The Integral Theory of Everything is based on finding a holistic mathematical acceptable manner of interpreting the dynamic relationship as between the 3 fundamental polarities (that underlie all experience of reality).
Once again these polarities relate to (i) the distinction as between internal and external within a given stage of development (horizontal polarities); (ii) the distinction as between whole and part between different stages of development (vertical polarities); (iii) the ultimate distinction as between form and emptiness both within and between different stages of development (diagonal polarities).
I identify 4 stages of integration corresponding with the qualitative interpretation of 1, 2, 4 and 8 dimensions respectively (relating in turn to the 0th, 1st, 2nd and 3rd powers of 2).
The standard conventional scientific approach - based on linear rational understanding - corresponds with the 1st dimension (Integral 0 approach).
Basically such an approach - which is based on clear separation of the opposite polarities in experience - does nor allow for corresponding complementary understanding. Therefore it necessarily deals with the key polar interactions through a form of reductionism. Thus typically in conventional science, the internal aspect is reduced in terms of the external; the whole in any context is reduced in terms of the part; finally emptiness is reduced in terms of form.
The first truly integral approach (Integral 1) allows for the dynamic complementarity of both internal and external through - what qualitatively represents - 2-dimensional understanding.
Here internal and external (conscious) phenomena are considered in holistic mathematical terms as both positive and negative with respect to each other in real terms. However the Integral 1 approach does not yet allow for appropriate interpretation of the relationship as between whole and part and form and emptiness.
The second approach (Integral 2) allows for additional dynamic complementarity as between whole and part (which are now qualitatively distinguished from each other). In holistic mathematical terms this corresponds with 4-dimensional understanding. Here both real and imaginary distinctions are made with both positive and negative directions. So in any context, if for example the "part" is designated as real (in conscious terms) then relatively the "whole" is designated as imaginary (i.e. pertaining to unconscious meaning).
So the Integral 2 approach allows fully for the necessary interaction of conscious and unconscious in experience; in physical terms this corresponds with the interaction of discrete phenomena with an underlying holistic ground (or field) of matter.
The third approach (Integral 3) then allows for further dynamic complementarity as between form and emptiness which in holistic mathematical terms corresponds with 8-dimensional understanding.
Such understanding is based on the four complex roots (of the 8 roots of 1) where both real and imaginary aspects are equal. The fascinating point here is that these equally constitute null lines (with no magnitude). So in corresponding qualitative terms, these allow for the ultimate unification of form and emptiness (with the complex relating to form and the null designation to emptiness respectively).
In psychological terms this would entail that the interaction as between real (conscious) and imaginary (unconscious) would now be - literally - so equal or harmonious that phenomena (of form) would not even appear to arise in experience this facilitating union with emptiness.