Saturday, October 8, 2016

Evolution of American Thought: The Law of Errors

Much of the foundation for modern American thought can be traced to a long defunct coffee shop in London:

Georgian London - Old Slaughters Coffee House
74 & 75 (old number) current number 77 St. Martins Lane, London, UK
Note: 77 St Martins Lane is the approximate location the building was torn down in 1843 to make way for Cranbourn Street.

In 17th century England, coffee houses tended to be fairly genteel places compared to other establishments like taverns. Women and open gambling were generally banned and alcohol was usually not served. Coffee houses were places where men of the same profession could congregate. The Old Slaughterhouse, in its day, was where the top artists, intellectuals and foreigners would gather to play games like chess, draughts (checkers) and whist (old version of bridge) and sometimes wager on them.

It was here that Abraham De Moivre earned money calculating odds for gamblers and, in the process, eventually developed the expression of the Gaussian function (Bell Curve) and related calculation of the  probability of error:

Statistics for the Behavioral Sciences by By Susan A. Nolan, Thomas Heinzen

In the 18th century, the math prodigy, Carl Friedrich Gauss would take up De Moivre's work on gambling odds and apply it to astronomy. In particular, Gauss worked resolve measurement errors that are inherent in any data but were particularly vexing to the astronomers of the day with their primitive equipment. In the process, Gauss developed the the method of least squares (data fitting) and the normal (Gaussian) distribution of errors:

A French contemporary of Gauss, Pierre-Simon Laplace would later popularize these theories. It was Laplace who pointed out the usefulness of these work in quantifying social phenomena. Laplaces's student, Quetelet was one of the first to put these ideas into practice:

Mathematics in Victorian Britain

This post was inspired by a chapter in Louis Menand's book, The Metaphysical Club

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