Does how we use numbers in language shape how we compare them?
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.
Source
Linguistic experiential priors account for notation-dependent numerical representations
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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What they did
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.
What they found
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.
The limits
What it doesn't show
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.
Key terms
- Numerical distance effect
- People are faster and more accurate at comparing numbers that are far apart (2 vs 9) than numbers that are close (8 vs 9).
- Approximate Number System (ANS)
- A proposed evolutionarily old system for representing quantities approximately, shared with other species, onto which number symbols are thought to be mapped.
- Distributional semantic model
- A computer model that represents word meanings as vectors based on which words they appear alongside in large amounts of text.
- Notation dependence
- The idea that different number formats, such as digits and number words, are represented partly separately rather than converted into one abstract code.
- Akaike information criterion (AIC)
- A score for comparing statistical models; lower values mean a better balance of fit and simplicity, and a difference above 2 is usually taken as meaningful.
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Quiz yourself
What did the language model provide in this study?
Common questions
How can a language model tell us anything about how people think about numbers?
The model learns from how often and in what contexts numbers appear in text. If people's comparison speed follows these usage patterns better than true numerical distance, it suggests people's number representations are partly shaped by their language experience.
Does this disprove the idea of an abstract number sense?
No. It shows that linguistic experience predicts symbolic number comparison well and that digits and words may differ somewhat, which the authors say means the ANS need not be the only explanation. It did not test non-symbolic quantities like dot arrays.
Why were some numbers left out?
In Italian, 'uno' also means 'a', 'sei' also means 'you are', and 'venti' also means 'winds', so their language-based vectors would mix in unrelated meanings. Those items were excluded from the analyses.
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