From Summetria to Symmetry: The Making of a Revolutionary Concept
Bibliographic record
Abstract
The basic idea of this fascinating book is that while symmetry has often been regarded as an innate concept of the human mind, there is no historical evidence to support this; and that in fact, the understanding of symmetry is basically a product of the 18th century.As the authors argue, there are two major aspects to this matter, one aesthetic, the other mathematical, both converging on the figures of Adrien-Marie Legendre, who was the first to formulate an exact mathematical definition of symmetry in terms of what he called 'incongruent counterparts', and Gaspard Monge, who was the first to use the term 'symmetry' in a textbook on statics written for students in the French naval academy (wherein symmetry was applied to the problem of determining the center of gravity of ships).In their consideration of the aesthetic aspects of the history of symmetry, the authors consider such thinkers as Plato and Archimedes, Galen, Vitruvius, Alberti, Dürer, Perrault, Montesquieu, and Diderot; whereas the mathematical side of the story includes the works of (again) Plato and Aristotle, Euclid, Archimedes, Boethius, Oresme, Kepler, Galileo, Barrow, and Newton, among others.Noteworthy is the authors' attention to such matters as the subject of harmony and its relations to symmetry in studies of the impact of Vitruvius on Copernicus and the architectural conception of a planetary system, Galileo and the significance of harmony in music, Kepler and Descartes on the structure of snowflakes, and the extent to which both Kepler and Leibniz regarded harmony as a fundamental concept in astronomy and metaphysics.The authors also consider the appearance of symmetry in natural history, specifically in the contexts of botany, crystallography, and zoology.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.003 | 0.023 |
| Scholarly communication | 0.006 | 0.011 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.002 | 0.005 |
| 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".