Integral Science

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 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 current understan...

Sometimes a degree of ignorance can be a virtue. I am by no means properly acquainted with the quantitative mathematical intricacies of modular functions (and the important expression relating to the j-function). However in attempting to look at issues from a holistic mathematical perspective, I am not surprised that intimate connections have been demonstrated as between dimensions in the Monster Group and coefficients of the j-function. After all the Monster Group relates to an amazingly symmetrical object as group of rotations in 196,883 (Euclidean) dimensional space with group order: |M| = 808017424794512875886459904961710757005754368000000000 = 2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 Modular functions likewise relate to objects with supersymmetrical properties that can be transformed in an (infinite) variety of ways while remaining unaltered. It is intriguing however from a holistic mathematical perspective that such functio...

In the early 1980's I was very interested in Jungian psychology (and especially with respect to his theory of Personality Types). Part of the attraction arose from the fact that implicitly Jung formed many of his key notions in a manner amenable to holistic mathematical interpretation. I mentioned in the last post the (true) qualitative circular notion of dimension and contrasted this with the merely reduced quantitative linear interpretation that predominates in conventional mathematical and scientific understanding. As four dimensional space-time is so important (as conventionally understood) it is only reasonable to assume that an important circular interpretation of such dimensions can be equally given. It was here that familiarity with Jungian concepts proved valuable. Jung organised his understanding of Personality Types around 4 key functions that are often shown as equidistant points on the circle. So this bears obvious comparison with the four roots drawn on the ci...

Perhaps the single greatest problem with respect to conventional mathematical understanding relates to the standard treatment of dimensions, which is both highly reduced and unsatisfactory. From my current perspective I see this problem as so fundamental that it is truly remarkable how it is persistently overlooked. I generally describe the standard method of mathematics as the linear rational approach. Now the line is literally 1-dimensional; so alternatively from a qualitative philosophical perspective, Conventional Mathematics is based on 1-dimensional rational understanding. To see what this actually entails we can consider for a moment the natural number system. Now, when we list the natural numbers i.e. 1, 2, 3, 4,...they are commonly defined - merely - with respect to their quantitative characteristics. However implicit within such understanding is a (default) qualitative aspect (as dimension 1). In other words implicitly each number as quantity is defined qualitatively with res...

As is well known the term "Monstrous Moonshine" was coined by John Conway with respect to an unsuspected mathematical connection demonstrated as between the Monster Group and the j-function (an important part of number theory related to modular functions). The Monster Group itself appeared somewhat like the final piece in a massive jigsaw puzzle. The whole area of Group Theory - that has now assumed great importance in Mathematics - arose out of the attempt to classify the different types of symmetrical objects that can arise. A simple geometrical example of a symmetrical object is provided by the 3-dimensional cube which has six similar faces. Now there are many different ways of rotating the cube (48 in all) so that its symmetry remains unchanged. So the quest that arose in the 19th century was to classify the "atoms of symmetry" or basic building blocks as it were for all symmetrical objects, in what were termed finite simple groups. In some respects this paralle...

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...