A Simple Explanation of Transfigural Mathematics and Natural Inclusionality

A few days ago a comment on one of my articles, Yearning for the Pleroma , opened my eyes to a line of published thought I should have heard about by now but hadn't. I deeply appreciate this reader for taking the time to leave me the following:

Your example of paper being the ground reminds me of this youtube video by Dr Rayner:[http://youtu.be/yVa7FUIA3W8]  

and

Here's one of Dr Rayner's papers. Essentially, for him (and me) Space itself all around and within is the infinite inductive source...but I need others to examine this. There is relation to Toridal model. [https://www.bestthinking.com/articles/science/math/logic/transfigural-approach-to-evolutionary-origin] 

The first link, to this short video by Dr Rayner, presents an easy-enough introduction to the concept of natural inclusionality. And, yes, the paper model used in Rayner's nifty little demonstration is conceptually the same as the paper used as the ground in my own posters of Gnostic cosmology. 

In my drawings of Gnostic cosmology, the paper itself is likened to the ground state of the Universe (aka God the Father) and the drawings on the paper are the figures differentiating out of, but staying one with, the Father.

I am glad the commenter asked about its possible relation to toroidal models, because the Simple Explanation's toroidal cosmology turns out to be closely aligned with the natural inclusionality model and what they call transfigural math.

Here's the simplest definition of natural inclusionality I could find on the Inclusional Research Forum and Learning Space:  

"The co-creative, fluid dynamic transformation of all through all in receptive spatial context"

The idea behind natural inclusionality is that nature is not divided into the neat, straight-sided and artificially bounded spaces that conventional mathematics and logic depend upon for their formulae to work. Nature is interwoven and interdependent, and it rarely stops moving long enough to take a traditional measurement of singular characteristics. The solution provided by inclusionality is to view nature as a fluid state, with all objects and subjects included within the same fluid flow. Once you are able to shift your perspective to see this fluidity, you recognize "a naturally continuous dynamic geometry of fluid flow, in which spatial and informational phases are mutually inclusive, not mutually exclusive" (Shakunle, L.O. and Alan D.M. Rayner, 2016). 

Transfigural geometry is a "post-Euclidean" geometry "based on the logic of 'the included middle,' 'inclusionality', whereby material 'content' is a dynamic local inclusion of non-local spatial context and vice versa" (Ibid.). For those of you who enjoy reading logic and math, the paper cited here goes into detail regarding the logic of transfigural geometry and its ability to describe and better represent the dynamic interplay of material objects as natural energy flow. At its simplest, transfigural geometry is represented by the figure below:

This figure is called the "superchannel" of transfigural geometry. It represents a line that has been transformed from discrete points to local spheres of non-local spatial influence, called 'zeroids'. (Shakunle, L.O. and Alan D.M. Rayner, 2008)

Readers of this Simple Explanation blog will recognize the above figure as a variant of my own toroidal doodles -- 

in which the "superchannel" depicted by Shakunle is formed through the interplay of infinitely nested toruses.

Now, let's look at some quotes from Shakunle and Rayner and translate them into Simple Explanation terms. That way, if you are already familiar with transfigural math and natural inclusionality you will see how it relates to the Simple Explanation's toroidal cosmology. I'll highlight the quotes and their Simple Explanations, and link them to the original Simple blog articles for fuller explanations.  

"At the philosophical core of transfigural mathematics is the recognition of two distinct but mutually inclusive and co-creative kinds of dynamic influence at work in the cosmos: figural and transfigural. Figural influence is energetic, resistive and brings local distinctiveness--but never complete discreteness--to natural, variable viscous flow-form. Transfigural influence is non-resistive, spatial and present everywhere, without limit" (Shakunle, Rayner).

In Simple Explanation terms, the figural is the stuff of our universe--the aggregations that bubble up, combine, and form Units of Consciousness that distribute themselves at larger and smaller scales throughout creation.

Transfigural refers to the "meta" level consciousness that forms the conscious ground that underlies and transcends our universe and its material and electromagnetic components--what the Simple Explanation refers to as the Universal Unit of Consciousness, the universal womb.

"Transfigural influence can be thought of implicitly as spreading radially, from 'zero identity centres' (called 'zeroids' in transfigural mathematics) distributed everywhere, although this radial influence cannot be manifested explicitly without figural influence" (Shakunle, Rayner).

The Simple Explanation cosmology sites these "zeroids" as the singular point at the center of the torus. As the Universal Unit of Consciousness brings information flowing inward, toward the center of the torus, passing through the shared middles of every thing, past the point of here and now, and then as history downward and back around again to become future potential.  At the same time, information passing through the shared middles explodes inward into our physical reality, bringing coherence, form, and consciousness into every thing in the universe.

"The underlying dynamic geometry of natural flow form and transfigural mathematics is hence primarily non-linear and space-including... Through the interplay of inseparable transfigural and figural, radial and tangential dynamic influence, spiral, linear and annular form emerges fluidly from primarily spherical form as a local figural inclusion of non-local transfigural influence" (Shakunle, Rayner).

I, of course, would amend their primarily spherical forms to read primarily toroidal forms, which contain within themselves both conventional and non-Euclidean geometries, and which otherwise fully satisfies the spherical requirement of natural flow form.

At this point, transfigural math and natural inclusionality take an interesting turn toward talk of gravity, love, and creative potential:

"Transfigural space is not only gravitational but it is also a dynamic presence of love and creative potential" (Shakunle, Rayner).

One-in-Other as a flow translates therefore to One knowing what it is through others, alongside One, and through these others, to and through All with All also reaching inside One. This also translates to the origins of human identity, the place of the person in society and the world, and how human beings are in Nature and Nature in them and how all are included in Space, a common habitat that includes them. The middle, in this transfigural outlook, is not only included but every fluid logic number which is distinct, flows in what comes before and after it that also flow in it..." (Shakunle, Rayner).

A Simple Explanation cosmology proposes that there is a Unit of Consciousness attached to every piece of material of our universe, and it is this inherent consciousness arising from the One consciousness of the shared middle that has an attractive quality that pulls it toward others in search of aggregation into larger and larger forms. We call that attractive quality "gravity" when it relates to physical matter, and we call that attraction "love" when it relates to Units of Consciousness.

"Samedifference--Its Sustaining Spirit:

In the oppositional logic of OR, it is lose, out, win, remain. There are no such grounds for conflict in samedifference. Underlying samedifference is the spirit of sharing: giving, receiving, and passing on in a natural flow of energy. There is no mutually exclusive game of winners and losers. In samedifference, the greatest pleasure comes from bringing joy to the heart of the other through sharing in the gift and promise of life as it waxes and wanes, like a child belonging in the community of a village that belongs in the community of the world and ultimately limitless cosmos that is its home."

As is the case with transfigural math and natural inclusionality, the Simple Explanation cosmology inevitably leads one to embrace others in love. We call this The Simple Golden Rule: Your job is to reach out to others with love, aid, and information for the betterment of all.

I hope this article hasn't muddied the waters in my attempt to relate these two different ways of looking at the unity of our universe. I urge you to read my book, A Simple Explanation of Absolutely Everything, for the clearest, most logical exposition. Feel free to leave a Comment and I'll do my best to give a simple answer.

Toroidal Symmetries and Fractal Divisions

Noodling around with a protractor, bisecting circles into smaller circles to make them into toroids. Along the way, the 2-D drawing displays beautiful symmetries of various kinds.

I drew this toroidal pattern using a pencil compass on paper. The lines you see at the circles' centers is where the compass dug into the paper. Pardon the mathematical imperfections, as this was done freehand.

I imported the drawing into Paint and airbrushed out the compass scratches. I can see toroids all over this drawing, but you may only be seeing the circles.

Here I've used the Paint program to highlight the largest torus in this drawing, which shows up if you imagine this as a cross-section of a sphere. The blue lines show the cross section of the torus cutaway. This inner torus has been subdivided again into two smaller tori (darker blue circles). The vertical yellow lines are the poles; the longest pole is for the central torus; the two shorter lines are the poles of the two subdivided tori. You can go on subdividing each torus this way, each time dividing the cutaway of the torus into half-sized tori.

This torus and its poles was used to illustrate "the great square within the torus." Same view as the blue lined cutaway above.

The darkest blue circles represent my clumsy eyeball method of illustrating how the torus is dividing fractally. Each torus cross section can divide into two more.
I wish I had a program that would draw these things more accurately. Any volunteers?

Notice the interesting way this fractal division works. It will go on forever, larger and larger or smaller and smaller, in true fractal manner.

Usually when I've thought about multiply-linked tori, they appear to nest at a single center pole, like Russian dolls. But these new drawings show how the tori can divide fractally along different lines. 

Concentric tori courtesy of http://www.multidimensionalmusic.com/review2.html

The Simple Explanation has also used nesting toroids to illustrate chakras.

 ******************************************

A little more fooling around in Paint gives us a "quasi torus" in the vertical direction (yellow). Look for more on this tie-in to quasi-particles in a future article.

Here I've used the poles to define a quasi torus perpendicular to the blue set. Following the logic of the Simple Explanation, I don't really think the tori divide up and down like this, along the poles, since the poles represent time and motion rather than space. I think the tori only divide in the horizontal (blue) space. But here we can see that this structure has room for a fully symmetrical set of divisions in the vertical (yellow) dimension.