Integral Science

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...