On the origins of logarithmic number-to-position mapping.
Why this work is in the frame
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Bibliographic record
Abstract
The number-to-position task, in which children and adults are asked to place numbers on a spatial number line, has become a classic measure of number comprehension. We present a detailed experimental and theoretical dissection of the processing stages that underlie this task. We used a continuous finger-tracking technique, which provides detailed information about the time course of processing stages. When adults map the position of 2-digit numbers onto a line, their final mapping is essentially linear, but intermediate finger location show a transient logarithmic mapping. We identify the origins of this log effect: Small numbers are processed faster than large numbers, so the finger deviates toward the target position earlier for small numbers than for large numbers. When the trajectories are aligned on the finger deviation onset, the log effect disappears. The small-number advantage and the log effect are enhanced in dual-task setting and are further enhanced when the delay between the 2 tasks is shortened, suggesting that these effects originate from a central stage of quantification and decision making. We also report cases of logarithmic mapping-by children and by a brain-injured individual-which cannot be explained by faster responding to small numbers. We show that these findings are captured by an ideal-observer model of the number-to-position mapping task, comprising 3 distinct stages: a quantification stage, whose duration is influenced by both exact and approximate representations of numerical quantity; a Bayesian accumulation-of-evidence stage, leading to a decision about the target location; and a pointing stage. (PsycINFO Database Record
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.005 | 0.003 |
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 it