Why are 'groups' symmetry? (Re-inventing representation theory)

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A quick off-the-cuff video trying to answer this math question from Reddit:
  1. K-Theory
  2. math
  3. maths
  4. mathematics
  5. group theory
  6. symmetry
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Комментарии
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Sylow, yet another math word that I've been pronouncing wrong.

josh
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I have literally no idea on how anybody ever understands math deeply

ToriKo_
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Great; but what's the point in ascribing a symmetry to a thing? The actual underlaying vectors for rotations are non-symmetric for identical 1-tick rotations (orientations). Isn't that a lot like not seeing the forest for the trees? - great in all other ways you can deal with the forest, it's symmetric, but when you get back to the original representations, there's how to say more of a congruent unbalance ...
But maybe I miss the whole point - and a wheel that's a rectangle mounted on one edge is still symmetric and works just fine?
(rotation vectors are pre-quaternion, pre-SU(2), pre-so(3) (hence pre SO(3)))

zdayz
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