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

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.