Cold & Warm Geometry — How Rigid & Fluid Structures Affect Our Human Relationships and Sense of Self

Alan Rayner
6 min readFeb 18, 2020
Y do U Turn Away?’ (Pen, ink and watercolour on paper, by Alan Rayner, 2018)

There are some conversations I have with people in which I sense a combination of honesty, reasonableness and kindness present, which makes me feel at ease. Conversation flows. And there’s an absence of pretence, expectation and meanness of the kind that make me feel ill at ease. As I reflect on this now, I am surprised to realise just how common those latter qualities are in my own and others’ conversations. They ring alarm bells in me signalling the need for a fight, flight or freeze response. Conversation falters and stalls. Well, perhaps I’m not so surprised, in view of the prevalent conception of ‘self’ as a centre of assertive or submissive will. In an adversarial culture that mentally isolates self- or group-identity from ‘other’, there is little recognition of ‘self’ as a centre of receptive and responsive will. How come?

As I reflect further on this, it becomes clear to me that very different perceptions of ‘self’ are associated with two radically different geometrical perceptions of space and material form. These are:- (1) ‘Cold Geometry’ — abstract, freeze-framed geometry, which is primarily straight-edged, and (2) ‘Warm Geometry’ — natural flow-geometry, which is primarily circulatory.

What I am calling ‘Cold Geometry’ — the kind of geometry many of us are taught in school — only considers material forms superficially, as they appear momentarily from outside. It could also be called ‘Spectator Geometry’, because it derives from standing apart from what are regarded as ‘things’ in order to fix their position and name them. It conveys no awareness of the inner existence of material forms, or how they come to be as they are, where they are.

Cold Geometry is therefore ‘uninvolved’, ‘objective’ and ‘definitive’, confining its attention within a pre-imposed, 3-dimensional box-frame of space. It may ‘experiment’ with the things it defines within the frame from outside, but it doesn’t get inside with them: the ‘tiger’ is a kept a safely caged distance away from its ‘keeper’. The frame is thought of as an independent ‘Whole’, complete in and of itself. Its individual material contents are likewise regarded as independent ‘wholes’, complete in themselves, rigidly defined by their boundaries and separated from one another by space. Each material ‘whole’ has an infinitesimally small material point at its centre. Cold Geometry can therefore be thought of as ‘Whole-centred’, both in its perception of space and of material form.

‘Warm Geometry’, by contrast, perceives the boundaries of all material forms as inherently fluid — continually in the process of forming and reforming within limitless space and around distinctive localities of space. It considers material forms both from outside and from within as well as over a sufficient duration to perceive their motion. It is immersed and involved with and within what it observes. Its all-inclusive field of awareness radiates outwardly in all directions without limit from an innermost ‘focal’ location into endless space. Since this innermost location literally has no size it is an intangible ‘zero-point’ of space, within an open hole into which no material substance even of the smallest possible size can fit: you can’t have ‘mass’ without ‘volume’.

Warm geometry is therefore ‘Hole-centred’, like a circle drawn on a sheet of paper around the hole made by the needle-point of a geometrician’s compass. And, like this drawn circle its boundaries are formed dynamically and never isolate the space inside any locality from the space everywhere else. They dynamically distinguish but do not rigidly define material bodies apart from one another and their surrounding space.

In summary, Cold Geometry ISOLATES what is inside any PARTICULAR box-frame from what is spatially or energetically outside the frame, like a photographic snapshot. The frame has straight edges and is therefore exactly divisible into equally sized straight-edged units that can easily be enumerated. Warm geometry, on the other hand, is both spatially and dynamically continuous. It has no fixed limits and its field of awareness is divisible only into sectors of equal angle (conventionally 360 degrees in a plane around any one focal point) expanding outwards.

These radically different kinds of geometry can only be transformed from one to the other by ‘freeze-thawing’. Freezing entails rigidly restricting a portion of reality within a box-frame or ‘whole’ that excludes ‘extraneous space and motion’ and so can be subdivided into equal ‘parts’ that can conveniently be added, subtracted, multiplied and divided according to the rules of elementary arithmetic. Nature is rendered DISCONTINUOUS. Thawing renders Nature CONTINUOUS by re-entering the ‘extraneous space and motion’ excluded by the box-framing. Think how an ice-cube is made by freezing liquid water in a rigidly straight-sided container. Then consider what happens when the cube melts.

Now we need to ask which of these two different geometries is actually truer to life and what would be the effect of imposing one upon the other — placing a ‘round peg in a square hole’ or vice versa? Quite clearly, cold geometry is inherently STATIC whereas warm geometry is inherently DYNAMIC. Only the latter is true to the lively life we actually experience. So, we have to ask, what is the psychological, social and environmental effect of attempting to live in accordance with the restrictions of ‘cold geometry’, and how does this shape our human relationships with one another and the natural world’? There can only be one real answer: DESOLATION. I once depicted this desolation in a painting that I called ‘Arid Confrontation’:-

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

Cold geometry instils a solidly whole-centred sense of self and groups. It speaks of ‘Wholes’ and ‘Parts’ as if these actually exist in reality as independent entities — and as if reality itself is a Whole composed of separable Parts. This is associated with assertive or submissive will. Assertive will is motivated primarily by a desire for power over other. This comes with a sense of total ‘certainty’, total ‘control’ and total ‘responsibility’. Submissive will is motivated by a desire to be instructed by other. This comes with a sense of ‘subservience’ and ‘passivity’. Such motivations are prevalent in the economic, political and academic superstructures of modern human cultures. They come with strong conceptions of ‘Success’ and ‘Failure’ and ‘Rights and Wrongs’. These are associated in turn with feelings of Triumph, Reward, Incompleteness, Loss, Self-Righteousness, Guilt, Innocence, Despair, Blame and Shame. Feelings of Faith, Hope & Love, on the other hand, are set aside and kept private, or mistaken for Obedience, Expectation and Lust.

Warm geometry instils a hole-centred sense of self from which the zero-point centre of space invites energy into local circulation, like the ‘eye’ of a storm. It speaks of material bodies as ‘flow-forms’ — dynamically distinguishable expressions of natural energy flow within and around continuous space. This is associated with receptive and responsive will. Receptive and responsive will comes with a sense of variability, humility and compassion. It is motivated primarily by a desire to contribute — to serve the needs of self and others within natural neighbourhood. Such motivations are evident in the ‘behind-the-scenes’ caring and distributive infrastructure of modern human cultures. They come with strong perceptions of ‘Benefit’ and ‘Harm’, ‘Truth’ and ‘Falsehood’. These are associated in turn with feelings of Fulfilment, Satisfaction, Insufficiency, Grief, Virtue, Fallibility, Honesty, Possibility, Involvement and Forgivingness. Feelings of Faith, Hope and Love are paramount.

Perhaps it’s time for us to turn the tables, and live in accordance with warm geometry!

See also:-

Rayner, A (2019) Honesty, Reasonableness & Kindness — the Three Core Values of Natural Inclusionality

Rayner, A (2019) Reason to Love — How natural inclusionality heals the rift between rationality and emotion

Rayner, A (2020) Leading Co-creatively, From Love, the Receptive Middle Way

Rayner, A (2020) Radiant Receptivity

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



Alan Rayner

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