In Conventional Mathematics both real and imaginary numbers are used with respect to their (merely) quantitative interpretation.
However the key starting point of Holistic Mathematics is the realisation that every mathematical symbol can also be given a corresponding qualitative meaning.
The limitation therefore of Conventional Mathematics is that it is confined in qualitative terms to merely real understanding (corresponding to default one-dimensional interpretation).
The role of Holistic Mathematics is to provide corresponding imaginary interpretation in qualitative terms.
Whereas real interpretation corresponds directly with conscious, imaginary interpretation - by contrast - corresponds directly with unconscious understanding. Once again the real aspect relates to linear logic (where opposite polarities in experience are clearly separated) whereas the imaginary aspect relates in turn to circular logic (where such opposite polarities are treated as complementary).
Thus when we separate two polarities (to concentrate on one as independent) we have linear understanding; however when we combine these two polarities as complementary (to concentrate on both as interdependent) we have (two-dimensional) circular understanding. Though in direct terms such circular appreciation is of an intuitive nature, indirectly it can be given a reduced (linear) rational expression (corresponding to the qualitative square root of interdependent unitary form). And this is imaginary understanding.
So in this way the qualitative nature of imaginary understanding corresponds closely with its quantitative counterpart.
In like manner whereas Conventional Science provides the real aspect of understanding , Holistic (i.e. Integral) Science provides the corresponding imaginary component.
So - from a qualitative holistic mathematical perspective - in these contributions on Integral Physics, I am attempting to provide the vital imaginary aspect of qualitative understanding (that is ignored entirely in the conventional scientific approach).
Such an approach requires that one establishes - for example in any physical context - a complementary psychological interpretation. Through realising such complementarity in experience, one can intuitively unite both aspects (in a true contemplative manner).
Thus if we go back to the previous contribution, it deals with the complementarity - in qualitative terms - of both the physical notion of the "black hole" and the corresponding psycho spiritual notion of the "dark night". Now it is important to stress that such a relationship cannot be - literally - seen without adopting a distinctive type of understanding (that is not provided through conventional scientific appreciation!)
From a true integral scientific perspective the ultimate goal of understanding is - not to attempt to know about reality but rather - to experientially become one with reality in an ineffable manner. So reality is truly utterly mysterious with any theoretical understanding - necessarily - of a limited and partial nature.
One advantage of the integral approach is the manner in which it enlarges one's philosophical perspective to clearly see that the quest for any final TOE (as with string theory) is futile. Of course exciting new discoveries can indeed be made in this way, and we should always rightly strive to know more; however the quest for any final (merely objective) reduced explanation of reality is not possible.
Of course a truly comprehensive approach to science would employ - in qualitative terms - a complex rational approach combining both real (analytic) and imaginary (holistic) understanding.
However once again in these contributions I am confining myself to the integral (i.e. imaginary) aspect which is so greatly neglected in present scientific understanding.