The Cage, The Climbing Frame and The Swimming Pool -

Alan Rayner
7 min readMar 28, 2020

How Real Life Bends the Rules of Intangible Mathematical Structure

Future Present’ (Oil painting on canvas by Alan Rayner, 2000)

Much of my privileged early childhood was spent playing in a Kenyan garden, which sloped down to the River Nairobi at its bottom. There were trees to climb, lawns to run, jump and sprawl on and a swimming pool to immerse in. There was also some potentially dangerous wildlife and a Mau Mau uprising to contend with as a constant source of fear in the ‘black-ground’. And, yes, there were dark-skinned, pink-palmed African servants and their children to care for me and play with as an extended family. But their living conditions in a hut near the chicken run were a far cry from those in our elevated large house and veranda overlooking all that lay below it.

Years later, having just taken my final exams in ‘natural sciences’ at King’s College, Cambridge, I painted this picture as a recollection of those vibrant but scary colonial times, transported into an English context.

Tropical Involvement’ (Oil painting on board by Alan Rayner, 1972)

One fateful day, I climbed too high up a jacaranda tree, a branch bent and broke under my weight and I was lucky only to suffer a severely broken arm and gashed leg. Not long afterwards my father suffered a stroke and required hospital treatment back in England.

Trauma followed upon trauma. Literally overnight I found myself transported from that tropical involvement, never to return. And before long I was confined within a London schoolroom trying to decipher the abstract mathematical mysteries of whole numbers, fractions and straight-sided figures. These mysteries converted the boundless freedom for movement of natural space into a three-dimensional cage, and time into a line of separate instants from beginning to end. They didn’t add up to anything resembling my actual experience of continuous real life outdoors. Nonetheless, they were supposed to define ‘The Laws of Nature’ as a fixed set of rules. They needed to be learned and adhered to, especially as a good, ‘objective’ scientist, if you were not to ‘go wrong’. So that is what I tried to do. But somewhere deep within me would have none of it.

A year after painting ‘Tropical Involvement’, as I was embarking on a PhD study on fungal ecology, I made another painting, entitled ‘Arid Confrontation’. This brought my by now unconscious discomfort with abstract scientific methodology and mathematics out into open expression.

Arid Confrontation’ (Oil painting on board by Alan Rayner, 1973)

There was something about this methodology that cut me as scientific observer off from the natural world I experienced, delighted in and wanted to understand. The effect was desolate. I felt the need to re-immerse in the flow of what I was observing, and over the years that lay ahead my work departed further and further from the ‘straight and narrow’ path of abstract rationality.

Eventually, after further trauma and at the same time that I painted ‘Future Present’ (above), I fully realized what it is about the objective view of reality that was causing me so much discomfort. It ignores and/or removes from material form what is actually vital for this form to exist and come to life! Far from being ‘realistic’ or ‘true to life’, it is a restriction to the straight and narrow that can have no tangible existence. And yet it purports to represent just that as a rigid structural framework within and against which to measure and plot the distribution and movement of ‘things’.

So what is it that is being removed or ignored, and what is it that this mathematical structure actually represents? A clue to the answer can be found by questioning what a dimensionless point, a breadth-less line, a depthless surface or a box-frame of depthless surfaces attached to one another can truly amount to. Clearly they can’t amount to anything substantial because there is no such thing as a substance without thickness!

Can you imagine what this natural presence removed or ignored by abstract mathematical definition could be? It took a long while for the answer to dawn on me. But when it did, it turned my painfully learned abstract world view outside-in, back to what I knew as a child playing in a Kenyan garden, and to what countless soulfully aware predecessors overlooked by scientific and mathematical rationalism have known before me.

Ironically, the answer to the question of ‘what’s gone absent without leave’ is one and the same intangible stillness of void space that exists eternally and everywhere without limit! This stillness is anything but rigid. Rather it is a receptive presence that freely both permits and attracts movement — as may be apparent when you vacuum clean your carpet! Being insubstantial, it cannot be cut or displaced by moving form, but simply slips silently through it.

So, it dawned on me that material form and immaterial space are neither mutually exclusive nor one and the same as is supposed by abstract thought, but in reality distinct but mutually inclusive presences. This set the scene for me to develop a new way of understanding evolutionary processes based on what I have called ‘natural inclusion’. This subsumes the abstract concept of ‘natural selection’, which envisages life as a competitive struggle to fit a pre-defined ‘box of space’ called a ‘niche’. The latter concept, and its entourage of ‘social Darwinism, eugenics and ‘selfish gene theory’ was also a source of great discomfort for me as someone with deeply compassionate values.

In order fully to develop my awareness of natural inclusion, however, there was one more imaginative leap I needed to make. I had to work out how material form and immaterial space actually could naturally include each other. This raised the question of how natural boundaries that distinguish material bodies from one another and the space they are immersed in could come into being. Clearly they couldn’t just pop instantaneously fully formed into existence as ‘something from nothing’ — not in my imagination anyway.

The realization came to me rather readily as a result of my enjoyment of painting. A blob of paint placed on a canvas remains just that: a blob of paint. To come to life as an image, it needs to flow. Aha! I realized that natural boundaries can only be formed dynamically, as an expression of energy flow, and that can neither happen instantaneously, nor can it come to a stop if the form is not to disappear instantaneously back where it came from. The dynamically bounded form of a whirlpool, for example, disappears if its circulation stops.

Natural boundaries are intrinsically dynamic, not rigidly fixed in place. Time cannot be abstracted from material form and neither can space if the form is to exist and persist for more than no time.

Gosh! The rigid cage of abstract space and time constructed by conventional mathematics and objective science for material forms to be pushed and pulled around within by external ‘force’ is nothing of the sort!

In place of the deterministic rules of abstract ‘lines of force’ and ‘boxed-in’ space, we have intangible guidelines — ‘channels of receptive spatial influence’ as inductive ‘attractors’. Energy pulses and circulates responsively along and around these channels between and around all tangible material forms, from subatomic in scale upwards. These forms come to life as ‘flow-forms’ — forms made of flow, not inert building blocks of mass. Instead of the independence of measurable distance, duration, energy and matter of particulate Newtonian mechanics, and the ‘space-time’ of Einstein’s relativity theories, we have the ‘place-time’ of natural inclusion. Here all material form exists as a locality — a ‘place somewhere’ as a dynamic inclusion of space everywhere.

The rigid cage becomes an intangible climbing frame for life to flow and blossom around. Space continuously pools all swimmingly together instead of splitting us apart. Knowing our selves to be centres of receptive-responsive awareness — dynamically enveloped holes, not definitively bounded wholes — compassion for one another as neighbours in natural spatial and energetic neighbourhood becomes second nature, not moral obligation. We look after one another and our environment as we look after our selves coming into and passing on life in natural relay. Doesn’t that bending of rules feel infinitely better, more realistic and more creative than struggling to fit ourselves in to a predetermined box of our own making?

How Compassion Fruits’ (Oil painting on canvas by Alan Rayner, 2008)

Further Reading:-


Rayner, A.D. (2011). Space cannot be cut: why self-identity naturally includes neighbourhood. Integrative Psychological and Behavioural Science, 45, 161–184.

Rayner ADM (2011) NaturesScope: Unlocking our natural empathy and creativity — an inspiring new way of relating to our natural origins and one another through natural inclusion. Winchester, UK; Washington USA: O Books.

Rayner, A. (2012) What are natural systems, actually? Advances in System Science and Application 12, 328–347

Rayner, A (2017) The Origin of Life Patterns In the Natural Inclusion Of Space in Flux Berlin/Heidelberg: Springer.

Rayner, A (2018). The vitality of the intangible: crossing the threshold from abstract materialism to natural reality. Human Arenas 1 pp 9–20.

Rayner, A (2020) From abstract freeze-frame to natural kinship

Rayner, A (2020) Cold & Warm Geometry: How Rigid and Fluid Structures Affect Our Human Relationships and Sense of Self.

Rayner, A (2020) The Natural Inclusion of Difference

Rayner, A (2020) Evolutionary Flow

Rayner, A (2020) Simplicity & Entanglement

Rayner, A (2020) Permafrost & Fertile GroundWhat

Rayner, A (2020) Beyond Objectification



Alan Rayner

Alan Rayner is an evolutionary ecologist, writer and artist, who is pioneering the philosophy of natural inclusion