Bibliographic record
Abstract
Abstract Among Alcuin’s 53 problems in his Propositiones there are a series of “story problems,” as they are called today—numbers 2, 3, 4, 7, 16, 36, 37, 40, 44, 45, and 48—involving basic algebraic thinking. The problems are solved nowadays by setting up an equation or system of equations; but in Alcuin’s era, there was no formal algebra as such. These problems nevertheless put on display what algebra is essentially all about—thinking about problems in abstract ways, rather than concretely in arithmetical ways. This chapter deals with Alcuin’s story problems, examining a few other famous ones, such as the well-known story problem devised by Sir Isaac Newton. It also schematically discusses the Fundamental Theorem of Algebra and its basis in complex numbers. Alcuin’s inclusion of algebraic problems in his text showed to his medieval readers that the topic of equations was not the daunting one that his readers might have thought it was. The main difference between carrying out an operation arithmetically and doing so algebraically lies in thinking about the operation in general rather than in specific numerical terms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.083 | 0.024 |
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".