Here are some milestones in the evolution of erodynamics.
Frederick William Lanchester (1868-1946) was an English engineer. A creative genius interested in economics, physics, military strategy, automobiles, and air planes, he was of one of the first to grasp the military advantage of aircraft. In this context, he conceived a dynamical model for armed conflict, in which numerical strength, firepower, strategy, and attitude were counted [newman world ].
Lewis Frye Richardson (1881-1953) was an English physicist, meteorologist, and Quaker. A conscientious objector in the first World War, he served as an ambulance driver on the front lines in France, and saw a great deal of death and suffering. He decided to devote his life to the elimination of war. He developed a linear model for the arms race between two nations, in which a spiral of increasing armaments in each nation resulted from mathematical laws. He felt that the individual nations caught in this kind of dynamic were innocent victims of an out-of- control global system. He submitted a paper on this model to a journal, fully confident that another war could be averted. However, the paper was rejected, and the second World War began. After this rejection, Richardson continued his work, trying to justify the model on the basis of actual armament statistics. In these efforts, he founded the field of politicometrics. Richardson's life work was published posthumously in 1960.
The word economics is derived from the Greek oikos nomos, meaning the management of a household. This is also the source of oikonomia, the Christian doctrine of the economy of salvation. In the last century, economics became an important social science. Because it is naturally equipped (since prehistoric times) with numerical data, it was one of the first of the social sciences to receive a mathematical treatment. In 1932, John Von Neumann (1903- 1957) created one of the first dynamical models for an economic system, giving rise to a whole industry of mathematical analyses, computer simulations, and data collection (econometrics) [goodwin chaotic ].
In 1935, Gregory Bateson (1904-1980) adapted the Richardson arms-race model to the process of the division of a culture into subcultures, analagous to differentiation in biological systems. He called this universal dynamical process for the development of a schism a Richardsonian process of schismogenesis [bateson steps ]. In fact, schismogenesis, a social form of bifurcation, was one of Bateson's main themes [bateson steps ]. Later, he would apply it to schizophrenia (see 4.3 below.)
Kurt Lewin (1890-1947) was influenced by the hermeneutics of Dilthey, with whom he had contact in Berlin, and Wertheimer, who had developed a field concept in Gestalt psychology as early as 1923. This was extensively developed by Lewin. His life space is a sort of psychological field, extending over a group of animals [Lewin field ]. He modeled social psychological objects by shapes within the life space, or field. He also introduced concepts of dynamics and bifurcations in these shapes, under the name Topological Psychology [lewin topological ]. The rigorous development of Lewin's ideas had to await complex dynamical systems theory, or chaos theory, in the 1960s and 1970s.
Nicholas Rashevsky (1895-1964) escaped from the Russian revolution to become the indefatigable pioneer of mathematical biology at the University of Chicago (Karre man, 1990). In 1939, he published an early erodynamic paper applying the methods of mathematical biology to sociology, and published a book on this subject in 1947. He edited the writings of Lewis Frye Richardson, the founder of erodynamics, for posthumous publication in 1968. In his Looking at History through Mathematics (Rachevsky,1968), he offers steps toward a mathematical model for Toynbee's theory of history. A ten tative prevision of Catastrophe Theory is included, to explain revolutions:
An explicit recognition of the hermeneutic circle is presented in the Preface of this book, as part of an extensive defence of mathematical modeling.
Carl G. Jung (1875-1961) came late in his life to some fractal awakening, expressed in his book, An Amswer to Job (1952), published in 1954. This presents an astonishly bold psychoanalysis of the god Yahwey, in which good and evil are combined in a fractal binary.
In the 1960s, Thom developed catastrophe theory, and published the theory in 1972, along with a number of ideas for its application in the sciences, linguistics, philosophy, and so on [thom 1972]. The final chapter, Chapter 13, sets out the modern formulation of erodynamics, in the context of proposed applications to sociol ogy and psychology.
In the 1970s, Isnard and Zeeman replaced the linear model of Richardson and Bateson with a nonlinear model, the cusp catastrophe of Thom's theory. They applied their model to the original arms race context of Richardson's work, showing how the model fit a situation of schismogenesis, in which the voting population of a democratic nation split into hawks and doves. Zeeman also adapted the cusp to model anorexia nervosa, an emotional disease in which phases of gluttony and fasting alternate [zeeman book], [postle].
In 1985, Mark Kushelman (under the pseudonym Kadyrov), a mathematician and systems scientist then in Moscow, put together two of these cusp models into a double-cusp model for two nations engaged in an arms race, completing the nonlinear version of Richardson's original model. It provides a map, in the two-dimensional space of sensitivities of each nation to armaments of the other, showing regions of different behaviors, such as hawks and hawks, hawks and doves, doves and hawks, and doves and doves. Surprisingly, in the north-west and south-east sectors of this map, Kushelman found oscillating behavior. This might be significant in situations of codependence or addictive behavior [abraham double cusp]. A slightly different double cusp map was used by Callahan and Sashin in the treatment of anorexia nervosa and affect-response [callahan sashin]. Some other nonlinear adaptations of Richardson's model for the arms race have been studied by Mayer-Kress and Saperstein, who found chaotic behavior in their model [mayer-kress saperstein nonlinear].
In Manifesto for Cyborgs, Donna Haraway analyzes the cyborg, an integral being who is part human, part machine. Without explicit reference to fractal geometry, Haraway's vision is essentially fractal. She describes three critical cases of the fractal deconstruction of a binary: human/animal, animal-human/machine, and physical/non-physical. She extends these examples to a long list of fractured identities: self/other, mind/body, culture/nature, male/female, etc -- of political significance. This pathfinding analysis leads the way to a fractal method for the deconstruction of all binaries, and the reconstruction of self-images (and scientific categories) as fractal identities. Thus, she introduced fractal geometry into anthropology, beginning a transformation ongoing today. Since 1985, there has been an erodynamic explosion.