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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. [ABSTRACT FROM AUTHOR]

We show that children in the Tsimane', a farming-foraging group in the Bolivian rain-forest, learn number words along a similar developmental trajectory to children from industrialized countries. Tsimane' children successively acquire the first three or four number words before fully learning how counting works. However, their learning is substantially delayed relative to children from the United States, Russia, and Japan. The presence of a similar developmental trajectory likely indicates that the incremental stages of numerical knowledge--but not their timing--reflect a fundamental property of number concept acquisition which is relatively independent of language, culture, age, and early education.

Infants must learn about many cognitive domains (e.g., language, music) from auditory statistics, yet capacity limits on their cognitive resources restrict the quantity that they can encode. Previous research has established that infants can attend to only a subset of available acoustic input. Yet few previous studies have directly examined infant auditory attention, and none have directly tested theorized mechanisms of attentional selection based on stimulus complexity. This work utilizes model-based behavioral methods that were recently developed to examine visual attention in infants (e.g., Kidd, Piantadosi, & Aslin, 2012). The present results demonstrate that 7- to 8-month-old infants selectively attend to nonsocial auditory stimuli that are intermediately predictable/complex with respect to their current implicit beliefs and expectations. These findings provide evidence of a broad principle of infant attention across modalities and suggest that sound-to-sound transitional statistics heavily influence the allocation of auditory attention in human infants.

A major open question in natural language research is the role of communicative efficiency in the origin and on-line processing of language structures. Here, we use word pairs like "chimp/chimpanzee", which differ in length but have nearly identical meanings, to investigate the communicative properties of lexical systems and the communicative pressures on language users. If language is designed to be information-theoretically optimal, then shorter words should convey less information than their longer counterparts, when controlling for meaning. Consistent with this prediction, a corpus analysis revealed that the short form of our meaning-matched pairs occurs in more predictive contexts than the longer form. Second, a behavioral study showed that language users choose the short form more often in predictive contexts, suggesting that tendencies to be information-theoretically efficient manifest in explicit behavioral choices. Our findings, which demonstrate the prominent role of communicative efficiency in the structure of the lexicon, complement and extend the results of Piantadosi, Tily, and Gibson (2011), who showed that word length is better correlated with Shannon information content than with frequency. Crucially, we show that this effect arises at least in part from active speaker choice. (Contains 2 figures.)

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful representational system. We provide an implemented model that is powerful enough to learn number word meanings and other related conceptual systems from naturalistic data. The model shows that bootstrapping can be made computationally and philosophically well-founded as a theory of number learning. Our approach demonstrates how learners may combine core cognitive operations to build sophisticated representations during the course of development, and how this process explains observed developmental patterns in number word learning. (Contains 6 figures and 2 tables.)

We present a general information-theoretic argument that all efficient communication systems will be ambiguous, assuming that context is informative about meaning. We also argue that ambiguity allows for greater ease of processing by permitting efficient linguistic units to be re-used. We test predictions of this theory in English, German, and Dutch. Our results and theoretical analysis suggest that ambiguity is a functional property of language that allows for greater communicative efficiency. This provides theoretical and empirical arguments against recent suggestions that core features of linguistic systems are not designed for communication. (Contains 3 figures.)

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 factorswere relatedtovariance inWeber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, corticalneurondensityanddomain-general cognitionwere 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. [ABSTRACT FROM AUTHOR]

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., an, (ab)n, and {a,b}+, context-free (e.g., anbn, anbn+m, and xxR), and context-sensitive (e.g., anbncn, anbmcndm, 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. [ABSTRACT FROM AUTHOR]