1.1 Networks as Polymerizing Gels

Against holism and atomism, White proposed a relational ontology that recognizes that in social life “there is no tidy atom and no embracing world, only complex striations, long strings reptating as in a polymer goo, or in a mineral before it hardens” (1992a, p. 4). Thus, social organization is “messy and refractory, a shambles rather than a crystal” (2008a, p. 18), captured by imageries of polymerizing gels in phase transitions (polymer gel metaphors replacing that of rigid structure). In his words:

We are creatures living within social goos, shards, and rubbery gels made up by and of ourselves. We, like gels, may dissolve into a different order under some heat. Even the frozen shards exhibit only limited orderliness, and even then an orderliness lacking in homogeneity […] (1992a, pp. 337–338).

Moreover, in theorizing social networks as polymer gels, White insisted that often chains of “ties and their stories are generated in an endogenous process without need for the analyst to call on attributes or ideology” (White, 2008a, p. 22; see also Baldassarri & Bearman, 2007; Bearman, 1993; Padgett & Ansell, 1993). In this view, topologies of networks emerging from multiple relational bonds are more significant to social life than any single dyadic bond, much like DNA’s complex temporal-spatial switchings are key to gene transregulation, or proteins’ 3D molecular shapes are more relevant to cells’ metabolic communications than single covalent bonds (White, 1992b, p. 211, on the significance of spatial models for vacancies and blockmodels).

In this connection, emergent topologies of network ties configure reflexive arrangements that are highly consequential for action in that, as Crossley puts it, “different patterns of connection generate different opportunities, constraints and dynamics for those connected in them” (2010, p. 14). Some of these relational patterns partly congeal into positive and negative feedback loops, resulting in control systems, including path dependence, technological or arms races, poverty traps, and social dilemmas or coordination problems, among others. White (2008a, p. 63) explores control orders within network turbulence through concepts such as social molecules and disciplines (Fontdevila, 2018, p. 241). His goal is to uncover underlying network mechanisms to “seek principles of social process which account for chaos and normality together” (White, 1992a, p. 4).

1.2 Scale-invariance and Nonlinearities

From complexity science, White incorporates to his model two principles of self-organization: self-similarity and dispersion (Fontdevila, 2018, p. 239). Self-similarity or scale-invariance is the principle “according to which the same dynamic processes apply over and over again across different sizes and scopes” (White, 1992a, p. 5). Complementing self-similarity is the principle of dispersion. This principle captures White’s view of social life as characteristically nonlinear with phase transitions. Thus, social process cannot be reduced to linear normal curves in that “it is not averages which are crucial, but rather spreads across locale and degrees of social connections” (White, 1992a, p. 5). White’s notion of comparability among structurally equivalent actors derives from this dispersion principle and is further developed in his theory of market profiles (White, 1981 & 2002).

In complexity thinking, self-similarity and dispersion are two sides of the same process of self-organization that exists at the “edge of chaos”, where systems thrive and adapt in the phase space between chaotic and congealed states (Kauffman, 1995; Langton, 1990; Lansing, 2003). At the edge of chaos is where power-law and other long-tailed distributions predominate, including many small, few medium size, and occasional large frequencies. In fact, long-tailed distributions signal that a complex system is self-organizing through nonlinear sensitivity to initial conditions.

Often small initial conditions create path dependencies that rapidly produce long-tailed distributions. For example, a few online songs can quickly go viral, disproportionately increasing their frequency as more and more people see their growing popularity and stream them. In this case, a self-organizing positive feedback loop sets in that started by small initial, often random, conditions rather than by the songs’ intrinsic qualities. Similarly, “an academic paper with 500 citations may owe its success as much to positive feedback as to quality” (Page, 2015, p. 29). Moreover, Fontdevila and White (2013) contend that in struggles for domination among rapidly polymerizing netdoms, identities manage ambiguity through reflexive and indexical language dimensions (metapragmatics, heteroglossia, poetics). They argue that “poetic control” of speech styles for esthetic and persuasive purposes transform identities into power-law constellations with robust footing that then decouple to preserve quality.

In self-organizing systems, both positive and negative feedback loops increase dispersion. Positive feedbacks create long tails because “more begets more” (e.g., multiplicative effects, power laws, Matthew effects, preferential attachment), but negative feedbacks also skew normal variance because they disproportionately reduce fluctuations (Page, 2015, p. 34). Most importantly, self-organizing runaway loops that accumulate continuous change may cross a threshold entering a phase transition (bifurcation) where a new emergent organization is born. Phase transitions are like a “dialectical transformation” in Hegelian parlance, where “changes of quantity become changes of quality” and new forms emerge (Byrne, 2005, p. 105; Mackenzie, 2005). In short, self-organizing complex systems have the capacity to produce the emergence of new properties and functions at a larger scale. For example, a city region can phase transition from industrial to post-industrial, reaching a threshold after which new emergent social properties arise, like unexpected health disparities and residential inequalities (Byrne, 2005, p. 105; Page, 2015).

Finally, self-organizing feedback loops and path dependencies occur at very different scales of the system. In fact, it is scale-invariance that is the hallmark of complexity, providing complex systems with flexible yet resilient hierarchical structures (Cilliers, 2001, p. 4). In this sense, complex systems are not chaotic but fractal systems. To adapt to their environments, all systems differentiate into hierarchies of parts that reduce the amount of information that any single part needs to keep track of and control. But in contrast to hierarchical models of nested systems in equilibrium, complex systems self-organize into hierarchies that interpenetrate at various scales to provide redundancies and resilience (more on this later).

The relational turn of social network analysis pioneered by White and collaborators was a radical breakthrough that helped move sociology away from the cybernetic model of structural functionalism — which was a poor model of the reality of social systems far from equilibrium (Byrne & Callaghan, 2023; Sawyer, 2005; Urry, 2005 & 2006). The relational turn developed innovative mathematical tools to explain network forms and emergent effects that work behind social actors’ backs. However, the network turn often remained at a meso-level of analysis with limited theoretical insight on complexity and emergence at broader historical scales. Although network mechanisms (scale-invariance and nonlinearity) dissolved many distinctions between physical and social systems, new theoretical frameworks were needed to explain emergence in what is specifically human, that is, the phenomenology of meaning.

2.1 Stories and System Boundaries

In Identity and Control, White develops “story” as phenomenological accomplishment of network tie. He draws on the paradigm shift from representational to ontological understandings of narrativity that had taken place in the social sciences and humanities of the 1980s (Somers, 1994 & 1996). In his words:

An apparently simple pair-tie can be seen to be a considerable social accomplishment […] There also must be ambivalence and complexity built into a tie, since it is a dynamic structure of interaction in control attempts. It is this structure which is being summed up as a “tie”, and interpreted in stories, both by its members and by onlookers (White, 1992a, pp. 68–69; 2008a, p. 25).

A story consists of a series of periodic reports, accounts, and updates variably linked through emplotment that provide a characteristic sense of temporality to a social tie — it provides a history. Through stories, network ties are reinterpreted by actors in ongoing interactions and control efforts. As discussed later, sets of stories are told and retold in speech registers and sublanguages appropriate for a particular type of tie. Stories deliver a characteristic sense of continuity to social ties, which otherwise would switch on and off in everyday disjointed snapshots. In this sense, narrative is the site where subjective experience of phenomenological “shock” — new times, new contexts, new trajectories — triggered by netdom switchings is “edited out” from the weavings of the social in order to preserve identities’ ontological continuity.

It is worth noting that already in the 1960s White was well aware of the significance of the phenomenology of network ties, expressing concerns about the co-constitution of objective structures and actors’ perceptions and experiences of them. White’s concept of category-network or catnet — sets of individuals interconnected and “alike in some respect, from someone’s point of view” — is an early exercise on the need to include cultural dimensions to network structure (2008b, p. 4 [1965]). As he put it in early lectures,

a net continues indefinitely […] Yet there must be a common culture to define a type of relation sharply and clearly, if there is to be a net defined by the presence or absence of that relation between pairs of persons (2008b, p. 2 [1965]).

Similarly, in his conceptualization of frame as folk theories used by people to categorize their indirect relations (e.g., a kinship group with names for indirect relations), White states that “people develop culture in part to meet their needs to visualize, operate in and modify the social structure to which they belong” (2008b, p. 11 [1965]). Moreover, White’s modeling of market profiles based on phenomenologies of mutual perception and signaling is a special case of his broader concept of comparability of ties (White, 1981 & 2002). Actors reduce uncertainty in social life by assessing courses of action taken by other actors with structurally equivalent standpoints and valuations.

White’s conceptualizations of the phenomenology of ties through stories, from catnets to netdoms, are important considering that one of the most intractable epistemological challenges in complexity thinking of the social sciences is the question of boundary formation (Cilliers, 2001; Sawyer, 2005). Human social systems are not physically bounded in the same localized way as biological systems. This is because interconnections between component parts in social systems are rarely physically visible but mostly constructed through intersubjectivities and semiotic practices. Hence, the same “parts of the [social] system may exist in totally different spatial locations [and] non-contiguous sub-systems could be part of many different systems simultaneously. This would mean that different systems interpenetrate each other” (Cilliers, 2001, p. 6).

In this light, White’s model enables us to think deeply about systems interpenetration and boundaries through mechanisms beyond isolated dyads attempting to stabilize the indeterminacy of their double contingency. Beyond dyadic reductionism, his model incorporates the complexity of multiple contingency, including identities’ second-order observations of shifting network shapes and expectations, taking into account changing positions and expectations of several nodes removed from their direct ties and located in different subsystems. As discussed later, multiple contingency is key to indexicalities of context-making (i.e., boundary formation) across netdoms since speakers perform reflexively not just to co-present ties but via them to absent and indirect ties as well — for example, indexing deferential demeanor in addressing a direct superordinate with the intent to indirectly target the latter’s higher-ups who are not present (Fontdevila & White, 2010 & 2013).

2.2 Control and Ambiguity

Moreover, White’s primitive of control also enables us to think about processes of open-ended boundary formation in complex systems. Identities, as sources of action triggered by stochastic processes in social life, seek control to reduce uncertainty by relentlessly switching netdoms.² In the process they produce phenomenological contrasts among ties that become interpreted through emplotment in stories. For White, these stories result from control efforts by identities to reduce uncertainty. But “control” is not just “domination over other identities. Before anything else, control is about finding footings among other identities. Such footing is a position that entails a stance, which brings orientation in relation to other identities” (White, 2008a, p. 1). He claims that footings must be reflexive with future anticipation as well as present response efforts (Fontdevila & White, 2013; White, 2008a, p. 2). Thus, there “must be ambivalence and complexity built into a tie, since it is a dynamic structure of interaction in control attempts” (White, 1992a, p. 69).

Moreover, White asserts that reaching through network ties to get robust action entails “keeping the state of interaction hard to assess through making very many possible evolutions continue to seem possible […] which prevents anyone from seeing clearly an outcome that would end the social tie” (White, 2008a, p. 288). He draws on Leifer’s (1991) characterization of expert chess players sustaining ambiguity, where a player’s ability to make sense of the game is often not determined by the capacity to see many moves ahead, but by the ability to sustain uncertainty in the relationship itself.

In short, “ties are stable only through being ambivalent and ambiguous at any particular instant and in any tangible action” (White, 1992a, p. 86). This strongly resonates with complexity thinking, since, as Cilliers indicates, the “boundary of a complex [social] system is not clearly defined once it has emerged […] and therefore the closure of the system is not something that can be described objectively” (2001, p. 5). In complex systems parlance, the boundaries of social ties constituted by their stories must remain open-ended to endure.

To close this section, in White’s model both ambiguity (i.e., sustaining ambivalence within a tie) and ambage (i.e., using direct ties to influence indirect ties) pervade network ties’ phenomenologies. These are also mechanisms that can unblock and get fresh action (White, 1992a, pp. 57 & 106). Hence, I argue these mechanisms produce resilience and flexibility to complex systems because open-ended boundaries of network ties enable hierarchies to interpenetrate different subsystems (contra the “operational closure” of autopoietic models à la Luhmann, more on this later). Note that if footing among identities is about keeping boundaries of stories open, then boundaries by their nature are objectively difficult to define. Thus, it goes without saying that the methodological challenges of operationalizing boundaries in complex social systems are formidable (see McLean & Song, 2023, for the operationalizing challenges of “side-directed behavior” in network configuration).³

3.1 Indexical Language and Metapragmatics

Indexes are more or less grammaticalized elements that point to features of the social or physical world, and that speakers use reflexively to create and lay out the contextual parameters of their social interactions. Unlike referential symbols, indexes are signs that signify by spatio-temporal contiguity.⁴ From shifters (e.g., here, now), pronouns (e.g., I, she), verb tenses, to code-switching, registers, deference markers, prosodic tones, silences, and so on, indexes anchor the linguistic code in practical contexts of use. Many linguistic indexical strategies can be used reflexively (i.e., metapragmatically) to constitute the social contexts in which they are uttered. For instance, two individuals “switching” to a first-name basis index a new context of status proximity, or coworkers “switching” from formal to casual speech index a more relaxed professional context. Indexes enable speakers to reflexively negotiate their footings and ties, rendering more complex semiotic processes (e.g., metaphor, myth, narrative) fully operational in communicative practice. In short, indexes are the primitives of meaning that bridge semiosis and communication in social life (Fontdevila, 2010 & 2025).

White recognized this constitutive capacity of language to shape context and the meaning of speakers’ interactions through switches in indexicalities. Switching is, thus, his model’s third primitive and a fundamental mechanism of context-making that embeds or decouples networks into different shapes and temporalities. For White, “[…] meaning emerges for humans only with switching, as from one netdom to another. Switching is central to this theory and will appear again and again at different scopes and levels” (2008a, p. 12). In short, language matters to networks because speakers via reflexive switches of indexical markers reshape their network topologies (e.g., switching forms of address, ironic tone, vernacular versus standard registers). Moreover, these switches are never performed in dyadic isolation. In White’s view (1995b, p. 4), Silverstein’s “heroics of indexicality” produced with phenomenological effort in face-to-face interaction need not be in “myopic messiness of dyads”, but channeled by broader patterns of network switchings.

In this light, White claims that switches of speech registers and specialized sublanguages across netdoms are fundamental “vehicles of meaning for identity and control” (2008a, p. 17). His reflections on the origins of speech registers as indexical devices of network tie are worth noting here. Thus, packs of vertebrates (e.g., wolves, primates) avoid constant injuries from competitive fights by being naturally selected for transitive dominance of pecking order across every domain of activity — “sex, food, resting site, first to the alpha male, then […] no talk needed” (1995a, p. 1037). However, in evolutionary or historical scale even greater fitness or subsistence, respectively, was attained by establishing subsystem boundaries along specializations of “task and caste and locale and breeding”. This is the strategy pursued by ant societies for millions of years, with pheromone chemical “signaling” as the key mechanism that demarcates caste and task boundaries.

Eventually, “over thousands of years, one vertebrate species (two, if you include Neanderthal) worked out specialization with talking, not pheromones. Like the ants, early human talkers may have switched only rarely, perhaps in the earliest mass ceremonials. At some point came frequent switching, perhaps situated around sleep patterns, and no longer necessarily in lockstep” (White, 1995a, p. 1037). White claims that “sociocultural reality was constructed only when there was switching back and forth between at least two domains, everyday and ceremonial, with their continuing networks” (1995a, p. 1035). In his own words:

Humans, unlike ants, switch back and forth between specialized domains of joint activity, and talk develops along with and sustains this differentiation. Talk and its languages are shaped primarily by this switching. Switches in talk between one and another domain are at the same time switches in which particular social ties of different sorts are being activated and deactivated (White, 1995b, p. 1).

In other words, complex communication by task and rank in human social organization is sustained through specialized speech registers and sublanguages. Now, all communication is metacommunication as we know since Bateson (1985[1955]), and thus any message provides context-markers to the addressee on how to decode it (e.g., tone to decode the opposite meaning of a remark in irony). Through its indexical devices, a speech register “metacommunicates” the type of network tie and its associated story, including its purpose, tasks and ranks. What is significant about human complex organization is that very different tasks can be performed by the same individual switching across different netdoms. Hence, it is critical to switch speech registers to signal and contextualize boundaries of netdom switches — a “switch” of speech register signals (indexes) the activation or deactivation of a particular type of tie within a relationship, for example, from coworker to friend. Speech registers are metacommunicative devices (equivalent to pheromones in ants) that enable the emergence of specialized subsystem boundaries among human beings when they perform multiple tasks and ranks across different domains — unlike ants, which are selected genetically for task and caste. Among humans, complexity only emerges after there is potential to switch registers and thus “social process even thousands of years ago could develop only in co-constitution with full-fledged language” (White, 2008a, p. xxi).

For complexity thinking, the aforementioned underscores that the indexical and reflexive functions of language constitute critical mechanisms of emergence in human systems of complex organization. In particular, the metapragmatic function of language (i.e., reflexive awareness of the pragmatic rules of linguistic interaction) is essential to speakers’ deployment of indexical devices and contextualization cues that accomplish types of netdom ties.⁵ As Sawyer notes, “speakers use the metapragmatic function of language to reflexively communicate about the emergent process and flow of the encounter or about the ground rules and the communication language itself” (2005, p. 182). Moreover, metapragmatic processes of context-making occur in real time and thus “the mechanisms by which relational information is signaled are inherently ambiguous, i.e., subject to multiple interpretations […] In conversation, such ambiguities are negotiated in the course of interaction” (Gumperz, 1982, p. 208).

3.2 Subsystems Interpenetration through Indexical Language

In light of the above, I argue that the capacity for indexical and reflexive switching that enables specialized differentiation across netdoms is also the key mechanism that undergirds subsystems interpenetration in complex social systems. Reflexive switches of transposable metapragmatic devices can reshape boundaries and enable subsystems interpenetration — for example, switching from standard to vernacular speech at the workplace signals solidarities and exclusions anchored in separate but interpenetrating subsystems of race and corporation. Against nested hierarchies of cybernetic models, complex social “systems can be overlapping, non-nested and not saturating of their space, and have different temporal and spatial reach” (Walby, 2021, p. 326). Because they are open to polysemic interpretation, indexical devices also create indeterminacies and redundancies that enable cross-communications between shifting systems hierarchies. As Cilliers has remarked, in complex systems, “hierarchies are not that well-structured. They interpenetrate each other, i.e., there are relationships which cut across different hierarchies” (2001, p. 7). In his words:

The cross-communications between hierarchies are not accidental, but part of the adaptability of the system. Alternative routes of communication are vital in order to subvert hierarchies that may have become too dominant or obsolete. Cross connections may appear to be dormant for long, but in the right context may suddenly play a vital role (Cilliers, 2001, p. 7).

Similarly, White has indicated that “any social formation whatever, complex or not, tends to settle into blocking action over time” (1992a, p. 255), but decoupling by netdom switchings “provides the lubrication that permits self-similarity of social organization across scopes and levels” (2008a, p. 280). In this connection, Fontdevila et al. (2011) have analyzed subsystems interpenetration via indexical switching. They agree with Luhmann that meaning is central to social life but challenge his claim that modern society is based on communicative self-closure of separate, functional subsystems (e.g., economy, science, law, arts). They contend that there is refuting evidence from sociolinguistics and argue that language’s indexical and reflexive devices are transported across institutional contexts with significant netdom consequences.

Thus, Fontdevila et al. (2011) claim that identities, in their struggle to secure footing, switch among different institutional rhetorics often producing “hybrid” rhetorics (see also Fontdevila & White, 2010, p. 339). These hybrid rhetorics enable identities to reflexively frame ambiguity and avoid “indexically” closing systemic meaning (e.g., gay marriage legalization reframing established institutional rhetoric). This proves crucial to boundary maintenance of rapidly differentiating subsystems, since it keeps boundaries permeable and porous to new meanings, avoiding systemic collapse. Similar to “story” discussed earlier, identities seeking reflexive footings across institutional rhetorics embrace ambiguity to keep their ties flexible in anticipation of change. Thus ambiguity should not be removed methodologically as measurement error but should instead become fully integrated into the analytical model.

In short, identities switching across subsystems bring new contextualizing and reflexive devices that change the communicative rules of specific subsystems, which are not impermeable to indexicalities from elsewhere. In contrast, Luhmann’s theory of communication is based on binary codes governed quasi-algorithmically within autopoietic subsystems to reduce uncertainty (e.g., legality/illegality in law, legitimacy/illegitimacy in politics). By establishing an ontological distinction between action and communication to justify systems operational closure, Luhmann falls back into structuralist and nonindexical understandings of meaning. But only actors seeking footing contextualize systems’ self-referential meanings to reach understanding. Institutional logics may constrain action but ultimately it is reframed and enabled by identities struggling for control. Fontdevila et al. (2011) contend that humans are not merely the system’s environment but the cornerstone of the system’s meaning generation. In other words, systems closure does not solve the problem of meaning and uncertainty in social life. In fact, lack of uncertainty is itself a problem. Order is necessary, but order at the edge of chaos.

In closing this section, I would like to highlight the relevance of systems interpenetration for current theories of power. In particular, this is relevant for theorizing intersectional mechanisms of power across global and postcolonial societies. In this respect, Walby (2007 & 2021) is unique in providing an analytical framework that incorporates intersectionality into complexity thinking. Contra nested models of cybernetic differentiation, Walby remarks that, in complex systems analysis,

there can be multiple systems having effects in the same space […] [allowing] for the analytic separation of institutional domains and regimes of inequality […] [and] the theorisation of multiple intersecting regimes of inequalities without identifying or reducing each one to a separate institution (2021, p. 320).

She further states that,

[…] for example, multiple regimes of inequality of class, gender and ethnicity can all structure the same institution of employment. This theoretical capacity to distinguish between institutional domains and regimes of inequality is only possible with this new way of thinking about systems […] There is no longer a difficult choice between a theory of society based on institutional differentiation and one based on regimes of inequality: sociology can have both (2021, p. 320).

Space limits prevent full elaboration of White’s understanding of power and systems interpenetration. Suffice it to say, like Bourdieu’s (1977) political economy of linguistic capitals, White sees domination as “the root process in what is specifically social” (1995b, p. 10). Any language is always a discourse of interpenetrating sublanguages, styles, and registers, laden at all scales with struggles for domination and identity. Thus, grammars may result from routinization, but by domination rather than innocent habituation, over historical choices of switchings in unequal networks and domains (Fontdevila & White, 2013). White provides a framework to theorize overlapping systems of domination via indexical language. He looks to insights from the sociolinguistics of pidgins and creoles as models for localized grammaticalization processes embedded in domination, and transposes them to any situation where actors fluent in different sublanguages and indexical systems must interact in a common lingua franca — so not only trade posts and plantations but multiethnic corporations traversed by global networks of transactions and peoples. Thus, reflecting on the grammaticalization choices of deictics and other indexical devices of business talk of the modern corporation, White & Godart (2010) remark,

Within your part of a firm, say a big New York bank, one has come to speak in the style which is at home there. Speaking with another firm, by contrast, could instead be analogous to using a different, coarser and more formal idiom, much as in the Djirbal tribe of Australian Aborigenes a man switches to a special mother-in-law language when speaking to affines (2010, p. 273).