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A nat (sometimes also nit or nepit) is a logarithmic unit of information
Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
 or entropy
Information entropy

In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the self-information contained in a message, usually in units such as bits....
, based on natural logarithm
Natural logarithm

The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e , where e is an irrational number constant approximately equal to 2.718281828....
s and powers of e
E (mathematical constant)

The mathematical constant e is the unique real number such that the function ex has the same value as the derivative, for all values of x....
, rather than the powers of 2 and base 2 logarithms
Binary logarithm

In mathematics, the binary logarithm is the logarithm for base 2. It is the inverse function of ....
 which define the bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
. The nat is the natural unit for information entropy. Physical systems of natural units which normalize Boltzmann's constant to 1 are effectively measuring thermodynamic entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 in nats.

When the Shannon entropy is written using a natural logarithm,

it is implicitly giving a number measured in nats.

One nat corresponds to about 1.44 bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
s , or 0.434 hartley
Ban (information)

A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or information entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and binary logarithm which define the bit....
s .

lass="link1" onMouseover='showByLink("m5312315",this)' onMouseout='hide("m5312315")'href="http://www.absoluteastronomy.com/topics/Alan_Turing">Alan Turing
Alan Turing

Alan Mathison Turing, Order of the British Empire, Fellow of the Royal Society was a British mathematician, logician and Cryptanalysis....
 used the natural ban
Ban (information)

A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or information entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and binary logarithm which define the bit....
 (Hodges 1983, Alan Turing: The Enigma).






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A nat (sometimes also nit or nepit) is a logarithmic unit of information
Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
 or entropy
Information entropy

In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the self-information contained in a message, usually in units such as bits....
, based on natural logarithm
Natural logarithm

The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e , where e is an irrational number constant approximately equal to 2.718281828....
s and powers of e
E (mathematical constant)

The mathematical constant e is the unique real number such that the function ex has the same value as the derivative, for all values of x....
, rather than the powers of 2 and base 2 logarithms
Binary logarithm

In mathematics, the binary logarithm is the logarithm for base 2. It is the inverse function of ....
 which define the bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
. The nat is the natural unit for information entropy. Physical systems of natural units which normalize Boltzmann's constant to 1 are effectively measuring thermodynamic entropy
Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
 in nats.

When the Shannon entropy is written using a natural logarithm,

it is implicitly giving a number measured in nats.

One nat corresponds to about 1.44 bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
s , or 0.434 hartley
Ban (information)

A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or information entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and binary logarithm which define the bit....
s .

History

Alan Turing
Alan Turing

Alan Mathison Turing, Order of the British Empire, Fellow of the Royal Society was a British mathematician, logician and Cryptanalysis....
 used the natural ban
Ban (information)

A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or information entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and binary logarithm which define the bit....
 (Hodges 1983, Alan Turing: The Enigma). Boulton and Wallace
Chris Wallace (computer scientist)

Professor Christopher Stewart Wallace was an Australian computer scientist notable for having devised:* The minimum message length principle — an information-theoretic principle in statistics, econometrics and machine learning which can be seen both as a mathematical formalisation of Occam's Razor and as an invariant Bayesian infere...
 (1970) used the term nit in conjunction with minimum message length
Minimum message length

Minimum message length is a formal information theory restatement of Occam's Razor: even when models are not equal in goodness of fit accuracy to the observed data, the one generating the shortest overall message is more likely to be correct ....
 which was subsequently changed by the minimum description length
Minimum description length

The minimum description length principle is a formalization of Occam's Razor in which the best hypothesis for a given set of data is the one that leads to the largest data compression....
 community to nat to avoid confusion with the nit
Nit (unit)

The candela per square metre is the SI unit of measurement of luminance; nit is a non-SI name also used for this unit. It is often used to quote the brightness of computer displays, which typically have luminances of 50 to 300 nits ....
 used as a unit of luminance
Luminance

Luminance is a Photometry measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle....
 (, ).