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How culture makes mathematics possible


Numerical capacity isn’t inherent but an abstract cultural product, says a neuroscientist. Stephen Fleischfresser reports.


Animals may have an innate understanding of quantities but counting requires understanding of symbols that can only come from culture, according to Rafael Núñez.
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Is numerical ability due to nature or nurture?

A spirited debate over whether the capacity for numbers and arithmetic is an evolved trait is soon to be published in Trends in Cognitive Sciences. At stake is whether the ability to use numbers is significantly biological, like the structure of the eye, or trivially biological, like the ability to snowboard.

Researchers in ‘numerical cognition’ widely accept there is an evolved capacity specific for numbers and arithmetic, a position supported by the observation that many non-human animals also seem to display numerical capacity.

Rafael Núñez, professor of cognitive science and director of the Embodied Cognition Laboratory at the University of California, San Diego, begs to disagree. Núñez, a veteran in the cognitive neuroscience of mathematics and numbers, says “numerical cognition is not biologically endowed”.

The notion of number is different to quantity, he argues, because it involves a symbolic element. Specifically, we refer to numbers using symbols, either written or spoken, something singular to Homo sapiens. “Developing socio-historically,” he says, “symbolic reference puts ‘number’ in a qualitatively separate realm from the quantity-related phenomena observed in nonhuman animals”.

This, he argues, “places ‘number’ outside the reach of biological evolution via natural selection”. In other words, ‘number’ is cultural.

Displays of non-human numerical ability are only possible through extensive training: they are expressions of culture.

What we share with non-human animals, Núñez argues, is ‘quantical cognition’, the capacity to discriminate quantity, not number. This takes the form of ‘subitising’, the ability to know how many objects there are in a small grouping without counting, and ‘large quantity discrimination’ (LQD), the very imprecise similar ability that applies to large numbers.

These are the ‘biologically evolved preconditions’ (BEPs) for number, Núñez suggests, with the concept of number being cultural in the same way as snowboarding. In the case of snowboarding, balance and the ability to navigate by eye are the BEPs. Just as snowboarding uses these biological roots evolved for very different purposes, the number capability hitchhikes on the evolved biological capacity to discriminate quantity.

He supports his argument by pointing to studies of hunter-gatherer societies that indicate the vast majority only have words for numbers up to five, neatly in the subitising range.

Beyond this, he provides evidence that speakers of English and Chinese use different parts of the brain when processing Arabic numerals, an indication that number is “mediated by cultural factors, such as writing systems, educational organisation and enculturation”.

Researchers in the field of numerical cognition will no doubt fight these findings. Andreas Nieder, a well-known neuroscientist of numbers, in the same issue of Trends, does offer a rebuttal of sorts.

Nonetheless, it will take a great deal more than this to settle the debate. Núñez’s argument is subtle and persuasive and may well shake up the field.

Stephen fleischfresser.jpg?ixlib=rails 2.1
Stephen Fleischfresser is a lecturer at the University of Melbourne's Trinity College and holds a PhD in the History and Philosophy of Science.
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