15 The companion space theorem:
self-other connectivity in infant and dyad

Revealing finely tuned intersubjective co-ordination in early infant-adult interplay, Trevarthen (1986) distinguishes alteroception as the motivated perception of others that depends on the specific cerebral response to the kinematic, energetic and physiognomic aspects of the other's body movements. Demonstrating how innate releasing mechanisms fail to account for neonatal and deferred imitation, Meltzoff & Moore (1977, 1989) and Meltzoff (1988) offer evidence of active equivalence mapping in virtue of a supramodal body scheme. I shall offer an account of the inversion mechanism requisite for such processes in face-to-face exposure, for example, in imitative learners, 9 month old, who face the model's pushing a button on a box out of their reach.
What enables them to invert the model's perspective as an appropriative basis for re-enactment on the next day?
A reply is proposed on the basis of a model of infant intersubjectivity in terms of a companion space with a "virtual other" (Bråten 1986/1988a, 1992b). The model has been applied to protoconversation by Bråten (1988b) and by Trevarthen (1990, 1992), and found by Murray (1991) to account for results of perturbation experiments by implying coherent infant reaction, not random, upon perturbations (cf. Figure 15.1).

Postulate and definition of the virtual other
The virtual other is an innate non-specific companion perspective (*A) which complements the bodily self perspective (B) with the operational efficiency (virtus) of an actual companion perspective (A).

The developing mind, in virtue of its inherent companion space with "a virtual other" that invites inclusion of actual others, recreates and transforms itself in the same coherent format in these two alternating modes:

(i) engagement with the actual other in felt immediacy (B A);
(ii) self-engagement (with the virtual other) (B *A).

Comment. - The first self-other connective circle (I) applies inter alia to the connectivity which even a neonate may established with a model who elicits imitation, and to the connectivity in unperturbed infant-adult protoconversation, including live occurrences in Murray's replay design when mother and two-month-old child establish felt immediacy (Murray & Trevarthen 1985, 1986) (cf. Figure 15.1 (left)). The second circle (ii) applies inter alia to circular re-enactments in infants, including the delayed self-concentrated effort in neonatal imitation, and to infant reaction to perturbation of protoconversation (cf. Figure 15.1 (right)).

The infant's self-other connectivity in Murray's replay design
In the live and unperturbed sequence in Murray's replay design, even though separated by a wall and only audio-visually linked, the mothers and children establish reciprocal connectivity. When this occurs, the infant constitutes with the mother a self-organizing dyad in which they complete and complement each other in the mutual constitution and operational closure (circularity) of the dynamic whole. Fig.15.1 (I) gives a static inscription of the first circle in which the child's bodily self, B, is complemented by the adult, A, as the child's live companion, and which will be re-established after the perturbed sequence.

Infant reaction to perturbation
In the perturbed sequence, when the baby is faced with a replay of the live mother from the preceding "happy" interplay conforming to (I), the live adult is no longer available to complement the baby's bodily self in the companion space in which they inter-operated. Hence, that space is again left open for the baby's virtual other to complement the baby's bodily self in the companion space. Fig. 15.1 (ii) indicates how the same operational format applies to the baby's self-comforting as a result of the baby's transition from (I) happy engagement with the live mother to (I) self-engagement upon exposure to the replay mother. While the contents and affected structure of the infant's companion space has been changed, the operationally closed format is the same.

Upon return to unperturbed interplay
When they are re-united after the perturbed sequence, the infant again includes the mother in his companion space to complement his bodily self, re-establishing the former cycle (I). The reverse transition occurs. The baby again connects with his mother and includes her in his companion space in felt immediacy.

Imitative learning
Meltzoff (1988) documents how 9-month-olds, exposed to model performance on an object out of their reach, for example, pushing a button that makes a beeping sound (Fig. 15.2 (right)), were found capable of deferred imitation with 24 hours delay. So what, then, enables the infant learner who faces an adult model pushing a submerged button on a black box -- to feel even at a distance the perspective and to appropriate the model's performance as a basis for re-enacting the pushing on the next day? The reply proposed is this: in virtue of the learner's virtual other, enabling inverted alteroception, the facing model's enactment affords and gives rise to a mirror-reversal of the performer's perspective as appropriating basis for the proprioceptively felt re-enactment. Thereby, even face-to-face exposure to manual enactment on some object of joint attention will leave the infant with the feeling of having been hand-guided by the author of the manual movement.

Imitative learning in the Balinese culture
In order to establish a baseline of the account to be offered, consider Gregory Bateson's snapshots of scaffolding or literal hand-guidance in the Balinese culture (Fig. 15.2 (left and middle)). The boy Karba (11 and 12 month) directly experiences his parent to complement his bodily self, as his mother guides his hands as they harvest food, and as his father moves Karba's hands as he sits on his father's lap, being taught to play a bamboo xylophone. The initial instruction and "scaffolding" of these complex acts are facilitated by the adult's placing himself literally and physically in the learner's companion space and moving with learner's bodily self in the same direction. The parent's hand-guiding affords Karba with the experience of feeling to co-enact the performance. On the basis of such repeated (e)motional experiences with his actual other, Karba may later try to re-enact the motions with his virtual other.

The inverted mirroring implied to occur in face-to-face situations
For exposure to less complex acts on objects, infant learners, including Karba, are capable of similar (e)motional experiences and memory, I suggest, even when facing the teacher and object from a distance.
Definition of (e)motional memory of engagement in felt immediacy. - In order to emphasize that such bodily felt experience (Erlebnis) of participant motions differs from conceptually ordered experience (Erfahrung), I say that the other is experienced in the mode of felt immediacy (as distinct from perceptions mediated by concepts and symbolic representations), and shall use the composite term '(e)motional' (literally 'out-of-motions') to qualify the affective experience and remembrance of moving with the other's motions affording the baby the feeling of participating in those motions.
Comment. - This probably involves and affects sub-cortical networks in emotional and motivational circuits interlaced with those that are evoked in proprioception. In terms of this (e)motional system, and differing from models of learning by (egocentric) observation or from conceptional memory, the model of imitative learning to be submitted concerns circular re-enactment from (e)motional memory of having co-enacted the model's motions in felt immediacy (cf. LeDoux's (1994) 'emotional memory').
Definition of circular re-enactment. - Imitative learning entails that what the learner previously has felt to be doing with the actual other (the model), the learner will later attempt doing with the learners' virtual other. This is here termed circular re-enactment.
Comment. - It follows from the postulate that the operational format of what Baldwin and Piaget terms 'circular reaction' is here qualified in a radically different way to involve the infant's virtual other in the same operational self-other format in which actual others complement the infant's bodily self.
Corollary about mirror asymmetry.- The relation between the bodily self perspective (evoked in proprioception) and the virtual other perspective (enabling alteroception) is chiral-like (from Greek for 'handedness'), that is to say, like the mirror asymmetry of the left and right hand.
Comment.- Let me demonstrate chirality with my hands: if my right hand is superimposed on my left, the two hands, even though resembling each other, show themselves to be unequal in form. Only if I let one my hands be reflected by a mirror, and not the other, do they coincide in form. Thus, in conjunction with the above corollary the postulated virtual other complement to the bodily self is implied to enable perceptual mirror inversion: Body movements of actual others included in the companion space afford alteroception in an appropriating sense, which in face-to-face situations entails perceptual inversion, i.e. perception of the other's movements and orientation from the other's stance.
Definition. - The perceptual inversion and supra-modal binding of somaesthetic and visual qualities afforded by actual companions is here termed inverted alteroception.3
Comment. - This mirror reversion arises in virtue of the asymmetry of the bodily self and virtual other perspectives, and may perhaps even account for the left-right inversion in human neonates who, after the model takes a pause, imitate clockwise head rotation in a clockwise and, hence, inverted direction (reported by Meltzoff & Moore 1989).

The companion space theorem
Deferred imitation and imitative learning presuppose successful completion (closure) of these two self-other connective circles:

(I) First, initial connectivity (in joint attention) with the actual other, whose bodily motions, affording alteroception in an appropriate (inverted) sense, is felt to be co-enacted with author of the motions.
(ii) Second, inward connectivity in preparation of re-enactment from (e)motional memory, sustained in the affected companion space in which the preceding feelings of co-enactment (with the actual other) connect to in-form own attuned re-enactment (with the virtual other).

Comment. - The first circle (i), conforming to (i), enables the infant to feel to be engaged in the performance with the author of the performance as if they were doing it together and facing the same direction. The second (i), irrespective of the delay, entails that what the infant has felt doing with the actual other -- in face-to-face exposure or otherwise -- the infant will try to re-enact with the virtual other. Sustained in the affected companion space, perhaps in the young infant as a crude kind of motivational or "emotional memory" (LeDoux's term), the alteroceptively felt enactment connects by interlaced pathways (involving amygdala ?) to in-form the proprioceptively felt attuned re-enactment.

A model of deferred imitation
Consider again the face-to-face situation in the deferred imitation experiment (Fig. 15.3 (left)). Here the learning infant is facing the adult, and denied access to the object during the initial model performance. Yet the learner is somehow capable to assume the performer's (inverted) perspective as appropriating basis for the proprioceptively felt re-enactment (Figure 15.3 (right))..
The asymmetric manner in which the learner's virtual other perspective complements the learner's bodily self, enables inverted alteroception of the teacher's movements as he complements the learner's bodily self. That leaves the learner with the (e)motional experience of having been "hand-guided". His proprioceptively felt re-enactment on the next day can thereby be in-formed by the alteroceptive feelings afforded by the facing other's performance on the black box out of reach. In order to attempt doing (with the learner's virtual other) what the learner has felt doing with his actual other, the alterceptively felt motions have to be retained and reactivated in the learner's companion space to in-form the proprioceptively felt re-enactment. Thus, what the infant previously has felt to co-enact with the actual other, the infant may later try to adjust to and re-enact in a semblant manner with the infant's virtual other (Figure 15.3 (right)). Such attempts at adjusted re-enactment (with the learner's virtual other) stem from the learner's (e)motional memory of felt co-enactment (with the learner's actual other).Thus, the learners' inverted alteroception of the model's motions enables them to feel to be doing the pushing of the button on the box out of their reach even though the facing model is the author of the motion. The learner is left with the bodily experience of having partaken in co-enacting the movements as if the learner were hand-guided by the facing instructor like the hand-guidance afforded by Karba's parent facing the same direction (Figure 15.2 (left and middle)).
Comment: Implications for autism? - The model and the learner need not face the same direction, unless the novel movements are very complex, or the child has learning problems that requires hand-guidance in front of a mirror in the teaching of skills that require reciprocal and complementary movements. In normal children, the relation between the bodily self perspective, evoked in proprioception, and the virtual other perspective, enabling (inverted) alteroception, has been defined as complementary, and is assumed to arise from interlaced neural cell networks that give rise to asymmetries that are chiral-like, like the mirror asymmetry of the left and right hand. Impairment of that relations is implied to prevent alteroceptive inversion. For example, the autistic model for the movie "Rainman" is reported to find it painful to face himself in the mirror. He closes his eyes while shaving himself in front of a mirror. Implied to stem from impairment of the (e)motional system in autism, difficulties in imitating asymmetric body movements from face-to-face exposure are predicted to be most acute in face-to-face situations that requires alteroceptive reversal and binding. The first of the two self-other circles (I), specified above, would be prevented from being closed and connect with the second (ii).
In contrast, successful closure of (e)motional self-other connectivity will nurture cultural development of higher-order modes of relating to self and others, like meta-representational ability, the impairment of which is the focus of the theory-of-mind hypothesis of autism (Baron-Cohen et al. 1993).

Postscript: Beginning of the path from simulation of motions to simulation of minds
The posited companion space with an inborn bodily-self/virtual-other complementarity differs from the functionally highly specific "innate companion schemata" applied in ethology by Uexkull and Lorenz. Eating food from the mother's hand might be described in terms of what Lorenz (1971) calls "a mother companion schema", but not so when the baby in return offers some of the food to the mother's mouth in a semblant manner. Such frequent occurrences invite, as I have attempted to show, this account: Including the mother in the infant's companion space, the infant feels to be taking part in her feeding movements as a basis also for reciprocal re-enactment. The caregiver's complementary perspective in enacting the feeding is felt in the reciprocal mode of felt immediacy. When the child in return offers food or milk to the adult's mouth, this proprioceptively felt re-enactment has been in-formed by previous alteroceptively felt enactments. The infant reciprocates by re-enacting in a semblant manner from (e)motional memory of having co-enacted the feeding with the author of the feeding.
Such (e)motional mode comprises the way in which own and others' bodily position, movements and sounds are directly experienced, out-of-motions, as it were, in contrast to experience mediated by symbolic representations or simulation.
The mode of engaging with others in felt immediacy clearly differs from the mode of simulating other minds upon break-down of dialogue (Bråten 1973ab, 1974, 1992). This difference is demonstrated by the mothers' behaviours during the unperturbed and perturbed sequences in Murray's replay design (Murray & Trevarthen 1985, 1986). First, the mother engages with her two-month-old child in live interaction (Fig. 15.1 a). Then, when unwittingly faced with a replay of her companion from the previous live interaction, the mothers continue to talk. Sensing that something is amiss, most of the mothers now talk to their replay companion in an imperative manner (Murray & Trevarthen 1985) in virtue of their models for simulating others (Bråten 1974; 1992).
Such higher-order modes of simulating or constructing others by culturally acquired means are mediate modes, unlike the inborn bodily self-feeling entailed in proprioception5 and the mode of relating to others in felt immediacy. Unless deprived of interactional nurture, or brought to collapse or divorce by severely distortive experiences or by biological impairments, the primary mode of relating to others in felt immediacy is expected to be at play also in the experienced child and in the adult, and not just a "stage" left behind in early ontogeny. For example, some of the mothers in Daniel Stern's (1985) experiments, when asked to get out of tune with their babies while watching them play, found it very hard to abort their affect attunement.

Teasing: infants' simulation of aborted motions in offer-withdrawal games
The caregiver who unwittingly opens her mouth as she feeds a spoonful into the baby's mouth, exemplifies attunement by participating in the baby's eating.
When the baby reciprocates by offering some of the food to the caretaker's mouth in a semblant manner, and opening his own mouth in the process, then the infant reveals himself to be participating in the caretaker's receiving motion. If the infant, however, withdraws his offer of food with a big smiler or laughter before the caregiver has grabbed the food, then something qualitatively different has occurred. The infant not only re-enacts the caregiver's feeding movements, but apparently wittingly and wilfully aborts his reciprocating movements, finding the offer-withdrawal game funny.
A qualitative leap has occurred for the infant to be able to accomplish this feat of anticipating the other's complementary response, and to break off before that complementary response completes the adult interaction scheme of feeding and being fed. Chevalier-Skolnikoff (1982) describes toddlers' teasing in this format: offers toy and smiles, withdraws toy and laughs. Reddy (1991) reports episodes of offer-and-withdrawal teasing in younger infants. In one case, following a few pleasant give and take exchanges of an object, the infant first offers and then withdraws the object with a broadening smile as the adult reaches for the object. When the adult has withdrawn his hand, she repeats the offer with a slight smile, and when the adult holds out his hand again, the infant repeats withdrawal with smile broadening as the adult's hand approaches (Reddy 1991:146). We may assume that the infant would not have found such abortion funny, were she unable to complete, as it were, in her companion space the complying movements resulting in the actual other's grasping the object.
This comes close to anticipatory simulation of own give-motion and the actual other's grasp-motions, completed in fancy, while aborted in actuality. In order to find the wittingly aborted offer funny, the infant must somehow be able to anticipatory complete in her companion space the complementary responding by the adult, that is, the adult's taking the bait or food, that is, pre-enact the adult's taking the food in a virtual manner, and contrast that with the actually aborted move when the offer is withdrawn. This is a creative and constructive act of anticipation by the infant. We may even say that what the infant does is to execute a predictory simulation of the adult's motion of complementing the infant's move of offering, aborted before that simulated response can be actualized. We need not attribute here the anticipatory or predictory capacity to simulate the adult's mind, that is, to anticipate the adult's mental expectation. But clearly, simulational fancy is involved in the child's imagination of the behavioural completing by the companion.
This may be precursory of the capacity later in ontogeny to simulate the co-actor's mental processes during (break-down) of conversations between symbol-processing participants. In the process of offering an utterance, the actor sometimes arrests himself, having anticipated by mis-understanding by means of internal simulation of the co-actor's understanding of the utterance to be produced (Bråten 1974). Restricting description to anticipatory simulation of behavioural response, not of mental interpretation, we may describe teasing toddlers in such offer- and withdrawal-games in an akin manner. If that is tenable, then such operational characteristics of anticipating the virtual completion of an aborted movement of the other, may be said to prepare for a higher-order leap that comes later in ontogeny: simulation of mind.

1 The various portions of this succinct paper have been successively presented at the King's College Research Centre Workshop on Perception of Subjects and Objects, Cambridge, 17-23 September 1992; at the ICIS Pre-conference on Imitation, Paris, 1 June 1994; and at the first Theory Forum symposium in Oslo, August 1994. The abstract (without figures, comments and footnotes) has been printed in S. Bråten (ed.) Intersubjective Communication and Emotion in Ontogeny. Symposium Pre-proceedings, The Norwegian Academy of Science and Letters, 25-30 August 1994:15-16, in preparation for Bråten (ed.) 1998.
2 Transition model: Let the name and value of the complementary process to the baby's bodily self, B, be symbolized by one marker, such that A is the name and value of B's actual other, and *A is the name and value of B's virtual other. Let the become-operator ":=" signify that the embodied values previously assigned to the processes in the (companion) space symbolized to the left of the operator are replaced by the embodied values in the (companion) space symbolized to the right of the operator. Then, the baby's transition from a) happy engagement with the live mother to b) self-engagement upon exposure to the replay mother entailing the absence of the actual mother may be expressed in this way:
the baby's reaction to perturbation: BA := B*A
That is, for the baby's bodily self B, deprived of the actual other A, the baby's actual other A is replaced by the baby's virtual other *A in the companion space in which the previous interplay occurred.
When re-united after the perturbed sequence, the infant again includes the mother in his companion space to complement his bodily self, re-establishing the former cycle (I). The reverse transition occurs:
the baby's experience of re-union: B*A := BA
That is, the value of the baby's actual other, A, now fills the space previously, during the perturbed sequence, assigned to B's virtual other, *A.

3 1999 addition: this is the defining characteristics of what I later term 'altercentric perception' (Bråten 1997ab) consistent with my definition of 'learning by altercentric participation' in more recent essays in this volume.
4 Transition model: Let the dot-notation "." signify appropriation or co-authorship, such that A.[] marks an object [] belonging to the actual other A, and BA.p[] signifies how A complements the infant's bodily self, B, in authoring the movement p on the object. Using the previously defined become-operator ":=" (cf. conventions in the note to Fig.15.1), we may then succinctly express in the same format the way in which exposure to the model and his box results in the infant's experience of co-enacting the pushing at time (t):
BA.p [](t) := B*A.'p [](t+d)
That is, complying with the invitation to attend to the model and his object, the learner includes in his companion space the model, whose motions, A.p, afford alteroception in an appropriate (inverted) sense, and, hence, is felt to be co-enacted in joint authorship at time (t). Thereby, the enactment of the object performance as felt by the learner to be co-enacted with the actual other at time (t), provides at some later time (e)motional basis for re-enactment (with the learner's virtual other), even efforts to reduce the difference between own movement p' and p as sustained in (e)motional memory.
Omitting the time and object markers, the above may be reduced to this succinct expression conforming to the state transition specified in the note to Fig. 15.1: BA.p := B*A.'p
(The text in diagrams is adjusted in accordance with Fig.5.1 in Bråten (ed.) 1998:111).
5 The way in which impairment of bodily self feeling calls for simulation of movements is illustrated by a patient with large fibre sensory neuropathy entailing loss of proprioception below the neck (Cole & Sedgwick 1991; Jonathan Cole reporting at a Cambridge workshop on perception Sept. 1992). Struck by this rare neurological illness at the age of 19, Ian Waterman lost the sense of light touch and the sense of proprioception. During the following 16 years, he was able to adapt to his impairment conditions. Since he has no feedback from his peripheral nerves, and hence no feeling of his bodily position and movements, he has to monitor every movement by sight to work out where his limbs are, and to develop strategies to control his movements, enabling him, for example, to reach for a glass of water. In so doing (demonstrated in a video documentation), he apparently uses his vision inputs and visuo-motor feedback as a basis for anticipating and monitoring his balance and motions. He manages this feat of reaching for and grasping the glass of water through planning and monitoring the deviations between his mentally planned and executed body movements mediated by the visual cues informing him about his actual whereabouts in the space in which he operates, without being in-formed by any direct (proprioceptive) feelings of his bodily action. I suggest that Waterman, deprived of a sensory prerequisite for engaging in the primary mode of felt immediacy, manages to engage in this reaching-for-a-glass-of-water situation in the re-presentational mode of simulational mediacy.