THE MERCURY MODELS OF IBN AL-ŠĀṬIR AND COPERNICUS
Bibliographic record
Abstract
Abstract Copernicus' complex Mercury model in De revolutionibus is virtually identical, geometrically, to Ibn al-Šāṭir's (ca. 1305 – ca. 1375). However, the model in his earlier Commentariolus is different and in many ways unworkable. This has led some to claim that the younger Copernicus did not understand his predecessor's model; others have maintained that Copernicus was working totally independently of Ibn al-Šāṭir. We argue that Copernicus did have Ibn al-Šāṭir's models but needed to modify them to conform to a “quasi-homocentricity” in the Commentariolus . This modification, and the move from a geocentric to heliocentric cosmology, was facilitated by the “heliocentric bias” of Ibn al-Šāṭir's models, in which the Earth was the actual center of mean motion, in contrast to Ptolemy and most Islamicate astronomers. We show that: 1) Ibn al-Šāṭir sought to reproduce Ptolemy's critical elongation at the trines(±120°), but changed the Ptolemaic values at 0, ±90, and 180°; 2) in the Commentariolus , Copernicus does not try to produce viable elongations for Mercury; and 3) by the time of writing De revolutionibus , Copernicus is in full control of the Mercury model and is able to faithfully reproduce Ptolemy's elongations at all critical points. We also argue that claims regarding “natural” solutions undermining transmission are belied by historical evidence.
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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 | 0.000 | 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 | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 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".