Topological Dynamics

Abstract

Giovanni Ceva, the first Galilean economist presented in this volume, tried to handle monetary relationships in the same way as he dealt with geometrical properties. Giuseppe Palomba (1908–1986), the last Galilean economist considered here, went back to geometry to discover a world in which different economic spaces revealed scaling properties, in the sense of some degree of invariance with changing space scales. These properties concern not specific shapes (as in the case of fractals), but certain economic rules, or uniformities, that remain valid even if the level of generalization changes. Palomba worked on the axiomatization of economic spaces from the 1940s until his death in 1986. This project on topological dynamics was preceded by an excellent work on economic dynamics (1939) and some contributions that drew on Pareto’s sociology (1935) to outline the issue of the growing generalization that Palomba subsequently developed. His attempt to axiomatize economic spaces was ignored by the mainstream economics of the time, and ended with Palomba himself.