The cultural challenge in mathematical cognition

Beller, Sieghard; Bender, Andrea; Chrisomalis, Stephen; Jordan, Fiona M.; Overmann, Karenleigh A.; Saxe, Geoffrey B.; Schlimm, Dirk

doi:10.5964/jnc.v4i2.137

Cited by 21 publications

(12 citation statements)

References 75 publications

(64 reference statements)

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“…Depending on the type of task, as well as on the conditions in which a given task is performed, different neural mechanisms might be invoked for disparate kinds of mental calculations (Curtis et al, 2016;Yusoff et al, 2016;Beller et al, 2018;Hickendorff et al, 2019). For example, complex addition or subtraction is based on mechanisms that are distinct from the ones for complex multiplication or division.…”

Section: Introductionmentioning

confidence: 99%

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

Klichowski

Króliczak

2020

Front. Psychol.

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One of the most critical skills behind consumer's behavior is the ability to assess whether a price after a discount is a real bargain. Yet, the neural underpinnings and cognitive mechanisms associated with such a skill are largely unknown. While there is general agreement that the posterior parietal cortex (PPC) on the left is critical for mental calculations, and there is also recent repetitive transcranial magnetic stimulation (rTMS) evidence pointing to the supramarginal gyrus (SMG) of the right PPC as crucial for consumer-like arithmetic (e.g., multi-digit mental addition or subtraction), it is still unknown whether SMG is involved in calculations of sale prices. Here, we show that the neural mechanisms underlying discount arithmetic characteristic for shopping are different from complex addition or subtraction, with discount calculations engaging left SMG more. We obtained these outcomes by remodeling our laboratory to resemble a shop and asking participants to calculate prices after discounts (e.g., $8.80-25 or $4.80-75%), while stimulating left and right SMG with neuronavigated rTMS. Our results indicate that such complex shopping calculations as establishing the price after a discount involve SMG asymmetrically, whereas simpler calculations such as price addition do not. These findings have some consequences for neural models of mathematical cognition and shed some preliminary light on potential consumer's behavior in natural settings.

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Section: Introductionmentioning

confidence: 99%

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

Klichowski

Króliczak

2020

Front. Psychol.

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“…As cultural objects go, numbers occupy a niche of their own; some can be surreptitious and veiled under a cloak of superstition, for example, the association of number 13 with bad luck in American culture, the link between number 4 and death in Chinese culture [2], the avoidance of counting people by numbers in Jewish orthodoxy on account of its bad omen [1]. Ongoing research of number words across languages paints a landscape of contrasts ( [3][4][5] inter alia). On the one hand, we observe extreme variation in the different types of systems that various cultures use (or not!)…”

Section: Why Numbers?mentioning

confidence: 99%

“…For most Indo-European languages, building higher numbers and extending number words to denote larger quantities involves following (existing) language-internal rules. Thus, excluding the lower numbers (1)(2)(3)(4)(5)(6)(7)(8)(9), which are encoded by unanalysable atoms, and the running numbers (11)(12)(13)(14)(15)(16)(17)(18)(19), given their considerable variation, for the remaining higher numbers, stable morphological patterns can be detected where the base (10s, 20s, 30s, 40s) is combined with the atom (3 in 23, 5 in 55) in a head-dependent manner, in accordance with patterns involving nominal and clausal word orders [2]. That is, morphological word-formation process ties in with syntactic constraints.…”

Section: Number Words-not a Privileged Categorymentioning

confidence: 99%

The history of number words in the world's languages—what have we learnt so far?

Calude

2021

Phil. Trans. R. Soc. B

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For over 100 years, researchers from various disciplines have been enthralled and occupied by the study of number words. This article discusses implications for the study of deep history and human evolution that arise from this body of work. Phylogenetic modelling shows that low-limit number words are preserved across thousands of years, a pattern consistently observed in several language families. Cross-linguistic frequencies of use and experimental studies also point to widespread homogeneity in the use of number words. Yet linguistic typology and field documentation reports caution against positing a privileged linguistic category for number words, showing a wealth of variation in how number words are encoded across the world. In contrast with low-limit numbers, the higher numbers are characterized by a rapid and morphologically consistent pattern of expansion, and behave like grammatical phrasal units, following language-internal rules. Taken together, the evidence suggests that numbers are at the cross-roads of language history. For languages that do have productive and consistent number systems, numerals one to five are among the most reliable available linguistic fossils of deep history, defying change yet still bearing the marks of the past, while higher numbers emerge as innovative tools looking to the future, derived using language-internal patterns and created to meet the needs of modern speakers. This article is part of the theme issue ‘Reconstructing prehistoric languages’.

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“…Number words are possibly one of the most paramount cultural tools for expressing numerosities. Different aspects of numerical cognition are indeed saturated with culture (Beller et al, 2018;Núñez, 2009;Núñez, 2017), with proprieties of numeration systems that vary across languages (Bender & Beller, 2012). One of these proprieties is certainly the extent of the system itself.…”

Section: Introductionmentioning

confidence: 99%

The use of number words in natural language obeys Weber’s law.

Rinaldi¹,

Marelli²

2020

Journal of Experimental Psychology: General

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It has been suggested that the origins of number words can be traced back to an evolutionarily ancient approximate number system, which represents quantities on a compressed scale and complies with Weber's law. Here, we use a data-driven computational model, which learns to predict one event (a word in a text corpus) from associated events, to characterize verbal behavior relative to number words in natural language, without appeal to perception. We show that the way humans use number words in spontaneous language reliably depends on numerical ratio -a clear signature of Weber's law -thus perfectly mirroring the human and non-human psychophysical performance in comparative judgments of numbers. Most notably, the adherence to Weber's law is robustly replicated in a wide range of different languages. Together, these findings suggest that the everyday use of number words in language rests upon a pre-verbal approximate number system, which would thus affect the handling of numerical information not only at the input level but also at the level of verbal production.

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The cultural challenge in mathematical cognition

Cited by 21 publications

References 75 publications

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

The history of number words in the world's languages—what have we learnt so far?

The use of number words in natural language obeys Weber’s law.

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