Model flexibility and number of parameters
This post is some thoughts I had after reading ‘Real numbers, data science and chaos: How to fit any dataset with a single parameter’ by Laurent Boué.
The paper above shows that any dataset can be approximated by the following single-parameter function:
$\sin^2 (2^{x \tau} \mathrm{arcsin} \sqrt{\alpha})$
Where $x$ is an integer, $\tau$ is a constant which controls the level of accuracy, and $\alpha$ is a real-valued parameter which is fit to the dataset in question.

