But still note, that even if some solution appears to be "pretty" or "obvious" mathematically for some specific scenario (like drawing the areas for inverse square rule, or looking at the galactic curve for a "fit" with MOND), it never means that it automatically follows that all of the measurements in all the experiments will match that.
The "better" theory must cover more, not less of the measurements. The one that at the moment certainly covers the most is dark matter, and the alternatives simply cover much less (or as I've posted even somewhere result in the wrong shapes). Once some alternative manages to cover the observations and bring even more predictive power, that one will eventually be accepted (although sometimes "one funeral at a time" was needed), even if it's less "pretty" and less "obvious."
The problem with the dark matter model is that it has more free variables so epistemologically it's just "able to fit more". At some level it feels like that time in high school physics (gravity lab with ball bearings) when one of my classmates proudly showed off a sixth order Excel polynomial fit of five data points with an R^2 of 0. (That doesn't mean dark matter is wrong)
More than what exactly? As far as I know, the https://en.wikipedia.org/wiki/Lambda-CDM_model is the
best we have, i.e. with the minimal number of parameters that still covers most of the observations. If there were a better one, it would already be accepted.
But unless you try to inform yourself, you wouldn't even believe how good it is, compared to the alternatives. Really, really good, as in, it actually predicted the future measurement results of the oldest signals reachable to us, and then later the measurements did match perfectly.
> epistemologically
Ah... I'd guess then that you don't write about physics but some non-scientific belief system.
the lambda-CDM model assumes the existence of a distribution of dark matter which is unique to each galaxy and empirically derived. That's potentially a (countably) infinite-dimensional free variable vector for each galaxy, although typically models assume dark matter is usually symmetrically distributed (which can still be a countably infinite-dimensional free variable vector, as a function of rho and phi at least). In any case it's got enough free variables to account for two drastically different cases - 'normal' galaxies, and diffuse galaxies, which apparently have no dark matter. How do you parameterize that without at least one free variable per galaxy?
> If there were a better one, it would already be accepted.
In 2 dimensions it would be just ~r.