Units of representation: Children’s perception of number in the “connectedness illusion”
Bibliographic record
Abstract
The developmental and evolutionary origins of abstract number reasoning have long been debated. Central to this debate is the underlying unit: whether the quantitative reasoning observed in infants and animals necessitates truly numeric object-level representation or can instead be inferred from covarying low-level spatial frequency. Recent studies with adults rely on the “connectedness illusion” to dissociate cardinality from spatial frequency, suggesting object-level representation is fundamental. However, whether these representations exist early in development remains underexplored. We use the connectedness illusion to test whether 3–6-year-old children enumerate objects or spatial frequency. Children complete a non-symbolic comparison task modeled after He et al. (2009). On 50% of trials, two dots are connected by a line, forming a “barbell.” Results show that, like adults, children underestimate connected displays despite instructions to ignore the connections. These findings suggest that object-level representations, rather than low-level spatial frequency, underlie children’s quantitative reasoning.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.022 |
| Science and technology studies | 0.000 | 0.008 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.014 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".