The role of nature and brain in demystifying the “unreasonable effectiveness of mathematics”
Bibliographic record
Abstract
In 1960, Eugene P. Wigner shared his observation of the unreasonable effectiveness of mathematics in formulating regularities in nature. Later, Jean Piaget recognized the functioning of the living organism as a source of harmony between mathematics and nature. However, not only did Piaget not demonstrate how more advanced mathematics could be linked to natural behavior, the unique functional feature of human behavior was absent in his explanation of its ultimate outcome (i.e. mathematics). The present analysis proposes that the effectiveness of mathematics seems puzzling because of the apparent disconnection between nature, the characteristics of the human brain and behavior, and the properties of mathematical constructs. The behavior of humans and other animals (i.e. rodents) will be the basis of comparison to meet the objective of the analysis in demystifying the effectiveness of mathematics in natural sciences by (1) showing the potential natural roots of some mathematical constructs in the organization of behavior with some specific examples in mathematics, (2) demonstrating a mechanism for the construction of mathematical reasoning as well as for the invention of mathematical constructs, and (3) discussing how mathematics seems disconnected from nature as a result of mathematical inventions guided by the symmetry principle.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.039 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".