In Nassim Nicholas Taleb's definition, a black swan is a large-impact, hard-to-predict, and rare event beyond the realm of normal expectations. Much of scientific discoveries for him are black swans – "undirected" and unpredicted. The event most commonly considered a black swan is the September 11, 2001 attacks. This term refers to the unexpected nature and unpredictability of the sudden observance of black swans that coincided with the discovery of Australia. Previously, the commonly held belief was that all swans were white in color.[1] Nassim Nicholas Taleb (b. ... A sequential look at United Flight 175 crashing into the south tower of the World Trade Center The September 11, 2001 attacks (often referred to as 9/11—pronounced nine eleven or nine one one) consisted of a series of coordinated terrorist[1] suicide attacks upon the United States, predominantly... Species 6-7 living, see text. ...

The high impact of the unexpected

Before Taleb, those who dealt with the notion of improbable, like Hume, Mill and Popper, focused on a problem in logic, in the limits of making general statements from specific observations. Taleb's Black Swan has a central and unique attribute: The high impact. His claim is that almost all consequential events in history come from the high impact events – while humans convince themselves that these events are explainable in hindsight. David Hume (April 26, 1711 – August 25, 1776)[1] was a Scottish philosopher, economist, and historian. ... John Stuart Mill (20th May 1806 – 8th May 1873), a British philosopher and political economist, was an influential liberal thinker of the 19th century. ... Sir Karl Raimund Popper, CH, FRS, FBA, (July 28, 1902 – September 17, 1994), was an Austrian born naturalized British[1] philosopher and a professor at the London School of Economics. ... Logic, from Classical Greek λόγος logos (the word), is the study of the principles and criteria of valid inference and demonstration. ... Hindsight bias, sometimes called the I-knew-it-all-along effect, is the inclination to see past events as being predictable and reasonable to expect, perhaps because they are more available than possible outcomes which did not occur. ...

One problem, according to Taleb, is that the unexpected is thought to be minimized through a too strong reliance on large numbers of observations (hence, the title of the book, relating to the fallacy of "all swans are white"), which assumes the nice properties of the Bell Curve. Taleb notes that other functions could very well be in order, such as the fractal, the awareness of which might help to temper expectations. In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are... A central limit theorem is any of a set of weak-convergence results in probability theory. ... The normal distribution, also called Gaussian distribution by scientists (named after Carl Friedrich Gauss due to his rigorous application of the distribution to astronomical data (Havil, 2003)) is a probability distribution of great importance in many fields. ... The boundary of the Mandelbrot set is a famous example of a fractal. ...