This doesn't refute the point. If there's a royalty dimension and then you rotate it, there's still a royalty dimension. It just isn't a basis vector. In a blog

This doesn't refute the point. If there's a royalty dimension and then you rotate it, there's still a royalty dimension. It just isn't a basis vector. In a blog post intended for introducing the idea, is that distinction really worth dwelling on? It could be a misunderstanding, or just a pedagogical simplification.