Lewin's colleagues blamed his use of topology to illustrate his theories for the fact that his work was underestimated during his lifetime. When he published Principles of Topological Psychology in 1936, the book received a number of harsh reviews. Some reviewers maintained that Lewin's diagrams were distractions that led readers away from his theories to his mathematical representations of them. He replied in an article on "Formalization and Progress in Psychology" (1940) that his main interest was not "formalization or mathematization." The value of these tools for psychology "exists only in so far as they serve as a means to fruitful progress in its subject matter, and they should be applied . . . only when and where they help and do not hinder progress."
A related criticism of Lewin's use of topology and mathematical formulae is that they do not add any new insights to the behavior they supposedly explain. In addition, they cannot be used to predict a person's behavior before it occurs; rather, Lewin's diagrams are after-the-fact representations of his data. Lewin admitted that this line of criticism had some validity:
It is true, however, that it is a clearer test of the adequacy of the theory if one can make predictions from it and prove these predictions experimentally. The reason for this difference seems to be that empirical data generally allow for quite a range of different interpretations and . . . therefore it is usually easy to invent a variety of theories covering them.
The diagram reproduced earlier as an example of Lewin's use of topology may also serve here to illustrate his critics' point. It is difficult to see what the mathematical formulae add to a verbal description of a situation of indecision. Moreover, the diagram has no predictive value. In order to indicate the child's decision, one of the two vectors would have to be measurably larger or longer than the other—which would imply that the outcome of the child's decision is already known to the psychologist drawing the diagram.
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