Problem Solving Redux — Formal Methods

To expand on my last entry, problem solving includes more than a disciplined pursuit of mentally active investigation as a consistent lifestyle. There are also several methodologies to help in the pursuit. They are all easier said than done, but cultivating the ideas leads to internalizing them, so they become second nature and you automatically use them without having to consciously apply them.

I already talked about one methodology in an earlier entry, root-cause analysis, so I’ll skip that one. A lot of people use trial-and-error, such as filling in numbers in Sudoku, then seeing if it works. Eventually you get good enough to “see” the right number and no longer need trial and error. Seeing the answer is really just sped up trial and error, or “Abstraction,” in which you calculate all the “no” answers in your head so quickly it seems like you just suddenly “see” the right answer.

You can also break the problem down to simpler parts and solve each part first to lead to the big solution. The problem of choosing a major in college might include breaking it down to “what are my interests,” “what are my talents,” “where those overlap, what career choices are there,” then “what are my lifestyle preferences” and see which ones fit into the career choice results, and narrow down from there (future income expectations, what doesn’t conflict with your values, etc.). This is also a kind of Output Analysis—what is my end result goal in four years, back to what college major to start with. This will also involve research skills as a problem-solving methodology.

Some people use brainstorming, which usually requires multiple people feeding off each other throwing out ideas, sparking ideas in each other, to get at an explanation or solution to a puzzle (what to name a new product, what to title your new book, how to spend a vacation, etc.). People associate the “hypothesis” method with science: assert a theory then try to prove it—or the reverse—disprove the theory, which leads to narrowing the theory to points that cannot be disproved, and go from there.

On TV mystery shows, you see the detectives saying, if I were doing something like this, what would I do? This is a “sympathetic” approach, putting yourself into someone else’s shoes/mind, as best as you can. It is also used by actors, known as “method acting,” where you go through a psychological and physical process to “become” the character. Solving problems can involve analogy methods, comparing to other similar scenarios that you’ve solved before, or reducing the problem to something more readily solvable.

Your effectiveness as a problem solver will match how mentally active you are, how persistent you are, and how serious a student you are of the formal methods of investigation. You can be a gifted intuitive problem solver, but still become much more effective if you learn, then internalize, the formal methods that others have already worked out.

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