In geometrical terms complementary opposites relate to both ends of a straight line diameter drawn through the centre of a circle (with an angle of 180 degrees at this centre).
Therefore we can speak of complementary opposites in terms of horizontal, vertical and diagonal polarities (where opposite poles are related to each other).
As we have seen in this context when we posit one pole i.e. give it a positive sign (+) the opposite pole is thereby - in relative terms of negative sign (-).
In dynamic holistic mathematical terms, the horizontal poles (exterior and interior) comprise complementary "real" opposites of form (+ 1 and - 1) which are relatively positive and negative with respect to each other.
The vertical poles (whole and part) comprise complementary "imaginary" opposites
of form (+ i and - i) which are again positive and negative with respect to each other.
Finally the diagonal poles (fundamental form and emptiness) comprise a double set of complementary "complex" opposites k(+ 1 + i) and k(- 1 - i); also k(- 1 + i) and k(+ 1 - i) which are once more positive and negative with respect to each other. (k = 1/square root of 2).
These diagonal poles also have an alternative "empty" interpretation as null lines = 0, indicating - at this level of understanding - that form is dynamically identical with emptiness (and emptiness with form).
However it is course possible to relate these polarities with each other (where bi-directional linear complementarity no longer strictly exists).
In analytic geometrical terms, the relationship between horizontal and vertical (and vertical and horizontal) line diameters is 90 degrees (i.e. half of 180).
Likewise in holistic mathematical terms, the dynamic relationship between horizontal and vertical polarities (and vertical and horizontal) is exactly half that of the bi-directional linear polarities (i.e. opposite horizontal or opposite vertical or opposite diagonal poles respectively).
Now if we refer to the overall dynamic relationship between poles (comprising horizontal, vertical and diagonal) in various combinations as holistic mathematical "spin" then the "spin" as between horizontal and vertical (and vertical and horizontal) when combined is exactly half their spin (when considered separately in relation to each other).
Furthermore in analytic geometrical terms, the relationship between diagonal and either the horizontal or vertical lines (and either the horizontal or vertical lines with the diagonal) at 45 degrees is exactly quarter that of the bi-directional straight line diameters (180 degrees).
Likewise in holistic mathematical terms, the dynamic relationship as between diagonal and either horizontal or vertical polarities (and either horizontal or vertical and diagonal) is exactly quarter that of the bi-directional linear polarities.
Thus if we arbitrarily assign the number 2 as the holistic mathematical "spin" of the bi-directional linear polarities (e.g. positive and negative horizontal) then the corresponding dynamic relationship as between horizontal and vertical (and vertical and horizontal) will be of "spin" = 1.
Furthermore the spin of the diagonal poles with either the horizontal or vertical (or the horizontal or vertical with the diagonal) will be of "spin" = 1/2.
Well a remarkably similar notion applies in quantum mechanics (where it is given a more analytic asymmetric interpretation).
Spin in this context refers to the pattern of rotation of sub-atomic particles.
All matter particles (and anti-matter equivalents) such as the electron have spin -1/2 (i.e. where the value = 1/2).
Also the non-gravitational particles of force carriers (such as photons and gluons) have spin -1
(i.e. where the value = 1).
Finally the hypothesised spin of the gravitational force has spin -2 (i.e. where the value = 2).
Now the values here follow a complementary pattern to holistic mathematical "spin".
Where matter particles have the "lowest" spin in quantum mathematical terms -1/2, material poles (i.e. "real" opposites) have the "highest" corresponding "spin" in holistic mathematical terms = 2.
Likewise whereas the force carrier particles of gravity have the "highest" quantum mechanical spin -2, the corresponding relationship as between diagonal (force carriers) and either horizontal (material) or vertical (dimensional) reality has the lowest holistic mathematical "spin" = 1/2.
The problem with analytic interpretations is that reductionism inevitably is involved (as with all asymmetrical type understanding).
We have seen this already in relation to object phenomena and dimensions.
In conventional analytic terms object holons are always to a degree reduced to their corresponding dimensions.
Therefore with a three-dimensional object such as a box the material object is defined in terms of its dimensional (space) characteristics (both in quantitative terms).
In other words in conventional science, though the dynamic relationships connecting phenomena always entail structures in relation to states (and states in relation to structures) both are reduced in terms of each other.
Thus the dynamic structure-state of the relationship of a phenomenon with its dimension and the dimension with its phenomenon (which are quantitative and qualitative with respect to each other) are collapsed with in either exclusively quantitative (empirical) or qualitative (theoretical) terms.
This leads in turn to the conventional asymmetrical interpretation of dimensions (3 space and 1 time).
The same problem then carries over into the understanding of forces (which again are approached in unduly empirical quantitative terms).
So just as the 3 space dimensions are appropriated in quantitative terms, in similar terms likewise with 3 of the 4 forces. So traditionally in physics the fourth force of gravity has remained separate from the other three (resisting integration) just as formerly the time dimension remained largely separated from space.
Now from an integral perspective the relationship between objects and dimensions (and dimensions and objects) is fully symmetrical. Likewise the relationship between the forces (and their corresponding relationship to both objects and dimensions) is fully symmetrical.
And the holistic mathematical Theory of Everything can precisely demonstrate the nature of these relationships in dynamic terms (as we have already shown in previous Chapters).
Of course in phenomenal terms these relationships will not appear symmetric and analytic science must necessarily deal with such phenomenal appearances.
However there is an essential relationship as between analytic and holistic interpretations, which is greatly missing from current understanding.
This is obvious in modern physics where exciting theoretical findings (as with String theory) are not backed with corresponding intuitive insight.
So I have been at pains here to explain a properly integral appreciation of the concept of "spin" (based directly on holistic mathematical appreciation of the TOE). It fundamentally arises - as I have demonstrated - from the dynamic interaction of opposite complementary poles, which are horizontal, vertical and diagonal with respect to each other.
In integral terms these are understood in relationship to each other. So "spin" always refers to the nature of a dynamic relationship connecting matter (structures), dimensions (states) and forces (embracing all).
Equally "spin" can be given a complementary interpretation relating directly to the Self and our psychological appreciation of the fundamental interactions governing material phenomena (structures) qualitative dimensions (states) and spiritual "forces" (volitional motivation).
And again it is this very appreciation of this deep complementarity relating to the Self and Reality that greatly facilitates the process of integration.
In asymmetric terms these fundamental integral dynamics become distorted with spin apparently relating solely to physical matter, dimensions and forces (considered separately).