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This essay tells the story of how the modern theory of vectors was gradually discovered, and covers the colorful yet often forgotten late-19th century quarrel b
by jamespropp 3y ago
This essay tells the story of how the modern theory of vectors was gradually discovered, and covers the colorful yet often forgotten late-19th century quarrel between quaternionists and vectorialists.
- 082349872349872 3y agoA tangent, and (for Dr Propp) suggestion and question: - Related: https://mathenchant.wordpress.com/2023/06/16/what-is-a-matrix/ https://mathenchant.wordpress.com/2023/06/16/what-is-a-matri... - May I suggest adding a link to https://mathenchant.wordpress.com/feed/ https://mathenchant.wordpress.com/feed/ somewhere more easily found than via "View Source"? - Since you (a) mentioned a working title "... Adventures of Plus and Times" and (b) have classroom experience, do you have any opinions on the following: when overloading the "high school" arithmetic operators for ring- and lattice-like structures, is it easier for people to learn (a) overloads with traditional use (ie × ↦ meet, + ↦ xor in Electrical Engineering), (b) overloads with mnemonic stories: "product makes things larger; modulo makes things smaller", or (c) any consistent overloads, because just making the abstraction leap is much more difficult than remembering any operator assignments?
- jamespropp 3y agoI don’t have classroom experience with this kind of teaching. I may write a companion to “When 1+1=0” called “When 1+1=1”, at which point I’ll have to think harder about these issues. (Are we using a different 0 and a different 1 here? Or a different +? Or a different =?)
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