Representing Chaos: Peircian Triads and 3-sided football

David Scott (Trinity College, Dublin, Ireland)

The nature of the relationship between 'Order and Chaos' implied by this conference's general heading is one of binary opposition. Not least in the light of the likelihood of a numerous attendance by Peircian semioticians, a challenge or problematisation of this polarisation was no doubt anticipated and a problematisation of an antonymic relationshiop between 'Order' and Chaos' expected. This paper duly explores ways of breaking out of the binary oposition 'Order/Chaos' using the Peircian triadic model that will be illustrated in part by the example of a recent ludic invention: three-sided football.

First, a few words of introduction to this entrancing game. Three-sided football was devised by the Danish COBRA artist, Asger Jorn, member of the 'International situationniste'. It provides three 7-a-side teams, using three goals on a hexagonal pitch. The game has been put in practice in the 1990s in Britain, Germany and Italy, where there are already three-sided football leagues. In Britain, a theory of the game has been articulated by David Essex who stresses that the game is devised to move away from the binary oppositions of conventional football - the agressive us-and-them approach. As opposed to the 'homerotic psychosexual drama' of regular soccer, three-sided football is a game in which successful attack implies cooperation, so the usual anally retentive techniques are absent. Each team has two opposite sides of the pitch, and the winner is the one which concedes the fewest goals. Teams must decide which goal to attack while defending their own against the two other teams. Alliances are built up with the other teams but change as each individual team seeks its own advantage. Persuading a second team to join the first's assault on the third's goal can be done in a number of ways: by begging, or threatening, use of body language or other collateral gestures, manoeuvring the ball into a position where one team realises its best chance is to swap sides. Team dynamics and concensus decision-making are developed when members of the same team disagree about which goal to attack. These splits have to be healed before opponents take advantage. Good communication and a talent for negotiation, rather than muscle or the killer instinct, make three-sided football the special game that it is. As David Essex says, the essence of the game is duplicity or organised chaos(1).

I use three-sided football in this paper as a model for Peircian sign functions, especially in so far as it exemplifies a triadic structure which stresses the role of the interpretant. In the three-sided game, firstness, the representamen, is represented by the ball; secondness, the object, is represented by the goal; thirdness, or the interpretative process, by the player or players. The 'ground' in which the object is grounded is, of course, the football pitch. The 'meaning' of the game is a function of the players organising themselves into an interpretative process which can never merely be the negotiation of a binary opposition. Chance and random change are integral to the process. With this structure in mind, I now turn back to the Order/Chaos problematic that is this conference's topic so as to explore ways out of the binary binds it proposes.

As a number of participants in the conference have observed, the opposite of 'order' is 'disorder'; 'Chaos', however, is more than just disorder: it is a type of disorder radical enough to render any relationship it might have with an antonym highly problematic. As a word, the dictionary defines chaos as 'complete disorder' or 'the disordered formless matter supposed to have existed before the ordered universe'. These definitions interrelate in an interesting way, for the disorder that chaos represents is a disorder of a radical or cosmic scale. Chaos is a disorder in which all traces of order or pattern seem to have been erased. But, the second dictionary definition, like Greek mythology, also suggests that Chaos preceded order, implying that any sense of order or system is a subsequent superimposition on a pre-existing chaos, a model created with the view to enabling meaning or sense to be made of the universe. But if order emerged from Chaos, there must already have been the potentiality for order in Chaos; in which case, Chaos is a kind of order, but one not generally knowable or verifiable; or it is an order that is virtually knowable, but one not yet known and perhaps never fully knowable. A truer antonym of Chaos might therefore be Design or System, words which have no natural antonyms: chaos is a phenomenon in which design or system seems lacking. If we focus on the 'seme' 'sign' buried in the word 'design', we can read Chaos as being a state of affairs where there are no signs , or rather, if there are signs, they are not (yet) recognizable as such (which amounts to the same thing). The question then arises: can we conceive of an object which does not present itself in terms of signs?

Some scientists, in seeking a principle of order in the apparent randomness not only of certain phenomena, but also in the randomness that is the ultimate basis of matter in the universe, have recourse to Chaos Theory in attempting to clarify their thinking. For Chaos theory proposes a number of hypotheses which enable us to conceive of ways in which Chaos may be 'structured'; they include constrained randomness, nonlinearity, self-similarity, entropy, feed-back loops and, perhaps most importantly, concealed order. What modern science, chaos theory and three-sided football suggest to us is that chaos may be a phenomenon not so much where there is no order or system, but one in which order and system changes , apparently at random, and that chaos becomes manifest when we look for particles and in fact see waves, or when we look for waves and in fact see particles. Or we look for linearity and find spatiality, or when we look for continuity and find instances of spontaneity. Viewed in this way, chaos could be seen as being fundamentally a semiotic problem. In responding to it, the semiotician in his turn would need to consider chaos both as an immediate object , a sign (in Peircian terminolgy), and as a preinterpreted or dynamic object, one whose sign status is more problematic.

If this is the case, how does the semiotician go about deciding on the best approach? If the semiotician is, by definition, committed to signs and to viewing all phenomena, all objects as potentially significant, some fundamental issues are raised. Three of them have been cogently articulated by Umberto Eco in Semiotics and the Philosophy of Language in which he asks: (a) Can one approach many, and apparently different, phenomena as if they were all phenomena of signification and/or communication? (b) Is there a unified approach able to account for all the semiotic phenomena as if they were based on the same system of rules[...]? (c) Is this approach a scientific one?(2) These questions were, of course, of major concern to Charles Sanders Peirce whose project, as a philosopher and founding father of Semiotics, was precisely to establish the nature of the relationship between phenomena and signs, between objects and meaning. As Carl R. Hausmann has shown, in his recent study of Peirce's evolutionary philosophy(3), 'the relationship between phenomenological categories and semeiotic', was fundamental to Peirce's establishment of a coherent philosophical architectonic. So 'what Peirce says about the evolution of the cosmos is a counterpart to what he says about the development of the interpretation of signs' (Hausmann 1993: 18). The triadic structures that constitute Peircian sign systems also structure his conception of the phenomenological world, or 'Phaneron' as he calls it.

The problem, then, of semiotics when facing chaos is one both of classifying and interpreting, activities that are mutually dependent. These activities may be conceived in terms analogous to what may be defined, in Peircian terminology, as of encompassing the Phaneron, - a concept that finds a parallel later in Umberto Eco's concept of the 'Encyclopaedia'. The Phaneron is all that which, from whatever point of view and in whatever sense, is present in the mind of whomever, everywhere and always, whether or not it corresponds to anything. Phaneroscopy, the study of phanerons, attempts to distinguish among them several classes or categories and to describe their characteristics even though no single class is completely isolatable from another; the characteristics of the different categories are nonetheless markedly different and can be classified and their principal subdivisions enumerated. For Peirce, these classifications resolve themselves into triple triadic schemes, much like his classes of signs. Thus Firstness , is the phenomenological category of quality: an immediate presence that offers the phenomenon as sheer possibility.Secondness, is the categority of phenomena encountered as recalcitrance or resistance: a fact of experience, a certain brute presence. Thirdness, is the category of mediation, the making intelligible of the possibilites of Firstness or the brute phenomena of Secondness. Thirdness operates triadically, through a mediation in which one thing is related to another by means of a third(4).

When Eco states that 'the regulative idea of encyclopaedia is the only way to outline the possibility of [the]universe [of semiosis] and to try tentative devices for describing it' (Eco 1984: 77-780), he could equally be referring to Peirce's Phaneron.. For Peirce's inspired combination of Pragmatics and Semiotics proposes a means of accounting for both continuity and change, system and (apparent or momentary) chaos in the world. Peirce's account of the relationship between continuity and spontaneity, (especially as analysed by Hausman) is an example of the way his thinking is able to account for an apparently chaotic or paradoxical situation, is able to show how one order can become another, that the cosmos can evolve without sacrificing its coherence as a system. For although intelligibily is broadly to be equated with continuity, every continuum is open to the possibility of more intelligibility. Peirce's system is based on a notion of continuity in which spontaneity is possible, where the latter originates new intelligibility which is in turn absorbed into the continuum. Again, three-sided soccer provides an analogy: new alliances or new truths do not necessarily totally invalidate 'old truths'or old allinaces, though the latter may take on a different status in the light of the former. So what Eco says about the structure of his model of the 'Encyclopaedia' is also further illuminating in relation both to Peirce's Phaneron and to three-sided football theory:

(a) It is structured according to a network of interpretants. (b) It is virtually infinite because it takes into account multiple interpretations realized by different cultures[...]. (c) It does not register only 'truths' but, rather, what has been said about the truth or what has been believed to be true as well as what has been believed to be false or legendary[...] (Eco 1984: 83).

In pointing out that the 'Encyclopaedia' is structured like a labyrinth, Eco could, like Hausmann, also be characterising the expression of Peirce's thinking in general; also the structure of three-sided soccer where the ground is not a symmetrical pitch but a maze. The important point to stress here, in relation to the Encyclopaedia and to the Phaneron, is the role of the interpretant and the complex strategies of inference and interpretation on which it draws. Eco underlines the multiple inferential processes which underly semiosis and the necessity of analyzing intuition semiotically as a 'complex cognitive process' (Eco: 1984: 9). But the Peircian concept which most helps clarify the nature and complexity of semiosis or meaning creation, here, one effectively highlighted by Hausmann in his analysis of Peircian signs and their conditions, is that of the Ground. For it is the grounding process that governs the status of the sign and the manner of its interpretation. For the ground qualifies the object and thus governs the way it will be represented by the interpretant. Peirce's distinction between the immediate object and the dynamic object, as I mentioned at the beginning of this exposé, is fundamental here. For in the case of the immediate object, the ground merges with the object, while in the case of the dynamic object, it remains independent of the semiotic process within which the sign arises (Hausman 1993: 73). Thus, when faced with a phenomenon such as chaos, the 'ground' for interpretation is not clear: as an object, it is dynamic ; to make sense of it, the interpretative process must itself become dynamic, drawing on the collateral experience of the dynamic interpretant in attempting to convert it into an immediate object by discovering ground or grounds for interpretation. In terms of three-sided football, the problem is that of deciding into which goal to kick the ball and with the collateral assistance of which side. Confronted by chaos, the semiotician resists consigning it to the category of what Peirce might describe as the 'absolutely incognizable' (cited in Hausman 1993: 65), and seeks out instead the virtually signifying elements that, for semioticians at least, are taken to underly all phenomena. Michel Costantini in his recent article in EIDOS seems to confirm this situation when he states the modern semiotician's position as being one which considers 'tout comme virtuellement signifiant'(5).

It is interesting to note that one of the leading proponents of the term 'Semiotic' in contemporary semiological discussion, Julia Kristeva, envisages the term precisely to describe a virtually significant state (a kind of chaos) anterior to the Symbolic order of Language and the Law, and, therefore, of knowledge. In La Révolutuion du langage poétique, Kristeva characterizes the 'chora sémiotique' paradoxically as an 'ordonnancement des pulsions', a provisional and mobile ordering, a 'rhythmic space', operating according to displacement or condensation, metonymy or metaphor, which both precedes and also underlies more conscious processes of mental activity and language use(6). Although these operations are, by definiton unconscious, signs of them manifest themselves in dreams and texts, and for Kristeva, these signs already constitute virtual propositions. Much of La Révolution du langage poétique is devoted precisely to pinpointing them in the writings of the French poets Mallarmé and Lautréamont.

In Peircian semiotics this virtuality is very apparent. Peircian semiotic theory is characterised by its allowance for the movement of sign functions and its recognition of the multiplicity of interpretative strategies. From the point of view of the interpretant, inference or abduction, as well as induction and deduction, constitute a fundamental part of the mechanism of interpretation, depending upon the combination and interrelationship of components constituting the sign and the varying grounds in which they operate.

Peirce's predelection for the triadic structure is significant in relation to the problem of chaos, for the triad is intrinsically unstable. Lacking the symmetry of the diad, the logical balance of the antonym or the binary opposition, it proposes a third term, whose relationship with the other two is always problematic, not least because the third can become a first in relation to the second or a second in relation to the first. It can also include within itself elements from the first or second while still remaining itself third. The problem of semiotics, or Phaneroscopy, or chaos theory, or three-sided football, or Eco's 'Encyclopaedia' is therefore to classify and separate, to find or impose order on objects that are constantly moving, - sometimes into complex patterns of interrelationship with eachother. Just as Peirce insists on the continuity of thought or experience, so also he stresses the random or arbitrary potentiality of sign theory. So, dicisigns can be both indexical and iconic where the interpretant is the object. And he concedes that it is difficult to instance an absolutely pure index, or to find any sign devoid of indexical quality: symbols commonly involve 'a sort of index' while indices involve 'a sort of icon'. The constant shifting of categories is a function not only of the collateral experience of the dynamic interpretant, but also of the sign context, as will become clear if you think of triadic soccer or a round table at a semiotics conference in São Paulo.

But although, in its essential instability the triad is potentially a 'sign of chaos', through taking the risk of reversibility, by allowing for movement and change, it is able, to a certain extent, to 'embrace' chaos, to allow for the elements of spontaneity or randomness that are part of human experience. The angle of the triadic structure that is potentially the most chaotic is that of the interpretant. For Peirce - and in this lies an important part of his originality and his continuing relevance - stresses and complexifies the role of the interpretant, subdividing the mechanisms of semiosis into a further triadic structure of immediate, dynamic and final interpretants. So whereas the immediate interpretant responds to the object as represented in the sign (along the lines of semiosis as communication), the dynamic and final interpretants operate according to various kinds of collateral experience (what one might relate to the concept of the semiosis of signification) which, though comparable, are infinitely variable, or, at least, never exactly the same. (Eco's account of the interpretation of a metaphorical text perfectly exemplies the massive potential flexibility on the part of the interpretant in processing or reinterpreting the lexicon. Indeed, it is interesting to note how the complexities of literary structure - especially metaphor ans metonymy - become the basis of discussion in confronting some funamental semiotic issues - cf Barthes and Derrida as well as Eco and Kristeva). Although Peirce is interested primarily in the logic of relationships, not the psychology of them (and, a fortiori , not a psychonalysis of them), he allows for the subjectivity of each individual receiver, the infinite possibility of the phaneron, and provides tools for the analysis of the signifying process which can identify, even if they cannot penetrate, unconscious activity.

System and Chaos, then, though antonyms, are no doubt, at bottom, mutually dependent, related through a dialectic of tension. Signification may be envisaged as a provisional rationalisation of the virtual chaos of the phaneron or the physical universe, or the hexagonal pitch, a constant renewal and readjustment according to the multiple collateral experiences or pressures that are brought to bear on mental processes. Chaos is a necessary supplement (in the Derridian sense) to signifying systems. Semiotics, to be effective and comprehensive as a science, recognizes within itself both a principle of chaos and a principle of order: it concerns itself with both the semiotic chora and the symbolic law. In a different but related way, Peircian semiotics enables us to confront Chaos by showing that it is integral to our mental processes. To make sense of a universe and an experience which are essentially dynamic and changeing, it offers a semiotic model which, like three-sided football, embraces dynamic change. To repress or ignore the virtual chaos of our experience is to oversimplify the universe and impoverish our understanding of mental activity; and to provide a less challenging and interesting football game.

NOTES

(1) I am grateful for much of this information to Dawn Gill's article on three-sided soccer in The Observer , 11 August 1996

(2) Umberto Eco, Semiotics and the Philosophy of Language (London: Macmillan, 1984), 7

(3) Carl R. Hausman, Charles S. Peirce's Evolutionary Philosophy (Cambridge University Press,1993), 12

(4) A fuller account, including a schematic tabulation of the Phaneron, is supplied by Gérard Deledalle at the end of Ch I of Théorie et pratique des signes (Paris: Payot, 1979), 64

(5) Michel Costantini, 'Six ou sept choses que l'on croit savoir sur le signe et l'image' in Eidos 11 (1995), pp. 3-35

(6) Julia Kristeva La Révolution du langage poétique (Paris: Editions du Seuil, 1969), 2. Kristeva takes the word 'chôra' from Plato's Timaeus , where the term expresses the link between the sensible and the intelligible.