Date: Jul 19, 2000 9:37 PM Author: Ralph A. Raimi Subject: [HM] Benford's Law

There is a "law" commonly called "Benford's Law" after Frank

Benford who wrote a paper (*The Law of Anomalous Numbers* was its title)

about it in 1938 (Proc. Am. Phil. Soc. vol 78, p551ff), with no indication

that it was not original with him. Many other papers about this "first

digit phenomenon" appeared in later years, usually naming it after

Benford, but it had in fact been announced and discussed by Simon Newcomb

sixty-seven years earlier (Amer. J. Math vol 4, 1881, p39-40). When I

wrote a history of the attempts at proving this law (*The First Digit

Phenomenon*, Amer. Math. Monthly vol 83, 1976, pp 521-538) I had the

pleasure not only of announcing for the first time in print, so far as I

knew, that it had been anticipated by Newcomb, but of comparing Benford's

Law with an alternate, though similar one I dubbed "Stigler's Law", which

was a slightly different proposed frequency distribution of first digits

in the tables of data that have reason to exhibit the phenomenon in

question.

However, the Stigler I referred to was apparently the real author

of that "law", or at least he was the one who had written me about it

(privately), explaining it had been the result of a lunch table

conversation between himself and other members of a certain group of

wartime statistical analysts of military efficiency in 1944, the actual

calculation having been made by Stigler himself after the lunch was over.

This 1944 Stigler was the famous economist George Stigler (Nobel Laureate

in later years), the father of the statistician Stephen Stigler whose

Law of Eponymy is the subject of the exchange I reproduce below.

George Stigler was also the author of another "law", this one a

law of economics, the name of which I've now forgotten. This Stigler law

says that all (economic) elasticities are small, if not zero. Since the

assertion is manifestly impossible his (humorous, but nonetheless serious)

essay on the subject is worth reading, and appears in one of his two or

three collections of more or less non-technical essays on economics. I

believe there is no question that this particular law of economics is

properly named Stigler's Law, and is unlikely to be discovered again.

On Mon, 17 Jul 2000, Julio Gonzalez Cabillon wrote:

>

> At 05:30 pm 17/07/00 -0500, Barry Cipra quoted:

> |

> | If you think I exaggerate, you are obviously not familiar with

> | Stigler's Law of Eponymy. This law, which in its simplest form

> | states that

> | "no scientific discovery is named after its original discoverer"

> | ...

>

> which is in fact an overstatement, and I do think you exaggerate.

>

> -- JGC

>

Ralph A. Raimi Tel. 716 275 4429 or (home) 716 244 9368

Dept. of Mathematics FAX 716 273 4655

University of Rochester Webpage http://www.math.rochester.edu/u/rarm

Rochester, NY 14627 (Webpage contains links to papers)