[OPE] Random laughs: Zipf's law and Benford's law

From: Jurriaan Bendien <adsl675281@telfort.nl>
Date: Sun May 17 2009 - 07:42:00 EDT

"Each individual will adopt a course of action that will involve the
expenditure of the probably least average of his work (by definition, least

- George Kingsley Zipf , "Human Behavior and the Principle of Least Effort:
An Introduction to Human Ecology", p. 18, Addison-Wesley, 1949.

"A compilation of some 20,000 first digits taken from widely divergent
sources shows that there is a logarithmic distribution of first digits when
the numbers are composed of four or more digits. An analysis of the numbers
from different sources shows that the numbers taken from unrelated subjects,
such as a group of newspaper items, show a much better agreement with a
logarithmic distribution than do numbers from mathematical tabulations or
other formal data. There is here the peculiar fact that numbers that
individually are without relationship are, when considered in large groups,
in good agreement with a distribution law - hence the name "Anomalous
Numbers." A further analysis of the data shows a strong tendency for bodies
of numerical data to fall into geometric series. If the series is made up of
numbers containing three or more digits the first digits form a logarithmic
series. If the numbers contain only single digits the geometric relation
still holds but the simple logarithmic relation no longer applies. (...)
The Law of Anomalous Numbers is thus a general probability law of widespread

- Frank Benford, "The law of anomalous numbers". Proceedings of the American
Philosophical Society 78 (4), March 1938, pp. 551.

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