Spectrum of Development

As we have seen, with the linear (analytic) interpretation of number, the ordinal notion is effectively reduced in cardinal terms. Therefore we must move to a circular (holistic) interpretation, so that the ordinal aspect - while necessarily existing in relationship to the cardinal - yet preserves its own distinct identity. When one reflects on it, the ordinal notion can only have meaning with respect to a group of numbers that are defined in a cardinal manner. So for example one can validly seek to interpret the ordinal notions of 1st and 2nd (in the context of 2), the ordinal notions of 1st, 2nd and 3rd (in the context of 3), the ordinal notions of 1st, 2nd, 3rd and 4th (in the context of 4), the ordinal notions of 1st, 2nd, 3rd, 4th and 5th (in the context of 5) and so on. So again to illustrate, if we have a class of 20 pupils (in cardinal terms), then we can provide ordinal rankings in an examination for 1st, 2nd, 3rd, .....20th positions. What is fascinating here is tha...

To recap again briefly, during the 3 levels that characterise Band 3 (in my map of development), I had come to realise the extraordinary potential importance of the holistic dimensional notion of number (according to its Type 2 aspect). Through this holistic mathematical interpretation of number, I could see how the dynamic interactive nature of experience is implicitly structured in mathematical terms, with each holistic dimension relating to a unique configuration with respect to the fundamental polarities of experience (internal/external, whole/part and form/emptiness).  Indeed as the 3rd polarity set here represents but a special requirement with respect to the first two sets, this entails that phenomenal reality (in physical and psychological terms) is fundamentally conditioned by the dynamic interaction of just two sets of polarities (i.e. internal/external and whole/part). In psycho spiritual terms the "higher" dimensions (> 1) represent increasingly refined int...

Before proceeding further, I will once again attempt to make clear the distinction that I make as between the two notions of number - in effect particle and wave aspects - that continually interact in experience as analytic to holistic (and holistic to analytic) respectively. I define firstly the Type 1 aspect (where the number in question is referred to as the base). So every base number here is defined with respect to a default dimensional number of 1. Thus 2, for example in Type 1 terms is defined as 2 1 . I then define the Type 2 aspect (where the number in question is referred to as the dimensional number). Every dimensional number here is now defined, in inverse fashion with respect to a default dimensional base of 1. Thus 2 now in Type 2 terms is defined as 1 2 . Now it is vital to appreciate these two aspects of the number system operate in a dynamic relative fashion as complementary, where they keep switching (both in base and dimensional terms) as between analyt...

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 notio...

I would like to convey here the true significance of the Riemann Hypothesis. However it is vital to appreciate from the outset that this significance cannot be properly understood within the accepted confines of Conventional Mathematics, which solely recognises, in formal terms, the quantitative (analytic) interpretation of its symbols. Indeed from one important perspective, the Riemann Hypothesis - when adequately interpreted - points directly to a critical limitation in the overall accepted framework of Mathematics.   The number system is fundamental to the reality we call Mathematics. And what in turn is central to the number system is the relationship between the primes and the natural numbers. Now a prime has no factors (other than itself and 1). So 7 for example is an early example of a prime. All other natural numbers (i.e. composites) can then be uniquely expressed as the product of primes. So for example 30 ( = 2 * 3 * 5) is therefore composed of 3 prim...

We return now to a personal account of the journey through the 3 main levels of Band 5. Once again these bear a complementary relationship (on the spiritual descent) to the same three levels (on the spiritual ascent). However whereas as the direction on the ascent is primarily of a transcendent nature, where nondual spiritual development is - to a considerable extent - at the expense of customary dualistic understanding, here a reverse immanent emphasis applies, where one now gradually attempts to incorporate the dual in a balanced manner with the nondual. And once again, these 3 levels (of Band 5) are characterised by a special emphasis on each of the corresponding key polarity sets. And just as with Band 3 the journey initially commences at Level 1 with intense exposure to the (horizontal) interaction of external and internal polarities, equally it is similar at Band 5. However whereas at Band 3, this largely represents the gradual breakdown of rational a...