Holistic Mathematics - Type 1 Integration

Integral Approach

Q  We move on now to Integral 1 approach providing the first of the genuine integral interpretations of development. Can you briefly start by clarifying what you mean by a "genuine integral approach"?

PC A genuine integral approach is inherently dynamic combining the interaction of both differentiated and integrated aspects of understanding. Because - in experiential terms - we can only integrate what has been already differentiated, integral interpretation is therefore based on the transformation from differentiation to integration in development (and in reverse manner on the reduction of such integration to differentiated understanding).

As we shall see in this context integration - that is directly spiritual - is always associated with a very refined type of (circular) bi-directional differentiated understanding, that initially derives from an alternative either/or logic.

In my approach the most comprehensive form of interpretation i.e. radial, incorporates this dynamic type of circular understanding (both integration and differentiation) with the more stable form of linear understanding encountered in our last discussion (incorporating both linear differentiation and integration).

Therefore in general terms we can distinguish three types of interpretation.

  • Linear (in holistic binary format 1). This defines analytic interpretation relating to rational Type 0 understanding corresponding to the middle level of the Spectrum (L0,H0). It uses asymmetric either/or logic based on the clear separation of polar opposites.

  • It is primarily suited as a means of stable differentiation and can only deal with integration by effectively reducing it to differentiation.
  • Circular (in holistic binary format 0). This defines holistic interpretation relating to transrational understanding (Type1, Type 2 and Type 3) corresponding to the three "higher" levels of the Spectrum H1, H2 and H3 (which also dynamically includes the three "lower" L1, L2 and L3). Such understanding is based on the circular transformation through which bi-directional differentiated understanding is "converted" using paradoxical both/and logic in an intuitive integral manner (and the corresponding reduction of such intuitive understanding in a bi-directional either/or fashion). Such both/and logic - which is dynamically symmetric in paradoxical manner - is based on the complementarity (and ultimate identity) of opposite poles.

  • It is primarily suited as a means of subtle integration (which properly preserves its qualitative distinction from associated differentiation).
  • Radial. This is both linear and circular (in binary format 1 and 0) This defines the more comprehensive understanding (both analytic and holistic) using rational and transrational understanding (Type 0, Type 1, Type 2 and Type 3) thus incorporating all levels of the Spectrum.

  • It combines both/and logic (suited for integration) and either/or logic (suited for differentiation) in equal balance.
As we shall see later these three main types of understanding can be further refined to yield - in my approach - eight distinctive types of intellectual interpretation.

Thus the linear (analytic) type interpretation is subdivided into three i.e. linear 1 (concrete and formal rational), linear 2 (vision-logic) and linear 3 (mirror understanding).

The circular (holistic) type interpretation is also sub-divided into three i.e. circular 1 (Type 1 complementarity), circular 2 (Type 2 complementarity) and circular 3 (Type 3 complementarity).

Finally the radial (comprehensive) type interpretation is sub-divided in two i.e. radial 1 (interpenetration of linear and circular with some restriction) and radial 2 (interpenetration of linear and circular without restriction).

Nature of Integral 1 Understanding

Q Can you now start to explain more fully the nature of Integral 1 understanding relating it closely to the circular (and linear) number system?

PC In holistic mathematical terms understanding is literally two-dimensional i.e. two-directional.

This means that - in any phenomenal context - two opposite polarities are necessarily involved (which are complementary).

Now if we go back to our vertical number 12 , the two here refers to this dimensional characteristic.

As I have stated before, in direct terms the meaning here is circular, where 2 refers to the complementarity (using both/and) logic of positive and negative polarities. So in spiritual intuitive terms - which is its direct expression - Integral 1 understanding is strictly non-dimensional and empty (i.e. where the two opposite polarities cancel out).

Thus we have a linear interpretation whereby we formally identify the two opposite polarities (in dualistic fashion); likewise we have a circular interpretation where we see the two poles as complementary (and ultimately identical).

Q Can you illustrate this, distinguishing clearly bi-directional differentiated understanding from corresponding integral understanding?

PC We have already dealt with the conventional scientific manner of relating perceptions (facts) and concepts (theories). Though these are - relatively - quantitative and qualitative, in the rational (Integral 0) interpretation, both are effectively reduced in terms of each other.

So rational science is unable to properly distinguish as between the differentiation of phenomena and their corresponding integration with - in any context - the (circular) integral reduced to the (linear) differentiated aspect.

Let us now look at the Integral 1 interpretation.

We start here with the positing of a linear perception such as a number (corresponding to the horizontal quantitative recognition of unitary form). In other words the very identification of an actual perception is quantitative (in a unitary manner).

Now the corresponding circular concept of number dynamically represents - in relative terms - the vertical qualitative dimension as emptiness (to which the actual number is related).

Thus if the initial perception is actual (in finite terms), the corresponding concept is - relatively - potential (and strictly infinite) in dynamic terms.

In other words in order to switch from the understanding of the (actual) perception to the corresponding (potential) concept, the positive direction of the perception must - at least implicitly - be dynamically negated thereby enabling the qualitative change to be made. Thus the fusion of both positive and negative polarities of the actual number perception leads to the (unconscious) generation of spiritual intuition as emptiness. This represents the general experience of the concept (i.e. as potentially applying to all number perceptions within its class).

Thus the integral number concept is primarily intuitive and experienced as emptiness, representing the complementary (and ultimate identity) of positive and negative polarities of form.

However this potential experience of the dimensional concept is then rationally differentiated in a linear fashion as applying to all actual perceptions (within its class).

Thus the number concept - as indeed every concept - has both a rational differentiated (as applying to all number perceptions) and an intuitive integral interpretation (as potentially applying to all number perceptions).

The rational differentiated interpretation is linear, based on either/or logic (arising from the unambiguous separation of polar opposites). However implicitly it requires the support of spiritual intuition (arising from integral understanding).

The intuitive integral interpretation is by contrast circular based on the both/and logic (arising from the ultimate identity of polar opposites). However indirectly this must be supported by rational differentiated understanding.

Therefore in a comprehensive understanding - which is radial - equal emphasis must be placed both on rational differentiation (which is primarily of an unambiguous linear nature) and intuitive integration, which is spiritually empty (and from a phenomenal perspective dynamically approached in a paradoxical circular fashion).

So integration (as spiritually empty) is serviced by a special form of bi-directional differentiation. Here dualistic distinctions which are valid in terms of isolated polar reference frames are rendered paradoxical in terms of each other.

Thus an integral approach must necessarily - in dynamic terms - entail both form and emptiness (and emptiness and form) in a special way.

In other words the spiritual emptiness which primarily defines any integral state is always dynamically associated with a bi-directional appreciation of differentiated phenomenal form. Both aspects mutually enhance each other with bi-directional differentiation facilitating the qualitative transformation to nondual integral awareness and equally such integral awareness equally facilitating the more ready paradoxical appreciation of form (at a reduced differentiated level).

However the key emphasis with integration is on transformation and emptiness (through increasingly dynamic appreciation of paradoxical phenomenal interaction)

A differentiated approach also - in dynamic terms - entails both form and emptiness (and emptiness) in a unique manner.

Here the one-directional appreciation of phenomenal form (through the separation of polar opposites) implicitly requires the intuitive energy (provided by the degree of spiritual integration already attained).

However the key emphasis is now on reductionism and form (through the stable - and unambiguous - identification of distinct phenomena).

So both aspects are necessary for each other. Lack of sufficient differentiation sets dynamic limits on the degree of integration that can be attained; likewise lack of sufficient integration sets limits on the degree of differentiation that is possible.
A radial approach then combines both aspects through the marriage of contemplative transformation with active engagement in the world of material forms.

Q You have already explained the process by which we move from differentiated appreciation of a perception to corresponding integral appreciation of its concept.
Can you now briefly explain the reverse process whereby we move from the differentiated appreciation of a concept to integral appreciation of its corresponding perception?

PC Here we start with our rational interpretation of the number concept (as applying to all actual number perceptions). Now the dynamic transformation enabling the qualitative switch to recognition of the corresponding number perception, implicitly requires recognition of the complementarity of opposites (in relation to both positive and negative polarities of the concept).

Again this paradoxical appreciation of the concept leads to an empty spiritual recognition of the perception as potentially containing (as immanence) the number concept. In other words in this spiritual recognition the perception is infinite (as reflection of the whole number concept).

However this potential recognition of the perception - as spiritually infinite - quickly collapses to the actual finite recognition of an actual number.

Q I can see what you are getting at here! You are attempting to explain a process - which customarily is explained in merely rational terms - in a more subtle manner, which preserves the dynamic interaction of both spiritual intuition and reason (and reason and spiritual intuition)!

PC Yes! Though the importance of spiritual intuition may well be recognised for all creative scientific endeavour, in formal terms it plays no role in its interpretations. So from a dynamic perspective, science offers a somewhat reduced and distorted interpretation of reality.

Put another way it reduces the integral in terms of the (merely) differentiated interpretation of phenomena.

Not alone does an appropriate dynamic approach open up vast possibilities for new interpretations of integral science, it also can greatly enhance appreciation of the established analytic approach.

Q Going back to our earlier discussions, where you commented on the holistic importance of 0, 1 and 2, I can see now how you have extended this appreciation to both phenomenal quantities and qualities (as dimensions). Can you briefly comment?

PC Again in holistic terms 1 can be associated with unitary form, 0 with spiritual nothingness (or emptiness) as the potential for actual form.

2 can be associated with duality (through the separation of polar opposites).

As we have seen - in any context - dual understanding arises from positive (+) appreciation of phenomena (i.e. based on the separation of polar opposites).

Differentiation thereby always arises from combining poles (e.g. exterior and interior) in a (merely) positive manner as two separated poles.

So 1 + 1 = 2 in holistic (as in analytic) terms.

Now - in dynamic terms - 1 and 0 are connected with each other through the corresponding negation of what has been posited.

So 1 – 1 = 0 again in holistic (as in analytic) terms.

In other words through appreciation of the complementarity and ultimate identity (of opposite poles) form (1) gives way to emptiness (0).

Thus integration and nondual awareness arises from both the positing and negating of opposite poles as complementary (and ultimately identical).

So differentiation is primarily based on either/or logic (and the positing of opposite poles)

Integration is primarily based on both/and logic (and the negation of what has already been posited).

We then went on to explain how the switch from quantity to quality (or dimension) and quality to quantity always entails a corresponding switch in logical interpretation from either/or to both/and (and both/and to either/or).

Integral 1 Interpretation of Dimensions

Q This new notion of dimension fascinates yet puzzles me at the same time.

It seems to based directly on mathematical notions (with a holistic interpretation).

However it does not seem to bear any obvious relationship to physical notions (3 space and 1 time). Can you clarify your dynamic interpretation further and show its relationship - if any - to conventional interpretation?

PC In dynamic terms, the four dimensions are synonymous with the fundamental polarities (horizontal and vertical) which are positive and negative with respect to each other.

In terms of an Integral 1 interpretation, space has both positive and negative aspects; time also has both positive and negative aspects.

We have already described this process. To experience and posit an object (in space) we thereby negate the dimension of space (to which the object is related).

In reverse fashion to posit the dimension of space we thereby negate the object (to which the dimension is related).

In this way object phenomena and dimensions are intimately related to each other (and ultimately interdependent).

The process is similar in relation to time. We can only posit an object (in time) by negating the dimension (to which the object is related); likewise we can only posit the dimension of time by negating the object (to which it is related).

This dynamic integral appreciation is naturally geared to deal with both physical and psychological experience of dimensions (and objects) which are - relatively - positive and negative with respect to each other.

Thus - for example - to switch from the experience of an object located in physical space to its corresponding experience in psychological space we must dynamically negate the former (physical) before then positing the latter (psychological) aspect.

Likewise to switch from this psychological back to the physical spatial experience of the object, we again must negate the former (psychological) before positing the latter (physical) aspect.

Q Can you go into these dynamics more fully to show how physical and psychological aspects are related?

PC As we have stressed so often from a nondual integral perspective, any ultimate identification of polar opposites such as exterior and interior and space and time is paradoxical.

So we can only attempt to approach this dynamic appreciation by fixing our frame of reference in an arbitrary dualistic fashion.

In this context it may initially helpful to identify the experience of space with the affective and the corresponding experience of time with the cognitive aspect of understanding respectively.

Therefore from this perspective we identify an exterior physical object phenomenon in space through the (affective) senses.

For corresponding interior psychological recognition of the object in space to take place we must first - to a degree - dynamically negate this exterior perception before positing its opposite aspect.

Whereas the affective sense recognition constitutes a means of response to the object, by contrast - in relative terms - the cognitive aspect represents a means of corresponding control.

Thus to experience in physical time we must posit the object phenomenon in an exterior cognitive manner. Once again the corresponding switch to psychological recognition of the object in interior time, requires the negation of its opposite (exterior) aspect.

Now equally we could initially start with the dimension (to which the object is related) and trace out similar switching dynamics for both exterior (physical) and interior (psychological) recognition of both space and time.

The important insight here is that whereas the object phenomenon (to which the dimension is related) arises from perception (in both an exterior and interior manner), the dimension (to which the object is related) arises from corresponding conceptual understanding.

Thus the manner through we dynamically switch from recognition of object phenomena to corresponding dimensions (and dimensions to corresponding object phenomena) coincides with the complementary manner through which we switch in experience from perceptions to concepts (and in reverse manner from concepts to perceptions).

Q. Can this understanding be generalised for all life forms?

PC Yes! In the most fundamental sense perception and conceptual understanding relate to the manner through which we switch from recognition of a part to whole (and whole to part) identity which is shared - however primitively - by all life forms.

Thus the creation of a space and time environment (physically) is inseparable from corresponding whole/part (and part/whole) recognition psychologically. So ultimately - from a dynamic integral perspective - it is futile to attempt to view phenomena (as for example membranes and strings) in a merely physical manner.

From a dynamic perspective, physical and psychological aspects are always complementary and vitally necessary for proper understanding of either aspect.

Q You seem to be implying that current notions of object phenomena and dimensions are clearly inadequate. It is true as you say that we attempt to look on objects and dimensions in science as if they have an independent merely physical interpretation. Are you saying that this is untenable?

PC My position is more subtle than that. I have always recognised the great value and achievements of analytic science which - in terms of my approach - is based on Type 0 understanding.

However when we come to a proper integral appreciation - which necessarily views all levels of reality in terms of the interdependence of its complementary physical and psychological aspects - conventional scientific interpretation indeed breaks down. This does not of course entail that we should abandon such science. Rather it means that in terms of a proper integral appreciation we require a very distinctive type of understanding that applies to all our fundamental notions.

Q How do we switch in dynamic integral terms from recognition of objects to their corresponding dimensions (and from dimensions to objects). How indeed do we fundamentally switch from recognition of space to time (and in corresponding manner from time to space)?

PC Clearly in an integral appreciation (where physical and psychological aspects are complementary) we cannot attempt to explain one aspect without proper recognition of the other. In other words our ability to recognise space and time (with associated object phenomena) in our physical environment is inseparable from the psychological dynamics through which we psychologically are enabled to form both perceptions and concepts.

Now the very nature of an Integral 1 approach is that it is based on Type 1 complementarily involving opposite poles (which are directly positive and negative with respect to each other).

Therefore we can satisfactorily explain in an Integral 1 approach how switching as between objects (in either space or time) takes place as between physical and psychological interpretation (which are - relatively - exterior and interior with respect to each other).

We can also show how switching as between dimensions (either space or time) takes place with respect to both physical and psychological interpretation.

However we cannot fully explain how switching as between objects in space and time (and in reverse manner objects in time and space) takes place; neither can we fully show how switching as between space and time (and time and space) dimensions takes place.

This ultimately requires an Integral 3 approach (with associated Type 3 complementarily).

However we can say a certain amount at this stage.

Dynamic negation - which psychologically relates to the intervention of the unconscious - always plays two important roles in experience.

Firstly it is necessary to enable dualistic switching as between (direct) polar opposites. In this way one for example one is enabled to switch from dualistic exterior recognition of an object in physical space to corresponding interior recognition in psychological space.

Secondly, as a result of negation a certain spiritual fusion of opposites occurs which indirectly expresses itself through a qualitative change in experience.

In other words experience switches from (conscious) recognition of localised phenomena to corresponding archetypal (unconscious) recognition of the universal nature of phenomena.

This enables the important switch as between perception and concept (and concept and perception); likewise it enables the equally important switch as between space and time (and time and space).

Q Are you thereby saying that a proper appreciation of the nature of space and time from a physical perspective, requires the full incorporation of conscious and unconscious in psychological terms?

PC Precisely! However this requires an Integral 2 approach (with Type 2 complementarity). We will see then how the holistic interpretation of mathematical symbols provides a remarkable means for encoding the precise relationship as between conscious and unconscious which is equally associated with the complementary similar encoding of the relationship between objects and their related dimensions.

Q Can we come back to you Integral 1 interpretation of the relationship between space and time. I am trying to get some insight into the implications of this dynamic viewpoint.

It seems that you are saying that - from the Integral 1 perspective - every object phenomenon (in space and time) has two directions (positive and negative) and likewise that the corresponding dimensions of space and time have two directions (positive and negative). But what this all mean?

PC If you think back to our earlier discussion on Heraclitus, we discussed how the very notion of direction is always inherently paradoxical. In other words to give unambiguous meaning to any direction, we must fix the polar frame of reference in an arbitrary manner (when the opposite frame is equally valid).

Thus in the context of any pair of polar opposites there are two equally valid means for defining direction (by fixing the frame of reference arbitrarily with each pole). Though each of these gives an unambiguous interpretation within its own frame (i.e. positive), in dynamic interdependent terms they are opposite (i.e. both positive and negative) with respect to each other.

Let us illustrate this with reference to the distance in space and time as between the Earth and the Sun (and Sun and Earth).

Now in conventional analytic interpretation, the Sun is roughly 90 million miles (in space) from the Earth and about 9 minutes in time (i.e. it takes 9 minutes for the light from the sun to reach Earth).

We can in fact measure this distance in two ways. Firstly we can fix the frame of reference with the Sun. So the Earth is 90 million miles (in space) and 9 minutes (in time) from the Sun. Alternatively we can fix the frame of reference with the Earth. So now the Sun is 90 million miles from the Earth (in space) and 9 minutes (in time).

When we treat both of these measurements in an isolated absolute fashion (i.e. ignoring the change in direction) they give the same unambiguous result.

This typifies analytic Type 0 interpretation.

However in dynamic relative terms (where both poles are viewed simultaneously) it looks very different. Thus if the Earth is viewed as 90 million miles forward in space from the Sun, then - relatively - the Sun is 90 million miles backward (in space) from the Earth.

Likewise if the Earth is viewed as 9 minutes forward in time from the Sun, then - relatively - the Sun is 9 minutes backward (from the Earth).

Thus in dynamic relative terms movements in both space and time are positive and negative with respect to each other.

So from an Integral 1 perspective, all objects are defined bi-directionally (with respect to space and time). Likewise the dimensions themselves of space and time are also defined bi-directionally (with respect to corresponding objects).

Q Can you explain how this integral bi-directional interpretation (of both object phenomena and dimensions) can be fully consistent with nondual spiritual awareness?

PC Spiritual experience - which is empty and ineffable - relates directly to the present moment (where phenomenal object and dimensional notions have strictly no meaning).

However phenomenal notions of form are dynamically defined with respect to relative notions of space and time.

Thus when we properly appreciate the truly bi-directional nature of all object and dimensional interpretations, phenomenal notions of measurement (which are positive and negative with respect to each other) continually cancel each other out. So therefore from one perspective, spiritual emptiness existing in the present moment finds temporary relative expression in a paradoxical world of forms where objects and dimensions are - relatively - positive and negative with respect to each other. Also the transparency of phenomenal form thereby experienced relates directly to the fluidity of interaction as between opposite poles so that when such interaction is limited phenomena assume a somewhat rigid appearance.

Equally from the other perspective, relative notions of phenomenal form cancel out in dynamic interactive terms giving way to nondual spiritual of emptiness (existing in the continual present moment).

So form and emptiness (and emptiness and form) are intimately connected through nondual awareness that is dynamically associated with paradoxical bi-directional appreciation of polar opposites.

Q And all of this has complementary psychological interpretation?

PC Yes! As we have seen in psychological terms, the bi-directional interaction of objects and dimensions (and dimensions and objects) is mirrored by the corresponding complementary interaction of perceptions and concepts (and concepts and perceptions).

Thus with Integral 1 appreciation, perceptions and concepts (and concepts and perceptions) are understood in a true bi-directional fashion (reflecting the growing interdependence in experience of both exterior and interior aspects).

Q It would follow from what you are saying that we can never experience phenomena of form in the present moment.

PC Good point! Phenomena of form (either as objects or dimensions) are always experienced with respect to what is - relatively - past and future in space and time.

This entails exactly the same dynamics as discussed in relation to measuring distances as between Sun and Earth (and Earth and Sun).

All measurements take place with respect to the nondual present moment (with positive and negative directions). Because object phenomena are necessarily to a degree separated, space and time distances are involved, which are - relatively - forward and backward (i.e. positive and negative) with respect to each other.

Thus if an (exterior) event is measured as forward with respect to the (interior) self in either space or time, then the self is thereby measured as relatively backward with respect to this event.

Once again, when direction is based on isolated polar reference frames (either with respect to the exterior or interior aspect taken separately) it appears absolutely similar. However when considered in dynamic fashion using interdependent reference frames, direction with respect to either space or time always has both positive and negative interpretations which - when fully related - cancel out as the nondual present moment.

Thus the analytic (differentiated) interpretation of space and time is fundamentally based on isolated polar reference frames.

By contrast the holistic (integral) interpretation is based on dynamically interdependent reference frames ultimately leading to the very dissolution of phenomenal notions of space and time in the nondual present moment.

Furthermore the integral interpretation is directly based on the holistic mathematical notion of (circular) dimension.

Conventional Understanding of Space and Time

Q How do you relate the conventional understanding of 4 dimensions (3 space and 1 time) with your dynamic integral interpretation?

PC The first point to recognise is that the conventional interpretation of dimensions is based on merely positive notions i.e. forward direction with respect to both space and time (which is what would be expected in an analytic approach).

Secondly the interpretation is asymmetric (with 3 space dimensions and 1 time).

However there are certain flaws in evidence (even from an analytic perspective).

The notion of 3 dimensions of space derives from the customary rigid dense nature of object phenomena observed in space. Thus when I now look at my computer it reveals 3 space dimensions i.e. length, breadth and height.

To recognise these 3 dimensions, one momentarily separates the interior aspect (which in this context represents the qualitative time dimension) from space (which manifests itself in terms of quantitative object manifestations).

However what is consistently overlooked in conventional interpretation is that we must necessarily reverse this process in order to establish the location of physical object phenomena in time.

Therefore when we perceive an object in time, once again we separate space and time.

However now the interior aspect represent the qualitative space dimension with time manifesting itself as 3 quantitative dimensions (length, breadth and height) that can be measured in terms of time.

Q What do you exactly mean by 3 quantitative time dimensions? I can readily appreciate how we can measure physical objects in terms of 3 space dimensions but I cannot yet see how this
applies to time?

PC Perhaps the best way of appreciating this is through a  common measuring device which is light. As you know light travels at 186,000 miles a second (approx). So therefore we can convert all space measurements into time (i.e. as the time taken by light to travel a certain distance). Therefore the three dimensions - which customarily are measured in terms of space - can equally be expressed in time units.

Once again there is a "shadow" analytic interpretation of dimensions that is overlooked in conventional terms. This is due to a failure to properly distinguish quantitative from qualitative notions.

Thus space and time measurements can be applied in quantitative terms to objects (within dimensions).

Equally space and time can be interpreted in qualitative terms as the dimensions (within which object phenomena are contained).

As we have seen the analytic recognition of object phenomena requires the separation of the quantitative from the qualitative aspects. This inevitably results in its characteristic form of reductionism (where quantitative and qualitative aspects are reduced in terms of each other).

Thus (exterior) object phenomena can be viewed in terms of 3 (quantitative) dimensions of space and 1 (qualitative) dimension of time.

Equally (exterior) object phenomena can be viewed in terms of 3 (quantitative) dimensions of time and 1 (qualitative) dimension of space.

Q Can you now relate this perspective on physical dimensions with your psychological interpretation of the relationship between perceptions and concepts?

PC In this context, perceptions equate with quantitative objects and concepts with qualitative dimensions respectively.

In order to view object phenomena in dual analytic terms we must separate (qualitative) concepts from (quantitative) perceptions.

There are two ways in which this can be done.

We can fix (exterior) perception in an (affective) sense and the corresponding (interior) concept in a (cognitive) rational fashion.

The perception will then correspond to the familiar case of a (quantitative) 3-dimensional object in space with the concept providing the corresponding (qualitative) 1 dimension of time.

Alternatively we can fix (exterior) perception in a (cognitive) rational and the corresponding (interior) concept in an (affective) sense fashion.

The perception will now correspond to the mirror unrecognised case of a (quantitative) 3-dimensional object in time with the concept providing the corresponding (qualitative) 1 dimension of space.

Our actual experience of phenomena (as objects and dimensions) necessarily entails the interaction of both perspectives. The very rigidity of both object and dimensional recognition that typically occurs in physical terms, largely results from the reduction of the alternative mirror perspective to conventional interpretation.

This rigidity of physical phenomena is directly associated with the corresponding rigidity of both perceptions and concepts in psychological terms with - again - the mirror perspective reduced to conventional interpretation.

Thus typically the perception of object phenomena (in space) is associated with the (affective) senses. However in dynamic terms such recognition necessarily entails the interaction of both rational and sense aspects. However as regards actual observation, the rational is reduced literally to common sense interpretation.

Q I see what you are getting at. You are trying to balance the analytic asymmetric interpretation of dimensions with alternative mirror explanations, both of which then serve as the appropriate basis for moving towards the more dynamic integral approach. So far you have shown that the four dimensions can be equally viewed in terms of 3 space and 1 time (or alternatively 3 time and 1 space). However is there not still an imbalance as between quantitative and qualitative in that the 3 dimensions in each case are defined in quantitative (rather than qualitative) terms?

PC Your observation is correct! However the prime focus so far has been on the exterior recognition of phenomena. Not surprisingly the position is exactly reversed when we look at recognition of such phenomena from an interior subjective perspective. Again we have two equally valid interpretations in terms of 3 qualitative space dimensions and 1 quantitative time (and alternatively 3 qualitative time dimensions and 1 quantitative space). In this way combining both exterior and interior recognition we have perfect (static) balance in terms of asymmetric interpretation.

This paves the way for the movement towards corresponding (dynamic) balance in terms of integral symmetric interpretation (combining positive and negative polarities).

Q This is all seems very novel and therefore very difficult to intuitively assimilate. Is there any practical basis for your assertions?

PC Yes! I have always been greatly interested in providing to my own satisfaction a proper philosophical basis for mystical type appreciation of reality and also developments in modern physics (both of which I believe have been greatly neglected). Indeed the first great influence on my philosophical development was Einstein’s Theory of Special Relativity.

When we move on to Integral 3 understanding we will be able to fully translate the above views on space and time in holistic mathematical language showing in the process how it provides a complementary holistic philosophical interpretation that exactly mirrors one of the key findings of Relativity Theory.

Indeed though I am critical in many respects of the reductionist nature of modern physics, I greatly admire the intellectual brilliance of its many pioneers at the cutting edge of enquiry. Also I find it immensely stimulating and a wonderful catalyst for fruitful philosophical speculation.

  Integral 1 Approach and Development
Q Can you now briefly describe the implications of the Integral 1 approach for development?

PC Once again this approach combines integration with a special form of bi-directional differentiation, both of which are dynamically interdependent with each other.

Now in terms of holistic mathematical interpretation, differentiation is based on either/or logic and is linear and sequentially asymmetric in nature.

However there are really two forms of differentiation i.e. uni-directional and bi-directional and it is this latter type that is properly compatible with an integral approach.

In the uni-directional approach development is viewed in an unambiguous manner where it is defined in terms of just one asymmetric sequence of relationships.

Such an interpretation for example characterises the holarchic approach to development where every (lower) holon is defined as part of a (higher) holon.

So in this way higher development is viewed as the progressive movement to more collective wholes.

One example of this holarchic approach is the view that atoms are contained in molecules, which are contained in cells, which are contained in organisms and so on.

However such one-directional differentiation is always based on an arbitrary fixing of the polar frame of reference (where we could equally choose the opposite pole).

Thus though the relationship of whole and part (and part and whole) is dynamically interdependent, holarchy fixes the frame of reference with the whole aspect.

This requires us in a sense to pre-define the lower whole in any sequence when in truth it can only get its meaning in the context of higher wholes.

So - as with every asymmetric sequence - there is an equally valid mirror interpretation based on switching of the polar frame of reference.

Thus the mirror counterpart of holarchy is partarchy, where ever (lower) part is whole (in the context) of a higher part.

Thus from the perspective of partarchy, development can be equally viewed - in asymmetric terms - as the progressive movement to ever more unique parts.

Though each of these interpretations (holarchy and partarchy) give unambiguous consistent interpretations within their own (independent) frames of reference, in terms of each other (where polar opposites are interdependent) they paradoxically move in opposite directions. Thus what is "higher" from one perspective is "lower" from the other and likewise what is "lower" from one is "higher" from the other perspective.

So integration is based on combining these bi-directional differentiated interpretations which are always positive and negative with respect to each other. Thus the keener the paradoxical appreciation of such dualistic relationships of form at a differentiated level, the purer can be the realisation of intuitive awareness in empty spiritual terms.

This realisation of spiritual emptiness in a transformed integral fashion in turn enhances the paradoxical bi-directional appreciation of form at a reduced differentiated level.

Holarchy and partarchy relate to the vertical poles of development.

An Integral 1 approach however also requires similar bi-directional differentiated appreciation in terms of both horizontal poles (exterior and interior) and diagonal (form and emptiness).

Hopefully we will be able to illustrate further the nature of the Integral 1 approach in future discussions.

Q How would you contrast the Integral 1 with the Integral 0 approach?

PC In the Integral 1 approach, differentiation is clearly distinguished from integration.

To make differentiation dynamically compatible with integration, a very refined bi-directional approach is required where every asymmetric interpretation (defined in terms of one arbitrarily fixed pole) is understood to have a mirror image interpretation. The attempt to view both interpretations in simultaneous interdependent terms then provides the appropriate basis for moving to integration.

In the Integral 0 approach, differentiation is not satisfactorily distinguished from integration. Development is essentially viewed in terms of unambiguous asymmetric type sequences (suited to differentiation) with integration then largely accommodated to these notions. In terms of intellectual interpretation, such an approach cannot properly distinguish qualitative from quantitative (and quantitative from qualitative) aspects of relationships and in effect reduces integration to differentiation.

Even when nondual spiritual awareness is viewed as of primary importance, the Integral 0 approach cannot properly incorporate nondual with dual notions leading to a considerable unresolved discontinuity as between both aspects.

Q. What are the main limitations with the Integral 1 approach?

PC It is based on one limited notion of dynamic complementarity (i.e. Type 1 complementarity) which is based on relating poles (horizontal, vertical and diagonal) that are directly opposite to each other. However it cannot yet deal with the other important forms (Type 2 and Type 3).

What this means from a psychological perspective is that the role of the unconscious for the understanding of all relationships cannot yet be satisfactorily interpreted in a satisfactory manner. This requires Integral 2 understanding. .

Even less can the combined dynamic interpenetration of conscious and unconscious be satisfactorily reconciled in dynamic fashion with spiritual understanding.

This requires Integral 3 understanding.

Also while the focus is primarily on integral understanding, there can be a temporary loss in capacity for differentiated understanding that characterises analytic type appreciation. Thus from a spiritual perspective the focus of such development can be unduly contemplative.

Thus it requires the unfolding of the radial stages to restore proper balance as between holistic (integral) and analytic (differentiated) type understanding.