This posting illustrates the use of this qualitative binary system to encode the Spectrum of Consciousness.
Firstly I will say a little about the overall approach.
My most general categories are - what I refer to as - life stages or journeys.
I have three of these.
The first is concerned with the task of differentiation of consciousness (and includes all "lower" levels of development). Western psychology largely limits itself to this journey which culminates with the specialisation of reason at a "middle" level. This is the way of activity.
The second - again starting from the "middle" level - is concerned with the task of integration (and includes all "higher" levels of development).
Mystical spirituality (East and West) is mainly concerned with this second journey which culminates with the specialisation of intuition. This is the way of contemplation.
The third - what I refer to as Radial Reality - is the most mature and dynamic of the life stages and is concerned with both the continuing differentiation and integration of consciousness. The great spiritual "transformers" of history are usually shining examples of this life stage. This is the way of compassion.
Now differentiation and integration in experience are related to two fundamental logical systems that can be precisely formulated in qualitative binary terms.
The first is based on the clear separation of opposite poles in experience (e.g. subject and object). This is the rational (linear) approach and corresponds to 1 (in holistic terms). Actual (unitary) form is thereby developed in experience.
The second is based on the complementarity of opposite poles in experience. This is the intuitive (circular) approach and corresponds to 0 (in holistic terms). Pure potential existence (void of phenomenal form) is thereby experienced.
In dynamic terms (circular) intuitive knowledge is developed through negation of (linear) rational knowledge. So just as quantitatively 0 = 1 - 1, likewise qualitatively, 0 = 1 - 1.
(Circular) Intuition is thereby developed through the bi-directional use of (linear) reason.
Also 1 - 1 = 0; bi-directional (linear) reason is developed through (circular) intuition.
Thus the first life stage is concerned with the specialisation of the qualitative digit "1".
The second life stage is concerned with the specialisation of the qualitative digit "0".
The third life stage is concerned with the continued specialisation of both qualitative binary digits (1 and 0).
The two earlier life stages are made up of differing levels (and transitions between levels). The final life stage involves the mature differentiation and integration of all previous levels.
Before dealing with the differing levels of the Spectrum, I must say a little about the three types of complementary relationships common to all holons.
The first type involves horizontal poles. The most common expression of this would be in terms of the relationship as between objective and subjective, external and internal, exterior and interior etc.
The second type involves vertical poles. These are extremely important. The usual expression of this would be in terms of the relationship as between qualitative and quantitative, wholes and parts, the general and the particular, higher and lower, cognitive and affective etc.
In physical terms the important interaction as between objects and dimensions represents the dynamic expression of vertical polarities. In psychological terms the interplay as between (all) perceptions and corresponding concepts in experience again is the expression of vertical polarities.
The third type involves diagonal poles. These can be looked on as the combination of both horizontal and vertical opposites. The most usual expression would be in terms of the relationship as between actual and potential, form and formlessness, the manifest and unmanifest etc.
The three polarities can be given precise qualitative mathematical expression as the holistic geometrical interpretation of the eight roots of unity (The Theory of Everything).
What is important about this qualitative binary Spectrum is that it represents the structure of both physical and psychological reality.
Now we start the Spectrum with the first life stage which includes all "lower" levels (and transitions between levels).
LL3 is the "lower" null level. It would precede the unfolding of sensori-physical development. It represents a state of total confusion of the qualitative binary digits. No differentiation of (linear) rational consciousness has yet taken place; no integration of (circular) intuitive consciousness is thereby possible. Form and emptiness have yet no meaning. They are neither 1 nor 0 (in qualitative terms).
The transition from LL3 to LL2 involves the first crucial transition. This will commence with the developing foetus in the womb and continue after birth.
It involves the gradual differentiation of diagonal polarities. In other words the infant learns to differentiate (actual) form from (potential) emptiness. However phenomena are initially very confused and transient. As yet no clear distinction is possible as between quantitative (conscious) or qualitative (unconscious) aspects (vertically) nor external (objective) or internal (subjective) aspects (horizontally).
So we have here initial linear differentiation (1) with respect to its diagonal poles.
LL2 is the "lower" point level preceding phantasmic-emotional development. It is characterised by confused complementarity in relation to vertical and horizontal aspects and continuing linearity in regard to the diagonal aspect. The infant cannot properly distinguish personal from impersonal or subject from object and still largely lives in a world that is characterised by a confused sense of relativity.
So we have here continuing (diagonal) linear differentiation (1) and confused (vertical and horizontal) circular integration (0).
The transition from LL2 to LL1 is characterised by gradual linear differentiation in relation to vertical poles of experience. In other words the infant begins to distinguish parts from wholes, objects from dimensions, the impersonal from the personal.
So we have here linear differentiation (1) with respect to its vertical poles.
LL1 is the "lower" circular level from which rep-mind or pre-operational development unfolds. It is characterised by confused complementarity in relation to remaining horizontal polarities and continuing linear differentiation in relation to diagonal and vertical polarities.
However there is still a somewhat mythical flavour to experience where subjective and objective interpretations are somewhat confused.
So we have here continuing (diagonal and vertical) linear differentiation (1) and confused (horizontal) circular integration (0).
The transition from LL1 to L0 is characterised by gradual linear differentiation in relation to the remaining horizontal pole of experience. The child now begins to distinguish (internal) self from the (external) world and develop a growing moral responsibility.
So we have here linear differentiation (1) with respect to its horizontal aspect.
L0 is the important "middle" rational linear level. This would include the three sub-levels of rule/role mind (conop), formal-reflexive (formop) and vision-logic. It is characterised by continuing specialised differentiated development of linear experience with respect to its diagonal, vertical and horizontal poles. So remaining confused complementarity in experience is now largely eliminated.
This level - which is the only level on the Spectrum where (circular) complementarity does not exist, is the firm basis for the conventional paradigm of science. Unfortunately when this paradigm is used to translate other levels, it inevitably leads to misinterpretation.
We have here therefore continuing linear differentiation with respect to diagonal, vertical and horizontal aspects of experience (1).
So the lower levels can be seen as the gradual movement from a state of instinctive circular complementarity (i.e. totally confused integration) towards a state of rational linear separation (i.e. fully specialised differentiation).
The higher levels are characterised by the movement towards (circular) integration this in a proper mature fashion.
The transition from L0 to HL1 involves the negation of the horizontal direction of linear consciousness (i.e. - 1). This leads to the generation of spiritual intuition in what I refer to as mirror understanding.
HL1 is the "higher" circular level. Its earlier stages would correspond to the psychic realm and its later stages to the subtle realm.
In intuitive terms it is characterised by growing (circular) integration in relation to the horizontal polarities of experience (0). In rational terms it is characterised by bi-directional linear understanding of these same poles (1 - 1). In other words objective and subjective poles are increasingly experienced as being ultimately identical. The vertical and diagonal poles are still however largely characterised by one-directional (linear) differentiation (1).
The transition from HL1 to HL2 involves the additional negation of the vertical direction of linear consciousness (- 1). This is mirror understanding in relation to indirect consciousness ("imaginary" understanding) i.e. unconscious projections where quantitative phenomena carry a qualitative archetypal meaning.
HL2 is the "higher" point level. This equates well with the causal realm.
This is a very intuitive level characterised by growing intuitive (circular) integration in relation to both horizontal and vertical polarities of experience (0). In rational terms there is now bi-directional (linear) understanding in relation to both sets of poles (1 - 1). However one-directional (linear) differentiation still remains in relation to diagonal poles.
The transition from HL2 to HL3 involves the final negation of the diagonal direction of linear consciousness (- 1). This is mirror understanding in relation to the most fleeting of conscious phenomena (i.e. "complex" understanding).
HL3 is the "higher" null level. It is also referred to as nondual reality.
This represents the most specialised development of spiritually intuitive consciousness and represents (circular) integration in relation to horizontal, vertical and diagonal polarities of experience (0). Equally in rational terms it is characterised by bi-directional (linear) understanding in relation to the three sets of poles (1 - 1). Experience is now so refined that both the circle and line have become identical as a common central point (representing equally reason and intuition. By definition no one-directional (linear) differentiation now takes place in experience.
So just as the "lower" levels culminate with the specialisation of (linear) differentiated consciousness at L0 (1), the "higher" levels culminate with the specialisation of (circular) integrated consciousness at HL3 (0).
However - as explained - this (circular) void is also a (linear-circular) plenum-void. This can be simply explained as follows. Let us draw the analogy of the development of pure intuition as a journey to the North Pole. Now until we reach this pole we will continue to journey North. However at the point of the Pole itself we lose all sense of direction. In a sense it is pointing both South and North. Likewise when we arrive at the (circular) point of pure intuition, it now simultaneously represents both a linear and circular state (1 and 0).
This pure nondual state as both unity and nothingness (1 and 0), then becomes the basis for the unfolding of Radial Reality. This involves the progressive dynamic interpenetration of nondual experience with all dual phenomenal levels of the Spectrum.
It represents a continual growth in both the depth and range of experience in terms of all levels both in analytical (differentiated) and holistic (integrated) terms.
Radial Reality represents the refined expression of nondual (simple) and dual (complex) experience. Referring to this state as (solely) nondual experience is mistaken. Paradoxically it offers the greatest opportunities for (linear) rational as well as (circular) intuitive experience.
It is important to stress once again that my holistic mathematical approach is designed to indicate the complementarity (in horizontal, vertical and diagonal terms) between the psychological and physical interpretations of the Spectrum.
For example in vertical terms the "higher" level psychological structure of one level interprets the corresponding "lower" level physical structure. Recently, I illustrated this in relation to the holistic interpretation of quantum physics where the psychological structure of HL1 interprets the physical structure of LL1.
This qualitative binary approach is very versatile and can be next extended to sub-levels (of given levels).
Again I use the same basic principle of horizontal, vertical and diagonal polarities to distinguish three key sub-levels.
Thus for example at L0, conop relates to the horizontal aspect, formop to the vertical aspect and vision-logic to the diagonal aspect of understanding. All the "higher" levels have sub-levels that are defined in similar terms. The "lower" levels are characterised by confusion regarding the divisions between these sub-levels.
Within each sub-level, I next define stages once more using the same directional approach. These stages only become precisely differentiated at the "higher" level.
Thus at HL1 one distinguishes horizontal directions through distinct external (objective) and internal (subjective) aspects.
At HL2 one distinguishes clearly vertical directions through distinct qualitative (cognitive) and quantitative (affective) aspects.
At HL3 one finally distinguishes clearly diagonal directions through potential (spiritual) and actual (physical) aspects.
Finally within each stage I distinguish phases again using an extension of the same principle.
Recently in my postings on an integrated approach to physics (Holophysics 1), I illustrated the nature of this extended approach. So far I have dealt with the scientific implications of the first sub-level of HL1 (relating to its unique conop understanding).
Using the differentiation of the horizontal direction, this then led to two distinct stages external and internal respectively. Each of these stages were then described in terms of five phases. The key point about these postings was to show that the very key to an integrated understanding of physical relationships, lies in the precise mapping of the (qualitative) mathematical structure of the corresponding psychological level.
The complete unfolding of the Spectrum therefore involves life stages (journeys), levels, sub-levels, stages and phases.. All of these can be interpreted in terms of the qualitative binary system using the fundamental directions (horizontal, vertical and diagonal) that are common to all holons. (I have confined myself to the structure of the life stages and levels in this post).
I wish now to make a key point. To properly translate any level, we must use the understanding appropriate to this level. Thus we translate L0 (the rational linear level) in terms of the understanding of L0. However there is a marked tendency to utilise the understanding of L0 to equally translate all other levels.
Ken Wilber - perhaps surprisingly - exemplifies this problem. He uses vision-logic (which is the most advanced sub-level of L0) to rationally translate all "lower" and "higher" levels.
Because this understanding is linear and one-directional, he fundamentally misrepresents in important ways the true nature of all these other levels.
For example this problem lies at the very root of his handling of the pre/trans fallacy.
Ken tries to sharply differentiate pre from trans. Thus in Ken's treatment the "lower" stages are prepersonal (pre) and the "higher" stages transpersonal (trans).
However this is unduly linear and one-directional and makes no sense from the qualitative binary perspective.
By definition all the "lower" stages are both linear and circular (in a confused fashion).
All the "higher" stages are also both linear and circular (in a progressively integrated manner).
Thus if we take the understanding of LL1, this is linear in relation to both diagonal and vertical polarities (though still somewhat confused). Insofar as pre and trans have been separated in terms of these directions we can speak of understanding as either pre or trans. However understanding is still circular in relation to horizontal polarities. So in terms of this direction understanding is both pre and trans (in a confused manner).
At HL1, understanding is still largely linear in relation to both diagonal and vertical polarities (but now in a differentiated manner). Understanding is still either pre nor trans (in relation to these directions). However it is now largely circular (intuitive) in relation to horizontal polarities. So in terms of this direction understanding is both pre and trans (in an integrated manner).
So the structure of the "higher" levels precisely matches (in integrated) form the structure of corresponding "lower" levels (that are confused). "Lower" levels implicitly contain "higher" levels. "Higher" levels explicitly contain "lower" levels. In dynamic terms "higher" and "lower" levels necessarily interact in experience. Indeed the continual correction of "lower" level confusion is the very means by which "high" level integration is achieved.
Thus the qualitative binary approach thus leads to a very different interpretation of the nature of pre and trans behaviour. Though it places Ken's ideas in context (with an important though limited validity), it goes considerably beyond his approach and highlights the true complementary dynamics of these important terms. Indeed the appreciation of this complementarity is the key to recognising the corresponding equality of immanence and transcendence in development. Because there is a marked lack of this (circular) complementary logic in Ken's approach he never really gets to grips with these important dynamics. Thus he continually views development in transcendent holarchical terms (which is unbalanced).
This qualitative binary approach is very fundamental. Again it is sufficient to encode all transformation processes. Nondual reality can be described in terms of the identity of the two binary digits (interpreted in holistic terms.
"Form is not other than Void
Void is not other than Form"
However all phenomenal reality can equally be translated in terms of this system (with varying degrees of separation and complementarity of the binary digits.
Using "The Theory of Everything" with its horizontal, vertical and diagonal polarities, we can indicate a precise means to encode the logical structure of each level of the Spectrum. This method can then be extended to precisely structure further sub-levels, stages and phases. The very key to integrated science lies in this holistic mathematical mapping of the Spectrum.
Question on whole and part
I have a question regarding the notions of part and whole.
I can experience an object in the world as both a part or a whole.
For example, when I am with a friend s/he is both a whole but is
also composite, ie. contains facial expressions, feelings, words,
thoughts, etc. This is similar to your examples of cake slices. Here
we have a part/ whole object in the world which corresponds to self.
I can though, similarily view me and my collection of friends as a
whole of which I myself am a part. This arrangement is again of a
part/whole structure but here I am a part inside a whole, so the
compositness is not of an object in the world (corresponding to
self) but includes the reference point of the observer within the
whole. Could you please in holistic mathematical terms speak about
the difference between these two whole/part notions.
Re: Question on whole and part
You have raised here one of the most fundamental of all issues. (It
was central to the very development of Holistic Mathematics).
The conventional answer to your question would be that every object
can serve as whole or part (depending on the context).
In your first example where you take your friend as "whole", all of
the various attributes you list - facial expressions, feelings,
words, thoughts - are thereby in rational terms "parts" (of this
In your second example the frame of reference has now changed. Your
collection of friends is now the defining "whole" so now - in
rational terms - you are "part" of this whole.
Thus every object depending on the frame of reference can serve as
part or whole.
The trouble about this conventional interpretation is that it
represents a very reduced interpretation of the key experiential
It offers in fact a merely rational quantitative interpretation. The
qualitative interpretation of the relationship - which is based
directly on intuition - is simply reduced to the rational. So in
effect "wholes" and "parts" are very much confused in this (merely)
rational (quantitative) interpretation.
So when we look at the true relationship of "whole" and "part" we
can approach it from two (vertical) directions.
Firstly we explain the transformation in experience occurs by which
"lower" level parts are transcended and included in a "higher" level
Equally we explain the transformation in experience by which the
"higher" level whole is made immanent and included in "lower" parts.
I am looking out of my window now at a number of objects. I see a
garage a window a roof, a chimney, a wall etc. Now in rational
quantitative terms this represents a set of "parts". However at some
stage a transformation in consciousness takes place by which these
fragmented objects now resolve themselves into a "new" object i.e. a
Now this crucial transition - through which the "parts" are
transformed into a new collective "whole" is qualitative and
intuitive in origin. However in terms of a (reduced) rational
interpretation, it becomes quickly lost. So we now understand the
"whole" house - as well as its constituent parts - in merely
So then in experiential terms objects are not just quantitative (in
rational terms). Equally they are qualitative (in intuitive terms).
The key dynamic through which parts are transcended and included in
"higher" level wholes is itself spiritual (representing this
interaction of quantitative and qualitative).
Now a reverse process in consciousness is required enabling the
transition from a "higher" level whole to "lower" level parts.
This time we start by understanding the "whole" in rational
quantitative terms. Then through a qualitative intuitive
transformation in consciousness we are enabled to move from this
composite "whole" to an appreciation of its unique constituent
"parts". However again - in a rational terms - this qualitative
aspect is quickly lost with a merely quantitative interpretation of
Again the key dynamic through which the "higher" level whole is made
immanent and included in "lower" level parts is itself spiritual
(representing again the interaction of quantitative and
Now the holistic mathematical interpretation of these dynamics
raises very important questions regarding our very notions of
The belief that we live in a "real" world directly comes from
this strong scientific bias by which we identify meaning with what can be
verified in quantitative terms. We have seen that the rational
interpretation of objects reduces them to quantitative "real" terms.
The "real" world is then made up of such quantitative objects.
However every object has in dynamic terms both a qualitative as well
as quantitative interpretation. Though this qualitative
interpretation is directly intuitive in origin it can be given a
fascinating indirect "imaginary" interpretation.
Thus every object - in holistic mathematics - has both a "real"
(quantitative) and "imaginary" (qualitative) interpretation. Reality
in holistic mathematical terms is "complex" (i.e. both "real" and
Actually this corresponds very closely with the distinction as
between the scientific and artistic interpretation of an object.
Ultimately indeed it is based on the distinction as between
cognitive and affective understanding. Properly understood when
cognitive understanding is "real" then affective understanding - in
relative terms - is "imaginary".
However conventional science misunderstands this key distinction and
reduces - in any context - the (qualitative) affective to a cognitive
All objects therefore have "real" (quantitative) and "imaginary"
(qualitative) interpretations (as archetypes).
Now we have a remarkable connection here with conventional
As you know the comprehensive number system is complex (with real
and imaginary components). This is commonly represented by the
Argand diagram where real numbers are represented by the horizontal
x axis (moving out from the central point of 0 (in both positive and
negative directions). The imaginary numbers are represented by the
vertical y axis (again moving out from the common central point in
both positive and negative directions).
The holistic mathematical representation is exactly similar. Real
(quantitative) polarities are represented in horizontal terms
(positive and negative). Imaginary (qualitative) polarities are -
relative to quantitative - represented in vertical terms (positive
Thus the relationship as between whole and part (and part and whole)
cannot be properly interpreted in horizontal "real" terms (i.e. quantitative).
The true relationship is more subtle and always involves a switch
from horizontal to vertical understanding ("real" to "imaginary")
and then from vertical to horizontal ("imaginary" to "real").
These very dynamics involve the very fundamental way through which
(all) concepts and perceptions are related. However I think I have
said enough for now.
Thanks Matt for your interesting intervention. I see you have become
more active on the Forum recently. Good luck with your