What you see in the illustration are two entirely different ways of approaching a square.
The problem of how to connect the nine dots with only four lines, without taking pen from the paper, can only be solved as shown here by going out of the square. The dots only appear to create a box, and if you see it that way, you cannot solve the problem.
The nine dots problem is commonly used to illustrate the process of lateral thinking, or thinking outside the box, and is a common approach to creativity. It involves changing your perspective and freeing yourself from self-imposed or apparent limitations. The problem is, once you know the solution to the problem, there is not much more that you can do with it. The nine dots problem has become a cliché of creativity.
By contrast, the Japanese art of paper folding, know as Origami, is the art of folding the square into an astonishing variety of distinct shapes, animals, geometric figures, and objects of all sorts. All done by folding and refolding a single square sheet of paper, without any scissor cuts. It is far more challenging than the nine dot problem, because it involves manual dexterity as well as visualization. On the other hand, although someone creates the original origami shapes, for the most part people practice the art by following instructions. What is remarkable is the degree of flexible focus that was needed to come up with idea of folding paper in this way in the first place.
The Art of Folding
The art of folding is deeply ingrained in Japanese culture, and is an essential aspect of the Japanese sense of creativity and aesthetics. Japanese have refined the art of folding not only paper and clothing, but furniture, bicycles, eyeglasses, even joints of the human body in the martial arts. You can see numerous examples of folding the square in Japanese culture in a video slide show I produced with Prezi software.
I recently made a blog post on my presentation in October for the international conference of the Japan Creativity Society, at which I presented a paper which you can download, Folding the Square: The Geometry of Japanese Creativity. To accompany this, you can also download a Mandala Chart called GEOMETRY OF JAPANESE CREATIVITY for taking notes on key words and ideas in the thesis.
Why is folding the square significant for creativity? The reason is that, not only does it result in a host of useful and practical solutions to problems and products, but it also illustrates how many possibilities open up when we work within a certain set of limitations. The discipline of working within a set of rules and restrictions can sometimes set you free to discover new levels of flexibility and finesse.
This is not always the case, or every person working in a cubicle would be flexible and creative. More often than not, restrictions can bind and tether your imagination, particularly when imposed from the outside. It is when you seek to work out solutions inside the square of your own initiative through self-discipline, that creativity comes into play.
The unity of discipline and spontaneity
The artist who casts all rules aside in search of freedom of expression may find that he is still trapped in the limited range of his own experience and habit. One of the things that is consistent and intriguing about the traditional Japanese arts is that they are exceedingly difficult in the beginning. The brush in calligraphy is soft and disobedient, defying your efforts to control it. In the beginning it is difficult to even produce a sound on the Shakuhachi, or bamboo flute. Aikido is challenging to the beginner, who finds finesse frustrating, and force useless.
Each of the traditional arts follows a process know as Shu-Ha-Ri (守破離), roughly translated as follow, breakaway, depart. It is this process which connects discipline and spontaneity. Students are expected to begin by repeating copying standard master patterns until they become second nature. These are difficult to master, and much of the discipline is in recovering a beginners mind which allows you to engage with the materials and artistic challenges in a fresh and curious manner.
However, simply making skillful copies is not considered to be anywhere near the level of mastery. This is why in the martial arts, the first level of black belt (shodan) is considered to be merely the first step. Real development in the art starts after you learn the basic vocabulary and steps.
First you learn to follow skillfully, then you learn to breakaway, that is deal with variations and adaptations of the basic forms. Eventually you depart from all forms and learn how to be spontaneous in your expression. Though this process is formalized in the Japanese approach, in fact it is how all artists and musicians progress. Picasso did not start out creating free and original shapes, but rather in making remarkably realistic drawings. Many art students want to skip this stage of disciplined learning, and become an overnight Picasso. It cannot be done.
The Mandala Chart can facilitate the process of connecting discipline and spontaneity through flexible focus. It takes you away from polarity thinking, and helps you see one in terms of the other. Study the Japanese approach to creativity in folding the square, and it will open new horizons for you in the creative process!
—William Reed specializes in applying practical wisdom from Japanese and Asian culture to solving the problems of modern business and living. He is the author of the Flexible Focus column on Active Garage, the syndicated column Creative Career Path and the book A Zoom Lens for Your life. William is also a Representative Director and Co-Founder of EMC QUEST Corporation, which provides Coaching for Communication and Change, World Class Speaking™, and Accelerated Action with GOALSCAPE™.