The ability to represent recursive structures is thought to be foundational for language, music, mathematics, complex tooluse, and theory of mind. However, we do not currently know what type of computational machinery is used to representrecursive structures, or when this ability develops. Here we measure the developmental trajectory in young childrenusing a sequence generation task. We also test two proposed mechanisms for representing these structures: a stack-likedata structure a first-in-last-out structure in which only the last item can be accessed, and a queue-like data structurean ordered list that can only be accessed from its beginning. Each of these mechanisms make different predictions forwhat types of sequential structures should be easier to generate and have specific item-by-item response time signatures.We show evidence that both children and adults use a queue-like representational system which iteratively runs forwardssearches through a stored queue.

Humans learn and generate languages, music, games, and seemingly limitless varieties of other structures across domains. Unlike many AI systems, we often do so from little data. How do we learn such large varieties of richly structured representations so efficiently? One possibility is that people ``learn by programming,'' synthesizing data-generating algorithms to explain what we observe. We examine the nature and origins of this learning mechanism in adults, children, and nonhuman primates (macaque monkeys), using a highly unconstrained sequence prediction task. Although adults and children quickly learn many richly structured sequences, monkeys learn only the simplest sequences (e.g. lines). We test multiple learning models, finding that adults are best explained by a ``Language of Thought''-like program-learning model and monkeys by a simpler extrapolation strategy. Children exhibit varied learning strategies but are best fit in aggregate by an intermediately expressive model. Paper available at https://sites.google.com/view/patternlearning.

Languages commonly use physical properties to discuss dis-tinctly non-physical states and events in the world (e.g., “I’mnot a huge fan of licorice”). Here, we investigate the degreeto which associations between physical properties and abstractconcepts are culturally specific constructs. To do this, wetested three distinct populations—US adults, US children, andadults from an indigenous group in the lowlands of Bolivia, theTsimane’—on their associations between the physical conceptof weight and a variety of abstract attributes (e.g., importance,emotional state, moral worth). We find a strong relationshipbetween the associations of US and Tsimane’ adults, but little-to-no relationship between US children and either adult popu-lation. These results suggest that the property of weight playsa similar role in everyday thought across cultures, but that ittakes time to develop. Further, we found that these associationscould not be recovered from a simple semantic embeddinganalysis, suggesting that the cross-culturally shared connec-tions between physical and abstract attributes may be learnedthrough more complex experiences than language alone.

By about age four, children in industrialized cultures can use verbal counting to correctly name the number of objectsin sets larger than four. On some accounts, this full counting ability signals abstract knowledge about the fundamentalprinciples governing number (e.g. the successor function and later-greater principle). However, many children who qualifyas full counters fail to grasp these principles. Why? This failure could reflect number-specific conceptual deficiencies ordomain-general cognitive immaturity. Here we tested these alternatives in the Tsimane, an indigenous group in whichage and numerical knowledge are largely unconfounded. Although many Tsimane performed at ceiling, a subset of full-counters demonstrated poor understanding of fundamental counting principles. Performance was not reliably predicted byage or schooling, but rather by highest verbal count. These findings suggest that at any age, the development of numericalabilities is characterized not by sudden induction of abstract principles, but by piecemeal procedural learning.

From early in life, people implicitly associate time, number,and other abstract conceptual domains with space. Accord-ing to the Generalized Magnitude System proposal, these men-tal mappings reflect a common neural system for represent-ing various magnitudes, and share a common spatial organiza-tion. In a test of this proposal, here we measured mappings ofsize, time, and number in the Tsimane’, an indigenous Ama-zonian group with few of the cultural practices (like readingand math) that spatialize size, time, and number in the expe-rience of industrialized adults. On three spatial axes, the Tsi-mane’ systematically arranged imagistic stimuli according totheir magnitudes, but they showed no directional preferencesoverall and individuals often mapped different domains in op-posite directions. The results are inconsistent with predictionsof the Generalized Magnitude System proposal but can be ex-plained by Hierarchical Mental Metaphor Theory, accordingto which mental mappings initially reflect a set of correlationsobservable in the natural world.