idempotents
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The Algebra’s Apprentice: Prelude – Part II
In The Algebra’s Apprentice: Prelude – Part I, I shared how my initial approach to learning about physics changed from one of awe and reverence to skeptical inquiry. This is the latter half of the prelude, wherein I will tell you the story of how I came to meet a most mysterious algebra. A Shape… Continue reading
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On the Insufficiency of Groupoids
Macfarlane’s hyperbolic quaternions are the source of unresolved mystery yet again. Idempotents play havoc with invertibility and give groupoids the boot. Continue reading
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The Emperor’s New Closure
This playful notebook entry is a story that came to mind after a very real algebraic surprise I ran into while working with matrix representations. Posh Properties There once was an algebra that loved to try on matrix representations. It seemed of a reasonable and regal character, governing by simple laws and properties. While the… Continue reading