Editing Distance (section)

==Metaphorical distances==
Many abstract notions of distance used in mathematics, science and engineering represent a degree of difference or separation between similar objects.  This page gives a few examples.

===Statistical distances===
{{main|Statistical distance}}
In [[statistics]] and [[information geometry]], [[statistical distance]]s measure the degree of difference between two [[probability distribution]]s.  There are many kinds of statistical distances, typically formalized as [[divergence (statistics)|divergences]]; these allow a set of probability distributions to be understood as a [[space (mathematics)|geometrical object]] called a [[statistical manifold]].  The most elementary is the [[squared Euclidean distance]], which is minimized by the [[least squares]] method; this is the most basic [[Bregman divergence]]. The most important in [[information theory]] is the [[relative entropy]] ([[Kullback–Leibler divergence]]), which allows one to analogously study [[maximum likelihood estimation]] geometrically; this is an example of both an [[f-divergence|''f''-divergence]] and a Bregman divergence (and in fact the only example which is both). Statistical manifolds corresponding to Bregman divergences are [[flat manifold]]s in the corresponding geometry, allowing an analog of the [[Pythagorean theorem]] (which holds for squared Euclidean distance) to be used for [[linear inverse problem]]s in inference by [[optimization theory]].

Other important statistical distances include the [[Mahalanobis distance]] and the [[energy distance]].

===Edit distances===
In [[computer science]], an [[edit distance]] or [[string metric]] between two [[string (computer science)|strings]] measures how different they are. For example, the words "dog" and "dot", which differ by just one letter, are closer than "dog" and "cat", which have no letters in common.  This idea is used in [[spell checker]]s and in [[coding theory]], and is mathematically formalized in a number of different ways, including [[Levenshtein distance]], [[Hamming distance]], [[Lee distance]], and [[Jaro–Winkler distance]].

===Distance in graph theory===
{{main|Distance (graph theory)}}
In a [[graph (discrete mathematics)|graph]], the [[distance (graph theory)|distance]] between two vertices is measured by the length of the shortest [[path (graph theory)|edge path]] between them.  For example, if the graph represents a [[social network]], then the idea of [[six degrees of separation]] can be interpreted mathematically as saying that the distance between any two vertices is at most six.  Similarly, the [[Erdős number]] and the [[Bacon number]]—the number of collaborative relationships away a person is from prolific mathematician [[Paul Erdős]] and actor [[Kevin Bacon]], respectively—are distances in the graphs whose edges represent mathematical or artistic collaborations.

===In the social sciences===
In [[psychology]], [[human geography]], and the [[social science]]s, distance is often theorized not as an objective numerical measurement, but as a qualitative description of a subjective experience.<ref>{{Cite web|title=SOCIAL DISTANCES|url=https://www.hawaii.edu/powerkills/TCH.CHAP16.HTM|access-date=2020-07-20|website=www.hawaii.edu}}</ref>  For example, [[psychological distance]] is "the different ways in which an object might be removed from" the self along dimensions such as "time, space, social distance, and hypotheticality".<ref name=psych>{{cite journal | vauthors = Trope Y, Liberman N | title = Construal-level theory of psychological distance | journal = Psychological Review | volume = 117 | issue = 2 | pages = 440–63 | date = April 2010 | pmid = 20438233 | pmc = 3152826 | doi = 10.1037/a0018963 }}</ref>  In [[sociology]], [[social distance]] describes the separation between individuals or [[social groups]] in [[society]] along dimensions such as [[social class]], [[Race (classification of human beings)|race]]/[[ethnicity]], [[gender]] or [[human sexuality|sexuality]].