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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]

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]

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. [ABSTRACT FROM AUTHOR]

What determines how languages categorize colors? We analyzed results of the World Color Survey (WCS) of 110 languages to show that despite gross differences across languages, communication of chromatic chips is always better for warm colors (yellows/reds) than cool colors (blues/greens). We present an analysis of color statistics in a large databank of natural images curated by human observers for salient objects and show that objects tend to have warm rather than cool colors. These results suggest that the cross-linguistic similarity in color-naming efficiency reflects colors of universal usefulness and provide an account of a principle (color use) that governs how color categories come about. We show that potential methodological issues with the WCS do not corrupt information-theoretic analyses, by collecting original data using two extreme versions of the color-naming task, in three groups: the Tsimane', a remote Amazonian hunter-gatherer isolate; Bolivian-Spanish speakers; and English speakers. These data also enabled us to test another prediction of the color-usefulness hypothesis: that differences in color categorization between languages are caused by differences in overall usefulness of color to a culture. In support, we found that color naming among Tsimane' had relatively low communicative efficiency, and the Tsimane' were less likely to use color terms when describing familiar objects. Color-naming among Tsimane' was boosted when naming artificially colored objects compared with natural objects, suggesting that industrialization promotes color usefulness. [ABSTRACT FROM AUTHOR]

We present evidence that pressures for early childcare may have been one of the driving factors of human evolution. We show through an evolutionary model that runaway selection for high intelligence may occur when (i) altricial neonates require intelligent parents, (ii) intelligent parents must have large brains, and (iii) large brains necessitate having even more altricial offspring. We test a prediction of this account by showing across primate genera that the helplessness of infants is a particularly strong predictor of the adults' intelligence. We discuss related implications, including this account's ability to explain why human-level intelligence evolved specifically in mammals. This theory complements prior hypotheses that link human intelligence to social reasoning and reproductive pressures and explains how human intelligence may have become so distinctive compared with our closest evolutionary relatives. [ABSTRACT FROM AUTHOR]

Sentence processing theories typically assume that the input to our language processing mechanisms is an error-free sequence of words. However, this assumption is an oversimplification because noise is present in typical language use (for instance, due to a noisy environment, producer errors, or perceiver errors). A complete theory of human sentence comprehension therefore needs to explain how humans understand language given imperfect input. Indeed, like many cognitive systems, language processing mechanisms may even be "well designed"-in this case for the task of recovering intended meaning from noisy utterances. In particular, comprehension mechanisms may be sensitive to the types of information that an idealized statistical comprehender would be sensitive to. Here, we evaluate four predictions about such a rational (Bayesian) noisy-channel language comprehender in a sentence comprehension task: (i) semantic cues should pull sentence interpretation towards plausible meanings, especially if the wording of the more plausible meaning is close to the observed utterance in terms of the number of edits; (ii) this process should asymmetrically treat insertions and deletions due to the Bayesian "size principle"; such nonliteral interpretation of sentences should (iii) increase with the perceived noise rate of the communicative situation and (iv) decrease if semantically anomalous meanings are more likely to be communicated. These predictions are borne out, strongly suggesting that human language relies on rational statistical inference over a noisy channel. [ABSTRACT FROM AUTHOR]

We demonstrate a substantial improvement on one of the most celebrated empirical laws in the study of language, Zipf's 75-y-old theory that word length is primarily determined by frequency of use. In accord with rational theories of communication, we show across 10 languages that average information content is a much better predictor of word length than frequency. This indicates that human lexicons are efficiently structured for communication by taking into account interword statistical dependencies. Lexical systems result from an optimization of communicative pressures, coding meanings efficiently given the complex statistics of natural language use. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to the article "Endogenous sources of variation in language acquisition" by Han C-h, J. Musolino and J. Lids in the 113th volume.

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.)