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Mathematical descriptions of financial markets with respect to the efficient market hypothesis (EMH) and fractal finance are now equally robust but EMH still dominates. EMH and other current paradigms are extended to accommodate situations having higher information complexity and interactions
coupled with positive feedback. The “herding behavior” literature in finance marks a significant recognition that interdependent trader behavior may result in deviation from normal distribution of returns, as does “chartist” trading. Further legitimization of the separate-but-equal
status of EMH and fractal finance is pursued. Research on the nonlinear models giving theoretical underpinning to equations representing mirror markets as complex dynamical systems is encouraged. Why some herding- and chartist-behaviors scale up and then die off whereas others result in significant
crashes is explained. The buildup to the 2007 liquidity crisis offers an example of nonlinear scale-free dynamics. Concepts from complexity science, econophysics, and scale-free theory are used to offer further explanation to physicists’ mathematical treatments.