Integral Science

I have for some time maintained that my scientific approach is designed as a - preliminary - Radial 1 account of reality. However, before we get carried away with this let's remind ourselves that Radial 1 is but the first of 9 radial levels! Using mathematical terminology, the Radial 1 level is based on the two fundamental digits 1 and 0 (when appreciated in a holistic sense). So the purpose of this approach is to clarify how all stages of development are basically configured in terms of the interaction of linear form (1) and circular emptiness (0) respectively. Though of course some level of duality is required even at this level it is confined to consideration of the three fundamental polarities internal/external), whole/part and form/emptiness that underlie all phenomenal processes (and which can be given a coherent holistic mathematical rationale). So the Radial 1 approach lies closest to the purely contemplative vision of reality translated rationally into its most universal s...

The number 137 has raised considerable interest. Its reciprocal (1/137) approx. is referred to as the fine structure constant in physics and is related to the probability of electrons (or other particles) emitting or absorbing particles. Much has been written regarding the "mystical" properties of this number. Indeed some years ago my attention was drawn to its significance through correspondence relating to Jungian archetypes. And just recently an interesting article by Giorgio Piacenza has been published on Frank Visser's Integral World web-site. Without wanting to claim too much for the "mystical significance" of this number, I would like to initially broaden the topic to highlight some important general properties of prime numbers (of which 137 is a specific example). From one perspective prime numbers can be viewed as the basic building blocks of the natural number system (which we literally view in a linear manner as stretched out on a strai...

I have already mentioned my Riemann Hypothesis article. The basic finding of this article led me to an even more fundamental conclusion than I had imagined. This conclusion can be summed up as follows. (i) All dynamic interactions entail two distinct logical processes that are linear (1) and circular (0) with respect to each other. Once again linear logic is of the standard either/or type based on the clear separation of polar opposites (such as objective and subjective in experience). Circular (both/and) logic by contrast is inherently of a dynamic nature based on the complementarity (and ultimate identity) of these same polar opposites.  (ii) The inherent nature of a prime number is based on the consistent interaction of these two processes  (iii) The Riemann Hypothesis is required to guarantee the consistent nature of this interaction. Thus the true nature of prime numbers is of a radial mathematical nature (i.e. entailing the twin dynamic interaction of these two logica...

Perhaps it will help to put my approach to integral science in better context by briefly discussing the range of possible stages that can unfold throughout human development. In my latest version there are 7 major bands - a band is defined as a general group of stages with the same basic structure - with three main levels within each band. Thus we have 21 main levels in all. Though all of these bands are open in some degree to all, very little specialised development takes place in Western culture beyond the first two bands. From a cognitive perspective, all of these bands are defined by the interaction of two distinct logical systems - the linear and circular - which form the basis in turn for the nature of science. The linear system can be described as the logic of form and is the appropriate basis for differentiated (i.e. analytic) interpretation of reality of a quantitative nature. The line is - literally - one dimensional and so likewise analytic science (which is currently ...

Just as standard i.e. conventional Mathematics provides the essential tool for analytic science (which we misleadingly define as "science") Holistic Mathematics provides the essential tool for a new form of integral science with a truly extraordinary potential for development. When properly understood in a more comprehensive manner, every (analytic) branch of science has its integral equivalent based on a truly holistic appreciation of symbols. So for example we can validly speak of Integral Physics and Integral Economics (just to give two examples with which I have been mainly concerned ). Though I had developed many general notions, with some important specific illustrations, concerning integral science, recently I returned to physics with a view to a more detailed investigation. So during the Summer I completed three main articles, which still require some minor revisions, with the promise of a fourth to come ( researched for, but not yet written). The first ar...

It is now some months since I completed the article A Deeper Significance: Resolving The Riemann Hypothesis . This is turn followed on more detailed work on the topic at my website on  Riemann Hypothesis. What I was attempting to do was indeed very ambitious i.e. resolving the Riemann Hypothesis. Now from one perspective it might seem absolutely presumptuous that an amateur with no special ability in - what is conventionally called - mathematics should even attempt to tackle such a problem. However through Holistic Mathematics - which I have been developing now for some 40 years - I was confident that I could approach the issue from an entirely new perspective. So in the end I indeed resolved the issue to my own satisfaction, with the Riemann Hypothesis in the context of this new perspective having a remarkably simple resolution. Just to briefly summarise my findings! The Riemann Hypothesis is true! however this cannot be proven (or disproven ) within the axioms of c...