Nassim Taleb's Extremistan is an interesting "place." It is a place dominated by power-laws, the "long tail" if you will. In these systems the vast majority of events are small and inconsequential, yet from time to, exceedingly rare, time, a massive event can occur which outweighs everything which occurred before. That is to say, this sort of system does not obey the Law of Large Numbers.
For example, consider human height verses human income. Human height is a system whose values (or events as I referred to them above) fall along the well known Gaussian distribution (or bell curve). This means that the average height of a random sample of humans is stable. If you measure the height of 10,000 people and then include the tallest person in the world the average will not change in any meaningful way.
We cannot repeat this experiment with incomes. Bill Gates' income utterly dwarfs the average person's income. The average income of the 10,000 people would not reflect the average income of the same set of people plus Bill Gates.
This has major consequences for prediction--induction, to be more precise. Inductive reasoning holds that if we observe an experiment return a certain result many times, then we are justified in expecting that it will continue to achieve that same result in the future. I will have more to say about induction, or Hume's Problem, in the future.
My next post will be a bit more technical. I'm going to drill into what I meant by: "the average will not change in any meaningful way." We'll see that there's circular reasoning going on at the heart of statistics, and that it is inescapable.
For example, consider human height verses human income. Human height is a system whose values (or events as I referred to them above) fall along the well known Gaussian distribution (or bell curve). This means that the average height of a random sample of humans is stable. If you measure the height of 10,000 people and then include the tallest person in the world the average will not change in any meaningful way.
We cannot repeat this experiment with incomes. Bill Gates' income utterly dwarfs the average person's income. The average income of the 10,000 people would not reflect the average income of the same set of people plus Bill Gates.
This has major consequences for prediction--induction, to be more precise. Inductive reasoning holds that if we observe an experiment return a certain result many times, then we are justified in expecting that it will continue to achieve that same result in the future. I will have more to say about induction, or Hume's Problem, in the future.
My next post will be a bit more technical. I'm going to drill into what I meant by: "the average will not change in any meaningful way." We'll see that there's circular reasoning going on at the heart of statistics, and that it is inescapable.
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