Parallel and serial processes in number-to-quantity conversion
Bibliographic record
Abstract
Converting a multi-digit number to quantity requires processing not only the digits but also the number’s decimal structure, thus raising several issues. First, are all the digits processed in parallel, or serially from left to right? Second, given that the same digit, at different places, can represent different quantities (e.g., “2” can mean 2, 20, etc.), how is each digit assigned to its correct decimal role? We presented participants with two-digit numbers and asked them to point at the corresponding locations on a number line, while we recorded their pointing trajectory. Crucially, on some trials, the decade and unit digits did not appear simultaneously. When the decade digit was delayed, the decade effect on finger movement was delayed by the same amount. However, a lag in presenting the unit digit delayed the unit effect by 35 ms less than the lag duration, a pattern reminiscent of the psychological refractory period, indicating an idle time window of 35 ms in the units processing pathway. When a lag transiently caused a display of just one digit on screen, the unit effect increased and the decade effect decreased, suggesting errors in binding digits to decimal roles. We propose that a serial bottleneck is imposed by the creation of a syntactic frame for the multidigit number, a process launched by the leftmost digit. All other stages, including the binding of digits to decimal roles, quantification, and merging them into a whole-number quantity, appear to operate in parallel across digits, suggesting a remarkable degree of parallelism in expert readers.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".