The Nine Dot Problem

Our guiding metaphor is the Nine Dot Problem. The goal is to connect the nine dots with four straight lines without picking up your pen from the paper.  It is best to try to solve this problem now before looking at the solution.

The Nine – Dot Problem

Most people struggle for a long time, and after much frustration conclude that it is impossible. There is no solution. Many experience the same futility about war, the nuclear threat, terrorism, and ethnic conflicts. Like the nine-dot problem, they seem impossible to resolve.  A common answer is that we haven’t tried hard enough, so it’s necessary to do more of the same — more show of force, retaliation, “sending a signal”, using threats and coercion, building new weapons systems, stirring up more fear of the enemy. No matter how hard we try, it seems impossible to solve the problem.

What prevents us from seeing a solution is that we limit ourselves by thinking in old ways

We are responsible to lift the burden from future generations.

that don’t work. When they fail, we say it’s impossible, or blame the parties. We are so boxed into our usual ways of operating that we don’t realize where we can look for a solution. In the book Change: the principles of problem formation and problem resolution, (Watzlawick, P.,Weakland, J.,  & Fish, R. (1974)W.W. Norton & Company, Inc., New York)the nature of change is elaborated.


Almost everybody who first tries to solve this problem introduces as part of his problem-solving an assumption which makes the solution impossible.  The assumption is that the dots compose a square and that the solution must be found within that square, a self-imposed condition which the instructions do not contain.  His failure does not lie in the impossibility of the task, but in his attempted solution. Having now created the problem, it does not matter in the least which combination of four lines he now tries, and in what order, he always finishes with at least one unconnected dot.  This means that he can run through the totality of first-order change possibilities existing within the square, but will never solve the task.  The solution is a second-order change which consists in leaving the field and which cannot be contained within itself….

Very few people manage to solve the nine-dot problem by themselves. Those who fail and give up are usually surprised at the unexpected simplicity of the solution. The analogy between this and many real-life situations is obvious.  We have all found ourselves caught in comparable boxes, and it did not matter whether we tried to find the solution calmly and logically or, as is more likely, ended up running around frantically in circles.  But, as mentioned already, it is only from inside the box, in the first-order change perspective, that the solution appears as a surprising flash of enlightenment beyond our control.  In the second-order change perspective it is a simple change from one set of premises to another of the same logical type.  The one set includes the rule that the task must be solved within the (assumed) square; the other does not.  In other words, the solution is found as a result of examining the assumptions about the dots, not the dots themselves.Or to make the same statement in more philosophical terms, it obviously makes a difference whether we consider ourselves as pawns in a game whose rules we call reality or as players of the game who know les are “real” only to the extent that we have created or accepted them, and that we can change them.” (P 25 -26)

Most strategies we use, such as deterrence, counter-terrorism, all forms of violent force, represent first order changes. A first-order change is that which occurs within a system, but in which the system itself remains unchanged. In second order change, the system itself is transformed. For example, arms negotiations or SALT talks are first-order approaches, as they remain locked into a framework of assumptions about enmity and a militaristic approach to problems. All words and actions occur in the context of a competitive relationship. Everything is interpreted in an environment of mistrust. By contrast, a friendly visit to China using ping-pong diplomacy, a joint space venture, and Gorbacev’s unilateral initiative to withdraw from the nuclear arms race that ended the Cold War represent second order approaches, since both alter the basic nature of the relationship and all of the assumptions about that relationship. It allows for new and different interactions to occur.

Solution to the Nine – Dot Problem


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