Review of: "Volume-Based Probability: Outcome Frequencies from Deterministic Geometry"
Bibliographic record
Abstract
This is a nicely written paper describing how probabilistic frequency values can arise from strict deterministic dynamics through coarse graining.A great many assumptions are required to support the proof.This result does not seem to be all that surprising given the extensive literature available on symbolic dynamics and chaotic systems theory.I am wondering what exactly distinguishes this result from what is already known in that literature.The author promises to demonstrate how the Born rule of quantum mechanics can arise from this approach.They state that that will be shown in a subsequent paper as it is certainly not clear here.After all, the determinism in quantum mechanics is not in the dynamics of measurement values of quantum systems (assuming that even has any meaning) but in the dynamics of the wave function, which relates to the probability distribution of values of a system.I will be interested to see what they show.I wonder if the author is aware of the work of Masao Nagasawa, who many years ago showed the equivalence between linear Schrdinger equations and non-linear diffusion equations, which have identical probability distributions both given by a Born rule.The derivation of this in the case of the diffusion equation is entirely classical.Likewise, there is an equivalence between linear diffusion equations and non-linear Schrdinger equations, again with identical probabilities.His is a very deep result.
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 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 | 0.016 | 0.065 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.007 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.097 | 0.003 |
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".