Divergent and Convergent Creativity Are Different Kinds of Foraging.

According to accounts of neural reuse and embodied cognition, higher-level cognitive abilities recycle evolutionarily ancient mechanisms for perception and action. Here, building on these accounts, we investigate whether creativity builds on our capacity to forage in space ("creativity as strategic foraging"). We report systematic connections between specific forms of creative thinking-divergent and convergent-and corresponding strategies for searching in space. U.S. American adults completed two tasks designed to measure creativity. Before each creativity trial, participants completed an unrelated search of a city map. Between subjects, we manipulated the search pattern, with some participants seeking multiple, dispersed spatial locations and others repeatedly converging on the same location. Participants who searched divergently in space were better at divergent thinking but worse at convergent thinking; this pattern reversed for participants who had converged repeatedly on a single location. These results demonstrate a targeted link between foraging and creativity, thus advancing our understanding of the origins and mechanisms of high-level cognition.

Brain responses to a lab-evolved artificial language with space-time metaphors.

What is the connection between the cultural evolution of a language and the rapid processing response to that language in the brains of individual learners? In an iterated communication study that was conducted previously, participants were asked to communicate temporal concepts such as "tomorrow," "day after," "year," and "past" using vertical movements recorded on a touch screen. Over time, participants developed simple artificial 'languages' that used space metaphorically to communicate in nuanced ways about time. Some conventions appeared rapidly and universally (e.g., using larger vertical movements to convey greater temporal durations). Other conventions required extensive social interaction and exhibited idiosyncratic variation (e.g., using vertical location to convey past or future). Here we investigate whether the brain's response during acquisition of such a language reflects the process by which the language's conventions originally evolved. We recorded participants' EEG as they learned one of these artificial space-time languages. Overall, the brain response to this artificial communication system was language-like, with, for instance, violations to the system's conventions eliciting an N400-like component. Over the course of learning, participants' brain responses developed in ways that paralleled the process by which the language had originally evolved, with early neural sensitivity to violations of a rapidly-evolving universal convention, and slowly developing neural sensitivity to an idiosyncratic convention that required slow social negotiation to emerge. This study opens up exciting avenues of future work to disentangle how neural biases influence learning and transmission in the emergence of structure in language.

Multimodality matters in numerical communication.

Modern society depends on numerical information, which must be communicated accurately and effectively. Numerical communication is accomplished in different modalities-speech, writing, sign, gesture, graphs, and in naturally occurring settings it almost always involves more than one modality at once. Yet the modalities of numerical communication are often studied in isolation. Here we argue that, to understand and improve numerical communication, we must take seriously this multimodality. We first discuss each modality on its own terms, identifying their commonalities and differences. We then argue that numerical communication is shaped critically by interactions among modalities. We boil down these interactions to four types: one modality can amplify the message of another; it can direct attention to content from another modality (e.g., using a gesture to guide attention to a relevant aspect of a graph); it can explain another modality (e.g., verbally explaining the meaning of an axis in a graph); and it can reinterpret a modality (e.g., framing an upwards-oriented trend as a bad outcome). We conclude by discussing how a focus on multimodality raises entirely new research questions about numerical communication.

Space in Hand and Mind: Gesture and Spatial Frames of Reference in Bilingual Mexico.

Speakers of many languages prefer allocentric frames of reference (FoRs) when talking about small-scale space, using words like "east" or "downhill." Ethnographic work has suggested that this preference is also reflected in how such speakers gesture. Here, we investigate this possibility with a field experiment in Juchitán, Mexico. In Juchitán, a preferentially allocentric language (Isthmus Zapotec) coexists with a preferentially egocentric one (Spanish). Using a novel task, we elicited spontaneous co-speech gestures about small-scale motion events (e.g., toppling blocks) in Zapotec-dominant speakers and in balanced Zapotec-Spanish bilinguals. Consistent with prior claims, speakers' spontaneous gestures reliably reflected either an egocentric or allocentric FoR. The use of the egocentric FoR was predicted-not by speakers' dominant language or the language they used in the task-but by mastery of words for "right" and "left," as well as by properties of the event they were describing. Additionally, use of the egocentric FoR in gesture predicted its use in a separate nonlinguistic memory task, suggesting a cohesive cognitive style. Our results show that the use of spatial FoRs in gesture is pervasive, systematic, and shaped by several factors. Spatial gestures, like other forms of spatial conceptualization, are thus best understood within broader ecologies of communication and cognition.

Do Metaphors Move From Mind to Mouth? Evidence From a New System of Linguistic Metaphors for Time.

Languages around the world use a recurring strategy to discuss abstract concepts: describe them metaphorically, borrowing language from more concrete domains. We "plan ahead" to the future, "count up" to higher numbers, and "warm" to new friends. Past work has found that these ways of talking have implications for how we think, so that shared systems of linguistic metaphors can produce shared conceptualizations. On the other hand, these systematic linguistic metaphors might not just be the cause but also the effect of shared, non-linguistic ways of thinking. Here, we present a case study of a variety of American English in which a shared, non-linguistic conceptualization of time has become crystallized as a new system of linguistic metaphors. Speakers of various languages, including English, conceptualize time as a lateral timeline, with the past leftward and the future rightward. Until now, this conceptualization has not been documented in the speech of any language. In two studies, we document how members of the U.S. military, but not U.S. civilians, talk about time using conventionalized lateral metaphors (e.g., "move the meeting right" to mean "move the meeting later"). We argue that, under the right cultural circumstances, implicit mental representations become conventionalized metaphors in language.

Where Does the Ordered Line Come From? Evidence From a Culture of Papua New Guinea.

Number lines, calendars, and measuring sticks all represent order along some dimension (e.g., magnitude) as position on a line. In high-literacy, industrialized societies, this principle of spatial organization- linear order-is a fixture of visual culture and everyday cognition. But what are the principle's origins, and how did it become such a fixture? Three studies investigated intuitions about linear order in the Yupno, members of a culture of Papua New Guinea that lacks conventional representations involving ordered lines, and in U.S. undergraduates. Presented with cards representing differing sizes and numerosities, both groups arranged them using linear order or sometimes spatial grouping, a competing principle. But whereas the U.S. participants produced ordered lines in all tasks, strongly favoring a left-to-right format, the Yupno produced them less consistently, and with variable orientations. Conventional linear representations are thus not necessary to spark the intuition of linear order-which may have other experiential sources-but they nonetheless regiment when and how the principle is used.

Today is tomorrow's yesterday: Children's acquisition of deictic time words.

Deictic time words like "yesterday" and "tomorrow" pose a challenge to children not only because they are abstract, and label periods in time, but also because their denotations vary according to the time at which they are uttered: Monday's "tomorrow" is different than Thursday's. Although children produce these words as early as age 2 or 3, they do not use them in adult-like ways for several subsequent years. Here, we explored whether children have partial but systematic meanings for these words during the long delay before adult-like usage. We asked 3- to 8-year-olds to represent these words on a bidirectional, left-to-right timeline that extended from the past (infancy) to the future (adulthood). This method allowed us to independently probe knowledge of these words' deictic status (e.g., "yesterday" is in the past), relative ordering (e.g., "last week" was before "yesterday"), and remoteness from the present (e.g., "last week" was about 7 times longer ago than "yesterday"). We found that adult-like knowledge of deictic status and order emerge in synchrony, between ages 4 and 6, but that knowledge of remoteness emerges later, after age 7. Our findings suggest that children's early use of deictic time words is not random, but instead reflects the gradual construction of a structured lexical domain.

Mastering algebra retrains the visual system to perceive hierarchical structure in equations.

Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

Of magnitudes and metaphors: explaining cognitive interactions between space, time, and number.

Space, time, and number are fundamental to how we act within and reason about the world. These three experiential domains are systematically intertwined in behavior, language, and the brain. Two main theories have attempted to account for cross-domain interactions. A Theory of Magnitude (ATOM) posits a domain-general magnitude system. Conceptual Metaphor Theory (CMT) maintains that cross-domain interactions are manifestations of asymmetric mappings that use representations of space to structure the domains of number and time. These theories are often viewed as competing accounts. We propose instead that ATOM and CMT are complementary, each illuminating different aspects of cross-domain interactions. We argue that simple representations of magnitude cannot, on their own, account for the rich, complex interactions between space, time and number described by CMT. On the other hand, ATOM is better at accounting for low-level and language-independent associations that arise early in ontogeny. We conclude by discussing how magnitudes and metaphors are both needed to understand our neural and cognitive web of space, time and number.

Doing arithmetic by hand: hand movements during exact arithmetic reveal systematic, dynamic spatial processing.

Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental "number-line", the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial-arithmetical bias, moreover, was distinct from-but correlated with-individuals' spatial-numerical biases (i.e., spatial-numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes.

The motion behind the symbols: a vital role for dynamism in the conceptualization of limits and continuity in expert mathematics.

The canonical history of mathematics suggests that the late 19th-century "arithmetization" of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice.