Cutting In Line: Discontinuities in the Use of Large Numbers by Adults

David LandyIndiana University
Arthur CharlesworthUniversity of Richmond
Erin OttmarUniversity of Richmond

Abstract

Perceptual tools such as telescopes allow the application of robust internal perceptual systems to apply beyond the range of their unadorned capacity. This paper explores how reasoning over culturally provided representations enables the perception of conceptually distant structures. In particular, this paper examines the behavior of typical adults estimating the position of large numbers (1 thousand to 1 billion) on a number line. Participants—even those who closely match linear placement—show discontinuities in placement in the immediate vicinity of 1 million. This pattern was predicted by a theoretical account in which linear behavior across many orders of magnitude is achieved through highly linear patterns of placement on smaller lines that are recycled and scaled to larger numerosities. Just as the telescope allows perception of the imperceptibly distant, reasoning processes over the natural numbers appear to allow intrinsically limited magnitude-perception systems to apply (with distortion) to much larger scales.

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Cutting In Line: Discontinuities in the Use of Large Numbers by Adults (347 KB)



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