In holistic mathematical terms, the structures of Level 2 (Band 3) can be characterized as of a 4-dimensional nature from a qualitative perspective.
Now we all accept in conventional scientific terms the quantitative importance of 4 dimensions (with our macro world seemingly structured in this manner).
However an equal (though largely unrecognised) importance attaches to 4 dimensions from a qualitative perspective (with again everyday reality seemingly structured in this fashion).
These the 4 qualitative dimensions correspond indirectly (in a reduced quantitative manner) with the four roots of 1 i.e. + 1, − 1, + i and − i respectively.
Now we have already dealt with the significance of the two real (horizontal) roots in the context of 2-dimensional interpretation. Again, in dynamic relative terms, these refer to the interaction of external (objective) and internal (subjective) polarities (which necessary underlie all experience).
As we have seen, these horizontal polarities are integrated with each other (to a substantial degree) during Level 1 (Band 3).
So now the focus in development largely switches at Level 2 to the corresponding integration of these vertical (i.e. imaginary) polarities.
I have frequently stated that in holistic mathematical terms, the imaginary notion i, represents the indirect linear rational expression of meaning that is properly of a qualitative holistic nature. Put another way it is the indirect conscious expression of unconscious meaning.
In experience therefore, the unconscious can only indirectly express itself through projections that are attached to conscious symbols. So correct interpretation requires seeing such symbols as but the indirect expression of a more universal holistic meaning.
Actually, all of this relates to the fundamental relationship between wholes and parts in experience.
Properly understood, in dynamic interactive terms, the relationship as between whole and part (and part and whole) is quantitative as to qualitative (and qualitative as to quantitative) respectively.
However in 1-dimensional terms (which defines Conventional Mathematics) a reduced quantitative interpretation is given, whereby in any context the whole is understood as the sum of its quantitative parts (both of which are interpreted in a real conscious fashion).
Now this equates in psychological terms with a merely rational interpretation of relationships.
But again actual experience is dynamically interactive in nature entailing both rational (quantitative) and intuitive (qualitative) elements.
Therefore, from a proper dynamic perspective, the collection of parts (in a quantitative manner) reflect the whole (which is understood in a - relatively - qualitative manner).
Likewise each part (in an individual quantitative manner) reflects the whole (again understood - relatively - in a qualitative manner).
From a Jungian psychological perspective these would both reflect symbols that are understood as mediating archetypes of a universal nature.
Thus in the former case, generalised symbols would be serving as archetypes; in the later case it would be individual symbols of a local nature that would reflect these archetypes.
It is here where the spiritual contemplative traditions can provide additional assistance.
When the collective whole becomes the reflection of universal meaning, this is referred to as the transcendent aspect of spirituality; then, in relative terms, when individual localised part symbols serve as the reflection of universal meaning this is now referred to in a complementary manner as the corresponding immanent aspect of spirituality.
So the transcendent (whole) and immanent (part) aspects of spirituality are once again truly complementary.
Therefore from this perspective, when collective symbols serve as the mediator of spiritual (unconscious) meaning we can refer to them as imaginary (in a positive manner).
Then when one attempts in reverse fashion to switch to corresponding appreciation of individual symbols likewise serving as mediators of spiritual meaning we must first negate the earlier imaginary understanding.
In this way we can see that the transcendent and immanent appreciation of the qualitative nature of phenomenal symbols in mathematical terms corresponds with the two imaginary roots (of the 4 roots of 1) as + i and − i respectively.
The main practical problem that is now experienced however is that up to this point an unduly transcendent emphasis will have characterised spiritual development.
This means in effect that whereas one may find it relatively easy to see "higher" collective universal phenomena serving as appropriate "imaginary" archetypes of spirit, it may for a long time be much more difficult to accept "lower" instinctive phenomena (such as erotic fantasies) as likewise serving as appropriate symbols of spiritual meaning.
In other words in most religious traditions, an undue emphasis is placed on the "higher" transcendent aspect of spirituality. This then can lead to considerable problems in fully accepting the "lower" physical aspect of human experience. However, until this is properly achieved, the immanent aspect cannot be properly integrated with the corresponding transcendent aspect of spirituality.
Put another way in vertical terms two types of psychological integration are required (that are ultimately fully complementary).
Thus from the transcendent aspect the emphasis is on top-down integration i.e. where one attempts to integrate the understanding of "lower" from the perspective of the "higher" levels..
However for proper balance an equal emphasis must be placed on bottom-up integration, where one attempts in reverse fashion to integrate all "higher"from the perspective of the "lower" levels (whose nature becomes increasingly enhanced through continual re-visitation).
Indeed this distinction is crucially important for true appreciation of the nature of the Zeta 1 and Zeta 2 zeros respectively (in the context of the Riemann Hypothesis).
In fact, quite remarkably, the true nature of these zeros relates to the manner in which both top-down and bottom-up integration (of a holistic unconscious nature) is attained throughout development.
Now we all accept in conventional scientific terms the quantitative importance of 4 dimensions (with our macro world seemingly structured in this manner).
However an equal (though largely unrecognised) importance attaches to 4 dimensions from a qualitative perspective (with again everyday reality seemingly structured in this fashion).
These the 4 qualitative dimensions correspond indirectly (in a reduced quantitative manner) with the four roots of 1 i.e. + 1, − 1, + i and − i respectively.
Now we have already dealt with the significance of the two real (horizontal) roots in the context of 2-dimensional interpretation. Again, in dynamic relative terms, these refer to the interaction of external (objective) and internal (subjective) polarities (which necessary underlie all experience).
As we have seen, these horizontal polarities are integrated with each other (to a substantial degree) during Level 1 (Band 3).
So now the focus in development largely switches at Level 2 to the corresponding integration of these vertical (i.e. imaginary) polarities.
I have frequently stated that in holistic mathematical terms, the imaginary notion i, represents the indirect linear rational expression of meaning that is properly of a qualitative holistic nature. Put another way it is the indirect conscious expression of unconscious meaning.
In experience therefore, the unconscious can only indirectly express itself through projections that are attached to conscious symbols. So correct interpretation requires seeing such symbols as but the indirect expression of a more universal holistic meaning.
Actually, all of this relates to the fundamental relationship between wholes and parts in experience.
Properly understood, in dynamic interactive terms, the relationship as between whole and part (and part and whole) is quantitative as to qualitative (and qualitative as to quantitative) respectively.
However in 1-dimensional terms (which defines Conventional Mathematics) a reduced quantitative interpretation is given, whereby in any context the whole is understood as the sum of its quantitative parts (both of which are interpreted in a real conscious fashion).
Now this equates in psychological terms with a merely rational interpretation of relationships.
But again actual experience is dynamically interactive in nature entailing both rational (quantitative) and intuitive (qualitative) elements.
Therefore, from a proper dynamic perspective, the collection of parts (in a quantitative manner) reflect the whole (which is understood in a - relatively - qualitative manner).
Likewise each part (in an individual quantitative manner) reflects the whole (again understood - relatively - in a qualitative manner).
From a Jungian psychological perspective these would both reflect symbols that are understood as mediating archetypes of a universal nature.
Thus in the former case, generalised symbols would be serving as archetypes; in the later case it would be individual symbols of a local nature that would reflect these archetypes.
It is here where the spiritual contemplative traditions can provide additional assistance.
When the collective whole becomes the reflection of universal meaning, this is referred to as the transcendent aspect of spirituality; then, in relative terms, when individual localised part symbols serve as the reflection of universal meaning this is now referred to in a complementary manner as the corresponding immanent aspect of spirituality.
So the transcendent (whole) and immanent (part) aspects of spirituality are once again truly complementary.
Therefore from this perspective, when collective symbols serve as the mediator of spiritual (unconscious) meaning we can refer to them as imaginary (in a positive manner).
Then when one attempts in reverse fashion to switch to corresponding appreciation of individual symbols likewise serving as mediators of spiritual meaning we must first negate the earlier imaginary understanding.
In this way we can see that the transcendent and immanent appreciation of the qualitative nature of phenomenal symbols in mathematical terms corresponds with the two imaginary roots (of the 4 roots of 1) as + i and − i respectively.
The main practical problem that is now experienced however is that up to this point an unduly transcendent emphasis will have characterised spiritual development.
This means in effect that whereas one may find it relatively easy to see "higher" collective universal phenomena serving as appropriate "imaginary" archetypes of spirit, it may for a long time be much more difficult to accept "lower" instinctive phenomena (such as erotic fantasies) as likewise serving as appropriate symbols of spiritual meaning.
In other words in most religious traditions, an undue emphasis is placed on the "higher" transcendent aspect of spirituality. This then can lead to considerable problems in fully accepting the "lower" physical aspect of human experience. However, until this is properly achieved, the immanent aspect cannot be properly integrated with the corresponding transcendent aspect of spirituality.
Put another way in vertical terms two types of psychological integration are required (that are ultimately fully complementary).
Thus from the transcendent aspect the emphasis is on top-down integration i.e. where one attempts to integrate the understanding of "lower" from the perspective of the "higher" levels..
However for proper balance an equal emphasis must be placed on bottom-up integration, where one attempts in reverse fashion to integrate all "higher"from the perspective of the "lower" levels (whose nature becomes increasingly enhanced through continual re-visitation).
Indeed this distinction is crucially important for true appreciation of the nature of the Zeta 1 and Zeta 2 zeros respectively (in the context of the Riemann Hypothesis).
In fact, quite remarkably, the true nature of these zeros relates to the manner in which both top-down and bottom-up integration (of a holistic unconscious nature) is attained throughout development.
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