Alan Rayner

In the twentieth century, two dramatic technical breakthroughs combined with a long-standing approach to philosophical inquiry to yield a distinctive new vision of the nature and origin of life and living things, including human beings. The discovery of the genetic code and advent of modern computers, when viewed in the light of objective scientific inquiry projected an image of evolution as the spread and diversification of genetic information, and of life forms as information processors - computational machines. Correspondingly, more and more effort has been put into discovering firstly the calculational procedures or 'algorithms' that underlie behaviour and pattern generation amongst life forms and secondly the physical and chemical mechanisms through which these algorithms operate. Once we know these procedures and mechanisms, it is assumed we can have a good understanding of what makes life 'tick', in essence like clockwork. Here, I wish to question this assumption. Is the representation of living things as computational machines accurate? How far can it help us to understand how life truly evolves and relates to other life? Are there ways in which it could be a dangerous misrepresentation, leaving something vital outside consideration, and hence potentially profoundly misleading and even damaging?

My questioning of the vision of life forms as computational machines has three main avenues:

1. A reflection on the ways we inquire into reality, and how the nature of the inquiry affects the representation of nature. Is this representation a reality, an abstraction or a virtual reality?
2. A consideration of the use and abuse of mathematical and logical reconstructions and simulations of reality and their implications.
3. A review of the real nature of living systems, seen 'more empathically' as 'embodied water flows'.

We are all equipped with two distinctive ways of seeing detached and immersed. The immersed way of seeing makes no separation between our inner and outer selves. We feel absorbed and involved - and inclined to lose our sense of control and where we are - in what we see around us in our horizontal field as a rich, never-ending tapestry of space and features that moves reciprocally around and along with us as we move through it. The detached view distinguishes our inner selves as subjects from what we regard as objects in our external surroundings. We gain a sense of independence, control and certainty about where we are in relation to these objects, but lose all sense of the interdependent relationship between our movements and theirs, between our own influence and their influence mediated through our common space.

I think we tend to reverse and even abandon the natural primacy of the immersed perspective in favour of the detached as we emerge through childhood and adjust to the survival needs of our terrestrial existence. Here, air seems like a separating nothingness and ground is what we stand abstracted from at right angles. In fact, I sometimes reflect that if we were aquatic mammals, how different might our relationships with one another and our common space be.

Our dry abstraction of spatial context out of material content has, moreover, been enormously reinforced by our predator's binocular 'sorting out' vision and rationalistic philosophies. In the west, these philosophies surfaced with the likes of Aristotle and Parmenides and culminated in the Enlightenment of Bacon and Descartes and the clockwork universe of Newtonian mechanics. To this day, they have become deeply embedded in the methods we use, and addictively entrain our offspring to use, to inquire into reality.

So, perversely, we inquire into nature by excommunicating ourselves, and the objects of our studies, from nature. We impose restrictive practices on our inquiries that may seem to increase our certainty and sense of control, but only do so by creating even greater uncertainties about how our conclusions actually relate to reality.

I unconsciously represented my personal feelings about the eclipse of the immersed by the detached view, and resultant excommunication of nature, around 30 years ago in two paintings:

   Slide: Tropical Involvement

This painting, made after my final examinations in Natural Sciences, depicts the immersed feeling of dynamic complexity in living systems. A turbulent river rushes between rock-lined banks from fiery, tiger-striped sunset towards unexpected tranquility where it allows a daffodil to emerge from its shallows. A night-bird follows the stream past intricately interwoven forest towards darkness. A dragonfly luxuriates below a fruit-laden tree, bereft of leaves. Life is wild, wet and full of surprises.

The restrictive practices resulting from and in our excommunication of nature, are, in their turn, both expressions of and expressed in the mathematical and logical tools we use to conduct and describe the results of our inquiries. Our mathematical foundations continue to be grounded in the use of so-called 'natural numbers' and Euclidian geometry, and our logic on notions of objectivity and falsifiability. What, you might ask, is natural or realistic about these mathematical and logical tools? And since use of the tools prescribes the findings we make, isn't there a danger of self-fulfilling prophecy through treating these findings as proof of the presuppositions inherent in use of the tools?

Perhaps it's easier to ask, given that our perception of reality depends on our senses and so can't be independently 'judged', 'what isn't natural or realistic' about the tools? So, what isn't natural about 'natural numbers'? And, what isn't realistic about Euclidean geometry?

I would suggest - as others like Henri Poincare have done before me - most fundamentally that the answer to both these questions lies in the discretization or exclusion of space, such that a numerical entity is treated as isolated and hence independent, and a point, line or plane is treated as less than three dimensional. In other words, both natural numbers and Euclidian geometry result from the abstraction of context out of content, and vice versa, through the imposition of a fixed reference frame that doesn't actually exist. We therefore attempt to reconstruct reality by assembling discrete contents with fixed boundaries, metaphorical 'building blocks', in linear sequence without regard to their transformative spatial relationships. We literally leave something vital out of our reconstructions, but don't notice because the reconstructions seem to validate themselves. A curve assembled from infinitesimal straight lines looks much like a curve. A virtual reality assembled from discrete bytes, looks much like reality - unless you get really close up to it and the steps in its soulless pixellated construction stand out. A digital recording sounds much like the original, unless you are sensitive to its breathless clarity.

By the same token, notions of objectivity and falsifiability rest on the supposed ability to judge the truth of discrete entities independent of their spatial context, from which no thing, in reality, can be isolated. We set about mathematical and legalistic proofs that are founded in the falsehood of imposing a discrete reference frame - an abstraction. By putting reality, like Schrodinger's Cat, in a fully fixed and sealed box, we are wrong before we even begin. Reality itself cannot lie: it is as it is. Only abstract definitions of reality lie, in the very act of claiming truth and proof.

These mathematical and logical limitations have been recognized in the development of non-linear dynamical systems theory and Godel's theorem of incompleteness [the latter is a mathematical formulation of the paradox of the Cretan liar who tells you that 'all Cretans are liars']. However, it is not often made clear that these theories implicitly demonstrate the need to include the reciprocal coupling (resonance) of inner with outer space (possibility for movement) in any explanation of dynamic natural features. Indeed, it is not often made clear that such coupling is a primary universal characteristic rather than a secondary property emerging from a primarily linear initial condition. Even current demonstrations of 'deterministic chaos' and 'fractal geometry' make the latter assumption and so don't acknowledge the implicit inclusion of space in the dynamics they describe.

A detailed description of the ins and outs of non-linear theory is not possible within the time limits imposed upon this lecture! However, I will try to give some preliminary indications of its implications for the way we understand numbers and the real geometry of nature.

Firstly, with regard to numbers, I could start by asking 'why is 2 not the same as two ones?' In fact, linear theory, based on the principle of 'superposition' which underlies Newton's so-called 'Laws of Motion', would presuppose that 2 is the same as two ones, or, more generally, that

F(a) + F(b) = F(a + b)

Clearly this cannot hold true for functions that include the interaction of one with an other together in space, notably power functions. For example:

(a + b)² =/= a² + b²

but does = a² + b² + 2ab

So 2, when included, via a power function, in its own dynamics, has a distinct identity from two independent 1s. In other words, 1 and 1 united in space have emergent properties not evident in 1 and 1 alone. The dynamic combination of one with another, which is a primary characteristic of universal features, is necessarily non-linear. No universal feature can be understood in isolation from what it contains and is contained in and that together forms its distinct, but never discrete, identity. Every feature is a couple: a dynamic threesome of one, other and both - inner, outer and inter phases. Linearity is only achieved either by excluding one from other or integrating (unifying) them completely. To represent numbers as units - discrete entities - is unrealistic.

With regard to geometry, to represent any point, line or plane literally as devoid of space - as content freed from context - is unrealistic, removing the heterogeneous relief that is characteristic of all natural structures and imposing in its place a monotonous uniformity. By contrast, in order to retain this relief, it is necessary to use a geometry that includes spatial context with the distribution of substantial content. In such a geometry, surfaces are always complex, holey arrays rather than perfectly smooth coverings. And as these holey arrays are examined from closer and closer range, more and more holey arrays come into view. This is a geometry of nested holeyness, of necessarily incomplete surfaces leading into and out of each other over scales ranging from sub-atomic to universal. Moreover it is a dynamic geometry of reciprocally shifting relationships between inner and outer inductive spaces - a geometry of participatory rather than excluded space.

I tried to represent this kind of geometry in a painting:

The Hole in the Mole – an 'inclusional' poem, by Alan Rayner

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

An approach to such a geometry of nested space has been described as 'Fractal Geometry', based on the notion of structures with 'fractional' rather than purely integral dimensions, according to the relation

M = kr^D

which describes the relation between the material content (M) and the radius of the spatial field (r) occupied by a structure in terms of a power function or dimension, which can be fractional.

Fractal geometry therefore goes some way towards a more realistic representation of natural form. However, it remains framed in conventional abstract mathematical terms of fractions of discrete numerical dimensions of 1,2 and 3.

This brings me to consider whether it can ever be possible to represent nature realistically, and to what extent we can continue to use abstract mathematics and logic for such representation. My current answer to the first question is 'I don't know, but I would at least like to try to be more imaginative'. My answer to the second question is that abstraction can continue to be a very useful tool as long as we remain fully aware of its limitations and appreciate that in the gap between abstract representation and reality may yet be found deep insights into the true nature of reality.

So, what insights into the real nature of living systems can be gained from comparing our dry depiction of 'artificial life' with real life? As you might gather from 'The Hole in the Mole', of primary concern to me is the need to combine detached and immersed ways of seeing to yield what I call an Inclusional view of Spatial Togetherness or coupling. Here the dynamic relationship (resonance) between inner and outer spaces is included (as opposed to excluded, as in rationalistic representations) in our understanding. Moreover, to appreciate how this relationship is mediated in organic life forms as we know them here on Earth, we need only add water to the dry ingredients of our artificial representations!

For me, rivers have always been a wonderful metaphor in fact more than a metaphor, actually an inclusional description, of the way life diversifies into its myriad of dynamic forms. As it erodes rock and deposits sediment, a river both shapes and is shaped by the landscape it flows through, both creating and following paths of least resistance opening up and closing down spatial possibility for movement. This shaping occurs at the rivers banks, which mediate the reciprocally changing relation between inseparable stream and catchment content and context.

And just the same kind of shaping occurs in all organic forms of life.

Life form is a co-dynamic reciprocity of inner phase and outer phase coupled through inter-phase (dynamic boundary). One (content) is inseparable from and cannot change without simultaneously and reciprocally changing Other (context). All evolution is co-evolution, the dynamic attunement of content with context. Life forms are not Newtonian Bodies, but rather dynamic embodiments of the space that they both include and are included within. As energetically open systems, they are necessarily at least to some extent indeterminate (dynamically bounded) and in communication with their neighbours and surroundings. As a result of their growth or movements, these forms incorporate and interact with their surroundings in dynamic contexts through which they traverse, excavate and follow interconnected, riverine paths of least resistance. Here, the physical properties of water as a receptive medium for energy assimilation and transfer, and the way the configuration of this medium depends on the permeability, deformability and continuity of its retaining boundaries, are key to the diversity and versatility of life patterns.

Organisms are not discrete computational Machines processing digital information. DNA is not transmitted on its own from one generation to the next, but flows through a continuum of watery space that ultimately includes even extinct ancestors. DNA is not information in itself, which means the same anywhere, but rather gives and is given meaning through its dynamic relation with protein in the contextual medium of water retained within boundaries of variable deformability, permeability and continuity. And this meaning can change with context, just as the meaning of words in this sentence can change in the context of other words and spaces and sentences. And context lies inseparably both within and around the boundaries of organic life forms, as we know them on Earth, as embodied water flows responding to and producing change, like a river that both shapes and is shaped by landscape.

So, what, actually is information in this dynamic context? It is no more and no less than the dynamic inter-phase boundary, or relational surface that gives shape (i.e. in-forms) to both inner and outer space, like the banks that mediate the relation between a rivers stream and catchment.

So, what might this INCLUSIONAL way of seeing offer for our future understanding of the diversity of life and its evolution?

Most fundamentally, it changes the way we understand change. No treatment that attempts to fix or ignore context whilst changing content, in effect by excluding space or regarding boundaries as stationary limits, can hope, in itself, realistically to represent change. Space is what provides POSSIBILITY for change, and as change occurs, so the shape of spatial possibility also changes. Change is autocatalytic.

More specifically, inclusionality changes the way we might ask questions or provide explanations on the basis of our biological and chemical knowledge.

As soon as the pivotal significance of boundaries as dynamic fulcra mediating the relationship between inner and outer space phases is appreciated, attention can focus on how the holeyness of these boundaries influences their permeability, deformability and continuity. It then becomes possible to appreciate the distinction between informed holes or spaces, incorporated during boundary generation, and exformed holes associated with degeneration, death and decomposition. I depicted this relationship between constructive 'information' and destructive 'exformation' in a painting:

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.

The fundamental role of the availability of reducing and oxidizing power in generative and degenerative processes can then in turn be appreciated.

And, from the point of view of genetic information, the co-evolutionary attunement of relational surface between DNA and protein (as opposed to adaptation of one to the other) in a watery medium is seen as an inescapable consequence of life. To quote Barry Commoner: "DNA did not create life; life created DNA". Space is vital to life, in all its rich heterogeneity of watery form.

I'd like to end by referring to a recent analytical study made of the structure of the Internet. Here is a map representing the findings of that study:

Take a close look at this map. Do you see anything 'wrong' with it? At first sight it looked to me rather like an image of a fungal mycelium. But then I looked again and realized that it actually looked like a very dysfunctional mycelium a research colleague had once isolated from an incompatible reaction between strains isolated from what at that time were the Soviet Union and USA!

So, what did the analytical map and the dysfunctional mycelium have in common?

You've guessed it: they both lacked internal spatial connections and so were unable to operate as efficient communications networks. Maybe that's what happens when you exclude space: communication breaks down!!

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My Hope: To help develop a more empathic, more fulfilling way of thinking/feeling about relationships amongst ourselves, other organisms and our living space, which acknowledges the fact that the boundaries we inhabit are not absolute and fixed but rather inform dynamic, interactive domains that allow a rich variety of patterns to emerge and transform our lives

A D M Rayner