I played with this with a colab notebook way back when. I can’t visualize things directly in 4 dimensions, but at the time I came up with the trick of visualizing the pairwise cosine similarity for each pair of features, which gives at least a local sense of what the angles are like.
Trying to squish 9 features into 4 dimensions looks to me like it either ends up with
4 antipodal pairs which are almost orthogonal to one another, and then one “orphan” direction squished into the largest remaining space
OR3 almost orthogonal antipodal pairs plus a “Y” shape with the narrow angle being 72º and the wide angles being 144º
For reference this is what a square antiprism looks like in this type of diagram:
[Epistemic status: 75% endorsed]
Those who, upon seeing a situation, look for which policies would directly incentivize the outcomes they like should spend more mental effort solving for the equilibrium.
Those who, upon seeing a situation, naturally solve for the equilibrium should spend more mental effort checking if there is indeed only one “the” equilibrium, and if there are multiple possible equilibria, solving for which factors determine which of the several possible the system ends up settling on.