History
The discovery of Benford's law goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables (used at that time to perform calculations) the earlier pages (which contained numbers that started with 1) were much more worn than the other pages. Newcomb's published result is the first known instance of this observation and includes a distribution on the second digit, as well. Newcomb proposed a law that the probability of a single number N being the first digit of a number was equal to log(N + 1) − log(N).
The phenomenon was again noted in 1938 by the physicist Frank Benford, who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of 335 rivers, the sizes of 3259 US populations, 104 physical constants, 1800 molecular weights, 5000 entries from a mathematical handbook, 308 numbers contained in an issue of Readers' Digest, the street addresses of the first 342 persons listed in American Men of Science and 418 death rates. The total number of observations used in the paper was 20,229. This discovery was later named after Benford making it an example of Stigler's law.
In 1995, Ted Hill proved the result about mixed distributions mentioned below.
Read more about this topic: Benford's Law
Famous quotes containing the word history:
“America is the only nation in history which, miraculously, has gone directly from barbarism to degeneration without the usual interval of civilization.”
—Attributed to Georges Clemenceau (1841–1929)
“The history of the world is none other than the progress of the consciousness of freedom.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“We are told that men protect us; that they are generous, even chivalric in their protection. Gentlemen, if your protectors were women, and they took all your property and your children, and paid you half as much for your work, though as well or better done than your own, would you think much of the chivalry which permitted you to sit in street-cars and picked up your pocket- handkerchief?”
—Mary B. Clay, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 3, by Susan B. Anthony and Ida Husted Harper (1902)