Daniel Kahneman's new book Thinking, Fast and Slow, describes and contrasts two "systems" in our brains-- fast thinking and intuitive System 1 and deliberate, tedious, and often lazy System 2-- and he describes his comprehensive research and experimentation observing how System 1 (though brilliant at detecting emotions, recognizing objects, and jumping to fairly accurate conclusions) often screws up our System 2 thinking . . . and I found this example at the start of "Chapter 10: The Law of Small Numbers" both fascinating and indicative: Kahneman explains that the lowest incidence of kidney cancer in the United States is found in counties that are "mostly rural, sparsely populated, and located in traditionally Republican states in the Midwest, the South, and the West" and then he asks you what you make of this information . . . perhaps you speculate that people are exposed to less pollution in these places or lead healthier lifestyles or do more physical work . . . but then he reveals something paradoxical: the highest incidence of kidney cancer in the United States is found in "mostly rural, sparsely populated, traditionally Republican states in the Midwest, the South, and the West" and he asks you to make sense of this conflicting data . . . and perhaps your mind can resolve this-- maybe it has to do with poverty, or tobacco use, or access to poor medical care-- and so both these populations exist in the same regions, but the fact of the matter is that there is no causal reason why this is so-- the reason is purely statistical, and the important part of the statement is "sparsely populated"-- when you have smaller numbers there is a greater chance for statistical anomaly . . . I have a better chance of picking two students at random that both have blue eyes then I do having an entire class of thirty that all have blue eyes-- the two person sample is too small to indicate anything-- and so the only reason that the highest and lowest incidence of cancer occurs in the same type of county, demographically, is that these counties tend to have less people than other regions; this logical fallacy is common, the Gates Foundation determined that smaller schools are often more successful and invested substantial funds in creating small schools, sometimes even breaking large schools into smaller units, but what they neglected to realize is that small schools are often the most successful and they are also often the least successful . . . because their smaller populations are more likely to vary statistically; I found this idea compelling enough to explain to several of my classes, and I made a discovery of my own: high school kids DO NOT find this interesting at all . . . they don't want to guess why the incidence of kidney cancer is low, they don't want to guess why it is high, they don't want to speculate on the nature of the paradox, and they are certainly not excited to find out that there is NO causal reason for it.
