The cultural origins of symbolic number.

O’Shaughnessy, David M.; Gibson, Edward; Piantadosi, Steven T.

doi:10.1037/rev0000289

Cited by 11 publications

(14 citation statements)

References 202 publications

(360 reference statements)

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“…With instruction, human beings may also come to understand symbolic representations of number (O'Shaughnessy, Gibson, & Piantadosi, 2021). We count arrays of objects and we use numerical symbols such as Arabic digits to refer to precise quantities.…”

Section: Introductionmentioning

confidence: 99%

A theory of perceptual number encoding.

Lourenco¹,

Aulet²

2023

Psychological Review

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There has long been interest in how the mind represents numerical magnitude, particularly in the absence of symbols. For humans and nonhuman animals, number represents a core dimension of perceptual experience by which objects in the physical world are delineated. The physical world is also well characterized by other dimensions, many of which covary with number. Yet, the general consensus is that number is perceived independently of other magnitudes that co-occur with it. Here, we present evidence against the independence of number perception. In particular, we use evidence from neuroimaging, computational modeling, visual illusions, and psychophysics to introduce a novel theory of visual number encoding, wherein nonnumerical magnitude information such as cumulative surface area is encoded along with number and sustained throughout visual perception. Moreover, we propose that the experience of number per se reflects the readout of a multidimensional (i.e., integral) representation vis-à-vis selective attention, not the independent encoding of number.

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Section: Introductionmentioning

confidence: 99%

A theory of perceptual number encoding.

Lourenco¹,

Aulet²

2023

Psychological Review

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“…They concluded that none of the predictions were supported: Not all human groups have developed numbers and symbol systems vary widely across those that have (Chrisomalis, 2010), numbers are difficult for children to learn (Baroody, 2006), and timing of learning depends on external factors such as the amount of data that children are exposed to (Levine et al, 2010). O’Shaughnessy et al (2022) concluded that symbolic number systems have developed in response to social and economic needs of particular cultures, rather than innate or biological causes. For example, “modern” Hindu-Arabic numerals only became widely used in Europe after Leonardo of Pisa published Liber Abaci (“The Book of Calculation”) in 1202, which showed that algorithmic calculation with Hindu-Arabic numerals was superior to existing methods with Roman numerals and abacus and was very influential among Venetian merchants and traders (Sigler, 2003).…”

Section: Discussionmentioning

confidence: 99%

“…Although the historical development of mathematics has clearly been affected by economic and cultural factors, O’Shaughnessy et al’s (2022) proposal overlooks the universal features of symbolic number systems. Chrisomalis (2010) provided a structural typology of all known notation systems—over 100 different systems that have been used in the past 5,500 years—which associate “numeral phrases” (i.e., strings of symbols) with particular exact numbers.…”

Section: Discussionmentioning

confidence: 99%

The psychological scaffolding of arithmetic.

Grice¹,

Kemp²,

Morton³

et al. 2024

Psychological Review

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Where does arithmetic come from, and why are addition and multiplication its fundamental operations? Although we know that arithmetic is true, no explanation that meets standards of scientific rigor is available from philosophy, mathematical logic, or the cognitive sciences. We propose a new approach based on the assumption that arithmetic has a biological origin: Many examples of adaptive behavior such as spatial navigation suggest that organisms can perform arithmetic-like operations on represented magnitudes. If so, these operations—nonsymbolic precursors of addition and multiplication—might be optimal due to evolution and thus identifiable according to an appropriate criterion. We frame this as a metamathematical question, and using an order-theoretic criterion, prove that four qualitative conditions—monotonicity, convexity, continuity, and isomorphism—are sufficient to identify addition and multiplication over the real numbers uniquely from the uncountably infinite class of possible operations. Our results show that numbers and algebraic structure emerge from purely qualitative conditions, and as a construction of arithmetic, provide a rigorous explanation for why addition and multiplication are its fundamental operations. We argue that these conditions are preverbal psychological intuitions or principles of perceptual organization that are biologically based and shape how humans and nonhumans alike perceive the world. This is a Kantian view and suggests that arithmetic need not be regarded as an immutable truth of the universe but rather as a natural consequence of our perception. Algebraic structure may be inherent in the representations of the world formed by our perceptual system.

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“…Our findings are consistent with this account: when there were discrepancies in performance across different versions of tasks, they tended to occur in formally educated children. There are other examples of practice and context influencing numerical ability including studies of market vs. school arithmetic in Brazilian [ 33 , 34 ] and Indian [ 35 ] children, and in anthropological analyses of the influences of economics and trade in numerical literacy [ 36 , 37 ]. Beyond context, different tasks may have different demands on domain-general cognitive load, or working memory.…”

Section: Discussionmentioning

confidence: 99%

Verbal counting and the timing of number acquisition in an indigenous Amazonian group

Boni

Jara‐Ettinger²,

Sackstein³

et al. 2022

PLoS ONE

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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.

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The cultural origins of symbolic number.

Cited by 11 publications

References 202 publications

A theory of perceptual number encoding.

A theory of perceptual number encoding.

The psychological scaffolding of arithmetic.

Verbal counting and the timing of number acquisition in an indigenous Amazonian group

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