Vector Calculus In Pictures?

"How to turn the complex mathematics of vector calculus into simple pictures":

Joon-Hwi Kim at Seoul National University in South Korea and a couple of colleagues who have come up with a similar innovation for vector calculus—a graphics-based shorthand for one of the most common and powerful mathematical tools in science. “We anticipate that graphical vector calculus will lower the barriers in learning and practicing vector calculus, as Feynman diagrams did in quantum field theory,” they say.

I've only skimmed the paper, and I'm not yet convinced of the ultimate benefit. But others can read the original paper and decide for themselves