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The Innate Mind Volume 2: Culture and Cognition$
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Peter Carruthers, Stephen Laurence, and Stephen Stich

Print publication date: 2007

Print ISBN-13: 9780195310139

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780195310139.001.0001

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Mental Number Line s

Mental Number Line s

Chapter:
(p.112) 8 Mental Number Lines
Source:
The Innate Mind
Author(s):

Marcus Giaquinto (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195310139.003.0008

Along with our numeral systems, we have an innate sense of cardinal size at par with our sense of duration and distance, refined by cultural practices. The SNARC effect suggests that our number sense representations are associated with positions along a horizontal axis in egocentric space, resulting from an innate propensity to represent familiar sequences in a spatial line with direction culturally determined. The number-space association can be affected by visual imagery; though probably not itself a representation in the visual imagery system. It may be one source of the genuinely visual number line we often use in mathematical thinking. Using Kosslyn's account of the visual imagery system, this chapter explains the sense in which a visual number line can be infinite with linear (as opposed to logarithmic) calibration, and yet gives rise to finite images of number line segments with apparent calibration that is sometimes linear and sometimes logarithmic. The fact that some of us form idiosyncratic visual number lines, possibly in addition to the standard one, provides further evidence of an innate propensity underlying the formation of visual number lines once a written numeral system is acquired.

Keywords:   linear calibration, logarithmic calibration, number comparison, number bisection, number sense, number-space association, reverse SNARC effect, SNARC effect, visual number line

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