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When eleven does not equal 11: Investigating exactness at a number's upper bound.

Ira Noveck¹, Martial Fogel², Kira Van Voorhees¹

¹Université de Paris-Cité, LLF, CNRS, Paris, France.

|April 28, 2022

Summary

Symbolic numbers like "11" provide exact readings, unlike verbal numbers which imply "at least." This study explored how number presentation affects exactness in French speakers using a numerical magnitude task.

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Area of Science:

Cognitive Psychology
Linguistics
Cognitive Anthropology

Background:

The approximate number system (ANS) treats numbers imprecisely, lacking mechanisms for exact readings.
Linguistic-pragmatic and cultural factors may influence number upper bounds for exact interpretations.
Symbolic number representations may differ from verbal ones in conveying exactness.

Purpose of the Study:

To investigate if symbolic number expressions (e.g., "11") yield exact readings, unlike verbal expressions (e.g., "onze") which imply "at least."
To test the hypothesis that symbolic number forms explicitly provide exact readings, while verbal forms provide lower-bounded readings.

Main Methods:

A Numerical Magnitude Task (NMT) was administered to French-speaking participants.
Participants judged if a number was greater or lesser than a benchmark (12).
Numbers were presented in three formats: symbolic (Hindu-Arabic), oral, and spelled-out-in-letters.
A Number Identification Task (NIT) controlled for individual recognition speed.

Main Results:

Spelled-out numbers like "onze" (eleven) led to longer decision times and more errors compared to "treize" (thirteen).
Symbolic numbers "11" and "13" showed comparable processing times.
Oral number forms did not differ significantly in decision times, aligning with symbolic presentation results.

Conclusions:

Number presentation format significantly impacts interpretation, with symbolic forms potentially facilitating exactness.
Linguistic and cultural influences shape the upper bounds of number interpretation, affecting exactness.
Further research is needed to fully understand the cognitive mechanisms underlying number representation and interpretation across different modalities.