The authors argue that the word “critical” in the title is not purely literary. Based on their and other previous work on nonlinear complex dynamical systems, they summarize present evidence, on the Oct. 1929, Oct. 1987, Oct. 1987 Hong-Kong, Aug. 1998 global market events and on the 1985 Forex event, for the hypothesis advanced three years ago that stock market crashes are caused by the slow bu...