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My Daimon Hates Me
Jan. 3rd, 2019 02:32 pmToday, in the shower, I had another small epiphany. The polygon classes I'm studying can be classed as "pure" or "mixed", and also by their order, a natural number. First order pure classes I figured out quite a while back; they will be the subject of Taxonomy IV. First order mixed classes have been a headache; there's a small subset of them that I understand as well I do pure classes, but in general I haven't had a good picture.
Until this morning. I'd been mulling the connection between mixed classes and the dot and cross product of vectors, the connection being that they aren't derived from them. Each mixed class is derived, so to speak, from *half* of a dot or cross product, and I couldn't see how to break the products apart. In the shower, though, I realized that the tool for breaking them apart was one I'd been using all along, for other purposes. (Dr. Herstein, thank you for those character-building lessons!) While walking the dogs, I tried the new idea out on hexagons, and It. Is. Beautiful.
So again I have stuff that I want to write down - but this belongs in Taxonomy *V*, and I still haven't written Taxonomy II!
:is frustrated again:
Until this morning. I'd been mulling the connection between mixed classes and the dot and cross product of vectors, the connection being that they aren't derived from them. Each mixed class is derived, so to speak, from *half* of a dot or cross product, and I couldn't see how to break the products apart. In the shower, though, I realized that the tool for breaking them apart was one I'd been using all along, for other purposes. (Dr. Herstein, thank you for those character-building lessons!) While walking the dogs, I tried the new idea out on hexagons, and It. Is. Beautiful.
So again I have stuff that I want to write down - but this belongs in Taxonomy *V*, and I still haven't written Taxonomy II!
:is frustrated again:
