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:
“We aspire to be something more than stupid and timid chattels, pretending to read history and our Bibles, but desecrating every house and every day we breathe in.”
—Henry David Thoreau (1817–1862)
“In all history no class has been enfranchised without some selfish motive underlying. If to-day we could prove to Republicans or Democrats that every woman would vote for their party, we should be enfranchised.”
—Carrie Chapman Catt (1859–1947)
“Yet poetry, though the last and finest result, is a natural fruit. As naturally as the oak bears an acorn, and the vine a gourd, man bears a poem, either spoken or done. It is the chief and most memorable success, for history is but a prose narrative of poetic deeds.”
—Henry David Thoreau (1817–1862)