Lorentz group
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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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The Compass and the Gyre
When gyrovector spaces and hyperbolic quaternions brush against one another, their shared symmetries shimmer — and richer geometric structures stir just beneath the surface. Continue reading
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Hyperbolic Quaternions
An introduction to Macfarlane’s hyperbolic quaternions, a quaternionic algebra whose chiral multiplication reveals a direct basis for the Lorentz generators. A primer on their structure, pathologies, and connection to spacetime symmetries. Continue reading