Physics is very much searching for a TOE and hopes are high in some quarters that present developments in String theory (and more recently M-theory) will answer this quest.
However whatever benefits may arise from such an approach scientists are still dealing with reality at the level of phenomena. Such a theory by its very nature cannot be final as the phenomena it utilises will still await a deeper explanation.
So any approach that is ultimate, must attempt to get to grips with the original ground state of reality (before phenomena arise) and also attempt to explain how subsequent phenomena emerge.
Now there is where the holistic mathematical approach can be of so much benefit as its very formulations point to the original ground state using very simple integral symmetries.
In my model I use 3 sets of polarities which are sufficient to encode all dynamic processes.
The first set relates to the "real" polarities (i.e. consciously observed phenomena) which always have exterior and interior (and interior and exterior) aspects.
Using these polarities we can show the dynamic relationship between (quantitative) phenomena from one perspective, and from another the relationship between (qualitative) dimensions with respect to both their exterior and interior aspects.
However we are not yet able with these polarities to successfully demonstrate the interaction as between the (quantitative) objects and the (qualitative) dimensions (without reductionism).
However the second set of "imaginary" polarities (i.e. phenomena that are the indirect expression of the unconscious) remedies this problem and enables the subtle interaction between wholes (dimensions) and parts (object phenomena) to be properly related.
Now, reality is defined in mathematically complex terms with quantitative (object phenomena) and qualitative (dimensions) that are "real" and "imaginary" with respect to each other.
Physical forces which establish the interaction as between (quantitative) object phenomena and (qualitative) dimensions have elements of both and are defined by the third set of "complex" polarities i.e. that have both equal "real" and "imaginary" aspects.
The forces - as is increasingly known - exhibit both wave and particle aspects - which are "real" and "imaginary" with respect to each other.
So for example when we observe the wave aspect of light it is thereby "real" (with the particle aspect remaining "imaginary").
However when we then observe the particle aspect it is now "real" (with the wave aspect "imaginary").
So light (as an example of the electro-magnetic force) and by extension all four forces adapt perfectly in their behaviour to the dynamic interaction of the "complex" (i.e. diagonal) polarities.
One of the great quests in Physics is the unification of the four forces.
When we use the holistic mathematical approach - which is directly designed for integral appreciation - this becomes remarkably easy and is represented by the four complex roots of unity (given their dynamic interactive interpretation).
As we have seen the diagonal polarities - in terms of their own frame of reference - operate as null lines = 0.
So in the state where forces are perfectly reconciled, they thereby become empty of any phenomenal characteristics and represent the void, which is equally the potential for physical existence.
However this potential void (as an empty physical state) can also be described as the perfectly symmetrical arrangement of what are - in asymmetrical terms - observed as four separate forces.
So the fundamental structures pertaining to this physical void (which paradoxically ultimately are without structure) are provided by the four complex roots of unity given their dynamic holistic mathematical interpretation. Therefore we can say that in this empty physical state, particles and waves (i.e. relatively "real" and "imaginary" aspects ) and interior and exterior (i.e. relatively positive and negative aspects) are perfectly interchangeable.
The emergence of physical reality from this empty void is associated in a primary sense with the splitting off of these diagonal polarities so that "real" and "imaginary" and exterior and interior aspects are now no longer fully interchangeable. In this manner we have the birth of the four asymmetrical forces in physical reality.
The very same sort of approach can be fruitfully applied to clarifying the precise nature of the goal of all reality i.e. as the ultimate spiritual void.
We have here an exciting complementary matching of physical and spiritual "forces".
Now the spiritual "forces" manifest themselves as that mysterious drive and motivation relating to the will which enables the interaction - in psychological experience - of all phenomenal perceptions and concepts.
So as the physical forces are necessary to establish the interaction between objects and dimensions which are mathematically "real" and "imaginary" (i.e. quantitative and qualitative with respect to each other), the spiritual forces are equally necessary to establish the interaction in our experience of such object phenomena (perceptions) and dimensions (concepts).
Just as there is ultimately one "force" in physics i.e. as the empty physical void (which represents the potential for physical phenomenal reality) equally there is just one "force" in psychological terms i.e. as the empty spiritual void (which equally represents the potential for psycho-spiritual phenomenal reality).
Of course ultimately the empty physical void and the empty spiritual void are themselves identical (as the present moment) representing complementary aspects which separate in phenomenal terms.
Now we could equally say - again in dualistic manner - that there are two absolute states of this double void i.e. as pure nothingness representing the state before life begins, where - by definition - absolutely no differentiation or integration in experience has yet taken place and as pure being representing the perfect complete state of both differentiation and integration (which can only be approximately realised through phenomenal existence).
Once again in absolute (realised) terms there is no difference as between these two states, which represents the present moment continually renewed. However, paradoxically, finite existence is always necessary before realisation of one's true eternal state - which always is simply present - can take place. In more emphatic dualistic terms one's absolute spiritual nature which has existed and will always exist throughout eternity - needs to be "grounded" in finite terms before this realisation can take place.
Complementarity of Physical and Spiritual Forces
Now remarkably there are very close structural parallels as between the four forces (as identified in physics) and the corresponding four "forces" which equally exist in psycho-spiritual terms. However precisely because we do not interpret the physical and psychological aspects of reality in dynamic complementary fashion, we fail to recognise this correspondence (which would be immensely helpful in terms of a truly integral appreciation of reality).
Some time ago I was struck when reading Evelyn Underhill's "Mysticism" as to the manner in which she relayed how spiritual conversion takes place.
Underhill clearly emphasises that conversion typically takes place in either an immanent or transcendent manner (the precise manner of which is largely is dictated by personality characteristics).
When one studies her accounts more closely both the immanent and transcendent have exterior and interior manifestations.
So in fact we have four types of spiritual conversions (which exactly correspond with the diagonal polarities I have identified in my holistic mathematical approach).
First we have immanence (of an exterior kind) which we can arbitrarily fix as the diagonal line that splits the Upper Right Quadrant (into two equal sectors).
We have also immanence (of an interior kind) which will - relatively - be represented by the diagonal line equally dividing the Upper Left Quadrant.
Then we have transcendence (of an exterior kind) which will be represented by the diagonal line dividing the Bottom Right Quadrant.
Finally we have transcendence (of an interior kind) which will be represented by the diagonal line dividing the Bottom Left Quadrant.
So according to Underhill, mystical conversion manifests itself in terms of one of four spiritual forces. However the ultimate goal is to unify these forces so that they will all coincide as one in Spirit.
In physical terms until comparatively recently only two great forces were recognised i.e. the electromagnetic and the gravitational. Einstein for example devoted a great many years to the attempted reconciliation of these forces.
More recently two other forces have been recognised i.e. the weak and the strong.
The weak can be fruitfully seen as an interior expression of the electromagnetic force (of which natural light is one manifestation) which indeed operates in a more exterior manner. (Indeed it is now accepted that the weak can be successfully reconciled with the electromagnetic!)
Likewise the strong force can be fruitfully understood as an interior expression of the gravitational force (confined to the most intimate particle interactions over very short distances) Again the gravitational force operates - in contrast to the strong force - extremely weakly over - potentially - vast distances.
Now using this interpretation, we have two major physical forces - electromagnetic and gravitational (with exterior and interior expressions) and two major spiritual forces - immanence and transcendence (again with exterior and interior expressions).
This indeed suggests that there are indeed close complementary structural parallels between both sets of forces and indeed when we look more closely this is revealed to be the case.
The exterior expression of immanence is usually associated with nature mysticism whereby concrete phenomena become bathed in new light (i.e. new spiritual energy).
Likewise as we have seen, natural light is one important expression of the electromagnetic force (operating likewise in an exterior fashion).
Indeed just as physical energy (electromagnetic radiation) has a spectrum of different manifestations (of varying waveband and frequency), likewise it is true of spiritual energy. Whereas the equivalent of natural light is associated in spiritual terms with normal perception, more subtle forms of light (of differing ranges and frequency) are associated with mystical forms of awareness (and remain invisible at the level of normal perception).
The interior expression of immanence corresponds well with the more sensitive affective type of personality. It relates to emotional experience that is directly inspired by the Spirit based on considerable acceptance of one's humanity. So it is usually associated with a strongly devotional religious expression.
Now the parallel here in physical terms would be the weak force.
It is amazing how often that the very word used in physical terms is suggestive of its psychological meaning.
Weakness in psychological terms is often misleadingly associated - especially from a masculine perspective - as emotional vulnerability. However it is precisely the open acceptance of such vulnerability (with accompanying reliance on the Spirit) that is the essence of the interior expression of immanence. Indeed even in physical terms the weak force is associated with a vulnerable state of matter i.e. that is subject to radio-active decay.
The exterior expression of transcendence relates to a holistic cosmic appreciation of creation (that is inspired by Spirit).
The correspondent here would be the gravitational force, which again is best exempified in a global universal context.
However much closer connections can be made.
Whereas light is generally associated with a more superficial concrete situation, gravity is - by contrast - associated with a deeper conceptual context.
If we refer for example to "light" reading we imply an activity that is not intellectually demanding (in a conceptual manner).
Indeed the stereotype of a person who indeed is deeply intellectual would be of someone who has a somewhat "heavy" personality and is thus serious and grave.
Likewise gravity in physical terms is associated with weight i.e. "heaviness". Where there is no gravity there can be no weight. However this applies equally in psycho-spiritual terms. So it is transcendence that truly gives "weight" and a degree of gravity to personality. A truly "weighty" personality e.g. an intellectual or spiritual "heavyweight" will - by definition - thus have achieved considerable transcendence.
The most profound development of transcendence is associated with the mystical "dark night". This involves considerable contraction in one's experience of space and time and is associated therefore with an immense increase in psychological gravity. It is not surprisingly accompanied by profound grief (which etymologically is closely related to gravity)
The dynamics of the collapse of matter into "black holes" is remarkably similar in structural terms representing in this case physical gravity. So the close parallels here as between a physical and its corresponding spiritual "force" are undeniable.
Finally transcendence in an interior manner can be associated with the nuclear force. Spiritual transcendence of the self is principally associated with the authentic growth in faith, which literally gives strength - sometimes to an amazing degree - to the personality. So it is this faith - representing a strong growth in motivational conviction that literally holds the elements of personality together, just like the strong force in physics holds the particles of a nucleus together.
There are even further parallels. In physics the unification of the four forces is associated with considerable increases in heat so that ultimately in is believed that at a sufficiently high temperature all forces would be unified.
Indeed in this context we often refer to high-energy physics.
In similar terms the unification of the spiritual "forces" is associated by marked increases in energy so that mystical development does indeed represent high-energy psychology as the dynamics of relationships are steadily increased.
Indeed the final stage of development where the closest approximation to the unification of the spiritual forces is obtained - is often characterised by heat and fire. St. John of the Cross refers for example to "The Living Flame of Flame", so that with peak mystical fervour it seems as if the whole Universe is ablaze with love.
In holistic mathematical terms - each of the four spiritual "forces", which are ultimately unified and identical as empty Spirit - can be represented by diagonals in the four Quadrants where they have dual interpretations as null lines = 0 (pointing to the empty spiritual state) and complex interpretations (with equal "real" and "imaginary" aspects).
So though the nature of Spirit (in itself) is utterly mysterious and incomprehensible (in phenomenal terms) indirectly it manifest itself - like the physical forces - though interactions with phenomenal matter.
There it reveals itself alternately in "real" and imaginary" terms (which are interchangeable).
Thus when we are aware of the transcendent aspect of Spirit in "real" terms (with respect to phenomena), the immanent aspect thereby is "imaginary". Then when we are aware of the immanent aspect as "real", the transcendent aspect is "imaginary".
Indeed if refer to the immanent as the particle aspect of Spirit (e.g. "to see a world in a grain of sand") the corresponding wave aspect of Spirit is thereby transcendent. However if we refer to the transcendent as the particle aspect (as with spiritually inspired scientific observation) then the immanent is "imaginary".
So the transcendent and immanent aspects of Spirit have both "real" and "imaginary" expressions (which are interchangeable).
Likewise as we have seen, immanent and transcendent have both positive and negative (i.e. exterior and interior) expressions respectively.
There is a remarkably interesting implication of this handling of the "spiritual" forces, where the transcendent and immanent (and immanent and transcendent) aspects are seen as "real" and "imaginary" with respect to each other.
Now because the physical corollary of the spiritual "forces" of transcendence and immanence are electromagnetic radiation and gravity then this clearly implies that there is an extremely close structural connection as between these two physical forces.
So quite simply the "real" aspect of electromagnetic energy is the "imaginary" aspect of gravity; likewise the "real" aspect of gravity is the "imaginary" aspect of electromagnetic energy. Now in the nondual empty state these are perfectly symmetrical i.e. identical. However in asymmetrical terms the truth of the relationship remains "unseen".
In mystical terms this connection as between the "spiritual" forces is more apparent.
Thus when the transcendental (gravitational) force is especially at work (as during the "dark night") the spiritual light though recognised as present remains unseen. Likewise when immanence is at work and phenomena are bathed in plentiful light, all grief (which is directly related to psychological experience of gravity) is forgotten.
So when one aspect is present in experience, the other - though in truth also present - remains unseen.
So from this perspective, in physical terms gravity is energy (i.e. electromagnetic) that is unseen. Likewise electromagnetic energy is gravity (that is unseen and therefore unobserved).
Now this mystery can be easily represented by formulating "reality" in holistic mathematical complex terms (i.e. with "real" and "imaginary" aspects that in dynamic terms keep switching).
Closed v Open Integral TOE's
I have been outlining above the basic nature of a closed integral TOE. Here ultimate reality is described in terms of the (merely) complementary aspects of the polar opposites of existence where they become fully symmetrical in "real" (horizontal), "imaginary" (vertical) and "complex" (diagonal) terms.
In an open integral TOE both the relationship as between the symmetrical and asymmetrical aspects of polar opposites with respect to the dynamic unfolding of phenomenal reality at all stages is mathematically encoded in holistic binary form.
So the closed version of the TOE is then appropriately seen as a special limiting case (i.e. where phenomena do not arise) of the more comprehensive open TOE.
In outlining the holistic mathematical nature of all stages of development, I will be making use therefore of the open integral TOE
Thus to sum up
1) the fundamental state of reality can be expressed through the holistic mathematical explanation of the diagonal polarities which in dynamic terms continually interact:
a) from a nondual perspective as a pure empty state provided by the interpretation of theses "diagonals" as null lines = 0
(b) from the corresponding dual state in terms of complex polarities (with equal real and imaginary aspects).
Here the structures corresponding to the empty state are expressed in terms of the perfect symmetry of opposite complex ("real" and "imaginary") polarities for both diagonal lines.
So whereas in phenomenal terms these polarities necessarily separate as waves and particles (with in turn - relatively - separate "real" and "imaginary" aspects) in terms of ultimate reality they perfectly coincide (in a pure non-phenomenal union of structure that is equally a pure empty state).
2) we can approach the ultimate nature of "reality" from two perspectives which - again from a nondual viewpoint - are identical.
(a) in terms of the ultimate nature of physical reality (before finite life emerges). This can be equally represented as a pure empty state (representing the potential for phenomenal existence). Alternatively it can be viewed as the ultimate union of the physical forces which as we have seen can be precisely structured - in terms of their ultimate nature - through the holistic mathematical explanation of the diagonal polarities (i.e. the four complex roots of unity).
(b) in terms of the ultimate nature of psychological reality (after finite life is completed) where it again can be equally represented as a pure empty spiritual state representing the fulfilment of the potential for psychological existence. Alternately it can be represented as the union of the spiritual "forces" which again are precisely structured with respect to their integration through the holistic mathematical explanation of the diagonal polarities.
(c) Of course ultimately these two perspectives are themselves identical and interchangeable so that our explanations lose all sense of any asymmetrical direction.
3) The very essence of the integral scientific approach is that there is deep structural complementary as between the interpretation of physical and spiritual forces which can be equally be precisely explained through the holistic mathematical interpretation of the four complex roots of unity (i.e. the diagonal polarities).
Therefore in an integral scientific approach the choice of terminology used to explain both sets of forces will be deliberately chosen as to reveal this deep - though as yet largely unrecognised - complementary similarity (which is ultimately rooted in a common holistic mathematical structure).