February 4, 2000

outside the box thinking

I know that this phrase means unconventional or creative thinking. But what is meant by the reference to a box here? Is it a specific kind of box or just any old box that's "square" and therefore ordinary?

You're so right. There is no reason that "any old box" wouldn't do to support the metaphor. If you want to think creatively--even within the limits of reality--you don't want your thoughts to be confined by rigid barriers or solid walls or anything else that limits the scope of your imagination and intelligence. And the opposition between the ordinary "square" box and free, unconventional thinking works too.

But a more likely source for outside the box thinking is a well-known mathematical puzzle called the nine dots puzzle. In it, you're asked to put nine dots on a piece of paper so that the first row has three dots, the middle row three dots directly under those, and the bottom row three dots lined up with the others. You've now formed a pattern like this:
. . .
. . .
. . .

Aha! The nine dots form a two-dimensional box! The fiendish puzzle makers want you to connect all nine dots, using only four straight lines, without lifting your pencil from the surface of the paper, and without drawing over any of the lines you already have. Lines may cross, however.

You've probably guessed by now that you just can't solve this puzzle unless you think outside the box. As Professor Daniel Kies of the College of DuPage points out on his Web site (oddly enough, a site dedicated to English, not math), "When most of us look at the field of nine dots, we imagine a boundary around the edge of the dot array. In doing so, we limit ourselves to trying solutions to the puzzle that only link the dots inside the imaginary border. The result is futility. We can only solve the puzzle if we realize that there is no border."

There are several sites on the Web that offer solutions to this puzzle, most of which are identical except for the direction in which the resulting design points. My favorite is Professor Kies' solution, slightly animated and very much outside the box: One Solution to Nine Dots Puzzle.

But why don't you try to solve it for yourself before peeking? After all, it's a children's puzzle.

Enid