Numerical cognition
Does how we use numbers in language shape how we compare them?
Open access · cc by · source: Europe PMC
How similar two numbers are in everyday language use predicted how quickly people could say which was larger better than the actual difference between the numbers did, with some sign that digits and number words are represented differently.
Study at a glance
- Design
- Human experiment — Experiment 1 was purely computational (fastText word-vector distances for Italian numbers); Experiment 2 had participants compare pairs of Arabic digits and of Italian number words, and mixed models compared real numerical distance versus language-derived distances as predictors.
- N
- N=55 · 55 Italian-speaking university students in the behavioural Experiment 2 (Experiment 1 used no participants, only a text-trained language model).
- Population
- Native Italian-speaking university students tested online
- Outcome
- Correct response times and accuracy in choosing the larger of two numbers, compared across predictors using AIC model fit
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Key findings
Language-based distances closely tracked real numerical distance for both digits and words. For response times, the language-based predictors fitted the data better than real numerical distance in both tasks; for digits, the digit-based language measure fitted best, but for number words both language measures did equally well. For accuracy, all predictors did equally well for digits, while only the word-based language measure significantly predicted accuracy for number words. So the evidence for notation-specific representations was partial rather than consistent.
Methodology
First, the researchers used a language model (fastText) trained on around 11 billion words of Italian text to measure how similarly each pair of numbers is used in language, separately for digits (like 7) and number words (like sette). They then had 55 Italian students choose the larger number in pairs from 1 to 9, once with digits and once with written number words. Mixed-effects models tested whether real numerical distance, digit-based language distance or word-based language distance best predicted each person's speed and accuracy.
Limitations
The notation-dependence pattern was only partial and flipped between speed and accuracy across the two tasks, so it could be fragile; several model differences were small. The language distances and true numerical distances are highly correlated, making it hard to separate their contributions, and the study is correlational at the level of stimuli rather than manipulating anyone's language experience. It used only single-digit numbers, excluded 1 and 6 because of Italian word ambiguities, tested adults online in one language, and did not examine children, so it cannot show how these links develop. Faster responses to digits than words may simply reflect shorter string length.
How this study connects
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