I’ve always enjoyed this framing of the subject, the idea of mapping anything as hyperplanes existing in a solution space is one of the ideas that really blew my hair back during my academic studies. I would nitpick at your “dots in a circle example - with the stoner reference joke” I could be mistaken, but common practice isn’t to “move to a higher dimension”, but use a kernel (i.e. parameterize the points into the polar |r,theta> basis). All things considered, nice article.