I've come accross this physical interpretation for $ [X,Y] $ which I don't understand :
- Follow $X$ for some time $\epsilon$;
- Follow $Y$ for $\epsilon$;
- Follow -X for $\epsilon$;
- Follow -Y for $\epsilon$;
In the limit as $\epsilon$ approaches 0, the result of the above motion approaches the Lie Bracket $[X,Y]$.
Maybe someone can elucidate this for me?