The Art of Problem Solving

The book “The Art of Problem-Solving” discuss problem-solving in a system-thinking paradigm which authors argue to be inadequate in real-world problem-solving. System thinking involves studying the interrelationship and interaction between components and how the system fits in the world.

A puzzle is a problem one cannot solve because of a self-imposed constraint. Self-imposed constraints shackle creativity. Therefore, the key to freeing it lies in developing an ability to identify and deliberately remove such constraints.

Ackoff discusses a general framework for any problem:

  1. decision maker(s)
  2. variables that the decision makers can control: controllable variables
  3. variables that decision maker(s) cannot control, but these affect the outcome of the problem: uncontrolled variables
  4. constraints on controllable and uncontrolled variables
  5. possible outcome combining everything

For the decision maker, the problem consists of the following:

  1. Objective: desired outcome
  2. Controlled variables: course of action
  3. Uncontrolled variables: environment
  4. Relationship on how the action affects the controllable variable and how it leads to the desired outcome

Objective

Problems involve negatively and positively oriented objectives. In negative-oriented objectives, we try to remove the source of dissatisfaction, while in positive-oriented objectives, we try to add the source of satisfaction.

Another classification of objectives is based on “means” and “ends” But these are relative terms: every less-than-ultimate end can be considered a means or more ultimate end, and every means can be regarded as an end of the satisfaction of the satisfactory as every means has some intrinsic, non-instrumental value.

One can enjoy the game others play but only have fun if played by oneself.

The end of a problem may be the beginning of another problem.

The effort to eliminate what we do not want is reactive, retrospective, oriented problem-solving. The effort to obtain what we want is proactive, prospectively oriented problem-solving. In the former, we move away from something; in the latter, we try to approach some specified ideals. Due to the focus on deficiency independently rather than the relationship between things in retrospectively oriented problem-solving, the chances of overlooking relevant consequences are minimized when we formulate a problem in terms of approaching one or more ideals.

Proactive planning consists of a desirable future and finding ways of moving toward it as effectively as possible. The design of a desirable future is best carried out when it is embedded in the idealized design: a description of what designers would have now if they were only subject to two constraints: technological feasibility and operational viability.

Controllable Variables

In a problematic situation, the number of variables we identify as controllable depends on education and past experiences. And by ready-made criteria, the number of modeled controllable variables is often less than the actual number of controllable variables.

Often in the process of understanding a problem, we tend to simplify it, and this simplified version of the problem becomes the basis of further understanding and reasoning. This simplification process (which is usually based on exhibited functional behavior in local time/space ) itself might cut down the number of variables that might be relevant.

In general, we simplify our problems by reducing the number of alternative solutions we consider. Simplifying problems can preclude solutions better than those we consider. The consequences of every simplifying assumption should therefore be seriously evaluated. Simplification is often simple-minded.

Uncontrolled variables

Variables that affect the outcome constitute the environment and condition of the problem, and some of them create constraints under which the problem is to be solved.

Self-evidentiality of something may hide the fact the controllability of some variables. Self-evidence often means we’re not willing to question the truthfulness rather than whose truthfulness is unquestionable. These self-evident facts should be questioned even more when self-evidentiality is more.

Sometimes uncontrolled variables can be controlled by enlarging the system, which is considered to be relevant; this might bring another uncontrolled variable, which can be used to cancel the consequence of controllability of the first one, i.e., sometimes 1 + 1 = 0

Relations

Action taken by the decision maker(s) on controllable variables affects the outcomes, but not all variables are equally significant in determining the outcome. The belief in the nature of the relationship determines the variables and the way they need to be controlled for the outcome. One of the primary reasons through which we understand this relationship is causality. The cause can be of either probabilistic nature or deterministic nature. In real-world scenarios, most of the causality is of probabilistic nature. Many times, we mistake association with causality causing incorrect formulation of the problem. Causality requires more than mere association; controlled testing is required to establish the same.