May 7, 2013

Make your ill-defined problem a well-defined one

Do you consistently beat Hercule Poirot at identifying the murderer in Agatha Christie’s novels? It might be that the legendary detective just isn’t quite in your league. Or it might be that you come with a head start.

The difference between Poirot’s problem and yours, is that Poirot needs to start with an infinite set of suspects. You, on the other hand, can reasonably assume that whoever committed the crime came up a few pages ago. So with a bit of memory, and an understanding of how Christie builds her dramatic climax, you get a serious advantage.

Poirot is solving an ill-defined problem—one in which the initial conditions and/or the final conditions are unclear. (That’s also our interest on this website—(complex, ill-defined, and non-immediate) CIDNI problems.) In this case, Monsieur Poirot can’t reasonably restrict the number of suspects before he does a bit of legwork.

You, on the other hand, are solving a well-defined problem: one for which you have been given all (or most) of the elements you need to get to the answer. This is also what happens when you solved math problems in class. Think about it—I know, no-one wants to think about the days when they were solving math problems in class, but indulge me—your typical math problem gives you all the info that you need to get to the solution. Not only that, it also usually gives you only the info that you need to get to the solution. No wonder the National Academy of Sciences (and others) think that solving those well-defined problems is a poor preparation for solving real-life problems.

The take away? If you can’t see the solution to your ill-defined problem, try to see if there is a way to make it a well-defined problem. This will reduce the number of potential solutions and, hopefully, get you in the right direction.