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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 ?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 -8, through 0, to +8 along a horizontal line, and all ‘imaginary’ numbers, from -8i, through 0, to +8i, 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 Barabási, A-L (2002) Linked: the New Science of Networks. Perseus Publishing. Bluehdorn, I. (2003) Inclusionality-exclusionality: environmental philosophy and simulative politics. In Towards and Environment Research Agenda – a second collection of papers (A. Winnett and A. 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 Todd, 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. |
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