Bibliographic record
Abstract
Abstract Alcuin’s arithmetic problems not only bring out essential properties of numbers and numerals, but also cultivate inquisitiveness about these properties. This chapter discusses the problems numbered 1, 15, 46, 49, 50, 52, and 53 in Alcuin’s Propositiones, in which arithmetic is highlighted. These stimulate fundamental arithmetical thinking, showing how it can be applied to common problems of life, such as dividing up an inheritance—a theme that was treated cleverly centuries later by the Italian mathematician Niccolò Tartaglia. Among the theoretical ideas that these problems embed are the number line and optimization. Also discussed in this chapter is the perceived relation between numeration and numerology, which was implied in several of the problems, focusing on the number 7, which has been treated numerically and mystically since antiquity, starting with the Egyptian Rhind Papyrus. Overall, Alcuin’s problems bring out that arithmetic is everywhere one looks, from figuring out how to divide money and efficient ways to plow a field to figuring out ways to transport something under limiting conditions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.014 | 0.013 |
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; both teacher heads agree on what is shown here.
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".