Some thoughts on mathematics in the workplace and in school
Bibliographic record
Abstract
Submittedfollowing a conversation with the Editor about the recent death of Benoit.B Mandelbrot.In 1989, I was a mathematics and compute!science teacher and had a Grade 10 student, Tim, in my Grade 12 computer science class who was well ahead of his peers and needed a challenge.Exploring fractals seemed to be the challenge that sparked his interest.It was a topic that fascinated me as well.Fractal work was relatively new: the Mandelbrot set appeared in 1980 and Ihe Fractal Geometry of Nature had been published in 1982 (Mandelbrot, 1982).While limited technology stood in the way of Tim and I modeling a full range of fractals, om exploration led to work with a range of concepts, such as complex numbers and seeded iterative processes Dming that year of exploration, Mandelbrot was giving a lectme at the University of Guelph, where he was being given an honorary doctorate.As this was just an hour away from our school, Tim and I took the afternoon to drive to Guelph to hear the lecture.We were mesmerized.Mandelbrot described Julia sets and proceeded to show us fractal images that resembled art-work and geographical configmations, well beyond any of the rough black ink blots we were getting with the low resolution computer technology available in om school.Mathematics came alive Fractals became a way of ''seeing mathematics" Fractals can be generated in a va1iety of ways.One way that Tim and I explored is tluough a quadratic mapping of
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".