Chapter

Mental Number Lines I thank Brian Butterworth, Susan Carey, Peter Carruthers, Robyn Carston, Stephen Laurence, Richard Samuels, Gabriel Segal, and Elizabeth Spelke for helpful comments.

Marcus Giaquinto

in The Innate Mind: Volume 2: Culture and Cognition

Published in print January 2007 | ISBN: 9780195310139
Published online May 2007 | e-ISBN: 9780199871209 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195310139.003.0008

Series: Evolution and Cognition Series

 Mental Number Lines I thank Brian Butterworth, Susan Carey, Peter Carruthers, Robyn Carston, Stephen Laurence, Richard Samuels, Gabriel Segal, and Elizabeth Spelke for helpful comments.

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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

Chapter.  8569 words.  Illustrated.

Subjects: Philosophy of Mind

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