Mathematical Modelling of Physical Reality: From Numbers to Fractals, Quantum Mechanics and the Standard Model
Bibliographic record
Abstract
In physics we construct idealized mathematical models in order to explain various phenomena which we observe or create in our laboratories. In this article, I recall how sophisticated mathematical models evolved from the concept of a number created thousands years ago and I discuss some challenges and open questions in quantum foundations and in the standard model. We liberated nuclear energy, landed on the Moon and built ‘quantum computers’. Encouraged by these successes many believe, that when we reconcile the general relativity with the quantum theory then we will have the correct theory of everything. Perhaps, we should be much more humble. Our perceptions of reality are biased by our senses and by our brain bending them to meet our priors and expectations. Our abstract mathematical models describe only in an approximate way different layers of physical reality. To describe the motion of a meteorite we can use a concept of a material point but the point-like approximation breaks completely, when the meteorite hits the Earth. Similarly, thermodynamic, chemical, molecular, atomic, nuclear, elementary particle layers of physical reality are described using specific abstract mathematical models and approximations. In my opinion, the theory of everything does not exist.
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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.009 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".