What is it about?

One might think that numbers presented symbolically (as in "11") have the same meaning when they are presented in a written-out form (as in "eleven"). Based on work in pragmatics (which concerns the way people understand the intended meaning of a signal), we were not so sure. Our hypothesis was that symbolic representations are more likely to be understood as "exact" (as in "at least and no greater than") compared to written out versions (which would have a solid lower bound, the "at least" part, but a fluid upper bound). To test our account, we had participants carry out a Numerical Magnitude Task, in which they repeatedly determine whether a randomly presented number (from 8-11 and 13-16) was lesser than or greater than a benchmark (12). This was done for numbers in two other conditions, one presented written-out in French ("huit" -"onze"; "treize" - "seize") and another that presented its numbers over headphones orally, e.g. “/ˈon.zə/”). As far as the written-out version goes, what we today refer to as glottographic cases, we expected participants to (make more errors) and to take longer to respond "lesser than," to "eleven" ("onze" in French) compared to cases in which one needs to respond "greater than" for "thirteen" ("treize") because, only for the former, is one required to pragmatically strengthen the presented stimulus by solidifying its upper limit. We did not expect this pattern of results for, what we now call ideographic (the symbolic) cases; for these, we expected participants to always come up with an exact meaning. Our results supported this prediction.

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Why is it important?

Many theories assume that our neural representation for number is largely unaffected by the way it is presented.


This project was great fun from beginning to end.

Ira Noveck
Centre National de la Recherche Scientifique

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This page is a summary of: When eleven does not equal 11: Investigating exactness at a number’s upper bound, PLoS ONE, April 2022, PLOS, DOI: 10.1371/journal.pone.0266920.
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