ABSTRACT
In order to better analyze the formation of symmetries that are not perceptually given but have to be constructed by the subject in terms of correspondences with reversals, it proves helpful not to stick to isolable symmetries. In other words, it is useful not to limit oneself to symmetries that arise from a single system as was the case with the roadmap presented upside down or the transparent pages of chapter 8. Instead, we need to employ polyvalent systems involving several possible symmetries all of which can be used in solving a single problem but which present quite different relationships among themselves. Once again, the equilibrium of a balance scale provides such a problem. In certain cases, the relationships involved in a such scale are logical in nature, that is the relationship between weight and the number of identical objects; in other cases, the relationships are looser, even at times resting on simply arbitrary conventions. The advantage of variety in relationships as well as in objects is twofold. On the one hand, it allows us to attain greater spontaneity on the part of the subject than is seen when the relationships in play are suggested by the material itself. On the other hand and more important, it permits one to differentiate different forms of symmetries in function of figural, spatial, physical, or logico-arithmetic factors.
