Sources of inspiration and historical background

Abstract

This chapter is written in the style of an acknowledgement of broad intellectual debts. All my scienfitic work fell under the influence of the branch of physics called thermodynamics, and of other independent traditions ranging from deep to very shallow. I came to scaling and renormalization by cross-fertilizing the influences of probability theory (Lévy) and the social sciences (Pareto, Zipf and the economists’ idea of aggregation.)

At a point where my views on scaling were already formulated, I became aware that this notion is also fundamental in the study of turbulence (Richardson, Kolmogorov.) The theories of disorder and chaos, which also make extensive use of scaling and renormalization, arose from a different and independent tradition, and did not influence my work until quite late. Furthermore, diverse scaling rules were recorded in geology, but not appreciated, and the biologists’ allometry is yet another expression of scaling.

As my study of scaling became increasingly visual and grew into fractal geometry, it became widely agreed that fractal aspects are present in many fields; their importance is limited is some and fundamental in others — including finance.