Is metarepresentation an effect

Wolfgang Wildgen (Bremen)

Is metarepresentation an effect of self-organization? 1 Introduction: Reflexion on the concept of metarepresentation Before we introduce the concept of metarepresentation or the set of definitions proposed for this term, we must try to specify what representation means. There are different avenues which lead to a definition of this term. It is a key notion in the philosophy of mind and language, in epistemology, semiotics, linguistics informatics, robotics, and cultural theory. One avenue is etymological and historical. Thus Lat. praesentatio refers to Lat.: praesentia, i.e., being present, to appear, having an immediate effect (prae-sum = I am personally here). Lat. repraesentatio is a technical term of banking, i.e., paying cash, the verb Lat. repraesento has beyond this technical meaning a more basic use which means: to put before ones eye, to refer to something using images, triggering a vivid memory of something. Historically the notion of an indirect reference to something not present via a means/tool which stands for the non-present can be found in the definitum of the sign by Augustine. It is basically a predicate with three arguments: (a) Some being, which is the container of the representation, e.g., a human mind, which perceives and thinks. We call it the repraesentans. (b) Some entity being represented which is not directly accessible (absent). We call it the the repraesentandum. In many cases it is considered as in the focus of the attention of (a), or it is the goal of the intention of (a) (in the vectorial sense defined by Brentano). (c) Some entity accessible to (a) which organizes the link between (a) and (b) and provides a specific organization for the system of such representations. Peirce calls it the repraesentamen. This three-valent predicate can be enriched, if further arguments are added, such as: -

-

-

The context of representation, e.g., the environment in which (a) must survive via representations or the action to which representations lead. It may be a subpart of (b). That part of the representing being (a) which is the recipient of representation, e.g., the mind (or body), the brain, the cortex, specific neural structures or processes in the brain. The partner (in the own or in another species) for whom something is represented. The social system of ritualized schemata to which all representamens, e.g., signs like linguistic expression must be fitted. This could be the grammar of a specific language

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or the ethnic rules of symbolic interaction of some group of beings (subpart of a set of (a)). If one side arguments (a), (b), (c) may be augmented, mainly by a specification of subparts, regions, specializations of the major arguments, one can on the other side choose a more parsimonious strategy and reduce the three-place to a two-place predicate. The most radical choice is to eliminate part (b) and to say that after all representations are just (statistical) correlations between states of (a), e.g., neural states and processes and aspects of (c), e.g., the environment perceived and acted on. The substance of such a correlation may be hidden in a black box. This would be the position of a radical behaviorist or more recently one subscribed by connexionist models. Another bivalent scenario would place the two-place relation of representation inside the individual brain and would distinguish between a bottom-up flow from the senses (linked to the immediate presence of an environment) and a top-down flow of memory schemata and expectations. The two poles of this continuum could be the arguments of the term representation, although the continuous and processual nature of this concept undermines the logical nature of the concept (as a two-place predicate). If one assumes the “temporal binding hypotheses” of neuropsychology (cf. Wildgen, 2006), the concept of representation looses its static-logical nature and becomes a highly transient, temporally bounded phenomenon and this asks for criteria of stability which enable human symbolic behavior to be (partially) calculable and thus socially accessible. In a sense, this discussion gives us rather two bad choices: -

-

A concept of representation to which we may add (theoretically) an unlimited number of arguments (beyond the classical three ones found already in Augustine) and which not only is static but becomes a kind of unspecific basket of components without a clear profile. A very rudimentary notion which refers to processes in the brain (as a proper part of a biological entity). As the details we know about the dynamics of the brain stem from studies in animals, this concept does not properly separate human from nonhuman representations. Insofar as the neurological mechanism may be reproduced in machines, even the difference between physical and living entities could be lost in the line of this strategy.

Any discussion of the term “metarepresentation” must account for the controversies and ambiguities linked to the notion of representation. I will now turn to the prefix: meta. The prefix “meta” (from the Greek adverb: μετα) means: inside of, after and the Latin noun meta means center, point of revolution. Therefore, a representation could be meta if it comes after the representation. If after is understood in evolutionary terms, then one would have first the faculty of representation, then at a later/higher stage that of metarepresentation. MetarepresentationWildgen

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I will come back in a similar definition given by Sperber (2000) in the next section. Meta in Latin has a rather clear meaning as the turning point in a circus (for races). If representation is a goal-directed process, then the turning point after which the race comes back to the start/goal could mark the process of metarepresentation. In more theoretical terms, metarepresentation is reflexive, insofar as the intentional vector going from the starting point (a; e.g. the subject) to the immediate goal (c; the object) is reversed and now points to (a) which becomes simultaneously start and goal. This means that metarepresentation is reflexive, and self-referential. In the picture of the Roman circus and a race, the field returns to the start and every time it reenters the circle, this field may have changed a bit. This opens different interpretations of the term metarepresentation: -

If two parties (A, B) in a communicative process using representations are taken as background, the transfer A  B is one phase, where A represents something for B. After the turning point the receiver B becomes the sender and in B  A the representation is sent back to A, which may become aware of the message insofar it was sent, received and sent back, i.e., the content of the message becomes apparent for A (after the next turning point also for B). The condition for such a metarepresentation is however that the message intended and sent is more a less identical with the feedback message, i.e., it must have an attractor. Here we can apply the notion of the Poincaré map. In a circular motion the path may return to a point identical with the start or deviate from it. If the deviations are damped, the path is stable; if differences grow progressively, the attractor becomes chaotic. Figure 1 illustrates this basic scenario of dynamical systems theory (cf. Wildgen, 1987/2005). The curve intersects with the plane at two different points h and P with a distance d between both.

-

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Figure

1:

The

Poincaré

map

of

a

normal

and

a

chaotic

attractor

(source:

http://www.cg.tuwien.ac.at/research/vis/dynsys/Poincare97/fig-pmexplanation.1024x512.fc.labels.jpg)

Now, if the attractor is stable, metarepresentation just stabilizes the representation and may be identified with it. In the chaotic case, every return produces a difference and differences augment. There is an intermediate case which is shown in pattern reproduction and its selforganization. Every cycle abolishes parts of the original pattern, but there are one (or several) attractors to which all divergences tend. In the examples discussed by Stadler and Wildgen (1987), a text is reproduced in different series of reproduction. Some elements of the text are preserved, others change and finally one or several core texts emerge from the process of cyclic reproduction. In the case of experimental visual patterns reproduction, the underlying mechanism becomes even clearer. Example 1: Path of point reproductions on a sheet of paper. The attractors lie near the corners of the paper (independently from the start position).

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Figure 2: Point reproductions (cf. Stadler and Wildgen, 1987 : 118))

The process of deformation in a series of reproductions with internal attractors is a simple example of self-organization. As evolution can be understood as a series of reproductions this concept is applicable to the question of the emergence of specific ordered forms under specific conditions (in the example above the shape of the white paper is the relevant frame). The scientific use of meta in modern philosophy is linked to the term “metalanguage” introduced by Tarski in distinction against the term “object language”. Beyond formal languages one may say that a metalanguage appears, if beyond the simple use of a language either parts of the language are cited (whereby the language is used and something is said about it) or if statements about the regularities of the language are made. In this sense a grammar of a language L is a metalanguage of L: M(L).1 This metalanguage is post hoc in relation to a language, i.e., in an intellectual reflexion on language (under specific conditions implied by the method chosen and some theoretical assumptions) a set of statements about the language is made. In this sense all kinds of theories about representations would be metarepresentations.

1

Medieval philosophers who distinguished intentio prima and intentio secunda already take such a view.

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A more interesting object of semiotic analysis is, however, the natural reflexion on language evolving in the normal use of language, which may be called language consciousness and which is constitutive for certain levels of language acquisition in the child. In order to reach the adult level of language competence, a metalinguistic reflexion is necessary and constitutive (cf. the “theory of mind”, ToM, and other fields of current research). In the case of representations such a type of metarepresentation is therefore an aspect of semiotic evolution (in ontogenesis and phylogeny). I will discuss this aspect in next section. In the literature on the topic metarepresentation many of the aspects our analysis of the notion “metarepresentation” has uncovered, are present, but some are highlighted and further aspects are added. Dan Sperber takes language to be one prototype of metarepresentation: “Linguistic utterances are public representations and typical objects of mental metarepresentation. Speakers in intending an utterance, and hearers, in interpreting an utterance, mentally represent it as a bearer of specified content, that is they metarepresent it.” (Sperber, 2000: 121)

In his view (ibidem: 122) “modern human communication is metarepresentational through and through.” One could conclude that every thing in human communication which was considered a representation is now metarepresentation. This could be the beginning of an inflationary regress. If language is throughout metarepresentation, what about the underlying representation, may it also be a “bearer of specified content”? This leads to the homunculusproblem (cf. Wilson, 2000). Every sub-meta-level may again be categorized as meta and the homunculus (the representation) becomes more and more intrinsic to the individual mind (to smaller and smaller subparts of it). Another line of argument is proposed by Dennett (2000), who considers a path “from outside in” (ibidem: 21). The overt public use of signs is a clear indication of their metarepresentational nature (every body can perceive them, reflect on them, they are a common good like space, light, air, etc.). If we follow this line, metapresentations first become supra-individual, then social and finally elements of a cultural context, to which individuals respond (elements of their life world). The concept of a metarepresentation seems to shift on the scale between smallest pats of the individual mind (mini-homunculus) and the external (cultural) world. This is illustrated in Figure 3 Homunculus in the brain

individual consciousness

cultural context

world

Figure 3: Scale of the shifting concept of metarepresentation

I shall now turn to the question of the evolution of systems of representation in order to involve more basic laws which are able to fix the shifting concept of metarepresentation.

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2 The phylo- and ontogenetic evolution of metarepresentation The operation “meta” in “metarepresentation” 2 refers to a process which may occur at different time scales: a) In actual behavior embedded in a situation. Such processes belong to “microgenesis” as it was called by the Gestalt-theorist Werner (1956). Microgenesis focuses on “fine grained temporal dynamics of psychological processes and on the categorical character of meaning and perception” (V. Rosenthal, 2006: 117). Thus, given a perception, its memory adds the temporal cue “different from now” and reorganizes its content. In a sense it produces a new version of the percept with the feature “past” and traces of transformations added (cf. the discussion of memory of trace of transformation by Leyton). Another example of microgenesis is spontaneous imitation. Whiten (2000: 146) calls the result of such a process: re-representation. b) In the ontogenetic development, studies have revealed that two- to three year old children do not yet distinguish between a state of affairs p and a belief that p (cf. D. Rosenthal, 2000: 277). At the age of four to five, children develop a kind of higherorder-thought (HOT), which means that they are aware of states of thinking, believing possibly different from the state of affairs. Nevertheless this awareness is still linked to “behavioral cues and environmental stimuli” (ibidem: 282). They may be called second order representations. A third-order-representation could be “thoughts about thoughts about mental states” (ibidem: 283). So far three developmental stages seem to emerge: 

Two to three years old children do not yet separate thinking and believing (although they may use these words) from the states of affairs (what is true).



Four to five year old children are able to distinguish the state of affairs from the propositional attitudes expressed by “think, believe,…”. Therefore they can also conceptualize pretence and false belief. Nevertheless they link these secondary representations to behavior cues and if people sleep or are inadvertent, they are still seen as thinking, believing, representing something. The relevance of consciousness is not yet understood.

2

As for many fundamental questions, the question of an evolution of metarepresentation depends on a proper definition of the term “metarepresentation” (cf. last section). If metarepresentation depends on human language or even on a level of reflexive use of human language than any discussion on stages prior to the evolution of human language is unfounded. If metarepresentation is rather independent from language, its nature has to be elucidated with the help of evolutionary data. MetarepresentationWildgen

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

Adults achieve a third order representation insofar as they can think about someone actually thinking about mental states (only if consciousness and attention to the topic arises, not as a steady state).

Besides these developmental studies some results of psychiatry report differences in the capacity of metarepresentation in humans: 

Autistic children and adults are impaired in their evaluation of the states of mind of others (often regarding emotions).



Schizophrenia “is a late-onset breakdown of a metarepresentational system” (cf. Frith, 1992, Cosmedes and Tooby, 2000: 103f).

Although many issues in this field are still controversial, it seems obvious that the ontogenetic evolution of cognition and language is linked to the emergence of higher order representations. c) If children only develop metarepresentation after some years, how do animals in our evolutionary lineage from primates to monkeys, mammals, birds behave in this respect? A first restriction concerns language. If it is a precondition of metarepresentation, it would be pointless to consider this question further. One must therefore first assume the possibility of nonverbal metarepresentations, which refer rather to nonverbal communication and bodily signals than to language. Current results of experimental studies and observations in the wild show that imitation and simple mind-reading as manifestations of metarepresentation are more common in great apes (e.g. chimpanzees)) than in monkeys. In terms of an evolutionary time scale, a first level of metarepresentation could have been reached some 7 my years ago (with the common ancestor of humans and chimpanzees), whereas monkeys which separated from the ancestral line some 30 my ago did not yet reach this level. Still very basic skills such as learning by observation, in the case someone else has hidden something, or by imitating the sequence of acts which allow the animal to reach a specific goal can be found in social animals far from our lineage. As the scenarios of the evolution of human language diverge vastly (between an origin two million years ago with the species Homo habilis/erectus or 50,000 years ago with the first manifestations of cave art), the rise of “true” metarepresentation could be very recent. As cave art may be interpreted as a magical practice, it is even unclear, if the animals in the cave were seen as represented or as present and one could, therefore, rather link the rise of metarepresentation with the public use of writing (starting with object-signs some 10,000 years ago). In this case, all current populations which do not have writing would still live in a stage before the rise of metarepresentation and finally one may come to the absurd conclusion MetarepresentationWildgen

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that only philosophically trained humans use metarepresentations as they think about thinking (in Descartes’ sense of “cogito ergo sum”). In order to avoid such a “reductio ad Iovem” with the quasi-exclusion of all living beings (“reductio ad bovem”), I shall take another avenue which may be given the etiquette “selforganization” or “emergent structure”. Under specific conditions (physical, chemical, biological, social, economic), a system of agents (entities with forces, reacting to contexts) may change and move to a higher level of organization complexity. If one assumes (in a continous Darwinian thinking) that the transition from non-living to living-systems, plants to animals, primates to men, did not create totally new structures and processes, but rather reorganized existing ones (with respect to matter, energy, and forces) to form a new level of organization, then the obvious transitions between non-speaking, to speaking, non-conscious to conscious beings is of basically the same kind as all other transitions and probably uses the same or at least similar mechanisms. I shall first consider the basic types of self-organization found in nature and then return to possible evolutionary processes responsible for the emergence of representation, higher order representation (metarepresentation), language and consciousness (for details on the evolution of language cf. Wildgen, 2004).

3 Processes of self-organization as the basis of representation and metarepresentation 3.1 Models of self-organization, emergence of higher complexity in nature The emergence of life, of different species of animals, of men, of language, and culture may be understood as a process which continues the series of processes from the big bang to the organization of the solar systems and the state of the earth in which life could appear. I shall just mention some basic notion in order to show what I mean by the term selforganization of order in the ecology of man. In the ecological niche of man (his physical and biological environment, his domain of bodily interaction with the environment and his mental domain) different types of order vs. disorder can appear. a) Real systems are in equilibrium. This state of a system or this selective view of a system allows us to observe the major components, forces and possibilities of a system. It is the best scenario for the purpose of scientific modeling. Unfortunately systems in perfect equilibrium are rare (the planetary system, for example, which is one of the archetypes of human model making) and in order to filter out this equilibrium aspect in systems which are not in equilibrium we must go beyond empirical knowledge and make assumptions about the system which are rather theoretical.

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b) Real systems are in transient equilibrium (far from thermodynamic equilibrium). For these structures (called "dissipative" by Prigogine and Nicolis, 1989) noise and a constant flow of energy are necessary to preserve or even build up ordered structures. All living systems in equilibrium are at this or a higher level of dynamic organization. c) Real systems are often locally ordered but globally chaotic, i.e. minimal perturbations of the system grow stronger instead of being absorbed and after a number of evolutionary steps they end up in a chaotic mode. A prototypical example of a system in equilibrium and of transitions between different phases is a state-space defined by several equilibriums. The American physicist Josiah Willard Gibbs (1839-1903) formulated a basic law of thermodynamic equilibrium for such systems (in 1876) which is called the phase rule of thermodynamics. If we consider a physical or chemical system, a phase is a domain of homogeneity in the system which can be distinguished from other phases. In a more general way every natural system can have such "phases" or states not altered by small changes in parameters. The phase is a locus of macroscopic stability. A physical system (any system) consists of a number of components (e.g. water in Figure 1, or a mixture of water and salt in other cases, etc.). These components are assumed to be independent of each other.

Figure 4: The phase space of water

Finally, there are a number of parameters which govern the behavior of the system, e.g. temperature and pressure. These parameters are macroscopic forces. Thus temperature is a macroscopic measure relative to the motion of the atoms and molecules. Figure 1 shows the (schematic) phase space of water. We can abbreviate: p = phase c = component MetarepresentationWildgen

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f = degree of freedom (i.e. the number of macroscopic parameters which can change). Gibbs' law, which is called the phase rule, is a very simple equation: First rule (Gibbs' phase rule):

p-c+f = 2.

This law is, however, not a specific rule for chemical analysis. One can show that it is related to the Platonic polyhedrons; as Descartes (1640) and Euler (1752) have shown a similar formula holds for the relation between: P = surfaces; C = edges; F = vertices. Euler's law is valid for all regular (convex) polyhedrons. As Wildeboer and Plath (1979: 165) show, the same regularity is found in Pascal's triangle, which serves as the basis for combinatorial analysis and statistics. All these parallelisms are not due to chance. They show that Gibbs' law, Descartes' and Euler's rules, and Pascal's formula concern not specific systems but regular systems or systems in perfect equilibrium in general. A further extension of Gibbs' law concerns dynamical systems in equilibrium; thus the hierarchy of elementary catastrophes is directly related to regular polyhedrons and Euler's formula (see Slodowy, 1988). A prototypical system in transient equilibrium is found in convection (Bénard)-cells. If a fluid is heated from below the flux of energy and the viscosity of the fluid create rotating cells, i.e. out of molecular chaos a specific order is created which itself can jump from one stage to another (different sizes or directions of the ‘rolls’). Other examples are magnetization (the spins of the atoms are coordinated) and coordinated motions (compare the different "phases" in the locomotion of a horse). Again we have phases of stability and transition points. If the energy flux is stopped, the initial unordered situation reappears, i.e. order is only present in the flux. Figure 2 shows the cycles of a Bénard-cell (cf. Nicolis and Prigogine, 1989: 11). This order can be called a spontaneous order which arises by co-ordination of subsystems and the domination of one or a few "slaving" parameters (cf. Haken, 1983).

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Figure 2: Bénard-cells (cf. Haken, 1990: 5 )

The transient order is imposed on stochastic motion of single molecules and depends on the critical value of the temperatures below and above the liquid, on the geometrical form of the vessel, etc. The patterns obtained are not only transient, normally multistability is observed, i.e. the system chooses between a range of possible states. Haken (1990: 7) extrapolated this situation to cognition: "Our results may be interpreted as follows: The fluid possesses a variety of different states because of its internal mechanisms. But which of these states is realized depends on the initial conditions, or, to put things in a different way, a partially given pattern is completed in a unique fashion. But this is at the cognitive level precisely what happens in associative memory. Part of a set of data is completed in a unique fashion. Multistability means that our system can internally store many patterns. Their restoration from initial states appears simultaneously in all volume elements of the fluid, i.e. our fluid acts as a parallel computer."

This image of a process based on stochastic dynamics with transient order is relevant for synergetics (cf. Haken, 1983) and its applications. A prototypical chaotic system is given by the multiple copying machine (MCM) described by Peitgen, Jürgens and Saupe (1992: 30-35). In general these processes include a type of self-referentiality, in which the product of an operation is taken again and again as input of the operation. If every operation introduces minor changes, especially if non-linear transformations occur, the result of a chain of operations is chaotic. Most real systems have a range of initial conditions under which chaos appears. Chaos is thus a very general behaviour of dynamical systems and order phenomena are particular islands in a landscape dominated by chaos. In general we focus on order phenomena because the observational techniques for an exact description of stochastic and chaotic dynamics in language have not yet been developed.

3.2 The emergence of language If ritualization and the formation of cultures (i.e., the transmission of behavioral patterns by emulation, imitation and teaching) are compared in chimpanzees and humans (cf. Boesch MetarepresentationWildgen

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and Tomasello, 1998), the characteristic features of human communicative behavior become obvious. Contrary to instrumental behaviors, communicative behaviors are created “by two individuals shaping one another’s behavior in repeated instances of a social interaction” (ibidem: 600). The authors call this process “ontogenetic ritualization” (ibidem). These results point to an important difference between instrumental and communicative learning. In the latter case, innovation does not originate with an individual but is based on play or interaction with a second agent whose feedback brings about ritualization. The results are not simply the product of individual invention constrained by the affordances of objects or materials or by identical needs and purposes. They are driven by chance and cannot be disseminated by parallel invention or emulation in practical contexts; imitation and in many cases instruction is necessary. They are neither pre-selected by the context nor do the results of such communicative learning follow stable and unique models. The major difference between young chimpanzees and children is that imitation (and teaching) is much more prominent in children. If humans create a rich environment for the training of chimpanzee gestures, these may come near to the semiotic capacity of young children, but this situation is artificial and does not belong to the natural environment of chimpanzees. The bias for imitation, which is more abstract than emulation as it is not controlled by an evaluative testing of the model, triggers another process called the “ratchet effect” by Boesch and Tomasello (1998: 602), i.e., the inventory of accumulated behavioral patterns does not decrease; change consists of further elaboration and sophistication of the accumulated “cultural goods”. The acquisition of such a very complex system, e.g., language, a ritual tradition, a religious or political system, requires a long and intensive learning and teaching period, which only human societies can afford. The general picture is that of a gradual shift from emulation, to imitation (and teaching); the accumulation of results of ontogenetic ritualization creates a distance between animal and human behavioral and semiotic systems. The result looks like a dramatic qualitative difference. It is true that the increase of complexity is astonishing but this should not make us think that the basic principles are radically different. A major difference between animal and human communication was thought to relate to the referential function unique to human language. I shall discuss, therefore, the results of research reporting referentiality in alarm calls and other vocalizations of apes. Animal calls can be referential in relation to objects and events external to the caller. In these cases, they are easily identified by human observers and may be controlled experimentally by checking response to playbacks. Fischer and Hammerschmidt (2001) label these vocalizations as “functionally referential”. Examples are food-associated calls and alarm calls in vervet monkeys (Cercopithecus aethiops), Barbary macaques, and others. Categories distinguished in the alarm calls may be: eagle, snake, leopard (vervet monkeys) or dog, snake, human (Barbary macaques). The calls can be acoustically distinguished by means of

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frequency amplitudes and formant like structures (cf. ibidem: 33), i.e. they use basically the same inventory of acoustic characteristics as human language.. A second class of calls is given in social contexts; they “are commonly viewed as expressions of the internal state of the caller, and the observer may experience difficulties not only in describing this state, but also in pinning down the context eliciting a specific vocalization” (ibidem: 29). Thus the major semiotic functions of Bühler’s instrumental (organon) model of the sign: expression – appeal – reference are fulfilled in these calls. The social meaning is difficult for human observers to assess, but one may guess a rather complex semantic space of caller external (referential) and social meanings (shared expressivity). In conclusion one may say that animal and human communication share basic techniques. Certain components have been amplified and specified for humans. Such a continuity has already been advocated by Darwin (1872).

3.3 Metarepresentation as an emergent feature of symbolic behavior It is not possible for the moment to decide in what order the basic symbolic forms (in Cassirer’s sense) emerged and if the emergence of consciousness is rather linked to one of them. The order of documentation by paleontological data is:  

 

lithic technology (after 2,3 million years BP) art (geometric engraving on tools at the stage of Homo erectus; high level iconic art after 40,000 BP) myth (probably implied by Paleolithic art, i.e., before 40,000 BP) language (only documented by first systems of writing in the Neolithic)

For simplicity sake, we just presume that the four types of symbolic forms (and subvarieties) emerged together and are linked to the protospecies: Homo erectus and Homo sapiens with a dramatic transition around 400-200,000 years BP. In contrast to representations of the ambient ecology by animals, the appearance of symbolic representations is eo ipso the emergence of metarepresentations. These open a new field of cultural evolution with different levels of reflection and a cycle of meta-metarepresentations. Consciousness and metarepresentation are therefore the distinctive achievement of human cultures. I hope that the contributions to the conference will elucidate this development further.

4 Metarepresentation and art I have chosen figurative art (and not verbal art) in order to fin arguments for metarepresentation independent from the logical and propositional frames mostly applied in the analysis of language (cf. for the discussion of non-propositional representations Wildgen 2006b). In the case of pictures, the special case of linear structures which dominate in MetarepresentationWildgen

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linguistic analyses can be overcome and some complexities resulting from the mapping of representations into metarepresentations become visible.

4.1 Self-reference in art as a kind of nonverbal metarepresentation I would like to restrict the label of metarepresentative art to pieces of art which have at least two content-levels of representation. Thus an auto-portrait is not really metarepresentative because it just shows the artist; the fact that he is sitting in front of a mirror and is shifting forth an backward between his picture in the mirror and the portrait he is producing on the canvas or on the paper belongs to the context of the painting and not to its content. The frame which “tells” us that this is the borderline of the represented view or its composition does not belong to the content of the painting. I shall first discuss two classical paintings by Jan Vermeer van Delft (as he was called; 1632-1675) and Diego da Silva y Velasquez (15991660). They are shown in the figures 5 and 6.

Figure 5 Vermeer: The painter and his model

At first view this picture fits the series of interieurs Vermeer had painted before; but if we assume that the painter in the scene is Vermeer himself, then the painting refers to his act of MetarepresentationWildgen

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painting; it is self-referential. Moreover, the picture which he is about to create has the same central topic as the painting, i.e. the young lady in front of the window. There is a kind of self-reference between the whole painting and the drawing shown in the painting (partially occluded by the back of the painter). There is good evidence that the painter on the chair is in fact Vermeer himself, but the drawing he is making has obviously another motif and structure than the one on which he appears himself. Thus the act of drawing by Vermeer is represented in the painting which is itself a representation. This cycle of self-reference fulfils already one condition of a metarepresentation. But the picture in front of the painter is not identical with the oil-painting by Vermeer; it only shares the central topic (and thus the object in the focus of the metarepresentation). In a stricter sense, this painting remains a genre painting in which the activity of painters is the topic. Beyond the genre motif is shares the identity of the person depicted with the painter and the identity of the main subject in both paintings. It is implicitly metarepresentative. Another famous painting discussed extensively by Foucault in the first pages of his book: Les mots et les choses, is : Las Meninas by Velasquez, shown in Figure 6.

Figure 6 Las Meninas by Velasquez

In this picture we can find at least three parties looking at the scene which is the central concern of the painting, i.e. the princess escorted by her ladies at left and right and accompanied by two dwarfs and a dog. The person standing behind the door and looking at MetarepresentationWildgen

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the scene looks simultaneously at the king and the queen. They appear in the mirror and are thus only represented indirectly (and with side inversion). The painter, who is Velasquez himself, looks also at the monarch pausing for a moment in his work. One may infer that, when he continues his work in one moment, he will again look at the scene with the meninas and at his painting. As he is probably not painting the back of the princess, she and her environment must turn around in order to continue this session of painting. As in the case of Vermeer we don’t have a simple metarepresentation, although it is clear that the person standing before the canvas is the painter himself. It is almost certain that the painting he is just achieving is not the one we see, but one where either the princess is represented or a totally different one. In this case the visit of the princess would be accidental. In the following I will discuss the effect of mirrors, which were implicit in Vermeers painting (although it is probably difficult to see one’s back in the mirror) and was explicit in Velasquez’ painting (the representation of the king and queen in the mirror).

4.2 The semiotic effect of mirrors The simplest secondary representation (also called re-representation by Whiten (2000: 146) is given in the case of a mirror. One may distinguish different levels: 

In the self-portrait on can assume that a mirror was used by the painter; such an inference may be sustained by the somewhat unnatural position of the person, because in a self-portrait in front of a mirror, the painter must after each action on the painting return to an identical position in front of the mirror.



The self-portrait can show a part of the mirror. A portrait may show the person looking into a mirror and thus both the painter and the painted person look into the mirror and the painting represents the effect of looking into a mirror (with the effect of the mirror (inversion and change of perspective). The mirror may show the painter and his model. Both may look into the mirror and this





can be shown in the painting. Salvador Dali has made such a painting called: Stereoscopic Painting (1976). Figure 7 shows this painting. In fact the action of the mirror could be repeated whereby the painter and his model would appear not only twice but three, four, … n times. In the latter case the mirrors constitute a group of deformations (in the sense of Leyton) re-establishing identity after a finite number of steps. As in the case of video-feedback it can also have a chaotic attractor and destroy the original input and be slaved by an internal standard (e.g. a Sierpinki-structure).

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Figure 7 Stereoscopic Painting; Teatro Museo Dali, Figueras

A different kind of repeated representation with deformation has rather the character of a very free citation; thus many classical paintings have similar biblical or mythological references and the later one use types of representation already present in earlier ones. I have made several analyses of the topic: “Last Supper” before and after Leonardo’s famous fresco painting in Milan (cf. Wildgen, 2001).

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4.3 Paintings as central motives of other paintings A very interesting case is the series of paintings achieved by Picasso following the already discussed painting by Velasquez: Las Meninas. I will show just one in Figure 7.

Figure 8 Picasso reinterprets the painting by Velasquez

The painting including the self-reference to Velasquez is reproduced under deformations (roughly described by the cubist style of Picasso in this period). In this case, Picasso is not represented, i.e. the metarepesentational character is only overt at one level (Velasquez) and not at the other (Picasso). Nevertheless Picasso’s characteristic style (in this period of his life) is like a signature of his presence. Is this a case of metarepresentation or even of metametarepresentation? If we take up the model of Poincaré map, in which in each cycle the return map adds some deformations (distance between the start and the passage near the starting position after one round), one may say the first round made by Velasquez shows a clear distance to the starting pole:  Pole position: Velasquez puts the Meninas in a proper position and works on his canvas.  After the arrival of the monarch the princess turns around and Velasquez makes a pause. During this time he has the idea to make a painting of the new configuration including a portrait of himself and of the kind/queen in the mirror.

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

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The new canvas repeats parts of the original scene and adds the three types of observers (and the two bystanders at the right) Picasso takes this picture as the topic of a series of paintings. In this series, every

painting is again a return to the object (Velasquez’ painting) and its adds new features (eliminating others).  In this cycle every earlier painting is again a reference for the next one and so on. In the same category of a representation referring to another representation we find examples where the pieces of the original representation are reassembled to form a new painting. A clear example is the treatment of Leonardo’s “Lat Supper” by Andy Wharhol.

Figure 9 Andy Wharhol “Last supper” (1986)

These few examples show us, that metarepresentation has many different facets. Its basic feature is a (mostly) deformed self-reference. This means that a given configuration with one set of:  Repraesentans Repraesentandum,  Repraesentamen is redefined by the addition of new repraesentans (a new observer, subject who sees, paints, describes, formulates). With such a meta-level, the original configuration is substantially 

modified. One may compare this transformation with the causative transformation in language. If we have the basic sentence:  Eve gives an apple to Adam and we add a new agent, e.g. the snail, we obtain a causative construction:  The snail makes Eve give an apple to Adam, By this addition the semantic roles of Eve changes (from nominative to accusative; from a direct agent to an experiencer / an indirect agent.

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We had two clear cases where the repraesentans is in the picture: Velasquez and Dali. In the case of Vermeer one may infer from the context that Vermeer is sitting and painting his model (a further indication is the identity of the central repraesentandum). At the same time Vermeer’s painting belongs to another category where a reflective process involves the topic (the repraesentandum), i.e. the picture drawn by the artist in the painting corresponds to parts of the painting. This line is further developed in Picasso’s series on the Meninas. A question for discussion is, if these processes fall into the category of metarepresentations. They are not referring back to a human repraesentans, but rather on a representamen. One could argue that Repraesentans

Selfreferential loop (1)

Selfreferential loop (2)

Repraesentamen

Figure 10:

Reflexion of (A, B) in C

Selfreferential loop (3)

Repraesentandum

Peirce’s triad and added loops (1), (2), (3) and corresponding new triads

they rather are cases of normal semiosis (in the sense of Peirce), where the repraesentamen becomes the object of representation. Thus one could distinguish three types of cyclic selfreference in the semiotic triad, as shown in Figure 9. The clearest case of metarepresentation would be loop (1), the last examples discussed (Picasso) belong to type (2) and one could ask if there are examples of case (3). It seems that there is a hierarchy of metarepresentations, where type (1) is the prototype, case (2) corresponds rather to an iterated semiosis and case (3) seems to be degenerate. This is in accordance with the order given by Peirce, where the interpretant is the highest level in the semiotic process, followed by the repraesentamen. Nonverbal representations show similar forms of metarepresentations as verbal ones, although they also have specific features, as I have shown in the case of the paintings by Vermeer, Velasquez, Picasso and Dali. The transformations occurring during the transitions between representation to metarepresentation have not yet been duly considered, because the standard examples came from language which is basically linear and thus has a different potential of transformations than pictures, sculptures, or architectures. MetarepresentationWildgen

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Another fundamental problem is the limitation of the cycle of metarepresentations. In the case of the painter showing himself while he is representing a scene (while he is in the scene), this cycle is probably limited to one such cycle. In the case of the citation of representations and their deformation, the example of Picasso’s series has shown that this operation is almost unlimited. The reason is probably that all cycles are mainly citing the original or parts of it. Thus the cycle stands, although it may be very long, in a constant relation to the original. The conditions on further cycles should be properly analyzed; one conjecture is that repeated metarepresentations in the narrow sense lead to a metarepresentative chaos (cf. Wildgen, 1998).

5 Many open questions The strategy followed in the last section is a very optimistic one, insofar as a basic continuity of laws and principles throughout the universe (possibly fixed in the period after the big bang and not valid for other universes existing beyond ours) is assumed. A less radical strategy could allow for rather autonomous levels of organization which only share some very basic laws with other levels and may be described independently from earlier stages, from which they have emerged. Thus one could postulate that with the rise of consciousness (or intentionality) (meta) representations became rather independent from the surrounding ecology and are characterized by their arbitrariness (in the sense of Ferdinand de Saussure). Such arbitrary systems would not only control our perception of the ecology, in which we live, they would even change this ecology from a natural to an artificial one and thus reverse the Darwinian law of fitness. Another path could start from the social organization of animals and the techniques (e.g., grooming in higher apes) of social control or peace. A shift in the social structure triggered by symbolic forms, could have allowed higher levels of cooperation, larger societies with a network of levels and social subdivisions, different role patterns and types of socialization. The biological potential would have been exploited to a degree impossible for socially less organized primates. In this view meta (meta …)representation would be a consequence of a social (economic, political) evolution rather than an effect of higher cognitive capacities. These two routes may be called: -

The route of cognitive enrichment and self-referentiality. The route of social complexity and higher levels of socialization.

I wonder if other routes can be proposed which are not specifications or varieties of these two routes. Still the question remains, where the laws of such a higher cognitive social organization come from. Are they just a re-organization due to the choice of slaving parameters (as in synergetics) and the elimination of other parameters, or is there something MetarepresentationWildgen

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really new? If the latter seems to be the case, then one should ask, if the new type of organization is just a clever innovation transmitted by imitation and learning (due to chance) or a new potential arising from a kind of phase transition and exploited with necessity by any member of a species either in a situation of leisure or under specific (social, ecological) pressure. The underlying question is the freedom of will (in humans, or even in primates), its restrictions and the reorganization of free decisions by individuals in the context of an ecology and a given society. I think that the consideration of processes of self-organization and emergence does neither imply specific answers to these questions, nor is it incompatible with specific answers to them. Any kind of free decision is either contextualized or its fate (success) depends on contexts, in which certain more general laws are valid.

Bibliography Cosmides, Leda and John Toobie (2000) Consider the source: The Evolution of Adaptation for Decoupling and Metarepresentation, in: Sperber (2000a: 53-115). Dennet, Daniel C. (2000) Making Tools for Thinking, in: Sperber (2000a: 17-29). Haken, Hermann. 1983. Synergetik. Eine Einführung. Berlin: Springer (2. ed.). Nicolis, Grégoire and Ilya Prigogine. 1989. Exploring Complexity. An Introduction. New York: Freeman. Peitgen, Heinz-Otto, Hartmut Jürgens and Dietmar Saupe. 1992. Bausteine des Chaos Fraktale. Berlin: Springer. (English edition: Fractals for the Classroom I. New York: Springer.) Rosenthal, David M. (2000) Consciousness and Metacognition, in: Sperber (200a: 265-299). Sperber, Dan (2000a). Metarepresentation. A Multidisciplinary Perspective, Oxford U.P., New York. Sperber, Dan (2000b). Metarepresenrtation in an Evolutionary Perspective, in: Sperber (2000: 117-137). Stadler, Michael und Wolfgang Wildgen, 1987. Ordnungsbildung beim Verstehen und bei der Reproduktion von Texten, in: SPIEL (Siegener Periodicum zur Internationalen Empirischen Literaturwissenschaft), 6 (1), 101-144. Whiten, Andrew (2000) Chimpanzee and Mental Re-representation, in: Sperber (139-167). Wildgen, Wolfgang, 1998. Chaos, Fractals and Dissipative Structures in Language. Or the End of Linguistic Structuralism, in: Gabriel Altmann und Walter A. Koch (Hg.). Systems. New Paradigms for the Human Sciences, de Gruyter, Berlin: 596-620. Wildgen, Wolfgang, 2004a. The Evolution of Human Languages. Scenarios, Principles, and Cultural Dynamics. Reihe: Advances in Consciousness Research, Benjamins, Amsterdam. Wildgen, Wolfgang, 2004b. Éléments narratifs et argumentatifs de l’«Ultime Cène» dans la tradition picturale du XIIe au XXe siècle, in: Stefania Caliandro (Hg.). Espaces perçus, territoires imagés en art, L’Harmattan, Paris: 77-97. MetarepresentationWildgen

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Wildgen, Wolfgang, 2004c. Conceptual Innovation in Art. Three Case Studies on Leonardo da Vinci, William Turner, and Henry Moore, in: Frank Brisard, Michael Meeuwis und Bart Vandenabeele (Hg.), 2004. Seduction, Community, and Speech: A Festschrift for Herman Parret, Benjamins, Amsterdam: 183-196. Wildgen, Wolfgang, 2005. Visuelle Semiotik der elementaren Kräftefelder der Hände (Gestik) und der Augen (Blicke) in einigen Werken von Leonardo da Vinci und Barocci, in: Winfried Nöth / Anke Hertling (Hrg.), 2005. Körper - Verkörperung – Entkörperung, Reihe: Intervall, Bd. 9, Kassel University Press, Kassel: 149-179. Wildgen, Wolfgang, 2006a. The Dimensionality of Text and Picture and the Cross-cultural Organization of Semiotic Complexes, in: Reinhard Köhler und Alexander Mehler (Hg.). Aspects of Automatic Text Analysis, Springer, Berlin. Wildgen, Wolfgang, 2006b. Cognitive semiotics and neurodynamics. Paper read at the Early Fall School in Semiotics11th to 18th of September 2006, Sozopol, Bulgaria. Wilson, Robert a. (2000) The Mind Beyond itself, in: Sperber (2000a: 31-52).

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