TITLE: Mere Skills AUTHOR: Eugene Wallingford DATE: July 07, 2011 12:58 PM DESC: ----- BODY: Last week I ran into this quote attributed to Einstein:
The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.
I don't like "merely" here, because it diminishes the value of "mere" mathematical or experimental skills. I understand why problem formulation is so important, usually more important than problem solution. For one thing, it is hard to solve a problem you have not formulated yet. For another, problem formulation is often more difficult than solving the problem. As a result, as skills go, problem formulation is the scarcer resource. But problem-solving skill matters. Most of us need to be able to execute, too. And, at some point, you gotta know stuff -- and be able to do the little things. Maybe if you are Einstein, you can get by without the skills you need merely to solve the problem. If you can discover ideas like relativity, you can probably find grad students to turn the crank. But the rest of us usually need those skills. (I'm even skeptical about Einstein. I've heard stories, perhaps apocryphal, perhaps exaggerated, about Einstein's lack of mathematical skills. But even if there is a grain of truth in the stories, I suspect that it is all relative. There is a big difference between the math skills one needs to work out the theory of relativity and the math skills one needs to do the kind of work most scientists do day-to-day.) One important reminder we get from the quote is that there are two skills, problem formulation and problem solution. They are different. We should learn how to do both. They require different kinds of preparation. One can learn many problem-solving skills through practice, practice, practice: repetition trains our minds. Problem formulation skills generally require a more reflection and thinking about. Lots of experience helps, of course, but it's harder to get enough practice to learn how to tame problems through only repetition. For most of us and most domains, mastering problem-solving skills is a useful, if not necessary, precursor to developing problem formulation skills. While developing our problem-solving skills, we get a lot of repetition with the syntax of semantics of the domain. This volume of experience prepares our brain to work in the domain. It also give our brains -- engines capable of remarkable feats of association -- begins to make connections, despite our own inattention to the bigger picture. Our brains are doing a lot of work while we are "just" solving problems. Then we need to take that raw material and work on learning how to formulate problems, deliberately. In that, I agree with Einstein. -----