I just started reading Black Swan which has been highly recommended to me. While I don’t have high hopes I do like the initial focus on deflating the myth of the Bell Curve. This has been an area of interest for me for years as you’ll soon find out.
If you’ve studied statistics you’re familiar with the basic bell-shaped distribution which is known as a “Normal” distribution. Actually, it is technically a Gaussian distribution as it follows a pattern known as a Gaussian function (http://en.wikipedia.org/wiki/Gaussian_function).
Anyway, almost all of popular statistical theory is based on Normal distributions. Don’t believe me? Ever used the word “average”? The average is also known as the arithmetic mean, which in a Normal distribution corresponds to the middle of the bell – meaning that it’s the most commonly occurring value. In modern parlance “average” is really just a synonym for “typical” or “common” which is a simple way of describing how the mean represents a Normal distribution.
The same is true if you’ve ever heard of a “standard deviation”, which is a way to determine how far away a given value is from the mean in a Normal distribution. These days “standard deviation” is used in passing to refer to how different something is from what you’d expect. “Six Sigma” processes actually refer to a process that covers six standard deviations from the mean (sigma is the Greek letter representing a standard deviation in mathematics).
All of that is a long way of saying that a lot of what comprises common knowledge about statistics is based on Normal distributions. There are a lot of distributions that fit the Normal pattern including the height of a given set of people or the size of raindrops in a rain storm. It’s widely used in all of the social sciences to simplify complex phenomena.
The problem is that we’re finding more and more distributions are not Normal. Social network connectivity and the size of world cities are two basic examples that follow something called a Power Law distribution (http://en.wikipedia.org/wiki/Power_law) which looks nothing like a Bell curve. The entire concept of the “long tail”, which has started to pervade almost every aspect of business strategy, is based on this kind of distribution.
Unfortunately, your average person does not have the tools to deal with this kind of distribution. Arithmetic Means (averages) are meaningless when used on a Power Law distribution. There is no standard deviation because the mean is so grossly misrepresenting the values. Nothing can help you take this kind of curve and fit it into the nice Bell curve that everyone knows so well.
It’s hard to represent how fundamental a shift this is in our understanding of statistics. Not as mathematicians (who have known about these for centuries) but as a society. Math is a tool in the macrocosm as well as the microcosm and we rely on a shared understanding to be able to make decisions as a society. Politicians know that you’ll understand it when they talk about the “average American”. Imagine if they started referring to the “long tail” of Americans – I wonder if anyone would understand.
Someday we’re going to have to encounter issues like the massive inequality of wealth in the world. Unfortunately, that follows a Power Law distribution so we’re not ready yet.