Came across this excellent piece on Lie geometry, thought I'd share.
For those of you into math, you probably already know about the relationships between groups and symmetries.
Lie groups are "continuous" symmetries, so for example on the Bloch sphere in quantum land, Lie groups handle "continuous" rotations.
If you followed my lengthy diatribe on human visual perception, you'll know that differential geometry describes curved surfaces, which are many of the objects we see.
This video describes how to de-complexify the idea of curved surfaces on a curved manifold (like, planets or black holes under the influence of gravity in curved spacetime), by reducing it to algebra on a flat surface.
For those of you into math, you probably already know about the relationships between groups and symmetries.
Lie groups are "continuous" symmetries, so for example on the Bloch sphere in quantum land, Lie groups handle "continuous" rotations.
If you followed my lengthy diatribe on human visual perception, you'll know that differential geometry describes curved surfaces, which are many of the objects we see.
This video describes how to de-complexify the idea of curved surfaces on a curved manifold (like, planets or black holes under the influence of gravity in curved spacetime), by reducing it to algebra on a flat surface.
