Groping Toward Linear Regression Analysis: Newton's Analysis of\n Hipparchus' Equinox Observations
Bibliographic record
Abstract
In February 1700, Isaac Newton needed a precise tropical year to design a new\nuniversal calendar that would supersede the Gregorian one. However,\n17th-Century astronomers were uncertain of the long-term variation in the\ninclination of the Earth's axis and were suspicious of Ptolemy's equinox\nobservations. As a result, they produced a wide range of tropical years. Facing\nthis problem, Newton attempted to compute the length of the year on his own,\nusing the ancient equinox observations reported by a famous Greek astronomer\nHipparchus of Rhodes, ten in number. Though Newton had a very thin sample of\ndata, he obtained a tropical year only a few seconds longer than the correct\nlength. The reason lies in Newton's application of a technique similar to\nmodern regression analysis. Newton wrote down the first of the two so-called\n'normal equations' known from the ordinary least-squares (OLS) method. In that\nprocedure, Newton seems to have been the first to employ the mean (average)\nvalue of the data set, while the other leading astronomers of the era (Tycho\nBrahe, Galileo, and Kepler) used the median. Fifty years after Newton, in 1750,\nNewton's method was rediscovered and enhanced by Tobias Mayer. Remarkably, the\nsame regression method served with distinction in the late 1920s when the\nfounding fathers of modern cosmology, Georges Lemaitre (1927), Edwin Hubble\n(1929), and Willem de Sitter (1930), employed it to derive the Hubble constant.\n
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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 | 0.011 | 0.048 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.005 | 0.005 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 0.004 |
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".