INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
An independent forum for a critical discussion of the integral philosophy of Ken Wilber
Publication dates of essays (month/year) can be found under "Essays".
Part 1 |
Part 2 |
Part 3 |
Part 4 |
As an economics’ student in Dublin in the late 1960’s, Peter Collins underwent a significant “scientific conversion”. Since then he has devoted considerable attention to the implications of a full spectrum developmental approach for radical new interpretations of mathematics and its related sciences. Though potentially of growing relevance for better understanding of our present problems, so far, he believes, these have been greatly overlooked by both the scientific and integral communities.
Part 4: Connecting Human Perspectives
with String Theory
In my previous article, I dealt with the 16 primary perspectives that arise directly from a dynamic interactive understanding of the four quadrants.
I then showed how these perspectives can be related to the dominant functions as defined by the 16 personalities in the Myers Briggs Type Indicator (MBTI). So the dominant functions (and corresponding perspectives) are thereby those which are most differentiated in development.
However though often much less developed, all functions (with their corresponding perspectives) must necessarily arise in experience.
I then showed how each of the personality types entails a unique configuration of the four functions, which in turn can be expressed as a unique configuration of the four main perspectives (i.e. 1st person, 2nd person, 3rd person and 4th person).
However, after years of reflection on the MBTI, I came to realise a certain weakness.
And as typical of the experiential approach that I have always adopted with respect to issues, this initially arose out of consideration of my own personality type.
As much as I tried, I could not see that this personality fitted easily with any of those (as listed in the MBTI).
From one perspective, I saw myself as an internal feeling type, which related to a continual preoccupation with the existential nature of experience.
However from another perspective, I possessed a strong desire to unravel the universal structures of reality in an impersonal rational manner.
So, from early development there had always been a conflict in reconciling the affective (experienced in an internalised subjective fashion) with the cognitive dimension of experience (operating in a detached objective manner).
Indeed the alternative Enneagram system seemed to describe these personality features more accurately. So I sometimes saw myself as a 4 (with a strong 5 wing) or alternatively, as a 5 (with a strong 4 wing).
And then when I reflected further on the matter, I realised that all those writers with whom I had especially identified throughout adult development, broadly fell into the same personality categorisation (in Enneagram terms).
So there was Einstein, whom I saw as a strong 5 (with a 4 wing), Kierkegaard as a strong 4 (with a 5 wing), Hegel a strong 5 (with a 4 wing), St. John of the Cross a strong 4 (with a 5 wing) and Jung a strong 5 (with a 4 wing).
And I found this very illuminating. In particular, for a long period I had resonated deeply with St. John's writings (esp. “The Dark Night”). However I had come to the conclusion that his particular experience could not be solely taken as a reliable blueprint for the stages of spiritual development.
So I now could see more clearly that his approach represented just one version of spiritual unfolding that might be best suited for a particular type, who broadly shared the same personality characteristics.
This then led to the search for a more generalised outline to the advanced stages of development based on distinctive personality types.
And then when attempting to relate my findings regarding this hybrid personality (involving the 4 and 5) back to the MBTI, I realised that there were in fact 8 missing personality types still awaiting identification.
Furthermore, I could see that these new types and the existing 16 (already identified) could be more simply obtained from the original four functions (with their corresponding perspectives) and illustrated through a fully interactive understanding of the four quadrants.
And this new finding relates to the simple mathematical fact that any four objects (containing all four at a time) can be permutated i.e. arranged in 24 ways.
So for example, when we take the four letters a, b, c and d we can give 24 distinctive arrangements of these four letters.
Likewise, using the four numbers 1, 2, 3, 4 now representing the four perspectives 1st person, 2nd person, 3rd person and 4th person respectively, we can give 24 distinctive arrangements of these four perspectives (16 of which refer to those already identified in the MBTI).
The 24 Personality Types
The first group of 8 perspectives relating to the S type (in the Myers-Briggs typology) comes from arrangements, where the horizontal matching of opposite perspectives regarding exterior and interior aspects, is preserved.
We saw for example how in personal (subjective) terms, 1st is matched with 2nd and in an impersonal (objective) manner 3rd is matched with 4th person.
So preserving this number order with respect to 1st and 2nd (and 3rd and 4th) perspectives, allowing for their reverse directions, gives rise to 8 distinctive arrangements:
12 34 (ISFP), 21 34 (ESFP), 12 43 (ISFJ), 21 43 (ESFJ),
34 12 (ESTJ), 43 12 (ISTJ), 34 21 (ESTP), 43 21 (ISTP).
The general feature here is that particular attention is given to the integration of the dominant with the auxiliary function in a somewhat dualistic manner, though the other two functions are also necessarily involved.
These 8 personality types may be referred to as “the realists” and where successful development takes place, substantial integration is likely to occur relatively early in adulthood. This enables such people, to become well adapted to life, pursuing fruitful careers and becoming accomplished in many activities.
The next category dealt with in the MBTI relates to the 8 intuitive types, who are more geared to unconscious recognition of the potential inherent in phenomenal events.
Here perspectives operate in an intersubjective and interobjective manner, where the nondual aspect of experience is more emphasised.
Successful development for this grouping requires a greater level of integration of the tertiary function (in Jungian terms), which is in the same location as the dominant i.e. interior or exterior respectively. So, the 4th person perspective is related to the 1st, with both being given an interior location. Likewise the 2nd is related to the 3rd, with again both relatively given an exterior location.
So, the 8 intuitive types relate to the following set of arrangements regarding the four numbers (representing perspectives):
14 23 (INFP), 14 32 (INFJ), 41 23 (INTP), 41 32 (INTJ),
23 14 (ENFP), 23 41 (ENFJ), 32 14 (ENTP), 32 41 (ENTJ).
However this leaves 8 more possible arrangements that are not addressed in the MBTI.
The need for these can be seen with reference to the manner I illustrated the quadrants in the last article.
The first two arrangements of quadrants related here to the S type, based on horizontal complementarity of perspectives, where personal and impersonal are treated separately.
So in one case, one for example learns to successively combine dominant and auxiliary functions with respect to feeling. (This then implies that tertiary and inferior are likewise combined in a less effective manner with respect to thinking).
And this describes the S type.
Then in the next case, the emphasis is on vertical complementarity, in a holistic manner (involving intersubjective and interobjective aspects).
Though this now requires a greater interaction with the tertiary function (and the corresponding second weakest perspective), again I displayed these in a relatively distinct manner, where personal and impersonal perspectives are still to a degree separated.
This implies that the most complete development entails that both the personal and impersonal perspectives be themselves integrated in a diagonal manner. This requires for example that the individual interior of an impersonal be related to the collective exterior of a personal (and individual exterior of an impersonal with the collective interior of a personal) perspective.
Diagonal integration of quadrants then implies that one keeps switching as between personal and impersonal perspectives with respect to both their individual and collective aspects in an interior and exterior fashion.
This now in turn implies that the inferior function is integrated to a substantial degree with the other three functions. Alternatively, the hitherto least developed can now be successfully integrated with the other three personal perspectives.
So this leads to a new mixed type (M) with 8 number arrangements:
13 24, 13 42, 31 24, 31 42,
24 13, 24 31, 42 13, 42 31.
These can be looked on as a composite mix of both the S and N types already listed.
So the dominant and auxiliary here relate to personal and impersonal perspectives.
Put another way, these types are especially sensitive to the shadow side of personality. So, as soon as the objective side is exercised, the countervailing personal shadow intrudes. Then when the personal aspect now enters experience, the impersonal shadow becomes apparent. In this way, one is repeatedly led to implicitly question the (separate) dualistic validity of any distinct perspective.
Thus for proper integration, considerable emphasis must be given to the substantial integration of all shadow elements.
And when successful, one solely identifies with the separate validity of any function (or perspective) in a relative manner, now seeing each in truth as ultimately interdependent with all others.
The first two groupings emphasise polar opposite distinctions (especially where S types are concerned).
So one is defined as either extravert or introvert (E or I), either sense orientated or intuitive (S or N) either a thinking or feeling type (T or F) or finally perceptive i.e. spontaneous and open or judgemental i.e. controlled and closed (P or J).
However for the new third mixed type, these categories no longer apply
Thus, one in a primary sense is neither extraverted nor introverted but rather centraverted. Here the self is identifiednot with any distinct perspective but ratherwith a spiritual centre (through which all perspectives are related). Thus phenomenal perspectives are now understood as temporary relative expressions, emanating from this centre of one's being, continually existing in the present moment.
Likewise, one identifies with neither sense nor intuition as such but rather a marriage of the two, where spiritual potential can be combined with actual form. And this provides the best possibilities for transformation of the world (both in psychological and physical terms). So we now have the situation where a marked capacity for creativity can be expressed in an eminently practical manner.
The third set of polarities in the MBTI relates to thinking and feeling. A major criticism here is that no explicit role is given to the volitional capacity of the will, which is central to integrating the other functions. Even when not initially present, one thereby possesses an amazing ability to move towards a yet unseen integration by trusting one's innate desire for ultimate meaning.
In Christian literature, the most advanced spiritual state entails the identification of one's will with the will God, so that everything one does is thereby an expression of the divine will. In more psychological terms, one could express this as the integration of the ego self with all created phenomena.
Then reality seems to act through the self, which has now become so refined as to be inseparable from one's universal cosmic identity.
Finally, one identifies with neither perception nor judgement but rather with what might be called a quality of discernment which is attuned to making the appropriate response in circumstances that can vary widely. So one can be open to others and likewisewhen for example an important moral principle is at stakefirm and unyielding. And the appropriateness of both is dictated by changing circumstances (where one attempts to act in a fully integral manner).
Now according to the binary model, as all stages, by definition, represent a certain configuration with respect to the two aspects of differentiation and integration respectively (regardless of how undeveloped), everyone already enjoys a certain access to the entire spectrum of development.
However, especially regarding the more advanced stages, in practice this can remain a somewhat attenuated access due to insufficient development of both dual (differentiated) and nondual (integral) aspects.
In general terms, I have come to realise that the route to true integration of personality varies in accordance with the three groupings that I have identified.
So again we have the first group of 8, which in terms of the MBTI comprising S types. Successful development for this group largely centres on effectively combining dominant and auxiliary functions. Though this necessarily entails a degree of integration, it usually remains at an implicit level, where the unconscious largely acts to serve the conscious needs of the personality.
This grouping tends to be adapted especially well to the real world of dualistic phenomena. Though of course this does not exclude intuitive type development with respect to certain modes, adjustment to the world and its responsibilities tends to take place comparatively early in life so that these types are often highly accomplished, as already mentioned, regarding their careers and a wide range of other activities. Even when the deeper needs of the unconscious can no longer be avoided somewhat later in life, this rarely threatens to completely disturb a ready identification with the world of form.
Thus in terms of the stages of development, successful integration for these types can largely take place by the centaur stage (which would be the highest level of what I refer to as Band 2). Adaptation then tends to take place in an increasingly extensive fashion over a wide range of dualistic type activities.
Though by no means excludedat least for some modes“higher” contemplative type development (associated with Bands 3, 4 and 5) would be unlikely to occur to any considerable degree. This would also imply that the most developed radial stages i.e. Bands 6, 7 and 8 (as far as these have meaning) would thereby be largely confined to their active expression.
The second personality grouping relates to the N characteristic in the MBTI as that based on holistic intuition. Thus whereas the S type is geared to the identification of the parts within a system (thereby identifying the whole with the sum of these parts), the N type is more directly geared to the identification of wholes in a qualitative manner (which arises through appreciation of the interdependence of related parts).
However in present day society, which is largely geared to a reduced interpretation of reality, successful development for this intuitive grouping is much more problematic and in fact rarely fully achieved. As intuition is primarily the expression of the unconscious mind, true integration here properly requires substantial development of the unconscious.
In former times, this was largely achieved in a spiritually confined contemplative type setting, where exposure to the world of phenomena could be more easily controlled. However it is much more difficult to achieve this development while remaining in the world and being subject to its many demands.
Thus intuitive personalities such as artists, writers, and creative thinkers often maintain a very uneasy balance as between the needs of their personalities and the demands of everyday living, with true integration rarely being achieved.
Even when the desire for integration and acceptance of the necessary discipline is present, there are two seemingly contrary directions in which such development can occur.
In the spiritual traditions, more emphasis has been placed on the transcendent ascent, in the movement to a refined collective spiritual notion of the whole that ultimately is beyond phenomenal form. And this is often associated with the masculine principle in a somewhat impersonal view of the spiritual that initially emerges in development through the refining of one's rational cognitive faculties.
However, there should be an equal emphasis on the immanent descent in a more individual notion of the whole (as uniquely contained in each part of creation). This in turn is more commonly associated with the feminine principle, operating through the corresponding refinement of emotional and aesthetic sensibilities.
So here the main focus is on the return to earlier development in the attempt to root out the primitive confusion that can serve so much to hamper one's true emotional response to others.
Thus, in terms of my stages, the first leads to Bands 3 and 4 and in a more limited manner Band 5. However the more extensive development associated with Band 2 might remain quite limited.
Therefore the radial Bands (6, 7 and 8) insofar as they later unfold may now be of the more passive contemplative variety, where one still operates with a large degree of caution with respect to phenomenal activities.
In the second case of the spiritual descent, Bands 3 and 4 could be largely bypassed. However the earlier Band 2 and what I refer to as the spiritual descent i.e. Band 5, would be much more developed.
This would entail that radial development when it unfolds, would be of the more active type, considerably devoted to creative engagement with others.
However a limitation here could be an undue identification of spiritual reality with the world of form (in what could thereby represent a refined form of pantheism).
However it is the new group of eight personality types that in the appropriate circumstances, provide the greatest scope for successful development over the entire range of stages.
The first can be referred to as the “real” group (related to actual reality) and the second as the “imaginary” group (related to potential reality).
However the final group represents a “complex” personality type that incorporates both “real” and “imaginary” aspects. And paradoxically, when successful development takes place, this group is equally the most spiritually simple of all types.
The basic feature here is that considerable shadow development takes place with respect to all functions (and corresponding perspectives).
From one standpoint, the dominance of the first two favoured functions is lessened; equally the weakness of the latter two is properly acknowledged and addressed.
When one looks at the MBTI profiles, ISFP for example is opposite to ENTJ. And when one looks at the associated functions (and perspectives) in the previous part of this series, they are indeed the exact reverse of each other.
So, with this third grouping, the shadow aspects are so comprehensively addressed that all functions can play an equal role fully harmonising with each other.
This means that the conscious expression of any one function is properly balanced with its opposite aspect (in horizontal vertical and diagonal terms).
Therefore, we have here the existence of complex functions (combining both real and imaginary aspects) in an exterior and interior manner.
Likewise in terms of perspectives, we equally have the situation where each perspective is balanced with its opposite in horizontal, vertical and diagonal terms.
So, exterior and interior aspects are reconciled regarding both personal and impersonal perspectives. Collective and individual aspects regarding personal and impersonal perspectives (still considered in a relative separate manner) are then holistically reconciled in interior and exterior terms. Finally, both personal and impersonal perspectives are reconciled with each other in diagonal terms.
This can likewise be the most problematic of groups, for when development does not properly unfold, deep psychological problems such as psychosis may be encountered.
However, where issues can be satisfactorily addressed, the greatest results may be achieved.
Space, Time and Perspectives
It has long fascinated me how each personality type represents a unique configuration of the manner that space and time is experienced. Likewise, the corresponding configuration of perspectives (implied by each personality) equally entails a distinctive manner of experiencing space and time, representing a unique notion of a dimension.
And in this regard we have defined 24 relatively distinct dimensions.
However as the conventional appreciation of space and time (in scientific terms) implies just one limited interpretation of dimensions, I will now attempt to clarify the more comprehensive situation at greater length.
Physical and Psychological Aspects
In the Myers Briggs typology, the first distinction is between extravert and introvert (E and I).
So in the terms of space and time, the former relates to the (objective) physical, whereas by contrast, the latter relates to the corresponding (subjective) psychological experience respectively.
In this sense, both the physical and psychological aspects of space and time operate in a dynamic complementary manner.
When I initially became aware of Einstein's Special Theory of Relativity, I began to realise that all the key notions that he had provided regarding the relativity of space and time in physical terms, equally applied in a psychological manner.
Thus, in psychological terms, space and time are clearly relative. I have often reflected on this, for example, when caught in a traffic jam. As the traffic slows down getting ever more congested in space, the experience of time itself slows down considerably, where in extreme situations, each second can feel like an eternity.
And in physical terms when an object travels at increasing speed (relative to a stationary observer), less time passes as registered by the object. Then in the limit, when travelling at the speed of light, no time at all passes, with the “object” continually existing in the present moment. Therefore, relative to its own speed, time does not pass for a photon of light, which exists in the continual present moment.
And this has a direct psychological counterpart. So contemplation can be looked on as a process where psychological interaction with respect to phenomena continually increases. Then when eventually dwelling in the pure spiritual light, one remains in the present moment (where no time passes).
Indeed, I have frequently pointed to the incongruous fact that when Einstein was once asked to give a simple explanation of relativity, he did so in terms of its psychological rather than physical meaning.
“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.”
So what Einstein implies is that sitting with a nice girl for two hours can literally be a de-light-ful experience (where phenomenal dualistic barriers melt away). Therefore while bathed in this light, time does not appear to pass.
However, the opposite experience of sitting on a stove creates a strong feeling of isolation from one's environment, resulting thereby in a significant increase of what can be termed psychological gravity. And with this, there comes a marked sense of the slowing down of time.
In fact there are intimate parallels to be drawn as between the physical phenomenon of “a black hole” and the psycho-spiritual experience of “the dark night”.
A black hole leads to the collapse of certain types of stars, causing an extreme contraction of matter in its spatial vicinity due to an immense force of gravity. And this causes a considerable slowing down of time (relative to an outside observer).
A dark night is a psycho-spiritual phenomenon commonly associated with certain types of spiritual “stars” who have already attained a substantial degree of spiritual illumination. However, the conscious expression of this creative energy can then place considerable strains on the psycho-physical apparatus, leading to the subsequent need for deep levels of unconscious regeneration. And this can then result in the marked negation of former conscious structures, where one collapses under the weight of an intense psychological experience of gravity.
In fact, there are close etymological connections as between the notion of grief and that of gravity. So grief in representing the loss of what literally matters most to us, represents the psychological equivalent of physical gravity (just as spiritual light represents the corresponding equivalent of electromagnetic energy).
So the “dark night” is typically associated with an intense experience of loss (ultimately of the presence of God). And this can be associated with a dramatic slowing down in the experience of time.
Remarkably, there are further close complementary connections as between the phenomenon of black hole radiation (as outlined by Stephen Hawking) and the psychological process, by which one emerges from a prolonged dark night episode.
Thus the gravitational nature of the black hole can be transferred into physical energy through radiation, just as the psychological gravity (i.e. grief) of the dark night can be transferred into spiritual energy (i.e. pure joy) through the refined projection of repressed psychological material.
So there is an important unrecognised holistic area of scientific research, where key notions linking psychology and physics can be fruitfully investigated.
And chief among these relates to the complementary behaviour of space and time in both domains.
Indeed, I have long considered that feelings of stress entail important changes in the manner in which space and time is psychologically experienced and that our understanding could thereby be greatly improved through investigating this ubiquitous condition in an entirely new manner.
To sum up therefore, there is an exterior aspect to perspectives relating to the physical experience of space and time and an interior aspect relating to the corresponding psychological experience. Thus the dynamic switching as between both aspects represents the unfolding of space and time with respect to both modes.
And remarkably, in holistic mathematical terms, this entails the recognition of both positive and negative dimensions (of space and time).
So when we are consciously aware, these dimensions are thereby posited in experience.
However corresponding unconscious recognition requires that we can to an extent dynamically negate these same dimensions.
Thus, the very ability to keep switching as between the exterior and interior aspects of experience, requires the continual positing and negating of the dimensions of space and time (and related objects) with respect to their physical and psychological aspects.
And the present limited scientific notion of dimensionwhich completely ignores the intrinsic dynamics of experienceallows for no direct recognition of this fundamental reality.
Real and Imaginary Aspects
In the MBTI, the first group referred to as the sense (S) type, relates to those who principally gravitate towards the conscious world of form. So these types tend to be “realists”, who experience events as they actually happen.
However the intuitive (N) type relates to those who by contrast gravitate more to the unconscious world of emptiness. These by contrast are “dreamers”, who are more geared to the recognition of the holistic potential inherent in (actual) events.
By definition, every personality necessarily combines both of these aspects to some degree, though the relative dominance of each can greatly vary.
Again in terms of perspectives, the former S type relates to those that are primarily orientated to the specific manifestation of perspectives (in an objective or subjective manner).
The N type relates by contrast to those orientated to the holistic manifestation of perspectives (in an interobjective or intersubjective manner).
And once again these two types of perspectives are associated with a distinctive experience of space and time.
Accepted scientific notions are based almost exclusively on the conscious “real” interpretation, where a whole in every context is essentially treated in a reduced quantitative manner as the sum of its constituent parts.
However, we can equally give an unconscious “imaginary” interpretation to all events, where the “whole” is now understood in a true qualitative fashion as representing the interdependence of its various parts.
Therefore, though it is completely overlooked by present science, the understanding of space and time necessarily requires both a “real” conscious and “imaginary” unconscious element.
So quite simply, whenever we are aware of part phenomena in a quantitative manner, “real” conventional scientific notions apply.
However, when by contrast we are aware of phenomena in a qualitative fashion as “wholes”, then unrecognised “imaginary” notions are now directly relevant.
So, for example, the aesthetic appreciation of a painting or indeed any work of art necessarily implies “imaginary” as well as “real” notions of space and time. It takes place thereforeas properly understood do all eventsin “complex” dimensions.
Actual experience entails that a dynamic relationship be maintained as between both “real” and “imaginary” notions.
For example, a very talented athlete may form an early childhood dream of one day winning an Olympic final.
So the arduous practice and discipline that such an achievement entails on a daily basis (in an actual manner) is geared towards the realisation of that childhood dream (still remaining as unfulfilled potential).
Actual “real” experience of space and time is thereby wedded to a corresponding “imaginary” aspect, representing the potential that is inherent in everyday events. In fact, it is this potential aspect that provides the qualitative “whole” dimension of experience that is so necessary for activity to be truly meaningful.
So if the athlete eventually wins that Olympic event, this represents the fulfilment of a cherished dream. The conjunction then of the actual real moment of victory with the long held potential dream of winning represents a truly transformative experience (perhaps never to be repeated).
Though the imaginary notion is now used in both science and mathematics, it carries but a reduced quantitative meaning that remains devoid of any true qualitative significance.
And as I have repeatedly stated, the very essence of the imaginary concept from a philosophical perspective, is that it provides the means of incorporating holistic notions of interdependence, with regard to both science and mathematics, in an indirect quantitative manner.
However, the revolution that is now so urgently required is the ability to clearly recognise the imaginary in a direct qualitative fashion.
All experience, when properly articulated, therefore necessarily entails both “real” and “imaginary” notions of space and time.
And in psychological terms, whereas the S types predominantly experience these in a “real” manner, N types by contrast more directly experience these dimensions in an intrinsically “imaginary” qualitative fashion.
Personal and Impersonal Aspects of Space and Time.
As we have seen, everyone necessarily uses both feeling (F) and thinking (T) with respect to experience. However in practise, each personality in the MBTI is defined by the predominance of one of these modes.
And likewise, experience can be dominated by either the personal or impersonal perspectives.
Once again, these two modes (and perspective types) lead to a distinctive notion of dimensions.
So where the (affective) feeling mode predominates, one obtains a personal notion of space and time. However, where the (cognitive) thinking mode is to the fore, then an impersonal notion predominates.
And once again science, as we know it, is solely geared to the impersonal interpretation.
In practice we well recognise the distinction as between the personal and impersonal aspects of dimensions.
For example, we often refer to the personal space that attaches to human behaviour and the great damage that can result when this space is violated.
Likewise, though we do not refer so much to personal time, we frequently employ a synonymous term i.e. quality time.
Therefore, though time is scientifically measured in a quantitative manner e.g. 24 hours in each day, with regard to personal relationships, we are aware of a distinctive qualitative notion. So, if I am to spend some quality time with a friend, this implies a degree of intimate sharing (where personal disclosure is involved).
So the feeling type engages with space and time in a very different manner from the corresponding thinking type and because of the dominance of scientific notions, this is not at all properly recognised.
Only recently have I come to clearly realise that the root of this distinctive experience of space and time i.e. personal and impersonal respectively, lies deep in the holistic appreciation of the two aspects of the number system.
Once again the additive approach is based on the two original numbers 1 and 0. Then, starting with 0, through the progressive addition of 1, the natural numbers can be generated.
However the multiplicative approach is based on the primes, where through the unique products of such factors, the natural numbers (other than 0 and 1) can be generated.
Now, properly understood in a full perspective approach to mathematics, these two systemswhich ultimately are fully interdependent with each other in dynamic fashionoperate as complementary opposites.
So when, as customary, we identify the additive approach with impersonal notions of space and time, then the personal experience becomes directly identified with the corresponding multiplicative approach.
There are even significant clues here in the ordinary use of language.
We often refer to early instinctive experience of the senses as primitive (where both conscious and unconscious aspects are not properly differentiated from each other).
However, as cognitive reason slowly unfolds in an impersonal manner, equally sensations and feelings develop in a more organised natural fashion (just like the formation of natural numbers arises from the unique factor ordering of the primes).
And I have frequently stated on this forum how the transcendent ascent can best be interpreted in a holistic mathematical manner that is based on the additive approach to number.
Then the corresponding immanent descent (where the roots of primitive desire are unravelled) can correspondingly be interpreted in a multiplicative number manner based on the primes.
And the Riemann Hypothesis, which is really about the reconciliation of both aspects of the number system, can then be holistically understood as the basic requirement for the full flowering of the radial stages of development.
So a precondition for radial development is that a very complete integration of both affective (personal) and cognitive (impersonal) modes can be obtained, which ultimately relates to holistic mastery of the very manner through which the notion of number emerges in experience.
In fact this distinction as between emotion on the one hand and reason on the other is central to proper understanding of how space and time are associated with both the affective and cognitive modes respectively.
And these operate in a dynamic complementary manner.
So, if we initially associate space (and objects in space) with personal feeling, then time (and objects in time) are then associated with impersonal reason in a complementary fashion.
And this can operate in reverse, so that if time (and objects in time) become associated with personal feeling, then space (and objects in space) are associated with impersonal reason, again in a complementary fashion.
So, a continual dynamic switching takes place as between affective and cognitive modes on the one hand and the experience of space and time on the other (in both a personal and impersonal manner).
This implies that ultimately for the affective mode to operate in a fully harmonious conscious manner, it must be perfectly balanced by unconscious experience of the corresponding cognitive mode; likewise for the cognitive mode to operate in a similar conscious manner, it must be perfectly balanced by the unconscious experience of the corresponding affective mode.
And this is why the additional missing group of 8 personality types is no longer primarily defined in terms of thinking or feeling (as in the MBTI) but rather in terms of volition (V) which is used to fully harmonise both affective and cognitive modes.
However though personal notions of space and time regarding all holons (and onhols) are of equal importance to impersonal, this is not remotely recognised yet in conventional scientific terms, as illustrated for example in the present limited interpretation of evolution.
Space and Time: Objects and Dimensions
Perceptions represent the psychological counterpart in experience to physical objects. So, when one observes an external object, this necessarily entails a corresponding internal perception.
Concepts then represent the psychological counterpart to physical dimensions.
Thus as we commonly understand objects as related to the physical dimensions of space and time, likewise perceptions are necessarily related to their corresponding concepts, which are equivalent to the corresponding psychological dimensions of space and time.
By definition, all personality types experience both objects and dimensions. However again the balance can vary significantly as between those who primarily identify with individual objects (related to dimensions) and those who primarily identify with the collective dimensions (to which objects are related).
And this distinction relates to the final polarity set in the Myers Briggs typology involving perception (P) and judgement (J) respectively. So perceptive types are primarily oriented towards objects (in space and time) and judgemental types to the corresponding dimensional structures (to which these objects are related).
And this distinction corresponds to the individual and collective aspects of perspectives.
Thus the perceptive type (relating to the individual aspect of perspectives) tends to inductively infer overall dimensional structures from initial engagement with phenomenal objects.
However the judgemental type (relating to the collective aspect of perspectives) tends to deductively recognise phenomenal objects through initial engagement with the dimensional structures of space and time.
Personality Types, String Theory and Monster Moonshine
I had developed this 24-dimensional interpretation of personality types by the early 90's and had indeed already posted a version on an old Shambhala forum (circa 1998).
And I had already come to clearly realise that in a similar manner to the way in which one can designate distinctive personality types for the psychological experience of reality, equally one can designate distinctive “impersonality types” through which all physical reality can be explained.
And in a comprehensive understanding, both of these explanations would appear as two complementary sides of the same coin, as it were, with neither possessing strict meaning in the absence of the other.
And this then led to an unexpected connection with the world of strings, where an earlier version known as bosonic string theory gave rise to the asymmetric vibration of strings in 24 dimensions.
The Magic of 24
Before proceeding further, it may be of benefit to explain a little why the number 24 possesses such special magical properties.
When we multiply the first four natural numbers, i.e. 1 * 2 * 3 * 4, we obtain 24.
And as we have already seen, there are 24 unique ways in which these four numbers can be permutated (i.e. arranged).
Interestingly, the sum of the first 24 natural numbers = 300. Then when we add all the primes to 24 we get 100. And of course, the 24 hour clock plays an important role in every day life.
24 is also unique in that it provides the sole means of adding a series of successive squares of the natural numbers to obtain the square of another natural number.
Therefore, when one adds up the squares of all the natural numbers from 1 to 24, this results in the square of 70 (i.e. 4900).
When one thinks holistically regarding the notion of squaring, it carries a special integral significance, with the simplest form of such interpretation defined with respect to 2-dimensions (which I have often referred to in my articles using the example of a crossroads).
Therefore this special property of 24 suggests that it in fact carries a unique integral capacity (from a holistic mathematical perspective).
Not surprisingly therefore, the number 24 keeps cropping up in fundamental mathematical research, and was especially explored by Ramanujan, who possessed an extraordinary intuitive capacity to discover important results.
So 24 forms the basis of the famous Ramanujan tau function. This is perhaps the best known example of what is called a modular function in mathematics, which is one that possesses amazing symmetrical (i.e. integral) properties.
The number 24 figures prominently in his famous solution (along with Hardy) to what is called the partition problem.
The partition problem is deceptively simple to state.
One could for example attempt to explain all the ways in which 4 stones can be divided into partitions.
A first way is to divide the stones into 4 independent units i.e. 4 = 1 + 1 + 1+ 1.
A second way is to take stones two at a time i.e. 4 = 2 + 2.
A third way is to break the second bundle of 2 (in the previous example) into two independent stones. So, 4 = 2 + 1 + 1.
A fourth way is to take one bundle of 3 combined with the remaining stone i.e. 4 = 3 + 1.
Finally, one could take all 4 stones as one bundle i.e. 4 = 4.
So in this case, we can see that there are five possible partitions for the number 4.
However, it becomes increasingly difficult to work out the number of partitions for larger numbers.
So the resolution to the partition problem was concerned with obtaining a general formula that could calculate the total possible partitions for any number (regardless of how large).
And as I say, this formula features the number 24.
Then the earlier bosonic string theory, which provided the first truly consistent interpretation, was heavily related in mathematical terms to Ramanujan's tau function.
Sphere packing is another fascinating area in which the number 24 plays a special role.
We can start with the simple example in two dimensions of how to arrange similar sized coins in the most efficient manner. Hexagonal packing (as illustrated below) provides the most efficient method.
We can then move to the consideration of the most efficient way of stacking 3 dimensional spheres. If we take an orange as a good representation of a 3-dimensional sphere, this problem amounts to the most efficient way of stacking oranges. And this entails that each (interior) orange will make contact with 12 other oranges. However for 2 dimensions and 3 dimensions, even the most efficient arrangement entails a degree of free space (9% in two dimensions and 26% in 3 dimensions respectively).
These notions can then be easily extended into higher dimensions relating to the packing of hyperspheres. Though one cannot envisage such higher dimensional objects in 3-dimensional space, they can be satisfactorily dealt with in a mathematical manner.
And it has been shown that when one considers spheres in 8 and especially 24-dimensional spaces respectively, that an amazingly efficient packing solution is available (that leaves virtually no free space).
In 24-dimensional space, each object is touched, would you believe, by 196560 other objects.
This is what is now known as the Leech Lattice and has a hugely practical application in terms of the elimination of errors in communication systems.
The original Jungian Theory of Personality was based on 8 distinctive types and my own elaboration of this theory, via the MBTI, led to 24.
Interestingly in a reverse manner, the original bosonic string theory was based on the vibration of 24 asymmetric strings, relating to 24 dimensions (with two additional added to give 26). Then the subsequent generalisation of this model reduced this to 8 (with again two additional strings added to give 10). The present accepted model (M-Theory) is now based on 11 dimensions i.e. (9 + 2). And the alternative widely known personality theory i.e. the Enneagram, is based on 9 basic types.
Just as personality types represent unique ways in which the experience of space and time can be configured (in psychological terms), likewise string theory represents the corresponding unique manner in which space and time can be configured (in physical fashion). And it is important to note here that the very notion of a dimension is quite distinct here from its standard usage in everyday science.
So properly understood, a dimension in the context of string theory relates to how all the distinctive notions of space and time, which I addressed in the previous section, are configured.
And each such configuration equally relates to a unique manner in which the primary perspectives are configured.
And this is why it remains non-intuitive, as conventional science is confined to just one impersonal notion where dimensions are considered as separate.
In this new dynamic context, it is commonly stated that an asymmetric string can vibrate in 24 distinct dimensions. And as we have seen, we can equally say that a personality can psychologically vibrate (as a distinctive type) with respect to 24 distinct dimensions.
In other words, just as we can distinguish 24 asymmetric states for the string, equally we can distinguish 24 (differentiated) personality types (representing corresponding unique states). So in fact by looking at the relationship between strings and personality types in a complementary manner, we are led to the realisation that in each case, we are referring to the 24 primary perspectives, already identified.
And in turn, each of these perspectives (as a relative momentary experience) is associated with a unique configuration of space and time.
So the 24 personality types (in psychological terms) and 24 impersonality types (as asymmetric strings in a physical manner) are really just two sides of the same coin, relating to the unique way in which space and time in both cases can be configured.
Thus my key point again is that properly understood, both the physical and psychological explanations are fully complementary with each other and in fact correspond to the same fundamental manner in which the key primary perspectives are related at two extremes of evolution relating to earliest matter and human development respectively.
And the implications of this realisation I believe are truly enormous.
However there is another important mathematical area which can throw additional light on the ideas mentioned here.
The field of group theory arose out of an attempt to classify the different types of symmetrical objects that can occur.
A simple example of such a symmetrical object is given by the 3-dimensional cube. There are many different ways of rotating a cube (24 in all) so that its symmetry remains unchanged i.e. where it remains indistinguishable from a previous state.
So the quest that arose in the 19th century was to classify “the atoms of symmetry” or basic building blocks, as it were, for all symmetrical objects in what were termed “finite simple groups”
A great number of symmetrical objects are based on the different rotations possible regarding various prime number permutations.
However other simple groups exist where the number of indivisible permutations does not correspond to prime numbers.
In the classification that followed most conveniently fell into four coherent families.
However like separated islands, exceptions remained (26 in all) that were lumped into a sporadic groups category.
And the largest of these groups (and the largest of all symmetrical objects) is known as the Monster with the total symmetries truly enormous (and many times greater than all the quarks in the Universe).
What is remarkable is that key numbers associated with the Monster, at every turn, are intimately related to 24.
Then an exciting new development suggested that the Monster Group was itself connected with a seemingly unrelated area of mathematics known as the j-function, which is another example of a modular function (which as already stated, exhibits amazing self repeating symmetrical features).
And thenwhat came to be known asthe Monstrous Moonshine Conjecture (since proven), suggested that both the j-function and the Monster group could be connected through the 24 dimensional version of string theory. In brief, numbers in the j-function explain the vibrations of individual strings (at various energy levels). Then the Monster Group explains the overall way in which these vibrations can be co-ordinated at these levels.
And there is a remarkable similarity here with the very way that perspectives are related.
I have already made the point that the word “perspective” is somewhat confusing as it can be used in two relatively distinct fashions.
So we have the notion of (differentiated) primary perspectives. Differentiated in this psychological context, equates well with asymmetric in physical terms. And just as with strings in physics, these perspectives can be experienced at different energy levels i.e. stages of development. So, for example, a 1st person perspective (of an individual subjective nature) will manifest itself differently at the mythic and centaur stages.
Then we have the corresponding notion of (integrated) holistic perspectives which ultimately are without any distinct perspective. And this equates well with symmetry in physical terms.
So in the Monster Moonshine Conjecture, the asymmetrical behaviour of each string is described by the j-function and the overall coherence of string behaviour explained by the symmetrical features of the Monster Group. And both are here connected through the 24-dimensional model of strings.
In corresponding psychological fashion, we have the identification of the primary perspectives (which are differentiated in a relative manner from each other). Also in the binary approach to development, we have an outline of how these perspectives can be coherently integrated, which varies at each stage of development.
And these two aspects are connected through the model of 24 personality types (where each type combines the four perspectives in a unique fashion).
In the past, I attempted to explain differentiated and integral aspects in a manner consistent with the development of just one of these personality types (with which I identified).
What I find remarkable is that recent developments in Monster Moonshine have led to a new conjecture known as the Umbral Moonshine Conjecture (likewise now mathematically proven). And in this conjecture, there are 23 other ways through which the behaviour of each string and the coherent behaviour of all strings can be connected.
And once again the number 24 is in evidence. Not alone is it now conjectured that the 24-dimensional model of strings provides the coherent means to connect the individual (asymmetric) with the overall (symmetric) behaviour of strings but that there are likewise 24 ways in all through which this behaviour can be interpreted.
And again this fits in beautifully with my own evolving understanding of the theory of 24 personality types.
So in principle, each personality type, not only provides a unique way of differentiating the various perspectives, but equally, where full mature development occurs, offers a unique manner of achieving integration of all perspectives.
In the past, not surprisingly perhaps, I emphasised a stages of development model that was chiefly based on my own personality type.
However, in principle, associated with each personality is a distinctive stage model of development, which in its most advanced form ultimately allows for both the consistent differentiation and integration of all perspectives.
There are even further fascinating parallels as between the physical and psychological approaches that I do not have sufficient space here to explore in detail.
For example, the Umbral Moonshine Conjecture is explicitly based on the notion of “shadow” elements regarding string behaviour that is very much in line with the corresponding notion in psychological terms.
Likewise in exploring mathematical symmetries in the physical approach, much use is made of four dimensional objects called K3 surfaces, which suggest hidden symmetries within their structure.
Likewise in psychological terms, integration regarding development comes, for each personality type, through deep exploration of the manner in which the four basic functions (and four personal perspectives) contain hidden complementary patterns within their structure, which ultimately open out to embracing all personality characteristics.
We have covered a great deal of ground in 3 main sections.
The first section extends the MBTI to 24 distinctive personalities (in three main groupings)
Then these 3 groupings provide distinctive profiles through which overall personality integration can take place.
The second section then concentrates on the distinctive ways in which space and time arise in experience, with each personality type representing a unique configuration of such space and time. And this represents a new dynamic notion of dimension.
The third then draws strong parallels as between this theory of personality types and an earlier model of string theory.
Recent exciting developments, relating to the moonshine conjecture in physical terms and even more recently to the Umbral Moonshine Conjecture are in turn connected to strings and thereby have close parallels in the psychological realm.
The clear overall conclusion therefore is that both are in fact offering (using very different language) an attempted explanation of the various perspectives that experientially arise in both physical and psychological terms (which in truth represent two sides of the same reality) and how best they can be coherently integrated with each other.
Science itself ultimately requires the use of all these perspectives. However because of a strongly reduced rational approach (in formal terms) the true significance of its various findings cannot be decoded in an intuitively acceptable manner. In particular the vital connections which key physical findings have with the psychological realm are completely overlooked.
So the article represents a long overdue attempt to coherently address this vitally important issue.
1. In Enneagram terms, a 5 would relate to the (scientific) thinking and 4 to the more (artistic) feeling type (with both having an interior location). Though potentially a rich combination, it can be very problematic with the two key perspectives so inward oriented. Therefore, when development goes wrong, this can easily lead to serious forms of mental illness.
2. The 24 arrangements are abcd, abdc, cdab, cdba, bacd, badc, dcab, dcba, acbd, acdb, bdac, bdca, cabd, cadb, bdac, bdca, adbc, adcb, bcad, bcda, dabc, dacb, cbad, cbda.
3. I am referring here to the situation where successful growth for a particular personality type takes place. It is important to remember that no personality type is in any fundamental manner “better” or “worse” than another with each offering a distinctive means through which development can unfold. Other factors such as personal and social circumstances, influential relationships and crisis events can also play a key role.
And for all types, we can have a wide spectrum from very maladapted to highly integrated development.
Don Riso for example in dealing with the Enneagram, outlines on a scale from 19, development profiles for each type, varying from the most healthy to least healthy respectively.
4. As soon as horizontal integration occurs, a degree of overlapping in vertical terms necessarily takes place. And then where more specialised vertical integration occurs, this inevitably leads also to a degree of diagonal integration.
However with the S type, because the emphasis is mainly on dualistic type distinctions, unconscious appreciation (in the recognition of mutual interdependence of complementary perspectives) remains limited, relative to such dualistic understanding.
Therefore, the corresponding degree of vertical and diagonal integration is not enough to disturb the primacy of the two main functions (and perspectives) linked in a horizontal manner.
So, once again with the S type, the unconscious primarily plays a supporting role in enabling the successful unfolding of conscious understanding.
5. True integration for members this third group is very difficult to obtain in our culture as it may require a willingness to be an “outsider” with respect to conventional norms, while remaining continually faithful to a deeper quest for meaning (not recognised by society).
And even for those seriously motivated to achieve integration, failure to a greater or lesser extent is the most likely outcome.
I am reminded here of the lines of Dryden:
“Great wits are sure to madness near allied
And thin partitions do their bounds divide”
6. Though, in a primary sense, one may be defined as a centravert, in secondary terms, one will still exhibit either introvert or extravert tendencies.
However, when for example appearing as an introvert to others at this stage, the shadow side of the state is fully recognised. Such a personality therefore will find it easier to assume the opposite extravert behaviour when this is required.
So, much greater flexibility in the authentic switching of roles is a key characteristic of this developed personality.
Again there are eight types, which are all based primarily on the CTVD categorisation where C = centravert, T = transformative, V = volitional and D = discerning.
However, in secondary terms, behaviour relates to 8 composite types made up of one of the 16 standard categorisations (in the MBTI) paired with its exact opposite. So each personality fully unfolds through recognition of the shadow elements represented by the initial secondary type.
CTVD 1 (INFP and shadow ESTJ); alternatively (ESTJ and shadow INFP)
CTVD 2 (INFJ and shadow ESTP); alternatively (ESTP and shadow INFJ)
CTVD 3 (INTP and shadow ESFJ); alternatively (ESFJ and shadow INTP)
CTVD 4 (INTJ and shadow ESFP); alternatively (ESFP and shadow INTJ)
CTVD 5 (ENFP and shadow ISTJ); alternatively (ISTJ and shadow ENFP)
CTVD 6 (ENFJ and shadow ISTP); alternatively (ISTP and shadow ENFJ)
CTVD 7 (ENTP and shadow ISFJ); alternatively (ISFJ and shadow ENTP)
CTVD 8 (ENTJ and shadow ISFP); alternatively (ISFP and shadow ENTJ)
Even at the radial level, there can be a distinction as between the more active (where S is in the initial type) and the more passive (associated with N) leading to radial 1 and radial 2 experience respectively. However at radial 3, the initial type and shadow (from both directions) become largely indistinguishable from each other, offering the purest expression of the CTVD personality.
7. Like a lot of quotes attributed to Einstein, there is a degree of doubt as to whether he actually said these words. One explanation suggests that as a result of being asked so often to give a simple explanation of relativity, he hired a personal secretary to provide this answer.
However, if Einstein had reflected on his deliberately witty reply, he might have recognised an unexpected problem.
Once again, the reply refers to a psychological rather than physical notion of time. The clear implication therefore is that both physical and psychological experiences are complementary in a relative manner. This implies that relative notions apply not only to the physical world but also to the psychological constructs used to interpret this world. Therefore, the classical approach that Einstein steadfastly maintained throughout his life, in the belief that one can formulate absolute laws regarding objective reality, is ultimately untenable. So just like Newton's theory before him, Einstein's relativity theory represents but an approximation regarding the true nature of reality, which inevitably will be replaced by a more complete explanation.
8. As we know, information technology is based on the fact that all data can potentially be encoded using the two binary digits 1 and 0.
And this is connected with the additive approach to the number system, which directly lends itself to an impersonal approach to reality.
The alternative multiplicative approach in essence relates directly to feeling rather than reason and is rooted in the behaviour of the prime numbers. Unfortunately however, the attempted understanding of the primes has developed solely in a (masculine) analytic rather than (feminine) holistic manner.
So the Riemann Hypothesis, which is the outstanding unsolved problem in mathematics is directly concerned with the relationship of two aspects of the number system that are analytic and holistic with respect to each other. It therefore cannot be fully understood in a merely analytic type manner (as at present).
Likewise the attempted reconciliation of quantum mechanics with relativity theory is the outstanding unsolved problem in physics. And once again, this cannot be properly understood in a mere analytic type manner.
9. In physics, two extra dimensions are added to those relating directly to the asymmetric vibrations of the string. So the 24 dimensional asymmetric model becomes 26 dimensions and the generalised 8-dimensional asymmetric model becomes 10 dimensions.
Likewise in the prime based model of the number system we must add the two extra digits 1 and 0 to obtain all the natural numbers.
In personality terms, this equates to the fact that the 24 relatively distinct perspectives identified are related to the nondual notions (of unity and nothingness) respectively.
10. I made a holistic mathematical discovery regarding the significance of 24 some years ago (which I have not seen mentioned anywhere).
The circular number system, related to the various roots of 1, is especially significant from a holistic mathematical perspective.
And there is an ingenious way to find these roots.
Now the full angle around the central point of a circle is 360 degrees.
To find say the 4th root of 1, we divide 360 by 4 and obtain the value of cos 90 + i sin 90 = 1 + 0 = 1.
Then when we square this number we also get 1.
So we can get the nth root of 1 in this manner by dividing 360 by n and then adding sin and cos values (while ignoring the imaginary sign). And when we square the result the answer always lies between 1 and 2.
Now with the 24th root, we obtain cos 15 + sin 15 = .96592... + .25881… =
And when we square the result we get 1.5.
So this value derived from the 24th root of 1, lies at the very centre of the possible range of values, suggesting that it represents, in holistic terms, a golden mean as between differentiated and integral notions respectively. The other key values lie at the outer extremes. So 1st, 2nd and 4th roots all give an answer of 1, whereas the 8th root gives an answer of 2.
11. Though greengrocers have for centuries used the most efficient way of stacking oranges that leaves a minimum of free space, it has proved fiendishly difficult to prove this result and finally was only achievedas with the 4-colour problemthrough the extensive use of computers, in 1998. And recently, the most efficient methods that were long considered to hold for packing hyperspheres in 8 and 24 dimensions respectively, have also been proven to be true. In 8 dimensions this is known as the E8 lattice and in 24 dimensions it is the Leech Lattice (already mentioned).
In this context when mathematicians refer to 24 dimensions, they are understood in an absolute type manner as relating to space.
However reality is of a dynamic interactive nature, entailing both space and time.
Therefore when one attempts to infer relationships with respect to the real world based on absolute notions of space, it leads in many respects to a considerable amount of misrepresentation.
The notion of time as 1-dimensional, which still dominates thinking in physics, is based on the untenable view that the world itself can be understood objectively in abstraction from the mental observer. So the one dimension of time arises from the fact that observation necessarily starts with the mental observer, who is then assumed to view relationships in space in a detached objective manner.
However when one accepts the inevitable interaction of the mental observer with what is observed in space, time now becomes fully complementary with space.
So associated with each dimension of space is a corresponding dimension of time.
Therefore, when one attempts to realistically understand to what the 24 dimensions of asymmetric strings relate, then dynamic configurations (which equally involve time as well as space) are necessarily involved. And these thereby constitute a completely new notion of “dimension”.
And in turn to obtain the best idea of what this entails, we are led back to our model of personality types, where a complete dynamic explanation of such space and time configurations can be given in a psychological manner. And then the physical explanation of these configurations as “dimensions” is understood as fully complementary with the psychological.
Therefore, the notion of 24 dimensions can now be understood in a truly interactive manner where both rational (analytic) and intuitive (holistic) understanding operate in a complementary fashion with each other.
12. The term “Monster Moonshine” was coined by John Conway (a major practitioner in the field). At that time it seemed highly unlikely that a connection between the j-function relating to number theory and the Monster, in a seemingly unrelated area of algebra, could be made.
However the very choice of this term reveals an important problem which mathematicians never explicitly address.
As we have seen in an earlier contribution, “moon” has always been given a feminine connotation in language and the term lunacy (relating to “la lune” as the French word for “moon”) is symbolic of the unconscious mind. Thus “moonshine” suggests holistic meaning based on the hidden light of the unconscious.
In fact, the new term that has emerged “umbral moonshine” is even more revealing in this regard. The Latin word “umbra” relates to the deepest or most inward shadow. Therefore to understand what the “Umbral Moonshine Conjecture” relates to, in true holistic terms, requires the deepest exploration of the unconscious shadow side of personality.
As I have repeatedly stated, there is no formalised recognition in mathematics at present of this important holistic aspect. And it is this very lack that leads to a failure for example to see the fundamental links as between a vitally important physical/mathematical area of research and corresponding psychological development.
In fact, it has struck me forcibly in reading about the classification of the finite groupsin what admittedly is an outstanding achievement in mathematicsthat many of its main contributors undoubtedly fitted the Asperger's syndrome category. Though this was associated with a remarkable capacity for abstraction, enabling the considerable mathematical problems involved to be satisfactorily solved in an analytic type manner, by the same token, complementary holistic insight into what this all entails has been greatly lacking.
And in the end, the very appreciation of symmetry in any context does not primarily relate to ability for abstraction but to a more aesthetic holistic appreciation of the very nature of beauty. I am in way denying that mathematicians can indeed be guided by a strong implicit sense of what beauty entails. However there is little or no recognition yet that the explicit interpretation of such beauty in their work requires an utterly distinctive holistic mathematical manner of understanding.
Symmetry and the Monster: The Story of One of the Greatest Quests in Mathematics;
Mark Ronan: Oxford University Press, 1st Edition (July 1st, 2006)
Finding Moonshine: A Mathematician's Journey through Symmetry; Marcus du Sautoy: Harper Perennial (May 14th 2009).
Superstrings and the Search for the Theory of Everything; F.David Peat: Contemporary Books 1st Edition (October 1st 1988)
Why 5, 8 and 24 Are the Strangest Numbers in the Universe: John Baez: Scientific American, May 2011
See also The Rankin Lectures, 2008 delivered in Glasgow (available on YouTube) where John gives separate talks on 5, 8 and 24 respectively.
Mathematicians Chase Moonshine's Shadow: Erica Klarreich: Quanta Magazine, March 12th 2015
Monster Moonshine: 24-Dimensional Space; Peter Collins: Integral Science blog, April 16th, 2010
Personality Types and Superstrings; Peter Collins: Science of Integration, circa 1998