Couze Venn on Benoit Mandelbrot, fractals and the realignment of the human sciences

Photo: Couze Venn

Following the death of Benoit Mandelbrot, the father of fractal geometry, on 14th Oct 2010, Couze Venn comments on the mathematician’s influence, on fractals and knowledge, and on the methodological and epistemological traffic between mathematics, the natural sciences, the social sciences and the humanities.

The recent death of Benoit Mandelbrot (Oct 2010) is an occasion to re-examine what fractals as well as a number of methodological and epistemological developments in the sciences and mathematics such as complexity, chaos, non-linearity, network, topology, indeterminacy mean for a reorganization of knowledge in the humanities and social sciences. We all know that multidisciplinary borrowings across the natural and social sciences happen regularly; for example, projects aiming to apply the kind of concepts just noted surfaced in the 1990s, incited by developments such as those of Illya Prigogine’s work – whose notions of dissipative structures, far-from-equilibrium systems and self-organization have had significant echoes in many disciplines – and the wider dissemination of concepts such as complexity and non-linearity. The implications have altered conventional notions of determination and causality and posed a challenge to all mechanistic paradigms – though much remains to be done. Also, one should remind oneself that major thinkers like Lacan, Deleuze, Guattari, Simondon, Bergson, Levi-Strauss, Whitehead, Latour, Badiou – amongst figures most frequently cited in the social sciences and humanities – have productively deployed concepts borrowed from the natural sciences and mathematics to the benefit of critique and a more complex understanding of the human world (in spite of Sokal and Bricmont’s attack in Fashionable Nonsense, 1998 ). More recently the work of people like Donna Haraway, B. Massumi, M. De Landa, E. Grosz, J. Urry, N.Thrift has shown the benefits of such borrowings.

TCS has been at the forefront in exploring this traffic between the natural sciences, mathematics and social science, e.g. in the special issues or sections on complexity (vol. 22, no 5 2005), life (vol. 24, no 6, 2007), new vitalism (vol.22, no 1, 2005), climate change (vol 27, no 2-3, 2010), topology (forthcoming 2011). Yet these cross disciplinary exchanges are neither easy, or unproblematic, nor properly recognised, in spite of the fact that from the beginning the social sciences have deployed concepts from the ‘hard’ sciences – for example, notions of energy (Freudian psychic economy), the organism (almost ubiquitous in the 19th century), thermodynamics, evolution, and subsequently relativity and quantum physics along with the mathematics of chaos and complexity. The latter period of developments in the ‘hard’ sciences, it must be said, have yet to be fully deployed in the social sciences.

A significant multi-disciplinary project which opened the way has been the Macy Conferences (March 1943 – April 1953) at which ideas about complexity and autopoiesis or dynamic feedback loops in open systems, developing in different disciplines and sites, were brought to bear on problems of information theory, human and social communications, living organisms, cybernetic machines, mind-brain inter-relationships, leading to the establishment of cybernetics as a cross-disciplinary field. These conferences were organized by a core group of mathematicians, engineers, social scientists, neurophysiologists, biologists, psychologists, including thinkers like Gregory Bateson, Margaret Mead, John von Neumann, Julian Bigelow, Norbert Wiener, Warren McCulloch, Paul Lazarsfeld, Kurt Lewin, supplemented by guests amongst whom one can note Roman Jakobson, Claude Shannon, Erik Erikson, Talcott Parsons. The effects of the insights generated by that collaboration continue to shape research today, say, in the take up of the work of Humberto Maturana, Francisco Varela, Claude Levi-Strauss, Claude Shannon, Gregory Bateson.

The reason for a focus on fractals in re-examinning the epistemological, methodological and ontological questions that new theories in the hard sciences raise for the human sciences is that it is possible to argue that knowledge generally, and the relationship of knowing and being, have reached a new state that is likely to lead to fundamental shifts in the domain of knowledge and technics, shifts which will condition the future for some time. For one thing, the ‘hard’ sciences and the technical world associated with them have more than ever entered daily life at all levels, from the most mundane, e.g. communication using mobile phones and the food we eat, to how we generate power to sustain contemporary lifestyles, as Latour, in Cogitamus, (2010,) underlines in his arguments for a ‘political epistemology’ (2010: 26). His arguments address two related levels of the problem of knowledge: on the one hand it is the recognition that scientific discourse and scientific claims now enter into almost everything which is the subject of policy decisions and public debate – amongst cases he cites are swine flu, tuna fishing, economic explanations for the financial crisis, green technologies – such that daily life is suffused with, and is possible only on the basis of, interlocking dispositifs or assemblages that put to work specialist knowledges and capabilities.

This condition is familiar enough, though visible only when encountering an event that challenges the taken for granted status of these knowledges; for Latour, the aim of political epistemology is precisely to study the translations and combinations which take place across disciplines and technics in the process of putting into place and setting in motion these assemblages. On the other hand, at the more fundamental level, a number of problems have come to the forefront like climate change, ecological damage, limits to growth, threats to biodiversity and so on, which raise questions of ontology, ethics and world views. In that regard, it is worth noting the special section on ‘The Folly of Growth’ (Oct. 18-24, 2008) which the journal New Scientist has devoted to the scientific, economic and human problems arising from the pursuit of unending growth.

Furthermore, the sciences increasingly constitute knowledge of both micro and macro systems and their interrelations, whilst new technologies have emerged around the manipulation of the very small and the deepest levels of matter – particles, genes, cells, nano- and bio-technologies. These developments pose problems of scale which require fundamental re-orientations for the whole domain of knowledge, implicating the refiguration of the relation of ontology to epistemology. Yet, this more and more intimate interpenetration of scientific knowledge and daily life has not been accompanied by a greater public understanding of either the sciences themselves, including the social sciences, or the economico-socio-political processes which generate the assemblages in which they are inscribed (or technologized) as part of public policy. The disputes around climate change centred on the Stern Review, 2006, and the IPCC 4th Assessment Report (AR 2007) clearly illustrate this lack of understanding, as well as the political motivations which seek to undermine findings inimical to particular ideologies or worldviews.

Fractals happen to be an ideal candidate for examining this problem of the relationship between the micro and the macro, as well as related ontologico-epistemological and cross-disciplinarity issues. Media illustrations have led us to associate fractals with snow flakes, fern leaves, the shape of waves crashing on the shore, that is, iterative, self-similar patterns that repeat across scales – say,producing snow flakes at the small scale or, at a larger scale, snow drifts. First developed by Mandelbrot from 1975 (The Fractal Geometry of Nature, 1977), fractals now apply to Brownian motion, explanations of how galaxies cluster, the process of brain growth, the small-world network architecture of brain function, computer design, graphics, and fields like metagenomics and finance, for instance, regarding problems of scaling and turbulence. Interestingly, well before the economic crisis of 2008, Mandelbrot criticised economists who misunderstand problems of complexity in applying mathematics to the market – in The (Mis)Behaviour of Markets. A Fractal View of Risk, Ruin, and Reward, 2004.

A recent example of the application of fractals will illustrate the point about the shifts in research programmes and in the effects of developments in the sciences for rethinking social phenomena generally. Almost coinciding with Mandelbrot’s death, the lead article in New Scientist of 5th October 2010, ‘Fractal life. The chaos theory of evolution’ (Keith Bennett, 2010: 28-31), discusses the effect of environmental change on species in the light of fractal theory, concluding that evolution is chaotic and, contra Darwin, that the relationship between environmental change and evolutionary change is a weak one at the level of species. It is not that evolution is random, or that natural selection does not happen, but that adaptation at the macroevolutionary scale, as opposed to the microevolutionary level, is less predictable. One of the reasons is that the fossil record – the case considered is that of populations of trees and some animal species from the last ice age – shows that most species remain morphologically unchanged over long periods of time, though their distribution responds to environmental change. New species, it appears, emerge all the time, independently of significant climatic change, and adapt continuously but at the individual level and in terms of distribution, that is, at the level of epigenetic co-constitution. The weak correlation between evolutionary and environmental change, and the current state of evidence, lead Bennett to several conclusions. First is the suggestion that the relationship between genotype and phenotype is non-linear and chaotic, for, though phenotype is dependent on the complex interaction between an organism’s genes and its environment, mutations occur all the time, independently of environment, and small changes can lead to substantial but unpredictable consequences. The broader conclusions however are more significant for wider issues about evolution and the character of life generally – with implications for how to theorise social phenomena. These are that the evolution of life have many characteristics of non-linear systems: they are deterministic – a change in one part of the system causes changes elsewhere in the system – but unpredictable; behaviour in the system is sensitive to initial conditions; the history of life is fractal: there is self-similarity across scales, such that, without labels, one cannot distinguish the taxonomic levels between classes, orders and species (e.g., reptiles – and amphibians, birds, finches); rewinding the clock does not guarantee similar outcomes (because of indeterminacy) . So, there are no ‘laws’ of evolution, but we know the process is complex; and we still have much to learn. Incidentally, Bennett points out from the evidence that all species extinction over the last 20,000 years, except one, are anthropogenic.

The details are presented here in order to underline that scientific claims are part of a discursive-material process of producing knowledge, and so open to controversies internal to the specialist discourses, and also to point out the extent to which current knowledge runs counter to the still widespread mechanistic and simple-minded or naive ‘translation’ from genetics to human and animal behaviour that one encounters in public discourse and pop psychology. In this respect, one could cite in evidence the fact that current research supports the view that epigenesis has an important role in altering behaviour at the individual level, adding to the recognition of the complex character of the biology-environment relationship. For instance, Coghlan (2010) reports that there is growing evidence showing that epigenetic changes due to environmental factors can be passed on inter-generationally to individual members of a population (come back Lysenko?). The experiments refer to the fact that experiences and activity due to specific environmental factors lead to chemical caps (methyl groups) becoming attached by enzymes to cytosine (one of the four bases that make up DNA) causing specific gene activity within a cell to be switched on or off. These caps act as markers, used for instance to detect cancer cells, and now extended to the investigation of psychological behaviour relating to trauma. One experiment reports findings (I. Mansuy, Biological Psychiatry, 2010.05.036) which relate to the inheritability of methylation as a result of trauma inflicted during infancy (D. Sweatt, 2008, M. Meaney, 2010). But the process is complex and not well understood, and the longevity of the effects is as yet unknown. The links are tenous if suggestive, and shows up both the limitations of present knowledge, as well as the possibilities thrown up by the standpoint of complexity, and the naivety of those who buy into the (positivist, deterministic, ahistorical and misguided) evolutionary psychology’s model of human behaviour, or who readily follow the sociobiology deterministic bandwagon. Claims made about autism or ADHD come to mind, bearing in mind that these are problematic categories of ‘psychological dysfunction’, relying on labelling procedures that often pathologise behaviour which may have psychosocial or environmental determinants , and are culturally shaped anyway (the American DSM manuals have undue influence in this labelling process).

Given the massive amount of data available, one could multiply these kinds of examples. The point is about how the concept of fractals, along with the range of concepts noted, has brought all the sciences to the threshold of a reinterpretation of the world, the place of humans in it, and the practical question of how to deal with the confluence of interrelated crises – ecological, environmental, economic, resource, ethical – with which we are confronted. Several themes can be highlighted which would enable the social sciences and humanities to intervene in this situation:

Biotechnology, particularly techniques which 1. aim to reconstitute, control, heal, ‘normalise’, amplify the body and its capacities or functioning; 2. Biotechnology and food production, raising issues to do with the human-animal relationship; 3. Biotechnology and the management of the environment and biodiversity. All play with ideas of fractals, complexity, indeterminacy, etc (even if some of the projects may be framed within a control apparatus)
∙ The application of complexity theory, fractals, etc in the neurosciences: implications for the control and management of behaviour through the psychsciences, and for theorising consciousness, the mind-brain co-relationship, the possibility of constructing sentient machines.
∙ Rethinking the nature-culture complex in terms of relationality, and implications for social theory. An interesting study (Kerri Welch, Fractal Topology of Time: Implications for consciousness and cosmology, 2010) uses, amongst other things, the case of the relationship between a pond and the field in which it dwells to point to the dynamic intertwining at the thresholds of two contiguous living systems; she shows that in terms of biodiversity, exchanges and activity are at their most intense at the thresholds. So there are degrees of both randomness and regularity in what’s going on inside the pond, and in the field; but biodiversity is maximal at the threshold of the two. All three sets of relations and domains determine – with probability functions – what goes on, and we need to take all the domains and relationalities into account in an explanation.
∙ Rethinking critical theory in the light of developments in the sciences (beyond Deleuze). This is clearly a big topic. Views from our readers would be most welcome.

Couze Venn is the Managing Editor of Theory, Culture & Society, and has been the Review Editor since 2002, and Review Editor of Body & Society since 2008. He is also a member of the TCS Books Series editorial board. Though he has taught Cultural Studies and Science and Technology Studies for about 30 years, his research interests cover a wide range of topics in cultural theory, postcolonial studies, social theory, science studies, ‘psychosocial’ studies. He is currently working on issues relating to the critique of neo-liberal capitalism, particularly the question of the foundation for alternatives to economies based on growth and the privilege of private property; he continues to keep abreast of developments relating to anything to do with subjectivity.

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