Fitting our models to the data, we find that both models accurately captured the downward trend as well as some local peaks, yet it failed to do so for decade numbers. Why?
Using the Google N-grams database, we looked at the frequency of number words from 1 to 99 in 6 languages.
Across the board, we found two patterns:
🔻 Frequency drops with size
📈 Local spikes at certain numbers—especially round ones and those with many small divisors
With the cumulative model, we get an added benefit: it yields precise hypotheses about the mental representation of each number.
For instance, 24 is most likely represented as 4×6, but also as 2×12, 3×8, or the successor of 23—in that order.
Some of this isn’t new.
Dehaene & Mehler (1992) already showed that number word frequencies follow a ~1/n² law.
They suggested that while cultural or environmental factors could explain some of the frequency curve, the psychological organization of number concepts must play a major role.
In short: number frequencies show consistent patterns across languages.
A simple model grounded in a Language of Thought—recursively using +, ×, and 1—captures these patterns remarkably well.
This supports the idea that number concepts are built compositionally in the mind.
doi.org/10.1016/j.co...
Our model was actually missing a crucial ingredient: approximation.
Locutors experience a tradeoff between accuracy of the expressed quantity and length of the expression. Adding a parameter to account for this accurately models the whole curve.
Building on this, we tested a new cognitive model based on a Language of Thought (LoT) introduced by Dehaene et al., 2025.
The idea: number concepts are constructed in the mind using simple building blocks—1, +, and ×.
Some numbers seem to show up everywhere. Think of 10, 12, 24, 36...
Others—like 26 or 34—don’t get the same attention.Why? In our new paper with @standehaene.bsky.social and @mathiassablemeyer.bsky.social, we argue it's because of how the mind builds number concepts.
🧵
doi.org/10.1016/j.co...
We developed two models to explain how often a number appears:
- Shortest-path: only the simplest construction determines frequency
- Cumulative: all valid constructions contribute to frequency, weighted by their complexity
Here's how:
Maxence Pajot
Our new study (Debray*, Karami* et al.) explores how the brain encodes basic math concepts (integers, fractions, shapes). Samuel Debray led the 7T fMRI & behavioral work; I led the MEG.
@danielavalerio.bsky.social
@chrplr.bsky.social
@standehaene.bsky.social
www.biorxiv.org/content/10.6...
