Relation between chaos theory and Lewis's development theory:

Hideaki Yanagisawa


In this paper, four levels of Lewis's development theory are compared with a representative chaos equation

                     Z (n+1) = p [1 - Z (n)] Z (n) 

and the counseling process. This equation is equal to the following two equations:

X (n+1) = p [1 - Y (n)] Y (n) 


Y (n) = X (n).

The first level is equivalent to the variable X with no "n," where n is equivalent to time.

Thus, X means no change with time. The second level is equivalent to X (n) with "n," which means X (n) changes with time. The third level is equivalent to one of the two equations. X (n) and Y (n), being I and you, change with time. The fourth level is equivalent to the two equations. Therefore, Lewis's theory can be explained with chaos theory. A mistake on the fourth level and that on the further level are called "transference" and "counter-transference" in the counseling process, respectively. There are fixed and chaotic states in chaos theory. When any condition does not change, a chaotic state never converges to a fixed state. Each variable is equivalent to a person or a circumstance factor. The fixed state with convergence is a common understanding. The chaotic state is each person's personal understanding. Covariation is required for obtaining common or personal understanding. However, common understanding is not obtained with covariation alone. Because common understanding is produced with convergence of each other's thoughts, it is never produced with only one's self alone. Therefore, we do not have to feel frustrated for reality without common understanding.


Communication; Covariation; Chaos; Convergence; Counseling

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