Integral Science

It is important to distinguish linear and circular, in holistic mathematical terms, from real and imaginary (which in many ways are closely related). Initially, linear relates - in a scientific context - to understanding according to either/or logic. Here the crucial polar opposites, which condition all phenomenal experience of reality (internal/external, whole/part and form/emptiness) are clearly separated in interpretation. This then enables rational linkages to be made in an unambiguous sequential fashion. So Conventional Science is characterised by linear (1-dimensional) interpretation. Such linear understanding is directly posited in a real manner. To posit in this dynamic context (which entails the holistic meaning of +) simply means to make conscious. Real in a holistic mathematical context means understanding that is of a direct conscious nature. So Conventional Science is linear, corresponding to real rational interpretation in a positive manner. However in dynamic experientia...

I will comment here on one more interesting connection that I can make as between the analytical findings of string theory and my parallel findings in holistic terms. As the energy of a string increases, its vibration intensifies. However this process does not continue indefinitely. Beyond a certain point additional energy with respect to the string may lead - rather than a further increase in vibration - to the lenghtening of the string. And theoretically its length can then continue without limit! Now there is a fascinating possible holistic counterpart which had puzzled me for many years. Once again, this can initially be expressed with respect to psychological development. However - as always - because physical and psychological reality are complementary, it has - I believe - an intimate bearing on the holistic interpretation of strings. As we have seen normal development in our Western culture largely plateaus with specialisation of 1-dimensional (linear) understanding. However wh...

I would like to briefly extend further here the holistic mathematical approach to the qualitative interpretation of strings that has the scope to open up new areas of refined understanding (not possible through the conventional approach). We will start with the very notion of a p-brane. In conventional terms this is defined in a (merely) positive manner. So for example when we speak of a string, it is defined positively in 1-dimensional terms. Now, in holistic mathematical terms every possible mathematical relationship that we define in conventional terms can be given a holistic (mathematical) interpretation with application to both physical and psychological reality (in complementary fashion). This implies therefore that a string can be holistically defined with respect to the negative (as well as positive) 1st dimension Well what does this all mean! It perhaps is easier to approach the manner initially from a psychological context. In holistic mathematical terms, to posit is to simpl...

It is amazing how in life if one waits long enough that things tend to come full circle. And this is true of the development of science itself. In earlier times, science was much influenced by the intrusion of confused holistic notions of a spiritual nature that significantly impeded proper analysis of physical behaviour. For example in the middle ages, largely to serve theological requirements, the Earth was believed to be the centre of the solar system. Therefore when Galileo supported an alternative viewpoint (based on objective empirical analysis), he was forced to detract his opinions so as to preserve religious orthodoxy. So it is only in the last 400 years or so - largely as a result of the monumental contribution by Newton - that science has successfully differentiated itself from subjective beliefs based directly, or indirectly, on religious notions. Indeed one could argue that the prevalence of the aether (which Einstein finally discarded in the early 20th centur...

An important part of my integral approach to science relates to the fundamental role that holistic appreciation of the various number types can play. In this holistic classification of numbers, I refer firstly to - what I call - the original numbers (1 and 0), then 2 and the other prime numbers, followed by the natural numbers (and integers) then the rationals, followed by the irrationals (algebraic and transcendental), the imaginary and complex and the transfinite. Of course all of these are well recognised in standard analytic terms. However their true holistic significance has been greatly missed. In what follows we will be confining ourselves to the holistic interpretation of the original, prime and natural nos. The original numbers 1 and 0 have their holistic equivalents as oneness and nothingness respectively. Now, we must realise that we are here referring to dynamic - rather than static - notions. Nothingness in this context thereby refers to a physical (and spiritual) ...

Another of the findings of M-theory is the realisation that 1-dimensional strings are not the only fundamental "objects". Rather a whole host of extended objects in higher dimensions also exist called p-branes, where p = no. of dimensions involved. Also in 11 dimensional M-theory, where we have 10 spatial dimensions, the number of possible branes ranges from 0 - 9 dimensions. In parallel fashion, I have long been aware of a similar situation with respect to its holistic counterpart, where we allow for differing dimensions of interpretation with respect to string concepts. Because this understanding initially arose with respect to clarification of the stages of psychological development, I will discuss my findings in this context. When understanding of a particular dimensional level unfolds, strictly one should refer to it as the default level of understanding. So for example, when the rational linear stages properly unfold in experience, one thereby obtains default 1-dimensio...

One the key ideas that Witten proposed in 1995 was the idea of dualities. Thus the five recognised string theories - which initially were believed to be separate - were in fact connected by duality transformations, so that by using the appropriate key one theory could be mapped on to another (revealing precious new insights in the process). Now interestingly my own holistic approach is based directly on polar dualities i.e. internal/external, whole/part and form/emptiness and immanence/transcendence. In the Type 0 approach - which concurs with conventional scientific interpretation - these dualities are considered as separate; however the four other Types revealing increasing levels of complementarity (and ultimate identity) as between these opposites. So in the (conventional) analytic approach the five recognised string theories provide unique perspectives on the ultimate nature of reality. Then through appropriate transformations they can be seen as in fact equivalent expressions. Li...

What is now known as "the second superstring revolution" took place in 1995 following publication of a paper by its acknowledged leading proponent, Edward Witten. Up to this, a well recognised problem with string theory was the lack of one unique theory. In fact five - seemingly - separate theories existed referred to as type I, types IIA and IIB and two heterotic (hybrid) string theories. The hope at the time was that just one of these would eventually win out to qualify as the long sought for TOE. However Witten was to surprise the string community by demonstrating very close links as between all the existing theories and postulated that they were in fact part of on an even grander synthesis (M-theory). He also argued that this overarching theory would find expression in an 11 - rather than 10 - dimensional framework. Now of course, I am by no means qualified to deal with the analytic issues involved. My purpose is rather to point to the integral (holistic) scientific signi...

The basic rationale for this new understanding of dimensions - which applies equally to both physical and psychological reality - is that is based initially on the two key polarities sets which necessarily underlie all phenomenal experience. Now these two polarity sets can be referred to as horizontal and vertical with respect to each other. The horizontal relates to the basic distinction as between internal (subjective) and external (objective); the vertical then relates to the further critical distinction - in any context - as between whole (general) and part (specific). Now we can represent these polarities as four equidistant coordinate points on the circle of unit radius with internal and external the end points along the horizontal line and whole and part end points along the vertical line respectively (dividing the circle). In physical terms, the dimensions of space and time arise through the interaction of these polarities; likewise in psychological terms, experience of space a...

I fully accept that enormous mathematical strides have been made with respect to the development of string theory. In many cases these resonate strongly with physical understanding of the Universe apparently offering the hope that many key difficulties (such as the integration of Quantum Mechanics with the Theory Of Relativity) can at last be successfully achieved. However from a philosophical perspective I would find that the attempted explanation of many of the fundamental concepts of string theory (such as the nature of a "string" and the meaning of "dimensions) remains very confused. Once again I would see the reason for this problem as representing the limits of what can be achieved through conventional scientific method (based on linear understanding). Strictly speaking the philosophical limitations of this approach had already been exposed through the paradoxical findings of Quantum Mechanics (though in practice largely ignored). Though clearly these philosophical...

It might be helpful to further extend the complementary connections as between the two notions of strings i.e. analytic and holistic, respectively. From the analytic perspective it is readily admitted that, as the string can vibrate in an infinite number of ways (with each unique vibration corresponding to a distinct matter particle) that potentially therefore we can generate an infinite no. of particles. Now so far, only a relatively small finite number of distinct particles have been found. The actual explanation for this fact is due to the fact that actual particles discovered correspond to extremely low eneregy levels of vibration of the string. These likewise entails less energy (corresponding to relatively low masses). New particles entailing greater vibration of the string would require extremely high amounts of energy (well beyond present technological capacity). The reassuring fact therefore is that in terms of "normal" energy states we need only concern ourselves wi...

As stated so frequently in these blogs, the standard linear (1-dimensional) approach employed in Conventional Science is unable to maintain the key qualitative distinction (in any appropriate context) as between whole and part. It can only operate therefore by essentially reducing whole to part notions (in real conscious terms) or alternatively part to whole notions (in a likewise real conscious manner). Fundamental therefore to maintaining the proper qualitative distinction as between both aspects is the recognition that unconscious (circular) and conscious (linear) notions must be formally incorporated with each other in interpretation. As we have seen, whereas in a direct sense the conscious aspect of understanding relates to (real) rational interpretation (corresponding to either/or logic)), the unconscious relates directly to corresponding intuitive recognition (relating to complementary both/and logic). However this latter intuitive aspect can be given an indirect rational interp...

I have always had philosophical problems with the definition of a string. Indeed my interest in the area originally arose out of an attempt to redefine some of its key concepts in a way that I - at least - could find intuitively satisfying. This relates to a deeper problem with the whole area in that theorists and practitioners seem unable to bridge the gap as between mathematically satisfying results and a coherent explanation of the physical concepts involved (that can evoke any acceptable resonance with the manner in which people understand reality). So at the moment string theory resembles a kind of secret code that undoubtedly can generate many exciting mathematical results (suggestive of deep physical connections). However without a much more coherent philosophical decoding of the nature of its concepts it cannot really qualify as a true physical explanation of reality. So the problem with strings not alone relates to the present difficulties in finding ways of experimentally tes...

In the previous post, I demonstrated the interesting fact that with respect to root quantitative values (and corresponding dimensional qualitative values) that both n = 8 and n = 24 play a special role. Here with respect to the relationship cos(360/n) + i sin(360/n) the square of sum of (absolute) real and imaginary values = 2, for n = 8, and = 1.5, for n = 24 (where all possible values range from 1 to 2). So the former represents the maximum that can be attained whereas the latter represents the mean average (of all possible values). Let us remind ourselves of the context out of which this has arisen! Earlier I explained how the original Jungian Theory of Personality Types was based on 8 distinctive types. Then in the holistic mathematical extension of this approach (based on permutations the four key coordinate points on the complex plane) 24 distinctive types could be defined. One way of looking on each Personality Type is that it provides a unique way of configuring ch...

24 in its own right is a fascinating number. Firstly it represents all the permutations of 4 (containing 4 elements) that can be made from 4 which is 4 * 3 * 2 * 1. However there is another very interesting property that if we add up the squares of the consecutive numbers from 1 to 24 (inclusive) that the result 4900 will be the square of an exact whole number i.e (70). This is the only case known where the sum of squares of successive natural numbers is equal to the square of another whole number! Interestingly the sum of 1 + 2 + 3 +....+ 24 = 300, while the sum of the prime numbers between 1 and 24 = 100! 24 - as we shall see - plays a key role in Ramanujan functions, which in turn provides a direct link to the number of dimensions in one of the earlier string theories. 24 also plays a crucial role in the search for the Monster Group (the largest known symmetrical object) which again provides a direct connection with string theory. As we know, if the proper divisors of ...