Nature of Holistic Mathematics
Q You make very bold claims regarding Holistic Mathematics. Do you really believe that every analytic mathematical symbol and relationship - regardless of how abstruse - can be given a distinctive holistic interpretation with a dynamic interactive meaning in integral terms?
PC Yes I do!
Associated with every major level of the Spectrum is a distinctive manner of interpreting reality (with its own uniquely logical way of dealing with relationships).
When approached in this manner it can perhaps be appreciated that conventional mathematics largely represents the logical understanding of the rational stages that comprise the middle level of the Spectrum.
However the "higher" stages are based on a very distinctive transrational logic where spiritual intuition and subtly refined cognition increasingly interpenetrate.
This logic constitutes the appropriate basis for the integral dynamic appreciation of complementary - and increasingly paradoxical - interactions in development.
In conventional mathematical understanding all symbols and relationships are based on rational logic (reflecting the analytic understanding based on the clear separation of polar opposites).
Thus when we consistently interpret these same symbols and relationships through the "higher" logic, a distinctive dynamic appreciation is revealed which constitutes the understanding that is Holistic Mathematics.
So in principle a unique alternative holistic appreciation can be given for all conventional mathematical understanding.
Q This is quite mind boggling. It implies for example that a complex partial differential equation has a dynamic holistic interpretation with a direct application to development!
PC This is true though holistic mathematical appreciation will need to considerably advance before such a relationship can be properly understood in dynamic experiential terms.
In fact the implications are even more startling than we might first imagine.
As you know in conventional mathematics an enormous amount of theory can be developed with no apparent practical relevance to the world.
This cannot be true from a dynamic interactive context.
The apparent mismatch that so often takes place as between theory and application in conventional terms is inherently due to the inadequate philosophical appreciation that pervades standard mathematical understanding.
However by defining all symbols appropriately in the dynamic interactive context in which they arise such a mismatch is not possible as concepts (theory) and perceptions (practice) now fully complement each other.
Therefore - again in principle - the very notion of an abstract theoretical concept with no practical application to reality has strictly no meaning from the dynamic holistic perspective.
Holistic mathematics also has another enormous advantage.
In conventional terms mathematics provides a set of mental constructs that can be successfully applied to the scientific interpretation of physical (exterior) reality. But we do not really see that they have a corresponding role in the interpretation of psychological (interior) reality.
Thus there is a clear polarised split evident here with interior constructs used asymmetrically to interpret exterior reality.
However from a dynamic holistic perspective this subtly changes so that mathematical understanding is now understood as arising from the dynamic interaction of what - in dualistic terms - we identify as separated opposite poles.
Thus Mathematics - by its very nature - has both objective and subjective aspects which necessarily interact in development.
Likewise therefore - in dynamic terms - mathematics always has complementary interpretations in relation to both physical and psychological reality.
Thus in relation to the dynamics of development when we look at it from an interior perspective it reveals itself as a psychological Spectrum with many distinct stages of self.
However equally from the - relatively - exterior perspective it reveals itself as a physical Spectrum with many distinct stages (or planes) of reality.
In dynamic terms these two aspects - which initially may appear separate - are deeply complementary with similar basic structural patterns at every stage (in horizontal, vertical and diagonal terms).
The fundamental nature of these structures can be most precisely - and scientifically - encoded using mathematical symbols given their holistic interactive meaning.
Q How easy have you found it to provide the holistic interpretation of mathematical symbols?
PC Extremely difficult in one sense! I would see two principal reasons for this.
Firstly, as I have repeatedly stressed, holistic mathematical interpretation intimately depends on contemplative type spiritual awareness. Therefore the more refined - and inherently dynamic - the nature of the cognitive mathematical interpretation, equally the more refined must be the corresponding level of spiritual intuitive awareness.
The precision and universality implied by mathematical type understanding makes the use of its phenomenal symbols much more demanding than traditional "looser" religious images when used in a contemplative context.
Indeed this supports the view associated for example with the Pythagoreans, Plato, Nicholas of Cusa and in more recent times Franklin Merrell-Wolff that mathematical symbols potentially provide the most refined means of spiritual meditation.
Secondly, in terms of any sustained development of holistic mathematical type awareness we are still very much at an early infancy stage.
For example I could find very little of - what I would consider - genuine scientific interpretation in relation to the use of holistic mathematical symbols.
Now I am aware that much of this understanding could be already somewhere out there which I have not accessed. Even if this is true - which I somehow doubt - in terms of a general cultural appreciation it clearly has remained very obscure.
However given the remarkable attention and development that has been given to analytic type mathematical understanding over the centuries I find it incredible that holistic interpretation - which has an incredibly powerful integral scientific potential - remains so completely ignored. So much so that it is hard to even have a meaningful discussion with anyone on the topic!
Perhaps we are at a stage in history where this form of scientific understanding is only beginning to properly emerge in our culture. It has been for some years now unfolding in my own psychic development so it could well be unfolding likewise in the minds of others. I would love to think so. Otherwise I would find it hard to understand my long-held passionate conviction regarding its enormous potential.
Q You say that every analytic interpretation of mathematical symbols has a corresponding holistic interpretation with an integral scientific significance.
Can you briefly illustrate at this stage?
PC As we were aware the digital revolution is fast changing the nature of our society. This is fundamentally based on the realisation that all information can be potentially encoded using the two binary digits 1 and 0.
Needless to say in this analytic system 1 is clearly separated from 0 (and 0 from 1) so that they mutually exclude each other in interpretation.
However what is not properly appreciated is that the binary digits have an alternative dynamic holistic interpretation where 1 and 0 are understood as complementary (and ultimately identical) and that all transformation processes can be potentially encoded in this manner.
So for example the varied stages of development can be precisely encoded through the use of the holistic binary digital system. This indeed is the very basis of my own approach to development as I will illustrate later in some detail.
Thus a comprehensive interpretation of the binary digital system i.e. radial, has both analytic and holistic aspects with the potential power to encode both information and transformation processes.
Number: Holistic Interpretation of Binary Digits
Q Let us now examine how you apply your holistic approach to mathematical symbols. We will start with the important notion of number.
Can you tell us what exactly is number?
PC The notion of number is deeply implicit in our attempts to structure reality.
The most important numbers - which I refer to as fundamental - are the
already mentioned binary digits 1 and 0. These are inherent in our ability to distinguish existence from non-existence.
The very identification of phenomena implies the notion of oneness (1).
Thus in distinguishing a (phenomenal) form we thereby identify it as a unit.
Likewise the absence of phenomenal form in any context implicitly implies the notion of nothingness (0).
What is nothing is thereby empty of phenomenal form. So the binary digits (1 and 0) are inherent in our basic notions of form and emptiness.
If I say that there is a chocolate in a box, the identification of this form implicitly requires the notion of oneness (1). We could equally say there is one chocolate in the box.
If I eat that chocolate I would then say that there is nothing (0) in the box.
In other words it is now empty (of chocolates).
Q How would you describe the important relationship as between the one and the many?
PC To properly appreciate this we have to understand reality in dynamic terms.
Phenomenal understanding necessarily entails the dynamic interaction of perceptions with corresponding concepts (and concepts with corresponding perceptions).
Now associated with every (individual) perception is a particular notion of oneness (with an actual finite interpretation).
By contrast associated with every (collective) concept is a general notion of oneness (with a potential infinite interpretation).
The interaction of the general (potential) with the particular (actual) notion of oneness leads to the reduction of the (infinite) one to the many ones i.e. as finite individual units (perceptions).
Likewise in reverse fashion the interaction of the particular (actual) with the general (potential) notion of oneness leads to the transformation of the many (finite) ones into the general notion of oneness i.e. as the infinite collective one (concept).
In this way the one keeps giving away to the many (as particular finite perceptions); likewise the many continually are transformed into the one (as a potentially infinite concept).
Q I see! The riddle of the one and the many and the many and the one is directly tied up with the interaction of the finite and infinite domains in experience. What puzzles me however is the manner that you identify oneness in both finite and infinite terms. Can you briefly explain?
PC We will explore this further. However it should be enough at this stage to recognise that from an analytic perspective (where polar opposites are separated in experience) the notion of oneness applies merely in finite terms.
However in holistic terms the notion of oneness ultimately applies in infinite terms. This is best exemplified in mystical experience (where the dynamics of polar interaction reach their free most unobstructed expression).
Thus the ultimate realisation of Spirit is often expressed as the experience of oneness (i.e. as infinite).
Indeed when one understood that in dynamic terms one - and by extension - all numbers necessarily have both finite and infinite expressions, it becomes easier to appreciate the apparent paradox whereby Cantor showed that - as with the finite - there are many infinite numbers (with the set of all infinite numbers itself infinite).
Q OK! You have been dealing with 1 with regard to its analytic and holistic interpretations. Where does 0 fit in?
PC Once again it is always implicit in the very dynamics of phenomenal understanding, through which perceptions and corresponding concepts (and concepts and corresponding perceptions) interact.
We will look even more closely at the mathematical significance of this shortly.
But for the moment it is important to realise that the very recognition of a phenomenal perception (as an actual finite unit) requires in dynamic terms a corresponding emptying of its related concept.
Thus we become aware of a particular box by momentarily emptying from recognition the corresponding general concept of "box".
So 1 here clearly implies 0 in that the unitary finite perception requires the voiding of the corresponding infinite concept.
In like manner to become aware of the general "box" concept (as potential infinite unit) requires the emptying of recognition of the corresponding particular perception of a box.
So 1 again implies 0, with in this case the unitary infinite concept requiring the voiding of the corresponding finite perception.
So the very dynamics of phenomenal experience entail a continual interaction of form and emptiness (and emptiness and form). This represents the holistic interaction of the binary digits (1 and 0) as between their finite and infinite (and infinite and finite) states.
Q This is fascinating! So what you are saying is that in the most fundamental sense phenomenal reality represents the dynamic interaction of form and emptiness (and emptiness and form) which implicitly entails the corresponding interaction of the holistic binary digits of 1 and 0 (and 0 and 1). In this way development processes can indeed be encoded in a binary digital manner. But surely you need more than this to provide a coherent structure for all the stages of development?
PC You are right! This is just the first step though it is indeed a very important one.
We will be taking another crucial step in a moment.
Q Before you do this can you comment further on the relationship between form and emptiness) and the holistic binary digits. From what I understand, though you maintain that the binary digits are inherent in the interaction of form and emptiness (and emptiness and form), they cannot be directly identified with each other. Therefore, as you do not maintain that all transformations in development can be defined solely as number, what then precisely is the relationship between them?
PC This is a very good question. The holistic interpretation of number provides a mathematical manner of phenomenal representation that is especially valuable in the context of an integral scientific appreciation of reality. There are however other types of phenomenal representation possible as for example provided through traditional religious symbols.
It might help in this context to consider from the analytic perspective, the relationship as between phenomena and their corresponding digital representation.
Thus if I e-mail a letter through my modem the phenomena (words and letters) will be encoded in a binary digital form for transmission down the phone line and then having arrived at the other end will be decoded into their original form.
Likewise from a developmental perspective, the phenomena that we recognise in experience follow a somewhat similar process of continual encoding and decoding though now in a dynamic transformational manner.
However in one very important sense the encoding-decoding relationship is now in reverse.
As the mystical traditions suggest, the phenomena that arise in experience are but appearances and strictly represent what is a mirage or illusion in terms of their true nature.
So the fundamental nature of reality is a plenum-void, where in binary terms (actualised) oneness is identical with (creative) nothingness.
When this perfect binary relationship is then decoded it results in the pure experience of Spirit. Now when these two aspects - which ultimately are identical - become separated in our experience the original binary encoding of reality - where oneness is identical with nothingness - becomes somewhat distorted. Thus the corresponding decoding of this binary relationship likewise becomes distorted resulting in the phenomenal appearances we identify as reality (thereby concealing its ultimately pure spiritual nature).
So inherent in all phenomenal appearances (as decoded reality) are - somewhat - rigid holistic binary configurations where the fundamental identity as between oneness and nothingness is to a degree separated and thereby misinterpreted.
This in turn leads to the separation in experience of form from emptiness (and emptiness and form) leading likewise to the appearance of rigid phenomena in experience.
However because of the interaction of emptiness with form (and form with emptiness) these phenomena necessarily undergo a degree of transformation and thereby change in appearance.
So form and emptiness (and emptiness and form) continually co-exist with the binary digits 1 and 0 (and 0 and 1) as the decoded and encoded aspects of continually transforming phenomenal reality.
Q So you would not accept the view that reality is just number?
PC This is too simplistic. Again number - and we are here dealing with the binary digits - provides one manner of representing the nature of reality, which - as we have seen - has special value in the context of an integral scientific interpretation.
However this manner of representation is necessarily interdependent with the (decoded) appearances of phenomenal form which then influence the subsequent manner of binary encoding.
So in a strictly qualified sense, number - in this context - the binary digits, represents the (hidden) encoded aspect of ever transforming phenomenal reality.
Q What distinguishes then - at the secondary phenomenal level - one form from another? For example if I am sitting at a desk and working on my computer what gives the desk and computer their distinctive phenomenal identities.
PC Again the clue here lies in the manner through which information data are successfully encoded in binary terms. Here each phenomenon is given a unique binary code which is interpreted in a static fashion.
It is basically similar in holistic terms (though now in a dynamic interactive manner). Thus every phenomenon carries a unique dynamic binary digital code which - when sufficiently stable - enables unambiguous recognition. This in turn helps the maintenance of a stable configuration of the relationship as between form and emptiness.
Thus the unambiguous identification of phenomena requires a certain limit to the
rate of transformation in evolution.
When the dynamic of binary interaction greatly increases as with mystical development, it is associated with a corresponding increase in the dynamics of interaction of form and emptiness (and emptiness and form). Phenomena become considerably transformed in experience thereby losing their unambiguous identity.
Q This is all very interesting. A physicist might say that reality is ultimately made of strings (or membranes) though I find it difficult to really understand what these are supposed to represent. How do you relate your own binary interpretation to this physical worldview?
PC The problem with the physicists approach is that it attempts to concentrate on form (without equal emphasis on emptiness).
It then tries to provide an explanation in terms of "objects" such as strings which - being phenomena - are necessarily of a secondary rather than a primary original nature. So at a deeper level we need to explain the relationship of secondary forms to the ultimate original ground of reality which is ineffable.
Furthermore it attempts to deal with reality in merely physical terms without relationship to the important psychological and spiritual domains.
Therefore - despite the considerable merits of this approach - it as reductionist in several important respects.
I would intend the holistic binary approach to be more fundamental and properly integral so as to correct the problems I have identified.
However having said this I do see certain similarities in the two approaches.
For example physicists attempt to represent strings in phenomenal terms as one dimensional structures which can acquire varying degrees of linear extension and also circular type properties (as loops). They then attempt to explain - in a somewhat mechanical fashion - how interactions as between strings and loops take place.
I would however see all this in a more dynamic manner as the most primitive type binary interactions inherent in the - likewise - most primitive type dynamic interactions as between form and emptiness. As I said earlier in the discussion a certain degree of stability in dynamic interaction processes is necessary for unambiguous phenomenal identity to emerge. So strings would relate to an earlier stage where the actual existence of phenomena (as form) is still confused with potential existence (as emptiness).
In other words at the level of "string" reality, though we may well admit to a dynamic transformation process in development, we cannot yet meaningfully distinguish phenomena (of form) from their original ground (as emptiness).
Q Can you now briefly summarise the distinction as between the analytic and holistic interpretation of the binary digits.
In the analytic interpretation, the binary digits 1 and 0 are clearly independent (representing in turn an interpretation based on the separation of the fundamental polar opposites).
Thus 1 is not equal to 0; likewise 0 is not equal to 1.
As we know this analytic binary system has the power to potentially encode all information processes.
However in the holistic interpretation 1 and 0 are clearly interdependent (representing in turn an interpretation based on the complementary and ultimate identity of the fundamental polar opposites).
Thus from this holistic perspective 1 = 0; likewise 0 = 1
In the famous Buddhist sutra
"Form is not other than Emptiness
Emptiness is not other than Form"
In the context of my approach this represents the ultimate nature of reality (as decoded experience).
Corresponding with this is the holistic binary digital interpretation
"Oneness (1) is not other than Nothingness (0)
Nothingness (0) is not other than Oneness (1)
This in turn represents the ultimate nature of reality (as encoded experience).
Of course in this ultimate state both the decoded and encoded aspects are identical (as pure Spirit).
However in terms of the phenomenal appearances of reality both aspects to a degree separate though continuing to also maintain a necessary interdependence.
Though not yet properly recognised, the holistic binary system has the power to potentially encode all transformation processes.
This in turn provides the integral scientific basis of subsequently unravelling the confused nature of the corresponding decoded phenomenal appearances in development.
Q Before leaving this section can you clarify the nature of the relationship as between the analytic and holistic interpretations of finite and infinite notions.
PC The analytic mathematical approach - as we would expect - separates finite and infinite notions. It subsequently deals with the infinite as a reduced (linear) expression of finite meaning.
Thus an actual number perception - such as 1 - is finite. However the concept of number - which potentially applies to "all" numbers without limit - is infinite.
Whereas the direct appreciation of what is actual (and finite) is provided through rational understanding, the corresponding direct appreciation of what is potential (and infinite) requires spiritual intuitive recognition.
However because in formal terms mathematics is understood as a (solely) rational pursuit, this necessarily leads to the reduction of the potential (infinite) in terms of the actual (finite) aspect.
Thus the concept of number, though strictly speaking potential and infinite is - in formal mathematical interpretation - misleadingly identified with actual (finite) numbers. In turn actual number perceptions are directly identified with - what is relatively - the potential number concept.
So perceptions and concepts are interpreted in mathematics in merely reduced finite terms.
As we have seen this leads to a fundamental problem with the very nature of mathematical proof which always involves a mismatch as between actual (finite) and potential (infinite) notions.
Holistic mathematics - by contrast - is based on the interaction of reason and intuition (and intuition and reason) which enables the preservation of the qualitatively distinct nature of both finite and infinite notions.
Thus the binary digits can have either finite or infinite interpretations, which in any dynamic context are defined through exclusion of the corresponding aspect.
Thus the finite understanding of the actual number perception "1" is defined through dynamic exclusion of the potential number concept (with an infinite application to "all" numbers). So in holistic terms the concept is thereby voided as "0".
Likewise - in this context - the infinite understanding of the potential number concept "1" (i.e. the one general concept of number) is likewise defined through dynamically excluding the actual number perception. So now in holistic terms the perception is thereby voided as "0".
Now when we try to encapsulate this relationship as between 1 and 0 in merely analytic reduced terms finite and infinite are separated as two extremes.
Thus 0/1 = 0
However 1/0 = infinity.
However from a dynamic holistic perspective the relationship between both aspects is complementary and ultimately fully identical.
So when the two-way holistic understanding as between the binary digits is totally free and unobstructed infinity and 0 become identical as the plenum-void (the everything that is nothing).
Q I suspect that the implications of this are far-reaching not only in terms of holistic mathematics but also in terms of analytic interpretations. But surely you are not suggesting that this analytic knowledge which has proved so valuable should be discarded.
PC Of course not! However from a dynamic perspective the understanding of conventional mathematical notions is defective.
Paradoxically, the analytic interpretation of mathematical symbols could be greatly enhanced through placing them in a perspective where they are properly understood as representing just one limiting - though admittedly exceptionally useful - reduced interpretation (with fundamental polar opposites considered as separate).
In other words the creative use of analytic mathematical interpretation could thereby be significantly improved.
In the context in which I define it, a comprehensive understanding of mathematics is radial arising from a proper dynamic appreciation of symbols and relationships.
This then has twin aspects as analytic and holistic mathematics respectively.
Operations: Holistic Interpretation of Addition and Subtraction
Q We will return again to number. However let us move on to mathematical operations. Now we are all familiar - in an analytic context - with addition and subtraction and multiplication and division.
What I want to understand is how can these operations be given a corresponding holistic meaning?
Let us start with addition and subtraction. (The holistic understanding of multiplication and division requires much greater subtlety)!
Now addition is associated with the positive sign of a number. So the addition of 1 and 1 entails 1 + 1 (i.e. + 1 + 1).
Likewise subtraction is associated with the negative sign. So the subtraction of 1 from 1 entails 1 - 1 = 0.
This perhaps provides the clue to the corresponding holistic interpretation.
So adding (in holistic terms) entails the positing of phenomena.
Subtraction (in holistic terms) entails their corresponding negation.
In dynamic terms phenomena are continually posited and negated in experience.
Indeed this operation is intimately connected with the holistic binary digits.
Thus the implicit identification of the unitary nature of form implies the (conscious) positing of that phenomenon in experience. Likewise the implicit voiding of a phenomenon as nothing requires its corresponding negation.
We will combine the binary digits with the operations of addition and subtraction to demonstrate both their analytic and holistic interpretations.
From the analytic perspective (+) 1 - 1 = 0. This understanding is based on the separation of polar opposites in experience.
So for example if I recognise a chocolate in a box, the chocolate is thereby posited in unitary terms. If I now take this chocolate out of the box it, (i.e. the box) is thereby made void and empty. So here both the positive and negative identification of unitary form are clearly separated resulting in a merely static nothing of nothingness.
Likewise from the holistic perspective (+) 1 - 1 = 0. This is based on the complementarity and ultimate identity of polar opposites.
Thus in dynamic terms we recognise a unitary phenomenon of form through a (conscious) positing in experience. The corresponding negation of this form leads to an (unconscious) fusion in spiritual intuitive terms. So the (conscious) recognition of form is thereby cancelled.
Unitary form - whereby the (conscious) positive pole is posited - thereby gives way through corresponding (unconscious) negation to the voiding of this form as spiritual emptiness.
Ultimately, when the dynamics of experience reach their pure unobstructed expression, the (conscious) positing of unitary form is simultaneously balanced by its (unconscious) negation as spiritual nothingness (i.e. empty of phenomenal form).
So in the purest mystical experience form is dynamically identical with emptiness and emptiness with form.
So when we now - in holistic terms - say that 1 - 1 = 0 both the positive and negative aspects of form are simultaneously interdependent leading equally to an inherently dynamic appreciation of emptiness.
So in this holistic context, oneness as the fulfilment of actualised form is the basis for the realisation of spiritual emptiness (as the free creative potential of nothingness).
Likewise from the complementary perspective 0 = 1 - 1, so that nothingness represents the creative potential for the full actualisation of oneness (as unitary form).
Thus once again we have both a (static) analytic and (dynamic) holistic manner of interpreting this fundamental relationship as between the binary digits.
In the analytic interpretation the operational signs are separated leading to an absolute interpretation.
In mathematical terms the absolute value of + 1 or - 1 is the same (the sign is not relevant).
Likewise when we separate the two poles of unity i.e. + 1 and - 1 in understanding we get an absolute interpretation.
So analytic interpretation is - by its very nature - absolute in this precise radial mathematical sense.
By contrast in the holistic interpretation, the operational signs are complementary and ultimately identical. So oneness in this context always combines both poles as 1 - 1.
Q Can you now use the holistic mathematical operation of addition (positing) and subtraction (negation) to explain the dynamic nature of the three fundamental polarities that we have already encountered in earlier discussions.
PC In dynamic holistic mathematical terms opposite polarities such as exterior and interior are positive and negative with respect to each other.
Thus to recognise an "objective" phenomenon as an exterior (unitary) form, one must thereby (consciously) posit it in experience. This requires the corresponding negation of the opposite interior pole which is thereby temporarily erased and voided.
Thus in dynamic terms the positing with respect to one pole necessarily entails negating with respect to the other.
Likewise - relatively in reverse fashion - to recognise the "subjective" phenomenal self as an interior (unitary) form, one must also (consciously) posit it in experience. This requires the corresponding negation of the opposite exterior pole which is now likewise temporarily voided.
The interaction of exterior and interior (and interior and exterior) poles therefore entails the continual positing and negating of each pole with respect to each other. Also when one pole is posited as unitary form, the corresponding pole is thereby negated and made nothing as emptiness.
By extension the same basic dynamics apply to the interaction of all polar opposites in development, which necessarily entail in holistic mathematical terms, the two fundamental numbers i.e. the binary digits 1 and 0 and also the two fundamental operations of positing and negating (i.e. dynamic addition and subtraction).
So whereas we initially started out by explaining all development as the interaction of form and emptiness (which inherently therefore entails the holistic interaction of the binary digits 1 and 0) we now can extend this somewhat to also include the holistic mathematical interpretation of the fundamental operations of addition and subtraction.
Thus phenomenal development is based on the interaction of polar opposites whereby the positing of one pole - in dynamic terms - always entails the corresponding negation of its opposite.
Q Let us return briefly to number. Can you now explain the holistic mathematical significance of 2.
PC In holistic mathematical terms 2 relates to the quality of "twoness" or - as more commonly expressed - duality.
In analytical mathematical terms 1 + 1 = 2 (i.e. + 1 + 1 = 2)
Thus whereas 0 results from combining both the positive sign of 1 with the negative sign, 2 results from combining the positive sign of 1 again with the positive sign.
In holistic mathematical terms it is similar so that 1 + 1 = 2
The significance of this is considerable.
Though in dynamic terms the positing of one pole in phenomenal terms e.g. exterior implies the corresponding negation of its opposite, in reduced analytic terms the role of negation is ignored.
Thus in this manner, opposite poles are separated in experience and thereby posited as if they had an independent existence.
Therefore for example in conventional science object phenomena (representing the exterior pole) are treated as if they existed independent of interior recognition.
So when understanding takes place in a reduced - merely - analytic manner, opposite poles are separately posited in an explicit manner in experience (without formal recognition of corresponding negation of the opposite aspect).
Now implicitly some degree of interaction as between poles must necessarily take place which serves to facilitate the switching from one pole to another.
So the exterior pole is posited leading to an appreciation of "objective" phenomena as independently existing. Then the interior pole is likewise posited (with the corresponding recognition of an independently existing self).
In this way, opposite poles (which in ultimate terms are identical as spiritual emptiness) are clearly separated in experience.
Quite simply this separation of opposite poles whereby each is - merely - posited, is the fundamental basis of duality in experience.
Thus if + 1 represents the (mere) positing of an exterior (unitary) phenomenon of form, and + 1 likewise represents the (mere) positing of the corresponding interior (unitary) phenomenon of form (i.e. as self) then in holistic mathematical terms
1 + 1 = 2.
In other words when both the exterior (i.e. understanding of the world) and interior poles (i.e. understanding of the self) are both (merely) posited and thereby separated, experience becomes dualistic.
Once again by extension this applies to the treatment of all polar understanding. (And remember that phenomenal experience is always necessarily conditioned by opposite poles!)
Q I can appreciate what you are getting at. The simpler the holistic mathematical relationship the more universal is its significance as regards the interpretation of development!.
PC Exactly! The most fundamental mathematical symbols from an analytical, are equally the most fundamental from a holistic perspective where they now provide the scientific means for explaining the universal dynamic features of development.
So, as we have seen inherent in all development processes are the holistic binary digits (oneness and nothingness) and the holistic operations of addition and subtraction (as positing and negating respectively).