How to win a beer with high-dimensional statistics

I recently did some analysis on how different style prompts like "be succinct" and "avoid mannered prose" affect LLM outputs and I also saw a ~circular relationship with a 2d dimensional reduction (MDS) of the similarity matrix. I wonder if it's some artifact of PCA/MDS + Gemma's output dist

A fun step-up would be to see if you can find an infinity shape by repeating the process with a set of points which are maximally far away from all points but 1 on the existing circle.