A ban, sometimes called a hartley, is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit. Like a bit corresponds to a binary digit, a ban is a decimal digit. A deciban is one tenth of a ban. Logarithmic units are abstract mathematical units that can be used to express any quantities (physical or mathematical) that are defined on a logarithmic scale, that is, as being proportional to the value of a logarithm function. ... Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ... Entropy of a Bernoulli trial as a function of success probability. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... Plot of log2 x In mathematics, the binary logarithm (log2 n) is the logarithm for base 2. ... This article is about the unit of information. ...

One ban corresponds to about 3.32 bits (log₂(10)), or 2.30 nats (ln(10)). A deciban is about 0.33 bits. This article is about the unit of information. ... A nat is a logarithmic unit of information or entropy, based on natural logarithms and powers of e, rather than the powers of 2 and base 2 logarithms which define the bit. ...

The deciban is a particularly useful measure of odds-ratios or weights of evidence. 10 decibans corresponds to an odds ratio of 10:1; 20 decibans to 100:1 odds, etc. In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing. ...

According to I. J. Good a change in a weight of evidence of 1 deciban (ie a change in an odds ratio from evens to about 55:45), or perhaps half a deciban, is about as finely as humans can reasonably be expected to quantify their degree of belief in a hypothesis. Irving John (Jack) Good (born 9 December 1916) is a British statistician who worked also as a cryptographer and developer of the Colossus computer at Bletchley Park. ...

History

The ban and the deciban were invented by Alan Turing with I. J. Good in 1940, to measure the amount of information which could be deduced by the codebreakers at Bletchley Park using the Banburismus procedure, towards determining each day's unknown setting of the German naval Enigma cipher machine. The name was inspired by the enormous sheets of card, printed in the town of Banbury about 30 miles away, that were used in the process. Alan Turing is often considered the father of modern computer science. ... 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ... During World War II, British and American cryptographers at Bletchley Park broke a large number of Axis codes and ciphers, including the German Enigma machine. ... Banburismus was a process invented by Alan Turing at Bletchley Park during the Second World War. ... A three-rotor German military Enigma machine showing, from bottom to top, the plugboard, the keyboard, the lamps and the finger-wheels of the rotors emerging from the inner lid (version with labels). ... The modern Castle Quay Shopping Centre in Banbury is built alongside the Oxford Canal Map sources for Banbury at grid reference SP4540 Banbury is a market town on the River Cherwell in Oxfordshire, England. ...

The term hartley is after Ralph Hartley, who suggested this unit in 1928 (Reza [1961] 1994:7). Ralph Vinton Lyon Hartley (November 30, 1888 - May 1, 1970) was an electronics researcher. ...

The units pre-date Shannon's bit by at least eight years. Claude Elwood Shannon (April 30, 1916 _ February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ...

References

• Hartley, R.V.L., "Transmission of Information," Bell System Technical Journal, July 1928
• Reza, Fazlollah M. An Introduction to Information Theory. New York: Dover, 1994. ISBN 0486682102
• David J. C. MacKay. Information Theory, Inference, and Learning Algorithms Cambridge: Cambridge University Press, 2003. ISBN 0521642981. This on-line textbook includes a chapter on the units of information content, and the game of Banburismus that the codebreakers played when cracking each day's Enigma codes.