Sunday, April 30, 2017

Number and Development (4)

Perhaps the most startling implication of this holistic mathematical understanding of the number "4" is that it leads to a completely new interpretation of the nature of space and time (which are now understood in an inherently dynamic interactive manner).

In this holistic understanding, space and time simply represent the manner in which the two fundamental polarity sets (external/internal and whole/part) - which necessarily condition all phenomenal reality - interact.

So just as in number terms, we can maintain that the four roots of 1 (representing the reduced 1-dimensional expression of 4 as representing a dimensional number) are real and imaginary with positive and negative directions respectively, equally we can maintain the same with respect to space and time.

Thus from one valid perspective, we can say that the 4 dimensions contain  two real dimensions of space  (1 positive and 1 negative) and 2 imaginary dimensions (again 1 positive and 1 negative).

And because, in a dynamic interactive sense, real space corresponds to imaginary time (and real time to imaginary space) we can equally say that the 4 dimensions contain two real dimensions of time (1 positive and 1 negative) and 2 imaginary dimensions (again 1 positive and 1 negative).

Then mixing both space and time, we can say that the 4 dimensions relate to 2 real space dimensions and 2 real time dimensions (or alternatively 2 imaginary space dimensions and 2 imaginary time dimensions).

The first key point regarding this dynamic holistic interpretation is that both time and space are directly complementary with each other in both an (external) physical and (internal) psychological manner (as + and   with respect to each other).

Indeed this can be fruitfully used to explain why authentic spiritual experience is understood as related to the present moment (and only in a secondary sense with movement in space and time).

Indeed conventional experience is characterised by a considerable illusion i.e. that time possesses just one positive direction in time. One then believes that all events move forward unambiguously from past to future!

However when one reflects on the matter, all events necessarily entail the relationship as between external and internal aspects.

So from one perspective, one is directly aware of an (external) world in relation to an (internal) self; then from the opposite complementary perspective, one is directly aware of an (internal) self in relation to an (external) world.

Now when one attempts to isolate both reference frames (i.e. external and internal), time does indeed appear to unambiguously move forward in a positive direction.

So time moves forward with respect to (external) events; time equally then moves forward with respect to the (internal) self, which can observe such events.

However when we realise that both external and internal aspects are necessarily interdependent, then the movement of time now acquires a merely relative meaning.

Thus if time is viewed as moving forward with respect to (external) events, then it is - relatively moving backwards with respect to the (internal) self. Likewise if time is viewed as moving forward with respect to the (internal) self, then it is - relatively - moving backwards with respect to (external) events.

So when one is strongly aware of the necessary interdependence of both external and internal polarities, movements in time (and indeed space) both acquire a merely secondary relative validity, that in a primary spiritual sense cancel out in direct experience of the present moment.

When I initially became fascinated with Einsteins' Special Theory of Relativity, it struck me strongly that a complementary psychological interpretation could be given for his explanation of the physical nature of space and time.

In then intrigued me when I later read an account of Einstein's attempt to give a simple explanation of relativity, when he stated,

When you sit with a nice girl for two hours you think it’s only a minute, but when you sit on a hot stove for a minute you think it’s two hours. That’s relativity.”

However Einstein is clearly referring to a psychological - rather than physical - notion of time in this quote.

So the bigger issue - which was not addressed by Einstein is how both physical and psychological notions of time (and space) can be properly integrated.

And quite simply, this requires going well beyond the classical scientific paradigm accepted by Einstein.

However it requires an even deeper realisation to recognise that in dynamic interactive terms, space and time are real to imaginary (and imaginary to real) with respect to each other.

So space and time do not exist - as in the Newtonian world view - as an empty theatre in which physical events take place.

Rather they are both continually created through the dynamic interaction of phenomena (with in turn phenomena created through the dynamic interaction of space and time).

So when space emerges (both in physical and psychological terms) in a "real" manner, then time emerges in a corresponding "imaginary" fashion (and vice versa, so that when time emerges in a  "real" manner, then space emerges in an "imaginary" fashion.

In fact, the physical behaviour of space and time can be linked in a very fundamental way with corresponding psychological dynamics.

Now for convenience, I identify three primary modes (which constitute all psychological experience).

These are cognitive, affective and volitional respectively.

The cognitive can best be understood as a means of (impersonal) control with respect to reality, while the affective in complementary terms represents a means of (personal) response. The role of the volitional is then to maintain dynamic balance between both, so that they mutually can serve other in the optimum fashion. So the fullest experienced complementarity as between cognitive and affective (in a highly refined transparent experience of phenomena) is then consistent with a state of spiritual union.

Now again - though ignored in scientific terms - one can have both an affective experience of space and time (where emotional response is evoked) and a cognitive experience (which conforms directly with scientific notions).

However the very reconciliation of affective with cognitive aspects requires going beyond the "real" world of science, based merely on conscious type interpretation, to embrace both "real" and "imaginary" aspects (where conscious and unconscious aspects are recognised).

So this is precisely what is enabled in holistic terms at these "higher" levels of Band 3.

Therefore from this new dynamic perspective, both the cognitive and affective experience of space and time are now understood in complementary terms as real and imaginary with respect to each other.

So when real (conscious) experience of time (and space) is of a cognitive nature, the corresponding implicit (unconscious) experience is now of an imaginary nature.

Likewise, when the real (conscious) experience of time (and space) is of an affective nature, the corresponding implicit (unconscious) experience is now in turn of an imaginary nature.

So once again, when correctly understood in their dynamic interactive manner, the very nature of space and time is rendered to be of a merely relative secondary nature, representing the temporary phenomenal expressions of an ever present reality.

And once again, we have direct parallels in the physical world. So just as the notion of the unconscious is widely accepted in psychology (with interacting links with the conscious mind), equally a complementary situation necessarily exists with respect to the real world. So underlying the "real" world of scientific reality (based on conscious means of interpretation) is an equivalent "unconscious" of an imaginary nature, in a holistic ground that intimately relates to all phenomenal reactions. So for example virtual (i.e. imaginary) particles can freely emerge from this holistic ground of reality.

And corresponding to cognitive and affective aspects, we have control and response patterns (which again apply to all phenomena). So both real and imaginary space and time emerge in the physical world through the continual complementary interaction of control and response patterns (independence and interdependence) respectively, applying to all phenomena.

One further advance - using this holistic notion of "4" - was a Theory of 24 Personality Types where I constituted each personality type as a unique permutation of the four original holistic numbers (external and internal and whole and part).

So each personality type therefore can be seen as representing a unique configuration of the manner in which external and internal and whole and part poles are related in experience.

Each personality type thereby in turn represents a unique configuration in the manner in which space and time are related.

And I found striking parallels here with the bosonic world of superstrings (representing unique "impersonality types"). This in turns provides a far more intuitively accessible manner of understanding the multi-dimensional nature of strings (requiring more than 4 dimensions).

So in my interpretation, the "many" dimensions of string theory simply represent a certain unique configuration of the existing 4 dimensions.

Saturday, April 29, 2017

Number and Development (3)

For a long time since the late 60's, I was aware of the fact that all phenomenal reality is conditioned by two key sets of polarities. The first of these relates to external and internal (which we have already briefly discussed). As we have seen in dynamic interactive terms, these two poles - constituting now 2 holistic dimensions of experience, are, relatively, + 1 and  – 1 with respect to each other.

The second polarity set relates to whole and part, which can also express itself as general and particular, collective and individual, qualitative and quantitative and so on.

I was studying Economics at University in Dublin at the time and was considering then a new dynamic methodology for the discipline that would involve these two sets of polarities.

So from one perspective all external economic events entail an internal psychological aspect of behaviour (that is dynamically inseparable from such events).

Likewise a key dynamic interaction characterises the relation between microeconomic (part) and macroeconomic (whole) events.

However the nature of this relationship as between part and whole is quite subtle requiring an understanding of the complementarity of opposites that goes beyond the 2-dimensional consideration of positive and negative aspects.

So in fact the true relationship as between whole and part (and part and whole) is in holistic mathematical terms as real to imaginary (and imaginary to real) respectively, which in turn both contain positive and negative aspects. And this in fact directly corresponds to a reality now considered in terms of 4 holistic dimensions (which dynamically interact with each other in both a horizontal and vertical manner). Thus in terms of the "higher" holistic understanding, all 4 dimensions are seen as mutually interdependent with each other. These can then be expressed (in a reduced 1-dimensional separate manner) as + 1, – 1, + i and – i respectively.
Probably the most common form of reductionism - which especially pervades scientific discourse - is the reduction of the whole to part notions (in a merely quantitative manner).

This is clearly in evidence when for example we add two numbers.

So when we maintain for example that 1 + 1 = 2, the new cardinal "whole" number, 2 is interpreted directly as merely the sum of its part unit components. So we have here the direct reduction of whole to part notions (in a merely quantitative manner).

However implicitly, this very recognition of the quantitative notion of 2 requires the corresponding ordinal notions of 1st and 2nd (which are of a qualitative nature). Thus a distinctive qualitative appreciation is required for the ordinal notions of 1st and 2nd (as opposed to the quantitative appreciation of 1 + 1). However because of its 1-dimensional nature, Conventional Mathematics lacks the means of avoiding the inevitable reduction of the qualitative ordinal notion in merely quantitative terms!

So in the dynamics of understanding, when one is explicitly aware of the quantitative nature of a phenomenon (in a conscious manner), then one is necessarily implicitly aware of the corresponding qualitative nature of the phenomenon (in an unconscious fashion); likewise when one is then explicitly aware of the qualitative nature of a phenomenon (in a conscious manner), then one is likewise necessarily implicitly aware of the corresponding quantitative nature of the phenomenon (in an unconscious fashion).

Thus it is the very intervention of the unconscious that enables the continual switching as between whole and part (and likewise part and whole).
And because the unconscious is indirectly expressed in a holistic imaginary fashion, this implies that the dynamic relationship as between whole and part (and part and whole) is as real to imaginary and imaginary to real, respectively.

However when one does not explicitly allow for the role of the unconscious, then the relationship as between whole and part inevitably becomes understood in a merely reduced fashion e.g. where the whole is interpreted as the quantitative sum of its constituent parts.

So properly interpreted, where the parts are understood in a quantitative phenomenal manner, the whole then - relatively - represents a qualitative spiritual notion.

Thus from one perspective, human development itself can be viewed as the movement away from a more limited phenomenal part to a more collective whole notion (whereby all the parts are thereby seen as spiritually integrated with the whole). This in fact represents the transcendent pole of spirituality.

However from an equally valid opposite perspective, human development can be viewed as the movement from limited spiritual notions of the whole to ever more unique part notions (whereby each phenomenal part is eventually seen as fully reflecting the whole). This then represents the immanent pole of spirituality.

Unfortunately however this two-way relationship of part and whole notions is rarely properly emphasised with respect to psychological accounts of development (even when the ultimate goal is understood as spiritual). Typically an unbalanced emphasis is placed on "holism" where each "higher" stage is seen as collectively including the "lower", without an equal emphasis on "partism" where each "higher" stage (which is - relatively - "lower" - in terms of the previous perspective of "holism") is seen as uniquely reflecting the "lower" (which again is - relatively - "higher" in terms of holism").

So as I define it, with the ultimate attainment of the radial levels, all hierarchical distinctions with respect to these two - relatively opposite top-down and bottom-up - vertical directions are fully eroded. Here spirit, now directly grounded in phenomenal reality, is mediated through the centre of one's being (which is equally now the centre of all created reality).

I will conclude this entry by briefly indicating the relevance of this 4-dimensional holistic appreciation for the nature of number.

Again if we take the number "2" to illustrate, in Type 1 terms this is written as 21. So 2 here is the base and 1 the dimensional number respectively.

Then in Type 2 terms it is written as 12. 1 here is now the base and 2 the dimensional number respectively.

Now in terms of the first polarity set, all these numbers (in both base and dimensional terms) have both external and internal polarities relating to the objective mathematical symbols involved and their corresponding subjective mental interpretations respectively.

However, intriguingly they all equally possess both a real and imaginary identity.

So when the base number is real, the corresponding dimensional number is imaginary (in this holistic mathematical context). Likewise when the dimensional number is real, the base number is - relatively - imaginary.

This means, that in dynamic interactive terms, all numbers necessarily keep switching as between both a real (quantitative) and imaginary (qualitative) status.

Put another way, this leads to the startling realisation that all numbers have both a particle-like (quantitative) and wave-like (qualitative) identity, which keep switching in the dynamics of experience.

Thus, properly understood, quantum behaviour is not just a feature of sub-atomic physical reality, but in a more fundamental sense is a feature of all numerical reality!

Friday, April 28, 2017

Number and Development (2)

In yesterday's blog entry, I attempted to outline succinctly the holistic mathematical nature of "2" (as representing a dimensional number).

This in turn is directly related to the unfolding of the various stages of Level 1 (Band 3).
What happens here is that one's former dualistic vision of reality becomes steadily eroded, through a marked acceleration in unconscious development, where phenomena become - literally - negated to a considerable extent. This then leads to a more spiritually refined intuitive worldview, where the dynamic relative nature of all phenomena can be readily appreciated.

In my own account, Level 1 is largely concerned with - what I refer to as - the horizontal polarities of external and internal (which are relatively + 1 and – 1 with respect to each other), which necessarily condition the experience of all phenomena.
And in holistic mathematical terms, this culminates in the coherent vision of the nature of 2-dimensional - as opposed to 1-dimensional - reality.

However, when one recognises that the number "2" can be given a distinctive holistic mathematical meaning, then this likewise implies that, in principle, the same should apply to all numbers.

In particular as the notion of 4 dimensions - as understood in conventional physical terms - is directly relevant to the manner we understand space and time, this implies that "4" should likewise carry an immense significance from a holistic mathematical significance.

I have mentioned on many occasions how I experienced an immediate affinity with Jung's writings (when I seriously studied them in the early 80's).

I could see holistic mathematical understanding was strongly implicit in his work.

For example his four functions can be illustrated as 4 equidistant points on the unit circle.

Likewise his mandalas, used as symbols of integration, are then often depicted in the same manner as dividing the circle equally in the same four-fold - or alternatively - 8-fold manner).

So when one of Jung's great followers Marie-Louise Von Franz stated "Jung devoted practically the whole of his life's work to demonstrating the vast psychological significance of the number four" it is this holistic mathematical "circular" notion of "4" that implicitly she had in mind.

In fact Jung came close to a more explicit holistic mathematical expression of "4" when he termed 2 of his functions as rational and 2 as irrational, setting up dynamic complementary links between them with respect to their respective conscious and unconscious usage.

However, after much reflection, I came to the firm conclusion that the true holistic mathematical nature of "4" is given by the four respective roots of 1 i.e. + 1, – 1, + i and – i respectively.

This in turn raises the all important issue of the holistic mathematical meaning of the imaginary number i (i.e. the square root of – 1).

Now we have already seen, in holistic mathematical terms that – 1 relates to the (unconscious) negation, in a dynamic manner, of - formerly - consciously posited ("real") phenomena, now entailing 2 dimensions of understanding!

If one then attempts to express such (unconscious) holistic understanding indirectly in a  conscious manner, this entails expressing what is inherently of a 2-dimensional nature, in a reduced 1-dimensional manner, which is the equivalent of obtaining the square root.

So the all important holistic mathematical conclusion is that the imaginary notion relates to holistic unconscious meaning that is indirectly conveyed in a conscious manner.

When one understands this, one realises that reality is necessarily of a complex nature (entailing both real and imaginary aspects).

The "real" aspect relates to the (local)  recognition of phenomena in a directly conscious manner.

The "imaginary" aspect is then related to recognition of the global nature of phenomena in an unconscious fashion. In fact without this imaginary aspect, it would be impossible to relate phenomena with each other!

And we have already seen how this problem lies at the heart of conventional mathematical understanding.

Though of course in standard analytic terms, such Mathematics recognises the importance of both real and imaginary numbers (as quantities), from a qualitative perspective it attempts to conduct all interpretation from within a solely "real" i.e. conscious framework.

So as we have already seen, in every context, it effectively reduces the distinctive holistic notion of number interdependence in a reduced independent fashion.

Thus symbols in Mathematics never possess a solely conscious meaning, for implicitly the very requirement for relating these symbols requires unconscious meaning (of a holistic nature).

However we can then indirectly attempt to relate this unconscious aspect in a conscious fashion through the adoption of the imaginary notion (in a qualitative manner).

Now when the unconscious aspect is nor properly recognised - as is this case in present accepted Mathematics - it is blindly projected on to objects (without of course its nature being recognised).

Therefore, though - certainly from my perspective - an obvious fundamental problem lies at the heart of all Mathematics, this can never be addressed while interpretation remains rigidly stuck within real (i.e. rational conscious) modes of expression.

So the clarification of the imaginary notion, which represented a significant further breakthrough in my holistic mathematical understanding, related very much to the on-going development of Level 2 (Band 3).

So just as all numbers in analytic terms can be expressed within a complex framework (allowing for real and imaginary quantities with positive and negative values), equally I now was in a position to elaborate on a similar complex framework in a holistic qualitative manner.

I will return to some of the enormous implications of this in the next few blog entries.   

Thursday, April 27, 2017

Number and Development (1)

Even as a small child I was fascinated with the nature of number and the fundamental mathematical operations of addition and multiplication.

This led me on at the age of about 5 to the discovery of my own system of logs (based on the power of 2) whereby multiplication of numbers could be conveniently "converted" into a simple operation involving addition.

Then about 5 years later, I made a much more important and life-changing discovery, when I clearly came to realise that every act of multiplication inevitably involves a qualitative as well as quantitative transformation. However the qualitative aspect is then completely edited out of conventional mathematical interpretation.

This initially arose from consideration of the the area of rectangular fields. So if a field was of length 80 metres and width 60 metres, the area, 80 * 60 = 4800 sq metres. So though the initial measurement of length and width are both 1-dimensional, the resulting area now represents 2-dimensional units. So both a quantitative transformation (i.e. 4800) and qualitative transformation (2-dimensional units) takes place.

However conventionally, when in arithmetic terms we multiply 80 * 60, the result of 4800 is expressed in an unchanged 1-dimensional quantitative manner (which thereby can be represented as a point on the real number line). Therefore I realised  - though I lacked the means then to resolve the issue - that the conventional interpretation of multiplication was simply not fit for purpose. 

So this represented an early "peak" experience into a far more advanced form of mathematical understanding, where both analytic (quantitative) and holistic (qualitative) aspects would be necessarily involved.

Furthermore this moment which crystalised as a very sober realisation was not so much the peaking of a "higher" state - though it certainly contained an important illuminative element  - but rather of a "higher" structure of understanding. This experience then in many ways  served as the crucial driving force over the next 50 years or so towards a greatly enhanced form of mathematical understanding, which I have only recently been able to finally articulate (to my own satisfaction).

Expressed simply, the key issue relates to the notions of number independence and number interdependence respectively, which are always reduced in terms of each other in conventional mathematical terms.

For example, if we take a cardinal number such as 3, it is represented in quantitative terms as the sum of independent component sub-units i.e. 1 + 1 + 1. So the units here of a homogeneous nature, which - literally - lack any qualitative distinction.

Then we add for example two numbers - say 2 + 3 - the result i.e. 5, then seemingly is likewise composed of merely independent units.

However things become subtly different where multiplication is involved.

So let's now consider the multiplication of 2 * 3 .

To make it concrete let us imagine 2 rows with 3 coins in each row!

Now the key to using the operator (i.e. 2) in this case is the recognition that the 3 coins in each row are similar (as duplicates of each other) so that we can make a one to one identification of each coin in the 1st row with each corresponding coin in the 2nd row.

However in the recognition of this shared similarity, we have now moved from the quantitative notion of number independence to the qualitative notion of number interdependence.

However in conventional mathematical terms, this crucial distinction is completely overlooked.

So putting it bluntly, the standard accepted interpretation of multiplication suffers from a fundamental confusion in the failure to properly distinguish the analytic notion of number independence (which is quantitative)  from the corresponding holistic notion of number interdependence (which is of a distinctive qualitative nature).

Now it is recognised that the Riemann Hypothesis is deeply connected with the relationship as between addition and multiplication. However this issue clearly cannot be properly understood within a mathematical paradigm that insists on mere quantitative type interpretation of its numerical symbols!

So on the long road to unravelling the true nature of addition and multiplication, I realised that the first major requirement was the development of the hidden aspect of Holistic Mathematics (where every symbol can be given a coherent qualitative - as opposed to quantitative - interpretation).

And the unfolding of this new holistic mathematical understanding formed a very important - though not exclusive - component of my cognitive development through the various levels of Band 3.

So associated with each of the "higher" levels of Band 3 i.e. Level 1, Level 2 and Level 3 respectively are both refined states (representing ever purer forms of spiritual intuition) and refined structures (representing increasingly dynamic forms that indirectly are defined in a circular paradoxical manner).

And these states and structures relate to cognitive, affective and volitional understanding respectively.

So we concentrating initially here on the cognitive mode with respect to the unfolding of new logico-mathematical understanding of a holistic nature.

In particular I formed then the holistic understanding of the important circular number system that - in quantitative terms - is defined by the various roots of 1 (in the complex plane).

So for example the 2 roots of 1 are + 1 and – 1 respectively, which in the standard analytic manner are separated in a static either/or fashion.

However these two numbers can equally be given a holistic meaning where + 1 and – 1 are now understood as interdependent in a dynamic interactive manner.

So from a holistic perspective, + 1  implies the dimension (i.e. direction) of experience whereby  phenomenal meaning is posited in a directly conscious manner. – 1 then implies the corresponding dimension whereby such meaning is then negated in a directly unconscious fashion.

Now there are two poles with respect to all phenomenal reality that are - relatively - external and internal with respect to each other. In holistic mathematical terms these poles are designated as + 1 and – 1 respectively.

So when the external direction is posited e.g. as a conscious object, this is designated (within its own independent frame of reference) as + 1.
Likewise when the internal direction is posited e.g. as a mental construct, this is likewise designated (within its own independent frame of reference) as + 1.

However crucially the dynamic switching as between both poles requires the unconscious direction which - literally - serves to negate the phenomenon already posited, resulting in a psycho spiritual fusion of intuitive energy, which then activates recognition of the opposite (unrecognised) pole..

Therefore though phenomena can indeed be consciously posited within their own independent frames of references, when these frames are related as interdependent, like matter and anti-matter particles in physics, a negative fusion with the positive, resulting in intuitive appreciation necessarily takes.

So therefore relative to each other, external and internal poles are positive and negative, which continually keep switching in the dynamics of experience.

I realised clearly at this point that conventional mathematical interpretation is defined in a holistic mathematical manner as 1-dimensional i.e. where formal  interpretation is merely of a conscious nature (taking place within isolated independent frames of reference).

However I had now defined for myself a new 2-dimensional framework whereby both conscious (posited) and unconscious (negated) directions of experience, for all mathematical symbols, are recognised in a dynamic interactive manner.

Therefore it is somewhat meaningless to attempt to define mathematical truth externally in an absolute objective manner as such truth necessarily entails subjective mental interpretation which is relatively of an internal nature.
So properly understood, all mathematical truth (from this 2-dimensional perspective) is of a dynamic relative nature, entailing external and internal poles (as complementary opposites).

So what is formally accepted as mathematical truth (i.e. 1-dimensional interpretation) - where interpretation is viewed in absolute corresponence with objective reality - represents but one special limiting case that is of a highly reduced nature. 

And of course the 2-dimensional interpretation in principle can likewise apply to all intellectual discourse.  So Hegel in many ways applied it to philosophy while Jung showed its relevance for psychology. Likewise it forms a  a staple part of expression in many mystical traditions such as Taoism, while more recently it has been seen to be deeply relevant in physics with respect to quantum mechanical behaviour.

So I had could see how a number such as 2, can be given two distinctive interpretations, which I term Type 1 and Type 2 respectively.

In the first case (Type 1) - which represents the standard analytical mathematical interpretation - 2 is more properly defined as 21. Here the number is defined in the default 1-dimensional quantitative manner.
So 21 = 11 +11 where the units are defined as homogeneous and independent.

In the second case (Type 2) - which represent the new holistic mathematical interpretation - 2 is more properly defined as 12, where the default base number 1 is raised to the power of 2 (i.e. in a 2-dimensional manner).

Here the two units of 2 are considered as interdependent with each other in a qualitative manner. Now such interdependence can only be directly appreciated in an intuitive fashion. However indirectly, one can attempt to translate such interdependence, in the standard 1-dimensional manner by taking the square root, resulting in the two answers + 1 and – 1.
Though these two results are necessarily separated in 1-dimensional terms (either + 1 or – 1) , from the 2-dimensional perspective they are considered as directly complementary (i.e. + 1 and – 1 simultaneously).        

Wednesday, April 26, 2017

Further Clarification

Perhaps at this stage I should offer further clarification on the nature of Band 5 on the spectrum, which I have referred to as the “Spiritual Descent.

In truth the dynamics are a little more complex that I had previously suggested.

Now in terms of my own classification system, I associate Band 2 with the specialisation of linear type understanding. So this represents the ground level of the personal stages, in the conscious understanding of the world of everyday dual phenomena.

Then I characterised Band 3 as an ascent through transpersonal stages representing increasingly more refined intuitive understanding  towards an ultimate spiritual reality of a nondual ineffable nature.

However because of the inherent complementarity, in a dynamic interactive manner, of transpersonal and prepersonal stages, this equally requires an underground journey back into the deep recesses of earlier development as one comes to encounter ever more starkly the primitive instinctive regions of personality (which normally get repressed and bypassed in many ways through the earlier journey towards the differentiation of conscious development).

So the ascent through the transpersonal stages of Band 3 necessarily requires a corresponding descent through the - earlier - traversed prepersonal stages of Band 1.

Thus the balanced drive towards vertical spiritual integration of the psyche encompassing affective, cognitive and volitional aspects structures, requires both top-down integration from the perspective of the unfolding of new “higher” transpersonal stages and bottom–up integration from the perspective of revisited “lower” prepersonal stages (where they can only now be properly disentangled with respect to their instinctive unconscious nature).

And this bi-directional manner in turn is how both the transcendent and immanent directions of spirit properly unfold.

However typically, as I characterise it in my account, this two-way development in the psyche is likely to remain somewhat unbalanced during Band 3.

So in vertical terms the personality can become increasingly stretched leading to acute psychological stress with the completion of Band 3 (Level 3). So from one perspective one has travelled up a high mountain into the thin air of spiritual contemplative understanding (requiring a considerable refinement in all conscious activity).

From another perspective one has journeyed in an opposite direction into the unconscious primitive depths of the personality, where one is subject to all sorts of instinctive promptings (again requiring the considerable surrender of conscious control).

So unfortunately when there is a pronounced vertical dimension to the spiritual journey (which certainly characterised my own experience), the middle level grounding in the everyday world of Band 2 can thereby become considerably eroded.

Though I characterise Band 4 as the specialisation of these holistic unconscious stages (which indirectly can be given a refined paradoxical conscious expression), in truth they are likely to largely overlap in development with the unfolding of the new stages of Band 5.

From the perspective of the “higher” transpersonal development attained, these require a descent as one slowly attempts to ground them once more in the everyday levels of Band 2.

However from the perspective of “lower” prepersonal, in the continual revisiting of these stages, this is likely to entail an even deeper descent into the primitive unconscious as one finally tries to fully unravel the repressions and hurts from early childhood still preventing the full bottom-up integration of the psyche.

So the culmination of Band 5 with the completion of Level 3, is consistent with a situation where one is now ready to properly ground the “higher” transpersonal in the middle levels (associated with personal development).
This is equally consistent with the full unravelling of the “lower” prepersonal, that have not yet however been properly integrated in a bottom-up fashion with the middle levels.

Thus the complete vertical integration of the psyche, requiring the bi-directional interaction of both “higher” and “lower” with the middle levels would therefore not fully occur before the unfolding of Band 6 (representing the radial stages).

And so Band 6 would then likewise entail the incorporation of ever more extensive horizontal integration within each level with the vertical integration of every level (already attained).         

Tuesday, April 25, 2017

Mysterious Journey

It is a while now since I contributed new material to this blog.

When I last posted, I was dealing with the refined cognitive development relating to Band 5 (Level 2) which in my account was intimately related to the unravelling of the mysterious nature of the number system. For I was now beginning to see clearly the remarkable implications, which the qualitative behaviour of the primes hold for psychological development.

In conventional mathematical terms, the primes are seen as the basic “building blocks” of the natural number system (in quantitative terms).

However a key realisation of this stage is a growing recognition that all mathematical symbols (such as number) can be given both quantitative (analytic) and qualitative (holistic) interpretations!

So this leads to an inherently dynamic appreciation of the number system, where both primes and natural numbers interact with each other in a bi-directional fashion. 

When the great German mathematician David Hilbert was once asked what mathematical problem was the most important (as quoted by Constance Reid in her biography) he replied:

“the problem of the zeros of the zeta function, not only in mathematics, but absolutely most important”

Thus it seems that Hilbert had some inkling that the zeros, which represent an infinite series of solutions to the Riemann zeta function (with the value = 0) possess an importance that far transcends their recognised mathematical significance.

In the accepted mathematical context, the zeta zeros are relevant because in a mysterious way they fully encode the nature of the primes. From the reverse perspective, we could equally maintain that the primes are important because they fully encode the nature of the zeta zeros.

Thus the relationship between these two key components is circular which directly implies that the number system can only be properly understood in a dynamic interactive manner entailing both quantitative (analytic) and qualitative (holistic) aspects. 

Unfortunately however, conventional mathematical interpretation is of a highly reduced nature where symbols (such as number) are given a merely quantitative interpretation.

Thus in every context the qualitative aspect (which is uniquely distinct) is thereby reduced in a quantitative manner.

For example, it is customary to view the individual primes (such as 2. 3, 5, 7,…) quantitatively as the “building blocks” of the natural number system.

And the key feature of each prime is that it has no factors (other than itself and 1).

 However, properly understood, the collective arrangement of primes (whereby they operate as unique factor groupings of composite natural numbers) represents in a dynamic relative manner, their qualitative aspect.

And whereas a highly random behaviour attaches to each individual prime, a highly ordered behaviour characterises the collective behaviour of the primes.   

And the zeta zeros reconcile as it were these two aspects (quantitative and qualitative) of the primes. However looked  at from an equally valid reference point, each individual zeta zero is likewise random while the collective behaviour of the zeros is highly ordered, with the primes now in turn reconciling these two aspects.

So the primes and the zeta zeros are thereby mutually encoded in each other (in both a quantitative and qualitative manner).

Likewise - though less well recognised - the primes and natural numbers are mutually encoded in each other.

Now, admittedly this does not seem apparent when - as in conventional terms - we admit solely the quantitative aspect of the primes.

Here again, the primes are considered unambiguously as the essential “building blocks”,  with each natural number representing a unique combination of independent prime factors (in cardinal terms).

However when we consider the qualitative aspect of the primes through switching to their ordinal nature, each prime is now uniquely defined as a group of natural number members. So 3 for example, entails the interdependent grouping of its 1st, 2nd and 3rd members.

So once we admit relatively distinct quantitative and qualitative aspects, the primes and natural numbers are likewise seen to be mutually encoded in each other.

Thus the fundamental role of the zeta zeros, in this dynamic interactive context, is to enable consistent switching as between both the quantitative and qualitative aspects of the primes (which equally entails the qualitative and quantitative aspects of the natural numbers).

This is a key issue that is entirely overlooked in conventional mathematical terms.

Once we recognise that all mathematical understanding properly entails both the quantitative (analytic) and qualitative (holistic) interpretation of its symbols, then the key underlying issue is the requirement for consistency in use with respect to both aspects.

And the famous Riemann Hypothesis, which postulates that all the (non-trivial) zeta zeros lie on a straight line drawn through .5 on the real axis, represents the crucial condition for this requirement to be met.

This is the much deeper reason as to why the zeta zeros are so important in that they somehow are mysteriously involved in consistently reconciling both the quantitative and qualitative aspects of mathematical understanding.

However this considerably transcends conventional mathematical boundaries as the issue is central to life itself.

When we look at human development, it starts with embryonic experience of a highly primitive instinctive level.

I had long been fascinated with such development, which I suspected bore a direct link with my enfolding dynamic appreciation of the nature of the primes.

The very essence of primitive behaviour is that both conscious and unconscious aspects of behaviour - which have not yet been sufficiently differentiated in development - thereby remain to a considerable extent entangled with each other.

Expressed another way, both quantitative (analytic) and qualitative (holistic) aspects are thereby greatly confused.

So solving the primitive problem as it were, requires that both conscious and unconscious aspects of experience be fully differentiated, before then eventually becoming fully integrated with each other. 

In corresponding fashion, I realised that fully solving as it were the prime number problem equally required that both quantitative (analytic) and qualitative (holistic) aspects of mathematical interpretation be both fully differentiated from each other as its Type 1 and Type 2 aspects, before eventually becoming fully integrated with each other as its Type 3 (radial) aspect.

Therefore in development - what I identify as - Band 5 (Level 2) represents the crucial stage, where at last mathematical understanding has now become sufficiently refined to enable - at least in general terms - this much sought after integration of both its Type 1 (analytic) and Type 2 (holistic) aspects.

Thus the mathematical quest to understand the fundamental nature of the number system (in the two-way relationship as between the primes and natural numbers) exactly corresponded in my experience with the inner quest for mature psychological integration (in the two-way relationship as between conscious and unconscious).

Thus I gradually came to the deep realisation not alone of how the zeta zeros objectively played a crucial role in enabling the consistent behaviour of the primes with the natural numbers, but subjectively in terms of my own development of how they equally played a crucial role in enabling the seamless integration of both conscious and unconscious aspects of experience.