Faster-than-exponential growth also occurs in computing power, as meas — Didier Sornette

"The assumption of perfectly rational, maximizing behavior won out until recently in the art of modeling, not because it often reflects reality, but because it was useful."

"According to the academic world view that markets are efficient, only the revelation of a dramatic piece of information can cause a crash, yet in reality even the most thorough post-mortem analyses are typically inconclusive as to what this piece of information might have been. For traders and investors, the fear of a crash is a perpetual source of stress, and the onset of the event itself always ruins the lives of some of them."

"Positive feedbacks, when unchecked, can produce runaways until the deviation from equilibrium is so large that other effects can be abruptly triggered and lead to ruptures and crashes."

"The concept of a random walk is simple but rich for its many applications, not only in finance but also in physics and the description of natural phenomena. It is arguably one of the most founding concepts in modern physics as well as in finance, as it underlies the theories of elementary particles, which are the building blocks of our universe, as well as those describing the complex organization of matter around us."

"It is difficult to assess how much this gambling spirit is active in the minds of individual investors. If it is, even to a small degree, it is relevant to our discussion since it makes investors prone to imitation and herding because they invest on little information. It may also explain the anomalously large volatility of prices and their potential instabilities."

"Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns."