Corresponding to the Spectrum of Consciousness is a Spectrum of Methods for scientifically translating reality.

A coherent logical structure can be associated with each level of consciousness in the Spectrum providing a precise rational basis for a wide range of different translation methods (each possessing an important validity).

The Centaur stage represents a very narrow range of the Spectrum. Vision-logic as the understanding appropriate to this stage provides the basis for one important - though necessarily limited - translation method. We cannot adequately interpret reality solely from this perspective.

Rather we need the full Spectrum of Methods to provide a comprehensive understanding of reality.

So from this enlarged perspective the pre/trans fallacy for example, can be given a wide range of differing interpretations (in correspondence with each of the translation methods).

So when we attempt to understand the pre/trans fallacy - or indeed any concept - through the filter of just one method (such as vision-logic), an unduly limited and ultimately distorted interpretation emerges.

However before we look at the scientific nature of the translation methods we need to clarify the nature of the Spectrum.


I define the Spectrum in terms of bands, levels, transitions (between levels), sub-levels, directions, stages and phases of development.

Let us look at each in turn.


The bands are defined in terms of "lower", middle and "higher", ultimately leading to - what I refer to as - Radial Reality.

The "lower" band corresponds to prepersonal development. It involves a gradual process of differentiating structures in experience (starting from an initial confused state).

The middle band corresponds to personal development and entails the specialized differentiation of structures.

The "higher" band corresponds to transpersonal development and entails the reverse process of properly integrating structures in experience (that have already been differentiated).

Radial Reality involves a dynamic process by which structures are both differentiated and integrated in experience. It involves the relative separation and mutual interpenetration of previous bands.


The bands can be subdivided into various levels.

The "lower" band comprises three levels L3, L2 and L1 (corresponding roughly to archaic, magical and mythic respectively).

The middle band comprises the - very important - rational level. Because it serves as a bridge between the "lower" and "higher" levels it can be referred to equally as L0 or H0.

The "higher" band comprises three levels H1, H2 and H3 (corresponding roughly to psychic, subtle and causal realms).

These levels throughout the Spectrum are designed in such a way as to demonstrate both their linear and circular aspects.

From a linear perspective, levels are relatively separate and distinct ascending from the "lowest" (L3) to the "highest" (H3) in a hierarchical fashion.

However, from a circular perspective, levels are relatively interdependent.

Thus there is a complementarity of structure existing between "highest" and "lowest" levels (and "lowest" and "highest"). .

Thus H3 is complementary with L3 (and L3 with H3).

H2 is complementary with L2 (and L2 with H2)

H1 is complementary with L1 (and L1 with H1).

Finally, H0 is complementary with L0. In other words the middle level is complementary with itself.

It is very important that both the linear (independent) and circular (interdependent) interpretations of levels be maintained for proper understanding.

Radial Reality involves the relative independence of each level with the relative interdependence of all levels. It involves the mature ability to effectively analyse and synthesize reality.

Transitions (between levels)

Bridging each level is an important psychological event that makes successful transition to the next level possible. For example the important transition bridging the middle and "higher" levels, involves mirror understanding (where every dualistic interpretations of reality is understood to have an opposite explanation that is equally valid).

A precise structure can be identified for each transition (between the levels).

In my model there are 7 levels (and 6 transitions between levels).


Each level has three sub-levels (which are not always clearly distinguishable).

For example in the important middle "rational" level, we have a concrete sense orientated (conop), a formal mental orientated (formop) and a more intuitive orientated sub-level (vision-logic).

Each of the other levels can also be identified - relatively - with respect to sense, mental and intuitive sub-levels.


Each sub-level can in turn be subdivided in terms of directions. These resemble closely the notion of quadrants. However the four quadrants are limited to horizontal (exterior-interior) and vertical (individual-collective) distinctions. Directions would allow additionally for diagonal (finite-infinite) distinctions.

Thus a sub-level can be defined in terms of eight directions. Proper differentiation of these directions does not take place however at each sub-level.

The sub-levels of H3 involve the most complete differentiation (and corresponding integration) of all eight directions (horizontal, vertical and diagonal). The sub-levels of L3 by comparison involve the most confused differentiation (and thereby confused integration) of the eight directions.

The sub-levels of H2 involve the differentiation (and corresponding integration) of four directions (horizontal and vertical). The sub-levels of L2 by comparison involve the confused differentiation (and confused integration) of these same four directions.

The sub-levels of H1 involve the differentiation (and corresponding integration) of two directions (horizontal). The sub-levels of L1 by comparison involve the confused differentiation (and confused integration) of these two directions.

The sub-levels of H0 (and L0) involve the proper differentiation and corresponding integration of just one direction.

What this in effect means is that the sub-levels of L0 (H0) basically confuse the process of differentiation with that of integration. (Integration is effectively reduced to differentiation). This is true of the "highest" of these sub-levels (i.e. vision-logic)!


Each direction can be subdivided in terms of stages. The stages relate to the unfolding of affective, cognitive and moral spiritual structures respectively. A scientific translation requires that special attention be given to the precise structure of cognitive understanding at each stage. At the highest level of H3 for example, the cognitive stage develops with respect to eight different directions (which are both differentiated and integrated with respect to each other).


Finally with respect to the unfolding of stages we can identify several different phases that highlight the dynamic nature of development.

So once again the Spectrum can be subdivided with respect to bands, levels, transitions (between levels), sub-levels, directions, stages and phases which are given both linear and circular interpretations.

What is fascinating is that all these structures of development - even at the most detailed level - have a coherent holistic mathematical interpretation (which greatly clarifies their precise nature).1


Digital technology is based on the principle that information can be encoded in terms of just two binary digits (1 and 0), with a distinct quantitative interpretation.

All information - despite its great complexity - can potentially be encoded in terms of these two digits.

However the binary digits have an equally important qualitative interpretation that is scarcely recognized.

So all transformation processes (e.g. human development) can potentially be encoded in terms of the holistic interpretation of these two digits.

Qualitatively interpreted, the two digits relate to the two systems of the logic of form (corresponding to the holistic interpretation of 1) and the logic of emptiness (corresponding to the holistic interpretation of 0).2

The logic of form is based on the clear separation of polar opposites (e.g. subject and object) and is the direct means for the differentiation of experience.

It is linear in nature and geared to making absolute distinctions where understanding takes place in a one-directional sequence.

Thus if we understand development as moving unambiguously from prepersonal through personal to transpersonal stages we are using the logic of form (which is uni-directional).

The logic of emptiness by contrast is based on the complementarity (and ultimate identity) of these same opposites in experience. Though in direct terms it relates to spiritual intuitive experience, indirectly it has an important rational interpretation (which by its very nature is paradoxical).3

It is literally circular in nature and geared to making relative distinctions.

It is based on the clear appreciation that all dualistic understanding requires an arbitrary fixing of polar frames of reference so that from the opposite perspective

equally valid interpretations are also possible.

Put another way all asymmetrical interpretations have mirror equivalent interpretations (which are equally valid).

Truth does not reside therefore in the (separated) positive pole but rather in the dynamic interaction of both positive and negative poles.

When both positive and negative poles are finely balanced it leads to the pure experience of spiritual emptiness (which is directly intuitive).

Indirectly however it leads to an enhanced appreciation of paradox arising from the complementary two-way nature of all explanations of reality.

In rational terms this leads to a bi-directional logic where opposite dualistic explanations are simultaneously embraced (each having a merely relative truth-value).

So the (linear) logic of form operates on an either/or notion of truth based on the separation of opposite poles. It is asymmetrical in nature with logical connections made sequentially in a uni-directional manner.

The (circular) logic of emptiness operates on both/and notion of truth based on the complementarity of opposite poles. It is symmetrical in nature with paradoxical logical connections made simultaneously in a bi-directional manner.

The logic of form (uni-directional) provides the appropriate means for analyzing and differentiating experience.

The logic of emptiness (bi-directional) provides the appropriate means for synthesizing and integrating experience.

Most translations of reality are based predominantly on the logic of form. Vision-logic for example represents the most flexible and sophisticated use of this logic.

However it is properly suited as a means of analyzing rather than synthesizing reality.

It does not therefore provide an appropriate basis for Integral Studies.

The key task now is to interpret the full Spectrum in terms of the qualitative binary system.

A unique binary code (based on both logical systems) can be applied to the Spectrum (even at its most detailed breakdown).

However it is sufficient for my purposes at this stage to indicate how this binary code can be applied to each of the major levels of the Spectrum.


To understand the basis of this logical coding it is necessary to look at the nature of the key polar distinctions.

There are three main types.4


Common manifestations of this type would be that between object and subject, external and internal, exterior and interior (as in the treatment of the quadrants).


Major manifestations of this type would be that between part and whole, quantitative and qualitative, individual and collective (as in the treatment of the quadrants).

In physical terms the relationship between space and time entails vertical polarities. Psychologically, the important relationship, as between cognitive and affective understanding, entails vertical polarities.


This involves the simultaneous combination of horizontal and vertical poles and represents the most basic of all distinctions. Significant manifestations would be the relationship as between finite and infinite, actual and potential and manifest and unmanifest.

To sum up, all holons can be fundamentally defined in terms of horizontal, vertical and diagonal polarities.

However a full appreciation requires that these polarities be interpreted in binary terms through the two logical systems (i.e. of form and emptiness).

The fundamental structure of each level of development can be interpreted in terms of precise configurations of these logical systems.

I will now outline the binary code for each of the major levels (and Radial Reality).5


It starts with the first differentiation of the diagonal direction; confused bi-directionality of other two directions (vertical and horizontal) remains.

The infant starts to separate (finite) form from (infinite) emptiness; however s/he cannot yet properly distinguish part from whole (vertical poles) and object from subject (horizontal poles).


It entails the differentiation of vertical directions; continued bi-directional confusion of horizontal directions remains.

The infant now starts to make proper part/whole distinctions (vertical poles); however object/subject confusion still remains.


It leads to the differentiation of horizontal directions.

The child now properly distinguishes remaining confused polarities.

L0 (H0)

The on-going differentiation of all three directions - leading to the specialization of rational (linear) understanding - now takes place.

This is the only level where circular understanding plays no explicit role (though it is implicitly required). Unfortunately most formal translations of reality are heavily based on this limited interpretation of reality.


The bi-directional integration of horizontal poles now unfolds; continued differentiation of vertical and diagonal poles remains.

In spiritual experiential terms, object and subject polarities are intuitively reconciled. In indirect rational terms a keen appreciation of the paradoxical nature of (horizontal) dualistic distinctions emerges.


The bi-directional integration of both horizontal and vertical poles now unfolds; the continued differentiation of diagonal poles remains.

In spiritual experiential terms, part and whole polarities are additionally reconciled in a deeper form of intuitive awareness. A very refined appreciation of rational paradox - in terms of both horizontal and vertical polarities - emerges.


The bi-directional integration of all three poles (horizontal, vertical and diagonal) unfolds.

In spiritual terms finite and infinite polarities are also reconciled in an intuitive awareness largely empty of distinct phenomena. This culminates in the experience of nondual reality (which represents the integration of horizontal, vertical and diagonal directions).

An extremely refined type of rational paradox emerges consistent with the lack of rigid dualistic understanding (in terms of all three polarities).

This represents the specialized development of (circular) intuitive awareness. It also represents - in rational terms - the culmination of refined bi-directional understanding (which is the appropriate basis for integrated translations of reality).

So development moves gradually from a confused bi-directional interpretation of reality (the "lower" band) towards the proper differentiation of structures with the middle band of L0 (H0) as the logic of form. It then moves from specialized differentiation towards a mature integration of structures (the "higher" band) which culminates with H3 as the logic of emptiness.

Radial Reality

This combines both the mature differentiation and mature integration of structures (which requires both logical systems). It incorporates the full interaction of uni-directional and bi-directional understanding.


In a previous article I proposed eight translation methods, based on the binary codes of the middle and upper bands of the Spectrum and Radial Reality. I excluded the translations of the "lower" band (as they do not lead to mature interpretations of experience).

I will once again outline these methods. They distinguish clearly as between one-directional (1), bi-directional (0) and both one directional and bi-directional forms of understanding (1 and 0).

Quite simply one-directional methods (largely relating to middle band) are suited for differentiation and analysis.

Bi-directional methods (relating to the "higher" band) are properly suited for integration and synthesis.

Methods that appropriately incorporate one-directional and bi-directional understanding (relating to Radial Reality) are properly suited for both differentiation and integration.

Differential Methods

Differential 1

This is based on the lower sub-levels (conop and formop) of L0 (H0). It leads to a narrow analytical approach that is exemplified by conventional science.

Differential 2

This is based on the higher sub-level of H0 (the centaur). It leads to a flexible and varied analytical approach (using vision-logic). Because this method is combined with intuitive understanding it may appear suitable for synthesis. However properly understood it provides a multi-differential (rather than a true integral) approach.

Differential 3

This is based on the understanding that bridges the middle and "higher" levels and is the most sophisticated of the differential approaches.

It leads to the clear appreciation that all asymmetrical explanations of reality have mirror image explanations that are equally valid. It is the subsequent pairing of these mirror image explanations that paves the way for symmetrical bi-directional understanding (leading to true integration at the "higher" levels).

Integral Methods

Integral 1

This is based on H1 and the application of bi-directional understanding to horizontal polarities (e.g. object and subject).

This is the starting basis for a very different type of qualitative scientific understanding (that is properly integral) which I refer to as Holoscience.

It is not directly concerned with the understanding of quantitative relationships. Rather it is based on close complementarity of physical and psychological structures. This means that any explanation of physical reality has a mirror explanation that is equally true of psychological reality.

Alternatively if we start from well-known psychological relationships we can find mirror image structures in terms of physical reality.

In principle this kind of understanding can be applied to any of the sciences. (I have concentrated mainly on Mathematics, Physics and Economics).

It leads to a radically different and inherently more balanced way of looking at relationships greatly enhancing the intuitively synchronistic appreciation of reality. From another perspective it provides a means of transforming scientific understanding into a natural type of spiritual meditation.

Integral 2

This is based on H2 and the application of bi-directional understanding to both horizontal and vertical polarities.

This leads to a much more refined appreciation of the qualitative scientific worldview (i.e. Holoscience).

One can now appreciate the complementary nature of all physical and psychological relationships (both in terms of horizontal and vertical polarities).

I will illustrate here just two important applications of this appreciation of vertical polarities.

Whereas clearly "lower" physical should not be confused with "higher" psycho-spiritual reality, yet a very subtle complementarity necessarily exists between both domains.

The "lower" the level of physical reality we are investigating the "higher" the corresponding understanding required for appropriate translation. Thus physical relationships at the "lower" sub-atomic level require the "higher" transpersonal levels (for meaningful interpretation).

Enormous progress could be made by accepting that a Spectrum of Nature exists (with varying levels), that is fully complementary with the Spectrum of Consciousness (with corresponding levels).

For any level of physical investigation, there is therefore a complementary level of psychological understanding that is appropriate. Though it is invalid to confuse "higher" and "lower" realms, yet similar structural characteristics apply to corresponding levels in both domains. Thus the "highest" (transcendent) physical level is required to explain the "lowest" (immanent) physical level. This is very relevant when one reflects on the reduced search in Physics for a "Theory of Everything".

Another important "vertical" application relates to the connection as between transpersonal and prepersonal development (and prepersonal and transpersonal).

We can only properly interpret the "lower" prepersonal in terms of the corresponding "higher" transpersonal levels.

So if we want to adequately translate the confused bi-directional understanding of a "lower" level such as L2, then we need the mature bi-directional understanding of the corresponding "higher" level of H2. Thus the attempt to translate the "lower" prepersonal levels through the lens of one-directional methods (such as vision-logic) strictly speaking is inappropriate.

Integral 3

This is based on the understanding of H3 and the application of bi-directional understanding to horizontal, vertical and diagonal polarities.

This leads to the most refined appreciation of qualitative science and is most suited to true integration of reality at all levels. In direct terms it culminates with the experience of spiritual emptiness (with erosion of rigid dualistic understanding in terms of all three polarities).

This form of understanding is best suited for a true holistic "Theory of Everything" (where physical and psychological structures are ultimately identical).

Radial 1

The Radial Methods are based on the mature combination of both one-directional and bi-directional approaches enabling one to properly analyze and synthesize reality.

With Radial 1 there is some division as between global and local understanding. In other words, one will have an overall worldview (combining the interaction of both differential and integral understanding) which will not be fully reflected in immediate responsibilities.

Radial 1 is the basis however for the most comprehensive scientific approach that combines both quantitative (analytic) and qualitative (synthetic) considerations.

The nature of this science can be given a precise holistic mathematical interpretation.

Mathematicians recognize the existence of both real and imaginary numbers. A complex number has both a real and imaginary component.

In holistic mathematical terms, conventional science, with its quantitative analytical bias (based on one-directional understanding) relates to the "real" world.

However Holoscience - by contrast - with its qualitative synthetic bias (based on bi-directional understanding) relates to the "imaginary" world.

Thus a complete scientific understanding is "complex" (combining both "real" analytic and "imaginary" synthetic components).

This comprehensive kind of science only properly unfolds with Radial 1 understanding (which in Christian mystical terms would relate to early development of the Unitive life).

However though the spiritual characteristics of the Unitive life have been outlined in the mystical literature, little or no attention has been given to precise clarification of the scientific worldview (consistent with this development).

Radial 2

It represents the most complete development possible where differential and integral understanding interpenetrate to a considerable extent.

Its is consistent with a very creative and dynamic involvement in secular affairs (combined with constant spiritual absorption).

Because differential and integral aspects are so harmoniously combined it approaches a state of pure simplicity.

So overall we have three different types of translation methods (which should not be confused).

1) "Real" Differential Methods
These are based on the either/or distinctions of the logic of form and are uni-directional in nature. They are directly suited to analysis of reality.

I have distinguished three such translation methods Differential 1, Differential 2 and Differential 3.

2) "Imaginary" Integral Methods
These are based on the both/and distinctions of the logic of emptiness and are bi-directional in nature. They are directly suited to synthesis of reality.

Again I have distinguished three such translation methods Integral 1, Integral 2 and Integral 3.

3) "Complex" Radial Methods
These harmoniously combine the two logical systems (with uni-directional and bi-directional aspects). They are directly suited to both the analysis and synthesis of reality.

I have distinguished two such translation methods Radial 1 and Radial 2.


Our notions of science have been greatly limited through a translation method based on just one band of the Spectrum. So often it is applied in ways that are not strictly appropriate leading to considerable reductionism and confusion.

When properly understood a wide range of translation methods are available (each with a limited range of validity). The recognition of this important fact within Consciousness and Integral Studies has the capacity to revolutionize the entire field.


1.The holistic mathematical model for this is based on a very simple idea. There is a well-defined circular number system (that complements the conventional linear interpretation). This circular system provides the direct basis for a qualitative (as opposed to quantitative) interpretation of mathematical symbols.

This circular system is found by using numbers to obtain roots of 1.

Of special importance are the roots obtained from using 2, 4 and 8.

Using 2 (obtaining the square root) we get the bi-directional "real" pairing of +1 and -1.

This provides us with our horizontal polarities (represented geometrically along the real x axis).

Using 4 (obtaining the 4th roots) we get the bi-directional "real" pairings of +1 and -1 and "imaginary" pairings of +i and -i. This gives us both horizontal and vertical polarities (represented geometrically along the x and y axes).

Using 8 (obtaining the 8th roots) we get bi-directional "real" pairings of +1 and -1 and "imaginary" pairings of +i and -i and "complex" pairings (with equal "real" and "imaginary" values).

This gives us horizontal, vertical and diagonal polarities (represented along the x and y-axes and intersection of both).

The geometrical representation of these simple mathematical relationships closely resembles many mandala diagrams (which are used to symbolize integration). However there is a very deep holistic mathematical explanation for their true nature.

Indeed when we interpret these three polarities in terms of the two logical systems (of form and emptiness) we generate a "Theory of Everything".

The entire Spectrum in terms of levels, transitions, sub-levels, directions, stages and phases can be precisely structured in holistic mathematical terms using these "real", "imaginary" and "complex" distinctions.

2. The logic of form literally involves the separation of opposite polarities (positive and negative) so that we identify truth with just one pole (i.e. the positive).

The logic of emptiness literally involves combining both poles (positive and negative) so that they are cancelled out (in phenomenal terms). So we identify truth with nothing in phenomenal terms (i.e. emptiness).

This tendency is very evident in the religious traditions.

In the West - where the logic of form predominates - the three major religions are monotheistic (based on the notion of One God).

In the East - where traditionally the esoteric traditions embraced the logic of emptiness - there is a greater emphasis on ultimate reality as a void (i.e. nothing in phenomenal terms).

3. In direct terms the void (0) is intuitively experienced in spiritual terms. However in dynamic terms this intuitive experience cannot be divorced from bi-directional rational understanding. In other words the first step in moving from rigid phenomenal (dualistic) to intuitive (nondual) awareness is to create paradox in terms of the dualistic interpretation (through bi-directional understanding). This prepares the mind for a qualitative transformation where the paradox is intuitively reconciled. This intuitive awareness in turn facilitates a greater recognition of the rational paradox of dualistic interpretations. So in dynamic terms, direct intuitive awareness and indirect bi-directional understanding are inseparable.

4. Again this is based on the holistic "Theory of Everything" (already mentioned).

5. Each level involves a unique configuration of both linear (1) and circular (0) understanding with "real" (horizontal), "imaginary" (vertical) and "complex" (diagonal) interpretations.

So there is a clearly defined (holistic) mathematical structure underlying every level.

In general "lower" levels represent confused configurations, and "higher" levels properly integrated configurations (involving similar structures).