Limitations of probabilistic analysis
The phenomena Taleb describes as "black swans" are events that are completely unpredictable according to the best available predictive techniques. Weather modeling, analysis of stock performance, and military and economic theory--to name just a few disciplines that rely heavily on statistics and probability--depend on the way people attempt to explain past events and form general notions about how a complex system ought to work. Sometimes an essential piece of knowledge or insight is missing. A computer generated analysis, for example, is only as good as the assumptions and input used to program the computer. When the best possible human knowledge fails to predict a major event or upheaval, frequently the problem is due to an incomplete understanding of system parameters. After the wrong assumption is corrected and the black swan event is factored in, the model can often "work" properly.
Human arrogance
Since the Age of Enlightenment it's been fashionable to believe that science has, or will soon have, solved all the world's most complex problems. It is now possible to design machines based almost solely on mathematical models and to manage stock portfolios solely based on mathematics. How to mitigate risk is the foundation of the insurance industry and the basis of a great deal of actuarial science. But when a low-probability disaster strikes, most mitigations fail because they are designed for less severe conditions. Throughout the book, Taleb shows how the experts are frequently and ironically blind to low-probability events.
Statistics as a poor predictor of individual performance
Taleb describes the standard-normal Gaussian curve, often called the "bell curve", in very negative terms because although it is useful for describing the distribution of natural related phenomena, most graphs describing human-related events follow fat-tailed, multimodal, or even Zipf related distribution. In any case, attempting to predict the outcome for any one individual or event based on past performances of similar events does not work. Positive black swans--such as the runaway stock market success of Microsoft or the selection of winning lottery numbers--cannot be predicted reliably enough. Taleb's take on the issue is that people tend to believe that standard-normal distributions themselves are normal, when the evidence shows that extreme phenomena are not the exception but the norm.
Randomness
According to Taleb, despite thousands of years' worth of trying to understand and control the circumstances around them human beings are still deluding themselves if they fail to acknowledge just how much of what occurs around them is essentially random. Instead of constantly adapting analytical models based on new observations, Taleb recommends an investment strategy designed to maximize profit in an extremely random and increasingly unstable world.
