AIC/BIC/MDL judge models after fitting. But we often need a before-fitting rule: the minimal set of genuinely informative variables for a stated accuracy. Let’s collect saturation cases: projects where adding one more variable stopped reducing the error; and, conversely, cases where a single new, independent quantity unlocked progress. Please post compact summaries: target accuracy, variables included, when improvement stalled, and why (hidden dependence, dimensional redundancy, etc.). The outcome could be a practical “required simplicity” rule of thumb for different fields: how to reach the goal with the fewest variables—without wasting effort.
Number of Variables in a Law of Nature
The number of variables required for a law of nature can vary greatly depending on the complexity of the phenomenon being described. There is no one-size-fits-all answer, but rather a balance between simplicity and explanatory power.
Simplicity vs. AIC/BIC
- *Simplicity*: Simpler models with fewer variables are often preferred due to their ease of interpretation and reduced risk of overfitting.
- *AIC/BIC*: Akaike information criterion (AIC) and Bayesian information criterion (BIC) are metrics used to evaluate model fit while penalizing complexity. They can help determine the optimal number of variables in a model.
Balancing Simplicity and Complexity
- *Parsimony*: The principle of parsimony suggests that models should be as simple as possible while still explaining the data adequately.
- *Model Selection*: Techniques like cross-validation can be used to evaluate the performance of models with different numbers of variables and select the best one.
Considerations
- *Domain Knowledge*: Domain-specific knowledge and expertise can guide the selection of relevant variables and the development of models.
- *Data Quality*: The quality and quantity of data can impact the number of variables that can be reliably included in a model.
No Fixed Number
- *Context-Dependent*: The number of variables required for a law of nature depends on the specific context and phenomenon being studied.
- *Ongoing Refinement*: Models and laws of nature are often refined over time as new data and evidence become available.
Ultimately, the number of variables in a law of nature is determined by the interplay between simplicity, explanatory power, and the complexity of the phenomenon being described
Article Unleashing the Power of Information Theory: Enhancing Accura...
The current understanding of the situation is that fundamental limitations are only part of the picture. The actual achievable measurement accuracy is determined by many additional factors: losses, noise, decoherence, and the specific experimental setup. However, in this literature, the model of the process under study is usually taken as given: it is assumed that the researcher initially knows which physical mechanisms are significant, which parameters need to be controlled, and which dimensionless groups adequately describe the phenomenon. In practice, on the contrary, it is the choice and structural completeness of the model that often predetermine the achievable accuracy even before statistical data processing or the use of additional quantum resources come into play. A methodological gap arises between the “fundamental limit” and the actual experimental results: there is no operational concept that would directly link the adequacy of the model with the upper limit of accuracy. In a number of works on the information method (hereinafter referred to as IM, or FIQ method), this gap is systematically closed. The concept of pre-experimental informativeness of the model is introduced, depending on the choice of the class of the phenomenon, the set of dimensionless criteria taken into account and the ranges of their change. This informativeness sets an a priori level of uncertainty, which is not eliminated by simply increasing the number of measurements: to reduce it, a modification of the model itself is required.
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