Chapter 2.

 

 Welcome to the Common Space - Where All Really Is Flow

 

 

The Emergence of ‘Inclusionality’ - The Inextricability of Space From Time, Energy and Matter

 

A few years ago, following a long period of intense, assisted self-exploration (i.e. psychodynamic psychotherapy) in search of the source of my uncertainty, and how I could understand and relate with this source, I woke up one morning from a startling, extraordinarily powerful dream. In the dream, I was preparing a demonstration class for students on the processes of decomposition in leaf-mould (literally the combination of fallen leaves and fungal mycelium that forms a kind of mulch, much beloved by gardeners, on the floor of woodlands and forest). I gathered together a sample of leaf-mould, taking very great care to exclude any kind of wildlife that might be dangerous to the students. I put this sample into a transparent, perspex box, so that it could be viewed readily from outside. To my horror, as I observed the contents of the box through the perspex, I saw a thin-bodied green and yellow snake emerging from the leaf-mould. I couldn’t tell whether this was the deadly venomous South African ‘boomslang’ or one of the several ‘harmless’ snakes that appear very similar to it. Then the snake found a hole in the side of the container and started to slither out through it. I realized that I now had no alternative. In the interests of the safety of the students I had no choice but to handle the snake, no matter how uncertain I might feel about its venomous potential. No sooner did this realization come upon me, than the snake coiled up into a tight spiral, like a millipede, and spun gyroscopically.

 

The rich symbolism of and prescience of dreams never ceases to amaze me - and of course there are many stories of the role of dreams in major breakthroughs for Humanity. How can it be, that in this unconscious realm we gain access to so much that relates so deeply to the concerns affecting us and our relationships with others? I have italicized some of the symbols in the above dream that seemed important to me when I had it and as I recall the dream now. But before I offer some of my own interpretations of these symbols, I want to outline some of the relevant experiences that led up to it.

 

From around the mid-1990s, I began to experience an intensification of the classical symptoms that in modern parlance are ascribed often rather dismissively to ‘mid-life crisis’, but which may more deeply be understood as a product of inhabiting an Anti-culture. I felt again those incongruities from my youth and childhood, between my life experience and values and what I was being asked to conform to in an academic system that I was trying to contribute to as a biological teacher and researcher. Not only did I suffer the agonizing doubts described in Chapter 1 about the validity and worth of my scientific findings, but I also felt an increasing sense of fraudulence, a sense that I had assumed a mantle that simply did not fit with who I am.  In short, I felt I had actually become akin to one of those dark Vampiric figures of the Wasteland depicted in my painting, ‘Arid Confrontation’ (Figure 1, Chapter 1). Apart from a few minor rebellions where I couldn’t help but put a spoke in the wheel of some one-sided scientific bandwagons, I had allowed myself, after all, to be defined and subsumed by others’ expectations of me, but couldn’t live either up or down to these expectations. And, symptomatic of my desolation was the fact that in a period of over twenty years I painted only four pictures - two for each of my two daughters.

 

These feelings grew as, like many University scientists, I struggled to keep my research activities alive and support my students and colleagues in an increasingly competitive, egotistic and commercially oriented culture focused on material gain and mechanistic interpretation. I had experienced an interlude, from1987-1991, when I was supported by BP Venture Research Unit - an unusual organization that actually recognized and valued research aimed at enhancing understanding rather than a predefined end product, and hence actively encouraged an open-ended approach. But apart from this interlude, when I experienced real intellectual freedom and a taste of extraordinary possibility, the attitude of most funding agencies towards scientific creativity was akin to that of Millstone Grit. [And it has got even worse since then, aided and abetted by the advent of the ‘Research Assessment Exercise’, which uses the most grossly unscientific and prejudicial techniques to rank UK University Research in alignment with Governmental demands for competitiveness]. One was effectively required to know in advance what the findings of the research would be, to show how these fitted with the prescriptive goals of the funding agency, and to describe how these findings would be ‘delivered’. Scientific research was regarded not as an uncertain exploration into the realms of the mysterious valley of serendipitous discovery, but instead as a production line. Many of my colleagues appeared to comply with this idiocy by applying to do research that they had already done, by playing political games, forming crony groups and inventing esoteric ‘buzzwords’ that would enable them to get the nod from their peers.

 

I found all this extremely distasteful, but still attempted to offer what was wanted, in so far as my values and abilities would allow. For a while, I just about managed to keep afloat, and our research group even got as far, whilst working with a Pharmaceuticals discovery company, as developing a new synthesis explaining the chemical ecology of fungi in terms of variable responses to oxidative stress in distinctive environmental contexts. But the funding agency wasn’t pleased - it wanted specific ready-made products with names and structures attached, not a general understanding of when, where and why these products were formed. Above all, it did not want to know about the nature of fungi as complex systems that couldn’t be expected to be controlled predictably, and simultaneously express their full biochemical repertoire, within the restrictive conditions of existing industrial production plant.

 

As the inevitable ‘crunch’ approached, the rebellions of my soul became ever more overt. I resumed painting in earnest in 1997, and helped to form a local group called Bath Bio*Art, feeling that an artistic perspective might help to cure the cancerous malaise I perceived creeping through the scientific community and enrich its prospects for a more creative, contextually sensitive way of working. In the same year, my book, ‘Degrees of Freedom - Living in Dynamic Boundaries’, was published, in which my questioning of the discretist underpinnings of conventional natural selection theory, and the associated ‘selfish gene’ and ‘its all in the genes’ (‘genetic determinism’) notions began to emerge.

 

The following year, 1998, I became President of the British Mycological Society, a position I regarded as an immense privilege, yet which exposed me more than ever to my own doubts and sense of others’ expectations. It took an enormous effort of will to keep myself going through this year, the end of which was marked by presenting a ‘President’s Address’. The latter took place in the famous Lecture Room of the Linnaean Society in London where Charles Darwin had presented his famous paper with Alfred Wallace in 1858 concerning ‘The Origin of Species’. So here was I, a ‘heretic’ in the making, presenting my address in the same place and under the gaze of a huge oil painting of the Great Man Himself!

 

I knew in my heart of hearts that this President’s Address would be my mycological ‘Swansong’, so I wanted to present something special. I was well past being able to present something full of technical data and scholarly references, in the manner of my predecessors. So I decided instead to present a celebration of the inspirations I had felt over the years as I searched for clues to the mysterious relationship between fungi and trees that had first entranced me as a boy on forays with my father. I called it ‘Fountains of the Forest’, and based it around the painting shown in Figure 3, which I made a gift of to the Society.

 

 

INSERT PICTURE HERE

 

 

Figure 3. ‘Fountains of the Forest’ (By Alan Rayner, Oil on Board, 1998).  Within and upon the branching, enfolding, water-containing surfaces of forest trees¾and reaching out from there into air and soil¾are branching, enfolding, water-containing surfaces of finer scale, the mycelial networks of fungi. These networks provide a communications interface for energy transfer from neighbour to neighbour, from living to dead and from dead to living. They maintain the forest in a state of flux as they gather, conserve, explore for and recycle supplies of chemical fuel originating from photosynthesis. So, the fountains of the forest trees are connected and tapped into by the fountains of fungal networks in a moving circulation: an evolutionary spiral of differentiation and integration from past through to unpredictable future; a water delivery from the fire of the sun, through the fire of respiration, and back again to sky, contained within the contextual boundaries of a wood-wide web. (From Mycological Research 102, 1441-1449, 1998).

 

 

Three months later, the crunch I spoke of in Chapter 1 finally came and I began the process of self-reclamation that continues to this day. I found myself working across disciplines and with all kinds of people who I would have been most unlikely to encounter in my former guise, whilst somehow still remaining employed within the Department of Biology and Biochemistry at the University of Bath.

 

In Spring 2000, I received ‘out of the blue’, an e mail message from Doug Caldwell, a Canadian microbiologist who had developed a ‘non-Darwinian’ view of evolution based on his work with ‘continuous culture systems’. He had published his ideas in an article in Advances in Microbial Ecology, to the great chagrin of many of his colleagues. He had, he told me, heard that I had expressed somewhat similar ideas, and would like to discuss whatever commonalities and differences we might have with one another.

 

I was delighted by Doug’s message. For me at least, such expression of interest in one’s work by another scientist from a different specialism, accompanied by invitation into discussion, was all too rare. Doug’s message contained a hint of something I had longed to hear – a ‘honk’ of encouragement. Maybe I wasn’t quite so scientifically alone as I had felt – the loneliness I had alluded to at the opening of ‘Degrees of Freedom’.

 

The conversation with Doug dived straight in at the deep end, assuming Universal proportions before I knew what had hit me. ‘Do you think that life is an infection of a dead Universe?’ Doug demanded. ‘Er…pass’. But, despite my hesitance, I was tickled to find, reflected in another, my own covert feeling that it wasn’t possible to understand the local details of biological diversity without addressing much larger, even more fundamental questions.  And Doug was expressing ideas he called ‘Universal Information Theory’ and ‘Nested Proliferation Theory’ which did indeed seem to correspond in many ways with the indeterminate (dynamically bounded/framed), ‘informational-content-with-spatial-context’ co-evolutionary thinking that I had begun to try to express in ‘Degrees of Freedom’. Moreover, Doug questioned the notion of ‘natural selection’, describing it as a ‘superstition’ rather than a ‘mechanism’, invoking a mythical, purely external agency making judgemental decisions about what was or wasn’t good enough, and eliminating the latter. On this, I agreed with Doug, even though at that stage I had not got as far as resisting the term altogether, as I have now.

 

Not long after our conversation began, Doug introduced me to two more correspondents, Dirk Schmid, a former research associate of his, and someone he described as ‘a very interesting person’, called Ted Lumley. Ted, a geo-physicist and disenchanted former oil company executive who had become interested in the way ‘exceptional teams’ work, at the same time as concerned about the social and psychological damage induced by rationalistic thinking, proved a prolific correspondent. In ‘no time’ (for absolute time, split apart from space, finds no place in Ted’s relativity-oriented thinking), our in-boxes started to groan under the load of accumulated messages. Prompted by Dirk, we began to think about how we might best organize and disseminate our missives as a discussion group, and hence how we might ‘label’ our ‘theme’, for ease of reference. Another deluge of correspondence followed as we each suggested candidates and got worried about having our style cramped by imposing inflexible, over-technical and/or inappropriate word-definitions. Eventually, Ted picked out ‘inclusionality’ as having the right kind of ‘flavour’ from one of my lists of candidates, and we decided to settle on that.

 

‘Inclusionality’ correspondingly arose simply as a convenient label. It expresses the idea, which developed as our conversations unfolded and included others, that space, far from passively surrounding and isolating discrete massy objects, is a vital, dynamic inclusion within, around and permeating natural form across all scales of organization, allowing diverse possibilities for movement and communication. Correspondingly, boundaries that from an orthodox perspective are regarded as discrete, fixed limits of isolated objects or systems, are seen inclusionally as pivotal, relational places. Here, complex, dynamic arrays of voids and relief both emerge from and pattern the co-creative togetherness of inner and outer domains, as in the banks of a river that simultaneously express and mould both flowing stream and receptive landscape.

 

At the heart of inclusionality, then, is a simple but radical shift in the way we frame reality, from absolutely fixed to relationally dynamic. This shift arises from perceiving space and boundaries as connective, reflective and co-creative, rather than severing, in their vital role of producing heterogeneous form and local identity within a featured rather than featureless, dynamic rather than static, Universe.

 

We hence move from perceiving space as ‘an absence of presence’ – an emptiness that we exclude from our focus on material things – to appreciating space as a ‘presence of absence’, an inductive  ‘attractor’ whose ever-transforming shape provides the coherence and creative potential for evolutionary processes of all kinds to occur. Correspondingly, we extend beyond orthodox impositional logic based on the notion of discrete objects or wholes, complete within themselves and so transacting within pre-set limits of Cartesian space, to the heterodox inclusional logic of distinct, ever-transforming relational, and hence incomplete, places.  These places have reciprocally coupled insides and outsides, which communicate through space-including, and hence permeable or holey, intermediary domains. In other words, we move from the one- (unitary) or two- (binary/dual) aspect ‘logic of the excluded middle’ to the three- (ternary) aspect ‘logic of the included middle’. Note that this logic is therefore neither entirely Holistic (assuming One Fundamental Whole or Unity) nor entirely Reductionistic (assuming Many Fundamental Wholes, interacting linearly as parts of larger Wholes), but rather a dynamic coupling of one together with the other over all spatial scales in ‘Holey Communion’.

 

When space is included in our perceptions of boundaries, it becomes inseparable from the energy that makes us alive. Darkness is included with light, gravity with electromagnetism, and time and matter cannot exist as separable, absolute quantities in their own right. We neither see the world and Universe about us as an incoherent assemblage of independent objects/closed systems surrounded by emptiness, nor do we lose ourselves in a featureless oceanic infinitude.

 

So, the logical premise of ‘inclusionality’ is of the incompleteness (holeyness) and interdependence of distinct places rather than the completeness and independence of discrete objects. Could inclusionality help to irrigate the deserted landscape desecrated by human Anti-culture, and allow the world of flowers to bloom once more?

 

Now, let’s revisit the dream I described at the outset of this Chapter and see how it may relate to the emergence of ‘inclusionality’. To begin with, the dream seems to be depicting something about the nature of the very particular scientific method of inquiry that arises though adherence to the discretism of the law of the excluded middle. The inquiry invariably begins with the selection and abstraction of a sample, which is placed within some actual or theoretical limiting boundary or reference frame and then studied in isolation from its natural context. A part of nature is excised and brought under scrutiny within the imposed framework of the sampling grid, laboratory, containing vessel, experimental apparatus or mathematical construct. Its properties and behaviour are thence defined and predicted in terms of rules, laws and principles that are discovered to apply within this framework through the proposition and testing of hypotheses. From this small picture contained within the part, it is expected or hoped that an understanding can be obtained of the big picture of the whole from which the part was derived.

 

The exclusion of the undesirable sources of uncertainty is very obvious in this dream as my attempt to keep out anything wild and potentially dangerous to the students. This attempt is obviously well intentioned, but also has the potential effect of preventing the students from apprehending reality and hence accepting an idealized view. The insertion of an invisible barrier compounds this abstraction, so that the contents of the box can be seen but not felt. These contents, meanwhile, consist of apparently particulate ‘units’ (leaves), which, in reality are collectively bound together through the tubular network and labyrinthine inner spaces of fungal hyphae. And, from the midst of these contents emerges the very aspect of nature that I had tried to exclude, in the other worldly, unpredictable, potentially deadly form of the snake with the profoundly resonant name. Like it or not, this form is inextricable from and vital to the dynamic reality of life. And it worms its way out of the box through a hole in its otherwise rigid boundary. But, like it or not, the moment I realize that I am going to have to handle this form, and hence establish a feeling relationship with it, it transforms from linear and dangerous into an innocuous spinning spiral. In this latter form, it dynamically balances reciprocal curved space potentials, like the rolling coin I described in Chapter 1.

 

The dream therefore seems to express what I, alongside others involved in the inclusional conversations, have come to view as the inextricability of space from energy, matter and time, in spite of our efforts to exclude it through analytical methods aimed at the elimination of uncertainty. Like it or not, space, and the uncertainty it implies is both intrinsic and extrinsic and can intrude and extrude everywhere through whatever kind of barriers we may try to put in its way. But if we are prepared to handle it, include it in our consideration, it can transform our understanding of the world about us.

 

In my own efforts, both conscious and unconscious, to include and handle space in my considerations of personal and scientific uncertainty, I have found myself getting into deeper and deeper, hotter and hotter water! I have found it necessary to venture into the realms of ideas and disciplines far beyond what might initially have been perceived, by others or myself, as my ken, based on my educational background and ‘qualifications’. But, like them or not, I felt that these realms were simply too important to ignore or hide away from if I was to follow through the implications of my thoughts and experiences. I simply had to try to make my own kind of sense of them, in language that I at least could follow. And in doing so, I have found my understanding of the world about me transforming in ways that have come as an enormous surprise, which both delights and frightens me. In the following sections I will try to relate something of this delightfully frightening, surprising interdisciplinary navigation into the deep, hot watery realms of uncertainty, naēve and foolish as I have honestly felt along the way. Doubtless I have followed in the wake of others whose findings and experiences might have helped if only I could have known them better. But at least I know that this is my locally subjective, uniquely situated and recreated story, what my friend Jack Whitehead would call my living theory, which I wish to share. 

 

 

 

Dynamic Boundaries

 

Up until our inclusional discussions began, I had not focused directly on space as such and its importance in understanding dynamic processes. Indeed, to focus on space would have seemed like a bit of a contradiction in terms – how can you focus on what appears to be nothing – an absence of presence? So, as with many other people, I suppose, space was a purely implicit background to my thinking, which I took for granted and didn’t attract my immediate attention. What I had focused on, however, as the result of my biological and especially my fungal studies, was the dynamic nature of living system boundaries. I had concluded that to regard these boundaries as sudden cut-off points that isolated life forms at any scale of organization as discrete individual entities or ‘units’ was unrealistic, and failed to recognize the very places where the wonderful variety of life patterns emerge. I also linked the pattern-generating potential of living system boundaries to ideas that were developing in the fields of chaos and complexity theory.

 

By focusing on boundaries as places of dynamic, co-creative relationship between adjacent domains over all scales, I found what felt to me like a much more satisfying way of understanding the evolution, interactions and development of life forms than the standard ‘pressure cooker’ world of ‘survival of the fittest’. This pressure cooker world, in which the growth of populations of independent individuals with selfish genes comes up against discrete limits imposed from outside, leading to intensive competition and the elimination of the less ‘fit’ or ‘adapted’ performers, least able to reproduce themselves, had never made much sense to me. It was just too full of contradictions and internal inconsistencies, arising ultimately from the fallacy of the excluded middle, whereby discrete limits are imposed between insides and outsides that do not and cannot exist in the reality of a dynamic biosphere on a dynamic earth in a dynamic Universe. How, in this pressure cooker world, can a process of elimination, which leads inexorably to monoculture, at the same time give rise to diversity? If you try to explain this by saying that there is a diversity of pressure cookers (known technically as ‘niches’), then where do these different pressure cookers come from? And how can you explain the occurrence of sex in a world in which more of the same is allegedly better? And why are there so many examples of distinctive life forms living in intimate association with one another in so-called ‘symbioses’? And how come natural communities of organisms are so elaborately and coherently structured? In all honesty, nothing in evolution to my mind makes sense in this abstract pressure cooker world of pure competition and selection, which both reflects and is an artefact of Anti-cultural human societies rooted in the impositional logic that dislocates content from context.

 

By accepting that boundaries were sites of dynamic, co-creative relationship rather than abrupt severance, I felt a much more fluid perception of living patterns emerge in my mind, which corresponded with my actual experience of Nature and the unconscious aesthetic awareness of my artwork. I found something joyous and inspirational in this perception, which brought a sense that life eases rather than bullies its way, by both creating and following paths of least resistance. I envisaged organic life, as we know it on Earth, as an embodied water flow forming droplets, pools, rivers and eddies everywhere, both deep and shallow, in the process of emerging locally in the flow forms we call organisms, populations and communities. I saw evolution as a process of continual contextual transformation, a necessary co-evolution of larger context with its locally expressed content, with each shaping and being shaped by the other. I saw genetic ‘nature’ and environmental ‘nurture’ as inextricably intertwined, with each other’s influence coinciding in the dynamic boundaries of living systems. I saw ‘niches’ not only as closed down pressure cookers imposing do-or-die constraints, but also as co-created, co-creative vacuums, forever opening up new creative possibilities.

 

So, what makes boundaries dynamic, and how does this influence the patterns produced by the flow forms of life? My first approach to answering this question was based on my observations of the overtly riverine growth forms of fungal mycelia. I recognized three basic relative properties of boundaries, which influence the patterns produced by such riverine forms by varying their resistance to the transfer and distribution of energy sources. The deformability of boundaries is reciprocally related to their rigidity, which resists expansion and contraction due to assimilation and release of energy sources between insides and outsides. The permeability of boundaries affects their resistance to passage of energy sources between insides and outsides. The continuity of boundaries affects the internal channelling of energy sources, the resistance to which is increased by various kinds of interruption and decreased by enhanced connectivity.

 

By varying the deformability, permeability and continuity of their boundaries, living systems can gather, conserve, explore for and redistribute energy sources in close and highly efficient correspondence with their local contextual circumstances. I suspect there is much that human societies could learn much from understanding the importance of all of these processes, if we are ever to live in truly sustainable relationship with our environment.

 

Only under circumstances of external plenty is it appropriate for boundaries to be both relatively permeable, allowing uptake of energy sources, and deformable allowing expansive growth and the consequent differentiation/ proliferation of boundary surface. These are the circumstances generally assumed to apply indefinitely by capitalist economic theory and neo-Darwinian models of evolutionary fitness [notwithstanding the paradoxical assumption that competition becomes most intense as resource ‘limits to growth’ are approached].

 

Under all other circumstances of external shortage (including those brought about by earlier uptake into the system), where the proliferation of permeable surface would promote net loss of energy sources due to leakage, growth-limiting or redirecting processes of integration become apposite. These processes minimize surface exposure by impermeabilizing, fusing and redistributing boundaries in various ways to serve distinctive life functions. Correspondingly, by rigidifying, fusing and impermeabilizing boundaries, living systems can conserve energy sources in resilient, dormant structures that survive adverse conditions, as with plant seeds, bulbs, corms and tubers. Alternatively, by impermeabilizing deformable boundaries it is possible to explore out across adverse terrain from a local feeding station, as in plant runners. And by partitioning off redundant parts, their energy sources may be redistributed to other parts of the system, as with the senescence and abscission of plant leaves.

 

Through focusing on these boundary properties, and the way they can be varied according to circumstances, a pleasing picture emerged for me of how I could account both for the different patterns observed at distinctive stages of an organism’s life history, and for the distinctive life histories of diverse organisms. But waiting in the wings, there was also another, wider and deeper answer to the question of what makes boundaries dynamic, which is implicit in their relative deformability, permeability and continuity. This answer became surprisingly obvious as soon as the discussions with Ted Lumley got under way and connected also to some other conversations I had been having with my Nigerian friend, Lere Shakunle, who had recognised a problem deep in the foundations of orthodox mathematics. And this answer appealed greatly to my own artistic aspirations. It is none other than the vital presence of space.

 

 

Eureka!  Space - The Ultimate Fluid and Source of All Fluidity!

 

So, what is space, really? Here are some of the kinds of questions I have asked myself in order to try to gain some deeper understanding of the vital role of space in evolutionary creativity.

 

Try to imagine a world or Universe without space: would there be any room to move? Now try to imagine a world or Universe of pure space: is there anyone there? Take a look at the sentences I have just written, or the one I am writing presently: what do you perceive? What do the sentences have in common? What makes them different? Perhaps you might consider that space is ‘distance’ – what comes between things. Perhaps you might consider that space is nothing, as it has no substance to it. In which case, nothing comes between things – so what is keeping them apart? Can the letters in this sentence have any meaning – make any difference – without space? Can the spaces have any meaning without the letters? What are the letters made of that makes them visible? Would they be visible if they were pure matter containing no space?

 

Through asking these kinds of questions, along with my conversations with others, I developed an increasingly powerful sense of two distinctive kinds of physical ‘presence’, one explicit and tangible, the other implicit and intangible, which together produce meaning. One of these presences informatively lines or surfaces the other, which nests within, through and around it to give rise to the expression of the distinguishable, heterogeneous natural features that characterize the Universe in all its rich diversity of form, over all scales.

 

In art, these two kinds of presence are known, respectively, as ‘figure’ and ‘ground’. All works of art can hence be thought of as configurations of information, contained in the working materials that the artist intentionally or assertively brings into dynamic relation with receptive space, which thereby induces the Art form to emerge. For example, the blank canvas invites the application of paint into an infinite variety of possibilities that the artist gives expression to. Meanwhile, the artist cannot help but be included in the emergence of the full complexity of the picture as the conveyor of paint inspired by the presence of the receptive space. The real artist (‘virtual artists’ may be another matter!) cannot sit, uninvolved like some distant voyeur regarding affairs through some transparent window. A feeling relationship has to be established between the paint and the receptive space, through the body of the artist who combines the two. And it is the engagement, as intermediary between one and the other that delights the artist; I can feel a chuckle of recognition rising in my chest as I write this.

 

In this deep sense, Nature appears to me as a Work of Art, brought into complex expression through the intermediary contextual agency that combines informational content with spatial possibility across all scales. The human artist is aping a Creative Agency who is not some eminent outsider, but both the combined and combining immanent presence in all of varying degrees of solidity and fluidity, neither of which can be absolute in a dynamic, featured, Universe. In these terms, Nature is the expression of what many might refer to as God. To Fall Out with Nature, in our quest for superior knowledge and control through the exclusion of Space, rather than to seek humble understanding, is therefore to Fall Out with this God. Likewise, to Fall Out amongst ourselves, to be alienated and feel guilt and shame in our differences as unique expressions of Nature is to Fall Out with this God. Such has been the Fate of all kinds of orthodox and fundamentalist Religions, evident implicitly in their Genesis stories. And the Fall Out from a Nuclear explosion is an expression of the implications of that ultimate Excommunication of Humanity from Nature. 

 

With these ideas in mind, my research companion, Songling Lin, has worked out a relationship between ‘complexity’, ‘information’ and ‘uncertainty’, which he expresses in the form of the following equation:

 

Complexity = Information + Uncertainty

 

By inclusionally incorporating ‘uncertainty’ as ‘spatial possibility’, this simple equation establishes a three-way relationship that overcomes the contradiction, which I will describe later, between space-excluding thermodynamic and biological/computational views of evolutionary processes. Due to their focus purely on figure, to the exclusion of ‘ground’, the latter views respectively regard information either as pure negative ‘entropy’ (‘uncertainty’/‘disorder’/’randomness’) or as pure complexity/diversity. Songling’s equation regards information as both negative spatial possibility and positive complexity operating together. It also relates to the notion of a ‘complex informational signal’ as having both an explicit or ‘real’ component and an ‘imaginary’ component, in the manner of a ‘complex number’ (which I will be discussing later). This notion was the basis for Dennis Gabor’s Nobel Prize-winning invention of holography.

 

In these terms, uncertainty as spatial possibility is a vital and inextricable inclusion in the complex, dynamic heterogeneity of the Universe, expressed over all scales. We begin to appreciate that space not only provides the common ground for the figurative expression of information, but also provides the fluidity, which mobilizes this expression into dynamic features. The greater the incorporation of space, the less solid these features become, much as paint is made more mobile by the artist through the incorporation of ‘solvent’ or ‘medium’. And as a river flows through a landscape, it conveys space into its own channels. In other words, the incorporation of space frees up creative possibility, whereas removal of space closes down possibility.

 

Space then, is the ultimate bathing fluid and dissolving fluidizer of the Universe, which, were it capable of being abstracted in pure form (which it isn’t in reality because it is always associated with information in some degree) would have zero viscosity and unrestricted possibility. This raises the question of the relation of space to the elusive ‘Ether’, which philosophers and scientists have pondered upon from time to time. 

 

The notion of the ‘Ether’, as some tangible aspect of space, arose from observations of the wave-like properties of light. Since the detached view of waves, such as those in the sea, implied ‘waves in something’, i.e. in a medium, it was natural to suppose that ‘light travelling through space’, as to the earth from the sun, was doing so in or upon this medium, the ‘aether’. Eventually, however, the existence of the ‘Ether’, was disputed because the necessary resistance or frictional influence of this medium on the velocity of light could not be demonstrated : indeed it was widely thought to have been disproved by the famous Michelson-Morley experiment, from which Einstein deduced his special Theory of Relativity based on regarding the speed of ‘light’ (in the general form of electromagnetic radiation, only a small portion of which is ‘visible’ to the human eye) as the only invariable (i.e. absolute) quantity in the Universe.

 

From an inclusional perspective, however, the notion of light travelling entirely in or upon a single tangible medium does not correspond with the real nature of a wave.  Inclusionally, a wave can be understood as a threesome of more viscous inner with less viscous outer phases reciprocally coupled through an intermediary phase, as with waves in the sea, which arise from a reciprocal coupling of seawater and air through their dynamic interface. So the notion of ‘light in or upon space’ does not make sense, whereas the idea of ‘light with space’ as a reciprocally coupled partnership does. Moreover, this coupling of informative electromagnetic (light) energy with inductive (gravitational) zero viscosity space, represents the most insubstantial (immaterial) waveform possible, and a light wave is simultaneously and reciprocally a gravity wave. All other waveforms are more substantial (matter-containing, where matter is a condensed form of space-including electromagnetic energy), whilst still requiring the inclusion of space to provide the necessary fluidity.

 

Likewise, the notion of the velocity of any waveform travelling independently through space is an illusion of a detached perspective and the abstraction of ‘time’. The inclusional view reveals that the apparent lateral movement of a wave is in fact the product of reciprocal coupling – inning and outing, upping and downing – of inner and outer phases. Similarly, the notion of purely self-defined ‘discrete particles’ uncoupled from (independent of) the space through which they are reciprocally moving and from which they draw energy, is an artefact of detachment. All journeys of inner ‘content’ in one apparent direction are reciprocally coupled with an outer contextual journey in the opposite direction and all forms of content are fundamentally waveforms, whether in ‘open interface’ (as in sea waves) or ‘encapsulating interface’ (as in a tennis ball) configurations.

 

You may find, like I do, that the following exercise may help you to visualize what is going on here. Find or purchase a toy ‘windmill’ of the kind children (and some adults who have retained their playful spirit) like to stick in sandcastles. Lay it to one side. Now, walk across a room. Ask yourself and any friends who might be watching you ‘what has just happened?’ Note your answers. Now ask, ‘what else has happened?’ Now, walk across the room again, holding the windmill out in front of you.

 

This exercise reveals just how prone we are to focus on the explicit/manifest ‘content’ and lose sight of the implicit/invisible spatial context. The usual response to the question ‘what has just happened?’ is to say ‘I/you have just walked across the room’. The usual response to the follow-up question ‘what else has just happened’ is mystified silence and/or expressions of puzzlement.

 

When we walk across the room holding the windmill in front of us, the reciprocal displacement of air-space that is invisibly coupled with our ‘own’ movement is made manifest in the spinning of the pinwheel. This reciprocal displacement by a ‘body’ immersed in a fluid was, of course, at the heart of the insight that is famously said to have induced Archimedes to jump out of his bath and run naked down the street crying ‘Eureka’; every schoolboy’s favourite story, mine included. Similarly, the coupling of inner with outer through intermediary interface was at the heart of the spiral transformations devised by Archimedes in his inventions of the ‘screw’ and ‘propeller’ represented in the blades of the windmill.

 

Of course, you may be thinking that the reciprocal displacement of a weightless, zero-viscosity fluid accompanying a moving body is of little consequence on the scale of our everyday human existence. And in some senses you would be right: this is why Newton’s laws of motion work perfectly well for us as an excellent approximation in predicting and plotting the trajectories of relatively large, solid, encapsulated waveforms (known to some as ‘particles’) such as cannonballs, spacecraft, moon and planets. These laws fail to be so predictive, however, whenever the relative solidity of the waveform ‘bodies’ decreases, as in all kinds of relatively mobile fluids (e.g. ‘bodies of air, water, etc) and at subatomic (‘quantum’) scales. Moreover, they fail at all scales to represent the dynamic possibilities of three or more bodies under one another’s mutual influence (i.e. inhabiting common space) - the so-called ‘three body problem’. The latter problem is apparent even with such seemingly hard objects as billiard balls arrayed on a pool or snooker table. Here, whenever one ball - a ‘place’ relating inner with outer through intermediary space - moves, arising from the assimilation of energy supplied through the prod of a player’s cue that it attracts to its surface, the shape of possibility space everywhere on the table transforms. This transformation is irreversible (because an exact repetition of the ball’s relational path is infinitely unlikely) and experienced locally, from the perspective of each ball, as a unique shift in the opportunity to have access to the attractive space of a pocket. It is patently not so that when one ball moves everything else stays the same - as might appear to be the case to a detached external observer unaware of the accompanying transformation of space. Similarly, a game of football uniquely experienced by each player as an ever-changing, breath-taking field of opening and closing possibilities, feels very different from the way it appears to a spectator in the grandstand purely as a complex set of transactions or exchanges. 

 

This reciprocal coupling of inner with outer is very familiar to artists, whose appreciation of the relationship of the ‘positive space’ of ‘figure’ with the ‘negative space’ of ‘ground’, enables them actually give primacy to the latter if they want to draw faithfully ‘in proportion’. By shifting the focus of attention from ‘positive’ figure to ‘negative’ ground, it is possible to avoid the inevitable prejudicial distortions that arise from focusing purely on the ‘figure’ and arrive at a deeper awareness of how the latter is ‘placed’. Moreover, this shift of attention is thought to involve increased activity of the spatially aware, verbally inarticulate ‘right hemisphere’ of the brain, relative to the analytical, articulate ‘left hemisphere’.

 

So, in terms of developing ‘contextual awareness’, the windmill exercise illustrates a valuable mental technique, which can aid our inquiries through the cultivation of an inclusional attitude of mind. Whenever you find yourself (as I often do) describing or explaining a phenomenon in a simple, small picture, linear cause and effect way, which focuses purely on the explicit ‘actions and reactions’ (‘transactions’) of local ‘positive content’, ask yourself ‘what else has happened/is happening?’ Then shift your attention to the big picture of the contextual field from which that phenomenon emerged. With practice, this call upon your inner artist will help to break you out of the paradoxical, self-referential, ‘positivist loop’ of orthodox, impositional logic.

 

Henri Poincaré, whose theory of relativity preceded and exceeded in scope that of Einstein, appreciated the issues only too well. ‘Space,’ he stated in “Science and Hypothesis”, ‘ is another framework we impose upon the world . . . here the mind may affirm because it lays down its own laws; but let us clearly understand that while these laws are imposed on our science, which otherwise could not exist, they are not imposed on Nature…..Euclidian geometry is . . . the simplest, . . . just as the polynomial of the first degree is simpler than a polynomial of the second degree. . . . the space revealed to us by our senses is absolutely different from the space of geometry.’ Here, Poincaré was in effect saying that the mathematical structure we impose on space is unlike the space that we sense, which provides possibility for movement and communication.

 

Einstein, by contrast, continued to take a detached, objective view of space, as is implicit in his description of his ‘environment’ as ‘everything outside of himself’ and in his famed imagining of travelling on, rather than in a light beam. Correspondingly, he retained the concept of the 'Ether' as the medium for light, as in his statement in 'Ether and the Theory of Relativity';

"This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials g(mu,nu), has, I think, finally disposed of the view that space is physically empty. . . . The ether of the general theory of relativity is a medium which is itself devoid of 'all' mechanical and kinematical qualities, but helps to determine mechanical (and electromagnetic) events. . . .Recapitulating, we may say that according to the general theory of relativity, space is endowed with physical qualities."

 

So, unlike Poincaré, who dismissed the notion of detached space altogether, Einstein substituted in the idea of space as a medium in itself.

 

The relation between the work of Einstein and his predecessor, Poincaré, the former rationalistic, the latter inclusional, echoed in many ways the relation between the work of Newton and his predecessor, Kepler. Although Newton acknowledged the lack of universal coherence implicit in his belief that matter consisted of ‘solid, massy, hard, impenetrable, moveable particles’ and his associated notions of fixed space and absolute time, he chose to leave understanding the necessary non-material co-ordinating agency to the domain of God or future philosophers:

 

“I wish we could derive the rest of the phaenomena of nature by the same kind of reasoning from physical principles; for I am induced by many reasons to suspect that they all may depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles laid down will afford some light either to this or some truer method of philosophy.” (, 'Philosophiae Naturalis Principia Mathematica', Isaac Newton, 1687, Author’s Preface)

 

                        and

 

“This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being”

 

 Kepler, on the other hand, saw space itself as God (or, more appositely, Goddess or Godhead), the great co-ordinating, harmonizing geometric influence orchestrating the ‘Music of the Spheres’.

 

“Why waste words?  Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?); geometry provided God with a model for the Creation and was implanted into man, together with God’s own likeness --- and not merely conveyed to his mind through the eyes.” (‘Memoir’ cited in ‘The Sleepwalkers’, Arthur Koestler, p. 264)

 

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

 

 

Ultimately, nothing in physics makes sense when space is included in the picture; everything in physics makes no sense when the space that permeates everywhere is excluded

 

 

Stating the Obvious - When Evidence of Absence is Evidence of Presence

 

Nothing I have said so far is based on new scientific knowledge or calls for conjecture about supernatural forces, extraterrestrial life etc. It all seems so surprisingly obvious, that I wonder why I have bothered to go to such lengths to try to understand and articulate it. Surely everybody knows it in their heart of hearts. And indeed many people tell me that they do, often accompanied by a patronising smile at my child-like naivety in suggesting that they don’t, a feature most noticeable amongst my academic colleagues. But, then why does what I am saying seem to bother them so much? And why do they not incorporate it into their own practice and communications, preferring instead to maintain a hard line attitude? And why, as a world community do we persist with this attitude, which engenders so much psychological, social and environmental damage? And why, when I have tried to convey the findings from my explorations to final year undergraduate students studying my ‘life, environment and people’ course at the University of Bath, have I found myself accused by colleagues and external examiners of being ‘anti-scientific’ and disturbing and misguiding the students? And why has the students’ ready acceptance and skilful artistic as well as formally scientific exposition of their understanding of the findings that I have discussed with them in open forum been said to lack evidence and scholarship and hence be scientifically worthless? And how, in the face of such contempt, have I managed, as I have so far, to continue to run the course for five years? It certainly hasn’t been easy!

 

I have already spoken of the ‘one-way filter’ that maintains the hierarchical power of the Vampire Archetype. But now I want to look a little closer at the psychological nature of this filter, through which people can admit - and indeed lay claim to - implicit knowledge, whilst at the same time opposing its implications.

 

Most fundamentally, I suspect that the one-way filter operates by controlling what is admitted as ‘evidence’, hence enabling us to turn a ‘blind eye’ to the blindingly obvious. As I have said already, inclusionality is fully consistent with the scientific finding that physical space permeates everywhere, over all scales and with the findings (if not the initial premises or explanations offered by) of relativity theory, quantum mechanics and non-linear dynamical systems theory. In other words there is ample implicit evidence for the presence of absence. But this evidence is of course unlike the kind of explicit evidence sought through orthodox logic, which dismisses ‘evidence of absence’ as ‘absence of evidence’, focused purely as this logic is on substantive, and hence tangible presence. The latter is then inappropriately regarded as ‘hard’ or ‘solid evidence’.

 

The very nature of what is perceived as ‘evidence’ is itself dependent on logical premise. The inadmissibility of implicit evidence - evidence of the presence or occurrence of nothing, buttresses the discrete presupposition of impositional logic, rendering it forever closed to the possibilities included in space, the presence of absence everywhere. The only way in which this impositional dominance of ‘material’ over ‘immaterial’ (explicit over implicit) evidence may be relaxed, is evident in the story of Doubting Thomas, who had to feel the holes (the presence of absence) in Christ’s ‘body’ in order to believe in the Resurrection.

 

And so it is that when I try to articulate our ideas about inclusionality, based on the physical presence of absence called ‘space’, that I find myself being challenged, often condescendingly, by the question, ‘where is your evidence’. But when I answer ‘everywhere’, this is treated as inadmissible. Meanwhile, those who regard implicit evidence as inadmissible, provide no evidence for the presence of a fully discrete limit. The one way filter can be a frustrating place to encounter!

 

 

Osmosis - The Realm of Positive Negativity

 

Organic life on Earth as we know it as an embodied water flow revolves around a very remarkable and, to me at least, mind-boggling phenomenon. In this phenomenon I think it may be possible to gain an insight into how the inclusion of space, as a zero viscosity fluid, participates in the dynamics of the Universe from microcosm to macrocosm. When I was first introduced to this phenomenon at School, I found it incomprehensible from the perspective of the particulate worldview that my teachers used to explain it. Yet these teachers seemed perfectly happy both with the existence of the phenomenon as such and with their incomprehensible explanation of it. They didn’t seem to see it as challenging the very principles of orthodox logic and mathematics that they clearly believed in and were trying to inculcate into the likes of me. I found this very worrying because my elder sister, who studied biology six years ahead of me, reliably informed me that this was perhaps the most important phenomenon to understand if I wanted to be a biologist. And I desperately wanted to be a biologist. So, I really did need to understand the curious world of counterbalancing inner with outer through intermediary domains in which the phenomenon of osmosis occurs.

 

When we drop a sugar cube into a glass of water, the sugar dissolves and its molecules disperse by the process of diffusion so that their concentration becomes uniform throughout the water. At least, that’s the standard description of what happens, along the lines I was told at School (hint: remember the ‘windmill’ exercise described earlier in this chapter, if you want to think about this a different way). If on the other hand, a living cell, or tissue containing many such cells, containing a sugary solution is put into the glass of water, the sugar will stay put, whereas water will flow into the cell or tissue by the process called osmosis. In the case of plant and fungal cells, the inflow of water results in a tendency for the cell to expand, which is counteracted by the resistance of the surrounding ‘cell wall’ resulting in the build up of internal ‘pressure’, known as ‘turgor’. Ultimately the expansion of the cell ceases when the resistance or ‘inward pressure’ of the wall exactly balances the outward pressure of the cell contents, and the cell is described as ‘turgid’. It is as though the cell ‘sucks’ water in until it can take no more due to the constraints of its containing boundary.

 

So, in one situation, solute particles are described as moving outwards, from high concentration to low concentration, whereas in the other, solvent (water) molecules are described as moving inwards from more dilute to less dilute solution. What could account for this difference? Well, actually, in some ways there is no difference between the two situations in terms of the process that is occurring; what differs is the frame of reference within which this process is being observed and interpreted.

 

What makes the difference between the two situations is the presence of a one way filter, in the form of the membrane between the insides and outsides of living cells, which is effectively semi permeable in that it allows passage of water molecules but not solute. In both situations, water flows inwards from more dilute to less dilute locations, but the reciprocal outward displacement of solute from more concentrated to less concentrated solution is constrained by the presence of the cell boundary. In the absence of this boundary our objective human attention tends to focus on the apparent action of solute particles moving from more dense to less dense locations as if being repelled by one another.

 

Without the filter in place, we are hence prone to impose our own reference frame and, in the same way as revealed by the windmill exercise, to lose sight of the reciprocal influx of solvent that accompanies the outward displacement of solute. In the presence of the retaining boundary, however, our attention flips to the apparent movement of the solvent. So we find our attention shifting back and forth between content and context in a way that can seem very inconsistent - which is what confused me when I was first introduced to the phenomenon at school.

 

If, on the other hand, we allow our attention to be drawn primarily by the distribution of the solvent, what becomes apparent is the relative affinity or attractiveness of the more internally informed/surfaced for the less internally informed/surfaced fluid. With regard to water, this affinity is technically described as osmotic potential, and it has a negative value referenced to a ‘pool of pure water’ of zero potential. Water is hence attracted to places with more negative potential, which gives rise to a positive osmotic or turgor pressure when these places have a restraining boundary that limits reciprocal displacement of solute (internal surface). In much the same way it may be possible to think at a fundamental level of the reciprocal relation of fluid spatial context with dynamic informational surface as a universal phenomenon, operating over all scales of organization.

 

 

Breathing Space - Inspiration and Expiration

 

In March, 2002, I visited Karlstad in Sweden, to participate in some debates about the nature of life and life forms. Rather than keep me permanently confined to the grey, box-like lecture rooms where I met with and discussed ideas with her colleagues, my host recognized that my eyes and lungs were longing to take in some of the surrounding scenery, and so took me out exploring. The weather was, for at least part of my stay, brilliantly sunny, but still very cold; the lakes were still frozen in places and huge icicles draped down the steep banks alongside the roads we travelled. My host asked me what inspired my paintings. I looked around and immediately knew what my next painting would feature.

 

When I returned to England, the spring-loaded potential I had left behind a few days beforehand had released an explosion of exuberant form of the kind that has never ceased to take my breath away since I left the tropics for the temperate zone as a seven-year old. I visited a local wetlands nature reserve where the sights of bursting leaf, flower and catkin melded with the flights, splashes, calls and swims of waterfowl. Towards the end of our visit a metallic twittering attracted our attention to the swoops and spirals of a party of sand martins, newly arrived from migration. It wasn’t long before I painted the picture shown in Figure 4.

 

 

INSERT PICTURE HERE

 

 

 

Figure 4. ‘Breathing Space’ (By Alan Rayner, Oil on Canvas, 2002). Spring IS Inspiring. New leaves open stomatal windows to sky. Sand Martins swirl down from migration towards water. Egrets flutter past. A white-ribbed Silver Birch, rooted to rocky diaphragm, transforms crimson lung-branches into leaves. Coral bark fires imagination. Pussy Willow erupts into incandescent catkins. Blackthorn snow-storms. Lichens pulsate with their own slow rhythm. Space moves within and without the embodied water flows of life. In, out, together, to gather. Implicit Human Being. In Formational Lining. Attuned.

 

 

Rhythm, I feel, is at the heart of life, the very expression of that dynamic, reciprocal relationship of inner with outer coupled through intermediary domains that waves and pulsates everywhere, from microcosm to macrocosm. The breath of life is the breathing of ever-present living space, continually transforming. When we breathe in, the outside breathes into us. When we breathe out, the outside breathes in from us. Breathing in, we become inspired, ready for action. Breathing out, we expire and relax. To exclude space is to stifle this breathing and reduce the world into dead objects, lacking internal agency, that respond like Newtonian bodies and neo-Darwinian ‘units of selection’ only to external force; the fish that swims only with the current, so they say, is a dead fish. To remove the dynamic, holey boundary that couples whilst differentiating the inner from the outer, is to dissolve the creative potential so that all becomes one - a lifeless, featureless conformity. 

 

To get a mental picture of how rhythmic patterns can arise from the reciprocal dynamic coupling of inner and outer space phases mediated by a permeable, deformable intermediary boundary, I find it helpful to think of a balloon, whose rubbery surface (skin) is full of holes. As fluid is transferred from outside to inside the balloon, so the holes in its inflating surface enlarge and increasingly release the contained fluid. The boundary expands until, providing the rate of input is sustained, a balance is reached where output and input are equal and the surface is held stationary in dynamic equilibrium, in the same way as the turgid cell whose uptake of water by osmosis is balanced by loss across its membrane and wall. If, however, the rate of fluid input exceeds a threshold amount, then the counteraction between the tendency of the balloon to expand as it gains fluid and to contract as it loses fluid through its enlarging holes, sets up a repetitive oscillation between alternative surface distributions. This oscillation, or cycle of ‘waving correspondence’, increases in complexity as input is raised further, so that the number of oscillations between repeats doubles and redoubles until yet a further threshold is reached. The balloon boundary then reconfigures apparently erratically and without ever repeating itself, like a fibrillating heart or turbulent body of fluid.

 

This picture corresponds with the patterns predicted by a relatively recently developed branch of mathematics, known as non-linear dynamical systems theory (which encompasses its more popularly known subsets, ‘chaos theory’ and ‘complexity theory’). This theory is based on ‘non-linear equations’, which contain ‘negative feedback’ terms that restrict a trend for amplification to ‘infinity’ when the equations are repeatedly ‘iterated’ (i.e. when their solutions or ‘outputs’ are ‘fed back’ as ‘inputs’ to calculate a further output). In other words, these equations generally simulate the counteraction between a drive for expansion or ‘growth’ (resulting from iteration) coupled to an increasing tendency for resistance to or dissipation (letting go) of further input, much as in the leaky balloon.

 

A well-known, relatively simple example of a non-linear equation on these lines is the ‘logistic difference equation’. This equation relates the actual number of entities (x) as a proportion of the maximum possible number (1) in a current population to the number of entities in the next generation (xnext) in terms of the net rate of reproduction (r) per head of population as follows:

 

xnext = rx – rx2

 

where x varies between zero and 1.

 

Here, the potential for increase in x, due to the reproductive drive, r, resulting from resource acquisition is countered by the negative feedback term, rx2. When this equation is iterated (i.e. when the output xnext value is used repeatedly to input the next x value) from some low initial positive value (if initiated from exact zero it will remain zero for eternity), the rx2 term increasingly constrains the increase in x. Ultimately, there is no net increase when x is equal to 1 – 1/r, representing the ‘equilibrium population size’ or ‘carrying capacity’ of the population.

 

For values of r between 1 and 3, the equilibrium population size ranges from zero to 2/3, and iteration of the equation from low values results in an initial increase in x. This increase either leads directly to attainment of the equilibrium value if r<2, or, if r>2 to a series of progressively smaller fluctuations (i.e. ‘damped oscillations) above and below the equilibrium value. For values of r<1, x becomes zero. For values of r>3, however, the population is driven over a threshold where it becomes unstable. Here it is unable to attain a single equilibrium state (known as a ‘fixed point attractor in ‘phase space’), unless arriving by some infinitesimally small chance at exactly the requisite value of 1-1/r, and instead subdividing or ‘bifurcating’ into a series of alternative states. Here, as r is increased, x values come to oscillate around first two, then four, then eight …2n values in a so-called ‘period doubling’ cascade. At r = 3.57, deterministic ‘chaos’ first becomes evident, as x values vary unrepeatedly and at r = 4, all x values between 0 and 1 become possible.

 

Note here that the ‘chaos’ produced via the logistic equation is described as ‘deterministic’ because all the ‘initial conditions’ are fixed at the beginning and there is a pre-set limit that the system cannot get beyond. The system is effectively contained within a fixed boundary and its behaviour can be predicted with complete certainty so long as the initial conditions are known precisely. The fact that in reality the initial conditions cannot be known precisely, and even tiny changes in initial conditions can be amplified by feedback into huge changes in behaviour (the so-called ‘butterfly effect’), makes the behaviour unpredictable in the longer term. But this unpredictability or uncertainty is not regarded as stochastic (due to randomness in ‘open space’) because the system is fully defined. But wait – isn’t there an inconsistency here?  In fact the system depends on the presence of open space because energy has to get from outside-in to drive the system and this energy can be dissipated through negative feedback (expanding holes in the balloon model). Space has got in through the back door – the supposed determinism is in the modelling assumptions using discrete numbers, not in the model itself. The non-linearity results from the inclusion of space. In fact that’s what non-linearity most fundamentally implies – the inclusion of space. And in real systems such non-linearity is primary, not a secondary product of forcing a primarily linear system.

 

Moreover, the balloon model is both limited in itself and exposes the limitations in current non-linear mathematics, for three further reasons.

 

Firstly, as already mentioned, it starts with a ‘given’ set of ‘initial conditions’ – a fixed amount of ‘material’ in the balloon’s skin, a fixed ‘holeyness’ of the skin and a fixed rate of input: in effect a self-contained, fixed set of ‘Rules’ imposed for all time. The story begins in an instant with no historical or future contextual influence. But what if more material can be added to the skin as the balloon expands, or if its ‘holeyness’ can be altered as its circumstances change? We would then have a truly dynamically bounded or ‘indeterminate’ system of the kind widely found in real life, like a growing fungal hypha, tree, blood vessel or nerve cell.

 

Let’s consider, as an example of a real life system, a fungal hypha growing in wood. The wall of this tube-like structure has a deformable, dome-shaped tip, which elongates as wood substance is effectively transferred from its ‘outer space’ through gaps to its inner space. Like a river eroding its way into landscape and depositing sediment, the hypha opens, closes and follows paths of least resistance (spaces) in close correspondence with its inseparable dynamic context. Branches form in this system whenever input exceeds throughput capacity to existing points of deformation on its informational boundary. These branches may form in a tributary-like pattern where they are formed at or near sites of input, or in a delta-like pattern where they are formed remote from these sites. Initially they are ‘dendritic’ (divergent from one another) and so linked ‘in series’, such that their internal (hydraulic) resistances to throughput (current) combine additively. But the branches can also fuse (‘anastomose’, self-integrate) when their self-created holey envelopes coincide, so converting a dendritic pattern into a parallel-distributing network with hugely increased internal conductivity. Now the system can, literally, ‘mushroom’, transcending its previous limitations and operating on a greatly amplified scale, like a river in flood or an erupting volcano supplied by anastomosed larva channels. We see here, then, how the variable fluidization of its boundary enables a dynamic system to evolve, both changing and being changed by its dynamic context and scale of operation.

 

The second limitation of current non-linear mathematics exposed by the balloon model, is related to the first in that it concerns the problem of imposing a discrete time-scale, independent of space. This problem is implicit in the use of algebraic formulations based on an underlying system of discrete (independent) numbers. The simulated dynamics are then necessarily referenced to a sequential time scale (hence the term ‘feedback’), even though it is clear from the balloon example that the reciprocal transformations in inner and outer space are simultaneous. As the surface informing inner and outer space moves in response to input or output, so both inner and outer space reconfigure.

 

The third limitation is that the balloon example concerns only one inner space, outer space and informational boundary. Yet in reality, as far as the human imaginative eye can see, it is clear that informational boundaries are nested in many-layers, essentially in triplicate (3-fold). Every inner space within an outer space is also an outer space enveloping an inner space of smaller scale, from sub-atomic to universal. I will return to this issue later.

 

 

Death As a Way of Life

 

As my dream about the boomslang may reveal, I am, like many people, scared of death, and would very much like, if I only could, to exclude its possibility from my own and my loved ones lives.  I do not relish the idea of death as an annihilation of the individual - as it is wont to be regarded in eliminative ‘survival of the fittest’ models of evolution. Nor do I fancy the idea of an eternal afterlife if the avoidance of pain in that realm is contingent on being ‘good enough’ in this one. Viewed impositionally, death is an absolute boundary with a finality all of its own. A severance from existence and/or place of awesome Judgement that makes life seem either pointless or a fearful trial in which even the heavenly prospect comes loaded with potential damnation of one’s Self and one’s life’s companions.

 

Viewed inclusionally, however, death seems to me like no more and no less than the ultimate expiration from inner to outer, the release of spatial potential for reconfiguration into new forms of correspondence between content and context in an ever-changing realm. It is nothing more and nothing less than the subsidence of the waveform into a place of deep calm from which new forms can emerge. That’s how it seemed as my mother, after hours of laboured breathing, let go her last sigh. I find solace in this view, a sense of ‘opening ending’, of the kind shown in Figure 5.

 

 

INSERT PICTURE HERE

 

 

Figure 5. ‘Opening Endings’ (By Alan Rayner, Oil on Canvas, 1999). An elm tree’s demise, its wing-barked boundaries opened by ravages of bark beetle and fungus, makes way for new life to fill its space. Maple leaves take over the canopy between earth and sky, but their coverage is only partial, leaving openings for arriving and departing flights of woodpeckers. Fungal decay softens the wood to allow the tunnelling of long-horn beetle larvae and probing and chiselling of beak-endings. A nest cavity provides a feeding station between egg and air.

 

 

This sense of death as an inextricable aspect of the vital inclusion of space in life, is perhaps most obvious in organisms like plants and fungi, whose absorptive means of gathering in energy sources is associated with an indeterminate pattern of development. Here, the body can potentially expand indefinitely, rather than attain a more or less specific adult size, as in many animals that move bodily from place to place in the pursuit of energy sources that they ingest.

 

In these indeterminately developing organisms, the role of local death as a means of feeding, supplying and protecting larger life comes in many guises. It appears in the senescence of leaves as they release their stores of nutrients and lose their greenness prior to their abscission and fall. It appears in the formation of wood, as a water-conducting system of open spaces, lined with strengthening walls, derived from dying cells in the core of stems and roots. It appears in the death of the centres of spreading plants and fungal fairy rings, which releases their peripheries to travel inexorably outwards. It appears in the way that local death of cells and tissue protects from incursion by potential parasites and other destructive agencies. And so on.

 

The same roles of death in animal bodies and communities also occur, but may take a little more imagination to perceive. The consumption of one organism by another is the basis for the formation of so-called ‘food webs’ that underpin the diversity of natural communities. The metamorphosis of larvae into adults, whether these be tadpoles into frogs or caterpillars into butterflies involves what can be a huge redistribution of resources from dying into living form. An intrinsic feature of the development of many animals is the process of ‘programmed cell death’ or ‘apoptosis’. This process ensures that the cells do not outstay their welcome and become cancerous (cancer is produced by potentially ‘immortal’ cells that in clinging to life drain the corporate body ion which they ultimately depend).

 

A remarkable example of the ‘making of space’ by programmed cell death in the life of a plant is found in the moss Sphagnum, which inspired the painting shown in Figure 6.

 

 

INSERT PICTURE HERE

 

 

Figure 6. ‘Sphagnum Moss’ (By Alan Rayner, Oil on Canvas, 2003). A labyrinthine network, Of Life, In a matrix of death; A close interdependence, Of One with the Other, Fills Like a Sponge, With Water, Or Blood; Cushioning; Soothing; Healing; Filtering; Raising Ground out of Water, For others to root in, Building on the Backs, Of past endeavours; Death Feeds Life, In a succession, Of amplifying Diversity; But a distanced humanity, Walled Into Itself, Feeds Death With Life

 

 

The leaves of Sphagnum contain two kinds of cells: a set of green (photosynthetic), elongated cells link together in a network of channels around a matrix of dead, empty cells, formed by programmed cell death. The latter cells readily take up water, like a sponge, and can hold as much as twenty times the dry weight of the plant. As a result, Sphagnum produces bogs on initially open water, in which other plants can take root, resulting in a succession that can eventually lead to the establishment of woodland. The dead remains of the Sphagnum forms peat. Sphagnum also can be used to treat human wounds, due to its ability to soak up blood - it is sometimes called ‘blood moss’. In the painting, I contrast the life-supporting role of death in Sphagnum, with the feeding of death with life that results from human ideological conflict. The latter is, ironically, a product of the fear of death that arguably excommunicates human from non-human Nature.

 

 

Feeling the Heat - The Thermodynamics of Spatial Inclusion

 

One of the most extraordinary tales of death and deconstruction that fascinated me at school, was the notion of the ‘heat death of the Universe’ arising from the second law of thermodynamics. According to this most fundamental Law, which I was told no scientist could ever dispute without revealing themselves to be a fool of the first order and endangering their career, everything in the Universe is dead set on an irreversible course to a condition of pure ‘disorder’ or ‘randomness’. This utterly incoherent state of maximum ‘entropy’ is understood in statistical terms as being like an infinite pack of shuffled cards, from which the emergence of any consistent ‘order’ in the form of connective arrangements (such as a ‘flush’) is ultimately impossible. However, as I alluded to earlier, such a ‘conclusion’, whereby ‘irreversibility’ is understood as the consequence of progressive degradation of structure seems at first sight to contrast with the notion of biological evolution, through the elaboration of structure from simple foundations. This apparent contrast has been the subject of much scientific debate, but ultimately it may be an example of the kind of paradoxical inconsistency that arises from the rationalistic imposition of discrete limits around and within dynamic systems, and associated focus on content dislocated from spatial context.

 

The second law of thermodynamics was deduced from studies that showed that heat engines could never be 100 % efficient because heat cannot flow from a cooler to a hotter body (whereas, in the absence of ‘insulation’ it readily flows in the opposite direction) unless ‘work’ is done. This means that in the process of heating a body from the outside, some ‘useful’ energy (i.e. coherent ‘free energy’ or ‘exergy’, the capacity to apply ‘force’ through a distance and hence do ‘work’), is irreversibly leaked or dissipated back as heat to the outside via the body’s boundary. In an isolated system, defined as a collection of matter unable to exchange energy or matter with its outside, and so fully self-contained, all irreversible change therefore entails a net degradation of energy from coherent into incoherent form and a corresponding increase in entropy. [Reversible changes, by contrast, involve zero change in entropy].

 

All of this begs the issues of what is ‘heat’, how does it differ from other forms of energy, and how relevant is the notion of an ‘isolated system’ to the real world and Universe? As I reflect on these issues, I cannot help but infer that thermodynamic theory is an artefact of imposing space-excluding definitions upon reality, arising from classical Newtonian mechanics, that fail to account for the dynamic reciprocity of inner and outer through intermediary domains, and hence make no consistent sense. Heat, and heat exchange, cannot be understood as a property purely of electromagnetic energy/matter abstracted from space. They can, however, readily be understood as a property of space in dynamic relation with energy/matter, in much the same way that osmosis can be understood as a property of solvent in dynamic relation with solute.

 

My feeling is that if we regard the inclusion of space within a dynamic system as the basis for an expansion of possibility for movement, then this can clearly explain what we perceive as an increase in temperature within the system. As illustrated by the ‘leaky balloon’ metaphor I described earlier, the transfer of heat from outside to inside a system is hence understood as a process of in-breathing (inspiring) space, leading to expansion, counteracted by the enhanced tendency of the system’s dynamic boundary to leak and hence contract. By the same token, the contraction of a system as it cools, and may also undergo phase transitions from gas to liquid to solid as its exposed surface minimizes, can be understood as out-breathing (expiring) space. Similarly, compression (application of suffocating pressure) of the system from outside will have the effect of concentrating internal space and hence an increase in temperature, whilst tensioning of the system (application of vacuum) will draw out internal space, lowering temperature.

 

The upshot of linking thermodynamics inextricably with spatial dynamics is the emergence of a very different view of the aspiration of a dynamic system towards inner-outer dynamic equilibrium, a condition of harmonic balance, rather than the ultimate disintegration apparent from a one-sided, space-excluding view.

 

Attunement - A Dynamic Balancing Act

 

By contrast with the orthodox, space-excluding view of ‘thermodynamic equilibrium’ as an incoherent ‘slough of despondence’ from which there is ultimately no escape, the inclusional view of ‘dynamic equilibrium’ is an exhilarating ‘high-wire act’, oscillating between reciprocally coupled potentials. Stasis, in the inclusional view, is located in the ‘still point’ where inner and outer potentials exactly balance, and as such, although it may be approached, is impossible to find and/or sustain because the slightest (i.e. non-zero) deviation will engender a ripple of movement and counter-movement. Far from being the default condition of the Universe, which can only be shifted through the application of external force, stasis is therefore the unattainable, ever-present attractor, around which the Universe revolves, from microcosm to macrocosm. Meanwhile, by pushing one-sidedly against this balance, through the exclusion of space, humankind may be potentiating violent disruption as a self-fulfilling prophecy of its own deepest fears of annihilation.

 

Inclusional dynamic equilibrium (which might be called spatiothermodynamic equilibrium, I suppose) is hence about as far from thermodynamic equilibrium as one can get. It differs also, however, from the notion of ‘self-organizing’, ‘far from equilibrium’, ‘dissipative systems’ at the ‘edge of chaos’ developed by Nobel Prize-Winner, Illya Prigogine, during the latter part of the last century, which became a hallmark of ‘Complexity Theory’. This notion arose from recognition that systems at or near thermodynamic equilibrium have little or no capacity to generate complex form. If the second law of thermodynamics was not to be flouted, the emergence of complex form, for example of the kind produced by biological evolution, could only be explained by the occurrence of ‘energetically open systems’. By gathering in sources of energy, these systems effectively generate a large potential difference between their insides and their outsides, which they dissipate to the outside through the proliferation of their informational surface, hence maximizing entropy gain overall. Hence the generation of structural ‘order’, apparently ‘out of chaos’, by these systems is seen as a natural, ‘self-organizing’ way of ensuring transit to the heat death of the Universe.

 

Much as I sympathized with these ideas about the emergence of complex forms as dissipative systems, far from thermodynamic equilibrium, when I first heard about them, I couldn’t make any consistent sense of them in my mind. They seemed to contain too many internal contradictions, ultimately through the hard-line imposition of a one-sided view of complex systems. ‘Chaos’ was conflated on the one hand with structural complexity and heterogeneity and on the other hand with randomness. Randomness was treated as ‘homogeneous’, even though, as I will discuss in the next chapter, it is so only as a global ‘average’ and is actually extremely heterogeneous locally. ‘Order’ was conflated both with homogeneity and with structural complexity. The double standards of the Vampire Archetype were being applied everywhere, and indeed boundary-proliferating dissipative systems are themselves powerful representations of this Archetype and its devastating potential. Moreover, the representation of life forms purely as dissipative systems seemed to me to omit at least half (and possibly much more than half) of their life stories, evident in the transformations of their dynamic boundaries.

 

As I alluded to earlier, my response to these inconsistencies was to view ‘self-organization’ in terms of balancing what I called the ‘self-differentiation’ of boundary-maximizing systems in circumstances of external ‘plenty’ with the ‘self-integration’ of boundary-minimizing systems in circumstances of external ‘shortage’. Moreover, I recognized that this dynamic balancing was mediated through the interfacial boundary that both reciprocally coupled and distinguished inner and outer domains, which, correspondingly and simultaneously, mutually influenced one another, in the manner of a river’s stream and catchment.

 

This dynamic balancing of inner with outer through intermediary implies complementary, mutually transforming relationship and so differs quite fundamentally from the notion, prevalent in Darwinian evolutionary theory, of ‘adaptation’. The latter implies the response of ‘one’ to the fixed frame of reference imposed by the other, which arises in turn from their dislocation rather than togetherness. I therefore prefer to use the word ‘attunement’ to signify this mutual harmony-seeking relationship of correspondence of one with another. Such attunement is also evident in the physical phenomenon known as ‘resonance’, which amongst other things makes suspension bridges form waves and collapse when troops march across them without ‘breaking step’.

 

 

Nested Holeyness - The Dynamic, Space-Including Geometry of Nature

 

The mutual correspondence of inner and outer via necessarily incomplete and hence ‘holey’ or ‘permeable’ intermediary domains implies a fundamental dynamic geometry of Nature, extending from microcosm to macrocosm, which differs radically from the hard-line discrete abstractions of Euclid. Given the inductive ‘pull’ of spatial attraction in its inextricable relation with its electromagnetic informational lining, this geometry is primarily non-linear or curved, giving rise to spheres, ellipsoids, spirals and tubes. Linear structure emerges secondarily from this geometry, as in the cylinders formed by trees extending from an apical dome or the hexagonal arrays formed in honeycombs and the regular surfaces of crystals derived from the close-packing of curved space domains. This natural geometry is also ‘nested’, with smaller domains contained within larger domains, due to the recurrent placement of dynamic intermediary interfaces adjoining inner and outer domains over all scales. The simplest form of expression of this geometry would be a set of concentric perforated spheres, but the elaboration of this structure through the reconfiguration of energy-space has the potential to become extremely complex. I tried to represent this geometry and the way it combines local with non-local identity over all scales in the painting and poem shown in Figure 7.

 

 

INSERT PICTURE HERE

 

 

 

Figure 7. ‘The Hole in the Mole’ (By Alan Rayner, Oil on Canvas, 2001). I AM the hole; That lives in a mole; That induces the mole; To dig the hole; That moves the mole; Through the earth; That forms a hill; That becomes a mountain; That reaches to sky; That connects with stars; And brings the rain; That the mountain collects; Into streams and rivers; That moisten the earth; That grows the grass; That freshens the air; That condenses to rain; That carries the water; That brings the mole; To Life

 

 

So-called ‘fractal geometry’ is the nearest approach that conventionally fixed-framed mathematics has made to this natural geometry of ‘nested holeyness’. It was developed by Benoit Mandelbrot to describe structures whose boundaries, unlike Euclidean surfaces, appear progressively more complex/irregular, in ‘self-similar’ patterns, the more closely they are observed. 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 ‘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 -į, through 0, to +į along a horizontal line, and all ‘imaginary’ numbers, from -įi, through 0, to +įi, 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 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 reciprocal relationship with sequential ‘feedback’, the natural requires the intermediary that holds inner and outer spatial possibilities reciprocally and simultaneously together. A realm of endless creative possibility then emerges.