TLDR: Math and models can aid with understanding, but fundamentally they're about divination, not explanation. And explanation is the core of science. Over application of models is as bad as p-hacking, in that false explanations for phenomena are promulgated. At least with p-hacking, one other paper can say that a correlation was not shown. Whereas with model-hacking, there is often a tendency to "tweak" the model to fit, ala the earth-centric model of the solar system with its epicycles.
> And what is it about comparing computational weather models to p-hacking?
P-hacking is just an extension of assuming p-values past a certain point are very good evidence of real-world correlation. The Princeton Engineering Anomalies Research has evidence showing human-operator specific effects on computerized random processes at the 7 sigma statistical level: https://pearlab.icrl.org/pdfs/1997-correlations-random-binar...
Do you believe that this evidence of possible psychic phenomena is real without validated mechanistic means?
> Good weather predictions provide value to lots of people, while p-hacking is looking for results where there are none, only benefitting the hacker.
Except when the p-hacking is, serendipitously, correct. P-hacked results are not necessarily wrong, they're just fraught.
> I'm pretty sure that to program good weather predictions, you need to know a lot about the mechanisms.
I'm not saying that all use of models and mathematics in science is bad. I'm saying that premature generalizations based on looks is bad.
Do you at least get my point regarding reducing the universe to a hologram or to cellular automata? Weather modeling is much better than these because of its predictive power, but most importantly because the weather modelers keep trying to refine their models based on actual mechanisms.
Knowledge of the mechanisms help guide the parameters used in the models. But the models are not the thing. The equations are not the mechanisms. And the approximations certainly aren't the thing.
And I'm sure that holograms and cellular automata are useful at times in predicting or thinking about reality, just as fractals are useful in some understanding of plants (despite not being accurate models). Just as the Earth-centric model of the solar system with its epicycles was pretty decent at predicting future positions of the planets.
Mathematical models are not the end of the scientific investigation. Mathematical models are the intersection of science (understanding of the universe) and divination (trying to predict the future). Statistics are most useful for trying to identify linkages which probably share mechanisms, or for testing a hypothesized mechanism's effect on particular parameters. In physics, equations for quantum stochastic processes does not mean we've finished with our quantum understanding of the universe.
Math is not science, it's a separate thing that helps with science. Generalized models are generalized models, not fully accurate representations.
And trying to prematurely universalize models is just as bad as p-hacking. Even worse is trying to universalize a single model idea (such as holograms, cellular automata, or fractals) to an entire field. Even if you are right, your model provides a divination understanding of the phenomena, not a scientific understanding of the phenomena.
Crap, I have some good points here, but it's probably TLDR at this point.