It's obvious that the Lie derivative defined in terms of Lie brackets is anti-symmetric. But what is an intuitive way to visualize the anti-symmetry in the 'differentiating along a flow' definition? 


Thanks!



How can I picture antisymmetry of the Lie derivative?
Whichever definition you use that involves differentiating along a flow, it ought to have the property that $L\_X X = 0$; in other words, for reasons that should be clear, the Lie derivative is alternating. In the presence of bilinearity, this is equivalent to antisymmetry. 


