Integral Science

One of the great contributions of Fractal Geometry is that it leads to consideration of the corresponding notion of fractal dimensions. For example this is beautifully illustrated with Koch's Snowflake. See Mathworld . So to construct this Snowflake we start with an equilateral triangle. Then marking each line into 3 equal divisions we take the middle third and erect another equilateral triangle on each side. Then we continue to proceed in the same manner (constructing a new equilateral triangle on the middle third of each exposed side). Theoretically, we can continue in this manner an infinite number of times. The implication of this is that the perimeter boundary of the Snowflake thereby increases without limit. In fact we can easily see that the initial construction of equilateral triangles on the middle third of the original 3 sides of the starting equilateral triangle increases the perimeter length by a factor of 4/3. Thus as we can keep repeating this procedure indefinitely (...

Like so many, my first introduction to the new science of Chaos and Complexity came from the book "Chaos" written by James Gleick back in 1987. Recently I returned to read this book wondering as to whether the intervening years had changed my perception or sharpened understanding of the issues raised. As on the first occasion of reading, I was left however with a vaguely dissatisfied feeling, rather like the various courses of a meal that promise a great deal in preparation, yet somehow fail to deliver on eating. So I stayed a little with this feeling so as to get to its roots. Basically I would summarise the position as follows. Chaos Theory and all the various versions of Complexity arise from the recognition that so much behaviour in nature is of a nonlinear nature. However Conventional Science, through its linear method, tends to approach nature through modelling it in the form of linear equations (frequently adjusted finally in some way to approximate living condit...

As one can see, my integral approach to science (and development) is heavily based on holistic mathematical interpretation of the 1st, 2nd, 4th and 8th dimensions respectively. However a key insight here is that corresponding to every number (in holistic terms) is a unique dimensional interpretation (with application to both physical and psychological reality). In psychological terms, this entails that all possible understanding entails both conscious and unconscious aspects. So a dimension in this sense corresponds to a unique configuration of these two aspects. In scientific physical terms, this equally entails that reality entails both specific (manifest) phenomena related to an underlying (hidden) ground of reality. So here, each dimension relates to a unique configuration connecting such phenomena to this underlying ground. And of course in holistic mathematical terms, a dimension (in either its psychological or physical state) is given as a unique mapping of real and imaginary co...

One way of viewing this integral TOE is in terms of the main contemplative stages required before full union (empty of manifest phenomena) can take place. Linear understanding (1-dimensional) by its very nature leads to phenomena being given an unwarranted rigidity (by which they have a seemingly independent existence). So the first task is to remove such rigidity at a conscious level. This is attained by recognising the inherent complementarity - with respect to all phenomena - of both internal and external polarities (2-dimensional understanding). In holistic mathematical terms these are positive (+) and negative (-) with respect to each other in real terms. In psychological terms this can be attained at either a rational (cognitive) or sense (affective) level without the full integration of either aspect. In corresponding physical terms this would relate to a failure to fully integrate both personal and impersonal aspects with respect to scientific phenomena. The second task is then...

I will elaborate further on the significance of the three key polarities (corresponding to the holistic mathematical interpretation of 2, 4 and 8 dimensions respectively). The first set of horizontal polarities (corresponding to the relationship between internal and external) as we have seen are positive and negative with respect to each other in integral terms. The significance of this is that all scientific understanding of reality necessarily entails an internal (subjective) observer in relation to what is observed in external (objective) terms. Now when we view this relationship in a linear manners, both external and internal frames can be given a merely positive identity (that correspond with each other). For example I can view the "sun" as in objective terms as an external object. However equally I can view the "sun" in - relative - subjective terms as relating to its internal perception. Fortunately for Conventional Science - based on a linear app...

The Integral Theory of Everything is based on finding a holistic mathematical acceptable manner of interpreting the dynamic relationship as between the 3 fundamental polarities (that underlie all experience of reality). Once again these polarities relate to (i) the distinction as between internal and external within a given stage of development (horizontal polarities); (ii) the distinction as between whole and part between different stages of development (vertical polarities); (iii) the ultimate distinction as between form and emptiness both within and between different stages of development (diagonal polarities). I identify 4 stages of integration corresponding with the qualitative interpretation of 1, 2, 4 and 8 dimensions respectively (relating in turn to the 0th, 1st, 2nd and 3rd powers of 2). The standard conventional scientific approach - based on linear rational understanding - corresponds with the 1st dimension (Integral 0 approach). Basically such an approach - whi...

We hear a lot these days in scientific circles regarding the search for a TOE (Theory of Everything). For example some people that developments with respect to String Theory could lead to a TOE (possibly in the near future). Personally I believe that such optimistic views are quite unfounded and that a TOE within the accepted confines of Conventional Science is simply not tenable. Current science is still of a highly reduced nature. Once again I will place this in the context of my own approach. Potentially, we can identify an infinite number of qualitatively different dimensions of understanding. Each corresponds to a unique holistic interpretation of number through which reality can be validly interpreted. However, Conventional Science uses just one of these dimensions i.e. the 1st corresponding to linear rational understanding. As we have seen this default linear model of interpretation is not able to preserve the qualitative distinctions pertaining to the key polarities that necess...

Back in the mid 60's the two greatest intellectual influences on my development were Albert Einstein and Teilhard de Chardin. What I subsequently found fascinating was the degree to which they were very close contemporaries. De Chardin was born in 1881 (two years after Einstein). However they both died in April 1955, within 8 days of each other, in the US (which had become their new adopted homeland). Indeed even geographically they were very closely united at the end with de Chardin dying in New York and Einstein just 50 miles away in Princeton. Though in my own person a raging internal debate was going on regarding their respective philosophical standpoints, I am not aware of any substantial contact taking place between the two men during their own lifetimes. What is similar in the work of both is a great drive towards understanding the unity governing all creation. However though Einstein was certainly inspired by deep wonder and intuitive insight (of a genuine religious...

Evelyn Underhill published her classic book "Mysticism" in 1911. This is interesting - for what might initially seem an entirely unconnected reason - in that neatly divides the period as between Einstein's "Special Theory of Relativity" in 1905 and his "General Theory of Relativity" in 1916. In his earlier contributions Einstein particularly focused on the nature of light (electromagnetic energy) and its intimate connections with spacetime. In the latter he probed the mysterious nature of gravity. Then for the final 35 years or so of his life he turned his attention to the task of properly integrating these two forces in a unified field theory providing the basis for understanding the whole of nature. As we have seen it is the nature of the integral approach that it establishes clear complementary connections - ultimately in holistic mathematical terms - as between all key physical concepts and their (unrecognised) psychological complements. So electro...

As we have seen, it is the every essence of the integral approach to find - in any given context - the complementary notion (with which it is intimately related).  So with Integral Physics the task is to find - for any established physical concept - a matching psychological partner (which is mathematically identical in terms of its holistic qualitative nature). Thus we are now looking for the matching psycho spiritual counterparts to the four physical forces (already defined in holistic qualitative terms). In physical terms the forces are essential to explain phenomenal notions of movement. In corresponding spiritual terms, complementary forces are required to explain phenomenal notions of psychological movement. This is what we refer to as (fundamental) motivation i.e. that volitional sense of purpose (desire for meaning) which serves as a precondition for all psychological understanding. Though ultimately there is just one force in this sense, with all subsidiary representation...

As suggested in the last contribution, the holistic mathematical nature of each of the physical forces is given by the four complex roots of unity. If we take the first of these roots it is in the form 1/k(1 + i) where k represents the square root of 2, and i the square root of - 1 respectively. In holistic terms 1 denotes the real manifestation of (unitary) form and i the corresponding imaginary manifestation. Now it is the very nature of light that it can reveal itself - phenomenally - in either wave or particle form. So when for example the wave aspect is manifest in experience as real, then the corresponding particle aspect remains imaginary; likewise when the particle aspect is manifest as real, then the wave aspect is imaginary. So both wave and particle aspects of light keep switching as between a real and imaginary identity depending on which one manifests itself (according to a chosen observational context). However what is fascinating about the complex roots of unity is that ...

When Einstein was seeking his Unified Field Theory only two forces were involved i.e. the electromagnetic and gravitational. Subsequently two additional forces have been recognised i.e. the electroweak and the (strong) nuclear. When one looks at it, these appear in holistic mathematical terms very much as internal counterparts to the other two forces (which operate extensively throughout nature). Indeed the weak force (which for example can be used to explain the radioactive disintegration of certain atoms) offers itself as the internal (negative) counterpart to the electromagnetic; likewise the nuclear force readily suggests itself as the internal (negative) counterpart to the gravitational. I have already drawn attention to the natural complementary relationship as between the electromagnetic and gravitational forces. Whereas we would - literally - see the first as "light" the latter by contract would be "heavy". In fact the holistic mathematical relationship as b...

In Conventional Mathematics both real and imaginary numbers are used with respect to their (merely) quantitative interpretation. However the key starting point of Holistic Mathematics is the realisation that every mathematical symbol can also be given a corresponding qualitative meaning. The limitation therefore of Conventional Mathematics is that it is confined in qualitative terms to merely real understanding (corresponding to default one-dimensional interpretation). The role of Holistic Mathematics is to provide corresponding imaginary interpretation in qualitative terms. Whereas real interpretation corresponds directly with conscious, imaginary interpretation - by contrast - corresponds directly with unconscious understanding. Once again the real aspect relates to linear logic (where opposite polarities in experience are clearly separated) whereas the imaginary aspect relates in turn to circular logic (where such opposite polarities are treated as complementary). Thus when we separ...

As we have seen, from a psychological perspective a sudden acceleration in the customary speed of interaction between polarities of experience (such as internal and external) leads to a dramatic increase in psychological gravity. In common language this represents an experience of grief which in the spiritual contemplative life is identified as a purgative period for the soul. The higher stages of development (defined by their unique number dimensions) therefore represent progressively greater interaction i.e. psychological velocity as between opposite polarities (associated in turn with purer experience of the spiritual light). The transitions as between such stages thereby requires an acceleration with respect to previous interaction (associated again with purgative phases of development). The most profound of such purgative phases is often referred to as the Dark Night of the Soul. In truth there can be many "dark nights" on the spiritual journey. However the most dr...

The next significant breakthrough that Einstein was to make was the realisation that space and time becomes curved in the presence of gravity. As however gravity is an especially weak force in normal circumstances this curvature is so small as to be undetectable. However in the presence of matter with a substantial degree of mass the gravity force can exercise a significant degree of influence in warping surrounding space and time. Einstein also postulated that gravity would cause light to bend in the vicinity of such mass. Indeed Rutherford's experimental verification of this in 1919 was accepted as proof of Einstein's General Theory thus paving the way for universal acclaim. Once again there is a fascinating holistic correspondent to the curving of spacetime. Not only is this of interest in its own right but ultimately it throws considerable light on the true relationship of the electromagnetic to the gravitational force (demonstrating why a fully unified field theory is ...

Though path breaking in several respects, Special Relativity was limited in scope in that it did not incorporate the effects of gravity. So Special Relativity in quantitative physical terms is based on relative comparisons of phenomena travelling at a constant velocity. In corresponding qualitative psychological terms, Special Relativity is based on relative comparisons of phenomena that are interpreted within given stages of development (defined - as we have seen - by their dimensional numbers). Einstein made an important breakthrough in his attempts to incorporate gravity in a more general theory when he realised in a moment of clear insight that - what we call - gravity is inseparable from the effect experienced through accelerated movement. So for example when a car suddenly accelerates in speed one can feel a force pinning one to the seat that is identical to that of gravity. This unlocked an important key for Einstein. He saw that he could include gravity in a General T...

Einstein's famous equation demonstrating the equivalence of mass and energy arose out of his reflections on Special Relativity. So physical energy and matter are intimately related to each other. From an integral perspective, the question then immediately arises as to the relationship between spiritual energy and (our cognitive experience of) phenomenal form. As we can see from the physical formula, the square of the speed of light is directly involved, with the speed expressed in two-dimensional terms. Now if we examine this equation from a holistic perspective, two-dimensional understanding entails the structure corresponding to the two roots of unity i.e. + 1 and - 1 respectively. The implication here is that for physical energy to be fully released from matter its opposite polarities must cancel each other totally. In physical terms, this can be expressed as the situation where matter (+) and anti-matter (-) annihilate each other. There is a remarkabl...

There is a famous quote by Albert Einstein on Relativity. "Put you hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. THAT'S Relativity." I have always found this an interesting quote - not so much for its instantly accessible message that can be readily appreciated by anyone - but rather for the hidden problem that it raises (which Einstein does not deal with in his work). Put briefly, this is a statement about Relativity - indeed about Special Relativity - which relates specifically however to its (qualitative) psychological rather than its (quantitative) physical meaning. And as Einstein's Theory solely relates to the physical meaning, his clever quickfire illustration here in fact relates to a much deeper issue (which he does not address). In other words Relativity - in this context Special Relativity - can be given both a (quantitative) physical and (qualitative) psychological interpretation...

In my last contribution, I distinguished as between the 1-dimensional and 2-dimensional qualitative interpretations of Special Relativity. This highlighted the distinction as between the conventional scientific approach (1-dimensional) where effectively holistic circular (paradoxical) notions of meaning are reduced in linear (unambiguous) terms and the more refined 2-dimensional interpretation where both types of meaning can be clearly distinguished. Essentially all other higher dimensional interpretations entail the same basic distinction as between (analytic) linear and (holistic) circular notions of meaning in an increasingly refined manner. However some further distinctions can be made (for which my radial mathematical investigation of the Riemann Hypothesis has proved invaluable). Properly speaking, purely integral understanding i.e. that ultimately is realised in an intuitive manner, is confined to the even dimensions while increasingly refined rational understanding is associate...

I will outline briefly the basic holistic mathematical rationale by which the qualitative approach to measurement with respect to Special Relativity can occur. Conventional Science is based qualitatively on a merely linear (i.e. 1-dimensional) interpretation of mathematical symbols. However corresponding to every number (as dimension) is a unique qualitative interpretation. So theoretically an infinite number of such interpretations is possible. All interpretations (other than the default linear) entail a unique configuration of both linear and circular aspects of understanding. In psychological terms this entails a complex mix of both conscious and unconscious (corresponding to rational and intuitive type appreciation). Phenomenal quantitative measurements of space and time correspond merely to linear type understanding. However when both linear and circular aspects are incorporated such linear measurements of space and time are seen as merely relative expressions of an und...