Monday, June 28, 2021

Have you heard of Benford's Law?

Simply stated, this law says that if you take any large group of multiple-digit numbers--U.S. city populations, numbers of arrests per year in multiple cities, vote counts in numerous American counties, the numbers of book buyers for the top 100 bestselling authors, even the number of fractions of seconds each note is held in a long piece of music--in short, any database of supposedly random numbers on any subject, the numbers will begin with 1 for 30% of the time. Moreover, more of the numbers will begin with 2 than 3, more will begin with 3 than 4, more will begin with 4 than 5, and so on through 9, which will begin a number sequence only 5% of the time. 

If you chart this with 1 through 9 on the X axis (horizontal) and each number's frequency of occurrence on the Y axis (vertical), you get a smooth downward-sloping curve called the Benford Curve.  Many, many statistical samplings of supposedly random numbers databases have borne this out consistently, and statisticians take the law into account in their work. This phenomenon has even been used to detect fraud if a given database does not follow the law.

Nobody knows why this law is true. 

It just is.

(Source: the "Connections" documentary series on Netflix)


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