I have spoken many times before how Band 3 development, in my experience, was characterised by a keen realisation of the holistic mathematical nature of number (as relating directly to dimensions).
Now Band 2 - on which conventional scientific notions are firmly based is strictly 1-dimensional in this qualitative sense. This entails the absolute separation - in formal terms - of the key polarities of experience i.e. external/internal, whole/part and form/emptiness respectively, so that in any context involving these polarities, interpretation takes place with respect to just one fixed pole.
So conventional mathematical and scientific interpretation is based on the attempt to abstract objective (external) reality from mental (internal) interpretation. Likewise it is based on a mere quantitative relationship as between whole and parts (whereby the whole is viewed in reduced terms as the sum of its parts). Finally it is based on the consideration of phenomenal notions of material form in separation from empty (formless) spiritual notions.
So all in all, 1-dimensional interpretation is based on the reduction of qualitative to mere quantitative notions.
Holistic mathematical understanding of number (as dimension) can only be properly realised when the 3 key polarity sets (already mentioned) are viewed in a dynamic interactive experiential fashion.
In holistic mathematical terms, I had associated the number "2" with Level 1 (Band 3). Here experience is mainly concentrated on the two-way interplay of the horizontal polarities (external and internal).
One therefore now understands all relationships as comprising the complementary interaction of external and internal polarities that are - relatively - positive and negative with respect to each other. This holistic intuitive appreciation of complementary positive and negative poles (+ 1 and – 1 respectively) as interdependent thereby parallels the corresponding analytic interpretation of the reduced linear nature of "2" as representing dimensions, where the two roots of 1 (.+ 1 and – 1) are considered in either/or terms as independent.
I then later holistically associated the number "4" with Level 2 (Band 3) where experience is now additionally concentrated on the two-way interplay of the vertical polarities. Here, whole and part retain their uniqueness through two "imaginary" poles (that are indirectly expressive of the holistic intuitive nature of the unconscious).
Thus the proper mediation of whole and part aspects in experience i.e. without undue reductionism, entails the refined mediation of the intuitive unconscious - in an indirect conscious manner - as imaginary.
So the dynamic interaction of both conscious and unconscious in experience is now expressed through the holistic dimensional appreciation of the number "4", where both real and imaginary polarities - that are relatively quantitative and qualitative with respect to each other - are considered as dynamically interdependent (in positive and negative terms). This in turn parallels the reduced analytic nature of 4 as a dimensional power (given by the 4 roots of 1).
Finally the most refined interaction of polarities comes at Level 3 (Band 3) with 8-dimensional holistic understanding, which entails the closest approach in experience to the simultaneous identity of form and emptiness.
This basically requires the ability to preserve both real and imaginary polarities in an extremely close balance (in the ultimate identity of both conscious and unconscious). Again this is paralleled in reduced analytic terms by the 8 roots of 1.
Though I have concentrated here on the holistic significance of 2, 4 and 8 respectively, the remarkable finding of Band 3 understanding is that every number has an important holistic dimensional significance, whereby its true qualitative significance is expressed.
Basically this entails that associated with each number (in holistic terms) is a unique means of configuring the dynamic relationship as between the 3 central polarity pairings, which necessarily underlie all phenomenal relationships.
Also in this regard, I came to understand that a significant distinction applies as between even and odd numbers, which has a parallel significance with respect to the Riemann zeta function (to which the Riemann Hypothesis applies).
Basically the even numbers are associated with "passive" (contemplative) states of experience where a dynamic equilibrium representing the balancing of complementary opposites applies. This again parallels the analytic situation, where one obtains an even number of roots with respect to a number.
However the odd numbers are associated with more "active" (asymmetrical) states, where one remains temporarily in a disequilibrium position from a psychological perspective. However the resolution of this problem then leads to the seeking of "higher" equilibrium states (that quickly give way in turn to further temporary states of disequilibrium).
However the problem with my Band 3 development was that experience was mainly geared to transcendent type development.
Though I was initially reluctant to accept this, it coincided with an unbalanced emphasis on specialisation of the even dimensions (especially 2, 4 and 8).
In other words I was placing too much attention in the ascent, with respect to "higher" contemplative states without sufficient emphasis on counterbalancing outward activity. So the odd numbered dimensions - including all the primes other than 2 - were effectively becoming bypassed to a considerable extent in the process. And remarkably this implied equally in psychological terms that the deeper instinctive primitive levels of the psyche were being avoided.
This in turn coincided with the significant bypassing of the linear levels of Band 2 through the attempted integration of the "higher" levels of Band 3 with the "lower" levels of Band 1.
So as the descent through the levels of Band 5 gradually ensued, this led to a significant new perspective on the holistic mathematical notion of number, which equally provided a remarkable manner of uncovering the most primitive areas of psychic development.