Friday, July 13, 2018

But what of Clusters? (The Clustering Illusion & Law of Large Numbers)

For my second post I’d like to take some time discussing my chosen book for this course: How we know what isn’t so by Thomas Gilovich. Specifically I want to talk about “the clustering illusion” and the “law of large numbers” that he brings up. First, to explain, the clustering illusion refers to a person’s intuition that random events, such as a coin flip, should alternate between heads and tails more than they do. That is to say that even though there is a 50% chance of landing on either heads or tails – we are often shocked when we land on heads many more times than 50% of our flips (imagining landing on heads 9 out of 10 flips – that’s 90%). So the clustering illusion describes chance in a random distribution. However, chance doesn’t mean that there is a pattern, just the opposite – it’s still a random distribution and this is something that statisticians would describe via the law of averages which is also called the law of large numbers. The likes of which ensures that  there will be a close to 50-50 split after a large number of tosses and that the illusion that there is a pattern is only seen when you only observe a small “cluster” of tosses. A fascinating yet simple concept that serves to remind us that we can’t always assume that there are patterns to potentially random, by chance, events that occur in clusters. However, I did take issue with one example – or perhaps not so much issue but merely felt like more needed to be said about it. He used an example of a German bombardment against London during World War II in which the areas of impact were randomly distributed, as the accuracy of the bombs were quite limited. However, at the time, Londoners asserted that the bombs appeared to land in definite clusters. As a result they evacuated people to these seemingly less bombarded areas. The author mentions prior to this that there is no “law of small numbers” but perhaps that’s an issue. For I couldn’t help but think, even though I understood and agreed with him that the distribution of the bombs were random and thus no area could be promised as an area of safe haven – it is none the less true that if people had not evacuated to these areas, many more lives would have been loss. Perhaps there is no reason to explain why certain events occur in clusters and I certainly don’t want to let my human nature get to me in assuming that everything has a pattern. Yet I find it highly illogical to ignore realities (such as for whatever reason – or no reason – that some areas did indeed experience less risk) and highly unscientific to be satisfied with no longer asking questions. If no law describes small numbers than perhaps, and only perhaps, it’s not because there is no law governing them but because we simply haven’t discovered those laws yet.

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