Chapter 2.
Welcome to the Common Space - Where All Really Is Flow
The
Emergence of ÔInclusionalityÕ - 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 couldnÕt tell whether this was the deadly venomous South African ÔboomslangÕ or one of the several ÔharmlessÕ 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 Ômid-life
crisisÕ, 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, ÔArid ConfrontationÕ
(Figure 1, Chapter 1). Apart from a few minor rebellions where I couldnÕt 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 othersÕ expectations
of me, but couldnÕt 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 ÔResearch Assessment ExerciseÕ,
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 ÔdeliveredÕ. 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 ÔbuzzwordsÕ
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
wasnÕt 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 couldnÕt 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 ÔcrunchÕ 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, ÔDegrees of Freedom - Living in Dynamic
BoundariesÕ, was published, in which my questioning of the discretist
underpinnings of conventional natural selection theory, and the associated Ôselfish
geneÕ and Ôits all in the genesÕ (Ôgenetic
determinismÕ) 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 othersÕ expectations. It took an enormous
effort of will to keep myself going through this year, the end of which was
marked by presenting a ÔPresidentÕs AddressÕ. 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 ÔThe Origin of SpeciesÕ.
So here was I, a ÔhereticÕ 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 PresidentÕs Address would be my
mycological ÔSwansongÕ, 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 ÔFountains of the
ForestÕ, and based it around the painting shown in Figure 3, which I made a
gift of to the Society.
INSERT PICTURE HERE
Figure
3. ÔFountains of the ForestÕ
(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 Ôout of the blueÕ,
an e mail message from Doug Caldwell, a Canadian microbiologist who had developed a Ônon-DarwinianÕ
view of evolution based on his work with Ôcontinuous culture systemsÕ. 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 DougÕs message. For me at least, such expression of interest
in oneÕs work by another scientist from a different specialism, accompanied by
invitation into discussion, was all too rare. DougÕs message contained a hint of
something I had longed to hear – a ÔhonkÕ of encouragement. Maybe I wasnÕt
quite so scientifically alone as I had felt – the loneliness I had
alluded to at the opening of ÔDegrees of FreedomÕ.
The
conversation with Doug dived straight in at the deep end, assuming Universal
proportions before I knew what had hit me. ÔDo you think that life is an
infection of a dead Universe?Õ Doug demanded. ÔErÉpassÕ. But, despite my
hesitance, I was tickled to find, reflected in another, my own covert feeling
that it wasnÕt possible to understand the local details of biological diversity
without addressing much larger, even more fundamental questions. And Doug was expressing ideas he called
ÔUniversal Information TheoryÕ and ÔNested Proliferation TheoryÕ which did
indeed seem to correspond in many ways with the indeterminate (dynamically
bounded/framed), Ôinformational-content-with-spatial-contextÕ co-evolutionary
thinking that I had begun to try to express in ÔDegrees of FreedomÕ. Moreover,
Doug questioned the notion of Ônatural selectionÕ, describing it as a ÔsuperstitionÕ
rather than a ÔmechanismÕ, invoking a mythical, purely external agency making
judgemental decisions about what was or wasnÕt 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 Ôa very
interesting personÕ, called Ted Lumley. Ted, a geo-physicist and disenchanted former oil company
executive who had become interested in the way Ôexceptional teamsÕ work, at the
same time as concerned about the social and psychological damage induced by
rationalistic thinking, proved a prolific correspondent. In Ôno timeÕ (for
absolute time, split apart from space, finds no place in TedÕs
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 ÔlabelÕ our ÔthemeÕ, 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 ÔinclusionalityÕ as
having the right kind of ÔflavourÕ from one of my lists of candidates, and we
decided to settle on that.
ÔInclusionalityÕ
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 Ôan absence of presenceÕ – an
emptiness that we exclude from our focus on material things – to
appreciating space as a Ôpresence of absenceÕ, an inductive ÔattractorÕ 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 Ôlogic of the excluded middleÕ to the
three- (ternary) aspect Ôlogic of the included middleÕ. 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 ÔHoley CommunionÕ.
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 ÔinclusionalityÕ 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,
letÕs revisit the dream I described at the outset of this Chapter and see how
it may relate to the emergence of ÔinclusionalityÕ. 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 ÔunitsÕ (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 ÔqualificationsÕ. 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, na•ve 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 didnÕt
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 ÔunitsÕ 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 Ôpressure cookerÕ world of Ôsurvival of the
fittestÕ. 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 ÔfitÕ or ÔadaptedÕ 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 ÔnichesÕ), 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 ÔsymbiosesÕ?
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 ÔnatureÕ and environmental ÔnurtureÕ
as inextricably intertwined, with each otherÕs influence coinciding in the
dynamic boundaries of living systems. I saw ÔnichesÕ 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 Ôlimits to growthÕ 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 organismÕs 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 ÔdistanceÕ – 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 ÔpresenceÕ, 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 ÔfigureÕ and ÔgroundÕ.
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 (Ôvirtual artistsÕ 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 ÔcomplexityÕ, ÔinformationÕ
and ÔuncertaintyÕ, which he expresses in the form of the following equation:
Complexity = Information + Uncertainty
By
inclusionally incorporating ÔuncertaintyÕ as Ôspatial possibilityÕ, 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 ÔgroundÕ, the latter views
respectively regard information either as pure negative ÔentropyÕ
(ÔuncertaintyÕ/ÔdisorderÕ/ÕrandomnessÕ) or as pure complexity/diversity.
SonglingÕs equation regards information as both negative spatial possibility and positive complexity operating together. It also relates to the notion of a Ôcomplex
informational signalÕ as having both an explicit or ÔrealÕ component and an ÔimaginaryÕ
component, in the manner of a Ôcomplex numberÕ (which I will be discussing
later). This notion was the basis for Dennis GaborÕs 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 ÔsolventÕ or ÔmediumÕ. 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 isnÕt 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 ÔEtherÕ, which philosophers and
scientists have pondered upon from time to time.
The
notion of the ÔEtherÕ, 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 Ôwaves in somethingÕ, i.e. in a medium, it was natural to suppose that Ôlight
travelling through spaceÕ, as to the earth from the sun, was doing so in or
upon this medium, the ÔaetherÕ. Eventually, however, the existence of the ÔEtherÕ,
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 ÔlightÕ (in the general form of electromagnetic
radiation, only a small portion of which is ÔvisibleÕ 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 Ôlight in or upon spaceÕ
does not make sense, whereas the idea of Ôlight with spaceÕ 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 ÔtimeÕ.
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 Ôdiscrete particlesÕ
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 ÔcontentÕ 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 Ôopen interfaceÕ (as in sea
waves) or Ôencapsulating interfaceÕ (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 ÔwindmillÕ 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 Ôwhat has just happened?Õ Note your answers.
Now ask, Ôwhat else has happened?Õ 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 ÔcontentÕ
and lose sight of the implicit/invisible spatial context. The usual response to
the question Ôwhat has just happened?Õ is to say ÔI/you have just walked across
the roomÕ. The usual response to the follow-up question Ôwhat else has just
happenedÕ 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 ÔownÕ movement is
made manifest in the spinning of the pinwheel. This reciprocal displacement by a ÔbodyÕ 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
ÔEurekaÕ; every schoolboyÕs 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 ÔscrewÕ
and ÔpropellerÕ 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 NewtonÕs 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 ÔparticlesÕ) such as cannonballs, spacecraft, moon and planets.
These laws fail to be so predictive, however, whenever the relative solidity of
the waveform ÔbodiesÕ decreases, as in all kinds of relatively mobile fluids
(e.g. Ôbodies of air, water, etc) and at subatomic (ÔquantumÕ) scales.
Moreover, they fail at all scales
to represent the dynamic possibilities of three or more bodies under one anotherÕs mutual influence (i.e.
inhabiting common space) - the so-called Ôthree body problemÕ. 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 ÔplaceÕ
relating inner with outer through intermediary space - moves, arising from the
assimilation of energy supplied through the prod of a playerÕs 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 ballÕs 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 Ôpositive
spaceÕ of ÔfigureÕ with the Ônegative spaceÕ of ÔgroundÕ, enables them actually
give primacy to the latter if they want to draw faithfully Ôin proportionÕ. By
shifting the focus of attention from ÔpositiveÕ figure to ÔnegativeÕ ground, it
is possible to avoid the inevitable prejudicial distortions that arise from
focusing purely on the ÔfigureÕ and arrive at a deeper awareness of how the
latter is ÔplacedÕ. Moreover, this shift of attention is thought to involve
increased activity of the spatially aware, verbally inarticulate Ôright
hemisphereÕ of the brain, relative to the analytical, articulate Ôleft
hemisphereÕ.
So,
in terms of developing Ôcontextual awarenessÕ, 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 Ôactions and reactionsÕ (ÔtransactionsÕ)
of local Ôpositive contentÕ, ask yourself Ôwhat else has happened/is
happening?Õ 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, Ôpositivist loopÕ of orthodox, impositional logic.
Henri
PoincarŽ, whose theory of relativity preceded and exceeded in scope that of
Einstein, appreciated the issues only too well. ÔSpace,Õ he stated in ÒScience
and HypothesisÓ, Ô 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 NatureÉ..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.Õ Here, PoincarŽ 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 ÔenvironmentÕ as Ôeverything outside of
himselfÕ 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 PoincarŽ, 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, PoincarŽ, 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 Ôsolid, massy, hard, impenetrable,
moveable particlesÕ 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:
ÒI 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.Ó (, 'Philosophiae Naturalis Principia Mathematica', Isaac Newton,
1687, AuthorÕs Preface)
and
ÒThis most beautiful system of the sun, planets, and
comets, could only proceed from the counsel and dominion of an intelligent and
powerful BeingÓ
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 ÔMusic of the SpheresÕ.
ÒWhy 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 GodÕs own likeness ---
and not merely conveyed to his mind through the eyes.Ó (ÔMemoirÕ cited in ÔThe
SleepwalkersÕ, 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 donÕt, 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 Ôlife, environment and peopleÕ course at the University of Bath,
have I found myself accused by colleagues and external examiners of being Ôanti-scientificÕ
and disturbing and misguiding the students? And why has the studentsÕ 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 hasnÕt been
easy!
I
have already spoken of the Ôone-way filterÕ 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 ÔevidenceÕ, hence
enabling us to turn a Ôblind eyeÕ 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 Ôevidence of absenceÕ as Ôabsence of evidenceÕ, focused purely as this logic is on substantive, and hence tangible presence. The latter is then inappropriately regarded
as ÔhardÕ or Ôsolid evidenceÕ.
The
very nature of what is perceived as ÔevidenceÕ 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 ÔmaterialÕ over ÔimmaterialÕ
(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 ChristÕs ÔbodyÕ 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 ÔspaceÕ, that I find myself being
challenged, often condescendingly, by the question, Ôwhere is your evidenceÕ.
But when I answer ÔeverywhereÕ, 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 didnÕt
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,
thatÕs the standard description of
what happens, along the lines I was told at School (hint: remember the ÔwindmillÕ
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 Ôcell
wallÕ resulting in the build up of internal ÔpressureÕ, known as ÔturgorÕ.
Ultimately the expansion of the cell ceases when the resistance or Ôinward
pressureÕ of the wall exactly balances the outward pressure of the cell
contents, and the cell is described as ÔturgidÕ. It is as though the cell ÔsucksÕ
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 Ôpool of pure
waterÕ 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 wasnÕt long before I painted the
picture shown in Figure 4.
Figure
4. ÔBreathing SpaceÕ (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 Ôunits of selectionÕ 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 Ôwaving
correspondenceÕ, 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, Ôchaos theoryÕ and Ôcomplexity
theoryÕ). This theory is based on Ônon-linear equationsÕ, which contain Ônegative
feedbackÕ terms that restrict a trend for amplification to ÔinfinityÕ when the
equations are repeatedly ÔiteratedÕ (i.e. when their solutions or ÔoutputsÕ are
Ôfed backÕ as ÔinputsÕ to calculate a further output). In other words, these
equations generally simulate the counteraction between a drive for expansion or
ÔgrowthÕ (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 Ôlogistic difference equationÕ. 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 Ôequilibrium
population sizeÕ or Ôcarrying capacityÕ 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. Ôdamped
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 Ôfixed point attractor in Ôphase spaceÕ), unless
arriving by some infinitesimally small chance at exactly the requisite value of
1-1/r, and instead subdividing or ÔbifurcatingÕ
into a series of alternative states. Here, as r is increased, x values come to oscillate around first
two, then four, then eight É2n values in a so-called Ôperiod doublingÕ cascade.
At r = 3.57, deterministic ÔchaosÕ 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 ÔchaosÕ produced via the logistic equation is described as ÔdeterministicÕ
because all the Ôinitial conditionsÕ 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 Ôbutterfly
effectÕ), makes the behaviour unpredictable in the longer term. But this
unpredictability or uncertainty is not regarded as stochastic (due to
randomness in Ôopen spaceÕ) because the system is fully defined. But wait –
isnÕt 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 thatÕs 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 ÔgivenÕ set of Ôinitial conditionsÕ –
a fixed amount of ÔmaterialÕ in the balloonÕs skin, a fixed ÔholeynessÕ of the
skin and a fixed rate of input: in effect a self-contained, fixed set of ÔRulesÕ
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 ÔholeynessÕ can be altered as its circumstances change? We would then
have a truly dynamically bounded or ÔindeterminateÕ system of the kind widely
found in real life, like a growing fungal hypha, tree, blood vessel or nerve
cell.
LetÕs
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 Ôouter spaceÕ
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 ÔdendriticÕ (divergent from one another) and so linked Ôin seriesÕ,
such that their internal (hydraulic) resistances to throughput (current)
combine additively. But the branches can also fuse (ÔanastomoseÕ,
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, ÔmushroomÕ, 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 ÔfeedbackÕ), 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.
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 Ôsurvival of the fittestÕ 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 Ôgood enoughÕ 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 oneÕs Self and oneÕs lifeÕs 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. ThatÕs 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 Ôopening endingÕ, of the kind shown in Figure 5.
INSERT PICTURE HERE
Figure
5. ÔOpening EndingsÕ (By Alan Rayner,
Oil on Canvas, 1999). An elm treeÕs 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 Ôfood websÕ 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 Ôprogrammed
cell deathÕ or ÔapoptosisÕ. This process ensures that the cells do not outstay
their welcome and become cancerous (cancer is produced by potentially ÔimmortalÕ
cells that in clinging to life drain the corporate body ion which they
ultimately depend).
A
remarkable example of the Ômaking of spaceÕ 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. ÔSphagnum MossÕ (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 Ôblood mossÕ. 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 Ôheat death of the UniverseÕ 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 ÔdisorderÕ
or ÔrandomnessÕ. This utterly incoherent state of maximum ÔentropyÕ is
understood in statistical terms as being like an infinite pack of shuffled cards,
from which the emergence of any consistent ÔorderÕ in the form of connective
arrangements (such as a ÔflushÕ) is ultimately impossible. However, as I
alluded to earlier, such a ÔconclusionÕ, whereby ÔirreversibilityÕ 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 ÔinsulationÕ it readily flows in
the opposite direction) unless ÔworkÕ is done. This means that in the process
of heating a body from the outside, some ÔusefulÕ energy (i.e. coherent Ôfree
energyÕ or ÔexergyÕ, the capacity to apply ÔforceÕ through a distance and hence
do ÔworkÕ), is irreversibly leaked
or dissipated back as heat to the outside via the bodyÕs 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 ÔheatÕ, how does it differ from other forms
of energy, and how relevant is the notion of an Ôisolated systemÕ 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 Ôleaky balloonÕ 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 systemÕs 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 Ôthermodynamic equilibriumÕ
as an incoherent Ôslough of despondenceÕ from which there is ultimately no
escape, the inclusional view of Ôdynamic equilibriumÕ is an exhilarating Ôhigh-wire
actÕ, oscillating between reciprocally coupled potentials. Stasis, in the
inclusional view, is located in the Ôstill pointÕ 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 Ôself-organizingÕ, Ôfar
from equilibriumÕ, Ôdissipative systemsÕ at the Ôedge of chaosÕ developed by
Nobel Prize-Winner, Illya Prigogine, during the latter part of the last century,
which became a hallmark of ÔComplexity TheoryÕ. 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 Ôenergetically
open systemsÕ. 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 ÔorderÕ, apparently Ôout of chaosÕ, by these
systems is seen as a natural, Ôself-organizingÕ 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 couldnÕt 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. ÔChaosÕ was conflated on the one
hand with structural complexity and heterogeneity and on the other hand with
randomness. Randomness was treated as ÔhomogeneousÕ, even though, as I will
discuss in the next chapter, it is so only as a global ÔaverageÕ and is
actually extremely heterogeneous locally. ÔOrderÕ 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 Ôself-organizationÕ
in terms of balancing what I
called the Ôself-differentiationÕ of boundary-maximizing systems in
circumstances of external ÔplentyÕ with the Ôself-integrationÕ of
boundary-minimizing systems in circumstances of external ÔshortageÕ. 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 riverÕs 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 ÔadaptationÕ. The latter implies the response of ÔoneÕ
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 ÔattunementÕ
to signify this mutual harmony-seeking relationship of correspondence of one
with another. Such attunement is also evident in the physical phenomenon known
as ÔresonanceÕ, which amongst other things makes suspension bridges form waves
and collapse when troops march across them without Ôbreaking stepÕ.
Nested
Holeyness - The Dynamic, Space-Including Geometry of Nature
The
mutual correspondence of inner and outer via necessarily incomplete and hence ÔholeyÕ
or ÔpermeableÕ 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 ÔpullÕ 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 ÔnestedÕ,
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. ÔThe Hole in the MoleÕ (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
Ôfractal geometryÕ is the nearest approach that conventionally fixed-framed
mathematics has made to this natural geometry of Ônested holeynessÕ. It was
developed by Benoit Mandelbrot to describe structures whose boundaries, unlike
Euclidean surfaces, appear progressively more complex/irregular, in Ôself-similarÕ
patterns, the more closely they are observed. A famous example is the ÔMandelbrot
setÕ, made by mapping the distribution of points in the Ôcomplex planeÕ 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 Ôcomplex numberÕ is a number that consists of a
combination of a ÔrealÕ and ÔimaginaryÕ component, the latter being a
derivation of, ÔiÕ, the square
root of -1. The complex plane is formed in the space defined by placing all ÔrealÕ
numbers, from -°, through 0, to +° along a horizontal line, and all ÔimaginaryÕ
numbers, from -°i, through 0, to +°i, along a vertical line, and using these Euclidean
lines as co-ordinates. In effect, it represents a way of increasing the Ôpossibility
spaceÕ 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 ÔattractorsÕ have more generally been referred to as Ôfractal basin
boundariesÕ, 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 ÔfeedbackÕ, the natural requires the intermediary that
holds inner and outer spatial possibilities reciprocally and simultaneously
together. A realm of endless creative possibility then emerges.