1. Simple, fundamental concepts from network science

Network science is an emerging discipline that formalizes the study of complex systems, which are those composed of many parts whose interactions are heterogeneous enough that they cannot be accurately modeled using mean-field approaches (Newman, Reference O’Craven, Downing and Kanwisher2011). A useful way to represent these systems is as a network, where a part of the system is referred to as a network node (and often visualized as a ball in ball-and-stick diagrams), and where interactions or relations between parts of the system are referred to as network edges (and often visualized as sticks in ball-and-stick diagrams). Networks are naturally mapped onto mathematical objects called graphs (Bollobás, Reference Bollobás2002), and can be manipulated and studied straightforwardly by encoding them in adjacency matrices (Newman, Reference Newman2010). A single adjacency matrix A is an N-by-N matrix, where N is the number of nodes in the graph (or network), and where each ijth element of the matrix gives the strength of the relation between node i and node j. From the structure of such an adjacency matrix, one can learn about a system’s organization, make educated guesses about its function, and build simple models of its development, growth, or evolution (Watts & Strogatz, Reference Watts and Strogatz1998).

When representing a system as a network, the first challenging question facing the curious person is: “What is the right subdivision of this system into parts?” which amounts to asking, “What is a node?” The question is a historical one, being reminiscent of Socrates’ penchant for diairesis, the practice “of dividing things again by classes, where the natural joints are, and not trying to break any part, after the manner of a bad carver” (Plato 1925, p. 265e). Answering this question can be difficult because many systems can be subdivided into rather large parts, rather small parts, or any scale in between. It is quite important to surmount this difficulty because from the choice of nodes stems the choice of edges (Butts, Reference Butts2009): the sort of interpart relations that can be studied. It is perhaps unsurprising that—in practice—the most useful subdivision of a system into parts depends greatly on the scientific question motivating the study, and whether that question can be isolated to a specific scale of the system’s structure or function. In the context of the human brain and human behavior, there certainly exist some cases in which a hypothesis can be fine-tuned to address natural processes occurring at a single scale. However, many other hypotheses cannot be simplified in this way, and must instead be interrogated in a cross-scale manner.

A natural complement to the formulation of a multiscale hypothesis is the construction of a multiscale network. Take, for example, the primary organ of human curiosity: the human brain can naturally be divided into cortical and subcortical areas whose boundaries can be drawn either by using anatomical information such as cytoarchitecture (Brodmann, Reference Brodmann1909), or by using functional information such as patterns of activity (Glasser et al., Reference Ghosh and Deriche2016). Each of these parcels is thought to perform specific computations or produce specific cognitive functions, with subdivisions into larger parcels mapping on to coarser functions and subdivisions into smaller parcels mapping on to finer functions (Betzel & Bassett, Reference Betzel and Bassett2016). The structural connectivity between parcels can be estimated from diffusion imaging data, which offers information regarding the location and strength of white matter tracts physically linking cortical and subcortical regions (Ghosh & Deriche, Reference Glasser, Coalson, Robinson, Hacker, Harwell, Yacoub and … Van Essen2016). In a complementary analysis, functional connectivity between parcels can be estimated from functional neuroimaging data, which offers information regarding how similar temporal fluctuations in activity are in two parcels (Craddock, Tungaraza, & Milham, Reference Craddock, Tungaraza and Milham2015). At smaller spatial scales, structural connections can be defined by synapses between neurons (Kleinfeld et al., Reference Klimm, Bassett, Carlson and Mucha2011); at finer temporal scales, functional connections can be defined as correlations between trains of action potentials (Brody, Reference Brody1999). The multiscale network of the human brain houses rich information about how complex patterns of thought arise, and how individual differences in neurophysiology can produce individual differences in personality traits such as openness to experience (Beaty et al., Reference Beaty, Kaufman, Benedek, Jung, Kenett, Jauk and … Silvia2016), manners of production such as creativity (Beaty, Benedek, Kaufman, & Silvia, Reference Beaty, Benedek, Kaufman and Silvia2015), and behaviors related to knowledge acquisition such as information seeking (Scherer, Taber-Thomas, & Tranel, Reference Scherer, Taber-Thomas and Tranel2015).

2. Network representations of knowledge

The complex and multiscale organization of the brain supports our curious human abilities, whereby we secure new knowledge, acquire language(s), and build models of our external world. What is particularly apropos about this fact is the striking conceptual symmetry between the organ of curiosity and the object of curiosity. Indeed, in Webster’s (Reference Webster1828) Dictionary of the English language, knowledge is defined as “a clear and certain perception of that which exists, or of truth and fact; the perception of the connection and agreement, or disagreement and repugnancy of our ideas.” Indeed, without adjudicating between correspondence and coherence epistemologies, it is possible to explore individual and collective epistemic networks as belief suites that are produced by both the pressure for beliefs to cohere with one another and the prompt that they correspond to things in the world (Grim, Modell, & Breslin, Reference Grim, Modell and Breslin2017). In other words, knowledge can be represented as a network of connections (or relations) between ideas, concepts, or bits of information just as the brain can be represented as a network of connections between neural units that process, store, and recall that information.

A simple yet concrete treatment of knowledge as a network can be intuitively considered in the context of language. The units of language span from small phonemes through syllables to words, and each scale at which such network nodes can be defined has a distinct representation in the human cortex (Peeva et al., Reference Perfahl, Hughes, Alaracon, Maini, Lloyd, Reuss and Byrne2010). At the smallest scale, any two phonemes (two nodes in the language network) can be linked by a network edge weighted by the probability that those two phonemes are found beside one another in a given language. This edge weight can be encoded as the value of the ijth element of the adjacency matrix A for that language network, and the complete pattern of all pairwise probabilities provides information about the architecture of the language itself. From this information, one can seek to derive rules by which grammars arose in human languages, and one can also define new rules that lead to artificial grammars (Fitch & Friederici, Reference Fitch and Friederici2012). At a larger scale, any two lexemes (one word or several words, considered as an abstract unit) can be linked if they are phonological neighbors (Luce & Pisoni, Reference Maddi and Berne1998), and the network composed of such relations provides important information about how words are retrieved from human memory (Vitevitch, Reference Vitevitch2008).

Thus, language—our most common formal means of encoding, storing, and transmitting knowledge—can be usefully represented as a multiscale network. However, are there natural (yet formal) ways of representing knowledge itself as a network, and is such a representation useful in understanding human curiosity? Initial answers to these questions can be obtained using semantic networks, where nodes represent concepts and edges represent semantic relations between them (Sowa, Reference Sowa1987). Our understanding of the architecture of semantic networks has evolved appreciably over the last several decades. An early study in the 1960s suggested that semantic networks were trees (in the sense of graph theory) (Collins & Quillian, Reference Collins and Quillian1969), although a couple studies a decade later suggested that many sets of concepts are not well characterized by such exact hierarchical architecture (Keil, Reference Kenett, Anaki and Faust1979; Slobin, Reference Slobin1973). Capitalizing on expanded computational capabilities and more extensive data collection efforts, studies at the turn of the century replaced the tree hypothesis (Bales & Johnson, Reference Bales and Johnson2006) with evidence for two other architectural properties thought to optimize formation and search of semantic memory (Anderson, Reference Anderson2000): (i) small-world organization which can be intuitively described as the presence of strong local clustering alongside a few long-distance connections, and (ii) scale-free organization, indicated by the distribution of node degrees (number of connections emanating from a node) following a power law (Steyvers & Tenenbaum, Reference Steyvers and Tenenbaum2005).

The exact nature of a semantic network’s architecture depends to some degree on the measure of semantic relatedness chosen to define the network’s edges. Many possible definitions exist, including those based on estimates of causal relations (Danks, Reference Danks2014). While including multiple edge definitions in a single network is possible (using multilayer network approaches) (Kivelä et al., Reference Kleinfeld, Bharioke, Blinder, Bock, Briggman, Chklovskii and … Sakmann2014), arguably a simpler place to start is to choose a single measure of semantic relation such as similarity in meaning. Such a choice narrows the object of inquiry from a semantic relatedness network to a semantic similarity network (Harispe, Ranwez, Janaqi, & Montmain, Reference Harispe, Ranwez, Janaqi and Montmain2015). For example, one could represent single words as nodes, and link two nodes with an edge if they are listed as synonyms in a dictionary; this approach would offer a single semantic similarity network for an entire language, as used by a population. Alternatively, if one is interested in studying individual differences in semantic networks, one could perform a set of behavioral experiments in which human volunteers are asked to list a sequence of words such that temporally contiguous words in the sequence have similar meanings (Kenett, Kenett, Ben-Jacob, & Faust, Reference Kenett, Kenett, Ben-Jacob and Faust2011).

Measuring, quantifying, and understanding the knowledge network of a single human is a necessary first step toward a principled study of how that knowledge network was built, and what role the practice of curiosity played in its construction. Common empirical tools to estimate knowledge networks in a single human include tests requiring verbal responses and tests requiring written responses. Particularly, successful examples of the former include free association tasks (Nelson & Zhang, Reference Newman2000), and tasks in which volunteers are asked to narrate tales either from their imagination or inspired by visual aids; such tasks can also be used to assess alterations in semantic network structure that accompany cognitive deficits associated with neurological disorders or psychiatric disease (Drummond et al., Reference Drummond, Coutinho, Fonseca, Assunção, Teldeschi, de Oliveira-Souza and … Mattos2015; Lee et al., Reference Leherissey2017; Renz et al., Reference Renz, Lorch, Milich, Lemberger, Bodner and Welsh2003; Spitzer, Reference Spitzer1993). Particularly, successful examples of the latter include posthoc analyses of an individual’s written work, in any form in which it is accessible. From both verbal and written data, one can also construct a second type of semantic network known as a word cooccurrence network (Lazaridou, Marelli, & Baroni, Reference Lee and Orsillo2017) in which words (nodes) are connected to one another if they occur less than some number of words away from each other. In principle, this approach could be used to study changes in semantic networks over an author’s lifetime, or over the course of a psychiatric disease.

3. Modeling how networks grow

While understanding the architecture of a human’s knowledge network at a single instant in time would be quite useful, that human’s personality may be even more associated with how they built that knowledge network up over time. If one wishes to understand the building of a knowledge network, one could consider developing a mathematical model of network growth, and fitting the parameters of such a model to empirically measured data. For example, one might wish to choose a rule by which new nodes in the network are acquired, and one might also wish to choose a rule by which new edges in the network are acquired, by linking existing nodes, linking new nodes, or linking a new node and an existing node. One might also wish to choose a rule by which nodes or edges are removed (a process related to network aging), or in which the strength of edges change (a process related to network plasticity). In networks that evolve by both additions and deletions of nodes and edges, it becomes interesting to consider whether there are conservation laws that balance constraints (e.g., energetic or spatial) over time. These considerations are certainly not exhaustive, but form a good set from which to start building a model of network growth.

To gain an intuition for how one might write down a model for the growth of a knowledge network, we first discuss a few canonical benchmark models built on simple topological principles. One of the simplest (and arguably most well-known) network growth models is the preferential attachment model which was first defined by Price (Reference Price1976), and later re-discovered by Barabási and Albert (Reference Barabási and Albert1999) with slightly different parameter settings. Generally, this network growth model begins with an edge linking node i to node j. Next, a new node is added by placing edges between the new node and m previously existing nodes, where these existing nodes are chosen with a probability related to their degree. The outcome of this process is a network in which a few high-degree nodes gain an even greater degree (“the rich get richer”), while the majority of nodes maintain a relatively low degree, as evidenced by a right-skewed degree distribution. The preferential attachment model can be altered by biasing the choice of the m previously existing nodes. For example, the affinity model creates a hierarchical organization by specifying a parameter that takes on a different value at each node; the m existing nodes are then chosen with a probability related to their affinity parameter (Klimm, Bassett, Carlson, & Mucha, Reference Knutson, Adams, Fong and Hommer2014).

While the preferential attachment model has proven relevant for understanding the sizes of cities (Simon, Reference Simon1955), the wealth of rich individuals (Bassett & Bullmore, Reference Bassett2016), the number of citations given to seminal publications (Newman Reference Newman2002), and the number of links to World Wide Web pages (Barabási and Albert, Reference Barabási and Albert1999), many real-world and particularly biological systems grow under constraints and pressures that do not allow the formation of very high-degree hubs. In the context of knowledge networks, it is intuitively plausible that such constraints could include limited memory and learning capacity, or spatial encoding constraints in the brain. Indeed, special consideration has been given to adding constraints to network growth models of neural systems, where the probability of two neurons synapsing onto each other depends upon the physical distance between them (Bassett & Bullmore, Reference Bassett2016). One can incorporate this fact in a distance drop-off growth model, where nodes are placed randomly in a Euclidean space, and edges are placed between two nodes with a probability inversely related to their spatial separation (Klimm et al., Reference Knutson, Adams, Fong and Hommer2014). The outcome of this growth process is a network with a degree distribution that is reminiscent of those observed empirically, and with clear assortativity (Newman, Reference Newman2002), or the preference for low-degree nodes to connect to other nodes of low degree, and high-degree nodes to connect to other nodes of high degree. Such models are useful both at the small scale of neurons, and at the large scale of cortical areas (Bullmore & Bassett, Reference Bullmore and Bassett2011).

Constraints on network growth may either directly or indirectly impinge on node–node connectivity. The constraint of physical distance between neurons discussed is an example of a direct constraint. An example of an indirect constraint is the growth (or otherwise temporal variation) of a tissue that either surrounds the network or serves as a substrate for the network. This sort of indirect constraint has recently been modeled in the context of vasculature networks, which are biological distribution systems that transport nutrients across spatial distances to support the health of an organism (Modes, Magnasco, & Katifori, Reference Nelson and Zhang2016). Here, the growth of the tissue that the vasculature supports is modeled as one dynamical process, and the growth of the vasculature network itself is modeled as a second dynamical process, coupled to the first (Ronellenfitsch & Katifori, Reference Ronellenfitsch and Katifori2016). Of course, one could also expand the model to include finer-scale biophysical factors as well (Perfahl et al., Reference Ives-Deliperi, Howells, Stein, Meintjes and Horn2017).

How might these notions of topological wiring rules, physical pressures, and direct versus indirect constraints assist us in understanding how knowledge networks grow? Let us first consider this question in the context of semantic networks, where the majority of efforts have focused over the last few years. Steyvers and Tenenbaum (Reference Steyvers and Tenenbaum2005) offer a model of semantic network growth whereby nodes (words) are acquired according to a rule that seeks to maximally differentiate nodal patterns of connectivity. Over long time scales, this model produces a network with a scale-free degree distribution and small-world organization, which they suggest provide good fits to existing empirical data. Hills, Maouene, Maouene, Sheya, and Smith (Reference Hills, Maouene, Maouene, Sheya and Smith2009) offer a preferential attachment model of word–word association networks to understand how children acquire nouns in the first few years of life; the model incorporates the frequency with which words are experienced, the diversity of a word’s phonological neighbors, and the relation between new words and existing words in the immediate environment. We speculate that such models would be a useful place to start to understand knowledge network building motivated by curiosity. Moreover, although both of these models are suggested to apply to humans generically, it may also be useful to consider variations of these or related models that would fit one individual more than another individual. Such an effort could shed light on individual differences in semantic networks, which are pronounced in empirical studies, and have previously been linked to a participant’s personality and creativity (Kenett, Anaki, & Faust, Reference Kidd and Hayden2014).

4. Informing models of network growth with an individual’s practice of curiosity

There are myriad ways in which a knowledge network could grow, and the exact nature of that growth could be passive (a person is exposed to concepts by their caregivers speaking to them) or active (a person purposefully allots 1 hr/day to studying an encyclopedia, and taking vocabulary tests). The previous models of semantic network growth fall in the former category (passive), while here we turn our focus to understanding how the practice of curiosity (active) can grow and reconfigure a single individual’s knowledge network. Exactly how such knowledge network reconfiguration should be modeled is an open area of scientific inquiry that will require novel experimental paradigms, as we discuss in more detail later.

Admittedly, a portion of the literature assumes that curiosity is an inborn trait (Litman & Spielberger, Reference Loewenstein2003), such that one has a natural degree of curiosity just as one has a natural degree of irritability (Stanton & Watson, Reference Stanton and Watson2017) and mindfulness (Zhuang et al., Reference Zhuang, Bi, Li, Xia, Guo, Chen and … Qiu2017). Yet, both irritability and mindfulness vary over time, and mindfulness training is becoming an increasingly popular method to alter one’s patterns of executive capacities including decision making (Kirk et al., Reference Kivelä, Arenas, Barthelemy, Gleeson, Moreno and Porter2016), memory (Ives-Deliperi, Howells, Stein, Meintjes, & Horn, Reference James2013), and cognitive flexibility (Lee & Orsillo, Reference Lee, Martin, Hogan, Hano, Gordon and Losh2014) by altering brain function (Scheibner, Bogler, Gleich, Haynes, & Bermpohl, Reference Scheibner, Bogler, Gleich, Haynes, John-Dylan and Bermpohl2017). Similarly, curiosity can vary over time (Sternszus, Saroyan, & Steinert, Reference Sternszus, Saroyan and Steinert2017), and can be altered by different environments (Tripathi, Sarkate, Jalgaonkar, & Rege, Reference Tripathi, Sarkate, Jalgaonkar and Rege2015; Berson & Oreg, Reference Berson and Oreg2016), suggesting the possibility of practicing curiosity to change, grow, and enhance one’s knowledge network. In his reflections on education, John Dewey suggests that knowledge is a body of learned connections between things. Geographical knowledge entails an understanding of spatial connections, while historical knowledge entails an understanding of human connections (Dewey, Reference Dewey2011). Curiosity, then, is the tendency to make connections between things perceptible. These connections are built in and through experience. It is therefore the educator’s task to facilitate experience, encourage curiosity, and thereby enable the growth of knowledge networks in and among their students. But how?

To make this discussion more meaningful, we must first offer an operational definition of the practice of curiosity. Our operational definition is the performance of mental tasks characteristic of curious thought (Bassett, Reference Bassett and BullmoreForthcoming). Curiosity training could then be said to be a process whereby individuals engage in the practice of certain mental states of curiosity, as well as of certain transitions between states that naturally occur along a direction of questioning. One could practice engaging different foci of curiosity, or performing different types of curious search (Zurn, Reference ZurnForthcoming). Perhaps even more fundamentally, one could simply make time to be curious, and to act on curious thoughts. From a network perspective, a person’s practice of curiosity amounts to a walk—either random (Pearson, Reference Peeva, Guenther, Tourville, Nieto-Castanon, Anton, Nazarian and Alario1905) or biased (Volchenkov & Blanchard, Reference Volchenkov and Blanchard2011)—along one’s knowledge network, choosing which new nodes to acquire and which new edges to add, either as independent units or as subgraphs or motifs (Shen-Orr, Milo, Mangan, & Alon, Reference Schapiro, Rogers, Cordova, Turk-Browne and Botvinick2002). One could also model the practice of curiosity as an explicitly physical dynamical process, where one could purposefully leap from their existing knowledge network into an external pool of the knowledge network of the general public (or some canonical “truth” network) in search of a specific expected or nonspecific unexpected idea. The way in which a human walks, and the webs that a human seeks to build, are likely to depend in quite a foundational way on our personalities, our prior experiences, and our mental capacities.

Let us now discuss a few important considerations when building a network growth model informed by the practice of curiosity. We must begin by choosing the sort of node for which we search: more likely an idea, or a rather broad concept, than a single word or word form. Next, we must choose the type of edge that we wish to place: perhaps a notion of similarity, or causality, or analogy. It would also be useful to determine if there are characteristics of nodes that would make us more likely to place an edge: for example, perhaps one prefers connecting distant versus close-by ideas, or one prefers drawing top-down versus bottom-up relations. At a larger scale, we must choose whether and how we will marry the new node and/or new edge with the previously existing network. Are we working towards a dense, highly ordered graph? A sparse, fairly loopy graph? Are the architectural principles of the network consistent across the whole graph? Or do they vary? If they vary, do they vary in some meaningful way with properties of the ideas located in that section of the graph? With Dominic Widdows (Reference Widdows2004), we can ask about the distance between ideas, the geometry of the network, and the space in which the network exists, while with Peter Gärdenfors, we can ask: “What is the geometry of curious thought?” (Reference Gärdenfors2004), “How does it relate to one’s conceptual space?” (Reference Gärdenfors2014).

Perhaps we learn how to build knowledge networks from those around us, as we hear them question, as we see them search, or as we peruse their writings. If so, then the geometries we build may be not altogether unlike the geometries that our mentors and compatriots build. This symmetry of geometries is likely to be the case if knowledge network building is learned in the same way in which we learn the statistics of our environment (Rebuschat & Williams, Reference Rebuschat and Williams2012), a process supported by neural computations that encode either pairwise or higher-order relationships between concepts (Karuza, Thompson-Schill, & Bassett, Reference Karuza, Thompson-Schill and Bassett2016). By learning the practice of curiosity from other humans (Engel, Reference Engel2015), we learn which sorts of ideas others seek, and how they link those ideas together into larger and larger webs. The speed and success with which we learn the practice of curiosity from others could depend on the degree of reinforcement provided following our decisions and actions. Reinforcement learning, in which a learner is given feedback about the accuracy of their responses (Schultz, Reference Schultz2015), could serve to strengthen curious behavior as it is validated by another person.

To the degree that the practice of curiosity can be learned from others, it would be important to understand how current educational practice might already support that learning. Further, it would be important to determine whether and how we could alter educational practice to better imbue youth with a healthy practice of curiosity, according to their proclivities and appropriate to their stage of life. Are there optimal ways of transmitting information about what sorts of new network nodes to search for, what sorts of edges to use to link them, what sorts of architectures to fill out? Is the traditional lecture format conducive to such transmission? Would mentorship or apprenticeship approaches be more effective? Should the tutelage be implicit (merely viewing the practice of curiosity in others), or explicit (being told that one is learning how to practice curiosity), or both? Answering these questions will require additional work at the interdisciplinary intersection of network science, personality neuroscience, education, and curiosity studies.

5. Bridging from curious knowledge network building to underlying neurophysiology

What are the neural processes that support curious knowledge network building? Answering this question requires that we first consider neural representations of knowledge networks. Most early work in mapping representations of concepts or objects focused on single items, such as comparing and contrasting the representation of a house versus that of a face (O’Craven, Downing, & Kanwisher, Reference Oedeyer and Kaplan1999). This work motivated broader questions about how the representations between different objects or concepts are related to one another, and how that similarity might impact memory and by extension the growth of one’s knowledge space (see Xue et al., Reference Xue, Dong, Chen, Lu, Mumford and Poldrack2010, for an early empirical study and see Haxby, Connolly, & Guntupalli, Reference Haxby, Connolly and Guntupalli2014, for a recent review). In a pioneering study, Constantinescu, O’Reilly, and Behrens (Reference Constantinescu, O’Reilly and Behrens2016) recently demonstrated that the brain can organize concepts into a two-dimensional mental map, allowing conceptual relationships to be navigated in a hexagonal grid-like network code, similar to the manner in which humans navigate space (Hafting, Fyhn, Molden, Moser, & Moser, Reference Hafting, Fyhn, Molden, Moser and Moser2005). Exactly how that organization takes place—or how we learn to represent concepts in the brain and to encode their network of relationships—is an active area of inquiry. One posited mechanism for such learning is temporal contingencies (Karuza, Thompson-Schill, & Bassett, Reference Karuza, Thompson-Schill and Bassett2016). Indeed, recent evidence suggests that humans can infer the community structure present in networks of visual stimuli, when those stimuli are shown to the participant in a continuous stream defined by a walk on the network (Schapiro, Rogers, Cordova, Turk-Browne, & Botvinick, Reference Schapiro, Turk-Browne, Norman and Botvinick2013). Follow-up studies demonstrated that learning could be modulated by the type of walk taken through the network (Karuza, Kahn, Thompson-Schill, & Bassett, Reference Kashdan and Roberts2017), and tracked by the representations, activity dynamics, and connectivity of the hippocampus (Schapiro, Turk-Browne, Norman, & Botvinick, Reference Shen-Orr, Milo, Mangan and Alon2016).

The fact that the learning and appropriation of network structure in stimuli can be modulated by the temporal sequence of stimuli supports our hypothesis that one’s practice of curiosity (or the manner in which one samples knowledge space) will impact the type of knowledge network built. Yet, an important open question lies in what neurophysiological mechanisms might drive individual differences in these processes. In a comprehensive and thought-provoking recent review, Kidd and Hayden (Reference Kirk, Gu, Sharp, Hula, Fonagy and Montague2015) summarize recent work probing the biological function, mechanisms, and neural underpinning of curiosity. This body of work links curiosity with behavioral characteristics that differ across individuals, including our preferences for novelty versus familiarity (Kang et al., Reference Karuza, Kahn, Thompson-Schill and Bassett2009), for exploring our environment in search of new information versus exploiting existing information (Daw, O’Doherty, Dayan, Seymour, & Dolan, Reference Daw, O’Doherty, Dayan, Seymour and Dolan2006), and for the temporal resolution of uncertainty (Blanchard, Hayden, & Bromberg-Martin, Reference Blanchard, Hayden and Bromberg-Martin2015). While the neural mechanisms of curious behaviors are not fully understood, one particularly interesting line of evidence shows that self-reported curiosity tracks the activation of the caudate nucleus and the inferior frontal gyrus, both key players in the human reward circuit, whose function is heavily dependent on the neurotransmitter dopamine (Kang et al., Reference Karuza, Kahn, Thompson-Schill and Bassett2009). Interestingly, the nucleus accumbens—also consistently implicated in reward circuitry (Knutson, Adams, Fong, & Hommer, Reference Lazaridou, Marelli and Baroni2001)—was not activated. When an answer to the question that the participants were curious about was revealed, areas involved in learning and memory (such as parahippocampal gyrus and hippocampus) were activated, indicating the tight link between curiosity and learning (Kang et al., Reference Karuza, Kahn, Thompson-Schill and Bassett2009).

These separate lines of inquiry motivate future experiments tracking neural representations of concepts as human participants seek information about those concepts and interconnections between concepts, as well as experiments addressing the question of how individual differences in (i) the acquisition and change in neural representations, (ii) preferences for novelty, exploration, and uncertainty, and (iii) reward circuit activity might relate to one another.

6. Current frontiers

In the previous sections, we have reviewed a range of empirical studies across disciplinary boundaries that inform our formal framing of the practice of curiosity in terms of the mathematics of network science. However, we note that direct empirical studies that capitalize on this framework have yet to be undertaken. It is natural to begin by measuring the characteristics of human objects of curiosity. Are there commonalities between them? Are we more likely to search for an idea or a causal relation? How well can we articulate what we are searching for, verbally, pictorially, or in written form? What sorts of relations between these objects are we most likely to seek? And how does the topology of our network change as we practice curiosity? To what degree does curiosity add to versus reconfigure our knowledge networks? How are these knowledge networks, or their architectural properties, represented in the brain?

One fairly straightforward way to begin answering these questions is to conduct laboratory experiments with human volunteers in which we measure evolving knowledge networks. Such studies could evaluate changes in knowledge networks during explicit curiosity training or during intrinsic information seeking with little or no external constraints. These data could be used to test the hypothesis that individual differences in the practice of curiosity are reflected in individual differences in the knowledge networks that are grown. Further, one could test the hypothesis that the manner in which knowledge networks are grown is correlated with more commonly studied aspects of one’s personality. During such studies, one could also consider mapping the neural correlates of different sorts of walks along knowledge networks, both in their baseline form, and as they evolve over time. One could use these data to test the hypothesis that circuitry supporting reward processing and information-seeking behavior differ across individuals in a manner that maps onto individual differences in their practice of curiosity. A complementary alternative is to measure the evolution of knowledge networks in the written work of moderately prolific authors. While laboratory experiments could provide controlled environments in which to modulate curiosity training and knowledge network growth, and to link this information to underlying neurophysiology, they will likely be constrained to short time scales. By contrast, studies of authors (particularly those who are either nearing the end of their careers or deceased) could provide more ecologically valid accounts of knowledge network growth over longer time scales.

Experimental studies could be usefully complemented by theoretical studies developing simple mathematical models of the observed phenomena. The models currently developed to characterize the acquisition of nouns in young children may contain rules that are also relevant for the growth of knowledge networks in adult humans actively practicing curiosity. Yet, it is also likely that the network evolution characteristic of the practice of curiosity will require additional or altogether different growth rules mapping the purposeful reaching for distant ideas. In any case, such models could be parameterized directly from the empirical data. It would be particularly useful to determine whether best fitting parameter values differ for different individuals, at different stages of their life, with different brain architectures, and across individuals experiencing different levels of mental health.

7. Summary

In summary, this perspective seeks to develop and offer a formal framework for the study of curiosity as embedded in the joint disciplines of personality neuroscience and network science. We provide a short primer on network science and describe how the mathematical object of a graph or network can be used to map the items and their relations that are characteristic of bodies of knowledge, real and artificial grammars, and language. We discuss how networks can grow, and a few simple models that have been developed to better understand growth in various networks, including semantic networks. We offer an operational definition of the practice of curiosity, and discuss how that practice can be formalized as a process of network growth. We place particular emphasis on individual differences in knowledge network growth, informed by various aspects of personality and by our previous and current educational experiences. We outline important current frontiers in empirical measurement and theoretical model validation with the aim of developing concrete training regimens and educational practices in the future to enhance the practice of curiosity in youth.

8. Epilogue. Beyond curiosity: The general relevance of network science for personality neuroscience

We began this article by noting that the behaviors reflecting our personalities, and the neural drivers thereof, are fundamentally multivariate and characterized by complex temporal patterns of transitions between behavioral units. Moreover, we posited that network science offers a powerful conceptual framework and mathematical formalism for quantitatively describing, modeling, and explaining such patterns of behaviors, whether present in the domains of thought, decision, or action. The majority of our exposition focused on one particular domain of personality: curiosity, composed of both internal and external behaviors related to the acquisition of networks of ideas or concepts. Yet, the framework and formalism of network science are relevant across other domains of personality neuroscience more broadly.

Perhaps the most direct extension of the ideas we have described here lies in considering other time-varying behaviors of single humans. For example, one could use network science to understand the manner in which cognitive, interpersonal, or affective states relate to one another, similarly to the manner in which knowledge states relate to another. One could also extend these tools beyond a single individual and consider a group of individuals: what is the architecture of the network in which individuals (nodes) are connected by similarities in their personality traits (edges)? Does a person’s placement in that network relate to real-world outcomes? Finally, one could consider expanding beyond a single network to understand the relationships between networks. In probing cognitive domains of personality, one can ask how one’s internal knowledge network is instantiated in one’s physical brain network. In probing sociocultural domains of personality, one can ask how one’s brain network relates to one’s placement in their social network (Falk & Bassett, Reference Falk and Bassett2017). In the future, we envision that such studies of individual, group, and multiscale network architectures across various domains of personality will be increasingly important for understanding the structure and neurophysiological drivers of the human condition.