Alan Rayner

Science, as it has come to be practised most widely, has been immensely successful in the invention and production of artefacts, whether these are in the form of conceptual frameworks within which to define, predict and constrain natural processes, or material technologies. This success has largely been based on an absolutely definitive logic that abstracts material ‘content’ from spatial ‘context’. Such abstraction greatly diminishes the dimensionality of natural, non-Euclidean, dynamic geometry by fixing reality within rectilinear structural limits of length, breadth and depth. It may therefore come at the expense of deeper understanding of natural dynamic processes, which is needed to address currently emerging environmental, social and psychological concerns bearing upon human well being.
Meanwhile, scientific research has itself provided evidence, implicit in relativity, quantum mechanics and non-linear theory, which undermines the logical foundations for definitive methods of enquiry and explanation. ‘Hard science’ is being revealed as inappropriately premised and simplistic, capable of complicating and obscuring rather than simplifying our understanding of natural creativity, through presenting a very partial (one-sided) worldview. Here I explore how science theory and practice may be made more comprehensive, so as to correspond in a truly more simple way with natural process, and hence enhance - not abandon - its successful application. Primarily, I suggest this is possible through a form of enquiry that transforms - but does not replace - objective rationality, by spatially fluidising - not absolutely removing - its boundary definitions.

Definitive Science and the Construction of Artefacts
At its simplest, Science may be described as a human endeavour to comprehend the nature of physical reality by means of unbiased observation and enquiry, which avoids distortion, misrepresentation and fantasy. This is, however, easier said than done. Bias is hard to avoid for three main reasons. Firstly, the practice of science cannot readily be isolated from its cultural context - the dynamic set of customs, expectations, aspirations and values that evolves in any human community. This community will only reward those scientists who conform to its demands, and may ignore or even punish those who don’t. In such circumstances, both intellectual honesty and the potential scope of enquiry are liable to be compromised, especially in a competitive community. Secondly, the community of practising scientists will impose its own demands, for example through the process of ‘peer review’, based on its current knowledge and paradigms. Thirdly, and perhaps most insidiously, any attempt to avoid bias itself depends upon making assumptions about the nature of bias and hence about the nature of ‘reality’. If these assumptions are inapt, then bias will be introduced by the very effort to avoid it.

So it can be that the mainstream of Science becomes diverted from the very course that it most honourably seeks to follow. Far from faithfully representing natural creativity, its products may be artefacts, man-made constructions incongruent with the world in and from which they are forged. Moreover, the more useful and convenient these artefacts may seem, the more powerfully will the stream be diverted until ultimately it proves to be unsustainable in the natural world of its origins that it sought to comprehend.

The most tangible artefacts of Science are those demanded by its ravenous sister, technology, in order to ease our human way of life. Some, not necessarily all, of these artefacts may, however, all too readily engender dis-ease. Many a technological ‘silver lining’ brings with it a ‘dark cloud’ that compromises human and environmental well being in one way or another, whether it be gunpowder, nuclear energy, cars, planes, wind-turbines, genetically modified crops, nitrogenous fertilisers, drugs, computers or whatever. Somehow, however, the ‘dark cloud’ always seems to take many of us  by surprise, looming from some neglected quarter of nature or human nature that wasn’t accounted for in the initial research and development. Maybe there’s something about our current accounting methods, which is intrinsically neglectful and therefore biased in its expectations. If so, what is being neglected? Could there be a form of enquiry and accounting that enables us to be more circumspect, more aware of and able to navigate unpredictable possibilities?

Less tangible, but ultimately far more profound and intractable artefacts of science lie deep in its mathematical and logical foundations. These were laid during a phase of human cultural evolution when our technologies had developed insufficiently to enable us to see much beyond or within what could be revealed by our naked eye. Ironically, we appear to have remained more attached to the definitive worldview arising from this restrictive vision, than what new technologies have actually revealed about the microscopic and macroscopic character of the cosmos and our own human physiology, biochemistry and anatomy.

To cut a long story short, current scientific orthodoxy continues to hold unswervingly to faith in objective rationality as the basis for unbiased enquiry, but in doing so produces artefacts in the form of abstract logical frameworks and explanatory concepts. This is because objective rationality depends on the supposition that nature can be defined absolutely into independent, singular ‘forms’, ‘bodies’ or ‘objects’. These objects obey the logic of the ‘excluded middle’ in that they cannot be other than themselves; everything, according to this logic, which originated with Aristotle and Parmenides and persists in various forms to this day, must be either A or not A.  For this logic to hold true an absolute demarcation must exist between ‘something’ and ‘nothing’ - ‘solid’ matter and ‘empty’ space. Space must, in other words, be discounted as ‘immaterial’, an absence of physical presence’, which cannot be included in matter. For if space is counted as a physical presence, no thing can be truly isolated from any other thing - all inescapably co-exist in a common, fluid dynamic pool, like fish in an ocean and solutes in a solution, distinct and distinguishable but not discrete and definable.

Correspondingly, by treating space as ‘nothing’, an absence that nonetheless puts distance between (i.e. isolates) one thing and another, objective rationality mentally subdivides nature into discrete and therefore independent factions and fractions. These may be atomic particles, genes, human bodies, plots of land, nation states, natural ecosystems, planets, galaxies or whatever. They are studied in objective isolation from one another by a distant observer, supposedly without bias, who does not allow his or her own feelings to affect interpretation or analysis of whatever presents itself to view. They are categorised, measured, counted, manipulated and analysed within a discrete, three-dimensional, Euclidean structural framework, with space and time abstracted as background and subdivided into identical units. They are added, subtracted, multiplied and divided according to the rules of elementary arithmetic.

All interpretation of natural form and process in terms of objective rationality, whether ‘deterministic’ or ‘stochastic’ (fate or chance-based) is therefore ‘definition-driven’. It is dependent upon the tacit assumption that material content can be fully separated from spatial context, and hence that nature is definable into entirely discrete entities. There is, however, no contemporary scientific evidence to support this premise, and much evidence and reason to suggest that it cannot possibly apply to any kind of natural evolutionary process because ‘space’ - as an omnipresence of structural absence - cannot be excluded from natural dynamic geometry at any scale (Rayner 2004). In short, without the physical presence of space, no movement or distinction of form would be possible. ‘All’ would be a self-referential ‘concrete point’ of the kind envisaged by ‘big bang’ cosmology and exposed mathematically by Gödel’s theorem to be a paradoxical axiom (definition) - an extrapolation or reductio ad absurdum (cf. Hofstadter, 1980). 

Objectivity is therefore liable to introduce profound bias, the very thing it claims to avoid, whilst also greatly restricting the scope of scientific enquiry and interpretation. It does so by presenting an ineluctably partial (one-sided and self-referential) view of reality, ironically through its very insistence on material completeness. Note, however, that this view is not entirely wrong, because it is partially based in reality! But it is utterly inadequate to account for natural creative possibility.

Since the vast majority of scientific concepts and mathematical procedures and proofs are artefacts of objective definition (what Poincaré, 1905, referred to as ‘hidden axioms’), serious reservations must attach to their application to real-world dynamics. They may well provide excellent tools of enquiry, if used wisely, with full awareness of their partiality, but they cannot substitute nature. In particular, they re-present, and hence to varying degrees misrepresent, fluid dynamic natural process in much the same way that a cine film does.

In effect, independent snapshots of natural flow are abstracted and frozen within a fixed, rectilinear spatial frame at discrete time intervals. These snapshots are then run together, leaving our imagination magically to restore the spatial continuity in the gaps between frames. Trouble begins when the re-animated sequence is considered equivalent to the original undisrupted animation, with the isolated frames treated as if they were its fundamental, independent, particulate ingredients.

In the resulting back-projection, the frames become regarded as the determinants rather than as isolated fragments or ‘fixed precipitate’ of the flow. We become prone, with hindsight, to interpret history back-to-front, as a regression line of best fit to present status quo, with most of the original ‘co-incidental’ behaviour off this line edited out. We then proceed to use this regression to forward-project or ‘predict’ an abstract future or ‘end’, and contrive ‘means’ to serve whatever we perceive to be desirable outcomes. Moreover, having dislocated each frame from the flow, we require some forceful agency or actor to re-animate the flow. We begin to ask paradoxically ‘what do we do to bring about our desired fate? In so doing, we imagine that our bodies are inhabited by some internal driver or ‘ghost in the machine’ decision-maker, notwithstanding that they are in the meantime being pushed and pulled about from outside. Our resulting actions may correspondingly prove fatally out of attunement with the flow in which they are inextricably immersed, engendering profound psychological, social and environmental distress and damage.

Such prescriptive, definition-driven enquiry and interpretation is evident in a very wide variety of positivistic scientific endeavours and their simplistic popularisation. Egged on all the more by research funding agencies, assessment exercises and pressures to publish or perish, scientific enquiry becomes ‘self-fulfilling prophecy’. We set out to concoct and test ‘falsifiable’ and thereby axiomatic hypotheses, with minds so closed off from indefinable possibilities that we can and do ignore observations that ‘don’t fit’ with our presuppositions. Meanwhile we pay little or no attention to where and how these hypotheses and presuppositions arise in the first place.

Potent examples are to be found in the fields of Sociobiology and Game Theory, where the mathematical convenience of defining individuals as discrete numerical entities has led to inapt depictions of ‘selfishness’ and ‘altruism’. These depictions unjustifiably attribute the association of particular behaviours with genetic relatedness directly to genetic motivation (cf. Wilson, 1998). They have in turn been incorporated into damaging socio-political models, which reinforce the Darwinian axiom of ‘survival of the fittest’ (Rayner 2006).  With such models holding sway in the public imagination it is difficult to imagine how human conflict can be minimised and environmental sustainability encouraged. Somehow, they need to be transformed into a more comprehensive understanding, by including the receptive space that they ignore by imposing prescriptive definitions.

Fluidising Science - the Natural Inclusion of Receptive Space
No sooner are the definitions relaxed that scientists supra-naturally impose for the sake of theoretical and methodological convenience, than Science may transform from the study and generation of artefacts into a more naturally attuned endeavour. The underlying logic for scientific enquiry and explanation can hence transform from the opposition of fixed alternatives assumed to be exclusively right or wrong, to the complementarity of inner and outer possibilities both distinguished and pooled together through their dynamic interfacial boundaries in common space. This transformed reasoning can be thought of as the logic of the ‘included middle’ or ‘mutual inclusion of one within other’. It accords with a kind of awareness that Ted Lumley and I have called ‘inclusionality’ to highlight its distinction from divisive forms of ‘rationality’ (Rayner 2003, 2004). Here, all form is regarded as ‘flow-form’, a dynamic inclusion - not an occupier - of space in space, which cannot be defined absolutely in an unfrozen world.

With inclusionality, the freeze-framed geometry of isolated form melts into a fluid dynamic geometry or ‘transformational topology’ where space pervades everywhere, throughout an electromagnetically informed thermal and gravitational field. This dynamic geometry extends from microcosm to macrocosm and differs radically from the hard-line abstractions of Euclid. Its primary character is non-linear, twisting and curving, due to the inductive receptivity of spatial attraction, giving rise to bubbling spheres, ellipsoids, spirals and tubes in which all are simultaneously included in and reciprocally shaping all. It includes the human observer who may vainly attempt to detach from the scene by dislocating inner feeling experience (‘proprioception’) from his or her outward gaze. 

Linear structure emerges secondarily from this geometry, as in the cylinders formed by trees or the hexagonal arrays formed in honeycombs and the regular surfaces of crystals. This natural geometry is also ‘nested’, with smaller domains contained within and communicating with larger domains. The simplest form of expression of this geometry would be a set of concentric perforated spheres, but has the potential to become extremely ‘involved’ or ‘complex’.

The nearest approach that conventionally fixed-framed mathematics has made to this natural fluid dynamic geometry of ‘nested holeyness’ or ‘holey communion’ is known as ‘fractal geometry’ (Rayner 2004). This idea is closely linked with the development of non-linear dynamical systems theory, versions of which have been popularised as Chaos and Complexity theories (e.g. Gleick, 1989). It was made famous by Benoit Mandelbrot (1977), as a way to describe structures whose boundaries, unlike Euclidean surfaces, appear progressively more complex/irregular, in ‘self-similar’ patterns, the closer they are observed. Almost anything we look at in nature from clouds, to snowflakes, to river valleys, to ferns, to trees, to lungs has this property, which makes them immeasurable in terms of discrete units of length, area and volume, because how much you see depends on how close you are. For example, the length of the coastline of Madagascar seems much less to an astronaut orbiting the Earth than it does to a mite crawling around its many indentations. At infinitesimal scales of closeness, the length is infinite.

The problem of quantifying fractal structures can be solved by relinquishing the Euclidean idealization that dimensions can have only integral values of 0, 1, 2, 3, 4 etc, and allowing them also to have fractional (hence ‘fractal’) values. The fractal dimension of a structure can be calculated from the equation:

M = krD

where M is the material ‘content’ of a portion of the structure, r is the radius of the field in which this portion of content is contained, and D is the dimension. D can readily be found from the relationship between the logarithms of M and r for different fields of view. If the structure is homogeneous, then D will have an integral value. If it is heterogeneous, D will be fractional.

Fractal patterns can be simulated mathematically by iterating non-linear equations.  A famous example is the ‘Mandelbrot set’ itself, which appeared in many guises as a colourful modern mathematical art form in the late twentieth century. This set is made by mapping the distribution of points in the ‘complex plane’ that do not result in infinity when iterated according to the rule, z →z2 + c, where z begins at zero and c is the complex number corresponding to the point being tested. Here, a ‘complex number’ is a number that consists of a combination of a ‘real’ and ‘imaginary’ component, the latter being a derivation of, ‘i’, the square root of -1. The complex plane is formed in the space defined by placing all ‘real’ numbers, from -∞, through 0, to +∞ along a horizontal line, and all ‘imaginary’ 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 ‘possibility space’ for numbers as discrete entities to inhabit, from one to two dimensions.

The remarkable feature of the Mandelbrot set is the extraordinarily complex boundary that occurs between points within and points outside the set, in effect between an inner attractive space of zero and an outer attractive space of infinity. Such complex boundaries formed between neighbouring attractive spaces or ‘attractors’ have more generally been referred to as ‘fractal basin boundaries’, and are clearly at least analogous to the complex boundaries of natural process geometry.

Such deterministic representations of complexity, however, still begin prescriptively with the implicit or explicit Euclidean framing or numerical definition of contents and containers as complete wholes or ‘sets of initial conditions’. They hence retain the paradoxical assumption of completeness and replace the simultaneous reciprocal dynamic correspondence – attunement or resonance - of coupled concave and convex domains with sequential ‘feedback’, fixed within a rectilinear structural frame of space and/or time. They remain firmly in the ‘box’, even though they may subdivide its contents indefinitely.

The ‘warm’, fluid dynamic geometry of inclusionality, by contrast, implies the continual emergence of intermediary, incompletely definable transition zones (dynamic boundaries) through which convex and concave spatial possibilities are coupled and transformed by one another (Rayner 2004; cf. Shakunle, 1994). The implications of this geometry for our understanding both of nature and human nature are profound. They radically shift the emphasis we have traditionally placed on isolated ‘figures’ by liberating them from definition against a fixed background and including them inextricably within dynamic spatial context. Through this shift we invert the priority analytical thought gives to ‘content’ over ‘context’ and appreciate that all content is by its very nature ‘contextual’ – a dynamic inclusion of all, not a sovereign ruler over all. We focus primarily on how the ‘field of animation’ transforms in the process of giving rise to and subsuming the local distinctions or concentrations of energy that we may define through our explicit senses as ‘material objects’, not upon how these objects define and animate the field.

Hence we may distinguish but not entirely define the immense variety of evolutionary flow form in terms of ‘natural inclusion’ as the co-creative, fluid-dynamic transformation of all through all in receptive spatial context. We recognise that we cannot change or move any local identity (distinct ‘somewhere’) without simultaneously and reciprocally transforming the non-local identity of all (heterogeneous ‘everywhere’), and vice versa, spatially and relationally. We understand evolution in terms of reciprocal relationship - resonance or dynamic attunement - not the perfect adaptation of discrete individuals to pre-defined niches through the Darwinian ‘preservation of favoured races in the struggle for life’. Having not fixed the flow through prescriptive definition, there is no need to re-animate it by means of some ineffable force. Instead of envisaging a world of independent objects acting and reacting against and to one another in linear chains of cause and effect, we appreciate a natural neighbourhood of receptive-responsive flow-forms pooled together in common space.

Nothing is lost in this inclusional view of nature apart from the sense of absolute, predictable control and individual freedom that we may have gained by imposing definition upon it. But if this sense is a false one, an artefact that does not correspond with reality and may prove utterly misleading in the long run, what is to be gained, and how much is to be lost by adhering to it?

There is no reason to believe that a more geometrically realistic logical and methodological basis for scientific enquiry would have prevented or even delayed any of our scientific discoveries. It may, though, have made us more circumspect about their technological development and application as destructive weapons, sources of pollution and exploitative means of exercising authoritarian power over both human and non-human forms of life. Inclusionality doesn’t prevent us from identifying, distinguishing and working with diverse natural manifestations in dynamic relationship – it only holds us back from imposing stultifying limits upon their expression. By the same token, there is every reason to believe that fully definitive approaches have restricted the scope of philosophical and scientific enquiry and contributed to the conflicts that have drained human energies and creative and loving potential throughout recorded history. Even if through the ‘wrong reason’ we can contrive in very specific circumstances to predict some apparently ‘right’ answers, the latter will only serve to entrap us in persistent habits until, eventually, they find us out through the collapse of our social, psychological and environmental relationships. Ultimately we can make life hard for others and ourselves by trying to make it easy, within prescriptive limits of right or wrong definition.

Becoming Involved, not Complicated
Einstein & Infeld (1938) referred to the ‘inertial reference frame’ and ‘absolute time’ as ‘two frightening ghosts’, whose oppressive influence would be relieved by the advent of relativity theory. But somehow the oppression has not lifted, and definitive abstraction has remained firmly nailed in the heart of much current scientific theory and practice. Why? Is there some even more frightening presence that we become aware of as absolute fixed structures begin to dissolve?

In my experience, to call for definitions to be relaxed in a culture that is addicted to definition is to come into close encounter with stony ground, if not something like the fury of a toddler threatened with separation from its favourite toy or security blanket! It is difficult to find receptivity amongst many who have become accustomed to exclude receptivity from their way of accounting for nature and human nature. Once the vital receptivity of space is lost, it cannot be regained, any more than Humpty Dumpty can be restored to life from his shattered fragments. Inclusionality is hence not accessible from objective rationality, by definition, even though objective rationality can always be derived from and/or transformed by inclusionality.

To regain spatial receptivity in the process of relaxing – but not completely removing – definitions is to encounter the ghost of deep uncertainty, involvement and vulnerability that most of us will recognise implicitly in our personal experience, if not our explicit portrayal of life. This is the ghost that objective rationality loves to deny, or not even talk about, in the quest to suppress sources of fear. The ‘ghost of the gaps’, which permeates everywhere, pooling All together in universal communion, variously alluded to by distinct but not discrete religious and scientific belief systems as ‘Tao’, ‘Buddha Nature’, ‘Brahman’, ‘Holey Ghost’, ‘Wakan-Tanka’, ‘Gravity’, ‘Heat’, ‘Dark Energy/Matter’ etc. The inclusional ‘Mother Space’ or loving Agape of Nature, which fills us with profound compassion for our mortal companions, who we include in our sense of Self as Neighbourhood – somewhere as an inclusion of everywhere. 

Correspondingly, principal among objectivity’s objections to inclusionality is that the razed down simplicity that comes from defining things will ‘get lost’. Personally, I rather wish that it would! But, seriously, this objection illustrates the addictive, all or none quality of false dichotomy: either we have total definition or no definition. Definition is something we must have if we are not to get totally lost in a sea of troubles. We exclude between two stools the dynamic ‘middle ground’ synthesis of ‘neither entirely one nor the other’ and ‘not even both one and other in parallel universes’ but ‘one incompletely within other’ as nested  ‘whirls within whirls within the whirl of common flow-field’. In that exclusion almost all possibility for natural creativity really does get lost.

In reality, nature will not become less simple to understand if we relax definition, but our understanding will become more involved through appreciating the simple underlying coupling of inner whirl with outer whirl over all spatial scales. By the same token, the complications and paradoxes that arise as artefacts from imposing an imaginary fixed reference frame upon natural field flow will disappear from view, in much the same way as did the Ptolemaic ‘epicycles’ following the Copernican Revolution. The latter were used to explain away the erratic planetary paths evident from a geocentric definition of the Universe, but became redundant no sooner had that definition been found wanting. 

Art Full Science - New Avenues for Creative Exploration and Communication
By excluding that which it defines itself not to be, objective science may not only alienate itself from the public whose appreciation, understanding and money it craves, but may also greatly diminish its own opportunities for creative evolution and correspondence with other human endeavours. Such exclusion is evident in the ‘Two Culture’ split between ‘Art’ and ‘Science’ notoriously brought to light by C.P. Snow (1959, 1963; see also Petroski, 2005), and the increasingly cantankerous collision between Darwinian evolutionary science and religious ‘Creationism’ or ‘Intelligent Design’ theory. In a non-linear inclusional perspective, there is no need for this split and the nastiness it engenders: the split is an artefact of definitive logic.

Inclusionality can transform science into a far more open, receptive-responsive endeavour, in tune with natural process. Inclusional Science welcomes diverse approaches and forms of expression and does not set itself up in antithesis to Art or Religion but searches for commonality and complementarity of meaning in all worldviews. Indeed the inclusion of forms of enquiry not conventionally regarded as ‘scientific’ could do much to loosen up prejudicial definition and ‘warm’ the language, mathematics and methodology of science, so helping to release a deeper spirit of human communion and creativity. This is the enduring dream that I dare, as one still happy to describe but not define himself as a scientist, to express as follows:

References

Einstein, A. and Infeld, L.  (1938) The Evolution of Physics: From Early Concepts to Relativity and Quanta. Cambridge University Press.

Gleick, J.  (1988) Chaos. London: Heinemann.

Hofstadter, D.R. (1980) Gödel, Escher, Bach: An Eternal Golden Braid. England: Harmondsworth.

Mandelbrot, B. (1977). The Fractal Geometry of Nature. New York: Freeman.

Petroski, H. (2005) Technology and the humanities. American Scientist 93, 304-307.

Poincaré, H. (1905)  Science and Hypothesis. Dover Publications. Walter Scott Publishing Company Ltd.

Rayner, A.D.M. (2003) Inclusionality – an immersive philosophy of environmental relationships. In Towards an Environment Research Agenda – a second collection of papers (A. Winnett and A. Warhurst, eds.), pp. 5-20. London: Palgrave Macmillan.

Rayner, A.D.M. (2004) Inclusionality and the role of place, space and dynamic boundaries in evolutionary processes. Philosophica 73, 51-70.

Rayner, A.D.M. (2006) Natural Inclusion – How to Evolve Good Neighbourhood. Bath: self-published on CD.

Shakunle, L.O. (1994). Spiral Geometry. The Principles (with Discourse). Berlin: Hitit Verlag.

Snow, C.P. (1959) The Two Cultures and the Scientific Revolution. Cambridge: Cambridge University Press.

Snow, C.P. (1963) The Two Cultures: And a Second Look. New York: Mentor Books.

Wilson, E.O. (1998) Consilience - The Unity of Knowledge. London: Little, Brown and Company.
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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