Dear All,

Well, just to add that 'circles of influence', or, to expand this, 'spheres 
of influence' is very much a phrasing that I have used to introduce the 
transfigural (through the figure) fluid geometry of natural inclusion. 
Attached and below is a short essay about this(NB, these days I prefer the 
word 'figural' to 'informational'). I have also attached a painting that 
goes with it.

In speaking about 'influence', it helps, in my mind to recognise that this 
means 'in-flux'. It relates to my natural inclusional understandings of what 
it deeply means to be an 'in-habitant' of Nature as a 'receptive, reflective 
and responsive' 'including middle' - a natural 'centre somewhere' as an 
energetic inclusion of 'everywhere' as a limitless pool of receptive space. 
Hence we can all be thought of as simultaneously 'pooled together' in 
one-another's mutual influence. cf the following video clip from last 
saturday's 'NaturesScope' workshop.


 http://www.youtube.com/watch?v=9wkIB8E6aMw .


Correspondingly, instead of describing us as all 'energetically connected', 
I prefer to describe us as 'all variably open to one anothers' energetic 
influence'. Our boundaries are energetic interfacings that make us distinct, 
as natural flow-forms, but not discrete, as independent singlenesses. There 
is no need to claim paradoxically that on the one hand there are 'bounded 
wholes' whilst on the other 'there are no boundaries between them'. Equally 
there is no need to speak paradoxically of 'an infinity of wholes', or 
indeed of an 'infinite whole' as a totality (independent singleness), which 
is a contradiction in terms (it is not possible to count up to infinity 
because infinity is a quality of space not a quantity of figures; neither is 
it possible to count down to zero, for the same reason).


Although what I have said above uses what may seem like high falluting 
language (because I am trying to relate to and loosen abstract language, 
logic and imagery that has already been set rigidly in place), I think the 
point can be made much more simply, given the chance to be heard by 
unencumbered minds. Attached is the opening of a 'children's book' I have 
started to write, at the prompting of my friend Rev. Roy Reynolds.  I think 
it lies at the heart of living educational theory and practice, which 
recognises truly and deeply and compassionately what it means to be and 
become an in-habitant as a 'receptive hole'.




Warmest

Alan

-------------------------------------------

Relativity and quantum mechanics - a collision between two space-excluding 
geometries and their resolution in transfigural geometry



By Lere. O. Shakunle and Alan D.M. Rayner





The apparent incompatibility between quantum mechanics and general 
relativity theory has long been a source of vexation and debate. Here we 
suggest that not only is the reason for this incompatibility simple, but so 
too is its resolution. The incompatibility arises from the reciprocal ways 
in which the localized Euclidean and non-Euclidean geometries upon which the 
two theories are founded exclude consideration of the absolute zero and 
infinity of non-local space as a receptive immaterial omnipresence 
everywhere. Neither of these foundational geometries can adequately 
represent natural energy flow in a cosmos without external spatial limit. 
Both, by axiomatic definition, impose absolute discontinuity between the 
informational (electromagnetic/ ‘material’) and spatial (‘immaterial’) 
phases of energy flow, but in radically different ways. The simple solution 
to their incompatibility is therefore to be found in a naturally continuous 
dynamic geometry of fluid flow, in which spatial and informational phases 
are mutually inclusive, not mutually exclusive. The ‘post-Euclidean’ 
transfigural geometry developed by Shakunle (1994, 2006) is of this kind. 
This geometry is 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 (Rayner, 2004).



The framing of nature within an infinitely extended cubical box with a fixed 
centre or origin but no outside is the basis for the idealistic geometry of 
Euclid. Here, the infinite (i.e. ‘non-local’ in the sense of ‘present 
everywhere’ or ‘omnipresent’, not in the quantum entanglement sense of 
‘action at a distance’) receptive presence of space is definitively 
localized within just three orthogonal, width-lacking (i.e. space-excluding) 
structural planes. Through this geometry, space, time and structure are 
conveniently homogenized and abstracted from one another in a way that 
enables them to be packaged and quantified in independent, uniformly linear 
units. These units can be added, subtracted, divided and multiplied as whole 
entities and fractions according to the rules of elementary arithmetic. But 
the convenience comes at the expense of paradoxically defining infinite 
space within a fixed structure containing isolated objects that can only be 
moved by ‘force’ exerted from somewhere ineffable within or beyond their 
discrete limits. Energy flow is effectively stalled within an ‘infinite but 
bounded’ structure that dislocates space from matter.



By contrast, Riemannian and Lobachevskian non-Euclidean geometries, the 
former of which is the foundation for general relativity, can be described 
as ‘finite but unbounded’ (i.e. without fixed corners). These geometries 
paradoxically exclude space from matter – and hence impose discontinuity – 
by completely confining movement to a depthless curved surface. Here, as 
Wheeler (ref) put it, matter tells space how to curve and space tells matter 
how to move. But there is no opening for their mutual inclusion in a natural 
communion of energy flow. Each is closed off from the other, just as they 
are, but in a different way, through the imposition of rectilinear 
co-ordinates.



The obvious resolution of the incompatibility between three-dimensional 
‘infinite but bounded’ Euclidean geometry and the ‘finite but unbounded 
geometry’ of a curved surface is some kind of synthesis that opens up the 
reciprocal forms of closure imposed by each, to yield an ‘infinite and 
dynamically bounded geometry’.  Such a geometry would neither lack depth nor 
be linearly constrained, and so would include the possibility for emergence 
of an endless, though not completely unrestricted, variety of dynamic 
relational ‘flow forms’ as fluid configurations of space that only assume 
linear proportions when frozen or crystallized.  This corresponds with the 
poetic observation that ‘in nature everything is distinct, yet nothing 
defined into absolute, independent singleness’ (Wordsworth, 1815).



A limited step towards understanding how the mutual inclusion of space and 
matter in energy flow could lead to more realistic, i.e. naturally 
representative, non-linear mathematical formulations has been provided by 
the development of fractal geometry and the associated ‘strange attractors’ 
of chaos theory (e.g. Mandelbrot, 1977; Gleick, 1988). These formulations 
still originate, however, in the subdivision of a prescriptively imposed 
rectilinear and discrete geometrical and numerical framework. They begin 
with the localization of initial conditions and structural limits instead of 
allowing local form to configure dynamically within a non-local spatial 
context (Rayner, 2004).



A new system of numbers and geometry has, however, been developed, called 
‘transfigural mathematics’, which, we think, solves the problem of 
continuity through the inclusional logic of dynamically including space in 
matter and vice versa (Shakunle 2006). Correspondingly, rather than treat 
numerical identities as dimensionless points along a discrete line, and so 
in effect excluding both zero and infinity, this mathematics envisages 
numbers as dynamic relational neighbourhoods. Here, overlapping local 
informational spheres of non-local spatial influence form a truly 
continuous, ‘dimension-full line’ or ‘resonant superchannel’ (Shakunle and 
Rayner, 2007; Figure 1) in which reciprocal, spiralling inflows and outflows 
are dynamically balanced through inner core identities called ‘zeroids’ 
(from zero identities). The zeroids are hence equivalent to ‘organisms’ or 
‘convection cells’ in simultaneously receptive and responsive fluid 
relationship with their immediate environmental neighbourhood, and through 
this neighbourhood with all Nature.









Figure 1.  The continuous ‘superchannel’ of transfigural geometry. This 
channel represents the spatial expansion of the discrete, one-dimensional, 
purely material line comprising contiguous but spatially discontinuous and 
dimensionless numerical point-masses upon which classical and modern 
mathematics are founded. Each discrete point is transformed from a static, 
lifeless entity to a dynamic, breathing identity as a local informational 
(electromagnetic) sphere of non-local spatial influence, known as a ‘zeroid’ 
(from zero identity). The zeroids reciprocally inspire from and expire to 
their immediate neighbours, creating a double helical energy flow through 
coupled numerical neighbourhoods of three.



With this development of transfigural geometry, in which the zero and 
infinity of non-local space are brought in from the cold outside, we think 
that not only can a resolution be found for the incompatibility between 
relativity and quantum mechanics, but also new understandings of 
thermodynamics and evolutionary processes become possible (cf. Rayner, 
2004).







References



Gleick, J.  (1988) Chaos. London: Heinemann.



Mandelbrot, B. (1977). The Fractal Geometry of Nature. New York: Freeman.



Rayner, A.D.M. (2004). Inclusionality and the role of place, space and 
dynamic boundaries in evolutionary processes. Philosophica, 73, 51-70.



Shakunle, L.O. (1994) Spiral Geometry.  The Principles (with Discourse). 
Hitit Verlag, Berlin, Germany.



Shakunle, L.O. (2006). Mathematics – Identity, continuity, and equality. 
Journal of Transfigural Mathematics, 1, 65-89.



Shakunle, L.O. and Rayner, A.D.M. (2007) Superchannel of zero spirals. 
Journal of Transfigural Mathematics, 1, 63-64, 104-105.



Wheeler,



Wordsworth, W. (1815) Essay Supplementary to Preface









----- Original Message ----- 
From: "Joan Lucy Conolly" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Thursday, April 15, 2010 2:07 AM
Subject: Re: Design as Research


> Dear Sue
>
> What a lovely thought ... "circles of influence ... to ask the I, we and 
> them questions differently"! May I quote you in our meetings please?
>
> Joan
>
>