Ban (information)
Encyclopedia
A ban, sometimes called a hartley (symbol Hart) or a dit (short for decimal digit), is a logarithmic unit which measures information
or entropy
, based on base 10 logarithm
s and powers of 10, rather than the powers of 2 and base 2 logarithms
which define the bit
. As a bit
corresponds to a binary digit, so a ban is a decimal digit. A deciban is one tenth of a ban, analogous to a decibel
.
One ban corresponds to about 3.32 bit
s (log2(10)), or 2.30 nat
s (ln(10)). A deciban is about 0.33 bits.
with I. J. Good
in 1940, to measure the amount of information that 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.
Jack Good
argued that the sequential summation of decibans to build up a measure of the weight of evidence in favour of a hypothesis, is essentially Bayesian inference
. Donald A. Gillies
, however, argued the ban is, in effect, the same as Karl Popper's
measure of the severity of a test.
The term hartley is after Ralph Hartley
, who suggested this unit in 1928.
The units pre-date Shannon's bit by at least eight years.
. 10 decibans corresponds to an odds ratio of 10:1; 20 decibans to 100:1 odds, etc. According to I. J. Good
, a change in a weight of evidence of 1 deciban (i.e., a change in an odds ratio from evens to about 5:4), or perhaps half a deciban, is about as finely as humans can reasonably be expected to quantify their degree of belief in a hypothesis.
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
or entropy
Information entropy
In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...
, based on base 10 logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
s and powers of 10, rather than the powers of 2 and base 2 logarithms
Binary logarithm
In mathematics, the binary logarithm is the logarithm to the base 2. It is the inverse function of n ↦ 2n. The binary logarithm of n is the power to which the number 2 must be raised to obtain the value n. This makes the binary logarithm useful for anything involving powers of 2,...
which define the bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
. As a bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
corresponds to a binary digit, so a ban is a decimal digit. A deciban is one tenth of a ban, analogous to a decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...
.
One ban corresponds to about 3.32 bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
s (log2(10)), or 2.30 nat
Nat (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 nat is the natural unit for information entropy...
s (ln(10)). A deciban is about 0.33 bits.
History
The ban and the deciban were invented by Alan TuringAlan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...
with I. J. Good
I. J. Good
Irving John Good was a British mathematician who worked as a cryptologist at Bletchley Park with Alan Turing. After World War II, Good continued to work with Turing on the design of computers and Bayesian statistics at the University of Manchester...
in 1940, to measure the amount of information that could be deduced by the codebreakers at Bletchley Park
Bletchley Park
Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Museum of Computing...
using the Banburismus
Banburismus
Banburismus was a cryptanalytic process developed by Alan Turing at Bletchley Park in England during the Second World War. It was used by Bletchley Park's Hut 8 to help break German Kriegsmarine messages enciphered on Enigma machines. The process used sequential conditional probability to infer...
procedure, towards determining each day's unknown setting of the German naval Enigma
Enigma machine
An Enigma machine is any of a family of related electro-mechanical rotor cipher machines used for the encryption and decryption of secret messages. Enigma was invented by German engineer Arthur Scherbius at the end of World War I...
cipher machine. The name was inspired by the enormous sheets of card, printed in the town of Banbury
Banbury
Banbury is a market town and civil parish on the River Cherwell in the Cherwell District of Oxfordshire. It is northwest of London, southeast of Birmingham, south of Coventry and north northwest of the county town of Oxford...
about 30 miles away, that were used in the process.
Jack Good
I. J. Good
Irving John Good was a British mathematician who worked as a cryptologist at Bletchley Park with Alan Turing. After World War II, Good continued to work with Turing on the design of computers and Bayesian statistics at the University of Manchester...
argued that the sequential summation of decibans to build up a measure of the weight of evidence in favour of a hypothesis, is essentially Bayesian inference
Bayesian inference
In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...
. Donald A. Gillies
Donald A. Gillies
Donald A. Gillies is a British philosopher and historian of science and mathematics. He is an Emeritus Professor in the Department of Science and Technology Studies at University College, London.-Career:...
, however, argued the ban is, in effect, the same as Karl Popper's
Karl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...
measure of the severity of a test.
The term hartley is after Ralph Hartley
Ralph Hartley
Ralph Vinton Lyon Hartley was an electronics researcher. He invented the Hartley oscillator and the Hartley transform, and contributed to the foundations of information theory.-Biography:...
, who suggested this unit in 1928.
The units pre-date Shannon's bit by at least eight years.
Usage as a unit of probability
The deciban is a particularly useful measure of information in odds-ratios or weights of evidenceWeight of evidence
Weight of evidence is a measure of evidence on one side of an issue as compared with the evidence on the other side of the issue, or to measure the evidence on multiple issues.Weight of evidence or WofE may be used in:...
. 10 decibans corresponds to an odds ratio of 10:1; 20 decibans to 100:1 odds, etc. According to I. J. Good
I. J. Good
Irving John Good was a British mathematician who worked as a cryptologist at Bletchley Park with Alan Turing. After World War II, Good continued to work with Turing on the design of computers and Bayesian statistics at the University of Manchester...
, a change in a weight of evidence of 1 deciban (i.e., a change in an odds ratio from evens to about 5:4), or perhaps half a deciban, is about as finely as humans can reasonably be expected to quantify their degree of belief in a hypothesis.
Further reading
- David J. C. MacKay. Information Theory, Inference, and Learning Algorithms Cambridge: Cambridge University Press, 2003. ISBN 0-521-64298-1. This on-line textbook includes a chapter on the units of information content, and the game of BanburismusBanburismusBanburismus was a cryptanalytic process developed by Alan Turing at Bletchley Park in England during the Second World War. It was used by Bletchley Park's Hut 8 to help break German Kriegsmarine messages enciphered on Enigma machines. The process used sequential conditional probability to infer...
that the codebreakers played when cracking each day's Enigma codes.