Toward a better approach to goodness: Comments on Van der Helm and Leeuwenberg (1996).

Abstract

Some resularities are more salient to the visual system than others. P. A. van der Helm and E. L. J. Leeuwenberg (1996) have proposed a new approach that quantifies the goodness of a pattern's regularity as the number of holographic identities constituting the regulartiy, relative to the total amount of information needed to describe the pattern. This holographic approach to goodness was compared with previous approaches and was presented in relation to metatheoretic al issues. Tnese 3 aspects are discussed further here. First, the theory is shown to contain implausible assumptions and unfortunate gaps with respect to the required processing. Second, Van der Helm and Lseuwenberg's critique on preceding theories is refuted. Third, some metatheorerical issues need to be qualified or at least clarified. Together, these concerns suggest that a better approach to goodness might result from a synthesis of the most useful aspects of diverse theories of goodness. In 1996, Van der Helm and Leeuwenberg presented a new theory of goodness that helped researchers understand the perceptual salience of regularities such as repetition and mirror symmetry in terms of properties of their mathematical representation. They argued that preceding theories of goodness failed either because they were process theories with contradictory ad hoc assumptions or because they were representation theories taking a transformational approach to goodness. In contrast, their theory is representation based and nontransformational. First, I summarize Van der Helm and Leeuwenberg's (1996) theory and discuss some problematic assumptions and unfortunate gaps. Then, I demonstrate that their critique of preceding theories such as the transformational approach and the bootstrap model is not completely justified. Finally, I raise some concerns about the metatheoretical framework within which their theory has been presented. The major message is that a synthesis of the most fruitful aspects of the new representation theory with those of preceding process theories might lead toward a better approach to goodness.