I mentioned in yesterday's entry that the "multiple intelligences", as outlined by Gardner do not necessarily develop through the entire spectrum. Most do, but not necessarily all!

One especially interesting case here relates to logico-mathematical ability.

As conventionally understood, this attains full development through specialised rational structures that are associated with Band 2 (in my model of the spectrum). And this equates directly with linear (i.e.1-dimensional) interpretation. What this simply entails is that the fundamental polar opposites, which dynamically condition all phenomenal reality, are separated in an absolute manner.

Chiefly this entails the absolute separation of external and internal and whole and part polarities with quantitative and qualitative poles, which in dynamic experiential terms are necessarily complementary with one another.

Thus with linear rational understanding, interpretation - in every context - takes place with respect to just one isolated pole of reference.

So for example, typically in Mathematics, objective truth is considered in absolute isolation from subjective considerations. Equally, this truth is considered in merely quantitative terms (where the qualitative aspect in effect is completely ignored). This in effect leads to a basic form of reductionism, where the whole is reduced to its constituent parts. This is therefore associated with the analytic aspect of mathematical interpretation.

However, what is not at all properly recognised is that further development - entailing utterly distinctive multi-dimensional forms of "circular" paradoxical understanding - can unfold at the "higher" more intuitively inspired contemplative levels of understanding.

The simplest example is 2-dimensional,where both the external pole (as objective truth) and the internal pole (as mental interpretation) are considered in a bi-directional relative manner.

This leads to the direct unfolding of the qualitative aspect in what corresponds to the holistic aspect of mathematical interpretation.

And such holistic understanding reaches its specialised development at Band 4 of the spectrum. This is dependent on a highly refined type of intuitive state that is then combined with dynamic paradoxical structures of a relative "circular" kind.

From a psychological perspective, the analytic aspect (of quantitative understanding) relates directly to the conscious interpretation of mathematical symbols. However the holistic aspect, relates by contrast, directly to unconscious appreciation, now brought fully into the conscious light, where it can be given a refined phenomenal expression.

So the startling realisation now dawns that all mathematical symbols can be given dual analytic and holistic interpretations (of equal importance).

However initially both the analytic and holistic interpretations unfold in a somewhat separate manner.

So the final stage of development entails the gradual merging of both types of meaning in - what I refer to as - the radial aspect of mathematics. So this form of understanding entails the mature interpenetration of both conscious and unconscious aspects of appreciation.

And this would reach its specialised development at Band 6 (of the spectrum).

However even though logico-mathematical ability can be rightly extended in entirely new forms of appreciation to embrace the entire spectrum of development, it is not it itself necessary for full integrated development to take place.

So cognitive development can indeed unfold at all levels without necessarily being tied specifically to mathematical type ability.

Therefore I would accept that certain enlightened sages and spiritual leaders have indeed managed to attain to the most advanced levels of realisation (Bands 6 and 7) without displaying explicit recognition of their associated mathematical structures. However having said this, such logical structures would necessarily have been implicitly required in their actual experience!

With respect to the other "multiple intelligence, it would be meaningful, I believe, to accept that the entire spectrum of stage development potentially applies to interpersonal, intrapersonal and in a somewhat modified sense, linguistic and visual-spatial categories.

I would find it more difficult to apply all stages to musical and - especially - bodily-kinisthetic intelligence.

However, I certainly would see all stages as potentially applying to the "additional" intelligences" i.e. naturalistic, spiritual existential and moral.

However the central point remains that these essentially comprise "secondary modes" that already entail a certain unique configuration with respect to the primary "colours", as it were, represented by cognitive, affective and volitional modes.

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