Counting on the motor system: Rapid action planning reveals the format- and magnitude-dependent extraction of numerical quantity
Bibliographic record
Abstract
Symbolic numbers (e.g., "2") acquire their meaning by becoming linked to the core nonsymbolic quantities they represent (e.g., two items). However, the extent to which symbolic and nonsymbolic information converges onto the same internal core representations of quantity remains a point of considerable debate. As nearly all previous work on this topic has employed perceptual tasks requiring the conscious reporting of numerical magnitudes, here we question the extent to which numerical processing via the visual-motor system might shed further light on the fundamental basis of how different number formats are encoded. We show, using a rapid reaching task and a detailed analysis of initial arm trajectories, that there are key differences in how the quantity information extracted from symbolic Arabic numerals and nonsymbolic collections of discrete items are used to guide action planning. In particular, we found that the magnitude derived from discrete dots resulted in movements being biased by an amount directly proportional to the actual quantities presented whereas the magnitude derived from numerals resulted in movements being biased only by the relative (e.g., larger than) quantities presented. In addition, we found that initial motor plans were more sensitive to changes in numerical quantity within small (1-3) than large (5-15) number ranges, irrespective of their format (dots or numerals). In light of previous work, our visual-motor results clearly show that the processing of numerical quantity information is both format and magnitude dependent.
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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 | 0.003 | 0.001 |
| 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) | 0.000 | 0.000 |
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; a candidate call from one teacher head, not a consensus.
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".