en>Daswerth at 13:34, 13 November 2013

2013-11-13T13:34:43Z

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A '''nat ''' (sometimes also '''nit ''' or '''nepit''') is a [[logarithmic unit]] of [[information]] or [[information entropy|entropy]], based on [[natural logarithms]] and powers of [[e (mathematical constant)|''e'']], rather than the powers of 2 and [[binary logarithm|base 2 logarithms]] which define the [[bit]]. The ''nat '' is the [[natural unit]] for information entropy. Physical systems of natural units which normalize [[Boltzmann's constant]] to 1 are effectively measuring [[entropy|thermodynamic entropy]] in nats.

When the [[Shannon entropy]] is written using a natural logarithm,

:<math> H = - \sum_i p_i \ln p_i \!\,</math>

it is implicitly giving a number measured in ''nats''.

One nat is equal to 1/([[Natural logarithm|ln]]2) [[shannon (unit)|shannons]] ≈ 1.44 Sh or, equivalently, 1/(ln10) [[hartley (unit)|hartleys]] ≈ 0.434 Hart.<ref>{{cite web|title=IEC 80000-13:2008|url=http://www.iso.org/iso/catalogue_detail?csnumber=31898|publisher=[[International Electrotechnical Commission]]|accessdate=21 July 2013}}</ref> The factors 1.44 and 0.434 arise from the relationships
:<math>\left (2^x=e^1\Rightarrow x=\tfrac{1}{\ln 2}\right )</math>, and
:<math>\left (10^x=e^1\Rightarrow x=\tfrac{1}{\ln 10}\right )</math>.
One nat is the information content of an event if the probability of that event occurring is 1/[[E (mathematical constant)|e]].

==History==
[[Alan Turing]] used the ''natural [[ban (information)|ban]]'' (Hodges 1983, ''Alan Turing: The Enigma''). Boulton and [[Chris Wallace (computer scientist)|Wallace]] (1970) used the term ''nit'' in conjunction with [[minimum message length]] which was subsequently changed by the [[minimum description length]] community to ''nat'' to avoid confusion with the [[nit (unit)|nit]] used as a unit of [[luminance]] ([http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005 Comley and Dowe, 2005], [http://www.csse.monash.edu.au/~dld/Publications/2005/ComleyDowe2005MMLGeneralizedBayesianNetsAsymmetricLanguages_p271.jpg sec. 11.4.1, p271]).

== References ==
*{{Cite book |first=J. W. |last=Comley |lastauthoramp=yes |first2=D. L. |last2=Dowe |chapterurl=http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005 |chapter=Minimum Message Length, MDL and Generalised Bayesian Networks with Asymmetric Languages |editor1-first=P. |editor1-last=Grünwald |editor2-first=I. J. |editor2-last=Myung |editor3-first=M. A. |editor3-last=Pitt |url=http://mitpress.mit.edu/catalog/item/default.asp?sid=4C100C6F-2255-40FF-A2ED-02FC49FEBE7C&ttype=2&tid=10478 |title=Advances in Minimum Description Length: Theory and Applications |location=Cambridge |publisher=MIT Press |isbn=0-262-07262-9 |year=2005 }}
*{{Cite book |first=Fazlollah M. |last=Reza |title=An Introduction to Information Theory |location=New York |publisher=Dover |year=1994 |isbn=0-486-68210-2 }}
{{reflist}}

[[Category:Units of information]]

Enumerative geometry - Revision history

en>Daswerth at 13:34, 13 November 2013