Friday, July 1, 2011

Three Types of Mathematics (3)

I have stated that psychological development in Western culture largely plateaus at the 2nd Band (Middle) which is associated with Type 1 Mathematics.

I have also stated that Type 2 and Type 3 Mathematics are associated with the intuitively refined rational structures that characterise the other 5 Bands on the Spectrum (with Type relating to Bands 3 and 4 and Type 3 to Bands 5, 6 and 7 respectively).

The question might be validly posed as to the relevance of Type 2 and Type 3 Mathematics for a culture that has not sufficiently attained development at the appropriate Bands required for such mathematical understanding.

However a more nuanced appreciation of the dynamic nature of development would indeed allow at least for limited appreciation at present of these latter two Types of Mathematics.

Though there is indeed a certain sense in which the stages of development unfold in a linear manner, of necessity a complementary type relationship also applies e.g. as between lower and higher stages. Thus some access to higher and indeed radial stages opens up through mastery of lower and middle levels. So in a dynamic interactive sense one necessarily has access to all Bands on the Spectrum. However mature access to each level requires a process of sustained exposure to each level through a process that largely occurs in a linear sequence.
Therefore though development in rational terms may indeed for most individuals largely plateau (in a specialised sense) at the 2nd Band, varying degrees of access might still remain to the higher numbered Bands thus providing some limited basis for appreciation of Type 2 and type 3 Mathematics.

Development in any case rarely takes place in an even balanced fashion. So once again it is certainly possible for one who in most respects operates at a Band 2 level of appreciation to attain significantly higher Band understanding with respect to some modes of understanding. Frequently for example higher attainment with respect to rational structures will unfold which then would provide the ready basis for an even deeper appreciation of Type 2 and Type 3 Mathematics.

Another argument which could be made is that as we have reached a stage of very rapid evolution with respect to technology (especially IT) that this will call forth the need very soon for dramatic shifts in consciousness so as to absorb the repercussions of such developments. And this could therefore lead to rapid evolution for many of at least some of the higher Bands on the Spectrum which again would facilitate Type 2 and Type 3 mathematical understanding.
In support of this last point I would specifically mention present key issues in both Mathematics and Physics that will require higher Type understanding.

Indeed most of my work in recent years has been geared to demonstrating this very fact!

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