Divergence and the Complexity of Difference in Text and Culture
Bibliographic record
Abstract
Measuring how much two documents differ is a basic task in the quantitative analysis of text. Because difference is a complex, interpretive concept, researchers often operationalize difference as distance, a mathematical function that represents documents through a metaphor of physical space. Yet the constraints of that metaphor mean that distance can only capture some of the ways that documents can relate to each other. We show how a more general concept, divergence, can help solve this problem, alerting us to new ways in which documents can relate to each other. In contrast to distance, divergence can capture enclosure relationships, where two documents differ because the patterns found in one are a partial subset of those in the other, and the emergence of shortcuts, where two documents can be brought closer through mediation by a third. We provide an example of this difference measure, Kullback–Leibler Divergence, and apply it to two worked examples: the presentation of scientific arguments in Charles Darwin’s Origin of Species (1859) and the rhetorical structure of philosophical texts by Aristotle, David Hume, and Immanuel Kant. These examples illuminate the complex relationship between time and what we refer to as an archive’s “enclosure architecture”, and show how divergence can be used in the quantitative analysis of historical, literary, and cultural texts to reveal cognitive structures invisible to spatial metaphors.
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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 | 0.014 | 0.108 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.009 | 0.008 |
| Science and technology studies | 0.003 | 0.023 |
| Scholarly communication | 0.013 | 0.026 |
| Open science | 0.002 | 0.008 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".