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Society of Mind

7.4 problem solving

In principle, we can use the generate and test method — that is, trial and error — to solve any problem whose solution we can recognize. But in practice, it can take too long for even the most powerful computer to test enough possible solutions. Merely assembling a simple house from a dozen wooden blocks would require searching through more possibilities than a child could try in a lifetime. Here is one way to improve upon blind trial-and-error search.

The Progress Principle: Any process of exhaustive search can be greatly reduced if we possess some way to detect when progress has been made. Then we can trace a path toward a solution, just as a person can climb an unfamiliar hill in the dark — by feeling around, at every step, to find the direction of steepest ascent.

Many easy problems can be solved this way, but for a hard problem, it may be almost as difficult to recognize progress as to solve the problem itself. Without a larger overview, that hill climber may get stuck forever on some minor peak and never find the mountaintop. There is no foolproof way to avoid this.

Goals and Subgoal: The most powerful way we know for discovering how to solve a hard problem is to find a method that splits it into several simpler ones, each of which can be solved separately.

Much research in the field called Artificial Intelligence has been concerned with finding methods machines can use for splitting a problem into smaller subproblems and then, if necessary, dividing these into yet smaller ones. In the next few sections we'll see how this can be done by formulating our problems in terms of goals.

Using Knowledge: The most efficient way to solve a problem is to already know how to solve it. Then one can avoid search entirely.

Accordingly, another branch of Artificial Intelligence research has sought to find ways to embody knowledge in machines. But this problem itself has several parts: we must discover how to acquire the knowledge we need, we must learn how to represent it, and, finally, we must develop processes that can exploit our knowledge effectively. To accomplish all that, our memories must represent, in preference to vast amounts of small details, only those relationships that may help us reach our goals. This research has led to many practical knowledge-based problem-solving systems. Some of these are often called expert systems because they're based on imitating the methods of particular human practitioners.

A curious phenomenon emerged from this research. It often turned out easier to program machines to solve specialized problems that educated people considered hard — such as playing chess or proving theorems about logic or geometry — than to make machines do things that most people considered easy — such as building toy houses with children's blocks. This is why I've emphasized so many easy problems in this book.