Story of Psychology - Morton Hunt [357]
The Newell and Simon theory of problem solving—for alphabetical reasons Newell’s name is first on their joint publications—on which they worked for another fifteen years is that problem solving is a search for a route from an initial state to a goal. To get there, the problem solver has to find a path through a problem space made up of all possible states he might arrive at by making all the moves that obey the path constraints (rules or conditions of the domain).
In most such searches, the possibilities multiply geometrically, since each decision point offers two or more possibilities, each of which leads to another decision point offering another set of possibilities. In the sixty moves of an average chess game, each move, as already mentioned, has an average of thirty alternatives; the total number of paths in a game is 3060—30 million trillion trillion trillion trillion trillion trillion—a number totally beyond human comprehension. Accordingly, as Simon and Newell’s research demonstrated, problem solvers, in finding their way through such problem spaces, make no effort to look at every possibility.
In the massive tome they published in 1972 and straightforwardly called Human Problem Solving, Newell and Simon presented what they considered its general characteristics. Among them:75
—Because of the limits of short-term memory, we work our way through a problem space in serial fashion, taking one thing at a time.
—But we do not perform a serial search of every possibility, one after another. We use that method only when there are very few possibilities. (If, for instance, you don’t know which one of a small bunch of keys opens a friend’s front door, you try them one at a time.)
—In many problem situations trial and error is not practicable; if so, we search heuristically. Knowledge makes this very effective. As simple a problem as solving an eight-letter anagram like SPLOMBER would take fifty-six working hours if you wrote out all 40,320 permutations at a rate of one every five seconds, but most people can solve it in seconds or minutes by ignoring invalid beginnings (PB or PM, for instance) and considering only valid ones (SL, PR, etc.).*
—One important heuristic commonly used to simplify the task is what Newell and Simon call “best-first search.” At any fork in the search path, or “decision tree,” we first try the move that appears to carry us closest to the goal. It is efficient to move toward the goal with every step (although sometimes we have to move away from it to circumvent an obstacle).
—A complementary and even more important heuristic is “means-end analysis,” which Simon has called “the workhorse of GPS [General Problem Solver].” Means-end analysis is a mixture of forward and backward search. Unlike chess, which uses forward searching, in many cases the problem solver sees that he cannot proceed directly toward the goal but must first reach a subgoal from which the goal is attainable, or perhaps has to get first to an even earlier subgoal or one still earlier than that.
In a relatively recent review of problem-solving theory, Keith Holyoak offers a homely example of means-end analysis. Your goal is to have your living room freshly painted. The subgoal nearest that goal is the condition in which you can paint it, but that requires you to have paint and a brush, so you must first reach the earlier subgoal of buying them. To do so requires reaching the even earlier subgoal of being at a hardware store. So it goes, backward chaining until you have a complete strategy by which to move from your present state to the state of having a painted living room.76
As major an achievement as Newell and Simon’s theory of problem solving was, it dealt only with deductive reasoning. Moreover, it considered only “knowledge-poor” problem solving—the kind applicable to puzzles, games, and abstract problems. To what extent the method described problem