G2 shall be my favorite group! Well, for now. For a while. Or maybe for longer. It's the smallest of the exceptional Lie groups. Found 1893 by Élie Cartan. It was he who suggested to think about it in terms of rolling balls.
en.wikipedia.org/wiki/G2_%28ma

Picture two spheres, one three times larger than the other. Imagine them rolling on another without slipping nor twisting. Rolling surfaces have their own branch of mathematics: contact geometry!

en.wikipedia.org/wiki/Contact_

Follow

A spinor is like an electron! If you turn an electron by 360° it's orientation somehow becomes negative. Only when you turn it another full round its orientation returns to the starting position.

Attach a ribbon to your electron, and to the ground. As a reminder of the EM field that connects the electron to the universe. Turn it once, and you get a twist. Twice and... well, did you know: you can undo a doubly twisted ribbon by itself!

Sign in to participate in the conversation
mastodon.cloud

Everyone is welcome as long as you follow our code of conduct! Thank you. Mastodon.cloud is maintained by Sujitech, LLC.