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for most of us. When it is my turn to play, I have a number of possible moves. For each of my moves, my opponent has a number of possible responses. And for each of my opponent’s responses, I have a number of possible counterresponses. The sequences can be represented on a decision tree, a diagram that in this case takes the current board position as a starting point and shows each of my possible moves, each of the possible countermoves, each possible counter-counter move, each possible counter-counter-counter move, and so on, as deep as time and energy permit. The size of the tree for chess is immense, for the number of choices increases exponentially. Suppose that at each spot there are 8 possible moves. At that spot I must consider 8 initial moves for me, 8 × 8 = 64 replies of my opponent, 64 × 8 = 512 replies I can make, 512 × 8 = 4,096 possible replies by my opponent, and then 4,096 × 8 = 32,768 more possibili-ties for me. As you can see, the decision tree gets large rapidly: looking ahead five moves means considering over 30,000 possibilities. The tree is characterized by a vast, spreading network of possibilities. There isn’t space here for the decision tree for chess. But even a simple game like tic-tac-toe (or naughts and crosses) has a similar structure, shown in figure 5.1.

5.1 Wide and Deep Decision Tree. The game of tic-tac-toe (naughts and crosses). The tree starts at the top, with the initial state, then deepens as each successive layer considers all the alternative moves by each player. Although this diagram looks a bit complex, it is a pretty simple structure as these things go. First of all, this picture is much simplified. Only one possible first move by 0 is shown, and the symmetry of the board is used to reduce the number of alternatives being considered. (Only two first moves by X need be considered: the eight possibilities are really equivalent to the two shown because of the symmetry.) In the full game, there are nine possible first moves for 0, eight possible replies by X, seven second moves by 0, and so on, up to the third move by 0, which is the first possible time for the game to be won; there are 15,120 possible sequences up to that point. Even this simple game leads to such a wide and deep decision tree that it is not possible to work out all the possibilities in the head. Expert players take advantage of simple strategies and memorized move sequences. (From Human Information Processing, Second Edition, by Peter H. Lindsay and Donald A. Norman, copyright © 1977 by Harcourt Brace Jovanovich, Inc. Reprinted by permission of the publisher.)

That decision tree for chess is even wider and deeper—wide in the sense that at each point in the tree there are many alternatives, so that the tree spreads out over a considerable area; deep in the sense that most branches of the tree go on for a considerable distance.

Everyday activities don’t require the kind of complex analyses required for something like chess. In most everyday activities, we need only examine the alternatives and act. Everyday structures are either shallow or narrow.9

SHALLOW STRUCTURES

The menu of an ice cream store provides a good example of a shallow structure (figure 5.2). There are many alternative actions, but each is simple; there are few decisions to make after the single top-level choice. The major problem is to decide which action to do. Difficulties arise from competing alternatives, not from any prolonged search, problem solving, or trial and error. In shallow structures, there’s no problem of planning or depth of analysis.

NARROW STRUCTURES

A cookbook recipe is a good example of a narrow structure (figure 5.3). A narrow structure arises when there are only a small number of alternatives, perhaps one or two. If each possibility leads to only one or two further choices, then the resulting tree structure can be said to be narrow and deep.

Just as the ice cream store menu is an example of a shallow structure, the multicourse, fixed menu meal can serve as an example of a deep structure. Although