Essays on Recursion, Difference, Dialectics, Maps and Territories in Celebration of Gregory Bateson’s centennial


This issue of SEED honours the work and life of Gregory Bateson in the centennial year of his birth, 1904. During his lifetime much of his work was misunderstood, or unappreciated, because it challenged people to think in new ways and because it defied disciplinary compartments, his ideas being integral to fields as widely separated as anthropology, psychotherapy, communication studies, education, general systems theory, the sociology of small group interaction, developmental biology and ecology. Nevertheless, situated within the overall thread of Bateson's discourse on ‘mind', and ‘pattern' his ideas are remarkably prescient; this is why a Bateson quotation elegantly capturing the contours of a new idea is to be t found in so many books today. Bateson made streams of ideas flow together, and in this confluence he developed a rigorous understanding of holism, systemic wisdom as he sometimes referred to it, both within and beyond culture.

One of Bateson’s central ideas was to establish a family of theories, or an epistemology, that would transform the western scientific tradition in so far as that tradition was committed to scientific materialism and dualism. This is no longer so radical or so obscure a position to hold, indeed, the same position appears in a wide variety of social science literature since the 1970s particularly in the writing of feminists and environmentalists. The dualism to which Bateson referred, and which scientific materialism relied upon in its explanation of events, was a dualism which separated body from mind, rationality from emotions, culture from the formal aspects of environment, subject from object, perception from cognition. In contrast, the one distinction he wished to maintain was that of information contexts (meaning) from the material means through which information was broadcast and received. Too many aspects of information are represented through the lens of materialism, he believed, with the information theory of his day engendering false reductionism.

Bateson stated in more than one text that his ideas were attuned to an epistemological monism, at first a notion of organicism, but after Bateson’s embrace of cybernetics in the mid-1940s, an epistemology built around information and the fundamental ideas of cybernetics. These had circularity as their central concern, though as Bateson pointed out, circularity did not mean a precise circle in which events repeat themselves in the same circular path. All living forms reproduce and in doing so re-enter the domain of their forebears. These are recursive events, but in the case of species reproduction, they never step into the precise spot in the same stream twice-over. The arrow of time intervenes. A truly circular path would preclude emergence of new forms, and other forms of change or adaptation which are characteristic sequences of evolution. The passing of time always inflects recursion in human events, and human events must also, in the long run, share this formal characteristic of recursion in biological events. Bateson believed, contra Vico, there was no historical circularity which rolls human history along from barbarism to civilization and then returns human society to its starting point of barbarism once more. In between there is an enormous amount of information continually undergoing contextual change, but there are also fundamental premises, constraints to human understanding that endure, a structure of fundamental premises or ‘verities’ that give both form to, but permit freedom in, the variety of recursive events.

Thus Bateson indicated that a characteristic form or topology that captures the recursiveness of both biological form and human cultural and historical experience, is that of a spiral, a circularity that rotates in time. Nevertheless, the spiral was always a metaphor, rather than an operational framework in Bateson’s epistemology. Instead, Bateson approached recursiveness in terms of the oscillations in heterarchical ordering. The idea of heterarchical (multi-level) order was first developed by the well known cyberneticist, Warren McCulloch. McCulloch suggested in his classic paper on the topology of human nervous nets (McCulloch, 1965: 40-45) that the topology of recursion in nervous nets not only differs between long-term memory and short-term memory but that within the overall recursiveness of neural nets are multiple hierarchies occurring among the synapses of the nervous system connected in recursive reverberation. This renders the relation between any nervous input and any outcome from nervous activity highly non-linear and - in terms of any linear expression - highly indeterminate. McCulloch admitted that he could not proceed much beyond this suggestion because the mathematics of his time could not deal with so profound a non-linear phenomenon.

Bateson took McCulloch’s idea of heterarchy and adapted this to Bertrand Russsell’s hierarchy of logical types in a rather peculiar way: logical types could systematically unravel circularity of information and how it becomes entangled in a multi-level universe, but logical typing cannot itself demonstrate appropriate communication. Another way of looking at this is to say that the hierarchy of logical types could denote how propositions that do not enter directly into the content of communicative messages create context for their meaning, but communication that is logically ‘straightened out’ through strict, on-going application of logical types will always end up bordering on the absurd. Communication that means anything to anybody presupposes the existence of strange loops and entanglement of levels of logical type. Moreover, the extraordinary human capacity to distinguish ordering of context-levels is integral to any meaning in messages. The problem is not the existence of a jumbled heterarchy of context levels that cannot be adequately represented through linguistic nor numerical description, strange as this may seem. The problem, as Bateson pointed out, is that the capacity to distinguish context levels appropriately in communication sometimes becomes blocked. A persistent blockage, a persistent pattern of communication in which context levels negate their own order gives rise to grave problems of miscommunication and even mental pathology. In some cases of mental pathology, for example, a person is unable to distinguish whether messages originate from inside his head or externally.

Peculiarly, the same problems of misplaced orientation of context arises with the introduction of computer technology and with the computer’s ability to operationalize iteration of data fed into it, and via an algorithm, create patterns from such iterations. The relation between iteration of complex numerical events seems to be able to mimic natural forms of recursion, so much so that the one can be taken for the other, the model for the external perception. In recent years chaos theory has revealed relations between fractals and the fractal dimensions of land sites, and this similarity carries with it a strange beauty that has made chaos theory the best known example of iterative procedures. Yet as, Bateson himself pointed out, the two, iteration and natural recursion, are complementary but not isomorphic. Chaos theory may very well represent the dynamics in crystal formation, but is unlikely to represent the dynamics of living organization. The dynamics of crystal formation can be expressed through continued iteration of the same, identical form; the dynamics of living systems depends upon difference, rather than similarity. In other words, difference, not similarity, is fundamental to the activity of living systems. The primary organizational aspects of living systems rely upon sensing differences.

This issue of numerical iteration and its contrast to natural forms of recursion is the first subject to be discussed in the following set of papers (McNeil). As McNeil states, patterns of iteration within computer models generate an intense interest in the ‘self-organization’ of that pattern, but to what extent do these iterations of formal self-reference actually demonstrate ‘self-ness’? Does the attribution of ‘self-reference’ hide an ‘otherness’ of technical machinations hidden in re-enterable programming procedures? If so, then he whole notion of ‘self’ in ‘self-organization’ is at stake, and any model of ‘self-organization’ must be clearly distinguish its own context of ‘self’ in generating order and make clear its reference to physical entitivity or to alternative relational dynamic of embodiment, i.e. specify ‘self’ or ‘other’ in all contexts of repetition, reverberation, re-volution and rotation,.

McNeil gives a broad a view of recursive forms, and taken together, all of the other articles probe as deeply into issues relating to information, feedback and recursive dialectics as McNeil’s.. Neuman takes up sequence in heterarchical ordering and explicates the novelty of Bateson’s ideas. As Neuman explains it, the key to understanding Bateson’s view of recursion lies in the relations that exist between levels of a heterarchy. This gives rise to a ‘logic of in-between.’ The recursive ‘logic of in-between’ requires oscillation between two dimensions so that the meaning of an event emerges from this oscillation rather than strict re-ordering that Russell’s version of logical proposed. Russell’s logical typing imposed a ’higher,’ or more inclusive level, on a ‘lower.’ By contrast, in Bateson’s writing, the product of the oscillation is the re-entering form and is the ‘meta-level.’ This version gives a more satisfying explanation of changed meanings than the simple descriptive correspondences of wholes and parts in mathematical set theory. It also highlights boundary phenomena of a meta- or more holistic level in a manner quite different from the post-modernist trend of ‘bottom-up’ signification which tends towards infinite regression as if in a hall of mirrors.

Not all of the articles deal specifically with Bateson’s formulation of recursion through heterarchical ordering Other papers explore Merleau-Ponty, Rosen specifically argues that Merleau-Ponty’s conception of depth is the additional dimension required to resolve paradoxes that inevitably occur in circular phenomena. McNeil expresses a preference for toroidal recursion, arguing that the ‘turning of a turning,’ a second order turning in the topology of toroids, gives much better expression to the notions of relative invariance, ambivalence, complementarity and recursion than any other and is at the heart of McCulloch’s notion of heterarchy. Ryan builds on C. S. Peirce conceptions of ‘firstness,’ ‘secondness’ and ‘thirdness’ as the framework of relational order, and conjoins these categories with Bateson’s notion of a cybernetic circuit, though in Ryan’s elaboration of process, he drops Bateson’s insistence on mapping discontinuity.

Two other papers deal with recursion as expressed by people who had a close association with Bateson’s ideas. One (Skibinski) traces this with reference to an intellectual forebear, Alfred Korzybski, in whose journal Bateson first published his metalogues. Skibinski argues that Bateson’s stylistic presentation of his epistemology, a metalogue, not only explains the necessary circularity in our cognition, but is also at the same time an escape from the ‘meta’ in metaphysics. The meta- of ‘metalogy’ (Skibinski’s term) re-frames subject-object splits; it escapes the embrace of solipsism, because metalogy shows how any self comes to know itself through a primary discovery of the non-self within its own recursive perception. Skibinski notes that when Bateson posed the definition of ‘self’ in Our Own Metaphor, he meant that metaphor of self always juxtaposed a ‘me’ with somebody that is a ‘not-me.’ The rule here indicates that we have to perceive two different sides before we can infer that we are either not ‘duals’ or ‘no-sided.’ In other words instead of there being a substantial, real, subject-object split between the ‘me and the ‘not-me’ Bateson’s resolution lay in an understanding of difference and how the pattern of difference is interpreted by ‘the self.’ The interface of difference distinguishes Bateson’s discussion of the paradox of self-consciousness from Merleau-Ponty. Skibinski thus supports Neuman’s explanation of the mirroring of self as an ‘in-between event,’ the emergence of pattern from the surfaces of in-betweeness .

Another article (M’Closkey) develops Anthony Wilden’s extension of the Bateson idea of ‘steps’ or sequence in logical hierarchy to show how phenomena regarded as ‘duals’ (work and spirituality which are opposed to one another in materialist explanation) are, in fact unified in a single Navajo aesthetic. The article indicates that anthropological investigation has misunderstood the appropriate coding of pattern with consequences for the Navajo which are exacerbated by the current practices of the commercial sector of North American society. Finally, Harries-Jones looks once again at Bateson’s posthumous publication, Angel’s Fear, in the light of its central themes about recursion and aesthetics. It would seem that Bateson, at the very last moments of his life, was trying to re-define his dialectic between structure and process that he had developed so well in relation to his scheme of heterarchy and logical types - in order to take account a notion of process that would better fit ecological continuities and recursive process.

Though the depiction of recursive forms, forms that re-enter their own domain, have become more widespread since Bateson’s death, the relation of recursive forms to empirical events, and the difference in explanation that results from attention to processes and forms of recursion, is still relatively rare. McNeil points out that the topologists have been of little help here, for though their vocabulary of closed surfaces, their connectedness, closeness and relative invariance is rich in significance for a whole range of disciplines, they are loath to give any examples that can be taken up outside the world of other topologists. There has yet to be a definitive study by topologists of the topology of meaning. Instead, the study of meaning continues to be attached to one particular topology, that of a sphere, and its metaphoric representation, for spheres fit closely with the western tradition of rationality, that is to say, they have an orientable surface i.e. they set apart an inside and an outside; they have inherent symmetry; they are simply rather than complexly connected, that is an arc of a circle is the only kind of shortest line that can be drawn between two points; and there is no condition in a sphere of second order circularity. Other topological forms, the torus, display very different characteristics while the more improbable forms such as the Klein bottle, have been largely ignored.

The topology dealt with in some of the articles below has, therefore, the aura of being an exercise in ‘thought experiments,’ until it is realized that any ‘thought experiment’ which can better represent embodiments of holistic, rather than particulate form, gives rise to a new understanding of dimensions in space-time and such insight, if achieved, is always fundamental to society’s understanding of itself. So toroids and Klein bottles on the one hand, and Möbius strips and heterarchies on the other, may be ‘thought experiments’ but they are fundamental to an understanding of human perception and how perception is associated with the recursive processes of mind.

Bateson was, if nothing else, a pioneer in stressing the importance of perception to the study of mind. This point is summarized in the expression that Bateson borrowed from Korzybski (see Skibinski) that ‘the map is not the territory.’ In recent years laboratory studies have caught up with this remarkable insight. The eye has no equivalent of a photographic plate in the visual cortex. Nor is there one place in the brain in which nervous electrical messages are retranslated into a faithful image of the world ‘out there’. There is not even a single all-encompassing visual cortex, instead there are a number of discrete cell ensembles, each analyzing different features of the world, some responding only to horizontal, some to vertical lines, some to edges and angles, some to colour and some to motion. Each ensembles creates its own map of the world, but which aspect of which cell responds to the topography of the world it interprets depends on its connectivity with other cells, and not upon its distinctive properties. Hence it is the brain itself, the whole organ that puts vision all together, the activity of the whole organ on its parts still remaining an unknown process (Rose, 2004). Perception, as Bateson stressed, is an unconscious process, over which an individual has no control. In an experimental context, one of the most appropriate means for the investigation of this unconscious process is by investigating perceptual illusions or through study of impossible objects, like Necker cubes and the Klein bottle (McNeil, Rosen, Ryan) or the Möbius strip (Rosen), or the strange loops of a hierarchy in graphics by M.C. Escher. All these yield perceptual confusions and in order for any meaningful interpretation to occur, require some ‘dialectic’ between orienting stabilities of form - usually forms that are subject to classificatory denotation - and perceptual signification (Neuman, Harries-Jones).

The notion of context is of central importance to the idea of a ‘map is not the territory,’ and is a common thread among these papers. As M’Closkey shows, in order to perceive any pattern, it is important to broaden our understanding of the ways in which information is differently coded . Her example is a Navajo rug, whose iconic coding in photographs can be discussed openly among Navajo or between Navajo and non-Navajo. Yet it is subject to different denotation in different social contexts. Among Navajo weavers, once rugs are re-translated into textual objects in books, they cannot be discussed in so open a manner. As the textual object the rug cannot be ‘read’ for no textile object is sufficiently inclusive of what rugs signify. To the weavers, rugs represent relationships, both between themselves and to their cosmology. This relational circuit is far too large to be captured in any textual form. Thus Navajo weavers have nothing to say about the many empirical descriptions of Navajo rugs that appear throughout the southwestern U.S. in various studies of Navajo textiles. Even bilingual speakers in the southwestern U.S. are reluctant to address the content of these texts. Distinguishing the appropriate coding of pattern, M’Closkey argues, is fundamental to understanding why Navajo women continued for more than 150 years in weaving rugs that sometimes cost them more to purchase in materials than the price they received for the finished product. Thus we may say that the coding of ‘difference’ is not trivial to social organization, rather it can refer to differences in fundamental patterns of ‘time binding’ in human societies (see Skibinski)

The ‘map is not the territory’ also engenders discussion of continuity and ‘gapiness’. There is ‘gapiness’ between the abstract topography of the map created by the brain and the territorial surface continuities from which the map is derived. Paradoxically, there is always a sense of continuity achieved in the process of visual perception of ‘the territory’ despite the fact that the blinking of the eye, a phenomena of our biology, cuts directly into that sense of visual continuity and sends an array of discrete electrical messages to the brain. In all our perceptions we are therefore in a situation which Rosen defines as a topological paradox, a continuum with a cut in it that is both discontinuous and continuous. He argues that the only way to wrestle with this Möbius - type phenomena is to interpret its paradox: the recursiveness of a continuum with a cut or a twist in it, that at one particular locality enjoins it as a two-sided phenomenon, but in reference to the actual temporal process when passing along the Möbius surface as a whole, remains continuum. Thus Möbius exemplifies a dialectical entwinement, a radical recursion that should be understood in a constant and in a thorough going manner ‘all the way down.’ Rosen notes that a structure which embodies the paradoxical interweaving of continuity and discontinuity is precisely the structure that postmodernism has failed to introduce. Radical recursion through engaging the paradox is able to counteract the progressive slippage of the signifier so typical of postmodernism where the subject is transformed into an evanescent flux of differences.

A characteristic of Bateson’s approach to perception, circularity and information was to carry all of these ideas, including illusion and perceptual twists, outside a laboratory setting and investigate them in interactive social contexts. Something similar is considered in Ryan’s article on ‘kleinforms.’ The kleinforms that Ryan portray are somewhat different to its topological prototype, the Klein bottle. The relational circuit of kleinforms are those of a torus that penetrates itself, whereas in surface topology a Klein bottle is a form that only appears to penetrate itself, but self-penetration can only occur with the addition of more than three dimensions (McNeil, Rosen). Ryan’s kleinforms, on the other hand, permit self-penetration and encourage reflection on this phenomenon. Ryan presents the process of self-penetration as a way in which people as ‘signs of themselves,’ operate in feedback relationships with themselves and with others in real time, self-penetration occurring by means of interactive relational positioning of people in a circuit. Ryan’s relational circuit is a type of a tubular topology rather than that of a layer of surfaces. The positions of people in a circuit are not so much mapped on to a surface but rather constitute positions within a tube- like media, the relational circuit. The tubular circuit enables participation in simultaneous self-other activities, thus developing participatory perception from recursive positions of those in the circuit. By this means Ryan shows how people defined in C.S. Peirce semiotic system as a sign of themselves, can become active participants in Bateson’s version of systemic cybernetics.

Kleinforms, Ryan admits, are a creative misinterpretation of surface topology. He also admits to creatively misinterpreting Bateson. Ryan’s relational circuits owes more to the a-temporal tradition of C.S. Peirce ideas, than the insistence on temporal properties of feedback in Bateson’s cybernetics. The resolutions of Bateson’s map-territory distinctions, the mapping of discontinuity, was always in concordance with the arrow of time. In Ryan’s relational circuits, the map and the territory are not distinct, nor are map and territory discontinuous. As Ryan points out feedback in the circuits map a map into themselves. Map-territory distinctiveness


disappears in favour of positional orientations, ‘firstness,’ ‘secondness,’ ‘thirdness.’ By presenting an overall circuit of positional difference without discontinuity, Ryan maintains that his scheme creates operative redundancy in a complex manner. Given that redundancy patterns are essential to communication, more complex patterns of redundancies in mutual differentiation yield a better understanding of emergent meanings and of the possibilities for mediating differences in meaning. As a last look, Ryan’s approach can be compared to the dialectical inter-penetration of continuity and difference that Bateson puts forward in his posthumous publication, Angels Fear (Harries-Jones). Here we glance here at Bateson’s dialectic as he comes to grips with a new form of recursion proposed by Humberto Maturana and Francisco Varela in their presentation of autopoiesis. Bateson applauded the way these authors showed how the whole re-entered into the parts in the course of the development but was worried by the structural determinism that they advocated in their version of recursion.


McCulloch, Warren. 1956. A Heterarchy of Values Determined by the Topology of Nervous Nets. in Embodiments of Mind. Cambridge: M.I T. Press pp. 40-45.

Rose, Steven. 2004. Review of Michael Morgan. The Spaces Between Our Ears: How the Brain Represents Visual Space. in Guardian Weekly, February 5-11 p. 17.