Painting the Aurbis - Understanding Subgradients

Imagine, if you will, two magic paintbrushes. One produces black paint, while the other removes paint of any color. Black paint, as any child who has played with paint knows, is the summation of all other colors.

Anywhere the first paintbrush alone paints, there is only static, inky blackness. Anywhere the second alone touches the canvass, there is nothing.

Mix the two, however, and something magical happens-remove all red from a section of black paint, and you are left with green. Remove a bit of blue, and now you have a yellowish green.

Don't get paint in your eyes.