Models of semiotic borders in psychology and their implications: From rigidity of separation to topological dynamics of connectivity

Abstract

In this article, I discuss some implications deriving from different models of the notion of border, starting from interdisciplinary contributions and in particular from semiotics, psychoanalysis, cultural psychology, and topology. The starting point is a reflection on the notion of sign, as a device used to realize at the same time both a first form of discretization and to instantiate a system of relations with the environment. The article goes on to describe the importance of borders for the construction of human experience and for the processes of psychic and relational development. Lastly, the differences between three different forms of conceptualizing borders are discussed: rigid boundaries, permeable boundaries, and topological boundaries of the Möbius strip type. For each of the three models, the different implications will be presented and discussed.

Keywords

border Moebian topology psychoanalysis psychology semiotics

When the psychological disciplines focus on category systems based on implicit ontological and naturalistic assumptions, for example, the psychological qualities assumed as given and defined; the common sense as the source of legitimization of the construction of reality; the psychic identity as a fixed and naturalized object; and so forth (Klempe, 2016; Salvatore, 2016; Smedslund, 1995), their attention risks being captured only by the stability of the phenomena and not by their transformation and their constant becoming.

The human experience is characterized by an incessant semiotic construction of meaning, namely a constitutive and primary operation of classification, categorization, and interpretation that enables acting, thinking, and relating. In such a semiotic perspective, the notion of border assumes a considerable relevance since the processes of organization and transformation of meaning are dynamic processes that take place along liminal areas given by the organization of boundaries. Neuman (2003b, p. 103) states that meaning-making in living systems is primarily a phenomenology of boundaries within a recursive-hierarchical structure. In fact, each form of life needs a defined domain, wherein specific conditions of existence are possible and guarantee the development of the organism. Boundaries work both as limits/constraints and as freedom degrees.

Every semiotic system is constantly involved in a process of signification and interpretation, starting from its own differentiation with the outside (see Lotman’s, 2005, concept of semiosphere; and Valsiner’s, 2014a, multilayer model with recursive internalization/externalization processes). In order to achieve this differentiation, it is necessary to establish borders. Borders are essential devices that all semiotic systems need—from the biological ones (think of the cell membrane or the skin of the body) to the psychic border of a subject, from the borders of social systems to the borders of cultural systems (Marsico, 2016).

When we deal with semiotic systems, it is not a matter of a simple process of encoding and decoding signals; what characterizes a semiotic system is the interpretative and constructive function of meaning. As Umberto Eco (1976) shows, the threshold between an informative process and a semiotic process comes from interpretation. Lotman (2005) argues that what allows a structure to be a thinking system is a dialogical process with the outside (precisely through the organization of borders). The passages between inside and outside are processes of translation and interpretation (De Luca Picione, 2020; De Luca Picione & Valsiner, 2017). Bateson (1979) defines the mind as the ecological and systemic relationship between an organism and its environment. In any case, he does not consider a pure holistic vision of the mind. Indeed, he provides several criteria to define the mind. The first two criteria are very relevant for our discussion:

1. A mind is an aggregate of interacting parts or components.

2. The interaction between parts of mind is triggered by difference, difference is a nonsubstantial phenomenon not located in space or time; difference is related to negentropy and entropy rather than to energy. (Bateson, 1979, p. 92)

Bateson states that every mental process is activated by difference. Furthermore, he defines the fifth criteria in this way: “In mental process, the effects of difference are to be regarded as transforms (i.e., coded versions) of events which preceded them” (1979, p. 92). In this way, effects of difference must be considered as transformed-elaborated versions of the difference that preceded them. A recursive trajectory of transformation in-between mind and world is triggered. The point at stake is that it is therefore necessary to have a device that distinguishes and marks the differences. Borders are structural devices, necessary for every system, in order to signify its actions.

The general point of these different theorizations consists in the fact that there is always a semiotic process of codification and translation of signs starting from constructing borders. This allows the mind to be able to manage the transformative dynamics that are occurring in the present to those already occurred and/or expected.

What is a semiotic border?

In general, we can assume that a border is a device that promotes the production of a discontinuity. Producing a discontinuity means extracting from an indistinct and continuous background a discrete form that allows you to create at least one difference. The first differentiation is precisely the creation of a border, which helps to build and delimit a form (De Luca Picione & Freda, 2016a, 2016b, 2016c). In the words of Marsico and Tateo (2017):

Tracing a border is an action of differentiation based on certain criteria. Hence, within the new established entity (i.e. group, territory, category etc.) those units (i.e. individuals, things, dimensions etc.) that meet the selected criteria will be included and acquire a special value, while the others that do not have those characteristics will be excluded. As a result, once a boundary is traced, it operates to strengthen this distinction, reducing the internal differences and making possible the perception, construction or even the invention of a homogeneous unit. (p. 540)

On this matter we find the general assumption about the necessity of a primary act of differentiation in many formulations: in Herbst’s (1995) Co-Genetic Logics, in Spencer-Brown’s (1969) Laws of Form, in Bateson’s (1979) Ecological-Systemic Perspective of Mind, in Thom’s (1972) Mathematics of Catastrophes, in the Generative Semiotics of Greimas (1983), and in Lotman’s (2005) Semiotic Moscow–Tartu School.

The various contributions of these authors in the semiotic field lead us to highlight a central issue: in order to have a semiotic activity it is necessary that a process of discretization is in progress (a process of discretization of the continuum), starting from which it is possible to activate processes of articulation, chaining, and transformation of such discretization. The basic unit of semiotics is the sign, that is, a discretized form starting from an undifferentiated continuum. What I have just stated is well summed up in a general principle of development: Werner’s (1926/1957) orthogenetic principle. It asserts that each process of development proceeds from a state of relative globality and lack of differentiation to a state of increasing differentiation, articulation, and hierarchic integration. The emergence of an ordered and more complex structure takes origin from something previously unstructured or poorly differentiated. Development was seen as a two-aspect process: differentiation of organismic functions from a primordial global and undifferentiated state to a state of hierarchic integration of the differentiated parts (Glick, 1992, p. 560).

It should be noted that this “undifferentiated vs. differentiated” processuality (expressed in different meanings such as inside/outside, part/whole, unit/system, identity/alterity, etc.) can be considered the focus of every semiotic theory: the different declinations of semiotics—from the biosemiotic one to the studies on language and culture—are all based on the notion of sign as a discretizing element of experience. The sign is able to create a difference, which acts primarily as a time discretization (before/after), a spatial discretization (here/there, inside/outside), and a subjective discretization (me/not-me, me/other, we/they, etc.; De Luca Picione & Valsiner, 2017). A sign therefore produces an effect of semiotic deixis: in other words, it allows the distinction and the indication of a subject, space, and time, starting from which a process of signification can be contextualized. Furthermore, each process of semiotic development needs not only a proliferation of signs, but an integration and dynamic hierarchization (about that point, see Valsiner’s 2007, 2014a, works about transitory hierarchies of signs).

Ambivalence and apparent paradoxicality of borders

A first question arises: is the sign an already-given object, starting from which the experience is constituted? In terms of Kantian memory, is the sign an “a priori form” of our experience?

The argument I’m going to develop to address this question is that the sign has a profoundly ambivalent and paradoxical nature: the sign is both a thing and a relationship.

Recalling the notion of gegenstand in terms of Meinong’s (1960) theory, the sign can be considered as something that opposes a certain resistance. A sign stands as an element of reality that makes a difference within it. The main point is that an object could not have existence (in Meinong’s theory, existence is a contingent quality; the subsistence precedes the existence¹) but it could, regardless, have an impact. As Valsiner states in a discussion on gegenstandstheorie: “we act in our real worlds (AS-IS) in ways that are ‘fueled’ by the non-existing world of AS-IF” (Valsiner, 2014b, p. 296). A sign works on the border of factual and possible dimensions. It produces a salience starting from an undifferentiated background, and yet at the same time it is always the result of a continuous and recursive process of relating and new possible connections. The definition of sign, dating back to the Stoic formulation (Eco, 1976), considers it as “aliquid stat pro aliquo” (namely, something that is in the place of another), therefore the sign has a primarily relational and dynamic nature as well (think of Peirce’s, 1935, triadic semiotic model of sign, based on the dynamic relationship between three elements: object/referent/interpretant).

Once the sign is realized—starting from a system of relations of a field—it assumes a specific consistency. We grasp such a consistency as an existing and consistent thing (De Luca Picione, 2015). In so doing, we lose the other side of each sign: its relational nature. A sign is always connected with processes of contextualization, pertinentization, and subjective positioning of observers/actors (De Luca Picione & Valsiner, 2017; Neuman, 2003b; Salvatore, 2013, 2016). These relational processes, due to the effect of a cognitive economy based on an affective dynamic of generalization and reification (i.e., aimed to reduce the infinite possibilities of articulation and interpretation of the sign; De Luca Picione & Freda, 2014; Salvatore & Freda, 2011; Tateo, 2018), end up in the background. What remains is a salience effect of the sign that therefore comes to be reified. It is relevant to note that this dynamic provides stability to the subject/environment system, conveying and channeling information systems, interpretations, assessments, actions, choices, habits, and so forth. (Valsiner, 2014a).

Let us consider now some clarifying examples with explanatory power. Think of the host a priest uses to celebrate the rite of the Eucharist: the host can be “any” object that is present in that precise situation starting from myriad relational plots (cultural, social, historical, economic, but even contingent and random). Yet, the host is felt, worshiped, and conceived by the participants as the divine body during the religious rite. The host is experienced by the faithful not “as if” the sign of Christ’s body, but exactly “as it is” Christ’s body.

Think of the flag in a battlefield: if it is lost and ends up in the enemy’s hands, that sign turns itself into a defeat. Think again of the extreme act of sacrificing oneself for one’s own national flag, for one’s ideals, arriving at performing extreme acts of heroism: there is here a process of overlapping between the sign as a thing and the sign as a relationship.

At any moment, we are able to create, use, transform, and dismantle signs with the confidence of acting on reality. They allow us to think, act, and choose (De Luca Picione et al., 2018, 2019; Tateo & Marsico, 2019). It is sufficient to consider the play as a universal human experience (in every culture of the world and at any age in people’s lives): starting from a relational dynamics of constructing frames (borders that delimit rules/roles/possibilities of action), the players use and interact salient signs “as if” they were real, existing things, endowed with ontological value. This last point is completely in line with Simmel’s (2007) conceptualization of borders: they are psychological and social devices that act as a principle of organizing experience. It is a way of cutting out reality to interpret the meaning of events.

In light of this, we get to the core of my proposal. We can understand the border as a conceptual extension of the sign.

The border is a semiotic device that articulates the subject/otherness/world relationship (Simão, 2003): on the one hand, it carries out a limit (reduction of possibilities); and on the other hand, it offers the same conditions for its crossing, that is, creating the conditions for thinking, decision-making, and creativity (Español et al., 2018; see also the notion of border liminality developed in De Luca Picione & Valsiner, 2017, Figure 1).

Figure 1.

Simultaneous operation of separation and connection performed by semiotic borders.

Paraphrasing St. Paul’s letter addressed to the Romans in which he states that “the law produces anger; but where there is no law, there is not even transgression” (Romans 4:15), we can say that the border, through its own nature of limitation, constitutes the first possible condition for experiencing the world.

The need and opportunity of borders in human experience from birth

The human experience has been marked since its origin by the creation, use, and dismantling/crossing processes of borders. The borders provide a spatial delimitation that allows the orientation and management of the territory. Borders can be natural elements, such as rivers, mountain ranges, ravines, and so forth, or can be artificially created by means of walls, fences, frontiers, and symbolic systems endowed with a highly evocative power. For example, a Christian cross may mark the passage from a secular area to a sacred one; a national flag marks the passage from the use of one national language to another; the sound of a bell or a trumpet marks the start and the end of an activity, and so forth.

The borders—starting from their semiotic matrix—have a temporal connotation as well. Just think of how people’s lives are marked by “turning points,” namely specific circumstances (unpredictable situations or premeditated decisions) from whose occurring transformations are instantiated and generated. A turning point in people’s lives is a constraint, a temporal limit to the continuity of experience (De Luca Picione et al., 2019). Marking a difference between a first time (“as I was”) and an after time (“as I am now”), the temporal boundary of an experience offers the possibility of constructing a person’s sense of identity and its processes of development (“how I imagine I can be in future”). Identity, in psychological terms, can be conceptualized as a hypergeneralized sign (Salvatore, 2016; Valsiner, 2014a), constructed from the effect of myriad differences, transformations, and reversals that occur over time. Identity can be considered as a “border effect,” in its dual role of reification and relationship. In these terms, psychological identity is not the repetition over time of something identical, but it is a dynamic construction that a person obtains through processes of identification with some and differentiation from others (Esposito et al., 2016). Identity is a system of semiotic borders that evolve over time and have different degrees of extension and intensity.

As highlighted by Lotman (2005), the organization of borders is essential for identity in order to allow both stabilization processes and transformation processes. On the one hand, borders allow the semiotic system to be protected, that is, by ensuring the continuity of identity through the maintenance of differentiation; on the other hand, they enable comparisons with what is outside (through a process of semiotic translation and interpretation) triggering possible transformation processes.

If we read this dynamic starting from a temporal perspective, Lotman observes that the central parts of a semiotic system are slower to change and are more stable: this means that an identity nucleus is characterized by gradual processes over time and tends toward conservation and homeostasis. In contrast to that, the borders are a place of “explosive processes” of sensemaking processes (Lotman, 2009). We have to acknowledge these explosive processes are at the same time a threat to the identity of the semiotic system but also the possibility of its development and the integration of new parts.

The border therefore assumes the characteristics of a potential area, capable of: (a) absorbing stimuli coming from the periphery, (b) accelerating possible transformations, and (c) transferring novelties to the central structures.

It is worthwhile to consider in our discussion some psychoanalytical argumentations. Psychoanalysis has highlighted, in the processes of identity and development, how the “I” is in relation to both a process of differentiation from external “objects” and a process of connection with the environment. In fact, the Ego can be considered as a body surface of distinction between the inside and the outside (Freud, 1923/1961), and it acts like a psychic skin. The process of constructing the psychic instance of the Ego² is realized by gradual processes of distinctions of the figures of caring and of the objects of the external environment:

The infant’s bodily surface is quite literally the birthplace of the self for it is on and along this surface that the infant has the most formative and fundamental experiences of the world around it. . . . This boundary, at times real at times imaginary envelope based on the experience of the skin, will ultimately serve as the “floor” of the infant’s personality. (LaFrance, 2009, p. 15)

This perspective has a long tradition in the theoretical and clinical efforts of psychoanalysis.

Esther Bick (1968) observes that the infant’s mind is unable to achieve any sort of introjection. The infant’s psyche appears to be chaotic and diffuse. The skin works as the most primitive physical container “functioning as a boundary” (p. 484). In fact, birth is experienced as a loss of the primitive envelope that contains the body, and the discovery of gravity and heaviness in the newborn cause a feeling of falling, explosion, or liquefaction, in other words, forms of archaic primitive anxieties. There is the need to constitute a container: the function of the skin is to realize a primary container. The skin holds together the parts of the self, which have as yet no coherence. Firstly, maternal containment supports the growth of the baby’s psychic skin. Yet, in all those cases where such containment is faulty, the baby reacts through a constitution of a “second skin.” It works as a defense, a sort of omnipotent pseudo-independent form of protection, by means of hypertonic muscular tension, in order to hold the self together and to prevent disintegration (Willoughby, 2004). In this dynamic and clinical perspective, the skin as bordering container represents a dynamic device to enable the first psychic processes of introjection and projection.

Winnicott (1962) corroborates the relationship between body, sense of identity, and skin in his long clinical experience as a pediatrician and child psychoanalyst:

The ego is based on a body ego, but it is only when all goes well that the person of the baby starts to be linked with the body and the body-functions, with the skin as the limiting membrane. (p. 59)

A very broad and complete development of the function of the skin as a border can be found in the theoretical and clinical work of the French psychoanalyst Didier Anzieu (2018), who develops the notion of “skin-ego.” According to him, the body cannot be considered as a simple bag container—it plays an active role in putting the psychism in contact with the outside world and gathering and transmitting information. Anzieu believes that the skin-ego constitutes a real “contact barrier” (i.e., a border) with multiple functions: protection from stimuli, delimitation of outside/inside, reception, mnemonic recording, transmission, contact, and relationship.

Exploring the conceptualization of the border in the psychoanalytic field, we observe a fundamental and very broad relational origin: the role and the function of the Other within a sociosymbolic scenario of parental care practices and cultural styles of caregiving. The skin, as an intra-interpsychic³ border, is therefore the intersubjective place of inscription of signs and meanings, representation, aesthetic expression, eroticism, ornamentation, transformation, and modification. The skin is the main and indispensable topos for the embodiment of the culture conveyed through the subjective action of the other.

Looking at earlier societies and contemporary ones, tribal communities and Western social forms, with different modalities (related to cleaning practices, cosmetics, hairstyles, tattoos, engravings, scarifications, perforations) and ornaments (jewelry, clothes, accessories), we come to the conclusion that the skin shows itself as a semiotic support to the processes of signification and symbolic representation loaded with values and meanings (Nedergaard, 2016; Valsiner, 2014a, 2018). The skin becomes a means of expression of subjective identity and, at the same time, of belonging, sharing, and identification. The skin appears simultaneously as both a potential and creative arena of the relationship between the subject and the cultural canons to which they belong. The skin is therefore a semiotic border device that connects the inside and the outside, identity and otherness, conservation/tradition and transformation/innovation.

Two antinomical models of border

So far we have dealt with two different characteristics of the boundary: on the one hand a function of reification of the border (i.e., substantialization in terms of the entity of what is being discretized) and on the other hand a relational function of the boundary (characterized by development, transformation, and exchange) with the environment.

The conceptual ambivalence of the borders, when not explicitly treated, leads to the generation of two reductionist and oversimplified models, polarized only on one of the two sides (objectification vs. relational matrix).

Starting from what has been presented so far, it is possible to highlight two extreme conceptual models of boundaries.

Ontological vision of borders

By a process of rigid distinction, borders are considered to define an entity based on total closure, characterized by spatial rigidity and temporal fixity.

This is the case where the border works as a semiotic device of referentiality, namely, it refers to a reality (a set of given objects) assumed as such, whose relational matrix is misunderstood. Borders are considered as naturalized object. Under this conceptual model of border, we find the most diverse phenomena. Let’s consider, for example: (a) the construction of walls and ditches to prevent contact and exchange between people or for racial discrimination; (b) the rigidity over one’s own perspectives in political and religious terms; (c) a narcissistic attitude of a person thinking of herself as autonomous, completely self-sufficient, and not dependent on others; (d) the rigid epistemic separation between the different disciplines and the different knowledges; (e) the reductionist positions of research aimed at finding empirical evidences and confirmations on the different locations of human action (specific brain areas, specific genes, specific hormonal substances and neuro mediators, etc.); and (f) rigid cultural models aimed at thinking of the human being as entirely conditioned by its own culture of belonging.

The graphic representation of this model is that of a closed line drawn on a flat surface (see Figure 2). This closed line is engaged to differentiate the inside from the outside, to differentiate the sign from itself (A ≠ non-A), but nevertheless the process is blocked in a fixed differentiation and the identity fails to evolve, transform, build new possibilities outside of this rigid distinction (see Figure 2).

Figure 2.

Rigid model of border on a plane surface.

Systemic-Processual vision of borders

Borders are conceived and modeled as pure processes of regulation of the exchange between inside and outside, as processes of communication, contact, transitions, and transformation. In this modeling, the contextual frame acquires greater relevance. Borders, as sign devices, are no longer at the service of the ontological definition of the things that delimit, but are understood as processes, as trajectories of development, as catalysts of transformation (De Luca Picione & Freda, 2014; Valsiner, 2007). The borders are considered as starting from their dynamic and temporal function: they are observed as “explosive processes” of meaning (Lotman, 2009) with potential effects of risk and/or resource on the identity and integration of new parts. The border is considered as a potential and interconnected place.

The graphic representation of this model that we choose to adopt has a three-dimensional frame where a spherical surface shows openings that are traversed by exchange flows (information and energy) both inbound and outbound (see Figure 3). The central role of this model is entirely based on the relational processes with the environment (from ordered transitions to chaotic and unpredictable oscillations).

Figure 3.

Dynamic borders. In this representation border is a regulative device that enables systemic and trasformative processes with context.

Looking for an alternative synthesis of models of semiotic borders: The topology of the Möbius strip

At this point, we question how we can model semiotic borders while contemplating both the reifying and the relational perspective.

It is not a matter of choosing in favor of the one or the other perspective, namely, in favor of the sign/border as presence or the sign/border as relationship. Either vertice expresses an essential characteristic of each semiotic process: weaving relationships and constructing “objects” for thinking and acting.

How to develop a model of the notion of semiotic border that manages the paradoxical aspects and the inherent ambivalences of boundaring devices?

Below, we are going to use the topological support of the Möbius strip (see Figure 4), which allows us to hold together—at an abstract and geometrical level—the two different perspectives on semiotic borders.

Figure 4.

The representation of a Möbius strip.

The Möbius strip is a unilateral and nonorientable topological surface, consisting of one side and one edge (Barr, 1964; Pickover, 2006). The construction of this surface can be easily obtained through the half-twisting of a belt and the gluing of the two ends (the number of semi-twists can also be greater than one but it must necessarily be odd; see Figure 5).

Figure 5.

Construction of a Möbius strip.

This surface generates some mysterious phenomena that continue to fascinate since its discovery in 1858 by the mathematician August Ferdinand Möbius.

First, a Möbius strip has a single face and therefore cannot distinguish an inside from an outside, a front from a back. Indeed, the Möbius strip undermines the same intuitive notion of dimension. This surface is located between two (necessary for the plane) and three dimensions (necessary for the space).

Second, the Möbius strip permits a different representation of space by altering the relationship between the local and the global. In fact, if from a local point of view, two faces can be observed (and therefore two inscriptions can be made simultaneously, one on a side and the other on the recto). Yet, we must recognize that as a whole—that is, globally—the Möbius strip has only one face. It means it is a seamless strip (there are no continuity solutions), namely we can pass from inside to outside without jumps, tears, or cuts. It is enough to move along the surface.

This characteristic finds an immediate exemplification: if we let a pencil pass through the Möbius strip (see Figure 6), we note that it passes through the Möbius strip like any surface, but the strip still has only one face. At the local level, in the pencil area, there are two faces, but the strip as a whole, as continuous, has only one face (De Luca Picione, 2019).

Figure 6.

The relation of local and global on the Möbius strip.

From a topological point of view, the semitorsion is always elsewhere and is a structural condition not noticeable to a supposed living being on that surface. We can pierce the strip at any point to observe how a local “bi-faciality” (double-sided position) is created. Between the static and the dynamic viewpoint necessarily is present an element that doesn’t appear in our representation.

Third, the nonorientable space property of the Möbius strip has important implications. In theory, it implies that it is not possible to distinguish an object on the surface from its reflected image. From a geometrical perspective, a surface is considered nonorientable if there is a path that reverses the orientation (see the notion of chirality) of the creatures that live on it (Pickover, 2006, p. 116). In other words, it is possible to obtain the inversion of a figure only after having done a complete round along the Möbius strip, whatever the starting point on it is. After a round on the surface of the Möbius strip, the figure is upside down in relation to its initial position (see Figure 7). Another round will be needed for the figure to return to its starting position and orientation.

Figure 7.

A figure – depicted on a Moebius strip - requires two complete round to come back in the same position.

In theory, an organism that walks along the surface would turn upside down on the other side, without perceiving that incongruity. Following the surface of the strip, a finger will be found, after a round on the lower side of its starting point without having been lifted and without crossing the edge. After a second complete round, it will return to the point of origin, on the upper side. This property can be read in terms of temporal process (De Luca Picione, 2019; Granon-Lafont, 1985; Neuman, 2003b; Pickover, 2006): it is exclusively a temporal event that differentiates the upper and lower parts. Practically, they are separated by the time required to complete an extra round.

The dichotomy between the two signs—(that are) lower and higher, inner and outer, straight or upside down—is overcome by the intervention of a new dimension, namely time. Time, as continuity, sets the difference between the two faces.

Semiotic implications of Moebian topological borders

There are several crucial issues at stake for psychological disciplines, and their theoretical and methodological implications.

Many polar antinomies and concepts that characterize the fundamentals of research in psychology, semiotics, cultural studies, and social sciences (Lury et al., 2012; Shields, 2012, 2019) can find a different configuration by means of a Moebian border model. Think of the pairs of subject/object, social/individual, opening/closing, continuous/discontinuous, homogeneous/discretized, separation/connection, perception/memory (the former as collection of data from the external world, the latter as recovery of information from past experiences), conscious processes/unconscious processes, abstraction/reification, externalization/internalization, identity/otherness, projection/introjection, learning/imagination (the former as a passive form of imitation or acquisition, the latter as an active form of development through creative processes), and so on.

Valisner’s (2020) invitation to keep to account the duality and bivalence of human mind processes reads as urgent:

Borders, as the various parts of the whole, are the location where the unification of the system takes place. The need to see the uniting function of borders within a whole makes the analysis of the systemic functioning of the human psyche possible. This is what psychology of the human ways of being needs . . . understanding the complexity of the actors who generate their meaningful acts and resistances (as well as enhancements) to these very same acts, in the very human search for finding out about our mental horizons. (p. 12)

The model of the Moebian border is capable of giving a new spatialization of the semiotic activity between sign as relation and sign as entity. At local level of bordering, sign is grasped as an entity, yet at global level, sign is meant as a system of relation.

In the same way, the notion of psychological identity that I have presented above can find a topological support in the Moebian border. The identity requires the acknowledgment of a system of relation of similarities and differences. A Moebian border allows for holding together the distinction between subject and object, namely it is capable of both separating the subject from the object in the local space and of reuniting the subject with the object in the global space. That leads us to consider identity not only as thing (an abstract reified entity provided of consistency), but also as a semiotic process occurring in time and able to negotiate continuities and discontinuities.

Another point needs to be discussed. The Möbius strip introduces the problem of the self-referentiality of each semiotic process: is it the sign based on a self-referential circularity? The paradoxical aspect of the semiotic border of pertaining inside/outside, continuous/discontinuous, open/close risks creating an impasse. What introduces novelty and transformation? We are prone to believing that it is precisely the dynamic relationship between the local and the global in a temporal dimension that generates this situation. This is a crucial issue of semiotics: the relationship between the synchronic level (i.e., the structure of the system of signs, which is based on differences in the present time) and the diachronic level (i.e., the processual dimension in which chains of signs are formed, and previous signs are modified by the following ones). The permeability and porosity of the border, that is, the openness—as exposed in the second model (i.e., the relational and systemic one)—is recovered, but in a different way. The Möbius strip is a semiotic border whose unilateral topological structure becomes a surface of transcription where the inside and the outside are placed on the same syntagmatic chain of signs.

These last assumptions enable us to enrich previous psychoanalytical considerations on the skin. Skin always implies a self-referential process. For example, if we touch our own body, we experience a double perception, both from inside and from outside. The skin, whatever it is—bodily or psychic—works in a double direction both to separate and to unify, to recognize one’s own self and the other. Reflexive processes always imply self-reference, and that recursivity requires a synchronic and diachronic process of opening/closing.

The mind—as a semiotic system that provides an interface for maintaining a dynamic balance between its internal and external environment—does not produce two elaboration processes that are separated from one another and work in parallel (i.e., on the one hand, perception of the external world, and on the other hand, the perception of the internal world). The mind transcribes in the same semiotic articulation both synchronously and diachronically what occurs both inside and outside its Moebian borders. This leads us to consider the Moebian topology of the semiotic border as both open and closed. In the same way, the Moebian border is a writing surface in which both perceptual processes and mnemonic processes are transcribed together (Brown, 2012).

Conclusions

The Möbius strip offers a topological support to model the semiotic process of borders. With a Moebian model, we are able to maintain two aspects of semiotics together: on the one hand the discretization and differentiation of object-signs and, on the other hand, recursive–systemic processes with the environment.

The Möbius strip is paradoxically both a border and a nonborder: locally, it differentiates an inside and an outside, a me and a not-me, a before and after; but as a whole (globally) these differentiations are lost and it is possible to think of them as the effect of the particular dimensionality of the Möbius strip (you can go from inside to outside without crossing any border but only through a temporal event that marks the time of passage along the strip). As shown by Neuman (2003a), border can be thought of as a “paradoxical event.”

The realization of an exact round along the Möbius strip rather than being considered in measurable spatial terms (“how much” space has been travelled) must be thought of in conceptually temporal terms (the transformation that takes place “when” a round has been completed). This round implies two effects that are relevant for our discussion: the passage of an object on the other side of the strip (locally speaking) and its reversal. This means that a semiotic system can perceive an object one time as outside and another time as inside without considering this object as the same.

In this sense, the Möbius strip offers us a model where the ambivalences of semiotic border devices can be read according to a dynamics of local discontinuity (before/after, inside/outside, me/not-me) and at the same time according to a dynamics of global and continuous transformations (in terms of recursivity and continuous renewal of relations). This model offers a way to read further the opening/closing dynamics of sense-making processes. Indeed, the implications of a topological model of semiotic border allow us to treat sense-making processes simultaneously (but also separately), both by differentiating objects (that is, by discretizing the flow of experiences into signs) and by maintaining a continuity of relationship with the world.

In the chapter, “Toward a Phenomenology of Boundaries,” Neuman (2003b) defines the semiotic border thus:

Boundary as an oscillatory function is not only a differentiating process (a dynamic) that constitutes Differentiated forms (e.g., the being and his or her environment) but also a mode for transferring the “outside” into the “inside” (and vice versa), though not in a simplistic, representational manner, as usually portrayed in orthodox cognitive science. The environment is evident in the observer (the system we describe as the loci of the cognitive activity) not through a mapping of the external world onto the mind but through memorization of the environment, which is the boundary’s mode of periodic movement. (p. 103)

All of this invites us to persevere in the development of semiotic border models that can be capable of dealing with ambivalence, paradoxicality, and the ongoing becoming of human experience.

Footnotes

Acknowledgements

I want to thank Arnaldo Viscardi, Professor of Advanced English at University Giustino Fortunato (BN, Italy), for his accurate work editing this paper for English language use.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Raffaele De Luca Picione

Notes

Author biography

Raffaele De Luca Picione, PhD, is an associate professor of dynamic psychology at the Giustino Fortunato University (Benevento, Italy), and a psychotherapist with psychoanalytic training. His researches focus on subjectivity, affectivity, modeling of the mind and semiotic borders, temporality and processes of sensemaking, health and illness narration, starting from perspectives of psychoanalysis, cultural psychology, and semiotics. He is the author of The Mind as Form: The Mind as Text (Mimesis, 2015), Lacan’s Topological Adventure (Mimesis, 2020/in press), and more than 80 international and national publications including articles, essays, and book chapters.

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