A Puzzle to Challenge: Solution and Commentary

Last week I put out to the blogosphere a little puzzle (see A Puzzle to Challenge) which asked those who tried to connect nine dots using only four lines without picking up your pen/pencil and no backtracking.



Seems simple enough and, apparently, was quite simple, at least for 5 of the 6 people who filled out the poll on the original post. As I mentioned in that post, I give this little puzzle to my students in my Introduction to World Religions course and, while nearly 80% of those who responded to my post solved the puzzle, well over 80% of my students, semester after semester, do not.

Here is the solution:


All nine dots connected using four lines, without picking up and without backtracking.

Of course we may think of the old cliche, “thinking outside the box.” And such would be appropriate. But is there more?

Before I address this question, a little background to the puzzle as it was explained to me when I was first exposed to it in my undergraduate studies. The test was designed by Canadian sociologists and given to both French-Canadian children and  Intuit/Eskimo children. Much like my students, an overwhelming majority of the French-Canadian children could not solve the puzzle while the overwhelming majority of indigenous children solved it–and solved it quite quickly.


Well, according to how my professor explained it, the sociologists concluded the French-Canadian children had difficulty because when they looked at those nine dots, they saw a square. Why? Because squares (and rectangles for that matter) dominate much of our day to day experience. Just look around you and you will see, too, that such shapes are all around us. The indigenous children living in the north arctic, however, are not dominated by such and, concluded the sociologists, did not immediately perceive a square. Their perception not limited by the shape, they easily “thought outside the box.”

BUT, I wonder, is solving the puzzle as simple as thinking outside the box?

I thought of posing this puzzle on my blog after writing “The Doors of Perception: Only Slightly Ajar” where I quoted Mary Douglas at length:

“It seems that whatever we perceive is organized into patterns for which we, the perceivers, are largely responsible. Perceiving is not a matter of passively allowing an organ–say of sight or hearing–to receive a ready-made impression from without, like a palette receiving a spot of paint…It is generally agreed that all our impressions are schematically determined from the start. As perceivers we select from all the stimuli falling on our senses only those which interest us, and our interests are governed by a pattern-making tendency, sometimes called a schema. In a chaos of shifting impressions, each of us constructs a stable world in which objects have recognizable shapes, are located in depth, and have permanence…Uncomfortable facts which refuse to be fitted in, we find ourselves ignoring or distorting so that they do not disturb these established assumptions. By and large anything we take note of is preselected and organized in the very act of perceiving. We share with other animals a kind of filtering mechanism which at first only lets in sensations we know how to use.”

                                                                                                                                           -Mary Douglas, Purity and Danger, emphasis added

So how does this apply to the puzzle?

“Thinking outside the box” only applies if we see, that is perceive, a box. Taking Douglas as a point of reference, if we see a box, we do so because “we select” that “which interest us” and that which interests us is “governed by a pattern making tendency” and thus we create “a stable world in which objects have recognizable shapes.” I wonder, then, if the difficulty in solving the puzzle (for those who don’t) is a result of Douglas’s “ignoring or distorting,” these “established assumptions.” Those who see a box, assume a box because the box fits the schema which is, according to Douglas, “determined from the start.”

In other words, it is only a box if the box fits what interests us, that which interests being predetermined. Taking Douglas further, the box that confines our perception keeps our perception confined to the box and again I wonder if the relative inability to perceive anything other than a box is the result of our “ignoring or distorting” the “uncomfortable facts which refuse to be fitted in.”

Is seeing a box in those nine dots, then, a distortion or the result of something we are ignoring?

What of the results of the study as given to the French-Canadian kids and the results I have found when I give my students this test?

What does the apparent inclination toward seeing a box in these nine dots suggest about the world in which these “test-subjects,” being Westerners of course, suggest about the Western tradition? It seems to me, at least at the onset, that there is something about the “box”–the box might serve as a root metaphor for a Western consciousness, an image, as it were, that has significant social, political, and economic consequences as I will explore in a future post.

So the nine dots are only a box when we make them into a box. The box, then, is a created “reality,” a “reality” that we are, according to Douglas, “responsible” for creating.

“Thinking outside the box” is a cliche, and has become such, like most cliches, because there is a certain truth to it. And a certain value. But “thinking outside the box” still suggests there “is” a box. Thus as much as “thinking outside the box” is to go beyond that which is limiting, such thinking is still governed by the limits of the box and thus, ironically,  remains inside the box.

That the perception of a box is something someone creates suggests that these nine dots are not a box until someone makes it so. There “is” no box.

What happens, then, to “thinking outside the box” when there is no box?


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