‘Nested Holeyness’..a neat treatment to enjoy

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`Nested Holeyness': the Dynamic `Inclusional' Geometry of Natural

Space and Boundaries

 

By Alan Rayner

Dept of Biology and Biochemistry, University of Bath, Claverton Down,

Bath BA2 7AY, U.K.

 

SUMMARY

Modern understanding of dynamic processes of all kinds, from subatomic

to universal scales and encompassing the evolution of living systems,

continues to be restricted by the rationalistic treatment of

boundaries as discrete limits and space as distance between material

objects. Such treatment is founded mathematically in the geometry of

Euclid and arithmetic of discrete numerical units, which formed the

basis for Newtonian mechanics and the development of objective,

quantitative science aimed at prediction and control. It is, however,

profoundly unrealistic in being based on the illusion that matter

ultimately consists of solid, massy particles surrounded by (and hence

excluding) non-interactive space. This illusion leads to the dualistic

`paradoxes of completeness' that underlie the interpretation of change

as the consequence of imposing purely external force upon discrete

(isolated) and hence independent bodies, seen in life forms as the

location of individual selves.

 

A radically more creative, realistic and ultimately less

environmentally, socially and psychologically damaging perspective

opens up when it is acknowledged that space, as insubstantial

`possibility for movement', permeates within, around and through every

`thing'. There are no paradoxes of completeness in this perspective

because there are no discrete bodies - no isolated wholes. Far from

being complete, fixed Euclidean surfaces that simply divide insides

from outsides, boundaries both form and are formed by the co-incidence

of inner and outer inductive realms as complex, variably resistive,

dynamic, space-incorporating transitions. As such, they both

distinguish and reciprocally couple the local, inner (`individual')

and non-local, outer (`collective') callings of uniquely situated

waveform features of energy-space - relational places rather than

discrete entities - nested over all scales and identifiable in life

forms as `complex selves'.

 

Rationalistic Detachment and the `Individual Self'

I have heard it said that aboriginal people, when asked to draw a

`self-portrait', draw their surrounding landscape. Likewise, as

children, we do not initially differentiate between what we see and

who we are - instead we feel utterly self-absorbed in an ever-changing

bubble of life, rich with toings and froings, comings and goings,

hunger and satiation.

 

Later in life we may yearn to recover this sense of `no separation',

`oneness' or `unity' and seek it through meditation or other means.

And in the wake of the emergence of deconstructive postmodern

philosophies and reaction to the harsher strictures of Enlightenment

dualism and scientific reductionism, this same search is a feature of

many current `holistic' movements.

 

It is as though something vital is lost or ignored when distinctions

are made between inside and outside, `self' and `other', and the

resulting pain leads to a desperate quest to return to a primordial

condition of `no boundaries'. Here, however, I suggest that it is not

the existence, but rather the perception of boundaries, through which

inner-outer distinctions are made, that can bring about loss. If we

change our currently predominant rationalistic view of boundaries as

discrete limits, to what I and others have called an `inclusional'

view of boundaries as pivotal places of co-creative relationship, i.e.

`togetherness', then the vital contextual space that otherwise would

be excluded is brought back into our consideration. We do not have to

abandon all we have learned and invented through making distinctions,

but we do need to recover all we have lost, and heal the

environmental, social and psychological damage we have engendered, by

regarding these distinctions as absolute. So, what form of perception

and logic has brought us to this pass, where we need to recover, and

how has it affected our understanding of our relationships with one

another and the living world we inhabit?

 

Solidity - A Divisive Illusion

As land-inhabiting creatures unable to digest herbage and so needing

to find and catch or grasp localized sources of food as well as to

avoid or overcome danger, we couldn't survive for long without being

able to make distinctions. Making distinctions is therefore an

essential part of our early learning, urged on by our caring elders

and aided by our physical senses, especially our primates' binocular

vision.

 

One of the most important distinctions we learn to make, aided by

peering into some reflecting surface like a pond or mirror, or the

facial expression of a friend, relation or adversary, is between what

lies within our skin and what lies outside it. Then, as our focus

swings from subjective to objective, we become conscious of our animal

body and its vulnerabilities as the location of our individual self,

and of other bodies as potentially threatening or useful other selves

or `things'. We become prone to lose our immersed sense of inclusion

of all we survey and, if we are not mindful, may come to regard that

sense as a childhood fantasy to be put aside as we grow up and adjust

to the `real' world. And that is when the trouble starts, because that

is when we really do become subject to a profoundly alienating

illusion that excommunicates us both from nature and the real nature

of ourselves: the illusion of solidity.

 

We become focused on the explicit substance that appears to constitute

our bodies and the ground beneath our feet that fixes our location,

and regard whatever is insubstantial, undetectable by our physical

senses, as `nothing' - an absence that isn't a presence yet puts

distance between one `thing' and an other. We abstract space from

matter, and regard matter, and where matter is located as if sealed

within a fixed boundary and hence definable as `property', as all that

matters - `everything'. We become `materialists' and `individualists'

inhabiting an incoherent world and universe of what appear to us as

independent, solid objects that have to be forced into motion.

 

The journey towards materialism and objectivism is not only a

feature of our developmental individuation as we approach adulthood,

becoming increasingly adept at making distinctions. As has been widely

documented, it is also a feature of the western philosophical journey

that culminated in the Scientific Revolution and Enlightenment (e.g.

Tarnas, 1991; Spretnak, 1999). It has become deeply ingrained in our

mathematics and our science and, thereby, in our modern culture. And,

for all the technological innovation this culture has spawned, far

from fulfilling its potential as a source of mutual support and

inspiration, it has become for many a deeply distressing

`Anti-culture'. Founded in an illusion of discreteness, the isolation

of matter from space, it is a culture riven by the conflict and

paradox implicit in what might aptly be called the `anti-logic' of

`one' (`self') against `other' (`non-self').

 

`Anti-logic' in the Foundations of Mathematics

Many of us, I suspect, must recall with some dismay those occasions

when as children we were called inside from the playground of our

imagination, to learn to count and add, subtract, multiply and divide

numbers. Maybe we felt, consciously or unconsciously, a profound sense

of imposition and alienation from the world in which we naturally

belonged. If so, we had good reason!

 

Numbers, as we have mostly come to define and use them and

ironically describe as `natural', are anything but natural. Rather,

they are an abstraction from nature - an expression of material

content freed from spatial context and so treated as discrete,

independent `units'. According to the underlying anti-logic, one thing

has to be distinguished from no thing, it can't be something and

nothing at the same time - either it is or it isn't. In the words of

the song, `Green Grow the Rushes - O', `one is one and all alone and

ever more shall be so'. So, what, then, is two? According to the

anti-logic, two is, quite simply, no more than two independent ones,

and this notion is indeed the basis for the `law of superposition' and

linear condition of proportionality, whereby `the whole is the sum of

its parts'. But the fact that two isn't the same as two independent

ones becomes evident as soon as we multiply it by itself (i.e. apply a

`power' function), whence it makes four rather than two. Two includes

`something extra' that enables the two ones to `act together' to

produce `something extra', sometimes described (because only its

manifestation rather than its latent presence is evident from an

external viewpoint) as an `emergent property', that makes the `whole'

greater than the sum of its parts - i.e. non-linear. And this

something extra that produces something extra is no more and no less

than the inter-permeating space that couples the two ones as distinct,

but not discrete, identities. But according to the anti-logic, space

is nothing…

 

Useful though it may be in performing linear calculations, it is

clear that the treatment of numbers as independent, space-excluding

entities representing pure `substance' or `content' freed from

`context' - as `figure' freed from `ground' - is deeply paradoxical.

As was demonstrated by Kurt Gödel in his mathematical formulation of

the famous Cretan liar paradox, in which a Cretan informs you that all

Cretans are liars, the problem is one of assuming `completeness'. Any

`complete' or `entire' object that thereby has nothing outside of

itself, is inescapably self-referential and so impossible to verify or

falsify `independently' (e.g. Hofstadter, 1980).

 

Yet further paradox arising from focusing on content abstracted

from context, is contained in the second great foundation of

mathematics, Euclidean geometry. How can a `point' have no dimension,

a line no width and a plane no depth? Only by distilling all the space

out of it until we are left with `something' infinitesimally `pure'-

the indivisible, solid, massy atomic particles - the `building blocks

of the Universe' envisaged by Democritus and Newton alike. In reality,

such `point masses' cannot exist, and indeed, not for want of trying,

we have never found them as we have probed deeper and deeper into the

fundamental nature of `matter'. All we have found is distinctive

places - waveforms that we nonetheless describe as `fundamental

particles', so habituated are we to the notion of `solid substance'.

 

`Anti-logic' in the Foundations of Mechanistic Science and Objectivity

Despite the logical and practical impossibility of isolating matter

from space (and vice versa), and despite its own findings in

relativity, quantum mechanics and the dynamics and irregular geometry

of non-linear (complex) systems, science continues to be practised by

many according to purely Newtonian/Cartesian, deterministic

principles. This is because these principles are deeply embedded in

`objective scientific methodology' and its underlying mathematical and

philosophical framework.

 

Objective scientific methodology always starts by imposing a rigid

frame, actual or theoretical, around some isolated fragment of nature

from which the observer is excluded, and then proceeds to test

`falsifiable hypotheses' about events occurring within this frame by

means of quantification and experimentation. Nature is brought into

laboratories, contained in various vessels, purified from

`contaminants' and located in `controlled environments' where the

effects of `one variable at a time' can be tested. But the question of

how what can be quantified within this frame actually relates to the

reality outside the frame cannot be addressed by this approach alone.

The `certainty' about whatever is in the frame therefore comes at the

expense of enormous uncertainty about the relevance of the findings to

the `real world'.

 

The forlorn hope is that all the `small pictures' of Nature captured

within the isolated frames will somehow `add up', like the pixels on a

TV screen, to yield the `big picture'. It is rather like trying to

study and represent a river based solely on an examination of the

behaviour of the contents of cups dipped into the river! The outcome

is a headlong fall into the paradoxes of completeness. These paradoxes

are implicit in Heisenberg's uncertainty principle and `wave-particle

duality' and expressed in such notorious conundrums as Schrödinger's

cat, whose uncertain `state' of `life or death' is an artefact of

being sealed in a box with a vial of cyanide (see, e.g. Coveney &

Highfield, 1992).

 

In reality, the process of abstraction decontextualizes and so

devitalizes the dynamic system under investigation, by fixing or

`freeze-framing' its contents so that they can only be moved by

external force. Investigation therefore begins by immobilizing and

sundering the system and its contents, and then uses the result to

conclude that the system is made up from discrete components that have

to be mobilized into action from a static initial condition. This

conclusion is a non-sequitur, because the common-space inner-outer

connection that gave the system its dynamic coherence in the first

place has been systematically removed in the process of investigation!

Once shattered, all the King's horses and all the King's men cannot

put a lively Humpty together again! Vitalism, for all the railings of

positivist thinkers, had a very `real' point, or - should I say -

connection to make!

 

All this is not of course to say that objective scientific methodology

is useless, only that it cannot in itself offer a realistic

representation of nature. If, however, an effort is made to compare

the behaviour of abstracted fragments from nature with an experiential

knowledge of natural systems, then real insights may be found in the

differences and similarities that show up. For example, a comparison

between the behaviour of water in a cup and in a river may revealingly

inform us about the effects of isolation on the natural mobility of

fluids, and hence deepen our contextual understanding of the latter.

 

`Anti-logic' in the Foundations of neo-Darwinian Evolutionary Theory

Nowhere is the anti-logical dislocation of discrete bodies from their

spatial context as `individual selves' more obvious, or more profound

in its influence on the way we regard our relationships with one

another and other life forms, than in the notions of `natural

selection' and `survival of the fittest'. Here, we have an archetypal

collision between the judgmental, externally imposed `other' force of

the surrounding `environment' and the `removable object'. Those

objects that do not conform, i.e. are not `adapted' to the

requirements of the environment, suffer the death penalty of

extinction in a competitive struggle for existence with their

neighbours. Behaviour that is not in the individual self-interest of

these objects (ultimately, genes) is, therefore, not tolerated by the

system (Dawkins, 1989).

 

The implicit `fixed framing' in this concept of evolutionary

processes, following on from Malthusian principles of limits to

population growth, is evident in the way that `natural selection' is

commonly portrayed as a `pressure' imposing restrictions on the

expansive potential of its subject objects. This pressure intensifies

as population growth squeezes out available resource/space so that

ultimately only those entities with particularly favoured

characteristics can endure.

 

There are deep contradictions in this representation, arising from

its failure to incorporate the creative interplay between life forms

and their living space, whereby each reciprocally transforms the other

in a simultaneous process of attunement rather than a sequential

process of adaptation of one to the fixed other. Far from creating

diversity, the effect of adaptation and competition in a fixed space

is actually the inexorable drive towards monoculture, implicit in the

notions of `competitive exclusion' and `adaptive peaks' (e.g. Futuyma,

1986). And far from enhancing `efficiency', the operation of systems

at their most intensely competitive greatly increases wastage. Natural

selection, as it is most widely and popularly represented, is

profoundly counter-evolutionary, dissipating energy and impeding

innovation (Rayner, 1997).

 

`Anti-logic' in the Foundations of Educational, Social and Economic

Institutions

Anti-logic has literally become `institutionalized' in our modern

Anti-culture, an abstractive, deeply self-contradictory, social and

economic reality that is diametrically opposed to the reality of

natural processes. Having intellectually and physically dislocated our

selves from one another and our living space, we get caught between

our requirement to perfect our individual selves as complete,

independent, entities in competition with others, and our need to

regain the social coherence that we lose in the process. In believing

our selves to be fundamentally `free', and prepared even to fight for

this principle, we simultaneously fear the `disorder' of a

`free-for-all' society, and so try to impose limits on our

intrinsically `selfish' behaviour. We do this by means of a multitude

of restrictive governmental frameworks and practices, characterized by

pyramidal hierarchies that redistribute power from the many to the

few. A common feature of these organizations is the presence of an

administrative centre, a purely internal `regime' that

self-perpetuates through the imposition of `rules of behaviour' that

militate against any kind of `otherness' (outside interference).

Conformity with these rules - in educational terms, the reproduction

of anti-logical `received wisdom' - is regularly tested and rewarded

with promotion to positions closer to the highly resourced centre.

Non-conformity - `indiscipline' - is punished and marginalized.

 

So we live by double standards, competing to conform and treating life

as a `game' whose rules we try to turn to our best individual

advantage. As Dawkins (1989), ironically puts it, `Let us try and

teach generosity and altruism, because we are born selfish'!

 

So much for our much vaunted `freedom' and `democracy'! If we look

carefully at the hierarchical structure of our Institutions, it

quickly becomes apparent that they are neither free nor democratic in

serving the interests of all the people. Even if the governing regime

is democratically elected, its executive processes exclude and stifle

the views and needs of minorities (`majority rule' is not democracy)

and place inordinate power in the hands of a few.

 

Our Institutions are also profoundly ineffective in their internal

communication, profoundly inefficient in the way they waste human

effort and profoundly unresponsive to change. This is because they

operate within fixed limits (artificial demarcations) along

predominantly radial lines of communication, which distance the centre

from the periphery - the few from the many at the interactive margin

of the system. They create bottlenecks and fail to allow lateral

links to by-pass the hub. As will be discussed below, the latter links

are vital to reduce resistance to flow and allow effective

redistribution in real life parallel-distributing networks like

nervous systems, blood systems and fungal mycelia.

 

In the end, everyone suffers in the Institutions of Anti-culture.

Those `winners', who `succeed' by `playing the game' according to

individual self-promoting rules, lose their opportunity to relate

complementarily with others. Those who `lose' by not playing the game,

become impoverished. Resentment, pain and conflict abound in all

directions. Creativity is impeded by central bureaucracies, which

impose restrictions but do nothing to ease flow.

 

`Inclusional' Togetherness and the `Complex Self'

Clearly, although it has its uses, there are profound limitations and

contradictions inherent in the detached view of individual selves,

abstracted from context like `babies from bath water'. On this, there

is widespread agreement in postmodern thinking. There is less clarity,

however, about what lies at the heart of the difficulties with

rationalism in terms of its underlying presuppositions, and the nature

of the context that it abstracts from. Consequently, a variety of

different responses to these difficulties have developed, some of

which have the character of `jumping from the frying pan into the

fire' and others of substituting one kind of fixed reference frame for

another.

 

One reaction, that of deconstructionists, to the rationalist claim

to have a hold on `reality' through objective, `value-free',

quantitative methodology, has been to argue that no-one can be free of

the power relations of their social context, and hence that reality is

beyond our individual reach. Every `truth' claim we make is thereby

seen as a `social construction', to be rigorously taken apart by

discourse analysis - something which I have myself been subjected to

when trying to express my thinking about `inclusionality' (Bluehdorn,

2003; cf Rayner, 2003). Although the deconstructive approach is most

commonly regarded as synonymous with `postmodernism', it is in fact

rooted in the very socio-political context of `Anti-culture', which

emerges from the excommunicative anti-logic of rationalism. It might

therefore be more aptly described as `hypermodern', in contrast with

what Spretnak (1999) describes as `ecological postmodernism' of which

I would regard `inclusionality' as a development.

 

Whereas deconstructionism therefore takes the unrealistic

consequences of abstraction to the opposite extreme by denying access

to natural reality and so `losing the baby whilst reclaiming the bath

water', ecological postmodernism questions the realism of objective

rationality's dualistic presupposition of `isolation' or

`independence' and implicit denial of `relationship'. This form of

postmodernism has been most widely expressed in the `Green' and

`Holistic' movements' claims for `unity in diversity', `wholeness' and

`interconnectedness' and associated metaphors like `web of life' (e.g.

Spowers, 2002). Protagonists of these movements have a strong

tendency, however, to deny the reality of the detached view of the

external observer by denying the existence of an `outside' and hence

developing a totally internalized, subjectively immersed view. In

effect, they equate the `baby with the bath' as an `ecocentric' or

`ecological' as opposed to `egocentric' `self' (Macy, 1991). They

substitute the binary/dualistic, `many wholes/parts' view of isolated

entities for a unitary/monistic `non-dual', `one whole' view of `no

boundaries' and `no separation', akin to that we may have before we

begin to develop the notion of a distinguishable `self'.

 

This `return to origin' is often accompanied by more than a little

hypocritical spiritual pride and `all sweetness and light' claim to

`higher consciousness'. It can be quite excluding and disparaging to

those who `haven't got there', demanding that they `must change' if

they are to be allowed entry to the `club of the righteous' and `save

the planet' (Laszlo, 2002). But the change demanded is from one kind

of unrealistically imposed framework (isolated boxes) to another (all

in one box) and so may be just as restrictive, subject to the

paradoxes of completeness and denying of the human condition, if not

more so. By explicitly or implicitly denying the existence of

boundaries, holistic thinkers are prone to ignore the very place

through which the dynamic relationships and diversity that they

propound are mediated. They end up speaking vaguely and mystically

about `interconnectedness', complex `webs' of relationship,

`self-organization', `subtle energies', `vibrations', `Gaia theory',

`tight coupling', `yin-yang' and the like, without anywhere to relate

these concepts to.

 

The Holeyness of Dynamic `Reality'

How very different the picture we have of reality becomes, as soon as

we acknowledge that space, in the sense of insubstantial `possibility

for movement', permeates within, around and through every `thing'.

There are no paradoxes of completeness in this perspective because

there are no discrete bodies - `complete wholes', only holey

embodiments that both include and are included in space. Far from

being fixed, depthless Euclidean plane surfaces, complete coverings

that isolate insides from outsides, boundaries both form and are

formed by the co-incidence of inner and outer inductive realms as

complex, variably resistive, dynamic, space-incorporating transitions

from one depth or region of heterogeneous space to another. As such,

they simultaneously both distinguish (differentiate) and reciprocally

couple (integrate) the local/inner and non-local/outer domains of

uniquely situated waveform features - relational places rather than

discrete, objective entities. And space, far from being the distancing

source of incoherence in the universe is actually an `attractor': the

resistance-less, `nothingness' that coherently pools or calls `every

thing' together through its gravitational, inductive influence, which

becomes more powerful the deeper (more curved/internal), and hence

more associated with mass, it is. We shift focus from the explicit

distribution of matter through space, to the implicit distribution of

space through matter, and in so doing glimpse the `bigger picture' of

our human place in the living world and universe, a dynamic `nested

holeyness' of inner within outer callings, across all scales.

 

In living systems, the waveforms resulting from the necessary

togetherness (distinctness but not discreteness) of inner, outer and

intermediary callings may be thought of as `complex selves'. Rather

than being unitary or binary, ecocentric or egocentric `beings', such

couplings represent ternary `becomings', dynamic `threesome-onesomes'

where `two' implies `one' and `three' simultaneously - babies combined

recreationally and unpredictably with water (twoness) via skin

(threeness) in the spatial commons (oneness) of the bath! Their

behaviour is therefore ultimately intractable to rationalistic logic,

as implicitly acknowledged by Newton `himself' in his analysis of the

`three body problem' (Montgomery, 2001).

 

The concepts of `complex self' and `nested holeyness' were

anticipated by Koestler (1976) in his descriptions of `holons' - as

`Janus-faced' entities combining individual and collective aspects,

and `holarchies' - as nested arrays of holons, in his `Open

Hierarchical Systems Theory' (Rayner et al., 1984). These descriptions

of a `Russian doll' kind of nesting, also alluded to by Caldwell et al

(1997) and Wilber (1996), are, however, made all the more pertinent to

our understanding of dynamic reality, when the necessary

incompleteness, and consequent transformability (indeterminacy) of

space-incorporating boundaries is introduced. We then move from a

`wholes within wholes' or `worlds within worlds' description of

`things' as objects, to a `holes within holes' or `whorls within

whorls' description of identifiable places. Not only is every `thing'

necessarily both a grouping of smaller `things' and grouped with

others in some `thing' larger, but the incompleteness of boundaries

ensures that there is communicative spatial relationship and the

possibility for transformation across all scales.

 

The pivotal role of boundaries as dynamic, co-created, co-creative

intermediary places reciprocally coupling the inner and outer callings

of complex selves was effectively recognised almost two millennia ago

in the T'ai Hsüan Ching of Yang Hsiung (Walters, 1983; Rayner 2002).

As with `inclusionality', the T'ai Hsüan set out to acknowledge an

essential presence (`Jen') coincident with and communicatively

balancing between emergent dualistic polarities (Ti and T'ien). These

polarities were akin to the reciprocally coupled Yin and Yang of its

predecessor, the I Ching, but the latter was extended into an

explicitly ternary logic through the introduction of a dynamically

balancing, intermediary agency. Walters (1983) argues that the

paradoxes of incompleteness or `fallacy of the excluded middle' could

be `avoided if only philosophers could train themselves to consider

that between the two extremes there is always a third force, Jen.

Progress continues by the interaction of T'ien and Ti, but only Jen

can change the direction, add the unknown quantity, and create.'

Ancient ternary logic is also evident in the Christian Holy Trinity of

Father, Son and Holy Ghost; in the Kabbalah's pillars of Severity,

Grace and Mercy, and the Threshold between `unreal' Knowledge and

truth-less Fantasy symbolized by elastic `male' and plastic `female'

statues in the Hibernian Mystery Centres (Steiner, 1997).

 

In terms of this ternary, `dynamic framing', complete sealing of

boundaries would disrupt and stifle flow, whereas total dissolution of

boundaries would end in featurelessness. So both the pursuit of

absolute individual autonomy (independence) through the completion of

external boundaries, and of absolute collective unity (dependence)

through the obviation of internal boundaries are evolutionarily

untenable. By contrast, a holey intermediary boundary provides the

possibility for `breathing space' and consequent energy transfer

between dynamically coupled inner and outer inductive domains. Closing

in (decreasing holeyness) of boundaries results in `information', the

constructive shaping of local `features' and increased resistance to

energy transfer both from outer to inner (inspiration/ in-welling) and

from inner to outer (expiration/out-welling). Opening out (increasing

holeyness) of boundaries results in `exformation', and consequent

decreased resistance to energy transfer.

 

The complementary interdependence of generative and degenerative

processes via dynamic boundaries between inner and outer is therefore

inescapable. Space, though we may perceive it rationalistically as

`darkness', `imperfection' and even `mortal sin', cannot be excluded

from a vital, evolutionary system, try as we might in the

rationalistic pursuit of `perfection' in the form of individual or

collective completeness (wholeness). To find such `perfection' would

imply eternal stasis, a profound inertia of the kind approached (but

even then, not absolute) by the noble gases and in deep meditation.

Rather, in the excitable, dynamic world and universe that is drawn

towards such perfection through balanced relationship, outside yields

to and feeds the growth of inside, which yields in turn to outside in

natural renewable cycles and spirals. These natural inspirations and

expirations are disrupted, and even reversed, by the rationalistic

severance of one from the other.

 

Consequently, when we simplistically abstract our individual human

`inner selves' from their complex relation with our collective `outer

self', the ensuing conflicts feed death and dysfunction with life

rather than allow death and dysfunction to feed life. We either act

`selfishly', by disregarding our outer calling or `sacrificially' by

disregarding our inner calling. To avoid such fates, it is necessary

both to inform (manifest) and exform (relax) our inner-outer

boundaries, in ways that attune rather than dislocate the needs of our

complex individual and collective natures, as they continually

transform our circumstances through their dynamic, reciprocal

relationship. And, by its very nature, there can be no fixed

rationalistic rules or formulae to guide such attunement: only a

sensitive, instinctive or experiential feeling, or empathic

`awareness' of one for the other can work, mediated through their

dynamic, interfacial boundary.

 

Inclusional Logic in the Mathematics of Dynamic Systems

Any mathematical formulation of ternary logic needs to account for the

reciprocal, simultaneous dynamic relationship between inner and outer

spatial domains or callings of embodiments identifiable as places

rather than objects. Correspondingly, rather than treating numbers as

an expression of pure material content, with `zero' representing

`absence' and `infinity' representing `limitless amount', it would

make sense contextually to regard zero as `inner-outer balance'

(stationary boundary condition) and infinity as inner and outer

spatial possibility. So, too, would the treatment of numbers as both

giving rise to and containing one another as potentialities, as

expressed in some variants of `Green Grow the Rushes - O' (Stewart,

1976), in the Kabbalah, in Hopi native American culture and,

conceivably, in some Neolithic rock art (cf. Bradley, 1995).

 

Given the rationalistic nature of the foundations of mathematical

practice, however, it is not surprising that, as yet, there has been

little explicit attempt made to incorporate inclusional or ternary

logic, with the notable exception of the fluid logic

(threesome-onesome) number system and associated spiral geometry of

Shakunle (1994). For the most part, even when dealing with dynamic

processes, mathematical analysis begins with discrete, space-excluding

definition(s) of its frame(s) of reference (entities and initial

conditions). Although the effect of incorporating space is evident

from analyses of `non-linear dynamical systems', `fractal geometry'

and associated `irrational' and `imaginary'/complex numbers (see

below), what appears as `emergent' from these analyses may therefore

`really' be a manifestation of what is already implicitly present in

natural process geometry.

 

Fractal geometry is the nearest approach that conventionally

fixed-framed mathematics has made to the natural geometry of `nested

holeyness'. This kind of geometry was developed by Mandelbrot (1977)

as a way of describing structures whose boundaries, unlike Euclidean

surfaces, appear progressively more complex/irregular, in

`self-similar' patterns, the more closely they are observed.

 

Fractal structures can be quantified by allowing their dimension,

expressed as a relation between the logarithms of their material

content and radius of spatial field (i.e. `context') containing this

content, to be fractional as well as integral. They can be generated

computationally by means of `iterative' processes in which the

`output' from the `input' (which, despite the claim that they are

`deterministic', imply continued openness to outside space) of a

number into a non-linear equation is successively `fed back' into the

equation as `input'. A famous example is the `Mandelbrot set', made by

mapping the distribution of points in the `complex plane' that do not

result in infinity when iterated according to the rule, z & #8594;z2 + c,

where z begins at zero and c is the complex number corresponding to

the point being tested. Here, a `complex number' is a number that

consists of a combination of a `real' and an `imaginary' component,

the latter being a derivation of, `i', the square root of -1. The

complex plane is formed in the space defined by placing all `real'

numbers, from - & #8734;, through 0, to + & #8734; along a horizontal line, and all

`imaginary' numbers, from - & #8734;i, through 0, to + & #8734;i, along a vertical

line, and using these Euclidean lines as co-ordinates. In effect, it

represents a way of increasing the `possibility space' for numbers to

inhabit, as discrete entities, from one to two dimensions.

 

The remarkable feature of the Mandelbrot set is the extraordinarily

complex boundary that occurs between points within and points outside

the set, in effect between an inner attractive space of zero and an

outer attractive space of infinity. Such complex boundaries formed

between neighbouring attractive spaces or `attractors' have more

generally been referred to as `fractal basin boundaries', and they are

clearly at least analogous to the complex, ternary boundaries of

natural process geometry. Where, however, the conventional abstract

mathematical representation of such complexity begins prescriptively

with an implicit or explicit definition of content and container that

replaces their simultaneous (resonant) reciprocal relationship with

sequential `feedback', the natural might be said to originate in

indefinition - a realm of endless possibility. Here, distinctions

inform, exform and interact as coupled threesome-onesomes of

energy-space, that co-create the phenomenal heterogeneity of dynamic

nature in which time and matter, as separable quantities, are

illusions. Abstraction can only hold a mirror up to this reality, and

so capture a localized, inverted, and potentially deeply illusory

image of it.

 

Inclusional Logic in the Science of Transformation

So what? What does this `inclusional' view of space and boundaries

change as far as our scientific perceptions of nature are concerned?

Most fundamentally, I suggest that it changes our understanding of

change. It becomes possible to assimilate our scientific discoveries

into a context where the dynamic nature of context can be adequately

accounted for rather than excluded from consideration as `external

interference' or `noise'. Rather than beginning, through the

imposition of a fixed reference frame, with an assumption of stasis

that has to be `forced' into action from `outside', the very nature of

nature is understood to be dynamic. And with this understanding, our

concepts of causality and uncertainty also change. Rather than

regarding change as externally enforced and hence reversible movement

measured as a progression through space against intervals of absolute

time, all change is understood to involve the transformation of space

and consequent simultaneous alteration in both content and context and

their reciprocal relationship. Since this transformation necessarily

involves a change in content-context, it is, by its very nature both

irreversible and unrepeatable - unable to return directly or

indirectly to exactly the same place that it emanated from. Far from

being reproductive, producing more of exactly the same, Nature is

continually recreative and autocatalytic- opening up and building upon

new possibilities for itself. As was said so long ago by Heraclitus,

`you can never step in the same river twice'. Content and context,

stream and catchment, continually re-shape one another in an

ever-transforming flow of place. This place is dynamically framed by

itself as a complex waveform - a resonant coupling of inner with outer

energy-space, as was effectively recognized, albeit in a conventional

mathematical framing, by the communication theory of Dennis Gabor

(1946). Long neglected scientifically, but now being rediscovered,

this theory provided the basis for Gabor's Nobel Prize-winning

invention of holography, key to which was the notion of a `complex

signal' as a reciprocal combination of real and imaginary components,

rather than an independent pulse of information.

 

Inclusional Logic in the Evolution of Community Life

As I have already alluded to, the conventional fixed framing of

reality, and consequent precedence given to explicit material content

over implicit spatial context, leads inexorably to an emphasis on

competition between independent entities in considerations of

evolutionary processes. Taken to extremes, this emphasis can result in

the suggestion that `there is no such thing as society/community',

because the requisite co-operation in such a collective organization

would compromize individual `self-interest'. Both diversity and

co-operation are deeply contradictory, if not `irrational' and

`unnatural' concepts according to this view, and so, if they are to be

desired or tolerated at all in human societies, can only be sustained

by legal and educational enforcement.

 

By contrast, an inclusional, dynamically framed view that

originates with spatial indefinition and the manifestation of distinct

features in the first place as ternary, resonant waveforms of coupled

inner-outer domains, sees both co-operation and diversity in the

attunement of one with the other, as primary qualities of a

heterogeneous universe. Competition, on the other hand, results from

the attempted enforcement of distinctive identities, through the

imposition of a fixed reference frame, into exactly the same space or

`niche'. For many sensitive human beings, such enforcement, which

either denies their differences or sets these `at odds with' rather

than `in complementation' with others', feels deeply unnatural and

disempowering, for good reason.

 

In the inclusional view of the `complex self', there is therefore

nothing unnatural or contradictory about co-operation and diversity,

nor, for that matter, about outwardly `aggressive' behaviour that

sustains diversity through the assertion of local identity (Rayner,

1991, 1996, 1997). Rather, what we have, as many ecologists implicitly

or explicitly recognize in natural `ecosystems' and their inhabitant

`communities', is a dynamic `togetherness in diversity' or

`complementarity of labour'. Here, the collective and individual,

`the forest and the tree', both necessarily incomplete, continually

reconfigure one another as they explore and manifest the realm of

possibilities.

 

The irony is that we continue to find it virtually impossible to

apply this understanding to our own human communities, even though it

is, for many, only `common sense', obvious from our everyday

experience of relationships with one another and our living space.

This may be because our logical predisposition to freeze-frame reality

continues to cause us to seek `consensus' as `sameness' rather than

`complementarity' of view, whilst aspiring to individual perfection

through competition in an adversarial anti-culture. Even when we

proclaim our `interconnectedness', we mentally insert the connections

between initially disconnected independent entities that have to be

`joined up' - and so appear as `nodes' in a `web' or `tree' of purely

transactional relationships, as in modern network theory (Buchanan,

2002; Barabási, 2002). We fail to recognize that, rather than needing

to be `added in,' the connection is implicit, already there to be

co-discovered through relaxation of individual boundaries. And this

failure brings dangers if it is used to identify entities at the `most

pivotal nodes' as `the least dispensable'. In conservation biology,

such entities are described as `keystone species', with the inference

that they should be `preserved at all costs' (Scott Mills et al,

1993). In fact, a close examination of the so-called networks upon

which such conclusions are based shows them actually to be

dendritically branched strings or webs of nodes, produced, as

described above, by joining up initially discrete entities. They

therefore lack the intrinsic lateral connectivity of true, functional

natural networks like fungal mycelia, but resemble aberrant,

dysfunctional forms of the latter (K.J.J. Tesson et al., in preparation).

 

Creative Boundaries and the Diversity of Organic Life as an Embodied

Water Flow

During the twentieth century, two dramatic technical breakthroughs

combined with rationalistic philosophical inquiry to yield a

distinctive new vision of the nature and origin of life and living

things, including human beings. The discovery of the genetic code and

advent of modern computers, when viewed in the light of a detached

perspective projected an image of evolution as the spread and

diversification of genetic information, and of life forms as

information processors - computational machines. Correspondingly, more

and more effort has been put into discovering firstly the

calculational procedures or `algorithms' that underlie behaviour and

pattern generation amongst life forms and secondly the physical and

chemical mechanisms through which these algorithms operate. Once we

know these procedures and mechanisms, it is assumed we can have a good

understanding of what makes life `tick', in essence like clockwork.

 

The inclusional bringing together of immersed with detached -

subjective with objective - views of the dynamic boundaries of nature

and self, challenges this dry, mechanistic depiction of life forms by

restoring the watery context that sustains life as an ever-changing

flow. Life forms are not discrete computational machines processing

digital information. DNA is not transmitted `on its own' from `one

generation to the next', but flows through a continuum of watery space

that ultimately includes even `extinct' ancestors. DNA is not

`information in itself', which means the same anywhere, but rather

gives and is given meaning through its dynamic relation with protein

in the contextual medium of water retained within boundaries of

variable deformability, permeability and continuity. And this meaning

can change with context, just as the meaning of words in this sentence

can change in the context of other words and spaces and sentences. And

context lies inseparably both within and around the boundaries of

organic life forms, as we know them on Earth, as embodied water flows

responding to and producing change, like a river that both shapes and

is shaped by landscape.

 

I therefore see rivers both as a valuable metaphor and an actual

description of the `complex self' as a dynamic embodiment of inner or

individual or local space with outer, collective or non-local space.

We see riverine form whenever we look at life as an ever-unfolding,

enfolding presence, rather than in freeze-framed snapshots giving the

illusion of discrete individual entities. We see it in the branching

and anastomosis of fungal mycelia, blood systems, trees, leaf veins,

nervous systems, wildebeest herds, ant swarms, phylogenies and

pathways of all kinds (Rayner, 1997, 1998; Rayner and Way, 1999).

 

Simply by `tuning' the `holeyness' and consequent permeability,

deformability and continuity of their inner-outer boundaries, to

relate to internal and external availability of oxidizing and reducing

agents, life forms change pattern and process as they create and

respond to changes in their dynamic context. They `self-differentiate'

outwardly, through the proliferation of inner-outer boundaries when

and where there is plentiful external energy-supply, and

`self-integrate' inwardly through the fusion, sealing and

redistribution of these boundaries when and where there is external

shortage (Rayner, 1997, 2000; Rayner et al., 1999). In this way they

have generated the expanding diversity of Earth's `biosphere'. Until now…

 

Acknowledgements

I would like to acknowledge the inclusion of many correspondences with

complex self-identities in what I have written here. I won't `single

them out', but I am sure they will know `who' they are!

 

References

 

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Publishing.

 

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philosophy and simulative politics. In Towards and Environment

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Warhurst, eds.), pp 21-45. London: Palgrave Macmillan.

 

Bradley, R. (1995) Making sense of prehistoric rock art. British

Archaeology 9

 

Buchanan, M. (2002) Nexus: Small Worlds and the Groundbreaking Science

of Networks. W.W. Norton & Co.

 

Caldwell, D.E., Wolfaardt, G.M., Korber, D.R. and Lawrence, J.R.

(1997) Do bacterial communities transcend Darwinism? Adv. Microbial

Ecol. 15, 105-191.

 

Coveney, P. and Highfield, R. (1992) The Arrow of Time. New York: Fawcett.

 

Dawkins, R. (1989) The Selfish Gene. New edition. Oxford University Press.

 

Futuyma, D.J. (1986). Evolutionary Biology, 2nd Ed. Sunderland,

Massachussets: Sinauer Associates

 

Gabor, D. (1946) Theory of communications. Jour. Inst. Elec. Eng.

(London), 93, 429-457.

 

Hofstadter, D.R. (1980) Gödel, Escher, Bach: An Eternal Golden Braid.

England: Harmondsworth.

 

Koestler, A. (1976) The Ghost in the Machine. London: Hutchinson

 

Laszlo, E. (2002) We Can Change the World: A Practical Guide to

Thinking and Living in the 21st Century. Club of Budapest.

 

Macy, J. (1991) World as Lover, World as Self. Berkeley: Parallax Press.

 

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

 

Montgomery, R. (2001) A new solution to the three-body problem.

Notices of the AMS 48, 471-481.

 

Rayner, A.D.M. (1991) The challenge of the individualistic mycelium.

Mycologia 83, 48-71.

 

Rayner, A.D.M. (1996) Interconnectedness and individualism in fungal

mycelia. In A Century of Mycology (BC Sutton, ed), pp. 193-232

Cambridge University Press.

 

Rayner, A.D.M. (1997) Degrees of Freedom - Living in Dynamic

Boundaries. Imperial College Press, London.

 

Rayner, A.D.M. (1998) Presidential address: fountains of the

forest¾the interconnectedness between trees and fungi. Mycol. Res.

102, 1441-1449.

 

Rayner, A.D.M. (2000) Challenging environmental uncertainty: dynamic

boundaries beyond the selfish gene. In Towards an Environment Research

Agenda vol. 1 (A .Warhurst, ed), pp. 215-236. London: Macmillan.

 

Rayner, A.D.M. (2002) Breathing Space, Inclusionality and the T'ai

Hsüan Ching, J. Transfig. Mathematics 8, 9-16.

 

Rayner, A.D.M. (2003) Inclusionality – an immersive philosophy of

environmental relationships. In Towards an Environment Research Agenda

– a second collection of papers (A. Winnett and A. Warhurst, eds.),

pp. 5-20. London: Palgrave Macmillan.

 

Rayner, A.D.M., Coates, D., Ainsworth, A.M., Adams, T.J.H., Williams,

E.N.D. and N.K. (1984) The biological consequences of the

individualistic mycelium. In The Ecology and Physiology of the Fungal

Mycelium (D.H. Jennings and A.D.M. Rayner, eds), pp. 509-540.

Cambridge University Press

 

Rayner, A.D.M., Watkins, Z.R. and Beeching, J.R. (1999)

Self-integration—an emerging concept from the fungal mycelium. In The

Fungal Colony (N.A.R Gow, G.D. Robson and G.M. Gadd, eds), pp. 1-24.

Cambridge University Press.

 

Rayner, A.D.M. and Way, C. (1999) Evolutionary waterways: the

contextual dynamics of biological diversity. Frontier Perspectives 8

(2), 33-37.

 

Scott Mills, L., Soule, M.E. and Doak, D.F. (1993) The

keystone-species concept in ecology and conservation. BioScience 43, 219.

 

Shakunle, L.O. (1994) Spiral Geometry. The Principles (with

Discourse). Hitit Verlag, Berlin, Germany.

 

Spowers, R. (2002) Rising Tides. Edinburgh: Canongate Books.

 

Spretnak, C. (1999). The Resurgence of the Real: Body, Nature and

Place in a Hypermodern World. New York: Routledge.

 

Steiner, R. (1997 ) Mystery Knowledge and Mystery Centres. 3rd

edition. London: Rudolf Steiner Press.

 

Stewart, R.J. (1988) Where Is St. George, Pagan imagery in folk song.

New edition. Blandford Press.

 

Tarnas, R. (1991). The Passion of the Western Mind: Understanding the

Ideas That have Shaped Our World View. New York: Ballantine Books.

 

Walters, D. tran. (1983) The T'ai Hsüan Ching: The Hidden Classic by

Yang Hsiung. Wellingborough, England.

 

Wilber, K. (1996). A Brief History of Everything. Boston: Shambhala

Publications.

 

 

..b b.b.

[Guest guest]

Heady, not

 

Holy

 

 

(a mere distraction)

 

 

 

 

 

 

Nisargadatta , " .b bobji baba "

<Roberibus111 wrote:

>

> `Nested Holeyness': the Dynamic `Inclusional' Geometry of Natural

> Space and Boundaries

>

> By Alan Rayner

> Dept of Biology and Biochemistry, University of Bath, Claverton Down,

> Bath BA2 7AY, U.K.

>

> SUMMARY

> Modern understanding of dynamic processes of all kinds, from subatomic

> to universal scales and encompassing the evolution of living systems,

> continues to be restricted by the rationalistic treatment of

> boundaries as discrete limits and space as distance between material

> objects. Such treatment is founded mathematically in the geometry of

> Euclid and arithmetic of discrete numerical units, which formed the

> basis for Newtonian mechanics and the development of objective,

> quantitative science aimed at prediction and control. It is, however,

> profoundly unrealistic in being based on the illusion that matter

> ultimately consists of solid, massy particles surrounded by (and hence

> excluding) non-interactive space. This illusion leads to the dualistic

> `paradoxes of completeness' that underlie the interpretation of change

> as the consequence of imposing purely external force upon discrete

> (isolated) and hence independent bodies, seen in life forms as the

> location of individual selves.

>

> A radically more creative, realistic and ultimately less

> environmentally, socially and psychologically damaging perspective

> opens up when it is acknowledged that space, as insubstantial

> `possibility for movement', permeates within, around and through every

> `thing'. There are no paradoxes of completeness in this perspective

> because there are no discrete bodies - no isolated wholes. Far from

> being complete, fixed Euclidean surfaces that simply divide insides

> from outsides, boundaries both form and are formed by the co-incidence

> of inner and outer inductive realms as complex, variably resistive,

> dynamic, space-incorporating transitions. As such, they both

> distinguish and reciprocally couple the local, inner (`individual')

> and non-local, outer (`collective') callings of uniquely situated

> waveform features of energy-space - relational places rather than

> discrete entities - nested over all scales and identifiable in life

> forms as `complex selves'.

>

> Rationalistic Detachment and the `Individual Self'

> I have heard it said that aboriginal people, when asked to draw a

> `self-portrait', draw their surrounding landscape. Likewise, as

> children, we do not initially differentiate between what we see and

> who we are - instead we feel utterly self-absorbed in an ever-changing

> bubble of life, rich with toings and froings, comings and goings,

> hunger and satiation.

>

> Later in life we may yearn to recover this sense of `no separation',

> `oneness' or `unity' and seek it through meditation or other means.

> And in the wake of the emergence of deconstructive postmodern

> philosophies and reaction to the harsher strictures of Enlightenment

> dualism and scientific reductionism, this same search is a feature of

> many current `holistic' movements.

>

> It is as though something vital is lost or ignored when distinctions

> are made between inside and outside, `self' and `other', and the

> resulting pain leads to a desperate quest to return to a primordial

> condition of `no boundaries'. Here, however, I suggest that it is not

> the existence, but rather the perception of boundaries, through which

> inner-outer distinctions are made, that can bring about loss. If we

> change our currently predominant rationalistic view of boundaries as

> discrete limits, to what I and others have called an `inclusional'

> view of boundaries as pivotal places of co-creative relationship, i.e.

> `togetherness', then the vital contextual space that otherwise would

> be excluded is brought back into our consideration. We do not have to

> abandon all we have learned and invented through making distinctions,

> but we do need to recover all we have lost, and heal the

> environmental, social and psychological damage we have engendered, by

> regarding these distinctions as absolute. So, what form of perception

> and logic has brought us to this pass, where we need to recover, and

> how has it affected our understanding of our relationships with one

> another and the living world we inhabit?

>

> Solidity - A Divisive Illusion

> As land-inhabiting creatures unable to digest herbage and so needing

> to find and catch or grasp localized sources of food as well as to

> avoid or overcome danger, we couldn't survive for long without being

> able to make distinctions. Making distinctions is therefore an

> essential part of our early learning, urged on by our caring elders

> and aided by our physical senses, especially our primates' binocular

> vision.

>

> One of the most important distinctions we learn to make, aided by

> peering into some reflecting surface like a pond or mirror, or the

> facial expression of a friend, relation or adversary, is between what

> lies within our skin and what lies outside it. Then, as our focus

> swings from subjective to objective, we become conscious of our animal

> body and its vulnerabilities as the location of our individual self,

> and of other bodies as potentially threatening or useful other selves

> or `things'. We become prone to lose our immersed sense of inclusion

> of all we survey and, if we are not mindful, may come to regard that

> sense as a childhood fantasy to be put aside as we grow up and adjust

> to the `real' world. And that is when the trouble starts, because that

> is when we really do become subject to a profoundly alienating

> illusion that excommunicates us both from nature and the real nature

> of ourselves: the illusion of solidity.

>

> We become focused on the explicit substance that appears to constitute

> our bodies and the ground beneath our feet that fixes our location,

> and regard whatever is insubstantial, undetectable by our physical

> senses, as `nothing' - an absence that isn't a presence yet puts

> distance between one `thing' and an other. We abstract space from

> matter, and regard matter, and where matter is located as if sealed

> within a fixed boundary and hence definable as `property', as all that

> matters - `everything'. We become `materialists' and `individualists'

> inhabiting an incoherent world and universe of what appear to us as

> independent, solid objects that have to be forced into motion.

>

> The journey towards materialism and objectivism is not only a

> feature of our developmental individuation as we approach adulthood,

> becoming increasingly adept at making distinctions. As has been widely

> documented, it is also a feature of the western philosophical journey

> that culminated in the Scientific Revolution and Enlightenment (e.g.

> Tarnas, 1991; Spretnak, 1999). It has become deeply ingrained in our

> mathematics and our science and, thereby, in our modern culture. And,

> for all the technological innovation this culture has spawned, far

> from fulfilling its potential as a source of mutual support and

> inspiration, it has become for many a deeply distressing

> `Anti-culture'. Founded in an illusion of discreteness, the isolation

> of matter from space, it is a culture riven by the conflict and

> paradox implicit in what might aptly be called the `anti-logic' of

> `one' (`self') against `other' (`non-self').

>

> `Anti-logic' in the Foundations of Mathematics

> Many of us, I suspect, must recall with some dismay those occasions

> when as children we were called inside from the playground of our

> imagination, to learn to count and add, subtract, multiply and divide

> numbers. Maybe we felt, consciously or unconsciously, a profound sense

> of imposition and alienation from the world in which we naturally

> belonged. If so, we had good reason!

>

> Numbers, as we have mostly come to define and use them and

> ironically describe as `natural', are anything but natural. Rather,

> they are an abstraction from nature - an expression of material

> content freed from spatial context and so treated as discrete,

> independent `units'. According to the underlying anti-logic, one thing

> has to be distinguished from no thing, it can't be something and

> nothing at the same time - either it is or it isn't. In the words of

> the song, `Green Grow the Rushes - O', `one is one and all alone and

> ever more shall be so'. So, what, then, is two? According to the

> anti-logic, two is, quite simply, no more than two independent ones,

> and this notion is indeed the basis for the `law of superposition' and

> linear condition of proportionality, whereby `the whole is the sum of

> its parts'. But the fact that two isn't the same as two independent

> ones becomes evident as soon as we multiply it by itself (i.e. apply a

> `power' function), whence it makes four rather than two. Two includes

> `something extra' that enables the two ones to `act together' to

> produce `something extra', sometimes described (because only its

> manifestation rather than its latent presence is evident from an

> external viewpoint) as an `emergent property', that makes the `whole'

> greater than the sum of its parts - i.e. non-linear. And this

> something extra that produces something extra is no more and no less

> than the inter-permeating space that couples the two ones as distinct,

> but not discrete, identities. But according to the anti-logic, space

> is nothing…

>

> Useful though it may be in performing linear calculations, it is

> clear that the treatment of numbers as independent, space-excluding

> entities representing pure `substance' or `content' freed from

> `context' - as `figure' freed from `ground' - is deeply paradoxical.

> As was demonstrated by Kurt Gödel in his mathematical formulation of

> the famous Cretan liar paradox, in which a Cretan informs you that all

> Cretans are liars, the problem is one of assuming `completeness'. Any

> `complete' or `entire' object that thereby has nothing outside of

> itself, is inescapably self-referential and so impossible to verify or

> falsify `independently' (e.g. Hofstadter, 1980).

>

> Yet further paradox arising from focusing on content abstracted

> from context, is contained in the second great foundation of

> mathematics, Euclidean geometry. How can a `point' have no dimension,

> a line no width and a plane no depth? Only by distilling all the space

> out of it until we are left with `something' infinitesimally `pure'-

> the indivisible, solid, massy atomic particles - the `building blocks

> of the Universe' envisaged by Democritus and Newton alike. In reality,

> such `point masses' cannot exist, and indeed, not for want of trying,

> we have never found them as we have probed deeper and deeper into the

> fundamental nature of `matter'. All we have found is distinctive

> places - waveforms that we nonetheless describe as `fundamental

> particles', so habituated are we to the notion of `solid substance'.

>

> `Anti-logic' in the Foundations of Mechanistic Science and Objectivity

> Despite the logical and practical impossibility of isolating matter

> from space (and vice versa), and despite its own findings in

> relativity, quantum mechanics and the dynamics and irregular geometry

> of non-linear (complex) systems, science continues to be practised by

> many according to purely Newtonian/Cartesian, deterministic

> principles. This is because these principles are deeply embedded in

> `objective scientific methodology' and its underlying mathematical and

> philosophical framework.

>

> Objective scientific methodology always starts by imposing a rigid

> frame, actual or theoretical, around some isolated fragment of nature

> from which the observer is excluded, and then proceeds to test

> `falsifiable hypotheses' about events occurring within this frame by

> means of quantification and experimentation. Nature is brought into

> laboratories, contained in various vessels, purified from

> `contaminants' and located in `controlled environments' where the

> effects of `one variable at a time' can be tested. But the question of

> how what can be quantified within this frame actually relates to the

> reality outside the frame cannot be addressed by this approach alone.

> The `certainty' about whatever is in the frame therefore comes at the

> expense of enormous uncertainty about the relevance of the findings to

> the `real world'.

>

> The forlorn hope is that all the `small pictures' of Nature captured

> within the isolated frames will somehow `add up', like the pixels on a

> TV screen, to yield the `big picture'. It is rather like trying to

> study and represent a river based solely on an examination of the

> behaviour of the contents of cups dipped into the river! The outcome

> is a headlong fall into the paradoxes of completeness. These paradoxes

> are implicit in Heisenberg's uncertainty principle and `wave-particle

> duality' and expressed in such notorious conundrums as Schrödinger's

> cat, whose uncertain `state' of `life or death' is an artefact of

> being sealed in a box with a vial of cyanide (see, e.g. Coveney &

> Highfield, 1992).

>

> In reality, the process of abstraction decontextualizes and so

> devitalizes the dynamic system under investigation, by fixing or

> `freeze-framing' its contents so that they can only be moved by

> external force. Investigation therefore begins by immobilizing and

> sundering the system and its contents, and then uses the result to

> conclude that the system is made up from discrete components that have

> to be mobilized into action from a static initial condition. This

> conclusion is a non-sequitur, because the common-space inner-outer

> connection that gave the system its dynamic coherence in the first

> place has been systematically removed in the process of investigation!

> Once shattered, all the King's horses and all the King's men cannot

> put a lively Humpty together again! Vitalism, for all the railings of

> positivist thinkers, had a very `real' point, or - should I say -

> connection to make!

>

> All this is not of course to say that objective scientific methodology

> is useless, only that it cannot in itself offer a realistic

> representation of nature. If, however, an effort is made to compare

> the behaviour of abstracted fragments from nature with an experiential

> knowledge of natural systems, then real insights may be found in the

> differences and similarities that show up. For example, a comparison

> between the behaviour of water in a cup and in a river may revealingly

> inform us about the effects of isolation on the natural mobility of

> fluids, and hence deepen our contextual understanding of the latter.

>

> `Anti-logic' in the Foundations of neo-Darwinian Evolutionary Theory

> Nowhere is the anti-logical dislocation of discrete bodies from their

> spatial context as `individual selves' more obvious, or more profound

> in its influence on the way we regard our relationships with one

> another and other life forms, than in the notions of `natural

> selection' and `survival of the fittest'. Here, we have an archetypal

> collision between the judgmental, externally imposed `other' force of

> the surrounding `environment' and the `removable object'. Those

> objects that do not conform, i.e. are not `adapted' to the

> requirements of the environment, suffer the death penalty of

> extinction in a competitive struggle for existence with their

> neighbours. Behaviour that is not in the individual self-interest of

> these objects (ultimately, genes) is, therefore, not tolerated by the

> system (Dawkins, 1989).

>

> The implicit `fixed framing' in this concept of evolutionary

> processes, following on from Malthusian principles of limits to

> population growth, is evident in the way that `natural selection' is

> commonly portrayed as a `pressure' imposing restrictions on the

> expansive potential of its subject objects. This pressure intensifies

> as population growth squeezes out available resource/space so that

> ultimately only those entities with particularly favoured

> characteristics can endure.

>

> There are deep contradictions in this representation, arising from

> its failure to incorporate the creative interplay between life forms

> and their living space, whereby each reciprocally transforms the other

> in a simultaneous process of attunement rather than a sequential

> process of adaptation of one to the fixed other. Far from creating

> diversity, the effect of adaptation and competition in a fixed space

> is actually the inexorable drive towards monoculture, implicit in the

> notions of `competitive exclusion' and `adaptive peaks' (e.g. Futuyma,

> 1986). And far from enhancing `efficiency', the operation of systems

> at their most intensely competitive greatly increases wastage. Natural

> selection, as it is most widely and popularly represented, is

> profoundly counter-evolutionary, dissipating energy and impeding

> innovation (Rayner, 1997).

>

> `Anti-logic' in the Foundations of Educational, Social and Economic

> Institutions

> Anti-logic has literally become `institutionalized' in our modern

> Anti-culture, an abstractive, deeply self-contradictory, social and

> economic reality that is diametrically opposed to the reality of

> natural processes. Having intellectually and physically dislocated our

> selves from one another and our living space, we get caught between

> our requirement to perfect our individual selves as complete,

> independent, entities in competition with others, and our need to

> regain the social coherence that we lose in the process. In believing

> our selves to be fundamentally `free', and prepared even to fight for

> this principle, we simultaneously fear the `disorder' of a

> `free-for-all' society, and so try to impose limits on our

> intrinsically `selfish' behaviour. We do this by means of a multitude

> of restrictive governmental frameworks and practices, characterized by

> pyramidal hierarchies that redistribute power from the many to the

> few. A common feature of these organizations is the presence of an

> administrative centre, a purely internal `regime' that

> self-perpetuates through the imposition of `rules of behaviour' that

> militate against any kind of `otherness' (outside interference).

> Conformity with these rules - in educational terms, the reproduction

> of anti-logical `received wisdom' - is regularly tested and rewarded

> with promotion to positions closer to the highly resourced centre.

> Non-conformity - `indiscipline' - is punished and marginalized.

>

> So we live by double standards, competing to conform and treating life

> as a `game' whose rules we try to turn to our best individual

> advantage. As Dawkins (1989), ironically puts it, `Let us try and

> teach generosity and altruism, because we are born selfish'!

>

> So much for our much vaunted `freedom' and `democracy'! If we look

> carefully at the hierarchical structure of our Institutions, it

> quickly becomes apparent that they are neither free nor democratic in

> serving the interests of all the people. Even if the governing regime

> is democratically elected, its executive processes exclude and stifle

> the views and needs of minorities (`majority rule' is not democracy)

> and place inordinate power in the hands of a few.

>

> Our Institutions are also profoundly ineffective in their internal

> communication, profoundly inefficient in the way they waste human

> effort and profoundly unresponsive to change. This is because they

> operate within fixed limits (artificial demarcations) along

> predominantly radial lines of communication, which distance the centre

> from the periphery - the few from the many at the interactive margin

> of the system. They create bottlenecks and fail to allow lateral

> links to by-pass the hub. As will be discussed below, the latter links

> are vital to reduce resistance to flow and allow effective

> redistribution in real life parallel-distributing networks like

> nervous systems, blood systems and fungal mycelia.

>

> In the end, everyone suffers in the Institutions of Anti-culture.

> Those `winners', who `succeed' by `playing the game' according to

> individual self-promoting rules, lose their opportunity to relate

> complementarily with others. Those who `lose' by not playing the game,

> become impoverished. Resentment, pain and conflict abound in all

> directions. Creativity is impeded by central bureaucracies, which

> impose restrictions but do nothing to ease flow.

>

> `Inclusional' Togetherness and the `Complex Self'

> Clearly, although it has its uses, there are profound limitations and

> contradictions inherent in the detached view of individual selves,

> abstracted from context like `babies from bath water'. On this, there

> is widespread agreement in postmodern thinking. There is less clarity,

> however, about what lies at the heart of the difficulties with

> rationalism in terms of its underlying presuppositions, and the nature

> of the context that it abstracts from. Consequently, a variety of

> different responses to these difficulties have developed, some of

> which have the character of `jumping from the frying pan into the

> fire' and others of substituting one kind of fixed reference frame for

> another.

>

> One reaction, that of deconstructionists, to the rationalist claim

> to have a hold on `reality' through objective, `value-free',

> quantitative methodology, has been to argue that no-one can be free of

> the power relations of their social context, and hence that reality is

> beyond our individual reach. Every `truth' claim we make is thereby

> seen as a `social construction', to be rigorously taken apart by

> discourse analysis - something which I have myself been subjected to

> when trying to express my thinking about `inclusionality' (Bluehdorn,

> 2003; cf Rayner, 2003). Although the deconstructive approach is most

> commonly regarded as synonymous with `postmodernism', it is in fact

> rooted in the very socio-political context of `Anti-culture', which

> emerges from the excommunicative anti-logic of rationalism. It might

> therefore be more aptly described as `hypermodern', in contrast with

> what Spretnak (1999) describes as `ecological postmodernism' of which

> I would regard `inclusionality' as a development.

>

> Whereas deconstructionism therefore takes the unrealistic

> consequences of abstraction to the opposite extreme by denying access

> to natural reality and so `losing the baby whilst reclaiming the bath

> water', ecological postmodernism questions the realism of objective

> rationality's dualistic presupposition of `isolation' or

> `independence' and implicit denial of `relationship'. This form of

> postmodernism has been most widely expressed in the `Green' and

> `Holistic' movements' claims for `unity in diversity', `wholeness' and

> `interconnectedness' and associated metaphors like `web of life' (e.g.

> Spowers, 2002). Protagonists of these movements have a strong

> tendency, however, to deny the reality of the detached view of the

> external observer by denying the existence of an `outside' and hence

> developing a totally internalized, subjectively immersed view. In

> effect, they equate the `baby with the bath' as an `ecocentric' or

> `ecological' as opposed to `egocentric' `self' (Macy, 1991). They

> substitute the binary/dualistic, `many wholes/parts' view of isolated

> entities for a unitary/monistic `non-dual', `one whole' view of `no

> boundaries' and `no separation', akin to that we may have before we

> begin to develop the notion of a distinguishable `self'.

>

> This `return to origin' is often accompanied by more than a little

> hypocritical spiritual pride and `all sweetness and light' claim to

> `higher consciousness'. It can be quite excluding and disparaging to

> those who `haven't got there', demanding that they `must change' if

> they are to be allowed entry to the `club of the righteous' and `save

> the planet' (Laszlo, 2002). But the change demanded is from one kind

> of unrealistically imposed framework (isolated boxes) to another (all

> in one box) and so may be just as restrictive, subject to the

> paradoxes of completeness and denying of the human condition, if not

> more so. By explicitly or implicitly denying the existence of

> boundaries, holistic thinkers are prone to ignore the very place

> through which the dynamic relationships and diversity that they

> propound are mediated. They end up speaking vaguely and mystically

> about `interconnectedness', complex `webs' of relationship,

> `self-organization', `subtle energies', `vibrations', `Gaia theory',

> `tight coupling', `yin-yang' and the like, without anywhere to relate

> these concepts to.

>

> The Holeyness of Dynamic `Reality'

> How very different the picture we have of reality becomes, as soon as

> we acknowledge that space, in the sense of insubstantial `possibility

> for movement', permeates within, around and through every `thing'.

> There are no paradoxes of completeness in this perspective because

> there are no discrete bodies - `complete wholes', only holey

> embodiments that both include and are included in space. Far from

> being fixed, depthless Euclidean plane surfaces, complete coverings

> that isolate insides from outsides, boundaries both form and are

> formed by the co-incidence of inner and outer inductive realms as

> complex, variably resistive, dynamic, space-incorporating transitions

> from one depth or region of heterogeneous space to another. As such,

> they simultaneously both distinguish (differentiate) and reciprocally

> couple (integrate) the local/inner and non-local/outer domains of

> uniquely situated waveform features - relational places rather than

> discrete, objective entities. And space, far from being the distancing

> source of incoherence in the universe is actually an `attractor': the

> resistance-less, `nothingness' that coherently pools or calls `every

> thing' together through its gravitational, inductive influence, which

> becomes more powerful the deeper (more curved/internal), and hence

> more associated with mass, it is. We shift focus from the explicit

> distribution of matter through space, to the implicit distribution of

> space through matter, and in so doing glimpse the `bigger picture' of

> our human place in the living world and universe, a dynamic `nested

> holeyness' of inner within outer callings, across all scales.

>

> In living systems, the waveforms resulting from the necessary

> togetherness (distinctness but not discreteness) of inner, outer and

> intermediary callings may be thought of as `complex selves'. Rather

> than being unitary or binary, ecocentric or egocentric `beings', such

> couplings represent ternary `becomings', dynamic `threesome-onesomes'

> where `two' implies `one' and `three' simultaneously - babies combined

> recreationally and unpredictably with water (twoness) via skin

> (threeness) in the spatial commons (oneness) of the bath! Their

> behaviour is therefore ultimately intractable to rationalistic logic,

> as implicitly acknowledged by Newton `himself' in his analysis of the

> `three body problem' (Montgomery, 2001).

>

> The concepts of `complex self' and `nested holeyness' were

> anticipated by Koestler (1976) in his descriptions of `holons' - as

> `Janus-faced' entities combining individual and collective aspects,

> and `holarchies' - as nested arrays of holons, in his `Open

> Hierarchical Systems Theory' (Rayner et al., 1984). These descriptions

> of a `Russian doll' kind of nesting, also alluded to by Caldwell et al

> (1997) and Wilber (1996), are, however, made all the more pertinent to

> our understanding of dynamic reality, when the necessary

> incompleteness, and consequent transformability (indeterminacy) of

> space-incorporating boundaries is introduced. We then move from a

> `wholes within wholes' or `worlds within worlds' description of

> `things' as objects, to a `holes within holes' or `whorls within

> whorls' description of identifiable places. Not only is every `thing'

> necessarily both a grouping of smaller `things' and grouped with

> others in some `thing' larger, but the incompleteness of boundaries

> ensures that there is communicative spatial relationship and the

> possibility for transformation across all scales.

>

> The pivotal role of boundaries as dynamic, co-created, co-creative

> intermediary places reciprocally coupling the inner and outer callings

> of complex selves was effectively recognised almost two millennia ago

> in the T'ai Hsüan Ching of Yang Hsiung (Walters, 1983; Rayner 2002).

> As with `inclusionality', the T'ai Hsüan set out to acknowledge an

> essential presence (`Jen') coincident with and communicatively

> balancing between emergent dualistic polarities (Ti and T'ien). These

> polarities were akin to the reciprocally coupled Yin and Yang of its

> predecessor, the I Ching, but the latter was extended into an

> explicitly ternary logic through the introduction of a dynamically

> balancing, intermediary agency. Walters (1983) argues that the

> paradoxes of incompleteness or `fallacy of the excluded middle' could

> be `avoided if only philosophers could train themselves to consider

> that between the two extremes there is always a third force, Jen.

> Progress continues by the interaction of T'ien and Ti, but only Jen

> can change the direction, add the unknown quantity, and create.'

> Ancient ternary logic is also evident in the Christian Holy Trinity of

> Father, Son and Holy Ghost; in the Kabbalah's pillars of Severity,

> Grace and Mercy, and the Threshold between `unreal' Knowledge and

> truth-less Fantasy symbolized by elastic `male' and plastic `female'

> statues in the Hibernian Mystery Centres (Steiner, 1997).

>

> In terms of this ternary, `dynamic framing', complete sealing of

> boundaries would disrupt and stifle flow, whereas total dissolution of

> boundaries would end in featurelessness. So both the pursuit of

> absolute individual autonomy (independence) through the completion of

> external boundaries, and of absolute collective unity (dependence)

> through the obviation of internal boundaries are evolutionarily

> untenable. By contrast, a holey intermediary boundary provides the

> possibility for `breathing space' and consequent energy transfer

> between dynamically coupled inner and outer inductive domains. Closing

> in (decreasing holeyness) of boundaries results in `information', the

> constructive shaping of local `features' and increased resistance to

> energy transfer both from outer to inner (inspiration/ in-welling) and

> from inner to outer (expiration/out-welling). Opening out (increasing

> holeyness) of boundaries results in `exformation', and consequent

> decreased resistance to energy transfer.

>

> The complementary interdependence of generative and degenerative

> processes via dynamic boundaries between inner and outer is therefore

> inescapable. Space, though we may perceive it rationalistically as

> `darkness', `imperfection' and even `mortal sin', cannot be excluded

> from a vital, evolutionary system, try as we might in the

> rationalistic pursuit of `perfection' in the form of individual or

> collective completeness (wholeness). To find such `perfection' would

> imply eternal stasis, a profound inertia of the kind approached (but

> even then, not absolute) by the noble gases and in deep meditation.

> Rather, in the excitable, dynamic world and universe that is drawn

> towards such perfection through balanced relationship, outside yields

> to and feeds the growth of inside, which yields in turn to outside in

> natural renewable cycles and spirals. These natural inspirations and

> expirations are disrupted, and even reversed, by the rationalistic

> severance of one from the other.

>

> Consequently, when we simplistically abstract our individual human

> `inner selves' from their complex relation with our collective `outer

> self', the ensuing conflicts feed death and dysfunction with life

> rather than allow death and dysfunction to feed life. We either act

> `selfishly', by disregarding our outer calling or `sacrificially' by

> disregarding our inner calling. To avoid such fates, it is necessary

> both to inform (manifest) and exform (relax) our inner-outer

> boundaries, in ways that attune rather than dislocate the needs of our

> complex individual and collective natures, as they continually

> transform our circumstances through their dynamic, reciprocal

> relationship. And, by its very nature, there can be no fixed

> rationalistic rules or formulae to guide such attunement: only a

> sensitive, instinctive or experiential feeling, or empathic

> `awareness' of one for the other can work, mediated through their

> dynamic, interfacial boundary.

>

> Inclusional Logic in the Mathematics of Dynamic Systems

> Any mathematical formulation of ternary logic needs to account for the

> reciprocal, simultaneous dynamic relationship between inner and outer

> spatial domains or callings of embodiments identifiable as places

> rather than objects. Correspondingly, rather than treating numbers as

> an expression of pure material content, with `zero' representing

> `absence' and `infinity' representing `limitless amount', it would

> make sense contextually to regard zero as `inner-outer balance'

> (stationary boundary condition) and infinity as inner and outer

> spatial possibility. So, too, would the treatment of numbers as both

> giving rise to and containing one another as potentialities, as

> expressed in some variants of `Green Grow the Rushes - O' (Stewart,

> 1976), in the Kabbalah, in Hopi native American culture and,

> conceivably, in some Neolithic rock art (cf. Bradley, 1995).

>

> Given the rationalistic nature of the foundations of mathematical

> practice, however, it is not surprising that, as yet, there has been

> little explicit attempt made to incorporate inclusional or ternary

> logic, with the notable exception of the fluid logic

> (threesome-onesome) number system and associated spiral geometry of

> Shakunle (1994). For the most part, even when dealing with dynamic

> processes, mathematical analysis begins with discrete, space-excluding

> definition(s) of its frame(s) of reference (entities and initial

> conditions). Although the effect of incorporating space is evident

> from analyses of `non-linear dynamical systems', `fractal geometry'

> and associated `irrational' and `imaginary'/complex numbers (see

> below), what appears as `emergent' from these analyses may therefore

> `really' be a manifestation of what is already implicitly present in

> natural process geometry.

>

> Fractal geometry is the nearest approach that conventionally

> fixed-framed mathematics has made to the natural geometry of `nested

> holeyness'. This kind of geometry was developed by Mandelbrot (1977)

> as a way of describing structures whose boundaries, unlike Euclidean

> surfaces, appear progressively more complex/irregular, in

> `self-similar' patterns, the more closely they are observed.

>

> Fractal structures can be quantified by allowing their dimension,

> expressed as a relation between the logarithms of their material

> content and radius of spatial field (i.e. `context') containing this

> content, to be fractional as well as integral. They can be generated

> computationally by means of `iterative' processes in which the

> `output' from the `input' (which, despite the claim that they are

> `deterministic', imply continued openness to outside space) of a

> number into a non-linear equation is successively `fed back' into the

> equation as `input'. A famous example is the `Mandelbrot set', made by

> mapping the distribution of points in the `complex plane' that do not

> result in infinity when iterated according to the rule, z & #8594;z2 + c,

> where z begins at zero and c is the complex number corresponding to

> the point being tested. Here, a `complex number' is a number that

> consists of a combination of a `real' and an `imaginary' component,

> the latter being a derivation of, `i', the square root of -1. The

> complex plane is formed in the space defined by placing all `real'

> numbers, from - & #8734;, through 0, to + & #8734; along a horizontal

line, and all

> `imaginary' numbers, from - & #8734;i, through 0, to + & #8734;i, along

a vertical

> line, and using these Euclidean lines as co-ordinates. In effect, it

> represents a way of increasing the `possibility space' for numbers to

> inhabit, as discrete entities, from one to two dimensions.

>

> The remarkable feature of the Mandelbrot set is the extraordinarily

> complex boundary that occurs between points within and points outside

> the set, in effect between an inner attractive space of zero and an

> outer attractive space of infinity. Such complex boundaries formed

> between neighbouring attractive spaces or `attractors' have more

> generally been referred to as `fractal basin boundaries', and they are

> clearly at least analogous to the complex, ternary boundaries of

> natural process geometry. Where, however, the conventional abstract

> mathematical representation of such complexity begins prescriptively

> with an implicit or explicit definition of content and container that

> replaces their simultaneous (resonant) reciprocal relationship with

> sequential `feedback', the natural might be said to originate in

> indefinition - a realm of endless possibility. Here, distinctions

> inform, exform and interact as coupled threesome-onesomes of

> energy-space, that co-create the phenomenal heterogeneity of dynamic

> nature in which time and matter, as separable quantities, are

> illusions. Abstraction can only hold a mirror up to this reality, and

> so capture a localized, inverted, and potentially deeply illusory

> image of it.

>

> Inclusional Logic in the Science of Transformation

> So what? What does this `inclusional' view of space and boundaries

> change as far as our scientific perceptions of nature are concerned?

> Most fundamentally, I suggest that it changes our understanding of

> change. It becomes possible to assimilate our scientific discoveries

> into a context where the dynamic nature of context can be adequately

> accounted for rather than excluded from consideration as `external

> interference' or `noise'. Rather than beginning, through the

> imposition of a fixed reference frame, with an assumption of stasis

> that has to be `forced' into action from `outside', the very nature of

> nature is understood to be dynamic. And with this understanding, our

> concepts of causality and uncertainty also change. Rather than

> regarding change as externally enforced and hence reversible movement

> measured as a progression through space against intervals of absolute

> time, all change is understood to involve the transformation of space

> and consequent simultaneous alteration in both content and context and

> their reciprocal relationship. Since this transformation necessarily

> involves a change in content-context, it is, by its very nature both

> irreversible and unrepeatable - unable to return directly or

> indirectly to exactly the same place that it emanated from. Far from

> being reproductive, producing more of exactly the same, Nature is

> continually recreative and autocatalytic- opening up and building upon

> new possibilities for itself. As was said so long ago by Heraclitus,

> `you can never step in the same river twice'. Content and context,

> stream and catchment, continually re-shape one another in an

> ever-transforming flow of place. This place is dynamically framed by

> itself as a complex waveform - a resonant coupling of inner with outer

> energy-space, as was effectively recognized, albeit in a conventional

> mathematical framing, by the communication theory of Dennis Gabor

> (1946). Long neglected scientifically, but now being rediscovered,

> this theory provided the basis for Gabor's Nobel Prize-winning

> invention of holography, key to which was the notion of a `complex

> signal' as a reciprocal combination of real and imaginary components,

> rather than an independent pulse of information.

>

> Inclusional Logic in the Evolution of Community Life

> As I have already alluded to, the conventional fixed framing of

> reality, and consequent precedence given to explicit material content

> over implicit spatial context, leads inexorably to an emphasis on

> competition between independent entities in considerations of

> evolutionary processes. Taken to extremes, this emphasis can result in

> the suggestion that `there is no such thing as society/community',

> because the requisite co-operation in such a collective organization

> would compromize individual `self-interest'. Both diversity and

> co-operation are deeply contradictory, if not `irrational' and

> `unnatural' concepts according to this view, and so, if they are to be

> desired or tolerated at all in human societies, can only be sustained

> by legal and educational enforcement.

>

> By contrast, an inclusional, dynamically framed view that

> originates with spatial indefinition and the manifestation of distinct

> features in the first place as ternary, resonant waveforms of coupled

> inner-outer domains, sees both co-operation and diversity in the

> attunement of one with the other, as primary qualities of a

> heterogeneous universe. Competition, on the other hand, results from

> the attempted enforcement of distinctive identities, through the

> imposition of a fixed reference frame, into exactly the same space or

> `niche'. For many sensitive human beings, such enforcement, which

> either denies their differences or sets these `at odds with' rather

> than `in complementation' with others', feels deeply unnatural and

> disempowering, for good reason.

>

> In the inclusional view of the `complex self', there is therefore

> nothing unnatural or contradictory about co-operation and diversity,

> nor, for that matter, about outwardly `aggressive' behaviour that

> sustains diversity through the assertion of local identity (Rayner,

> 1991, 1996, 1997). Rather, what we have, as many ecologists implicitly

> or explicitly recognize in natural `ecosystems' and their inhabitant

> `communities', is a dynamic `togetherness in diversity' or

> `complementarity of labour'. Here, the collective and individual,

> `the forest and the tree', both necessarily incomplete, continually

> reconfigure one another as they explore and manifest the realm of

> possibilities.

>

> The irony is that we continue to find it virtually impossible to

> apply this understanding to our own human communities, even though it

> is, for many, only `common sense', obvious from our everyday

> experience of relationships with one another and our living space.

> This may be because our logical predisposition to freeze-frame reality

> continues to cause us to seek `consensus' as `sameness' rather than

> `complementarity' of view, whilst aspiring to individual perfection

> through competition in an adversarial anti-culture. Even when we

> proclaim our `interconnectedness', we mentally insert the connections

> between initially disconnected independent entities that have to be

> `joined up' - and so appear as `nodes' in a `web' or `tree' of purely

> transactional relationships, as in modern network theory (Buchanan,

> 2002; Barabási, 2002). We fail to recognize that, rather than needing

> to be `added in,' the connection is implicit, already there to be

> co-discovered through relaxation of individual boundaries. And this

> failure brings dangers if it is used to identify entities at the `most

> pivotal nodes' as `the least dispensable'. In conservation biology,

> such entities are described as `keystone species', with the inference

> that they should be `preserved at all costs' (Scott Mills et al,

> 1993). In fact, a close examination of the so-called networks upon

> which such conclusions are based shows them actually to be

> dendritically branched strings or webs of nodes, produced, as

> described above, by joining up initially discrete entities. They

> therefore lack the intrinsic lateral connectivity of true, functional

> natural networks like fungal mycelia, but resemble aberrant,

> dysfunctional forms of the latter (K.J.J. Tesson et al., in

preparation).

>

> Creative Boundaries and the Diversity of Organic Life as an Embodied

> Water Flow

> During the twentieth century, two dramatic technical breakthroughs

> combined with rationalistic philosophical inquiry to yield a

> distinctive new vision of the nature and origin of life and living

> things, including human beings. The discovery of the genetic code and

> advent of modern computers, when viewed in the light of a detached

> perspective projected an image of evolution as the spread and

> diversification of genetic information, and of life forms as

> information processors - computational machines. Correspondingly, more

> and more effort has been put into discovering firstly the

> calculational procedures or `algorithms' that underlie behaviour and

> pattern generation amongst life forms and secondly the physical and

> chemical mechanisms through which these algorithms operate. Once we

> know these procedures and mechanisms, it is assumed we can have a good

> understanding of what makes life `tick', in essence like clockwork.

>

> The inclusional bringing together of immersed with detached -

> subjective with objective - views of the dynamic boundaries of nature

> and self, challenges this dry, mechanistic depiction of life forms by

> restoring the watery context that sustains life as an ever-changing

> flow. Life forms are not discrete computational machines processing

> digital information. DNA is not transmitted `on its own' from `one

> generation to the next', but flows through a continuum of watery space

> that ultimately includes even `extinct' ancestors. DNA is not

> `information in itself', which means the same anywhere, but rather

> gives and is given meaning through its dynamic relation with protein

> in the contextual medium of water retained within boundaries of

> variable deformability, permeability and continuity. And this meaning

> can change with context, just as the meaning of words in this sentence

> can change in the context of other words and spaces and sentences. And

> context lies inseparably both within and around the boundaries of

> organic life forms, as we know them on Earth, as embodied water flows

> responding to and producing change, like a river that both shapes and

> is shaped by landscape.

>

> I therefore see rivers both as a valuable metaphor and an actual

> description of the `complex self' as a dynamic embodiment of inner or

> individual or local space with outer, collective or non-local space.

> We see riverine form whenever we look at life as an ever-unfolding,

> enfolding presence, rather than in freeze-framed snapshots giving the

> illusion of discrete individual entities. We see it in the branching

> and anastomosis of fungal mycelia, blood systems, trees, leaf veins,

> nervous systems, wildebeest herds, ant swarms, phylogenies and

> pathways of all kinds (Rayner, 1997, 1998; Rayner and Way, 1999).

>

> Simply by `tuning' the `holeyness' and consequent permeability,

> deformability and continuity of their inner-outer boundaries, to

> relate to internal and external availability of oxidizing and reducing

> agents, life forms change pattern and process as they create and

> respond to changes in their dynamic context. They `self-differentiate'

> outwardly, through the proliferation of inner-outer boundaries when

> and where there is plentiful external energy-supply, and

> `self-integrate' inwardly through the fusion, sealing and

> redistribution of these boundaries when and where there is external

> shortage (Rayner, 1997, 2000; Rayner et al., 1999). In this way they

> have generated the expanding diversity of Earth's `biosphere'. Until

now…

>

> Acknowledgements

> I would like to acknowledge the inclusion of many correspondences with

> complex self-identities in what I have written here. I won't `single

> them out', but I am sure they will know `who' they are!

>

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>

> .b b.b.

>