"Models, Models, Models: The Social Sciences and Non-Linear Dynamics Enter Into The Big Picture"
From French soil during the last 120 years there has sprung forth at least three persons who made contributions of significance in the social sciences and/or mathematics, which are of interest to technical market analysts. Each one of those persons helped to foster a unique optic or model that can place technical market analysis upon a more solid, scientific and secure foundation. These three persons of French heritage or education are Gustave Le Bon, Rene Thom and Benoit B. Mandelbrot.
"The Crowd", the celebrated book by Gustave Le Bon, underpins the behavioral model, the "Life Cycle Modeling Crowd behavior". The adoption-diffusion life cycle model, which is widely used in social science and in marketing research, can also be modified to fit the stock market. The Life Cycle Model shows how the four major parameters of technical analysis - price, volume, time, and sentiment - are interrelated. Further, the model can be used to specify and interrelate indicators to measure those parameters. It also reveals how these parameters can combine to form continuation or reversal patterns.
A technical analyst can apply the logic of the Life Cycle Model to construct a mechanical trading system. In addition, the Life Cycle Modeling adoption-diffusion characteristics help to explain the accumulation, markup distribution and markdown phases of a market cycle. Therefore, technical analyses are urged to continue to extend their applications of The Wyckoff Method and other pattern recognition approaches with the aid of The Life Cycle Model from behavioral finance.
Rene Thom's CUSP Model from Catastrophe Theory can assist the technical analysis and technical-trader to deal with and to capitalize upon extreme speculative moves or bubbles. Increasingly, markets appear to be ending with more spike reversals. Hence, the cusp model of Thom can assist the technician and the trader to supplement and complement the more tranquil studies engendered with the Le Bon inspired Life Cycle Model.
Mandelbrot's fractal analysis offers further refinement to the behavioral / mathematical models of Le Bon and Thom described above. The scaling principle of fractal analysis provides a sound vision for the Elliott Wave Principle. Thus an analyst could presumably use fractals to "Zoom in" to smaller and smaller time frames of data in an effort to fine tune a technical turning point. Moreover, there may exist other richer applications of Mandelbrot's fractal geometry. | 
