One of the many ways in which we have become cognitively lazy is to accept our initial impression of the problem that it encounters. Once we settle on an initial perspective we don’t seek alternative ways of looking at the problem. We close off all other lines of thought. Like our first impressions of people, our initial perspective on problems and situations are apt to be narrow and superficial. We see no more than we expect to see based on our past experiences in life, education and work.
By now most everyone has been challenged with the nine dot puzzle. The challenge is to draw no more than four straight lines which will cross through all nine dots without lifting your hand from the paper.
The first time a person tries to solve this puzzle they are stymied. This is because of our ingrained habits of labeling, categorizing, and our perception of the arrangement of the dots as a box or square. Once perceived as a box, most people will not exceed the imaginary boundaries of the imaginary box and are unable to solve the puzzle.
There is nothing in the challenge statement that defines the arrangement as a box and nothing demands the line must be drawn within the box, but people make the assumption based on past experiences and find the puzzle difficult.
The answer, as I’m sure you all now know, involves drawing a line that goes beyond the limitations of the imagined box. This is where the cliché “Think out of the box” comes from. To solve it, you have to start the line outside of the imaginary box.
The nine-dot puzzle was popularized by William North Jayme, a direct-mail copywriter who was hired by Esquire magazine in 1958 which wanted to abandon its unwholesome image for a more sophisticated one. Mr. Jayme came up with the ”puzzle letter”: an envelope with nine dots on it and a challenge to the recipient to connect them using no more than four uninterrupted lines. The enclosed letter showed that to do so, one had to go outside the box. Or, in other words, you had to break normal thinking patterns, something that the new Esquire said it could help modern men do. The letter was a phenomenal success, Esquire’s image was changed overnight and the subscriptions poured in.
Over time the puzzle became synonymous with creative thinking and the phrase “thinking outside the box” has now become a cliché for creativity. A cliché because the puzzle has become commonplace and most people remember the solution from their past experience with it. When the brain recognizes the pattern and we solve the problem it seems like a new insight has been sparked. However, when asked to search for other ways to solve the puzzle, the rationalizations begin. We think “If I can’t see it right away, it either isn’t there or not worth finding.” Apparently, if we think “outside the box” once, we are done and our thinking is done. Surrendering to this rationalization limits our thinking, our creativity, and our ability to apply ideas and skills to novel situations.
This has always troubled me somewhat as creative thinking means to approach a problem on its own terms using multiple perspectives to generate many different alternatives without judgment before deciding which alternative is best suited to the challenge
To begin with, the original “Think Outside the Box” solution was just one way to solve the puzzle. THERE IS NO ONE RIGHT ANSWER. Reality is ambiguous. Aristotle said it is either A or not-A. It cannot be both. The sky is either blue or not blue. This is black and white thinking as the sky is a billion different shades of blue. A beam of light is either a wave or not a wave (A or not-A). Physicists discovered that light can be either a wave or particle depending on the viewpoint of the observer. The only certainty in life is uncertainty. When trying to get ideas, do not censor or evaluate them as they occur. Nothing kills creativity faster than self-censorship of ideas while generating them. Think of all your ideas as possibilities and generate as many as you can before you decide which ones to select. The world is not black or white. It is grey.
NEVER STOP WITH YOUR FIRST GOOD IDEA. Always strive to find a better one and continue until you have one that is still better. In 1862, Phillip Reis demonstrated his invention which could transmit music over the wires. He was days away from improving it into a telephone that could transmit speech. Every communication expert in Germany dissuaded him from making improvements, as they said the telegraph is good enough. No one would buy or use a telephone. Ten years later, Alexander Graham Bell patented the telephone.
Spencer Silver developed a new adhesive for 3M that stuck to objects but could easily be lifted off. It was first marketed as a bulletin board adhesive so the boards could be moved easily from place to place. There was no market for it. Silver didn’t discard it. One day Arthur Fry, another 3M employee, was singing in the church’s choir when his page marker fell out of his hymnal. Fry coated his page markers with Silver’s adhesive and discovered the markers stayed in place, yet lifted off without damaging the page. Hence the Post-it Notes were born.
APPROACH A PROBLEM ON ITS OWN TERMS. Approaching the puzzle with this perspective “In what ways might I connect all nine dots with a continuous line without lifting my hand from the paper?” liberates the mind to think more freely about alternatives.
Looking at the puzzle from the perspective of the lines gets you thinking of the number of lines, the lengths of the lines, and the width of the lines. THREE LINES. For instance, there is no requirement that you must use four consecutive straight lines. Why not three, two or even one line? When linking things such as dots, we are used to linking the centers and our first attempts are to draw lines through the centers of the dots. This is another false assumption based on past experiences. The way to link up the dots is to have the line just touch the dots as illustrated.
ONE LINE. Another dimension of the puzzle is the instrument used to draw the line. Most people assume you must use a pencil or pen and draw a normal-sized line. But there is nothing in the challenge statement that prohibits the person from using an alternative instrument. One solution is to use a wide paint brush, dip it in paint and connect all nine dots with one straight continuous wide swipe.
LENGTH OF LINE. There is no limit on how long you can draw the straight line. So another solution is to draw the line around the world three times intersecting and linking up all nine dots.
This, of course, is impossible to do. Your brain is a dynamic system that evolves its patterns of activity rather than computes them like a computer. It thrives on the creative energy of feedback from experiences real or fictional. You can synthesize experience; literally create it in your own imagination. The human brain cannot tell the difference between an “actual” experience and a fantasy imagined vividly and in detail. This discovery is what enabled Albert Einstein to create his thought experiments with imaginary scenarios that led to his revolutionary ideas about space and time. Imagination gives us the impertinence to imagine making the impossible possible. Einstein, for example, was able to imagine alternatives to the sacred Newtonian notion of absolute time, and discovered that time is relative to your state of motion. Think of the thousands of scientists who must have come close to Einstein’s insight but lacked the imagination to see it because of the accepted dogma that time is absolute, and who must have considered it impossible to contemplate any theory.
In the nine dot puzzle, we take the impossible solution of going around the world three times and imaginer the essence of this idea into a solution that is realistic and practical as illustrated.
CHANGE THE BOX. Now, let’s look at from the perspective of the way the dots are arranged. There is nothing that prohibits us from rearranging the dots, so another one line solution is to cut out the dots and tape them into one straight line and draw one line straight through.
And another is to fold the puzzle over and over following the below steps until you have one line of dots and then link them with one straight continuous line.
Another way to change the pattern is to cut the dots out and line them up in a row. Then punch a pencil through the centers linking all nine dots.
The more ideas you generate, the more connections you make. These connections and their associated ideas often spark new ideas and new questions. The creative mind synthesizes all that is created and goes beyond them to create more creative products. For example, the above idea of stabbing a pencil through the cut out dots triggers another idea. That is to rumple up the puzzle into a small wad of paper and punch a pencil through the wad. You may have to do this several times, but probability being what it is, sooner or later you will punch the pencil through the dots linking them together.
In genius there is a patience for the odd and the unusual avenues of thought. This intellectual tolerance for the unpredictable allows geniuses to bring side by side what others had never sought to connect. In 1979, for instance, physicist Alan Guth was playing with the idea of hypothetical chunks of magnetic north divorced from the south. He was also playing with the odd notions of false vacuums. These odd notions led him to an astounding new theory of genesis which posits that the universe began with a hyper explosion. His theory answers mysteries of cosmology which other physicists had not been able to comprehend.
An unusual and imaginative solution is to widen the dots with a pencil so that each dot touches the adjacent dots? Now the nine dots are linked together with no lines.
Einstein said it best when he remarked “Imagination is more important than knowledge.”