A Visual Approach to Extremistan/Mediocristan
Taleb illustrates Mediocristan with a rug whose small irregularities disappear at a distance, and Extremistan with mountains that remain jagged across a range of scales. The analogy contrasts fluctuations that average out with extremes that can continue to dominate.
THE IDEA
A Visual Approach to Extremistan/Mediocristan
I am looking at the rug in my study. If I examine it with a microscope, I will see a very rugged terrain. If I look at it with a magnifying glass, the terrain will be smoother but still highly uneven. But when I look at it from a standing position, it appears uniform—it is almost as smooth as a sheet of paper. The rug at eye level corresponds to Mediocristan and the law of large numbers: I am seeing the sum of undulations, and these iron out. This is like Gaussian randomness: the reason my cup of coffee does not jump is that the sum of all of its moving particles becomes smooth. Likewise, you reach certainties by adding up small Gaussian uncertainties: this is the law of large numbers.
The Gaussian is not self-similar, and that is why my coffee cup does not jump on my desk.
Now, consider a trip up a mountain. No matter how high you go on the surface of the earth, it will remain jagged. This is even true at a height of 30,000 feet. When you are flying above the Alps, you will still see jagged mountains in place of small stones. So some surfaces are not from Mediocristan, and changing the resolution does not make them much smoother. (Note that this effect only disappears when you go up to more extreme heights. Our planet looks smooth to an observer from space, but this is because it is too small. If it were a bigger planet, then it would have mountains that would dwarf the Himalayas, and it would require observation from a greater distance for it to look smooth. Likewise, if the planet had a larger population, even maintaining the same average wealth, we would be likely to find someone whose net worth would vastly surpass that of Bill Gates.)
The referenced Figures 11 and 12 are not included in this excerpt.
Consider the coast of Britain. If you look at it from an airplane, its contours are not so different from the contours you see on the shore. The change in scaling does not alter the shapes or their degree of smoothness.
When to use it
Model insurance losses by checking whether rare catastrophic claims dominate the total and whether the chosen model represents those losses adequately.
Analyze stock market returns: daily fluctuations may appear Gaussian, but extreme crashes and booms are characteristic of Extremistan.
Assess earthquake risk by distinguishing the distribution of magnitudes from the distribution of resulting losses, and examining how extreme events affect the estimate.
Assess wealth distribution: the presence of billionaires in a large population is an Extremistan effect not captured by average wealth.
FROM THEORY TO EVERYDAY LIFE
In practice
Rug vs Mountain
A rug appears smooth from standing height because small undulations cancel out (Mediocristan). A mountain range remains jagged at 30,000 feet because large features persist at all scales (Extremistan).
Coffee Cup Stability
A coffee cup does not jump because the sum of its particle movements is Gaussian and cancels out, illustrating the law of large numbers in Mediocristan.
Bill Gates Analogy
If Earth were larger, even with the same average wealth, an individual could have net worth vastly surpassing Bill Gates, similar to how Extremistan distributions have extreme outliers.
A MOMENT TO REFLECT
Put it to work.
Can you identify a real-world situation that behaves like Mediocristan, where variations cancel out with scale? How about an Extremistan situation?
How does changing the scale of observation affect your perception of risk in financial markets or natural disasters?
Why is it dangerous to apply Gaussian statistics to phenomena that follow a power law or fat-tailed distribution?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)