Great quote! (and a great eye shown in your galleries)
Here's one answer to your question about the invisible essential --
and I think you've already found other answers, from what we see.
I just found Cartier-Bresson's mind-bending intro to his "The Decisive Moment"
which is online (along with the images) thanks to his publisher for all to read
http://e-photobooks.com/cartier-bresson/cartier-bresson.html