A Cognitive-Structural Sociological Account of the Emergence of Novel Worlds

Individual Level

We begin by considering individual cognition and establishing the notions on which we build an account of collective concepts. A concept is a mental representation by a person that provides expectations and beliefs about entities (e.g., people and events), which we call objects. These expectations concern the values of a set of relevant “features.” A person’s mental representation of a particular entity, such as a software product, a sports contest, or an academic publication, can be represented as a position in semantic space. The dimensions of such a space are the possible values of the features for which the concepts provide expectations and that matter for judging whether entities are instances of the concept. Concepts are generally paired with labels (linguistic tags) because people cannot directly share their mental representations but do communicate using labels. Our formalization uses labels to indicate concepts.

A contemporary rendering treats a concept as a probability density function, π(c | x), defined over a semantic space. Here, x denotes the position of the mental representation of an object in the space. This function, called a “concept likelihood,” gives the subjective probability (or belief) that an object that is an instance of a concept will have some combination of values of relevant features (a specific position in the semantic space). Contemporary quantitative semantics (including that built into large language models) treats this probability measure as providing the “meaning” of a concept (e.g., Boutyline and Arseniev-Koehler 2025).

The foundational empirical work on concepts and categories did not pay much attention to semantic spaces. Work in the style of the pioneer Eleanor Rosch uses commonly understood concepts and subconcepts (e.g., fruit: apples, grapes, and tomatoes). ² Researchers reasonably take for granted that subjects from the same culture use a common semantic space to represent such concepts. If researchers have doubts that people use common semantic spaces, they generally conduct experiments in which they teach subjects novel concepts. That is, researchers design the space and use it to represent stimuli. ³ However, when attention shifts to concept learning in natural settings, attention must be paid to the space. How do agents come up with featural representations? Previous research reveals that some features of the context, such as the task at hand, induce agents to engage in this cognitive work. We argue that the emergence of a distinctive cluster of objects simplifies the task. Collective action by interested agents supplies the necessary motivation.

Categorization means labeling, or assigning observable entities to concepts, for example, “That is a large language model.” Because concepts lack boundaries, categorization involves some uncertainty. The modern Bayesian approach looks at categorization as a problem of statistical inference (Anderson 1991; Tenenbaum and Griffiths 2002). Such an analysis considers a person deciding whether an object is an instance of a concept. The instance-of idea can be expressed formally with the predicate IS-A(c, o), which has the intended reading of “The focal person believes object o is an instance of concept c.” This approach interprets the strength of an agent’s belief in the truth of hypothesis IS-A(c, o) as a subjective probability.

Suppose one must answer “yes” or “no” to the question, “Is this researcher, o, a cognitive sociologist, c?” The Bayesian approach holds that the probability of answering “yes” is given by the Bayesian categorization probability:

Pr ( I S − A ( c , o ) | x ) ≡ Pr ( c | x ) = π ( x | c ) Pr ( c ) P r ( x ) ,

(1)

where π(x | c) is the concept likelihood and x is the position of object o in the semantic space. The other terms on the right side, Pr(x) and Pr(c), are the agent’s priors on the general distribution of feature values in the domain and on the likelihood an entity in that domain is an instance of the concept. This formulation links the notion of a concept to judgments about objects.

It might be helpful to give a toy example of a probabilistic concept. Suppose someone’s concept “circus” involves three binary features: (1) a traveling troop of performers, (2) high-wire acrobatics, and (3) trained animal acts. The semantic space here is a cube with eight vertices ([111], [110], and so forth). An individual’s circus concept assigns probabilities to the eight feature combinations, and the concept is given by π(f₁,f₂,f₃ | c). For instance, it might assign 0.70 to (111), 0.15 to (110), 0.15 to (101), and zero (epsilon) to the others. Entities with all three features are highly likely to be categorized as a circus, those with troops of performers and one other feature have a low likelihood, and all other configurations have extremely low (essentially zero) likelihood.

A category is a stochastic realization of an underlying Bayesian categorization process. In formal terms, a person’s category for the concept labeled c is the crisp set of objects the person judges to be instances:

C a t ( c ) ≡ { o | IS - A ( c , o ) } .

Collective Level

The analysis of worlds requires the concepts and categorizations of individuals be aggregated at a collective level. What groups of agents “think” reflects the concepts of each member because collectives do not possess concepts in the usual sense. But exactly how do collectives think? This is an unresolved question. We address it with a formulation of the degree to which a set of agents believes their meanings are the same or at least highly similar.

Taken-for-Grantedness

The taken-for-grantedness of concept c for individual m, in notation, g(c, m), is related to the categorizations of other members of the group. Because others’ concepts are not knowable, agents learn what others think by attending to their observable categorizations of objects. The more an agent observes that categorizations by other members agree with their own, the higher the likelihood of relying on such categorizations for inferences about objects when its feature values are unobserved. We refer to this process as involving taken-for-grantedness.

We use the model proposed by Hannan et al. (2019), which begins with the effect of an object’s categorization by one group member on the inference made by another. The postulated process works as follows. A Bayesian agent faces a situation that calls for an expectation about the feature values of a not-yet-seen object. A Bayesian will use the prior probability distribution of the feature values in the domain, Pr(x) in Equation 1, to form an expectation. If a member learns of another member’s categorization and treats it as credible, then her expectations about the relevant feature values will be based on her own concept likelihood, π(x | c).

The postulated process treats inference in the case of possible social influence as involving a mixture distribution, a weighted combination of Pr(x) and π(x | c) with weights that reflect social influence at work. If alter’s categorization has no effect on ego’s beliefs, then the mixture puts all the weight on the prior—there is no information update. Otherwise, the weight on the concept likelihood increases with the strength of the influence. ⁴

The next step considers one member and the group. The taken-for-grantedness of a concept for an individual in the context of a group is the strength of the individual’s propensity to accept the implications of categorizations by any other group member for whom they lack observations of prior categorizations. An agent takes the meaning of a concept for granted in the context of a group if she treats categorizations by any of its members as informative, even without prior information about the member (Hannan et al. 2019:236).

We assume taken-for-grantedness in a group is about the meaning of a concept, G ( c , M ) , given by the average over the members of individual taken-for-grantedness (g(c, m)):

G ( c , M ) = 1 | M | = ∑ m ∈ M g ( c , m )

If all group members rely only on their own categorizations (there is no social influence), then G is zero. Otherwise, G increases with the average over all (ordered) pairs of members of the weight placed on others’ observable categorizations (Hannan et al. 2019:241).

In defining a collective version of categorization and other judgments, we carry over the perspective built at the individual level. Doing so encounters complex aggregation issues (Hannan 2022a, 2022b). Some members of a collective might regard an object as an instance of a concept and others not.

Introducing a complicated account of the nature of aggregation can deflect us from the substantive issue. We simply refer to collective-level categorization and other judgments and leave open exactly what this means. We refer to general agreement to identify situations in which the level of agreement among members is high enough to justify concluding the collective thinks (nearly) alike about the matter.

We introduce a predicate, TFG(c, M), to express such an aggregation. Its intended reading is “The concept denoted by c has a generally taken-for-granted meaning for the set of agents M.” The following meaning postulate fills in the meaning of this predicate, links it to taken-for-grantedness, and instantiates the existence of the threshold.

∀ c , M ∃ ω > 0 [ TFG ( c , M ) ← → G ( c , M ) ≥ ω ) ] .

The tendency to update expectations about objects from categorizations by others comes from learning that other group members use the concept nearly the same way (Hannan et al. 2019). This means observing that others’ categorizations largely agree with one’s own. Because linguists and logicians dealing with concepts and categorization generally refer to a category as an extension of the concept, the argument we follow is expressed in terms of extensional agreement.

Group-level conceptual agreement is not observable because this requires measuring the distances between members’ concepts, and concepts are not observable. In contrast, agreement about categorizations can be observed and measured (Hsu 2006). This means empirical tests of the theory we present will likely depend heavily on the agreement on categorization.

We next consider an agent’s experienced agreement in categorization, first with another group member and then with the group as a whole. Let ea(c, a, b) denote the similarity of the categorizations in c by the focal agent, a, and by another group member, b, and let e a ¯ (c, m, M) denote the average experienced by members m with other members of group M. Finally, let EA(c, M) denote the average over pairs of group members. Then we assume the following:

∂ g ( c , m , M ) ∂ e a ¯ ( c , m , M ) > 0 .

To connect the individual and group levels, we need to specify the relation between extensional agreement and individual-level taken-for-grantedness. We assume a linear relationship exists between the two quantities. We formulate this in the following auxiliary assumption ⁶ :

∀ c , M ∃ α , β [ ∀ m [ ( β > 0 ) ∧ ( m ∈ M ) → g ( c , m , M ) = α + β e a ¯ ( c , m , M ) ] ] .

(2)

With this additional assumption, G(c, M) is increasing in the group-level experienced extensional agreement, EA(c, M) (Hannan et al. 2019:248).

∂ G ( c , M ) ∂ E A ( c , M ) > 0 .

The Cognitive Level: Concepts

Our representation of a world has two components: cognitive and material. The cognitive part consists of a triplet of concepts. The first is the organizing or focal concept c that gives meaning to a set of observable objects, as described in the previous section. The other two concepts are “producer of c” and “audience for c.”

Agents have concepts that provide meanings for producer of c and audience for c. Fit to expectations about the values of relevant features, these concepts shape judgments about who gets regarded as a producer or audience member. Concepts that give the meaning “producer of c” establish expectations about the making and public presentation of objects. For example, a producer of science, or a scientist, is expected to pursue the creation of new knowledge by conducting research, publishing their findings in journals or books, presenting these results at conferences, and giving lectures or teaching.

Similarly, the concept “audience of c” establishes expectations about agents who have some significant involvement with the objects presented by producers. For example, in banking, the audience includes the consumers making deposits and borrowing money and the regulators supervising the conduct of financial institutions. The audience role is not passive; enacting this role requires conceptual work and social behavior. Take the role of the critic in cultural production. Critics proclaim that some objects are exemplary, and they provide interpretations, cultural context, and aesthetic or quality judgments (Caves 2000).

Often, all that is expected of audience members is that they engage with what producers present publicly. But sometimes, the roles are more detailed. For example, in education and medical care, the roles of student and patient come with expectations that involve hierarchical components of authority, power, and prestige (Parsons 1975). Given that our model of taken-for-grantedness depends on agents learning from others’ categorizations, we consider only public engagement, or actions observable to others.

The concepts of producer and audience presumably have a probabilistic structure. Some configurations of feature values are highly likely, and others are less likely or unlikely for incumbents in these roles. The meanings of these concepts can vary in different contexts and over time. However, introducing such extreme flexibility introduces too much complexity. For tractability, we rely on the simplifying assumption that the meanings of the producer and audience roles are inherited from higher-order worlds, not newly created in a context. For instance, the role of professor varies little over the nature of the subject (e.g., literature or logic), as does the role of peer evaluator or student (the audience). With this simplification, we can identify worlds by labels or their focal coordinating concepts.

The Material Level: Objects and Agents

So far, our construction is purely cognitive. We fill out the meaning of a world by considering the agents who take on the roles and what they produce and evaluate. Objects have a central role because they are public demonstrations of private representations, carriers of forms both produced and observed. This notion reflects Sperber’s (1996, 2005) framework for cultural evolution, which treats culture as a set of private representations diffusing via public discussions of these interpretations of objects that manifest these representations.

Producers and objects are interdependent. An observable realization of a concept is the result of a producer’s thoughts and actions, and an agent is a producer by virtue of creating and presenting objects intended to exemplify the concept. To take the producer role with respect to a concept, an individual must have conceptualized it and presented an object as an instance. We denote the set of producers of the focal concept as “P.”

An agent is an audience member because the actor has conceptualized an object as a realization of c, inspected it, and engaged with it. We denote the set of audience members for the focal concept (at a time point) as “A.”

Production and engagement are social. Developing a new concept in complete isolation can produce novelty and, in principle, can sow the seeds of the emergence of a novel world. However, unless the work is shared with others and allows others to become interested, connect, and participate, the concept and its observable realization will remain private and will not have sociological significance.

Engagement requires nontrivial individual participation in a social context. It can take different forms and vary in intensity. In a music world, for example, attending a concert, opening a music club, performing music in public, signing an artist to a record label, and reviewing music performances each represent a form of engagement. Delivery of cleaning supplies to the club where music is performed, in general, does not. ⁷

Concept-related engagement means engagement in light of the concept. Engagement differs from consumption because audience members can engage with an object or performance with the goal of making a purchase decision or simply inspecting it out of curiosity. Similarly, consumers can buy without paying attention to the aesthetics that informed production.

We define the audience for a concept (genre, style, or form) as the set of agents that exhibit nontrivial levels of concept-related involvement (levels exceeding a threshold). The producer concept involves attending to the work of other producers. For instance, in science worlds, expectations for scientists include evaluating the work of other scientists, for example, as referees for publication or funding, for promotion and recognition as part of professional committees, or providing developmental feedback in a mentorship relationship. In general, producers are audience to one another.

The notions of object, producer, and audience are tied to a particular coordinating concept. This matters because two agents might engage an object in light of different concepts that come from different higher-level worlds. For example, a customer in a restaurant might consider the meal an instance of Japanese fusion, and another might consider it an instance of luxury dining.

Finally, membership of a world is the collection of producers and audience members, M = P ∪ A = A, where the second equality follows from the assumption that producers are audience to each other. We complete the ontology by combining the three components to define a producer-audience world, using the predicate WORLD(c, O, M).

This definition does not require members of a world share ongoing social ties or an identity. We opt for this less restrictive definition to accommodate situations in which the organizing concept has been highly institutionalized. In such worlds, such as classical Western music or medical care, the nonproducer audience does not typically share a common identity and interact outside the world. Nonetheless, many worlds (e.g., political movements) have a more social character and develop shared identities.

Stage 1: Distinctive Clusters of Objects

When do novel worlds arise? This process starts with the rise of what get perceived as distinctive clusters of objects in a parent world. Hannan, Pólos, and Carroll (2007) argue that new organizational forms are created when distinctive clusters of producers/products appear in some setting, are labeled, and gain collective meaning. Explaining where these objects and producers exactly come from is not the focus of our theory. However, we expect that producers experimenting with ongoing activities will originate such transformations, for example, scientists conducting research that introduces new ideas or artists composing, painting, and designing new aesthetic solutions to creative problems. New producers in a setting using new methods also contribute to these dynamics.

Sperber’s (1996) model of cultural evolution provides a representation of how the process can start. An object connects the mental representation of its “creator” to that of another agent, who then goes on to produce something of their own. In this transmission process, either by direct communication or by imitation, objects transform; they do not necessarily reproduce exactly. This happens because some information might be lost in the process or because the agents do not seek to produce a replica but rather something that follows their own dispositions and preferences (Sperber 2005).

Another aspect of Sperber’s (1996) model helps explain how object clusters arise. Objects and their mental representations do not, he argues, depart randomly from those that preceded them. Instead, they tend to gravitate around existing variants in the space of what is seen to be possible. Existing objects and concepts, in other words, function as “attractors.” With cultural items clustering around these attractors, culture allows for change while also maintaining some stability.

The key is that a subset of members of the focal world applies a new collective label to the cluster of distinctive objects. In building this construction, we use a label function, lab(o, a), that maps pairs of objects and agents to a collection of labels. This notion of label differs from the IS-A predicate introduced previously. The latter is a conceptual statement: The agent regards the object as an instance of the concept. The label function does not require this. This function is extensional: It points to a set of objects.

A subset of the existing world’s membership that applies the same label, say l, to some subsets of the world’s objects is given by

{ m | ( m ∈ M ) ∧ ∃ o [ ( o ∈ O ) ∧ l a b ( o , m ) = l ] } .

(3)

This generic construction does not identify a unique set. Suppose M(l) contains two agents, a and b. The formula says that both members apply the label under consideration. But then the sets that contain only a and only b also satisfy the condition defining the l-applying membership (Equation 3). This is a problem if we want to connect this formulation to a research design that supports tests of hypotheses about properties of worlds that make them more (or less) likely to generate clusters. Doing this requires a definition that identifies a unique set of members. It seems natural to single out the most inclusive set.

We can do this by examining the powerset of the set of members, denoted ℘(M). ⁸ We define a maximal l-cluster in a world as follows. First, consider the elements of the power set that satisfy Equation 3. We call this set M(l). The supremum of this collection of sets, sup(℘(M(l)), is the largest subset of the world’s membership that applies l to objects in the world. We refer to this supremum as M^*.

O ∗ = { o | ( o ∈ O ) ∧ ∃ m [ ( m ∈ M ∗ ) ∧ l a b ( o , m ) = l ] } .

Finally, there is an issue of the social significance of the cluster. According to the proposed definition, a single member can be responsible for a cluster. We want to restrict attention to clusters that are large enough to serve as a basis for the emergence process. We introduce a threshold on the minimum size of the maximal membership that applies a particular label. For example, one might impose the restriction |M^*| > θ.

We see no basis on which to predict what clusters emerge, just that some do. In this view, the natural way to model the emergence of clusters in a world is as an arrival process. Let N(W, t) denote the number of labeled clusters (of any label) that have emerged in the world W until time t. The arrival process is defined in terms of the following hazard.

κ ( W , t ) = P r ( N ( W , t + u ) = n + 1 | N ( W , t ) = n ) u .

Stage 2: Exploring the Meaning of a Cluster—Scene

A cluster of objects recognized by producers and other audience members in a world is a candidate novel world. Whether a candidate becomes a full-fledged world depends on whether the world’s membership comes to conceptualize the label and then generally takes for granted that others attribute the same meaning to this label.

The cognitive and behavioral work of conceptualizing a cluster and coordinating concepts and categorizations generally takes place in localized structures characterized by repeated patterns of perception, interaction, and discussion among social agents concerning objects. As visible representations, objects have mental representations as their cause and effect. Sperber formalized this idea in a model of cultural evolution that treats constructive cognitive processes as involved both in representing mental inputs and producing observable outputs (Claidiere and Sperber 2007; Sperber 1996). Mental representations sparked by perceptions of objects can, in turn, cause the production of further objects that can spark revisions of mental representations, and so on.

We focus on a localized high-energy social structure, which we call a scene. ⁹ The concept of a scene has been used in sociological studies of the production, performance, and reception of popular music. Such work focuses on situations in which spatially close groups of producers, musicians, and fans come together to share their common musical tastes, create music for their own enjoyment, and distinguish themselves from others (Lena 2012; Lena and Peterson 2008; Peterson and Bennett 2004; van Venrooij 2015).

Consider, for example, the scene that developed from 1973 to 1975 in New York City’s East Village and Gramercy neighborhoods. During that time, famed music clubs, such as CBGB and Max’s Kansas City, opened to book young, untested talent to play urgent, edgy, anti-establishment music (Lena 2012). This “new wave” of music came to be referred to as “punk” (Kristal 2005). ¹⁰

CBGB’s owner, Hilly Kristal, recounted there were many young bands in New York at the time but just a few places where they could perform and play their own music. The new clubs offered them a home. Tommy Ramone of the band the Ramones, who had an early residency at CBGB, recalled that the initial patrons were “artists, bohemians, drag queens, and Hell’s Angels” (Kristal 2005). Others started coming around, musicians primarily, and then customers, too. Magazines such as Creem started reporting on the scene. The reputations forged at these clubs would lead many bands to sign record-label deals, with Patti Smith among the first to do so in 1975 with the new Arista label.

Despite its widespread use, the notion of scene lacks a precise definition. Silver and Clark (2015) describe it as an open idea, and Woo, Rennie, and Poyntz (2015:288) consider it a “sensitizing concept” used to give a general sense of reference and guidance. We try to be more specific about what we mean by a scene: an interaction of producers and audiences characterized by high energy. This use appears consistent with the original interpretation of scenes in cultural studies. For instance, Straw (1991, 2015) characterizes scenes as social spaces of effervescence, perhaps echoing Durkheim’s notion of the feeling of belonging and assimilation produced by collective ritual action, where agents express an excess of sociability. Collins (2004) developed a related notion of emotional energy, a feeling of enthusiasm, confidence, and motivation individuals derive from participating in a group.

High energy is a subjective state, but it is connected to cognitive and behavioral processes that appear critical in a scene. Becker (1982) claims that groups that become interested in new artistic work do not simply observe and choose favorites among known producers but also engage in actions requiring significant effort. In a scene, individuals take producer and audience roles and interact to understand and refine the meaning of the core activity and associated aesthetics. In doing so, they explicitly reflect on conceptual issues.

Scenes, in our view, are not restricted to arts worlds but occur in all kinds of domains. Consider, for example, this description of the early days of cognitive science:

In some respects, Cognitive Science was most successful at the very moment it was born. It is difficult to recapture the excitement of the first Cognitive Science Society meeting, but it was palpable. Each of the subdisciplines associated with cognitive science was well represented. It was like going to an exotic marketplace and sampling an intriguing variety of products. That there was not a common language only added to the interest and desire for commerce. (Bender, Hitchins, and Medin 2010:374)

Negro, Hannan, and Olzak (2022) examine such a dynamic in the domain of winemaking, specifically, the production of Barolo and Barbaresco wines (considered among the world’s best). Until the late 1970s, producers of these wines used a method that had not changed in a century. This traditional method produced very tannic wines that needed long aging in large barrels that were difficult to clean, which often gave a “barnyard” odor to the wine (appreciated mainly by connoisseurs). Younger producers looked to France for superior methods and began to use the small barrel common in the Bordeaux region. Soon, more young producers joined them. About 20 producers started meeting as a group, talking to each other about their experiments in vineyard and cellar practices, tasting and comparing each other’s wines, and learning from these critiques. By the mid-1980s, as these meetings continued, the members began to produce a distinctive cluster of wines, which critics called “modern.”

As these examples highlight, scenes are social structures in which a membership explores the meaning of a cluster of objects. As we see it, such structures heighten the chances for the emergence of collective taken-for-grantedness. The model of this process sketched prevoiusly requires that agents in a group can observe each other’s relevant categorizations. The intense interaction and communication that characterize scenes supply the needed opportunity.

Insofar as meanings diverge for members of the scene and the rest of the world, “disfluent” exchanges require effort at clarification over the boundary of the scene. ¹¹ Sorting out misunderstandings and disagreements requires effort to articulate, discuss, share, compare, and contrast ideas and experiences. In other words, such situations can be characterized as involving high-energy states.

The onset of taken-for-grantedness lowers the collective energy state. Once members assume they have (nearly) the same meaning for the key coordinating concept, they are less likely to engage in discussion and debate about it. For this reason, we restrict the meaning of scene to the higher-energy state characterized by a lack of taken-for-grantedness.

We introduce a predicate to express the idea that the membership that attends to a cluster is exploring its meaning, seeking to understand how the cluster differs from what is usually encountered in the focal world. Let EXP(l, M(l)) indicate “the membership M(l) is actively exploring the meaning of the cluster labeled l.” The high-energy activity of exploring meaning by introspection and communication with others is inconsistent with the low-energy state characterized by general taken-for-grantedness.

We now turn to a formal definition of the scene.

The hazard of emergence of a scene is the limiting probability that those who attend to a cluster begin this search for meaning. So we express the hazard that a cluster becomes a scene as follows (here and in what follows, we must make the time points explicit in the notation).

λ ( W , t ) = P r ( E X P ( l , M * , t + u ) | ¬ E X P ( l , M * , t ) ∧ ¬ T F G ( l , M * , t ) ] ) u .

(4)

Stage 3: Emergence of a Novel World

Once a cluster has emerged, there are two labels in the picture: c and l. The two labels have a different standing: c is associated with a taken-for-granted concept, but l has only an extensional collective meaning. The last stage in the emergence of a novel world is for l to gain an intensional meaning, to become paired with a new taken-for-granted concept.

According to Definition 4, a scene is not a world (because its core concept is not taken for granted), but it would become one if the taken-for-grantedness grew to reach the threshold ω. The conversion of a scene into a world occurs if and when its membership takes for granted the meaning of the coordinating concept. Therefore, we define the hazard of the emergence of a world as follows.

μ ( W , t ) ≡ P r ( W O R L D ( W ′ , t + u ) | ∀ v [ ( 0 ≤ v < u ) → S C E N E ( S , v ) ] ) u ;

≡ P r ( T F G ( l , M * , t + u ) | ∀ v [ ( 0 ≤ v < u ) → P r ( ¬ T F G ( l , M * , v ) ] ) u ;

≡ P r ( G ( l , M * , t + u ) | ∀ v [ ( 0 ≤ v < u ) → P r ( G ( l , M * , v ) < ω ] ) u .

The first line in this definition gives a literal statement of the limiting probability of a transition from a scene to a world. The second line gives a logically equivalent restatement using Definition 4, which holds that the only difference between a scene and a world is the lack of taken-for-grantedness of the coordinating concept of a scene. The third line gives an equivalent statement using Meaning Postulate 1.

Transition 1: Arrival of Distinctive Object Clusters in a World

What properties of a world make it likely to spawn clusters of objects similar to each other and dissimilar from those in the rest of the world? Producers’ decisions and actions shape the features of objects, so we focus on producers. Producers are generally tied to other producers. They share new ideas with each other, and sharing new ideas in subgroups of producers can result in new clusters of objects. From this perspective, the degree of localization of social ties, generally called “network clustering” (Holland and Leinhardt 1971; Watts and Strogatz 1998), plays a key function. Clusters in a network of producers result in producers making objects that are similar to each other but different from the rest of the objects in the world.

The experiences, interactions, and communication shared in a group of producers are instrumental in achieving consensus on concepts. Research in cognitive science suggests that repeated interactions allow individuals to discuss and integrate different experiences and knowledge and to derive shared abstract representations of a problem (Fjaellingsdal et al. 2021). Sociological research has developed arguments consistent with this idea. Farrell (2003) studied groups of collaborators in art, science, and politics. These groups, which he called “circles,” are small scenes of peers who, through periods of dialogue and collaboration, construct a collective vision on how to produce new kinds of artworks, literary works, and social reform actions.

As Farrell’s (2003) analysis shows, the escalating reciprocity among scene members who work together leads them to experiment and discover new ideas or techniques that none would imagine alone. Members of circles generally show commonalities in beliefs, attitudes, and values. Their communication reinforces such commonalities so that they cohere into consistent cultural assumptions. These conditions appear to facilitate cognitive consensus: “[T]hinking aloud together, the collaborative process draws on each other’s memories, ideas, and thought processes. They operate almost as one mind” (Farrell 2003:285).

We formalize these ideas in terms of the coefficient of clustering in the network of ties among a world’s producers (in notation, PC). Our main line of argument here links the rise of clusters of objects to the degree of producer clustering. Producer clustering is measurable with the clustering coefficient, or degree of “community” structure as it is described in contemporary network science (Girvan and Newman 2002).

In the foregoing equation, we use a symbol ↑ to denote a positive monotonic temporal relationship between the term to the left and the one to the right. More specifically, φ ↑ ψ means that if the level of ψ is the same for 2 units, say x and x′, at a time point and for a subsequent interval φ(x) > φ(x′), then ψ(x) > ψ(x′) at the end of the interval. The Appendix provides the formal definition.

What accounts for the high clustering of producers? We propose that heterogeneity plays an important role. A producer network with high social heterogeneity is likely to fracture into relatively disconnected clusters due to homophily effects. Homophily draws together socially similar producers. When the overall level of heterogeneity is high, distinct clusters of producers form that are more similar within and more dissimilar between.

A cluster, by definition, is characterized as having a relatively high level of interaction (Ertug et al. 2022) and communication (Bang and Frith 2017). Evidence consistent with these claims comes from studies at multiple levels of analysis. Sociological research at the individual or dyadic level finds that culturally similar individuals are more likely to voluntarily sort into social connections (Lizardo 2006; Mark 1998). At the meso level, Farrell (2003:285) found that more social and cultural similarities among peers in professional collaborations were positively associated with the formation of groups, particularly egalitarian groups. For example, members become more knowledgeable about each other’s work. They provide intellectual, emotional, and material support helpful for producing new kinds of objects and developing collective meaning. These groups also stand out from the rest, presenting what they do as an alternative—sometimes even an opposition—to the status quo. This situation is positively associated with homogeneity within producer clusters and heterogeneity between them and with the degree of clustering in the overall producer network.

Postulates 3 and 4 warrant the main result about the effect of heterogeneity in clustering.

The proof of this proposition, and most that follow, applies the chain (or cut) rule: If φ, ψ, and χ are formulas, then φ → ψ and ψ → χ imply φ → χ. We supply proofs for the other cases.

Transition 2: The Emergence of Scenes

The previous stage focuses on the arrival of clusters of objects and producers. Cognitive work is involved in this process, with producers thinking about their activity and sharing their experiences with their peers. It does not necessarily follow that clustering leads to a collective representation of these objects and producers by the full membership.

How does social structure contribute to the likelihood a cluster gets conceptualized by a group? Hannan et al. (2007) argue that agents are unlikely to engage in cognitive and social effort to coordinate on a new label unless the cluster is relatively distinctive and large. Distinctiveness matters because it improves perception and comprehension (Murphy 2002). Distinctive clusters are sets of objects that are similar to each other, closely spaced in the semantic space, and distant, on average, from objects in the parent world. Size also matters because very small clusters (e.g., songs by a single artist recorded at nearly the same time or publications of a single research group about the results of related experiments) will generally have the greatest average similarity. The principles of cognitive economy, which discourage the formation of a great multiplicity of concepts for a world, imply that very small clusters are unlikely to be conceptualized. However, very large clusters are also unlikely to be conceptualized because they are unlikely to be distinctive from the rest of the world. Due to these opposing forces, clusters are most likely to be conceptualized at some middle levels of size and distinctiveness. For a Bayesian concept learner, this is a rational way to make sense of the world (Anderson 1991; Dasgupta and Griffiths 2022; Tenenbaum and Griffiths 2002).

This conclusion is similar to Rosch’s claim about the importance of basic-level concepts (Rosch et al. 1976). Rosch argued there is a trade-off between descriptive accuracy and parsimony. Suppose we want to use concepts that provide detailed and accurate distinctions. To do so, we would use very narrow concepts that create very high similarity among the items included. However, this cognitive strategy involves making a very large number of conceptual distinctions. The generally accepted view holds that humans are cognitive misers who seek to economize the use of scarce cognitive resources; this results in a tendency to form what Rosch called basic-level concepts. “Chair,” for example, is a basic-level concept; people find it easier to use “chair” than “furniture” (higher level) or “bar stool” (lower level). A large body of research supports Rosch’s claims (Murphy 2002).

We now build on the static image developed in this previous work using the notion of salience. Taylor and Fiske (1978) defined (perceptual) salience as the quality of a stimulus that makes it prominent, conspicuous, or otherwise noticeable compared with its surroundings; they describe salience as the “figure” that stands out against the less noticeable “ground.” Let salience(c, m, t) be a nonnegative real-valued function that records the perceptual salience of the object cluster k at time t for individual member m, and let Salience(t) denote the average salience of the focal cluster for members at time t.

Transition 3: The Emergence of Novel Worlds

A novel world is more likely to emerge from a scene when participation in it is more stable and coordinated. High consensus on the collective concept underlies such stability and coordination. This consensus is achieved when the taken-for-grantedness of the concept reaches a high level, which, as Berger and Luckmann (1966) argue, gives “cognitive validity” to shared meanings.

Empirical network science suggests that systematic engagement within a group generally increases the likelihood of consensus (Baronchelli 2018). However, sociological research following Simmel (1904) suggests that interaction and communication can also spark disagreement and cause conflict, even division within a group. Disagreement can arise from divergence in members’ vision of the scene as its activity becomes more intense. Or preexisting disagreement, not previously recognized, can become apparent from more active discussions among members that reveal different motives for participating in the scene. Or disagreement can reflect competition to gain higher status within the scene. The drive for control over interpretation of the activity can precede or be the by-product of scene emergence. Either way, disagreement can result in scene members developing different interpretations (concepts).

We do not need to adjudicate between these rival claims. Either path can yield the pattern we claim. On one path, engagement allows many opportunities to learn categorizations of other members. If these categorizations generally agree, possibly due to the updating of concepts to move closer to the group, then the resulting taken-for-grantedness will be high (Hannan et al. 2019). On another path, members who find their categorizations do not agree with the consensus are likely to leave the scene.

We denote the average level of engagement for members of a scene as Eng(S). The main intuition is that high average engagement promotes the development of extensional agreement for the coordinating concept.

Now we have implications that connect member heterogeneity with extensional agreement and the hazard of emergence.

Proposition 1, Lemma 1, and Definition 6 imply the main result.

We want to develop the implications of the argument chain that warrants Proposition 4 for the hazard of emergence. It seems intuitive that the higher G at one time increases the likelihood that G at a later time will have crossed the threshold ω. However, this does not follow logically from the information contained in the argument. One would need a model of the dynamics of G to learn the conditions under which intuition can be proven. Lacking such a model, we offer a hypothesis that builds on the argument behind the proposition but does not follow logically from it. We do this so we can tie the argument back to the hazard of emergence.

In stating the hypothesis, we need to impose the condition that G lies below the threshold for TFG, denoted here by ω, during the interval that ends just before the hazard is evaluated because the hazard is undefined otherwise. We do this as follows (the Appendix explains the notation):

Role Heterogeneity in Scenes

Social heterogeneity, as discussed previously, concerns sociodemographic characteristics. Another relevant form of heterogeneity involves role differences among scene members. When a high proportion of members adopt the producer role, the membership engages in conceptual work and responds to one another’s ideas. One can expect communication to flow more freely and openly.

Participating in a scene as a producer does not simply mean making an object and presenting it to an audience. Producing something novel requires several activities that take time and effort. Research on creativity suggests the production of novel objects is a multistage process (Mumford 2003). The production process starts with investing effort in learning and practicing the knowledge, skills, and expertise for work in a domain. After this preparation stage, ideas can flow through conscious reflection or unconscious incubation. A stage of insight follows where a producer experiences the emergence of new ideas. Subsequently, the ideas are evaluated to determine whether to discard, retain, or review them. The final stage is the externalization of an idea in a concrete and observable form.

Producers thus engage with a concept before they make an object, and the very activity of making the object also results in engagement. Nobel laureate Morrison (1993) described herself as someone who “practices and practices and practices,” and by her own admission, it was this sustained application of ideas that made her aware of formal structures in her art and promoted literary inventions.

The practice of production also contributes to agreement about the collective concept. Farrell (2003) studied groups of scientists, social activists, and artists, including the Impressionists, who in the 1860s challenged the rules of French academic painting. The Impressionists lived and worked in proximity; they often painted alongside one another, observing and commenting on each other’s work. They participated in aesthetic experimentation, collectively judging their innovations, incorporating some and rejecting others, and effectively working out a consensus on what their new art was and was not. Farrell (2003) calls this engagement process “instrumental intimacy,” a situation in which individual members align their cognitive processes. When such alignment occurs, group members feel validated in challenging established concepts and authority because their individual ideas “feel” stronger because they are shared by others in the group. In such social contexts, high engagement sustains the scene, and the associated shared experience facilitates consensus on the focal concept.

Because producers are audience to one another, our model does not require the presence of nonproducer scene members for a world to emerge. In practice, many scenes include nonproducers. Members of a scene not directly involved in production, of course, engage with objects and their producers. They communicate and interact. Some of these members develop enough expertise to become intermediaries, such as professional critics paid to share their assessments and opinions with the public. At the same time, nonproducers have less access to and know less about the production activity than producers themselves. In scientific worlds, the output of academic knowledge looks fully interpretable; nonetheless, scientists find it illuminating to discuss their work with their peers. In seminars or project collaborations, they can share their discovery process and discuss ideas they explored but that did not work out or results that do not get reported in research publications.

More direct knowledge of the production process contributes to shared participation in an activity and agreement about what is or is not part of that activity. However, with a larger share of nonproducers, fewer scene members will have developed an understanding of the scope of the preproduction process and therefore share all the relevant information. Cognitive processes are less aligned across the membership as a result, and extensional agreement will also be lower. In this situation, different understandings and perspectives can coexist, which we call heterogeneity in orientation (in notation, OHet).

Because we assume that producers also adopt the audience role, we implement the intuition described in the preceding paragraphs in terms of the proportion of membership in a scene only in the audience role ¹² :

A − o n l y ( M ) = | M \ P | | M | .

Now we turn to the postulate that codifies our intuition that proliferation of nonproducer members in a scene lessens engagement by some producers in introspective and conceptual work and in interaction and communication that sustain common mental representations. In general, less engagement can undermine consensus among producers and reduce the chance of world emergence.

There are several reasons to expect that greater heterogeneity in orientation will reduce agreement about what is and is not c (extensional agreement). First, such divergence will cause networks of producers to fragment, thereby reducing opportunities to discuss marginal objects and possibly reducing agreement. Divergence in orientations will also generally cause fractions to pay attention to different (new) objects. Finally, nonproducer scene members might activate different sets of motivations for engaging with the scene (e.g., market success in a purely aesthetic activity), which can shape members’ perspectives on the focal activity and their patterns of collaboration.