Yesterday, we saw how the Enneagram has a built-in dynamic quality,
portraying for each personality type (designated by one of the numbers from 1 -
9) the paths for integration and disintegration respectively.

However one significant weakness here (which also indeed applies to the
Myers-Briggs typology) is that it remains neutral as to the various levels of
development (on the full spectrum).

For example in Western Psychology, adult development is largely confined to -
what I designate as - the first two Bands on the Spectrum with adult development predominantly based on the second.

And this band relates to the specialisation of (linear) analytic
type understanding of a merely conscious nature.

In particular this understanding completely dominates the present
mathematical and scientific worldviews which in many ways serve as the new
religion for the present age!

However a crucial weakness of this worldview - despite its admitted great
triumphs - is that it is greatly lacking a true holistic dimension (which
directly relates to unconscious development).

In like manner the very capacity for true integration with respect to the
personality entails significant growth with respect to the unconscious.

Therefore one can seriously question the extent to which true integration
for the various personality types (with respect to any preferred system) can
take place without dealing with the vertical - as well as horizontal -
profiles for the various types.

As always, my initial interest in this area of development sprung directly
from personal experience.

Through most of my 20's, I found myself completely immersed in a profound
darkness that seemingly bore no relationship to the normal experience of others (as I then
imagined).

For one day in the week some calm would reign with respect to the inner storms and
travails prevailing and I would pursue some quiet spiritual reading in a Dublin library. There
I discovered the "The Dark Night" by St. John of the Cross which
resonated to a remarkable degree with my own experience.

Some years later, when this stage had passed I began to realise that St.
John's account itself reflected a particular personality type (that we both
shared).

So using The Enneagram, I would classify him as a 4 (with a strong 5
wing). In Enneagram terms every primary number type, is linked to a
secondary number
(as wing) on either side. So a 5 for example will therefore have either a
4 or
a 6 wing!

Therefore while undergoing the most intense inner subjective experience, he
could still view it in a detached objective manner.

Then in somewhat complementary manner I had come to see my own personality as
a 5 (with a strong 4 wing).

Now when one looks at the diagram for the Enneagram there is one unusual
feature.

Whereas all the other numbers are approached through criss-crossing lines
(in the close vicinity of the numbers) this is not the case between 4 and 5.

Therefore this would tend to signify that for this personality mix (in
particular) that an especially important gap in the personality must be bridged
to achieve true integration.

In fact, Jung - though not a spiritual contemplative in the accepted sense
- writes about a similar type crisis or "night sea
journey".

And again I was to realise that my later resonance with the writings of Jung
again reflected a very similar personality profile!

However it took me some time to properly accept that other personality
types could pursue a very different path to integration.

Therefore the "dark night" crisis - as portrayed by St.
John - that I long accepted as the gold standard for authentic spiritual
integration - in fact reflects but one extreme version that especially applies to
people with a particular personality mix.

At the same time, I made another interesting discovery.

I was reading a book "the Philosophy of St. Thomas Aquinas and
attempting to find a modern explanation as to why Angelology was seen as such
an important part of the medieval theological system.

Then the following sentence triggered the crucial insight that I was looking
for!

"The angels are creatures whose existence can be proved and in
exceptional cases observed; their suppression would render the universe as a
whole unintelligible."

I had been just been reflecting on the holistic significance of
transcendental numbers (such as π) when in immediately struck me that by
replacing angels with transcendental numbers we get the following equivalent statement:

"The transcendental are numbers whose existence can be proved
and in exceptional cases observed; their suppression would render the system of
numbers as a whole unintelligible."

So in fact Cantor (who
proved the unique existence of transcendental numbers without reference
to any actual examples) and St. Thomas could therefore be seen to have
been pursuing the same intellectual issues regarding the nature of the
infinite under the separate veils of Mathematics and Theology
respectively.

Now the significance of transcendental numbers in a holistic context is that
they relate to a highly refined spiritual intuitive type of understanding, where
both conscious and unconscious aspects of understanding are closely linked.

This then led me to a modern psychological way of looking at Angelology as a somewhat
mythical attempt of exploring the higher powers of the unconscious mind (which
especially find development through authentic spiritual contemplation).

In other words, from this perspective, Angelology points to the hidden unconscious potential of the
human personality.

In this sense it is remarkable that the Thomistic system - derived
from the Pseudo-Dyonysius - in fact represent a (vertical) Enneagram.
Here three
hierarchical ranks of angels are distinguished (with three degrees in
each hierarchy) which ascend from initial
contact with the material world to their most purely spiritual
manifestation
(as Seraphim and Cherubim).

In like manner spiritual contemplation starts from the a dualistic
base where spirit intermingles with (gross) phenomena before
eventually - all going well - culminating in pure union with God.

It is also interesting in this regard that the same Pseudo-Dyonysius equally
had an important influence on developing the doctrine of the via negativa with respect
to mystical development (which ultimately culminated with "The Dark Night" exposition of St. John of the
Cross).

So we have two Enneagrams, the standard (horizontal) version which
implicitly assumes the same level of development for all types and a (vertical)
Ennegram, which in a somewhat mythical manner portrays the various stages that
all types must pass through to achieve full spiritual union.

However a severe dichotomy still exists as between both types!

My own considerations on this issue initially centred on consideration of the - extended - 24 personality types classification.

Again these are divided into 3 main groups (of 8 types).

The first group comprising “real” types are most firmly rooted in the
actual world of form.

Therefore personality integration for these personalities is unlikely to require substantial exploration
of the “higher” vertical levels.

In fact the centaur - which would be the highest of the middle levels -
represents a good model of what is required here for successful integration.

Therefore with sufficient centaur type development, such
personalities would
be freed to engage with the (actual) world in a flexible and creative
manner. However this involvement would not require specialised
development with respect to the unconscious.

The second group are made up of “imaginary” types that gravitate naturally
to the creation of a potential reality (expressive literally of the
imagination).

Integration is likely to be more problematic for these types, who can experience considerable difficulty in integrating their unconscious instincts with
the demands of actual living.

For successful integration, such personalities may require a much
greater degree of “higher” contemplative development to cleanse their
creative desires of
excessive ego involvement. They may also require greater sustained
involvement with the conventional middle levels.

In practice however, as we see so with creative writers, actors etc. successful integration is rarely achieved, with substantial
personality difficulties often preventing satisfactory adaptation to
every day life.

The third group are made up of the “complex” types (paradoxically also
intrinsically the most simple) where the desire for authentic being chiefly defines
the personality.

The secret for integration here lies in the innate capacity of the will to navigate
the perilous route to true being.

When successful this offers the greatest opportunities for substantial
exploration of the more advanced levels on the spectrum.

However even then life is more likely to resemble a continual journey, where
one’s final destination can be approached but never quite fully attained.

I did then - combining the insights of the two Enneagram models - attempt to express both aspects as a Septagram
(with both horizontal and vertical developmental dimensions).

The first grouping (based on the 4 personality types) related to the number
1463 (in base 8, which again is a cyclic prime).

So all personality types - allowing for the dynamic interaction of positive
and negative directions in a real and imaginary manner - can be derived from
these 4 fundamental modes.

The second group based on 3 levels relates to the number 275 (again in base
8). This now relates to the possibility
of vertical growth between levels. Depending on type, 1, 2 or 3 hierarchical
levels will here in general be required for successful integration.

## Thursday, January 21, 2016

## Wednesday, January 20, 2016

### Personality Types (7)

As well as the Myers-Briggs (based on Jungian insights), I have also found special merit in the Enneagram system, once again attempting to view it from a holistic mathematical rationale.

Whereas the Myers Briggs is based on "4" with all possible profiles (16) representing the square of this number, The Enneagram is based on "3" with again all possible profiles (9) based on the square of this number.

Indeed "9" seems especially suitable from an integral perspective, and indeed in several respects I have found the Enneagram system better suited to deal with the dynamics through which successful integration of personality may take place.

Indeed it is easy to demonstrate some special holistic mathematical attributes of "9". In the denary (base 10) number system we employ, 9 represents – 1 (with respect to 10). And – 1 in turn represents the unconscious direction of development (which is directly relevant for personality integration).

Here is another interesting feature of 9! Take any number and then write its mirror version (reverse number)!

For example based on today's date, we can construct the number 200116. The reverse of this is then 611002. Now subtract these two numbers (with the smaller subtracted from the larger, we get 611002 – 200116 = 410886. Now divide by 9 and we obtain 45654. And this number is a palindrome (i.e. where the number and its reverse are identical).

Now a perfect palindrome will not always emerge from this procedure. However very frequently, one will arise. In most other cases the number will be very close to a palindrome, where with a small adjustment (e.g. changing the last digit by 1) a perfect palindrome emerges.

The holistic mathematical significance of this is that personality itself is based on the integration of complementary opposite directions. Thus when one successfully balances one polar tendency with its opposite, integration thereby results (with both opposite directions now identical with each other).

And as we have seen, just as "9" is especially useful in analytic terms for generating palindromes (from the combination of numbers with opposite sequences), equally "9" can play a special holistic role in terms of the successful integration of opposite tendencies in the personality.

Indeed the number 11 (which is + 1 with respect to 10) is also very interesting in this regard. It is holistically consistent with the positive (i.e.) conscious direction of personality!

Fascinatingly, when we attempt to generate palindromes in the same manner for 11, a polar split is in evidence.

When the number has an even number of digits, we must add the number and its reverse before dividing by 11. However when the numbers have an odd number of digits, we must subtract before dividing by 11.

So in this case (with 6 digits) we must add i.e. 200116 + 611002 = 811118. (Now in fact we already have a perfect palindrome, which will arise when the total contains the same number of digits. However such numbers will always be divisible by 11 (with again strong palindromic tendencies in evidence).

There are further fascinating number aspects.

With respect to the Enneagram, two distinct number groups (for integration purposes) are singled out.

The first is built around the unique sequence of digits for the reciprocal of 7!

Now 7 is especially interesting in this regard as it is the first - and best known - example of a full cyclic prime (in the denary system). For a full cyclic prime, the unique sequence of digits occurring in the decimal expansion of its reciprocal is just 1 less than the number in question!

And with 7, the unique sequence of recurring digits is 142857.

What is remarkable from a holistic mathematical perspective is that the primes represent the most independent of linear numbers (with no factors other than 1 and the prime number itself).

However when you then obtain the reciprocal of a prime, a complementary opposite picture emerges with its unique sequence of digits exhibiting amazing circular properties.

So for example if you multiply 142857 by 2, 3, 2, 5 or 6, the same circular sequence of digits will appear. For example when we multiply by 2 we get 285714 (which is the same number sequence with the circular position simply switched).

Therefore in holistic terms, this unique sequence of digits (for the reciprocal of 7) serves as a complementary model of interdependence (i.e. integration) in personality terms.

And remarkably with respect to the Enneagram, this circular sequence of digits (of the reciprocal of 7) plays a unique role.

For one attempts to achieve integration strictly with respect to an ordered movement through this circular number sequence. So for example a 4 (the Individualist) in Enneagram attempts to achieve integration by moving in the opposite direction (with respect to the circular sequence of digits).

Therefore the 4 would move to 1 (the Reformer) and then to 7 (the Enthusiast), 5 (the Investigator), 8 (the Challenger) and 2 (the Helper) respectively to achieve integration. The opposite direction then defines the process of disintegration. So the unhealthy direction for a 4 would be to move to 2 (and then to 8, 5, 7 and 1).

The other number (made up of the remaining digits) is 396.

This is already a very composite number with 5 factors (2.* 2* 3 * 3 * 11) again serving well for holistic integrative purposes. So for a "3" (the Achiever) to achieve integration movement would be in the opposite circular direction, to 6 (the Loyalist) and then 9 (the Peacemaker) with the opposite direction leading to disintegration.

Interestingly, in view of my earlier discussion on the holistic significance of palindromes, both 142857 and 396 are divisible by 9 and 11 respectively!

In fact Don Riso, who is perhaps the most authoritative writer on the Enneagram, provides an excellent blueprint of 9 different versions (from the healthiest to the most unhealthy) for all the 9 Enneagram types.

Whereas the Myers Briggs is based on "4" with all possible profiles (16) representing the square of this number, The Enneagram is based on "3" with again all possible profiles (9) based on the square of this number.

Indeed "9" seems especially suitable from an integral perspective, and indeed in several respects I have found the Enneagram system better suited to deal with the dynamics through which successful integration of personality may take place.

Indeed it is easy to demonstrate some special holistic mathematical attributes of "9". In the denary (base 10) number system we employ, 9 represents – 1 (with respect to 10). And – 1 in turn represents the unconscious direction of development (which is directly relevant for personality integration).

Here is another interesting feature of 9! Take any number and then write its mirror version (reverse number)!

For example based on today's date, we can construct the number 200116. The reverse of this is then 611002. Now subtract these two numbers (with the smaller subtracted from the larger, we get 611002 – 200116 = 410886. Now divide by 9 and we obtain 45654. And this number is a palindrome (i.e. where the number and its reverse are identical).

Now a perfect palindrome will not always emerge from this procedure. However very frequently, one will arise. In most other cases the number will be very close to a palindrome, where with a small adjustment (e.g. changing the last digit by 1) a perfect palindrome emerges.

The holistic mathematical significance of this is that personality itself is based on the integration of complementary opposite directions. Thus when one successfully balances one polar tendency with its opposite, integration thereby results (with both opposite directions now identical with each other).

And as we have seen, just as "9" is especially useful in analytic terms for generating palindromes (from the combination of numbers with opposite sequences), equally "9" can play a special holistic role in terms of the successful integration of opposite tendencies in the personality.

Indeed the number 11 (which is + 1 with respect to 10) is also very interesting in this regard. It is holistically consistent with the positive (i.e.) conscious direction of personality!

Fascinatingly, when we attempt to generate palindromes in the same manner for 11, a polar split is in evidence.

When the number has an even number of digits, we must add the number and its reverse before dividing by 11. However when the numbers have an odd number of digits, we must subtract before dividing by 11.

So in this case (with 6 digits) we must add i.e. 200116 + 611002 = 811118. (Now in fact we already have a perfect palindrome, which will arise when the total contains the same number of digits. However such numbers will always be divisible by 11 (with again strong palindromic tendencies in evidence).

There are further fascinating number aspects.

With respect to the Enneagram, two distinct number groups (for integration purposes) are singled out.

The first is built around the unique sequence of digits for the reciprocal of 7!

Now 7 is especially interesting in this regard as it is the first - and best known - example of a full cyclic prime (in the denary system). For a full cyclic prime, the unique sequence of digits occurring in the decimal expansion of its reciprocal is just 1 less than the number in question!

And with 7, the unique sequence of recurring digits is 142857.

What is remarkable from a holistic mathematical perspective is that the primes represent the most independent of linear numbers (with no factors other than 1 and the prime number itself).

However when you then obtain the reciprocal of a prime, a complementary opposite picture emerges with its unique sequence of digits exhibiting amazing circular properties.

So for example if you multiply 142857 by 2, 3, 2, 5 or 6, the same circular sequence of digits will appear. For example when we multiply by 2 we get 285714 (which is the same number sequence with the circular position simply switched).

Therefore in holistic terms, this unique sequence of digits (for the reciprocal of 7) serves as a complementary model of interdependence (i.e. integration) in personality terms.

And remarkably with respect to the Enneagram, this circular sequence of digits (of the reciprocal of 7) plays a unique role.

For one attempts to achieve integration strictly with respect to an ordered movement through this circular number sequence. So for example a 4 (the Individualist) in Enneagram attempts to achieve integration by moving in the opposite direction (with respect to the circular sequence of digits).

Therefore the 4 would move to 1 (the Reformer) and then to 7 (the Enthusiast), 5 (the Investigator), 8 (the Challenger) and 2 (the Helper) respectively to achieve integration. The opposite direction then defines the process of disintegration. So the unhealthy direction for a 4 would be to move to 2 (and then to 8, 5, 7 and 1).

The other number (made up of the remaining digits) is 396.

This is already a very composite number with 5 factors (2.* 2* 3 * 3 * 11) again serving well for holistic integrative purposes. So for a "3" (the Achiever) to achieve integration movement would be in the opposite circular direction, to 6 (the Loyalist) and then 9 (the Peacemaker) with the opposite direction leading to disintegration.

Interestingly, in view of my earlier discussion on the holistic significance of palindromes, both 142857 and 396 are divisible by 9 and 11 respectively!

In fact Don Riso, who is perhaps the most authoritative writer on the Enneagram, provides an excellent blueprint of 9 different versions (from the healthiest to the most unhealthy) for all the 9 Enneagram types.

## Tuesday, January 19, 2016

### Personality Types (6)

Yesterday, I mentioned how each personality type represents a unique configuration with respect to the manner in which space and time is experienced.

Ultimately, all configurations are based on the holistic mathematical interpretation of the two fundamental polarity sets (i.e. external/internal and whole/part) that underlie every phenomenon of form.

So once again, in holistic mathematical terms, external and internal are bi-directionally positive and negative, whereas whole and part are bi-directionally real and imaginary with respect to each other.

However this equally means that the same structures of space and time apply in a physical - as well as psychological - manner.

So just as in psychological terms we can define distinct personality types - representing unique configurations with respect to space and time - equally it should be possible to define in physical terms, distinct "impersonality" types, that likewise represent the same unique dimensional configurations.

So if we were to refer to the world as being composed of holons (whole/parts) and in reverse onhols (part/wholes) - where both external and internal directions apply - all holons (and onhols) would thereby be comprised of the same structural configurations with respect to space and time.

Indeed we could generalise even further, interpreting both cognitive and affective modes as representing - again in relative fashion - fundamental means of both control and response with respect to the environment.

So one could look at both physical and psychological reality as comprising an intricate web of control and response patterns. So the very capacity for phenomenal existence requires that a holon (and onhol) can exercise some degree of independent autonomy (control) while equally being able to relate (respond) to its environment.

Also though we would not apply the term "unconscious" to physical matter, in more general terms, the unconscious represents the holistic - as opposed to analytic - nature of reality.

Therefore in more general terms, we can perhaps recognise that all holons (and onhols) possess both an analytic identity (with respect to a local existence) and a holistic identity (with respect to an overall interdependence - ultimately - with all other phenomena in creation).

Unfortunately, Conventional Science very much distorts the nature of physical reality by attempting to understand it in a merely analytic (conscious) manner. This then leads to an enormous shadow in a total failure to recognise its counterpart holistic nature (where everything in truth is connected to everything else).

And of course the only way of healing this enormous split is through full incorporation of both conscious and unconscious in a psychological manner, which can then naturally reflect both the holistic and analytic aspects of physical reality in complementary terms.

Some years ago, when I was reading Michio Kaku's book "Hyperspace", I was suddenly enabled to make a vital connection as between my 24-Personality Type Model and the world of strings, which are postulated by many physicists as the fundamental "stuff" comprising the physical universe.

Kaku makes mention of the Ramanujan function, where in string theory each of the 24 modes appearing in the function corresponds to a physical vibration of the string. Then since physicists add two more dimensions when they count the total number of vibrations appearing in a relativistic theory, this leads to 24 + 2 dimensions of space-time.

Now these dimensions appear mathematically in what is known as the elliptic modular function. Suffice it to say that this entails definition in the complex half-plane (using real and imaginary numbers)!

So what I deeply suspected on reading this, is that I had arrived at the holistic mathematical counterpart of these notions, which are understood analytically in Conventional Mathematics.

However though their treatment is greatly advanced in a highly specialised manner, physicists seem to be especially lacking in the intuitive ability to explain what their findings really imply. And this is where holistic understanding is so valuable!

I was now able to see clearly that the very use of the word "dimension" in string theory is confusing. Therefore I suggest that in this context, each "dimension" (vibration of the string) represents a unique configuration with respect to the 4 dimensions (that only become properly separated at the macro level of phenomenal investigation).

So intuitively, it would seem perfectly reasonable to assume that the four dimensions (with which we are accustomed) are still very much entangled with each other. Thus at this level a "dimension" represents a certain unique configuration with respect to the entangled confusion of these 4 dimensions.

A more detailed version of my thinking at the time (20 years ago) is available at "Personality Types and Superstrings" .

Now the 26 dimensional version of Superstrings was soon replaced by a 10 dimensional version.

However as Kaku explains this in fact represents a generalisation of the Ramanujan function (on which the earlier version was based).

Thus the critical number for the 10-dimensional version is 8 (to which again 2 is added).

Interestingly the original Jungian approach to personality is based on the identification of 8 distinct types!

Then with the advent of M-theory, another space dimension has been added. So now the convention is to treat string reality as composed of 11 dimensions (9 + 2) bearing comparison with the alternative Enneagram approach.

So the critical point that I am making is that whether at an advanced psychological or primitive physical level, reality is fundamentally structured in terms of the same basic "dimensions" i.e. configurations with respect to space and time.

Furthermore, our understanding of space and time needs to change profoundly as we are presently locked into a merely reduced analytic interpretation, which distorts its true nature.

For example, we have been accustomed to treat space and time in an asymmetrical manner. Indeed this is very true even at the level of string theory, where all but 1 dimension are customarily postulated as of space!

However in true holistic terms, space and time dimensions are fully complementary and thereby symmetrical with each other. So it requires an enormous shift in mind-set to intuitively adopt the holistic approach as the appropriate model.

Also the holistic approach gives equal emphasis to imaginary as well as real dimensions.

Once again it will not be possible to "see" what imaginary dimensions entail until the unconscious is fully incorporated with conscious interpretation.

The holistic approach likewise gives equal emphasis to negative as well as positive dimensions. So in the very interaction of the (internal) self and (external) world, negative dimensions - in switching as between both poles - are necessarily involved.

Finally the holistic approach gives equal emphasis to personal as well as impersonal dimensions.

Put simply conventional scientific understanding conforms to the impersonal aspect of dimensions; however artistic appreciation conforms directly with their personal aspect.

So actual experience necessarily entails both personal and impersonal aspects.

However once again, conventional science simply acts to reduce the personal aspect in a distorted - merely impersonal - manner.

Ultimately, all configurations are based on the holistic mathematical interpretation of the two fundamental polarity sets (i.e. external/internal and whole/part) that underlie every phenomenon of form.

So once again, in holistic mathematical terms, external and internal are bi-directionally positive and negative, whereas whole and part are bi-directionally real and imaginary with respect to each other.

However this equally means that the same structures of space and time apply in a physical - as well as psychological - manner.

So just as in psychological terms we can define distinct personality types - representing unique configurations with respect to space and time - equally it should be possible to define in physical terms, distinct "impersonality" types, that likewise represent the same unique dimensional configurations.

So if we were to refer to the world as being composed of holons (whole/parts) and in reverse onhols (part/wholes) - where both external and internal directions apply - all holons (and onhols) would thereby be comprised of the same structural configurations with respect to space and time.

Indeed we could generalise even further, interpreting both cognitive and affective modes as representing - again in relative fashion - fundamental means of both control and response with respect to the environment.

So one could look at both physical and psychological reality as comprising an intricate web of control and response patterns. So the very capacity for phenomenal existence requires that a holon (and onhol) can exercise some degree of independent autonomy (control) while equally being able to relate (respond) to its environment.

Also though we would not apply the term "unconscious" to physical matter, in more general terms, the unconscious represents the holistic - as opposed to analytic - nature of reality.

Therefore in more general terms, we can perhaps recognise that all holons (and onhols) possess both an analytic identity (with respect to a local existence) and a holistic identity (with respect to an overall interdependence - ultimately - with all other phenomena in creation).

Unfortunately, Conventional Science very much distorts the nature of physical reality by attempting to understand it in a merely analytic (conscious) manner. This then leads to an enormous shadow in a total failure to recognise its counterpart holistic nature (where everything in truth is connected to everything else).

And of course the only way of healing this enormous split is through full incorporation of both conscious and unconscious in a psychological manner, which can then naturally reflect both the holistic and analytic aspects of physical reality in complementary terms.

Some years ago, when I was reading Michio Kaku's book "Hyperspace", I was suddenly enabled to make a vital connection as between my 24-Personality Type Model and the world of strings, which are postulated by many physicists as the fundamental "stuff" comprising the physical universe.

Kaku makes mention of the Ramanujan function, where in string theory each of the 24 modes appearing in the function corresponds to a physical vibration of the string. Then since physicists add two more dimensions when they count the total number of vibrations appearing in a relativistic theory, this leads to 24 + 2 dimensions of space-time.

Now these dimensions appear mathematically in what is known as the elliptic modular function. Suffice it to say that this entails definition in the complex half-plane (using real and imaginary numbers)!

So what I deeply suspected on reading this, is that I had arrived at the holistic mathematical counterpart of these notions, which are understood analytically in Conventional Mathematics.

However though their treatment is greatly advanced in a highly specialised manner, physicists seem to be especially lacking in the intuitive ability to explain what their findings really imply. And this is where holistic understanding is so valuable!

I was now able to see clearly that the very use of the word "dimension" in string theory is confusing. Therefore I suggest that in this context, each "dimension" (vibration of the string) represents a unique configuration with respect to the 4 dimensions (that only become properly separated at the macro level of phenomenal investigation).

So intuitively, it would seem perfectly reasonable to assume that the four dimensions (with which we are accustomed) are still very much entangled with each other. Thus at this level a "dimension" represents a certain unique configuration with respect to the entangled confusion of these 4 dimensions.

A more detailed version of my thinking at the time (20 years ago) is available at "Personality Types and Superstrings" .

Now the 26 dimensional version of Superstrings was soon replaced by a 10 dimensional version.

However as Kaku explains this in fact represents a generalisation of the Ramanujan function (on which the earlier version was based).

Thus the critical number for the 10-dimensional version is 8 (to which again 2 is added).

Interestingly the original Jungian approach to personality is based on the identification of 8 distinct types!

Then with the advent of M-theory, another space dimension has been added. So now the convention is to treat string reality as composed of 11 dimensions (9 + 2) bearing comparison with the alternative Enneagram approach.

So the critical point that I am making is that whether at an advanced psychological or primitive physical level, reality is fundamentally structured in terms of the same basic "dimensions" i.e. configurations with respect to space and time.

Furthermore, our understanding of space and time needs to change profoundly as we are presently locked into a merely reduced analytic interpretation, which distorts its true nature.

For example, we have been accustomed to treat space and time in an asymmetrical manner. Indeed this is very true even at the level of string theory, where all but 1 dimension are customarily postulated as of space!

However in true holistic terms, space and time dimensions are fully complementary and thereby symmetrical with each other. So it requires an enormous shift in mind-set to intuitively adopt the holistic approach as the appropriate model.

Also the holistic approach gives equal emphasis to imaginary as well as real dimensions.

Once again it will not be possible to "see" what imaginary dimensions entail until the unconscious is fully incorporated with conscious interpretation.

The holistic approach likewise gives equal emphasis to negative as well as positive dimensions. So in the very interaction of the (internal) self and (external) world, negative dimensions - in switching as between both poles - are necessarily involved.

Finally the holistic approach gives equal emphasis to personal as well as impersonal dimensions.

Put simply conventional scientific understanding conforms to the impersonal aspect of dimensions; however artistic appreciation conforms directly with their personal aspect.

So actual experience necessarily entails both personal and impersonal aspects.

However once again, conventional science simply acts to reduce the personal aspect in a distorted - merely impersonal - manner.

## Monday, January 18, 2016

### Personality Types (5)

I have always been fascinated by the manner in which we experience space and time and the complementary links which connect both psychological and physical notions.

As I have mentioned several times before on these blogs, I find it striking that when Einstein was once asked to give a simple account of Relativity he stated:,

"Put you hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. THAT'S Relativity."

However, this in fact relates to the psychological - rather than the physical - experience of time and Einstein seems to miss the highly important point that the psychological and physical aspects of time are themselves relative in complementary fashion!

The implications of this realisation are then enormous, for it implies that we cannot strictly hope to properly understand - as Einstein attempted - the physical world of relativity through the rigid mental apparatus of Classical Theory (which assumes that the world can be objectively interpreted independent of the inquiring mind).

When we move to the holistic - as opposed to the present analytic - interpretation of dimensions, complementary symmetrical relationships define the nature of both space and time.

Using our 4-dimensional model (as the circular holistic interpretation of "4") we have seen that all phenomena are defined by bi-directional positive and negative directions with respect to both real and imaginary aspects. As we have seen the directions are - relatively - external and internal, whereas the aspects are also conscious and unconscious with respect to each other.

This entails therefore that space and time are likewise defined by bi-directional positive and negative directions, with respect to both real and imaginary aspects.

And what does this precisely mean with respect to the dynamics of experience?

Basically, when for example we experience an object in space, this is thereby (consciously) posited in an external physical manner.

However, through the dynamics of experience, this will then be likewise (unconsciously) negated - to a degree - causing a switch in an internal psychological direction. One can then (consciously) posit the object in internal space (relating to the psychological construct involved in its understanding).

So, for example, the physical experience of an object e.g. a cat in space, entails both the positing of the external "object" and the internal perception of "cat", which are - relatively - positive (external) and negative (internal) with respect to each other.

Thus, the explicit recognition of spatial objects requires the implicit use of psychological perceptions. In like manner the explicit use of spatial perceptions requires the implicit recognition of physical objects!

However here the emphasis is primarily on object phenomena (in space).

So we also have the complementary experience of space dimensions (in relation to objects).

Therefore at one moment we are aware directly of object phenomena (that indirectly imply space dimensions). Then, at the next moment, experience has switched so that we are now directly aware of their space dimensional characteristics (and only indirectly of the objects contained therein).

And in psychological terms this experience is governed by the corresponding interaction of perceptions (objects) and concepts (as general space characteristics).

So again to come back to our cat, we keep switching from recognition of this phenomenon as an object (in space) to the more direct recognition of the general space dimensions (to which all cats relate).

However we also have the direct experience of subjective space (as self in relation to the environment).

Indeed we could refer to both subjective and objective experience of space and time as their personal and impersonal aspects respectively.

So again, experience keeps switching from experience of the physical world (in relation to the self) to the corresponding experience of the psychological self (in relation to the world).

Therefore we have physical and psychological interpretation of both objects in space dimensions (and space dimensions in relation to objects) in - relatively - external (positive) and internal (negative) terms.

And equally, these dynamics all apply in like manner with respect to time. Thus, when we experience an object phenomenon externally, this implies a corresponding mental perception internally in time.

And equally experience of both perceptions and concepts takes place with respect to time as well as space. And finally, we have the psychological subjective experience of time in contrast to the objective physical experience.

Then we can have both a real (conscious) and imaginary (unconscious) experience with respect to space and time.

And in the very dynamics of experience, real and imaginary keep switching in complementary fashion, through the corresponding switching of both cognitive and affective modes.

Thus, when experience say of an object in space is real (conscious), the corresponding experience with respect to time remains imaginary (unconscious). Then through interaction, experience of time now becomes real with corresponding experience of space imaginary.

It then struck me forcibly that the 16 Personality Types (based on either/or distinctions) with respect to the fundamental modes and directions, in fact represent unique configurations with respect to the manner in which space and time can be experienced.

So each Personality Type represents a distinctive manner in which space and time is holistically configured (in both physical and psychological terms) with respect to - relatively - real (conscious) and imaginary (unconscious) aspects of experience in positive (external) and negative (internal) directions.

Now to finish here, I will just briefly elaborate on the distinction as between real and imaginary dimensional experience.

The experience of a real object, for example in space relates directly to the conscious local nature of that object.

However the imaginary experience refers to its more holistic unconscious nature whereby one sees the object as an archetype (ultimately of an unseen ineffable meaning).

Fro example an Olympic final - say 100m - has a definite location in conscious space representing its "real" significance from this perspective..

However its "imaginary" significance relates to the holistic unconscious meaning that this event holds for the athletes taking place e.g. as the possibility for the fulfilment of a life-long dream!

Therefore because all experience entails the interaction of conscious with unconscious, this means in effect that all events necessarily entail a complex location in space and time (i.e. entailing both "real" and "imaginary" aspects).

Put even more simply, whereas the real is identified with actual, the imaginary is identified with potential meaning! And in dynamic interactive terms experience represents the continual transformation of the actual through reference to an emerging potential meaning!

Thus the belief that we live in a "real" world simply reflects the scientific approach used in its interpretation (where the unconscious is reduced to conscious meaning).

Finally, one may ask to what notions of space and time do the "missing" 8 personality types relate!

Well the answer here is, that in a primary sense, they all relate to the (spiritual) present moment.

This is especially evident, where these personalities achieve a substantial amount of integration. Then in a primary sense, their experience is deeply rooted in the present moment, though in secondary terms, varying relative configurations with respect to space and time necessarily apply.

This then leads to the profound realisation of the absolute nature of the present moment, from which all relative phenomenal expressions continually emerge in space and time.

As I have mentioned several times before on these blogs, I find it striking that when Einstein was once asked to give a simple account of Relativity he stated:,

"Put you hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. THAT'S Relativity."

However, this in fact relates to the psychological - rather than the physical - experience of time and Einstein seems to miss the highly important point that the psychological and physical aspects of time are themselves relative in complementary fashion!

The implications of this realisation are then enormous, for it implies that we cannot strictly hope to properly understand - as Einstein attempted - the physical world of relativity through the rigid mental apparatus of Classical Theory (which assumes that the world can be objectively interpreted independent of the inquiring mind).

When we move to the holistic - as opposed to the present analytic - interpretation of dimensions, complementary symmetrical relationships define the nature of both space and time.

Using our 4-dimensional model (as the circular holistic interpretation of "4") we have seen that all phenomena are defined by bi-directional positive and negative directions with respect to both real and imaginary aspects. As we have seen the directions are - relatively - external and internal, whereas the aspects are also conscious and unconscious with respect to each other.

This entails therefore that space and time are likewise defined by bi-directional positive and negative directions, with respect to both real and imaginary aspects.

And what does this precisely mean with respect to the dynamics of experience?

Basically, when for example we experience an object in space, this is thereby (consciously) posited in an external physical manner.

However, through the dynamics of experience, this will then be likewise (unconsciously) negated - to a degree - causing a switch in an internal psychological direction. One can then (consciously) posit the object in internal space (relating to the psychological construct involved in its understanding).

So, for example, the physical experience of an object e.g. a cat in space, entails both the positing of the external "object" and the internal perception of "cat", which are - relatively - positive (external) and negative (internal) with respect to each other.

Thus, the explicit recognition of spatial objects requires the implicit use of psychological perceptions. In like manner the explicit use of spatial perceptions requires the implicit recognition of physical objects!

However here the emphasis is primarily on object phenomena (in space).

So we also have the complementary experience of space dimensions (in relation to objects).

Therefore at one moment we are aware directly of object phenomena (that indirectly imply space dimensions). Then, at the next moment, experience has switched so that we are now directly aware of their space dimensional characteristics (and only indirectly of the objects contained therein).

And in psychological terms this experience is governed by the corresponding interaction of perceptions (objects) and concepts (as general space characteristics).

So again to come back to our cat, we keep switching from recognition of this phenomenon as an object (in space) to the more direct recognition of the general space dimensions (to which all cats relate).

However we also have the direct experience of subjective space (as self in relation to the environment).

Indeed we could refer to both subjective and objective experience of space and time as their personal and impersonal aspects respectively.

So again, experience keeps switching from experience of the physical world (in relation to the self) to the corresponding experience of the psychological self (in relation to the world).

Therefore we have physical and psychological interpretation of both objects in space dimensions (and space dimensions in relation to objects) in - relatively - external (positive) and internal (negative) terms.

And equally, these dynamics all apply in like manner with respect to time. Thus, when we experience an object phenomenon externally, this implies a corresponding mental perception internally in time.

And equally experience of both perceptions and concepts takes place with respect to time as well as space. And finally, we have the psychological subjective experience of time in contrast to the objective physical experience.

Then we can have both a real (conscious) and imaginary (unconscious) experience with respect to space and time.

And in the very dynamics of experience, real and imaginary keep switching in complementary fashion, through the corresponding switching of both cognitive and affective modes.

Thus, when experience say of an object in space is real (conscious), the corresponding experience with respect to time remains imaginary (unconscious). Then through interaction, experience of time now becomes real with corresponding experience of space imaginary.

It then struck me forcibly that the 16 Personality Types (based on either/or distinctions) with respect to the fundamental modes and directions, in fact represent unique configurations with respect to the manner in which space and time can be experienced.

So each Personality Type represents a distinctive manner in which space and time is holistically configured (in both physical and psychological terms) with respect to - relatively - real (conscious) and imaginary (unconscious) aspects of experience in positive (external) and negative (internal) directions.

Now to finish here, I will just briefly elaborate on the distinction as between real and imaginary dimensional experience.

The experience of a real object, for example in space relates directly to the conscious local nature of that object.

However the imaginary experience refers to its more holistic unconscious nature whereby one sees the object as an archetype (ultimately of an unseen ineffable meaning).

Fro example an Olympic final - say 100m - has a definite location in conscious space representing its "real" significance from this perspective..

However its "imaginary" significance relates to the holistic unconscious meaning that this event holds for the athletes taking place e.g. as the possibility for the fulfilment of a life-long dream!

Therefore because all experience entails the interaction of conscious with unconscious, this means in effect that all events necessarily entail a complex location in space and time (i.e. entailing both "real" and "imaginary" aspects).

Put even more simply, whereas the real is identified with actual, the imaginary is identified with potential meaning! And in dynamic interactive terms experience represents the continual transformation of the actual through reference to an emerging potential meaning!

Thus the belief that we live in a "real" world simply reflects the scientific approach used in its interpretation (where the unconscious is reduced to conscious meaning).

Finally, one may ask to what notions of space and time do the "missing" 8 personality types relate!

Well the answer here is, that in a primary sense, they all relate to the (spiritual) present moment.

This is especially evident, where these personalities achieve a substantial amount of integration. Then in a primary sense, their experience is deeply rooted in the present moment, though in secondary terms, varying relative configurations with respect to space and time necessarily apply.

This then leads to the profound realisation of the absolute nature of the present moment, from which all relative phenomenal expressions continually emerge in space and time.

## Friday, January 15, 2016

### Personality Types (4)

I mentioned the significance in yesterday's blog entry of the 2-dimensional, 4-dimensional and 8-dimensional approaches, which concur with the circular holistic interpretation of the numbers 2, 4 and 8 respectively.

Jung in his writings frequently highlighted the holistic psychological role of mandalas i.e. pictorial images, serving as archetypes for the totality of the self.

The most important of these mandalas are based on the division of the circle into 4 or alternatively 8 equal segments, often presented in a highly ornate visual fashion.

So the basic structure of these mandalas equate directly with the geometrical presentation of the four and eight roots of 1 respectively i.e. the holistic interpretation of 4-dimensional and 8-dimensional (as the holistic circular interpretation of "4" and "8" respectively).

Therefore the deeper reason as to why these mandalas serve such a powerful integral purpose is that all fundamental psychological processes can be successfully interpreted, in a dynamic interactive fashion, through the holistic interpretation of the 4 and 8 roots of unity respectively.

Now as we have seen, using the 4 basic modes of reason, judgement, sense and feeling - all dynamically coordinated through the central volitional mode - we can derive 16 distinct aspects of personality.

So again, each of the 4 modes can be - relatively - defined with respect to real (conscious) and imaginary (unconscious) aspects, in both positive (external) and negative (internal) directions.

Now, allowing for slight differences in terminology from Jungian use, these equate extremely well with the corresponding 16 Personality Types (in the Myers-Briggs formulation).

However, I gradually began to suspect a certain limitation with this approach.

The Myers-Briggs Personality Types are all based on either/or distinctions. So with the first letter describing one's type, one is basically described as either E (extrovert) or I (introvert).

Then with the second one is described as either S (sense) or N (intuition). With the third letter one is described as either a T (thinking) or F (feeling) type. And then with the final letter one's decision-making is based on either J (judgement) or P (perception).

However, initially based on closer examination of my own personality, I began to realise that such either/or distinctions did not properly fit in this case.

So I gradually came to the conclusion that for certain personalities a both/and rather than either/or designation of these opposites was more appropriate.

So for example, I saw myself primarily neither as an extrovert or introvert as such but rather as a centrovert.

Now in secondary terms, I may have appeared to others as introvert, but then in early childhood, I am told that I was in fact very extroverted.

So one characteristic of this mixed type is that secondary characteristics e.g. as extrovert or introvert can undergo considerable change throughout life, as one deeply seeks for that primary balance (which is central to personality).

Then again I had problems in terms of the S and N classification. Though my general approach is indeed very holistic (N), I have always sought for a mathematically precise formulation (that would indicate S). In other words, I do not see either conscious or unconscious reality as primary, but rather the ineffable interface as between both aspects.

So the midpoint of both S and N (or real an imaginary) is an ineffable spiritual quality that is utterly mysterious. So I describe this conveniently as M (mystical).

Then in relation to the third distinction of T and F, again I would never have seen either as primary. In my case I am conscious of using T strongly with respect to the outer world, but F equally strongly in relation to inner reality. So the holy grail here once again is to obtain the successful balance of both modes.

And this leads to a primary emphasis on the volitional capacity of the will.

So therefore for the mixed type, neither T nor F is primary but rather V (volition).

Finally, again with respect to the last, with respect to decision-making, the common ground as between J (judgement) and P (perception) would be a quality of discernment for what is appropriate in any particular circumstance. So this again this middle ground as between J and P, I refer to as D (discernment) .

So therefore, I now was able to define a new mixed grouping, which essentially comprised complementary opposites with respect to the accepted polar opposite Types i.e. CMVD.

For example using the Myers-Briggs typology I would probably classify my present personality (in secondary terms) as an INFJ. Thus the complementary opposite here would be an ESTP. And indeed I can remember in early life that I did operate somewhat as an ESTP!

Put another way, this mixed grouping of types is likely to prove extremely sensitive to the shadow side of personality with the attempt to achieve proper integration a life-long journey continually confronting one's shadow.

Whereas in ideal circumstances the types from this group provide the best possibilities for true integration, in practice they are likely to be most prone to severe psychological problems (reflecting serious failures in achieving integration ).

"Great wits are to madness near allied

And thin partitions do their lines divide"

So along with the 16 Types (based on either/or divisions) I now had a new grouping of 8 mixed Types (based on complementary opposite pairings with respect to the 16 Types).

This therefore now led to the definition of 24 fundamental personality types.

I then realised that these could be formulated in a simpler fashion from the original 4 modes.

The idea here was to look at each personality as based on a combination of the 4 modes, with the first mode the most dominant, the next mode the auxiliary, followed by the two weakest (with the last representing the inferior mode).

Now, if for simplicity we represent the four modes as a, b, c and d respectively, then 24 distinct permutations of these letters are possible.

So each Personality Type is therefore defined as representing a unique permutation (or configuration) of the 4 basic modes.

Now of course considerable variation is still possible (with respect to the spectrum of healthy to unhealthy versions of each type)

For example in some cases the first mode may be especially dominant (therefore limiting possibilities for subsequent integration with the 3 weaker modes).

In other cases the inferior mode may be especially weak this operating in a blind unconscious manner, which would again pose special problems for successful integration.

In general however, there are three distinct groupings (the first two which equate well with the S and N Types on the Myers-Briggs scheme).

Thus for the first group (of 8 Types) real (conscious) reality is likely to dominate experience. This is due to the operation in the same horizontal direction (i.e. either external or internal) applying to the two leading modes. This then leads to a somewhat rigid conscious experience of actual phenomena.

Then for the second group (of 8 Types) imaginary (unconscious) reality is likely to be more important. This is now due to the two prominent modes of the same nature (either cognitive or affective) operating in a vertically opposite manner (where for example external is counterbalanced by the internal direction of the opposite mode). This inherent conflict of directions then tends to generate a substantial degree of intuition leading to the more holistic (unconscious) generation of potential phenomena.

Then for the third mixed group (of 8 Types), complex (both conscious and unconscious) reality is likely to predominate.

We have here the most acute clash, where the two dominant modes are both of opposite aspect and opposite direction (i.e. diagonal in nature). So, for example, we could have an external cognitive counterbalanced by an internal affective mode. This renders the attempt to rest, as it were, in either (real) or unconscious (imaginary) reality especially difficult. In fact it is here that a radical spiritual solution may be most required to enable effective integration.

The paradox is that if successful spiritual integration does then take place, these inherently complex personalities can equally attain the greatest degree of true spiritual simplicity.

Jung in his writings frequently highlighted the holistic psychological role of mandalas i.e. pictorial images, serving as archetypes for the totality of the self.

The most important of these mandalas are based on the division of the circle into 4 or alternatively 8 equal segments, often presented in a highly ornate visual fashion.

So the basic structure of these mandalas equate directly with the geometrical presentation of the four and eight roots of 1 respectively i.e. the holistic interpretation of 4-dimensional and 8-dimensional (as the holistic circular interpretation of "4" and "8" respectively).

Therefore the deeper reason as to why these mandalas serve such a powerful integral purpose is that all fundamental psychological processes can be successfully interpreted, in a dynamic interactive fashion, through the holistic interpretation of the 4 and 8 roots of unity respectively.

Now as we have seen, using the 4 basic modes of reason, judgement, sense and feeling - all dynamically coordinated through the central volitional mode - we can derive 16 distinct aspects of personality.

So again, each of the 4 modes can be - relatively - defined with respect to real (conscious) and imaginary (unconscious) aspects, in both positive (external) and negative (internal) directions.

Now, allowing for slight differences in terminology from Jungian use, these equate extremely well with the corresponding 16 Personality Types (in the Myers-Briggs formulation).

However, I gradually began to suspect a certain limitation with this approach.

The Myers-Briggs Personality Types are all based on either/or distinctions. So with the first letter describing one's type, one is basically described as either E (extrovert) or I (introvert).

Then with the second one is described as either S (sense) or N (intuition). With the third letter one is described as either a T (thinking) or F (feeling) type. And then with the final letter one's decision-making is based on either J (judgement) or P (perception).

However, initially based on closer examination of my own personality, I began to realise that such either/or distinctions did not properly fit in this case.

So I gradually came to the conclusion that for certain personalities a both/and rather than either/or designation of these opposites was more appropriate.

So for example, I saw myself primarily neither as an extrovert or introvert as such but rather as a centrovert.

Now in secondary terms, I may have appeared to others as introvert, but then in early childhood, I am told that I was in fact very extroverted.

So one characteristic of this mixed type is that secondary characteristics e.g. as extrovert or introvert can undergo considerable change throughout life, as one deeply seeks for that primary balance (which is central to personality).

Then again I had problems in terms of the S and N classification. Though my general approach is indeed very holistic (N), I have always sought for a mathematically precise formulation (that would indicate S). In other words, I do not see either conscious or unconscious reality as primary, but rather the ineffable interface as between both aspects.

So the midpoint of both S and N (or real an imaginary) is an ineffable spiritual quality that is utterly mysterious. So I describe this conveniently as M (mystical).

Then in relation to the third distinction of T and F, again I would never have seen either as primary. In my case I am conscious of using T strongly with respect to the outer world, but F equally strongly in relation to inner reality. So the holy grail here once again is to obtain the successful balance of both modes.

And this leads to a primary emphasis on the volitional capacity of the will.

So therefore for the mixed type, neither T nor F is primary but rather V (volition).

Finally, again with respect to the last, with respect to decision-making, the common ground as between J (judgement) and P (perception) would be a quality of discernment for what is appropriate in any particular circumstance. So this again this middle ground as between J and P, I refer to as D (discernment) .

So therefore, I now was able to define a new mixed grouping, which essentially comprised complementary opposites with respect to the accepted polar opposite Types i.e. CMVD.

For example using the Myers-Briggs typology I would probably classify my present personality (in secondary terms) as an INFJ. Thus the complementary opposite here would be an ESTP. And indeed I can remember in early life that I did operate somewhat as an ESTP!

Put another way, this mixed grouping of types is likely to prove extremely sensitive to the shadow side of personality with the attempt to achieve proper integration a life-long journey continually confronting one's shadow.

Whereas in ideal circumstances the types from this group provide the best possibilities for true integration, in practice they are likely to be most prone to severe psychological problems (reflecting serious failures in achieving integration ).

"Great wits are to madness near allied

And thin partitions do their lines divide"

So along with the 16 Types (based on either/or divisions) I now had a new grouping of 8 mixed Types (based on complementary opposite pairings with respect to the 16 Types).

This therefore now led to the definition of 24 fundamental personality types.

I then realised that these could be formulated in a simpler fashion from the original 4 modes.

The idea here was to look at each personality as based on a combination of the 4 modes, with the first mode the most dominant, the next mode the auxiliary, followed by the two weakest (with the last representing the inferior mode).

Now, if for simplicity we represent the four modes as a, b, c and d respectively, then 24 distinct permutations of these letters are possible.

So each Personality Type is therefore defined as representing a unique permutation (or configuration) of the 4 basic modes.

Now of course considerable variation is still possible (with respect to the spectrum of healthy to unhealthy versions of each type)

For example in some cases the first mode may be especially dominant (therefore limiting possibilities for subsequent integration with the 3 weaker modes).

In other cases the inferior mode may be especially weak this operating in a blind unconscious manner, which would again pose special problems for successful integration.

In general however, there are three distinct groupings (the first two which equate well with the S and N Types on the Myers-Briggs scheme).

Thus for the first group (of 8 Types) real (conscious) reality is likely to dominate experience. This is due to the operation in the same horizontal direction (i.e. either external or internal) applying to the two leading modes. This then leads to a somewhat rigid conscious experience of actual phenomena.

Then for the second group (of 8 Types) imaginary (unconscious) reality is likely to be more important. This is now due to the two prominent modes of the same nature (either cognitive or affective) operating in a vertically opposite manner (where for example external is counterbalanced by the internal direction of the opposite mode). This inherent conflict of directions then tends to generate a substantial degree of intuition leading to the more holistic (unconscious) generation of potential phenomena.

Then for the third mixed group (of 8 Types), complex (both conscious and unconscious) reality is likely to predominate.

We have here the most acute clash, where the two dominant modes are both of opposite aspect and opposite direction (i.e. diagonal in nature). So, for example, we could have an external cognitive counterbalanced by an internal affective mode. This renders the attempt to rest, as it were, in either (real) or unconscious (imaginary) reality especially difficult. In fact it is here that a radical spiritual solution may be most required to enable effective integration.

The paradox is that if successful spiritual integration does then take place, these inherently complex personalities can equally attain the greatest degree of true spiritual simplicity.

## Thursday, January 14, 2016

### Personality Types (3)

I mentioned yesterday the complementary nature of the cognitive and
affective modes, which are relatively, both real (conscious) and imaginary
(unconscious) with respect to each other, in both external (objective) and internal
(subjective) directions.

However, perhaps the truly primary mode is that of volition (which expresses a fundamental purpose or orientation towards meaning, with respect to experience).

It serves therefore in effect as the key manner through which the attempt to achieve successful balance as between both the cognitive and affective modes is itself maintained.

When the personality is operating at the optimum level, substantial harmony therefore will be in evidence with respect to the complementary manner in which both cognitive and affective modes interact (without either attempting to dominate the functioning of the other). In such circumstances the will itself will tend to operate at the optimum level in enabling the further enhancement of the harmonious development as between the two other modes.

Indeed in such circumstances, the personality can operate with true freedom.

However when the initial relationship as between cognitive and affective is somewhat unbalanced, this sets limits to the freedom in turn in which the will can operate.

In other words, the will is likely to misinterpret the signals from the two other modes, thereby perpetuating a situation whereby just one mode maintains dominance.

However even here substantial readjustment is possible provided a person can keep tuning in with discernment to the quality of ultimate meaning being attained.

Therefore when this desire for true ultimate meaning is very marked - which is manifest for example in personalities with a strong spiritual orientation - the will can operate is such a way as to enable substantial transformation regarding any previous unsatisfactory relationship with respect to the cognitive and affective modes.

Thus the true nature of the volitional mode is rooted in the innate desire in the personality for ultimate meaning!

Therefore - though considerable overlap in practice necessarily takes place - the volitional, cognitive and affective modes are closely related to the spiritual domain of (ultimate) being, the rational world of (logical) thinking and the emotional world of (responsive) feeling respectively.

Though, again while stressing that every personality is unique, it is not really possible to attain true meaning without successfully balancing these three modes (without reduction of one domain to another).

These three domains in turn are commonly associated with the three great
cultural pursuits of religion, science and the arts.

In this context, the considerable problem of the scientific worldview, which dominates our present culture, is that it does in practice lead to the unbalanced - and therefore highly undesirable situation - where both the volitional and affective modes are substantially reduced in terms of the cognitive!

Though both cognitive and affective modes can indeed be given - as we have seen - a coherent holistic mathematical interpretation, this cannot be directly achieved in terms of the volitional.

However a fascinating indirect representation is indeed possible.

This entails adopting an 8-dimensional perspective.

Now in standard mathematical terms, the eight roots of 1 are,

However, perhaps the truly primary mode is that of volition (which expresses a fundamental purpose or orientation towards meaning, with respect to experience).

It serves therefore in effect as the key manner through which the attempt to achieve successful balance as between both the cognitive and affective modes is itself maintained.

When the personality is operating at the optimum level, substantial harmony therefore will be in evidence with respect to the complementary manner in which both cognitive and affective modes interact (without either attempting to dominate the functioning of the other). In such circumstances the will itself will tend to operate at the optimum level in enabling the further enhancement of the harmonious development as between the two other modes.

Indeed in such circumstances, the personality can operate with true freedom.

However when the initial relationship as between cognitive and affective is somewhat unbalanced, this sets limits to the freedom in turn in which the will can operate.

In other words, the will is likely to misinterpret the signals from the two other modes, thereby perpetuating a situation whereby just one mode maintains dominance.

However even here substantial readjustment is possible provided a person can keep tuning in with discernment to the quality of ultimate meaning being attained.

Therefore when this desire for true ultimate meaning is very marked - which is manifest for example in personalities with a strong spiritual orientation - the will can operate is such a way as to enable substantial transformation regarding any previous unsatisfactory relationship with respect to the cognitive and affective modes.

Thus the true nature of the volitional mode is rooted in the innate desire in the personality for ultimate meaning!

Therefore - though considerable overlap in practice necessarily takes place - the volitional, cognitive and affective modes are closely related to the spiritual domain of (ultimate) being, the rational world of (logical) thinking and the emotional world of (responsive) feeling respectively.

Though, again while stressing that every personality is unique, it is not really possible to attain true meaning without successfully balancing these three modes (without reduction of one domain to another).

In this context, the considerable problem of the scientific worldview, which dominates our present culture, is that it does in practice lead to the unbalanced - and therefore highly undesirable situation - where both the volitional and affective modes are substantially reduced in terms of the cognitive!

Though both cognitive and affective modes can indeed be given - as we have seen - a coherent holistic mathematical interpretation, this cannot be directly achieved in terms of the volitional.

However a fascinating indirect representation is indeed possible.

This entails adopting an 8-dimensional perspective.

Now in standard mathematical terms, the eight roots of 1 are,

+ 1 , – 1, + i, –
i, k(1 + i), k(1 – i), k(– 1 +
i) and k(– 1 – i) respectively,
where k = 1/√2.

Now
we have already dealt with the first four of these roots. The last four are all
complex roots where the magnitude of both real and imaginary parts is the same.

In
holistic mathematical terms, they enables us to provide an expression for the purest attainment of will where form = emptiness.

Thus
from the perspective of form, at the highest level of personality,
both real (conscious) and imaginary (unconscious) phenomena can be seamlessly
integrated (without undue attachment to either aspect).

In
this sense both real and imaginary are equalised with each other.

However
using the Pythagorean Theorem, where both adjacent (real) and opposite
(imaginary) sides are equal, the hypotenuse, which is the sum of the square of
both = 0.

(For
1

^{2}+ i^{2 }=^{ }1 – 1 = 0).
Now these diagonal lines, representing the hypotenuse
of a right angled triangle are referred to in physics as null lines (literally
without quantitative magnitude).

So
the holistic mathematical interpretation is that when both real
(conscious) and imaginary (unconscious) aspects of personality are brought into
close equal balance with each other - entailing a highly dynamic seamless
interaction of phenomena, experienced without undue attachment - a state of
spiritual emptiness (i.e. nothingness in physical terms) results.

Thus
we can see perhaps how beautifully the 2, 4 and 8 roots of 1 are related in
holistic mathematical fashion to the dynamics of development.

The
two roots (+ 1 and – 1) enable us to provide, relatively, positive
(external) and negative (internal) directions for both cognitive and affective
modes.

Then
the four roots ( + 1 , –
1, + i, – i) then enable us to provide real
(conscious) and imaginary (unconscious) aspects for both cognitive and
affective modes, in both positive (external) and negative (internal)
directions.

The
eight roots then enable us to provide
expressions of form (complex, with real and imaginary parts equal)) and
emptiness (null lines = 0) for the relationship of will - in all four quadrants
of the unit circle - with cognitive and affective modes relating to real
(conscious) and imaginary (unconscious) aspects in both positive (external) and
negative (internal) directions.

And
this enables us, in holistic mathematical terms, to provide a complete model of
Personality Types.

In fact, even for the most
sophisticated models currently in vogue, we solely require a 4-dimensional
(rather than 8-dimensional approach).

## Wednesday, January 13, 2016

### Personality Types (2)

Yesterday, I mentioned the holistic circular number system.

So each number that has a recognised quantitative (analytic) meaning in the conventional number system, has equally an unrecognised qualitative (holistic) meaning in a corresponding circular fashion.

This alternative circular system in truth leads to a new holistic understanding of the notion of a number dimension, which in turn paves the way for a radical new interpretation of the true nature of space and time (in both physical and psychological terms).

And just as "4" has a special significance in relation to dimensions from the conventional scientific perspective, equally this this true in holistic terms.

When Marie Louise Von Franz made the remarkable claim that "Jung devoted practically the whole of his life work to demonstrating the vast psychological significance of the number "4", she was referring implicitly to this circular holistic notion of "4".

And we can now briefly reveal in more mathematical terms why this is so important!

Just as in analytic terms the four roots of 1 define the four co-ordinates of the complex number system, which thereby enables the comprehensive treatment of all numbers, likewise this is true in holistic qualitative terms.

Therefore, in this context, we can now use the holistic notion of "4", which in linear terms is defined by real and imaginary co-ordinates (with respect to the unit circle in the complex plane).

Now once again, my basic model of personality is built directly on this holistic mathematical basis.

So we have the two complementary psychological modes (i.e. the cognitive mode of reason and the affective mode of sense) that are real (conscious) and imaginary (unconscious) with respect to each other.

Thus when the cognitive mode is made conscious (real), then in relative terms, the affective is thereby unconscious (imaginary).

However, in reverse manner, when the affective is now conscious (real) in experience, the cognitive is thereby unconscious (imaginary).

Therefore, both cognitive and affective modes keep switching, through the dynamics of experience, as between conscious (real) and unconscious (imaginary) aspects.

Likewise both modes have external (positive) and internal (negative) expressions.

Now to clarify a little more, I generally refer to the external (objective) cognitive mode as reason (R)!

Then with respect to the more internalised (subjective) expression of this mode, I customarily refer to it as judgement (J).

Likewise, I customarily refer to the external (objective) affective mode as sense (S) and then the more internalised (subjective) expression as feeling (F).

I must admit - though very much in broad agreement with Jung's treatment of personality functions - I have always found his definition of feeling as somewhat confusing (referring to it in rational terms).

However in my own terminology, feeling has clearly an affective - rather than cognitive - meaning.

So in this way, through the switching of polarities as between external and internal (and internal and external) we can thereby identify 4 modes (two cognitive and two affective) which in turn have both external (positive) and negative (internal) directions.

For example, when reason (R) is applied to some external objective - say scientific - issue, we thereby have its positive direction. However associated with this is a corresponding internal interpretation (using mental constructs).

We could validly refer therefore to the former external direction as the extrovert aspect (E) and the latter internal direction as the introvert aspect (I) respectively.

The fallacy therefore of belief in the "objective" nature of science, is that it inevitably reduces such subjective (internal) interpretation in a merely objective (external) manner.

However properly understood, objective reality has no strict meaning independent of subjective interpretation! Therefore our understanding of the world properly represents a two-way dialogue of interactive meaning.

Likewise judgement (J) has both an internal and external (i.e. introvert and extrovert) interpretations.

For example, in attempting to make an appropriate moral judgement with respect to individual behaviour, one's unique subjective experience (of an internal nature) will be critically important. However there is also an inescapable external dimension in the application of objective guidelines.

In fact, here we have a big problem with institutional religion, which attempts in many circumstances to reduce moral behaviour (e.g. in the case of abortion) to rigid conformity with unambiguous objective rules!

However once again properly understood, every moral decision should reflect a two-way dialogue as between external (objective) and internal (subjective) meaning.

Then with the sense mode (S), the external aspect relates to recognition of the object (that induces an affective reaction). The internal aspect then relates more directly to the affective feelings (induced by the object).

Then with the feeling mode (F), the internal aspect relates directly to subjective awareness of one's private feelings, where again the external aspect entails recognition of those events (that trigger such feelings).

So with the 4 modes (each with two directions) we have now defined 8 relatively distinct aspects of personality. However then we must remember that these have all both conscious (real) and unconscious (imaginary) expressions. In the Jungian system, this distinction is referred to as that between S (sense) and N (intuition). However once again, though very much in agreement with the general Jungian thrust, I prefer to use my own holistic mathematical terminology (to avoid confusion).

However what is clear is that when we allow for both conscious (real) and unconscious (imaginary) expressions with respect to the modes, we can now define 16 relatively distinct aspects of personality.

The Myers-Briggs Personality Types - which have arisen directly from Jungian notions - does indeed define 16 distinct Personality Types.

Each Personality Type is defined by 4 letters.

The first is either E (extrovert) or 1 (introvert). This concurs readily with external (positive) and negative (internal) directions (in my own approach).

The second letter is either S (sense) or N (intuition). This - as we have seen - relates to conscious (real) and unconscious (imaginary) in my approach.

The third letter is either T (thinking) or F (feeling). This concurs directly with cognitive and affective functions R (reason) and F (feeling) in my approach.

The last letter is either P (perception) or J (judgement). This concurs directly with cognitive and affective functions J (judgement) and S (sense) in my approach.

Thus each Personality Type is built around a certain dominance with respect to just one of the 16 possible Types.

Of course in some ways this is very unbalanced as all 16 aspects have an important role to play with respect to experience.

Though I recognise that in certain circumstances e.g. work, a person may indeed exhibit certain tendencies identifiable with one of these Types, I prefer now to see personality as a composite - however unbalanced - of all Types.

What I personally find of great significance is that all 16 Types can be directly related back to the holistic mathematical understanding of "4"!

And remember now we are speaking of a 4-dimensional reality that is structured - not in quantitative but rather - in a qualitative manner!

So each number that has a recognised quantitative (analytic) meaning in the conventional number system, has equally an unrecognised qualitative (holistic) meaning in a corresponding circular fashion.

This alternative circular system in truth leads to a new holistic understanding of the notion of a number dimension, which in turn paves the way for a radical new interpretation of the true nature of space and time (in both physical and psychological terms).

And just as "4" has a special significance in relation to dimensions from the conventional scientific perspective, equally this this true in holistic terms.

When Marie Louise Von Franz made the remarkable claim that "Jung devoted practically the whole of his life work to demonstrating the vast psychological significance of the number "4", she was referring implicitly to this circular holistic notion of "4".

And we can now briefly reveal in more mathematical terms why this is so important!

Just as in analytic terms the four roots of 1 define the four co-ordinates of the complex number system, which thereby enables the comprehensive treatment of all numbers, likewise this is true in holistic qualitative terms.

Therefore, in this context, we can now use the holistic notion of "4", which in linear terms is defined by real and imaginary co-ordinates (with respect to the unit circle in the complex plane).

Now once again, my basic model of personality is built directly on this holistic mathematical basis.

So we have the two complementary psychological modes (i.e. the cognitive mode of reason and the affective mode of sense) that are real (conscious) and imaginary (unconscious) with respect to each other.

Thus when the cognitive mode is made conscious (real), then in relative terms, the affective is thereby unconscious (imaginary).

However, in reverse manner, when the affective is now conscious (real) in experience, the cognitive is thereby unconscious (imaginary).

Therefore, both cognitive and affective modes keep switching, through the dynamics of experience, as between conscious (real) and unconscious (imaginary) aspects.

Likewise both modes have external (positive) and internal (negative) expressions.

Now to clarify a little more, I generally refer to the external (objective) cognitive mode as reason (R)!

Then with respect to the more internalised (subjective) expression of this mode, I customarily refer to it as judgement (J).

Likewise, I customarily refer to the external (objective) affective mode as sense (S) and then the more internalised (subjective) expression as feeling (F).

I must admit - though very much in broad agreement with Jung's treatment of personality functions - I have always found his definition of feeling as somewhat confusing (referring to it in rational terms).

However in my own terminology, feeling has clearly an affective - rather than cognitive - meaning.

So in this way, through the switching of polarities as between external and internal (and internal and external) we can thereby identify 4 modes (two cognitive and two affective) which in turn have both external (positive) and negative (internal) directions.

For example, when reason (R) is applied to some external objective - say scientific - issue, we thereby have its positive direction. However associated with this is a corresponding internal interpretation (using mental constructs).

We could validly refer therefore to the former external direction as the extrovert aspect (E) and the latter internal direction as the introvert aspect (I) respectively.

The fallacy therefore of belief in the "objective" nature of science, is that it inevitably reduces such subjective (internal) interpretation in a merely objective (external) manner.

However properly understood, objective reality has no strict meaning independent of subjective interpretation! Therefore our understanding of the world properly represents a two-way dialogue of interactive meaning.

Likewise judgement (J) has both an internal and external (i.e. introvert and extrovert) interpretations.

For example, in attempting to make an appropriate moral judgement with respect to individual behaviour, one's unique subjective experience (of an internal nature) will be critically important. However there is also an inescapable external dimension in the application of objective guidelines.

In fact, here we have a big problem with institutional religion, which attempts in many circumstances to reduce moral behaviour (e.g. in the case of abortion) to rigid conformity with unambiguous objective rules!

However once again properly understood, every moral decision should reflect a two-way dialogue as between external (objective) and internal (subjective) meaning.

Then with the sense mode (S), the external aspect relates to recognition of the object (that induces an affective reaction). The internal aspect then relates more directly to the affective feelings (induced by the object).

Then with the feeling mode (F), the internal aspect relates directly to subjective awareness of one's private feelings, where again the external aspect entails recognition of those events (that trigger such feelings).

So with the 4 modes (each with two directions) we have now defined 8 relatively distinct aspects of personality. However then we must remember that these have all both conscious (real) and unconscious (imaginary) expressions. In the Jungian system, this distinction is referred to as that between S (sense) and N (intuition). However once again, though very much in agreement with the general Jungian thrust, I prefer to use my own holistic mathematical terminology (to avoid confusion).

However what is clear is that when we allow for both conscious (real) and unconscious (imaginary) expressions with respect to the modes, we can now define 16 relatively distinct aspects of personality.

The Myers-Briggs Personality Types - which have arisen directly from Jungian notions - does indeed define 16 distinct Personality Types.

Each Personality Type is defined by 4 letters.

The first is either E (extrovert) or 1 (introvert). This concurs readily with external (positive) and negative (internal) directions (in my own approach).

The second letter is either S (sense) or N (intuition). This - as we have seen - relates to conscious (real) and unconscious (imaginary) in my approach.

The third letter is either T (thinking) or F (feeling). This concurs directly with cognitive and affective functions R (reason) and F (feeling) in my approach.

The last letter is either P (perception) or J (judgement). This concurs directly with cognitive and affective functions J (judgement) and S (sense) in my approach.

Thus each Personality Type is built around a certain dominance with respect to just one of the 16 possible Types.

Of course in some ways this is very unbalanced as all 16 aspects have an important role to play with respect to experience.

Though I recognise that in certain circumstances e.g. work, a person may indeed exhibit certain tendencies identifiable with one of these Types, I prefer now to see personality as a composite - however unbalanced - of all Types.

What I personally find of great significance is that all 16 Types can be directly related back to the holistic mathematical understanding of "4"!

And remember now we are speaking of a 4-dimensional reality that is structured - not in quantitative but rather - in a qualitative manner!

## Tuesday, January 12, 2016

### Personality Types (1)

I have always been fascinated with personality types and their relationship as to the manner in which personal spiritual development subsequently unfolds.

Of course, I should stress right away that each personality is unique with characteristics that belong to many different personality types!

However, having said that, many people do certainly exhibit in varying circumstances marked characteristics that would be associated with distinctive personality types (in the major classification systems).

For example, at work I shared for many years an office with colleagues lecturing in IT disciplines and could not but notice - what in Jungian terms would be described as - their strong sense (S) characteristics. These then contrasted considerably with my own more intuitive (N) personality!

However even here, one has to be careful for it is possible to exhibit certain strong - say thinking (T) - aspects with respect to one's work and then to express complementary feeling (F) aspects in one's leisure pursuits.

And then personality characteristics can change considerably over time so for example someone with marked extrovert (E) tendencies in early life may discover a neglected introvert (I) side in later life.

Also there are both healthy and unhealthy expressions of all these personality characteristics, with actual behaviour often varying considerably as between the varying extremes.

So again we must recognise the unique identity of each individual personality, whilst also recognising the way in which identifiable distinct general characteristics can be manifest in actual behaviour.

Therefore just as all colours can be shown to represent different mixes (or configurations) with respect to 3 or 4 primary colours, one of the earliest uses of my holistic mathematical approach was the attempt to precisely identify the primary ingredients - as it were - involved in relation to the formation of all personality types.

And - because of the holistic complementarity of psychological and physical realms - this also served as the identification of the primary ingredients with respect to corresponding impersonality types which was to lead to a remarkable unexpected connection with string theory!

In the late 60's and early 70's, I had become deeply aware of two fundamental polarity sets, which I now realised as underlining all phenomenal relationships (in both physical and psychological terms).

The first were - what I referred to as - the horizontal polarities of external and internal which operate at any given level of development.

So therefore the recognition of any object (as external) implies - relatively - a corresponding (internal) mental perception with respect to the observing self.

So the act of recognition therefore necessarily entails both external and internal polarities that are in holistic mathematical terms positive and negative with respect to each other.

And in the dynamics of recognition positive and negative continually switch positions. Therefore at one moment we are aware of the external world (in relation to the observing self). Then at the next we are now aware of the observing self (in relation to the world).

Now, the big mathematical breakthrough that I made in 1970 was to see both of these polarities as the holistic expression of a circular number system (that represents the number "2").

So just as there is a well recognised linear (i.e. 1-dimensional) system for the recognition of all real numbers (in a quantitative manner), I was now starting to recognise that a corresponding - though not yet recognised - circular system existed for the recognition of all real numbers (in a corresponding qualitative manner).

Therefore when a "higher" dimension of 2 is expressed indirectly in a linear fashion, the two directions (i.e. dimensions) are represented as + 1 and – 1 respectively. Though these remain separate at the reduced 1-dimensional level of formal rational interpretation, they are intuitively combined (in an ineffable spiritual manner) at the "higher" 2-dimensional level.

So 2-dimensional appreciation therefore directly represents the intuitive recognition of interdependence, where both positive and negative polarities are now fully integrated with each other.

This holistic idea of interdependence is then directly associated with the developmental notion of integration, with the corresponding analytic idea of independence associated directly, in corresponding fashion, with differentiation.

Therefore to the extent that we recognise both external and internal poles as independent, we are thereby differentiating with respect to development.

However to the corresponding extent that we can equally recognise both external and internal poles as interdependent, we are by contrast integrating the experience.

Therefore the proper interpretation of both differentiation and interpretation with respect to development requires both analytic and holistic aspects (which cannot be reduced in terms of each other).

Alternatively it requires both linear and circular notions of direction.

However because accepted intellectual discourse is heavily weighted in a merely analytic manner, this inevitably leads to a reduced interpretation of development (where integration is explained in terms of differentiated processes).

This is turn exemplified by an unduly linear approach to the various stages where, for example, the paradoxical holistic relationship as between "higher" and "lower" is continually misinterpreted!

Though I was also aware of the equal importance of - what I referred to as - the vertical polarities of whole and part, it took me much longer to properly appreciate their true nature in holistic mathematical terms.

A growing familiarity with Jungian Psychology in the early 80's was of great assistance here.

Jung in fact implicitly formulated many of his notions in a holistic mathematical manner.

For example with respect to his four functions he distinguished two (T and F) as rational and two (S and N) - in complementary manner - as irrational.

However, I gradually came to the view that an alternative formulation, whereby two modes (or functions) would be classified as "real" and two other modes as - relatively - "imaginary" was more appropriate.

The two "real" modes had both positive and negative directions (which continually interchanged with each other). Likewise the two "imaginary" directions had both positive and negative directions (which again interchanged with each other in relative manner).

So one might inquire as to the distinction as between "real" and "imaginary" modes!

In this holistic context what is "real" relates to what is consciously understood in a direct manner. This corresponds in scientific terms with - what I refer to as - analytic understanding.

However "imaginary" understanding is of a much subtler nature. In a direct fashion it relates to holistic appreciation (that is unconscious in origin). However indirectly, such holistic appreciation can be indirectly expressed through conscious type symbols. And this indirect conscious expression (of what is primarily of an unconscious holistic nature) represents the "imaginary" aspect of understanding.

For example in a refined fashion, key spiritual archetypes (whereby conscious symbols are used to convey a deeper holistic meaning) represent the "imaginary" aspect of understanding.

Then in a less refined fashion, psychological projections represent the unrecognised "imaginary" aspect of understanding.

In both cases, though specific symbols are used to mediate, the meaning of the experience is thereby primarily of a holistic non-local nature.

However, one cannot properly conceive of the "imaginary" aspect in static rigid terms as it continually interchanges with the "real" in a dynamic relative manner.

One important connection I now made was the recognition that the interchange as between whole and part (and part and whole) entails both "real" and "imaginary" aspects, which dynamically interchange in relative fashion.

So when the part aspect is (consciously) "real" in experience, the corresponding "whole" aspect remains implicitly (unconsciously) "imaginary". Then in the dynamics of experience, the complementary opposite aspects switch so that the whole is now (consciously) "real" and the part aspect implicitly "imaginary" (in an unconscious manner).

Therefore both whole and part aspects can be "real" or "imaginary" depending on context.

However, when one attempts to understand the relationship between whole and parts in a merely conscious manner (as "real") we have inevitable reductionism, whereby both aspects are defined in terms of each other (in a merely quantitative manner).

And science as we know it is riddled through and through with such reduced interpretation!

I also made the vital connection that whole and part are mediated through the cognitive and affective aspects of personality respectively.

The volitional aspect then serves the vitally important function of striving to maintain appropriate balance as between "real" (conscious) and "imaginary" (unconscious) aspects with respect to both cognitive and affective modes of personality respectively.

All this dynamic understanding was then enshrined within the holistic mathematical interpretation of "4".

In other words, when expressed in the standard 1-dimensional fashion, the holistic notion of "4" has four directions (i.e. dimensions) that are real and imaginary (in a positive and negative manner). In mathematical fashion, these are expressed as the four roots + 1, – 1, + i and – i respectively.

However, whereas in an analytic sense these are understood as clearly separate, in corresponding holistic fashion, they are understood as identically interdependent (through direct intuitive understanding).

So by the early 80's, I had formulated the holistic mathematical modelling of the 4 key polarities (external/internal and whole/part) which again underline all phenomenal relationships (in physical and psychological terms).

Then at a somewhat later stage, I was able to see how this could be precisely used in the clarification of the fundamental personality types.

Of course, I should stress right away that each personality is unique with characteristics that belong to many different personality types!

However, having said that, many people do certainly exhibit in varying circumstances marked characteristics that would be associated with distinctive personality types (in the major classification systems).

For example, at work I shared for many years an office with colleagues lecturing in IT disciplines and could not but notice - what in Jungian terms would be described as - their strong sense (S) characteristics. These then contrasted considerably with my own more intuitive (N) personality!

However even here, one has to be careful for it is possible to exhibit certain strong - say thinking (T) - aspects with respect to one's work and then to express complementary feeling (F) aspects in one's leisure pursuits.

And then personality characteristics can change considerably over time so for example someone with marked extrovert (E) tendencies in early life may discover a neglected introvert (I) side in later life.

Also there are both healthy and unhealthy expressions of all these personality characteristics, with actual behaviour often varying considerably as between the varying extremes.

So again we must recognise the unique identity of each individual personality, whilst also recognising the way in which identifiable distinct general characteristics can be manifest in actual behaviour.

Therefore just as all colours can be shown to represent different mixes (or configurations) with respect to 3 or 4 primary colours, one of the earliest uses of my holistic mathematical approach was the attempt to precisely identify the primary ingredients - as it were - involved in relation to the formation of all personality types.

And - because of the holistic complementarity of psychological and physical realms - this also served as the identification of the primary ingredients with respect to corresponding impersonality types which was to lead to a remarkable unexpected connection with string theory!

In the late 60's and early 70's, I had become deeply aware of two fundamental polarity sets, which I now realised as underlining all phenomenal relationships (in both physical and psychological terms).

The first were - what I referred to as - the horizontal polarities of external and internal which operate at any given level of development.

So therefore the recognition of any object (as external) implies - relatively - a corresponding (internal) mental perception with respect to the observing self.

So the act of recognition therefore necessarily entails both external and internal polarities that are in holistic mathematical terms positive and negative with respect to each other.

And in the dynamics of recognition positive and negative continually switch positions. Therefore at one moment we are aware of the external world (in relation to the observing self). Then at the next we are now aware of the observing self (in relation to the world).

Now, the big mathematical breakthrough that I made in 1970 was to see both of these polarities as the holistic expression of a circular number system (that represents the number "2").

So just as there is a well recognised linear (i.e. 1-dimensional) system for the recognition of all real numbers (in a quantitative manner), I was now starting to recognise that a corresponding - though not yet recognised - circular system existed for the recognition of all real numbers (in a corresponding qualitative manner).

Therefore when a "higher" dimension of 2 is expressed indirectly in a linear fashion, the two directions (i.e. dimensions) are represented as + 1 and – 1 respectively. Though these remain separate at the reduced 1-dimensional level of formal rational interpretation, they are intuitively combined (in an ineffable spiritual manner) at the "higher" 2-dimensional level.

So 2-dimensional appreciation therefore directly represents the intuitive recognition of interdependence, where both positive and negative polarities are now fully integrated with each other.

This holistic idea of interdependence is then directly associated with the developmental notion of integration, with the corresponding analytic idea of independence associated directly, in corresponding fashion, with differentiation.

Therefore to the extent that we recognise both external and internal poles as independent, we are thereby differentiating with respect to development.

However to the corresponding extent that we can equally recognise both external and internal poles as interdependent, we are by contrast integrating the experience.

Therefore the proper interpretation of both differentiation and interpretation with respect to development requires both analytic and holistic aspects (which cannot be reduced in terms of each other).

Alternatively it requires both linear and circular notions of direction.

However because accepted intellectual discourse is heavily weighted in a merely analytic manner, this inevitably leads to a reduced interpretation of development (where integration is explained in terms of differentiated processes).

This is turn exemplified by an unduly linear approach to the various stages where, for example, the paradoxical holistic relationship as between "higher" and "lower" is continually misinterpreted!

Though I was also aware of the equal importance of - what I referred to as - the vertical polarities of whole and part, it took me much longer to properly appreciate their true nature in holistic mathematical terms.

A growing familiarity with Jungian Psychology in the early 80's was of great assistance here.

Jung in fact implicitly formulated many of his notions in a holistic mathematical manner.

For example with respect to his four functions he distinguished two (T and F) as rational and two (S and N) - in complementary manner - as irrational.

However, I gradually came to the view that an alternative formulation, whereby two modes (or functions) would be classified as "real" and two other modes as - relatively - "imaginary" was more appropriate.

The two "real" modes had both positive and negative directions (which continually interchanged with each other). Likewise the two "imaginary" directions had both positive and negative directions (which again interchanged with each other in relative manner).

So one might inquire as to the distinction as between "real" and "imaginary" modes!

In this holistic context what is "real" relates to what is consciously understood in a direct manner. This corresponds in scientific terms with - what I refer to as - analytic understanding.

However "imaginary" understanding is of a much subtler nature. In a direct fashion it relates to holistic appreciation (that is unconscious in origin). However indirectly, such holistic appreciation can be indirectly expressed through conscious type symbols. And this indirect conscious expression (of what is primarily of an unconscious holistic nature) represents the "imaginary" aspect of understanding.

For example in a refined fashion, key spiritual archetypes (whereby conscious symbols are used to convey a deeper holistic meaning) represent the "imaginary" aspect of understanding.

Then in a less refined fashion, psychological projections represent the unrecognised "imaginary" aspect of understanding.

In both cases, though specific symbols are used to mediate, the meaning of the experience is thereby primarily of a holistic non-local nature.

However, one cannot properly conceive of the "imaginary" aspect in static rigid terms as it continually interchanges with the "real" in a dynamic relative manner.

One important connection I now made was the recognition that the interchange as between whole and part (and part and whole) entails both "real" and "imaginary" aspects, which dynamically interchange in relative fashion.

So when the part aspect is (consciously) "real" in experience, the corresponding "whole" aspect remains implicitly (unconsciously) "imaginary". Then in the dynamics of experience, the complementary opposite aspects switch so that the whole is now (consciously) "real" and the part aspect implicitly "imaginary" (in an unconscious manner).

Therefore both whole and part aspects can be "real" or "imaginary" depending on context.

However, when one attempts to understand the relationship between whole and parts in a merely conscious manner (as "real") we have inevitable reductionism, whereby both aspects are defined in terms of each other (in a merely quantitative manner).

And science as we know it is riddled through and through with such reduced interpretation!

I also made the vital connection that whole and part are mediated through the cognitive and affective aspects of personality respectively.

The volitional aspect then serves the vitally important function of striving to maintain appropriate balance as between "real" (conscious) and "imaginary" (unconscious) aspects with respect to both cognitive and affective modes of personality respectively.

All this dynamic understanding was then enshrined within the holistic mathematical interpretation of "4".

In other words, when expressed in the standard 1-dimensional fashion, the holistic notion of "4" has four directions (i.e. dimensions) that are real and imaginary (in a positive and negative manner). In mathematical fashion, these are expressed as the four roots + 1, – 1, + i and – i respectively.

However, whereas in an analytic sense these are understood as clearly separate, in corresponding holistic fashion, they are understood as identically interdependent (through direct intuitive understanding).

So by the early 80's, I had formulated the holistic mathematical modelling of the 4 key polarities (external/internal and whole/part) which again underline all phenomenal relationships (in physical and psychological terms).

Then at a somewhat later stage, I was able to see how this could be precisely used in the clarification of the fundamental personality types.

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