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
>
>
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