We have briefly defined the 3 Types of Mathematics - Type 1, Type 2 and Type 3 respectively.
In terms of my own treatment of the full Spectrum of Development, Type 1 is associated with the first two Bands (i.e. Lower and Middle) with specialised understanding associated with the Middle Band.
Not surprisingly as development in Western culture largely plateaus at the 2nd level, what is understood as Mathematics has become synonymous with Middle Band understanding. However correctly understood this in fact is Type 1 Mathematics (geared to quantitative appreciation of symbols).
Type 2 Mathematics is then correctly associated with both the 3rd and 4th Bands (i.e. Higher and Upper Middle) with specialised appreciation related to the 4th Band.
Though the development of these Bands is generally associated with the contemplative mystical traditions and has been well articulated from a spiritual religious perspective. However the great potential importance of the refined cognitive structures associated with such development for both Mathematics and Science has been greatly overlooked. So a key motivation for my own writing has been to outline the nature of these increasingly circular type structures and then sketch out their qualitative integral scientific significance.
Finally Type 3 Mathematics is associated with the 5th, 6th and 7th Bands (i.e. Radial).
For both Type 3 (a) and Type 3 (b) such understanding would properly unfold with the 5th and 6th Radial Bands (with specialised appreciation in each case related to the 6th Band).
Full specialised appreciation of Type 3 (c) Mathematics - which offers the greatest scope for the mature balanced interpenetration of both its quantitative and qualitative aspects - would then unfold with the 7th Band.
Mathematics of course provides an indispensable tool for scientific understanding.
So matching the 3 Types of mathematical we equally have 3 corresponding Types of scientific understanding.
Once again Type I relates to conventional quantitative notions of science. Once again in our culture Science is misleadingly identified with mere Type 1 appreciation.
Type 2 relates to qualitative notions in - what I refer to as - Integral Science.
Type 3 then relates to a more comprehensive form of scientific understanding where the mature interpenetration of both quantitative and qualitative aspects takes place.
Type 3 (a) entails a mainly quantitative analytic emphasis that is however appropriately informed with corresponding qualitative notions.
Type 3 (b) entails by contrast a mainly qualitative holistic emphasis that is appropriately informed with corresponding quantitative notions.
Type 3 (c) entails the most balanced mix of both quantitative and qualitative appreciation enabling greatest scope for scientific work that is both highly creative in vision and immensely productive of results.
My own mathematical and scientific contributions are mainly designed to be of the Type 2 variety (as these in practice are largely unrecognised and greatly misunderstood).