The Black Swan: The Impact of the Highly Improbable

Taleb discusses how the Gaussian bell curve—named after its ideator, mathematician Carl Friedrich Gauss—has been used to inaccurately convey the probability of an event happening. The bell curve is a probability distribution. According to the model, data points near the mean are more frequent in occurrence than data far from the mean.

In Taleb's view, using the Gaussian bell curve as a tool for understanding past and current events increases our blindness to Black Swans. Taleb demonstrates a sense of revulsion, referring to the Gaussian bell curve as a "monstrosity" (240), or, as even the chapter title suggests, "great intellectual fraud" (229).

This chapter explores the limitations of human knowledge. Mathematicians have produced models to quantify probabilities. However, as Taleb points out, Black Swans defy traditional mathematical models, and including Black Swans within models like the bell curve conveys a false idea about how the world really operates.

For Taleb, the topic of Black Swans is deeply personal, as he has devoted years of his life thinking about the impact of Black Swans on human history. At the very end of the chapter, he alludes to a model of thinking that has truly understood the nature of randomness: Mandelbrotian fractal randomness, which he explains in detail in the next chapter.

Taleb explains the concept of Mandelbrotian randomness, named after French-American mathematician Benoit Mandelbrot. Mandelbrotian randomness relies on geometric fractals, defined as "the repetition of geometric patterns at different scales, revealing smaller and smaller versions of themselves" (257). Taleb is drawn to the Mandelbrotian model primarily because it does not decrease the probability of a Black Swan from a statistical, predictive perspective. Additionally, Mandelbrotian fractals can turn Black Swans into Gray Swans, as "fractal randomness is a way to reduce these surprises, to make some of the swans appear possible, so to speak, to make us aware of their consequences, to make them gray" (272). Gray Swans, like Black Swans, can profoundly impact society. Unlike Black Swans, they are somewhat easier to account for and explain.

For Taleb, having a model serve as a frame of reference serves as a comfort, even though he admits that the fractal model does not yield precise, absolute answers. Taleb again emphasizes the limitations of human knowledge. As complex and sophisticated as Mandelbrot's model is, it still falls short when considering the fundamentally unpredictable nature of Black Swans. As much as human knowledge can improve through new discoveries, we are still limited in our ability to predict large-scale events that impact the world on a global scale.

Taleb discusses his observations of the misuse of mathematical theories, such as the Gaussian bell curve, as they are transferred to interpretations of social science. According to Taleb, this misuse often occurs when people adopt domain-specific thinking, which causes them to think differently, even abstractly, when they are at a conference, removed from their office environment, but when they return to the office they revert to the familiar. After the stock market crash of 1987, even after the Gaussian bell curve was proven to be an ineffective way of understanding what had happened to cause the crash, many once again used the bell curve to understand economics and finance. Taleb cites the Nobel Prize in economics as an exercise in futility; many of its recipients have based their theories on examining economics through the Gaussian bell curve.

Thematically, Taleb returns to the idea of confirmation bias versus objective analysis. When people are confronted with concepts that challenge their status quo, they may consider changing their mind. However, when crisis hits or when they need to take a major risk to put their new thinking to the test, they often revert to their previous beliefs and biases. Objective analysis is discarded in favor of what is comfortable, as evidenced in the case of businesspeople who go back to using the Gaussian model even after they have realized its limitations and inaccuracies as a predictive tool.