the nature of problem-solving

This weekend, I was doing something I don’t really like to do: home repair. My facility with tools is about a 4 out of 10. My knowledge of home repair is about a 2 out of 10. My interest in home repair is about a 3 out of 10. You get the idea. Luckily, my LIFELINE is a 10 out of 10!

When I realized I was trying to fit a 5/16 inch drill bit in a 1/4 inch electric drill . . . well, I had no idea where to go from there. The trusted lifeline — my brother (who is incredulous that anyone would pay $80/hour for the “simplest” of home repair tasks (which I have often done, with much gratitude to the service provider)) — came to the rescue. He told me that my 1/4 inch drill bit could, if carefully manipulated, create a hole large enough for a 5/16″ plastic anchor to be pushed into. It sounds so simple, but my knowledge and experience are so limited. Could I have come to that solution on my own? Maybe, in 3 years, if left to my own devices . . . there is much that is already known, however, and having someone who can share that knowledge is a God-send.

I was dealing with a known problem, and the circumstances and facts were not that unusual. While we can always learn from accumulated knowledge and should do so when there, unique circumstances, conditions, personalities, and lives present problems that are novel. Indeed, the “utopia” in which all foreseeable problems are solved and the solution recorded is a unreliable, undesirable (and frightening! . . . more in a future post), and unlikely, scenario. The need for ongoing problem-solving will be with us for eternity (I hope).

What is problem-solving, anyway? Problem-solving seems to fall into two major domains: 1) mathematics and 2) problem-solving where some difficulty or obstacle is encountered where one needs to overcome the obstacle to get from the current state to the desired state. Even though those types of problem-solving are often considered separate, there can often be overlap and knowledge gained from the mathematics discipline to other disciplines.

Consider George Polya’s classic book, How to Solve It. Polya was a teacher of mathematics and wrote How to Solve It to provide teachers a way of assisting their students in learning to solve problems, and students a direct means of discovering the same. It is considered “one of the most successful mathematics books ever written” (Forward by John H. Conway), but many readers through the past decade have found it “of help in attacking any problem that can be ‘reasoned’ out — from building a bridge to winning a game of anagrams.” (From reviews of the original edition.)

I will be bringing more of Polya’s wisdom to you in future posts, but today, I offer you a link to a summary of Polya’s “list,” by Richard Neufeld of California Polytechnic State University.

What do you think?

triumph of discovery

A great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

G. Polya
From the Preface to the First Printing
August 1, 1944
How to Solve It