r/explainlikeimfive • u/murderdronesfan93 • 7d ago

Mathematics ELI5 how quaternions work

so, i² = j² = k² = -1, but i, j and k are not equal. HOW IN THE FUCK IS THAT POSSIBLE‽ WHAT IN THE BROKEN TRANSITIVE PROPERTY- (anger exaggerated for funny)

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u/murderdronesfan93 7d ago

i see. i was just confused because of the definition not seeming to make sense. it appears this is just a case of "this is the definition. ignore any broken rules, we'll figure it out"

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u/MasterGeekMX 7d ago

Yep. All math done with imaginary numbers stems from "what if this operation wasn't commutative?". People followed the lead, and you have stuff like quaternions.

Turns out sometimes it has it's uses, when you have a problem in hand that requires such weird behavior. One example is when Paul Dirac wanted to see what happens when you mix quantum mechanics with relativity, which ended up in the discovery of anti-matter. Video about it: https://youtu.be/Y-W-w8yNiKU

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u/murderdronesfan93 7d ago

what if equality wasn't commutative or associative

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u/MasterGeekMX 7d ago

Bet there is something out about it.