Back in elementary school, I ran into a major learning obstacle. For years, I'd been taught arithmetic, and I had adeptly mastered addition, subtraction, multiplication and yes, even long division and fractions. However, one day my teacher sprung a new concept on me -- the idea that numbers can be represented by letters, and that you can take those letters and perform addition and all those other functions on them just as you could with numbers.I'll never forget how many times I thought I finally understood the concept but failed miserably on each test. My own personal "test case" was the formula for calculating the volume of a cylinder. This formula appeared on a test, and I solved the problem incorrectly. When I thought I'd finally grasped the concept, I asked the teacher to put the problem on the next test. Well, I failed again...asked again, failed again...and so on, until finally one day it "clicked," and I understood the concept of variables and solved the problem.
There are two kinds of problem-solving in math. You can solve by rote -- such as using a memorized "times table" to multiply -- or by general concepts, such as with variables. Rote works well for simple problems, but bigger problems require conceptual thinking. Just try to calculate the volume of a cylinder using a pile of counting stones and no variables!
It's the same with painting. You can either follow a specific set of instructions for every possible situation you run into, or you can use general principles. For example, I have beginning students who want to know exactly what I use to mix my cloud color. I can say I use two teaspoons of Permalba white, a pinhead of Ultramarine Blue, a pinhead of Alizarin Crimson plus a half-pinhead of Sap Green to warm the mixture. You can't go wrong with this. But what if you don't have Sap Green? If you're a student who work from specifics, you'll be lost, and you'll experiment with everything on your palette to get the right color. (And you'll end up with a muddy mess!)
However, you'll succeed quickly if you apply the principle that any warm color on your palette will add warmth. So, you might try a half-pinhead of Cadmium Yellow Red or even Cadmium Yellow Deep. Don't have those? Then if you've arranged your paints in a color wheel, like I do, just move away from Alizarin Crimson in a warm direction, and you'll find the hue you need.
I became pretty good with algebra -- and geometry and even calculus -- and the concept of variables. Once I made the leap of understanding, I discovered they're not that hard and, in fact, they make life a whole lot easier. Whenever I paint, I try to take what I learn and generalize it into a concept. From a handful of concepts, I can find the answers to a multitude of problems.
The above painting, "Sisters in the Snow," a little 5x7 plein air oil I did last week, is a painting that would have been hard to make, were I to work from a list of specific "tricks." The painting was born of experience -- and the application of general principles of warm and cool colors.
