi-directional with a purely relative meaning.
Dynamic Nature of Holons
Once again, every holon has both quantitative and qualitative aspects which dynamically interact in simultaneous bi-directional fashion. A holon (whole/part) is thus equally an on-hol (part/whole).
It is most important to appreciate that from an integral perspective, movement with respect to holons always takes place therefore simultaneously in two opposite directions.
So from one perspective we can portray development in transcendent terms whereby each whole is (quantitatively) included as part of a "higher" whole. (Emphasis here is on the whole/part nature of the holon). In this context the atom is (quantitatively) included in the molecule.
However equally we can portray development in immanent terms, whereby - relatively - each part is (qualitatively) included as the whole of a "lower" part. (Emphasis is now on the part/whole nature of the holon). So the molecule is (qualitatively) included in the atom. 5 Thus, from a true integral perspective, development simultaneously unfolds in both transcendent and immanent directions.
However to further clarify this crucial point we need to say a little regarding the nature of dynamic switching.
Basically it is quite simple. The quantitative and qualitative aspects of experience are complementary (in vertical terms). Thus when we consciously identify with one aspect – say the quantitative – an (unconscious) switch takes place in experience, so as to restore the neglected (opposite) aspect. 5
So from a dynamic perspective, understanding continually changes as between quantitative and qualitative aspects (and qualitative and quantitative).
This can be represented in binary terms. When the quantitative state is on, the qualitative is off; likewise when the quantitative is on, the quantitative is off.
This movement between quantitative and qualitative states (and qualitative and quantitative) likewise causes a switch in terms of cognitive and affective states (which are likewise dynamically complementary in experience).
Both cognitive and affective modes have quantitative and qualitative aspects.
If we initially identify the cognitive aspect in quantitative terms, the switch takes place to the corresponding affective aspect (which can now be identified in qualitative terms).
However if we identify the cognitive qualitatively, the corresponding switch is to the affective aspect (in quantitative terms).
I will now illustrate these dynamics in detail with respect to the relationship as between the atom and the molecule.
1 (a) The atom is transcended and included in the molecule (in quantitative terms).
(b) The atom is transcended and excluded in the molecule (in qualitative terms).
Quantitative inclusion dynamically implies qualitative exclusion. In
this context, when cognitive appreciation is turned on, affective appreciation
is turned off.
2 (a) The molecule is made immanent and included in the atom (in qualitative terms).
Understanding switches – relatively – from cognitive (mental) appreciation of the "higher" molecule to affective (sense) appreciation of the "lower" atom (which now includes the molecule).
(b) The molecule is made immanent and excluded in (quantitative) terms.
Here qualitative inclusion implies quantitative exclusion; thus when affective appreciation is turned on, cognitive appreciation is turned off.
So in these cases, transcendence is associated with cognitive (scientific) and immanence with affective (artistic) appreciation respectively.
However transcendence can equally be associated with the affective
mode and immanence with the cognitive.
3 (a) The atom is transcended and included in the molecule (in qualitative terms).
Understanding now switches from cognitive (mental) appreciation of the "lower" atom to affective (sense) appreciation of the "higher" molecule.
(b) The atom is transcended and excluded in the molecule (in quantitative terms).
Qualitative inclusion again implies quantitative exclusion; so when
the affective mode is now on, the cognitive is off.
4 (a) The molecule is made immanent and included in the atom (in quantitative terms).
Understanding here switches from affective (sense) appreciation of the "higher" molecule to cognitive (mental) appreciation of the "lower" atom.
(b) The molecule is made immanent and excluded in the atom (in qualitative
terms). Once more, quantitative inclusion implies qualitative exclusion;
so we now switch on the cognitive by switching off the corresponding affective
The very purpose of this integral translation is to render all dualistic interpretations paradoxical (in vertical) terms. Explanations must therefore be given a purely relative validity before they can be fully consistent with the nondual experience of reality.
Thus, in (circular) integral terms, inclusion always implies exclusion (and exclusion implies inclusion).
Transcendence implies immanence (and immanence implies transcendence).
Higher implies lower (and lower implies higher).
Quantitative implies qualitative (and qualitative implies quantitative).
Whole implies part (and part implies whole).
Cognitive implies affective (and affective implies cognitive).
Thus an integral (synthetic) translation is based on the complementarity of polar opposites in experience. It requires circular both/and logic (i.e. bi-directional) where understanding takes place simultaneously in opposite directions. This identifies the nondual symmetry inherent in all relationships.
By contrast a differential (analytic) translation is based on the separation of polar opposites. It requires linear either/or logic (i.e. uni-directional) where understanding takes place sequentially in one direction. This identifies the corresponding dual asymmetrical nature of all phenomenal relationships.
Perhaps the greatest single difficulty with conventional approaches to development is the misguided attempt to use analytic translations for the task of overall synthesis. At best this leads to a reduced interpretation of integration that is one-sided and inconsistent.
Though this methodological issue has been greatly ignored, it is of fundamental importance.
The very purpose of an integral translation is to provide an interpretation of reality that is consistent with nondual experience (in spiritual intuitive terms).
Paradoxical appreciation of the purely relative nature of all dualistic explanations is the basis for this transforming spiritual insight. This in turn greatly facilitates the appreciation of paradox and relativity. So spiritual intuitive and bi-directional understanding dynamically interact in experience.
When properly understood, integral translations of reality are inseparable from spiritual meditation.
Differential translations - though vitally important in their own right - are not directly compatible with nondual experience. They are inherently based on asymmetrical interpretations (where truth is identified in polarized terms). Thus they tend to view arbitrary phenomenal explanations in an absolute fashion (encouraging rigid attachment).
True integral translations - by their very nature - have immense potential
for the undoing of this rigid attachment (thus freeing one for the nondual
experience of reality).
Application to Development
This is a brief summary.
Linear analytic translations are directly suitable for interpreting reality in its phenomenal dual aspects.
Circular synthetic translations by contrast are directly suitable for interpreting reality in its empty nondual aspects.
Comprehensive translations - which I refer to as radial - combine interpretations in both dual and nondual aspects.
One of the implications of the (circular) synthetic approach is that it can provide the basis for a greatly expanded range of asymmetrical models of development (each with an equal partial validity).
The task then for the (linear) analytic approach is to flesh out these
models sequentially in detailed fashion.
Eight Asymmetrical Models of Development
We can in fact identify eight such asymmetrical models of development (from the above vertical translations). I will now briefly outline the nature of each model. 6
The first four are holarchical reflecting the whole-part nature of holons
(where each whole is a part of a "higher" whole).
The second four are "partarchical" reflecting the reverse part-whole
nature of holons (where - relatively - each part is a whole of a lower
The proper identification of opposite models at an analytic level serves as the means for creating the symmetrical (complementary) pairings which constitute the starting basis for the integral approach.
The key problem with scientific translation is as follows.
In formal terms, science adopts a cognitive mode of interpretation. However the very dynamics of experience necessitate that both affective and cognitive modes interact in whole/part (and part/whole) recognition.
Because science ignores the affective aspect in translation, it inevitably reduces the very nature of reality interpreting it merely in impersonal terms. 8
Reality at all levels involves the interaction of quantitative and qualitative aspects (and qualitative and quantitative). However science has no means of adequately translating this interaction (in terms of its existing paradigm).
The satisfactory translation of these dynamics requires a radically different philosophical approach and alters the very nature of what is scientifically meant by reality.
Remarkably the basis for this translation is rooted in an important mathematical notion (when given its deeper holistic interpretation). 9
I will deal with this in the second part of the article.
Spiritually refined aesthetic experience requires a
large measure of detachment from phenomenal characteristics so as to identify
directly with the spiritual light (mediated through the object symbols).
This detachment comes from the cognitive aspect.
Likewise when associated with the affective, cognitive perception acquires an immanent focus. Conventional science has both transcendent and immanent aspects (which are closely associated with the deductive and inductive approaches respectively).
With the deductive approach the "higher" wholes (theoretical constructs) are used to interpret the "lower" parts (empirical data).
With the immanent approach, the "lower" parts (empirical
data) suggest the "higher" wholes. Theoretical constructs then arise –
as it were – out of the empirical data.
5. In integral terms, "higher" and "lower" are purely relative. Thus if we define "higher" in terms of a transcendent perspective, then – in relative terms – immanent will be "lower". However if we switch our frame of reference, immanence will now be "higher" and transcendence will be "lower".
This reflects an asymmetrical approach (based on an analytic rather than a true synthetic approach).
Though containing an important partial validity it is somewhat unbalanced reflecting one of several equally valid asymmetrical interpretations.
Ken here – as one would expect in a holarchical approach – gives primacy to the whole (rather than the part) aspect. Thus he defines a holon as a whole/part (and not a part/whole) where a whole is also a part of other wholes. So the partness of holons is defined here in the context of wholes.
However a "partarchical" approach would give primacy to the part (rather than the whole aspect). Here a holon would be defined as a part/whole where a part is also a whole of other parts. So the wholeness of holons is here defined in the context of parts.
When Ken says for example that an atom is part of a molecule, he is identifying this relationship in transcendent terms (All of the atom is in the molecule; not all of the molecule is in the atom).
However when we look at this from the complementary perspective, the relationship works in reverse. The molecule is now a whole of an atom i.e. the molecule is immanent in the atom. In this context, all of the molecule is in the atom; not all of the atom is in the molecule. In other words qualitative appreciation requires the exclusion of quantitative characteristics.
Also when Ken says that each senior holon enfolds, envelops, and embraces its juniors, and this is the very nature of whole/parts, holons, and holarchy, again it has an important – though limited – validity.
However it is very one-sided for from the opposite immanent perspective, each junior holon enfolds, envelops and embraces its seniors, and this is the very nature of part/wholes, holons (or should we say on-hols) and "partarchy".
It is unbalanced to try and offer a consistent view of development that relies on an asymmetrical interpretation.
The very basis for moving on to a true synthetic approach is the recognition that all asymmetrical models can be given opposite interpretations (which are equally valid).
Integration then comes from the dynamic realization
in experience of this symmetry (of opposite explanations).
9. The very nature of analytic scientific translation is that it views reality in either/or terms (though in dynamic terms it is both/and). Thus science in its empirical aspects views phenomenal reality in merely quantitative terms. Strictly speaking in its theoretical aspects it views reality in merely qualitative terms. (A theory by its very nature is not directly related to specific phenomena).
So the great reductionism of science is to assume a direct correspondence as between these quantitative and qualitative aspects. Thus when scientists assume those theoretical constructs directly correspond with empirical data they are reducing the qualitative to the quantitative aspect.
Equally when they assume that empirical data correspond with theoretical constructs they are reducing the quantitative to the qualitative aspect.
So properly understood the disaster of modernity is not that the qualitative aspect has been reduced in terms of the quantitative but rather that reality which - in dynamic terms - is both quantitative and qualitative (and qualitative and quantitative) has been reduced in terms of polarized explanations that are either quantitative or qualitative. This is even more damning as it implies that (conventional) science gives a merely reduced interpretation of reality in both its quantitative and qualitative aspects (greatly limiting spiritual appreciation of both).
The root of this problem is the overuse of the (linear) either/or logic in interpretation with remarkably little appreciation of (circular) both/and logic.
This is why I am so passionately committed to the dynamic notion of integral science based directly on both/and logic.