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Despite proportional information being ubiquitous, there is not a standard account of proportional reasoning. Part of the difficulty is that there are several apparent contradictions: in some contexts, proportion is easy and privileged, while in others it is difficult and ignored. One possibility is that although we see similarities across tasks requiring proportional reasoning, people approach them with different strategies. We test this hypothesis by implementing strategies computationally and quantitatively comparing them with Bayesian tools, using data from continuous (e.g., pie chart) and discrete (e.g., dots) stimuli and preschoolers, 2nd and 5th graders, and adults. Overall, people's comparisons of highly regular and continuous proportion are better fit by proportion strategy models, but comparisons of discrete proportion are better fit by a numerator comparison model. These systematic differences in strategies suggest that there is not a single, simple explanation for behavior in terms of success or failure, but rather a variety of possible strategies that may be chosen in different contexts., Competing Interests: Declaration of competing interest None., (Copyright © 2024. Published by Elsevier B.V.)

We develop a mathematical approach to formally proving that certain neural computations and representations exist based on patterns observed in an organism's behaviour. To illustrate, we provide a simple set of conditions under which an ant's ability to determine how far it is from its nest would logically imply neural structures isomorphic to the natural numbers ℕ . We generalise these results to arbitrary behaviours and representations and show what mathematical characterisation of neural computation and representation is simplest while being maximally predictive of behaviour. We develop this framework in detail using a path integration example, where an organism's ability to search for its nest in the correct location implies representational structures isomorphic to two-dimensional coordinates under addition. We also study a system for processing a n b n strings common in comparative work. Our approach provides an objective way to determine what theory of a physical system is best, addressing a fundamental challenge in neuroscientific inference. These results motivate considering which neurobiological structures have the requisite formal structure and are otherwise physically plausible given relevant physical considerations such as generalisability, information density, thermodynamic stability and energetic cost., (© 2024 The Authors. European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd.)

For decades, cognitive scientists have debated what kind of representation might characterize human concepts. Whatever the format of the representation, it must allow for the computation of varied properties, including similarities, features, categories, definitions, and relations. It must also support the development of theories, ad hoc categories, and knowledge of procedures. Here, we discuss why vector-based representations provide a compelling account that can meet all these needs while being plausibly encoded into neural architectures. This view has become especially promising with recent advances in both large language models and vector symbolic architectures. These innovations show how vectors can handle many properties traditionally thought to be out of reach for neural models, including compositionality, definitions, structures, and symbolic computational processes., Competing Interests: Declaration of interests No interests are declared., (Copyright © 2024. Published by Elsevier Ltd.)

Throughout their lives, humans seem to learn a variety of rules for things like applying category labels, following procedures, and explaining causal relationships. These rules are often algorithmically rich but are nonetheless acquired with minimal data and computation. Symbolic models based on program learning successfully explain rule-learning in many domains, but performance degrades quickly as program complexity increases. It remains unclear how to scale symbolic rule-learning methods to model human performance in challenging domains. Here we show that symbolic search over the space of metaprograms-programs that revise programs-dramatically improves learning efficiency. On a behavioral benchmark of 100 algorithmically rich rules, this approach fits human learning more accurately than alternative models while also using orders of magnitude less search. The computation required to match median human performance is consistent with conservative estimates of human thinking time. Our results suggest that metaprogram-like representations may help human learners to efficiently acquire rules., (© 2024. The Author(s).)

Humans and other animals are able to perceive and represent a number of objects present in a scene, a core cognitive ability thought to underlie the development of mathematics. However, the perceptual mechanisms that underpin this capacity remain poorly understood. Here, we show that our visual sense of number derives from a visual system designed to efficiently encode the location of objects in scenes. Using a mathematical model, we demonstrate that an efficient but information-limited encoding of objects' locations can explain many key aspects of number psychophysics, including subitizing, Weber's law, underestimation, and effects of exposure time. In two experiments ( N = 100 each), we find that this model of visual encoding captures human performance in both a change-localization task and a number estimation task. In a third experiment ( N = 100), we find that individual differences in change-localization performance are highly predictive of differences in number estimation, both in terms of overall performance and inferred model parameters, with participants having numerically indistinguishable inferred information capacities across tasks. Our results therefore indicate that key psychophysical features of numerical cognition do not arise from separate modules or capacities specific to number, but rather as by-products of lower level constraints on perception. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Language is a defining characteristic of our species, but the function, or functions, that it serves has been debated for centuries. Here we bring recent evidence from neuroscience and allied disciplines to argue that in modern humans, language is a tool for communication, contrary to a prominent view that we use language for thinking. We begin by introducing the brain network that supports linguistic ability in humans. We then review evidence for a double dissociation between language and thought, and discuss several properties of language that suggest that it is optimized for communication. We conclude that although the emergence of language has unquestionably transformed human culture, language does not appear to be a prerequisite for complex thought, including symbolic thought. Instead, language is a powerful tool for the transmission of cultural knowledge; it plausibly co-evolved with our thinking and reasoning capacities, and only reflects, rather than gives rise to, the signature sophistication of human cognition., (© 2024. Springer Nature Limited.)

In a large ( N = 300), pre-registered experiment and data analysis model, we find that individual variation in overall performance on Raven's Progressive Matrices is substantially driven by differential strategizing in the face of difficulty. Some participants choose to spend more time on hard problems while others choose to spend less and these differences explain about 42% of the variance in overall performance. In a data analysis jointly predicting participants' reaction times and accuracy on each item, we find that the Raven's task captures at most half of participants' variation in time-controlled ability (48%) down to almost none (3%), depending on which notion of ability is assumed. Our results highlight the role that confounding factors such as motivation play in explaining individuals' differential performance in IQ testing., Competing Interests: Competing Interests: The authors declare no conflict of interests., (© 2024 Massachusetts Institute of Technology.)

The study of how children learn numbers has yielded one of the most productive research programs in cognitive development, spanning empirical and computational methods, as well as nativist and empiricist philosophies. This paper provides a tutorial on how to think computationally about learning models in a domain like number, where learners take finite data and go far beyond what they directly observe or perceive. To illustrate, this paper then outlines a model which acquires a counting procedure using observations of sets and words, extending the proposal of Piantadosi et al. (2012). This new version of the model responds to several critiques of the original work and outlines an approach which is likely appropriate for acquiring further aspects of mathematics., (© 2023 The Authors. Child Development © 2023 Society for Research in Child Development.)

We investigate number and arithmetic learning among a Bolivian indigenous people, the Tsimane', for whom formal schooling is comparatively recent in history and variable in both extent and consistency. We first present a large-scale meta-analysis on child number development involving over 800 Tsimane' children. The results emphasize the impact of formal schooling: Children are only found to be full counters when they have attended school, suggesting the importance of cultural support for early mathematics. We then test especially remote Tsimane' communities and document the development of specialized arithmetical knowledge in the absence of direct formal education. Specifically, we describe individuals who succeed on arithmetic problems involving the number five-which has a distinct role in the local economy-even though they do not succeed on some lower numbers. Some of these participants can perform multiplication with fives at greater accuracy than addition by one. These results highlight the importance of cultural factors in early mathematics and suggest that psychological theories of number where quantities are derived from lower numbers via repeated addition (e.g., a successor function) are unlikely to explain the diversity of human mathematical ability.

Words that are more surprising given context take longer to process. However, no incremental parsing algorithm has been shown to directly predict this phenomenon. In this work, we focus on a class of algorithms whose runtime does naturally scale in surprisal-those that involve repeatedly sampling from the prior. Our first contribution is to show that simple examples of such algorithms predict runtime to increase superlinearly with surprisal, and also predict variance in runtime to increase. These two predictions stand in contrast with literature on surprisal theory (Hale, 2001; Levy, 2008a) which assumes that the expected processing cost increases linearly with surprisal, and makes no prediction about variance. In the second part of this paper, we conduct an empirical study of the relationship between surprisal and reading time, using a collection of modern language models to estimate surprisal. We find that with better language models, reading time increases superlinearly in surprisal, and also that variance increases. These results are consistent with the predictions of sampling-based algorithms., (© 2023 Massachusetts Institute of Technology.)

The capacity to generate recursive sequences is a marker of rich, algorithmic cognition, and perhaps unique to humans. Yet, the precise processes driving recursive sequence generation remain mysterious. We investigated three potential cognitive mechanisms underlying recursive pattern processing: hierarchical reasoning, ordinal reasoning, and associative chaining. We developed a Bayesian mixture model to quantify the extent to which these three cognitive mechanisms contribute to adult humans' performance in a sequence generation task. We further tested whether recursive rule discovery depends upon relational information, either perceptual or semantic. We found that the presence of relational information facilitates hierarchical reasoning and drives the generation of recursive sequences across novel depths of center embedding. In the absence of relational information, the use of ordinal reasoning predominates. Our results suggest that hierarchical reasoning is an important cognitive mechanism underlying recursive pattern processing and can be deployed across embedding depths and relational domains., (© 2023 The Authors. Cognitive Science published by Wiley Periodicals LLC on behalf of Cognitive Science Society (CSS).)

Many social and legal conflicts hinge on semantic disagreements. Understanding the origins and implications of these disagreements necessitates novel methods for identifying and quantifying variation in semantic cognition between individuals. We collected conceptual similarity ratings and feature judgements from a variety of words in two domains. We analyzed this data using a non-parametric clustering scheme, as well as an ecological statistical estimator, in order to infer the number of different variants of common concepts that exist in the population. Our results show at least ten to thirty quantifiably different variants of word meanings exist for even common nouns. Further, people are unaware of this variation, and exhibit a strong bias to erroneously believe that other people share their semantics. This highlights conceptual factors that likely interfere with productive political and social discourse., (© 2023 Massachusetts Institute of Technology.)

Standard models in quantitative linguistics assume that word usage follows a fixed frequency distribution, often Zipf's law or a close relative. This view, however, does not capture the near daily variations in topics of conversation, nor the short-term dynamics of language change. In order to understand the dynamics of human language use, we present a corpus of daily word frequency variation scraped from online news sources every 20 min for more than 2 years. We construct a simple time-varying model with a latent state, which is observed via word frequency counts. We use Bayesian techniques to infer the parameters of this model for 20,000 words, allowing us to convert complex word-frequency trajectories into low-dimensional parameters in word usage. By analyzing the inferred parameters of this model, we quantify the relative mobility and drift of words on a day-to-day basis, while accounting for sampling error. We quantify this variation and show evidence against "rich-get-richer" models of word use, which have been previously hypothesized to explain statistical patterns in language., (© 2022 Cognitive Science Society LLC.)

Spatial cognition is central to human behavior, but the way people conceptualize space varies within and across groups for unknown reasons. Here, we found that adults from an indigenous Bolivian group used systematically different spatial reference frames on different axes, according to known differences in their discriminability: In both verbal and nonverbal tests, participants preferred allocentric (i.e., environment-based) space on the left-right axis, where spatial discriminations (like "b" versus "d") are notoriously difficult, but the same participants preferred egocentric (i.e., body-based) space on the front-back axis, where spatial discrimination is relatively easy. The results (i) establish a relationship between spontaneous spatial language and memory across axes within a single culture, (ii) challenge the claim that each language group has a predominant spatial reference frame at a given scale, and (iii) suggest that spatial thinking and language may both be shaped by spatial discrimination abilities, as they vary across cultures and contexts.

It is popular in psychology to hypothesize that representations of exact number are innately determined-in particular, that biology has endowed humans with a system for manipulating quantities which forms the primary representational substrate for our numerical and mathematical concepts. While this perspective has been important for advancing empirical work in animal and child cognition, here we examine six natural predictions of strong numerical nativism from a multidisciplinary perspective, and find each to be at odds with evidence from anthropology and developmental science. In particular, the history of number reveals characteristics that are inconsistent with biological determinism of numerical concepts, including a lack of number systems across some human groups and remarkable variability in the form of numerical systems that do emerge. Instead, this literature highlights the importance of economic and social factors in constructing fundamentally new cognitive systems to achieve culturally specific goals. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane', an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane' children may be shy in providing behavioral responses to number tasks, (b) Tsimane' children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane' children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane' children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words., Competing Interests: The authors have declared that no competing interests exist.

We examine the conceptual development of kinship through the lens of program induction. We present a computational model for the acquisition of kinship term concepts, resulting in the first computational model of kinship learning that is closely tied to developmental phenomena. We demonstrate that our model can learn several kinship systems of varying complexity using cross-linguistic data from English, Pukapuka, Turkish, and Yanomamö. More importantly, the behavioral patterns observed in children learning kinship terms, under-extension and over-generalization, fall out naturally from our learning model. We then conducted interviews to simulate realistic learning environments and demonstrate that the characteristic-to-defining shift is a consequence of our learning model in naturalistic contexts containing abstract and concrete features. We use model simulations to understand the influence of logical simplicity and children's learning environment on the order of acquisition of kinship terms, providing novel predictions for the learning trajectories of these words. We conclude with a discussion of how this model framework generalizes beyond kinship terms, as well as a discussion of its limitations., (© 2021. The Author(s).)

Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., "one, two, three . . ."). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population-the Tsimane' of Bolivia-in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants ( N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants' verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability. This article is part of the theme issue 'Systems neuroscience through the lens of evolutionary theory'.

A major goal of linguistics and cognitive science is to understand what class of learning systems can acquire natural language. Until recently, the computational requirements of language have been used to argue that learning is impossible without a highly constrained hypothesis space. Here, we describe a learning system that is maximally unconstrained, operating over the space of all computations, and is able to acquire many of the key structures present in natural language from positive evidence alone. We demonstrate this by providing the same learning model with data from 74 distinct formal languages which have been argued to capture key features of language, have been studied in experimental work, or come from an interesting complexity class. The model is able to successfully induce the latent system generating the observed strings from small amounts of evidence in almost all cases, including for regular (e.g., a n , [Formula: see text], and [Formula: see text]), context-free (e.g., [Formula: see text], and [Formula: see text]), and context-sensitive (e.g., [Formula: see text], and xx ) languages, as well as for many languages studied in learning experiments. These results show that relatively small amounts of positive evidence can support learning of rich classes of generative computations over structures. The model provides an idealized learning setup upon which additional cognitive constraints and biases can be formalized., Competing Interests: The authors declare no competing interest., (Copyright © 2022 the Author(s). Published by PNAS.)

In industrialized groups, adults implicitly map numbers, time, and size onto space according to cultural practices like reading and counting (e.g., from left to right). Here, we tested the mental mappings of the Tsimane', an indigenous population with few such cultural practices. Tsimane' adults spatially arranged number, size, and time stimuli according to their relative magnitudes but showed no directional bias for any domain on any spatial axis; different mappings went in different directions, even in the same participant. These findings challenge claims that people have an innate left-to-right mapping of numbers and that these mappings arise from a domain-general magnitude system. Rather, the direction-specific mappings found in industrialized cultures may originate from direction-agnostic mappings that reflect the correlational structure of the natural world., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution License 4.0 (CC BY).)

Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations-whatever they are-must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an "assembly language" for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems.

It is now a common practice to compare models of human language processing by comparing how well they predict behavioral and neural measures of processing difficulty, such as reading times, on corpora of rich naturalistic linguistic materials. However, many of these corpora, which are based on naturally-occurring text, do not contain many of the low-frequency syntactic constructions that are often required to distinguish between processing theories. Here we describe a new corpus consisting of English texts edited to contain many low-frequency syntactic constructions while still sounding fluent to native speakers. The corpus is annotated with hand-corrected Penn Treebank-style parse trees and includes self-paced reading time data and aligned audio recordings. We give an overview of the content of the corpus, review recent work using the corpus, and release the data., (© The Author(s) 2020.)

People can identify the number of objects in sets of four or fewer items with near-perfect accuracy but exhibit linearly increasing error for larger sets. Some researchers have taken this discontinuity as evidence of two distinct representational systems. Here, we present a mathematical derivation showing that this behaviour is an optimal representation of cardinalities under a limited informational capacity, indicating that this behaviour can emerge from a single system. Our derivation predicts how the amount of information accessible to viewers should influence the perception of quantity for both large and small sets. In a series of four preregistered experiments (N = 100 each), we varied the amount of information accessible to participants in number estimation. We find tight alignment between the model and human performance for both small and large quantities, implicating efficient representation as the common origin behind key phenomena of human and animal numerical cognition.

The scope of human learning and development poses a radical challenge for cognitive science. We propose that developmental theories can address this challenge by adopting perspectives from computer science. Many of our best models treat learning as analogous to computer programming because symbolic programs provide the most compelling account of sophisticated mental representations. We specifically propose that children's learning is analogous to a particular style of programming called hacking, making code better along many dimensions through an open-ended set of goals and activities. By contrast to existing theories, which depend primarily on local search and simple metrics, this view highlights the many features of good mental representations and the multiple complementary processes children use to create them., (Copyright © 2020 The Authors. Published by Elsevier Ltd.. All rights reserved.)

The question of what computational capacities, if any, differ between humans and nonhuman animals has been at the core of foundational debates in cognitive psychology, anthropology, linguistics, and animal behavior. The capacity to form nested hierarchical representations is hypothesized to be essential to uniquely human thought, but its origins in evolution, development, and culture are controversial. We used a nonlinguistic sequence generation task to test whether subjects generalize sequential groupings of items to a center-embedded, recursive structure. Children (3 to 5 years old), U.S. adults, and adults from a Bolivian indigenous group spontaneously induced recursive structures from ambiguous training data. In contrast, monkeys did so only with additional exposure. We quantify these patterns using a Bayesian mixture model over logically possible strategies. Our results show that recursive hierarchical strategies are robust in human thought, both early in development and across cultures, but the capacity itself is not unique to humans., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).)

The frontotemporal language network responds robustly and selectively to sentences. But the features of linguistic input that drive this response and the computations that these language areas support remain debated. Two key features of sentences are typically confounded in natural linguistic input: words in sentences (a) are semantically and syntactically combinable into phrase- and clause-level meanings, and (b) occur in an order licensed by the language's grammar. Inspired by recent psycholinguistic work establishing that language processing is robust to word order violations, we hypothesized that the core linguistic computation is composition, and, thus, can take place even when the word order violates the grammatical constraints of the language. This hypothesis predicts that a linguistic string should elicit a sentence-level response in the language network provided that the words in that string can enter into dependency relationships as in typical sentences. We tested this prediction across two fMRI experiments (total N = 47) by introducing a varying number of local word swaps into naturalistic sentences, leading to progressively less syntactically well-formed strings. Critically, local dependency relationships were preserved because combinable words remained close to each other. As predicted, word order degradation did not decrease the magnitude of the blood oxygen level-dependent response in the language network, except when combinable words were so far apart that composition among nearby words was highly unlikely. This finding demonstrates that composition is robust to word order violations, and that the language regions respond as strongly as they do to naturalistic linguistic input, providing that composition can take place., Competing Interests: Competing Interests: The authors have declared that no competing interests exist., (© 2020 Massachusetts Institute of Technology.)

It remains unclear whether and, if so, how nonhuman animals make on-the-fly predictions during pursuit. Here we used a novel laboratory pursuit task that incentivizes the prediction of future prey positions. We trained three macaques to perform a joystick-controlled pursuit task in which prey follow intelligent escape algorithms. Subjects aimed toward the likely future positions of the prey, which indicated that they generate internal predictions and use these to guide behavior. We then developed a generative model that explains real-time pursuit trajectories and showed that our subjects use prey position, velocity and acceleration to make predictions. We identified neurons in the dorsal anterior cingulate cortex whose responses track these three variables. These neurons multiplexed prediction-related variables with a distinct and explicit representation of the future position of the prey. Our results provide a clear demonstration that the brain can explicitly represent future predictions and highlight the critical role of anterior cingulate cortex for future-oriented cognition.

A logical rule important in counting and representing exact number is one-to-one correspondence, the understanding that two sets are equal if each item in one set corresponds to exactly one item in the second set. The role of this rule in children's development of counting remains unclear, possibly due to individual differences in the development of language. We report that non-human primates, which do not have language, have at least a partial understanding of this principle. Baboons were given a quantity discrimination task where two caches were baited with different quantities of food. When the quantities were baited in a manner that highlighted the one-to-one relation between those quantities, baboons performed significantly better than when one-to-one correspondence cues were not provided. The implication is that one-to-one correspondence, which requires intuitions about equality and is a possible building block of counting, has a pre-linguistic origin., Competing Interests: We declare we have no competing interests., (© 2019 The Authors.)

The approximate number system (ANS) has attracted broad interest due to its potential importance in early mathematical development and the fact that it is conserved across species. Models of the ANS and behavioral measures of ANS acuity both assume that quantity estimation is computed rapidly and in parallel across an entire view of the visual scene. We present evidence instead that ANS estimates are largely the product of a serial accumulation mechanism operating across visual fixations. We used an eye-tracker to collect data on participants' visual fixations while they performed quantity-estimation and -discrimination tasks. We were able to predict participants' numerical estimates using their visual fixation data: As the number of dots fixated increased, mean estimates also increased, and estimation error decreased. A detailed model-based analysis shows that fixated dots contribute twice as much as peripheral dots to estimated quantities; people do not "double count" multiply fixated dots; and they do not adjust for the proportion of area in the scene that they have fixated. The accumulation mechanism we propose explains reported effects of display time on estimation and earlier findings of a bias to underestimate quantities., Competing Interests: The authors declare no conflict of interest.

We introduce theory-neutral estimates of the amount of information learners possess about how language works. We provide estimates at several levels of linguistic analysis: phonemes, wordforms, lexical semantics, word frequency and syntax. Our best guess is that the average English-speaking adult has learned 12.5 million bits of information, the majority of which is lexical semantics. Interestingly, very little of this information is syntactic, even in our upper bound analyses. Generally, our results suggest that learners possess remarkable inferential mechanisms capable of extracting, on average, nearly 2000 bits of information about how language works each day for 18 years., Competing Interests: We declare we have no competing interests.

Humans naturally group the world into coherent categories defined by membership rules. Rules can be learned implicitly by building stimulus-response associations using reinforcement learning or by using explicit reasoning. We tested if the striatum, in which activation reliably scales with reward prediction error, would track prediction errors in a task that required explicit rule generation. Using functional magnetic resonance imaging during a categorization task, we show that striatal responses to feedback scale with a "surprise" signal derived from a Bayesian rule-learning model and are inconsistent with RL prediction error. We also find that striatum and caudal inferior frontal sulcus (cIFS) are involved in updating the likelihood of discriminative rules. We conclude that the striatum, in cooperation with the cIFS, is involved in updating the values assigned to categorization rules when people learn using explicit reasoning.

Zipf famously stated that, if natural language lexicons are structured for efficient communication, the words that are used the most frequently should require the least effort. This observation explains the famous finding that the most frequent words in a language tend to be short. A related prediction is that, even within words of the same length, the most frequent word forms should be the ones that are easiest to produce and understand. Using orthographics as a proxy for phonetics, we test this hypothesis using corpora of 96 languages from Wikipedia. We find that, across a variety of languages and language families and controlling for length, the most frequent forms in a language tend to be more orthographically well-formed and have more orthographic neighbors than less frequent forms. We interpret this result as evidence that lexicons are structured by language usage pressures to facilitate efficient communication., (© 2018 Cognitive Science Society, Inc.)

Humans have great difficulty comparing quotients including fractions, proportions, and probabilities and often erroneously isolate the whole numbers of the numerators and denominators to compare them. Some have argued that the whole number bias is a compensatory strategy to deal with difficult comparisons. We examined adult humans' preferences for gambles that differed only in numerosity, and not in factors that influence their expected value (probabilities and stakes). Subjects consistently preferred gambles with more winning balls to ones with fewer, even though the probabilities were mathematically identical, replicating prior results. In a second experiment, we found that subjects accurately represented the relative probabilities of the choice options during rapid nonverbal probability judgments but nonetheless showed biases based on whole numbers. We mathematically formalized and quantitatively evaluated cognitive rules based on existing hypotheses that attempt to explain subjects' whole number biases during quotient comparisons. The results show that the whole number bias is intrinsic to the way humans solve quotient comparisons rather than a compensatory strategy. (PsycINFO Database Record, ((c) 2018 APA, all rights reserved).)

Background: Seasons affect many social, economic, and biological outcomes, particularly in low-resource settings, and some studies suggest that birth season affects child growth., Aim: To study a predictor of stunting that has received limited attention: birth season., Subjects and Methods: This study uses cross-sectional data collected during 2008 in a low-resource society of horticulturists-foragers in the Bolivian Amazon, Tsimane'. It estimates the associations between birth months and height-for-age Z-scores (HAZ) for 562 girls and 546 boys separately, from birth until age 11 years or pre-puberty, which in this society occurs ∼13-14 years., Results: Children born during the rainy season (February-May) were shorter, while children born during the end of the dry season and the start of the rainy season (August-November) were taller, both compared with their age-sex peers born during the rest of the year. The correlations of birth season with HAZ were stronger for boys than for girls. Controlling for birth season, there is some evidence of eventual partial catch-up growth, with the HAZ of girls or boys worsening until ∼ age 4-5 years, but improving thereafter. By age 6 years, many girls and boys had ceased to be stunted, irrespective of birth season., Conclusion: The results suggest that redressing stunting will require attention to conditions in utero, infancy and late childhood.

Complex systems are often built from a relatively small set of basic features or operations that can be combined in myriad ways. We investigated the developmental origins of this compositional architecture in 9-month-old infants, extending recent work that demonstrated rudimentary compositional abilities in preschoolers. Infants viewed two separate object-occlusion events that depicted a single featurechange operation. They were then tested with a combined operation to determine whether they expected the outcome of the two feature changes, even though this combination was unfamiliar. In contrast to preschoolers, infants did not appear to predictively compose these simple feature-change operations. A second experiment demonstrated the ability of infants to track two operations when not combined. The failure to compose basic operations is consistent with limitations on object tracking and early numerical cognition (Feigenson & Yamaguchi, 2009). We suggest that these results can be unified via a general principle: infants have difficulty with multiple updates to a representation of an unobservable., Competing Interests: The authors declare no conflicts of interest.

A dominant mechanism in the Judgment and Decision Making literature states that information is accumulated about each choice option until a decision threshold is met. Only after that threshold does a subject start to execute a motor response to indicate their choice. However, recent research has revealed spatial gradients in motor responses as a function of comparison difficulty as well as changes-of-mind in the middle of an action, both suggesting continued accumulation and processing of decision-related signals after the decision boundary. Here we present a formal model and supporting data from a number comparison task that a continuous motor planner, combined with a simple statistical inference scheme, can model detailed behavioral effects without assuming a threshold. This threshold-free model reproduces subjects' sensitivity to numerical distance in reaching, accuracy, reaction time, and changes of mind. We argue that the motor system positions the effectors using an optimal biomechanical feedback controller, and continuous statistical inference on outputs from cognitive processes.

Classification of neurons into clusters based on their response properties is an important tool for gaining insight into neural computations. However, it remains unclear to what extent neurons fall naturally into discrete functional categories. We developed a Bayesian method that models the tuning properties of neural populations as a mixture of multiple types of task-relevant response patterns. We applied this method to data from several cortical and striatal regions in economic choice tasks. In all cases, neurons fell into only two clusters: one multiple-selectivity cluster containing all cells driven by task variables of interest and another of no selectivity for those variables. The single cluster of task-sensitive cells argues against robust categorical tuning in these areas. The no-selectivity cluster was unanticipated and raises important questions about what distinguishes these neurons and what role they play. Moreover, the ability to formally identify these nonselective cells allows for more accurate measurement of ensemble effects by excluding or appropriately down-weighting them in analysis. Our findings provide a valuable tool for analysis of neural data, challenge simple categorization schemes previously proposed for these regions, and place useful constraints on neurocomputational models of economic choice and control. NEW & NOTEWORTHY We present a Bayesian method for formally detecting whether a population of neurons can be naturally classified into clusters based on their response tuning properties. We then examine several data sets of reward system neurons for variables and find in all cases that neurons can be classified into only two categories: a functional class and a non-task-driven class. These results provide important constraints for neural models of the reward system.

Objectives: We assessed associations between child stunting, recovery, and faltering with schooling and human capital skills in a native Amazonian society of horticulturalists-foragers (Tsimane')., Methods: We used cross-sectional data (2008) from 1262 children aged 6 to 16 years in 53 villages to assess contemporaneous associations between three height categories: stunted (height-for-age Z score, HAZ<-2), moderately stunted (-2 ≤ HAZ≤-1), and nonstunted (HAZ>-1), and three categories of human capital: completed grades of schooling, test-based academic skills (math, reading, writing), and local plant knowledge. We used annual longitudinal data (2002-2010) from all children (n = 853) in 13 villages to estimate the association between changes in height categories between the first and last years of measure and schooling and academic skills., Results: Stunting was associated with 0.4 fewer completed grades of schooling (∼24% less) and with 13-15% lower probability of showing any writing or math skills. Moderate stunting was associated with ∼20% lower scores in local plant knowledge and 9% lower probability of showing writing skills, but was not associated with schooling or math and writing skills. Compared with nonstunted children, children who became stunted had 18-21% and 15-21% lower probabilities of showing math and writing skills, and stunted children had 0.4 fewer completed grades of schooling. Stunted children who recovered showed human capital outcomes that were indistinguishable from nonstunted children., Conclusions: The results confirm adverse associations between child stunting and human capital skills. Predictors of growth recovery and faltering can affect human capital outcomes, even in a remote, economically self-sufficient society., (© 2017 Wiley Periodicals, Inc.)