Integral Science

I have found the odd numbered dimensions more difficult to understand than the even. As we have seen the even are more properly geared for holistic integral interpretation of reality and as my main concern over the years has been to articulate such an approach in appropriate mathematical terms, it is not surprising therefore that the even dimensions held more resonance for me. The clue to understanding however of the higher odd dimension (focusing initially on the positive) is the realisation that human development necessarily entails both differentiation and integration which need to be maintained in healthy balance. So even for one committed to the process of growing in pure contemplative awareness, a certain level of activity at each stage must be maintained. Thus for example when one returns to active involvement (following the development of the more passive even numbered dimension), the next odd numbered dimension will then unfold. Thus arriving at the first of ...

We have looked at the positive even numbered dimensions. These are the most suited for pure integral interpretation of reality and are always based on the matching complementarity of opposites. Within the even numbered dimensions 2, 4 and 8 would command a special importance (as suited for integral interpretation of reality). However so far we have only considered the positive numbered even dimensions! So our next task is to give a meaning to the corresponding negative numbers. I have mentioned the philosopher Hegel as proving initially inspirational in terms of formulating the holistic mathematical meaning of 2-dimensional understanding. However I gradually became disenchanted with Hegel's approach. It seemed to me that that he was led into a fundamental error in elevating the mere formal rational interpretation of his logic above the very spiritual intuition that it really illustrated. In other words though one can formulate in rational terms the basic principle that all ...

As one may perhaps appreciate, the qualitative use of numbers (as dimensions) plays a key role in holistic mathematical understanding. So I have spent at this stage more than 40 years in the slow - and often painful - task of unravelling the hidden meaning contained in all numbers (as dimensions). In the attempt here to explain my present position, I will relate how this understanding actually unfolded in development. The first key insight was in recognition of the linear nature of the rational paradigm which underpins interpretation of both mathematics and science. So in qualitative terms, such understanding is defined in holistic mathematical terms by the number 1 (i.e. 1-dimensional interpretation). As we have seen this entails in Conventional Mathematics that all number quantities are ultimately defined in terms of a (default) power of 1. For example 2 ^ 2 = 4 (i.e. 4 ^ 1). In physics it implies for example that object phenomena are unambiguously posited in just one (external) dire...

I have already contributed a number of posts to this personal blog on the subject of String Theory. Though most of the unease within the conventional physics community relates to the difficulties in empirically testing String Theory (for some considerable time to come) I have been concerned with a deeper problem! For in terms of offering a coherent philosophical view of the nature of physical reality the present position is utterly impoverished. Now this failure to properly recognise a key weakness, relates to the traditional bias of science i.e. that is geared merely to quantitative analysis - rather than qualitative synthesis - of reality. Though it is certainly possible that ingenious ways of an indirect nature may be found to remedy the empirical testing deficit, little hope however exists of offering any coherent explanation as to what the theory is supposed to represent. Now scientists may immediately retort that they are not in the business of qualitative (i.e. philosophical) sp...

In the last post I addressed the fact that corresponding to each number in Holistic Mathematics is a unique scientific interpretation of reality. So the range of possible interpretations is infinite with Conventional Science based on just one of these numbers (i.e. 1). This I believe is a truly remarkable finding - which if even remotely grasped - should end all notions of science having reached its zenith! Indeed we can make further remarkable statements based on holistic mathematical interpretation. For not alone does every number possess a unique qualitative dimensional significance (as indicated) but equally every symbol and relationship - with an already established significance in Standard Mathematics - can likewise be given a unique holistic mathematical explanation with intimate relevance for psychological interpretation of reality. And those theories and hypotheses that already have been shown to have a special importance in standard quantitative terms would possess an...

Just as the standard analytic approach to science is ably served by its corresponding mathematical tool i.e. Conventional Mathematics, likewise the (qualitative) integral approach to science is likewise potentially served by its own respective mathematical tool i.e. Holistic Mathematics. A great barrier however that I have continually faced is the recognition that Holistic Mathematics - though using the same symbols - is radically different from what most people understand as Mathematics. So what certainly is not intended here is the standard use of Mathematics to deal with holistic type problems (which represents the old reductionist approach)! Rather it requires a new interpretation of mathematical symbols that inherently depends on corresponding appropriate level of intuitive insight for correct usage. To put this in context, one must appreciate that just as there are many bands on the electromagnetic spectrum (with natural light comprising just one), likewise it is true with respec...

I have been reading again "The End of Science" by John Horgan which I find interesting on several levels. Firstly, whether one agrees or not with its conclusion it puts forward a most provocative hypothesis i.e. that the great era of theoretical scientific discovery is at an end with diminishing returns with respect to further development now to be expected. Secondly it attempts to cover a wide range of different scientific fields conveying in the process some flavour of the rich developments that have already taken place. Finally - and most notably - Horgan managed to do an impressive amount of research in interviewing a significant number of the biggest names associated with these fields (at least at the time of writing in the mid 90's). What I like most about his approach is a certain innate scepticism which prevents him from ever appearing unduly awestruck with their strongly held beliefs. My own approach would be somewhat different to Horgan's and more ...

As we have seen science is based directly on the cognitive mode of reason. More specifically - as conventionally understood - it is based almost exclusively on the use of linear reason. This requires standard either/or logic where opposite polarities can be clearly distinguished. So for example this assumes that "objective" can be clearly abstracted from its opposite subjective pole, that parts in any relevant context are distinct from wholes and - perhaps crucially - that phenomena of form can be distinguished from the emptiness (in material terms) of spiritual reality. So the focus of science is to gain knowledge of reality in an impersonal detached manner. Though the affective and volitional faculties are likewise necessarily involved in experiential terms, their use is of a supporting indirect nature. For example even in the most abstract forms of mathematics, use must necessarily be made of symbols (that can only be verified at a sensible level). Also the very pursui...

In terms of successful psychological development we can identify - for convenience - three key personality functions in need of integration. These are 1) the cognitive function related to the pursuit of knowledge and order; 2) the affective function related to love and beauty and finally 2) the (primary) volitional function related to motivation and fulfilment. Corresponding to these functions are the three great domains of science, art and religion respectively. Therefore for successful integration in society, ultimately science, art and religion must be reconciled. However a great limitation at present is the manner in which science and religion especially - as presently understood - seem in many ways to be mutually in conflict with each other. As I have always been greatly interested in both domains, a key issue for me has related to attaining their mutual compatibility. Basically I would see that such compatibility requires two major revolutions with respect to curren...