Nassim Taleb, one of the more colorful, controversial, and cosmopolitan commentators about the science and philosophy of uncertainty, has started a new blog. This is not to be confused with the notebook on his site which he takes pains to note is “not a blog“.

Taleb’s most recent notebook entry on the logic of prediction errors has some interesting observations about our perception of “conditional expectations” and randomness:

One main life expectancy is from Mediocristan, i.e. is subjected to mild randomness. In a developed country a newborn female is expected to die at around 79, according the insurance tables. When she reaches her 79th birthday, her life expectancy, assuming that she is in typical health, is another 10 years. At the age of 90, she will have another 4.7 years to go. At the age of 100, 2 ½ years. At the age of 119 , if she lives miraculously that long, she will have about nine months left. As she lives beyond the expected date of death, the number of additional years to go decreases. This is the major property of random variables related to the bell-curve. The odds of a large number is small, so the conditional expectation of additional days drops.

With scalable variables, the ones from Extremistan that we encounter in real life, you will witness the exact opposite effect. Say a project is expected to terminate in 79 days, the same expectation in days as the newborn female has in years. But the errors are scalable, i.e. power-law distributed. On the 79th days, if the project is not completed, it will be expected to take another 25 days to completion. But on the 90th day, if the project is not completed, it will have about 58 days to go. On the 100th, it will have 89 days to go. On the 119th , it will have an extra 149 days. On day 600, if the project is not finished, you will be expected to need to wait an extra 1590 days. As you see the longer you go, the longer you are expected to wait.

This subtle, but extremely consequential property of scalable randomness is unusually counterintuitive. I believe that this is the core reason for our missing in our forecasts as we do not take into account the logic of the large deviations from the norm. The distribution is Mandelbrotian.

This idea can illustrate many phenomena; it applies to the completion date of your next opera house, the time a refugee is expected to wait until he can finally return home, or the day when the next war will end.