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Sometimes, I read passages like:

Languages X, Y and Z in region A are closely related to each other, comparable to French, Italian and Spanish in Western Europe.

The discussion in the question "Do distantly related languages have a lower incidence of false friends?" also implies that languages can be considered "closely related" or "distantly related" to each other.

How would one measure such distance and do linguists make that measurement for any purpose? Sometimes it's logically obvious, as a commenter in the linked question point out, that "it is uncontroversial to say that, given German as a reference point, Flemish (both West Germanic languages) is closer than Danish (both Germanic languages), which in turn is closer than Italian (both Indo-European)". How about comparison across different families? For example, How would one determine if Mandarin and Cantonese are (relatively) more closely related to each other than French and Spanish?

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There are qualitative and quantitative measures for 'distance'.

Qualitatively, many languages are easier to compare simply by know something about their family tree, which is implicitly recognizable (if one is lucky enough to know so many languages so well), by comparing vocabulary lists, syntax rules/systems, and phonology. The more common elements the closer they are. Mandarin and Cantonese are not mutually intelligible, but both have rich tonal systems, similar isolating grammars, and fairly simple phonological rules to map cognate words. Likewise French and Italian have a set of comparisons (similar conjugation/gender rules) and fairly regular rules mapping cognates. And the two sets of differences, those between Mandarin/Cantonese, and those between French/Spanish are of the same scale. The difference between French and German is so much larger than between Mandarin/Cantonese that one would be hard pressed to say they are of similar distance.

Quantitatively, one can define distance mathematically, by collecting a set of quantitative features in each language, and then defining a distance function that calculates an exact positive real number out of a combination of all the differences of these features. Then one can do a simple numerical comparison, the distance between X and Y and the distance between Z and W. One can go further and use a clustering algorithm to create a formal family tree of all languages of concern.

Presumably, the utility of a distance function would be to predict the difficulty in language learning or translation (machine or human); the further the distance, the more changes would need to be navigated. At some point, a distance will be meaningless; the difference between French and Swahili is just too much to settle qualitatively or quantitatively to then bother comparing with some other distance.

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    Has anyone performed this clustering analysis of languages? – Otavio Macedo Dec 28 '11 at 11:02
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    In comparison, another source suggests the 'lexical similarity' between French and German is 29% [en.wikipedia.org/wiki/Lexical_similarity], which is larger than the 19% similarity between Mandarin and Cantonese suggested by the above quoted passage. – Kenny LJ Jul 22 '14 at 9:32
  • @KennyLJ I'm not sure lexical similarity is the best way to measure distance. Languages can have a lot of lexical similarity but differ significantly in terms of grammar. – martinkunev Feb 12 '17 at 19:54
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There is a wealth of research on how to measure the distance between languages. Google the following: lexicostatistics, glottochronology, cladistics, Morris Swadesh and Robert Lees, Donald Ringe, April and Robert McMahon (esp. their 2005 book, Language classification by numbers), Sergei Starostin (esp. this paper).

However, I would recommend to read a intro textbook on historical linguistics (chapters on lexicostatistics and glottochronology) and chapter 6 in Keith Johnson's Quantitative methods in linguistics. Also, have a look at http://www.cs.rice.edu/~nakhleh/CPHL/

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People have looked at how distantly related languages are to determine when the proto-language existed, in much the same way as biologists try to determine when a common ancestor of two species existed. The more distantly related they are, the older the proto-language.

In fact, they sometimes present at the same conferences.

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Within the school of quantitative linguistics there is a kind of measurement methodology for dialects. A scientist called Hans Goebl used surveys to metricate differences between certain dialects inside of France. Here is the website for it: http://www.dialectometry.com/. The idea and methodology behind it is described in his article "On the nature of tension in dialectal networks" in "Systems: New Paradigms for the Human Sciences".

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One of several examples of a distance function is the Levenshtein edit distance. It works by producing a value based on how many 'edits' a word has to go through to match another. For example, English 'make' and Dutch 'maken' have a distance of 1, as only 'n' needs to be added or removed for both words to match. Better results can be achieved by assigning different values for more relevant edits, such as 'p' to 'b' (corresponding to predicable phonological changes), as opposed to the rather unlikely 'b' to 'z'. This can be useful in searching for cognates.

The values produced by calculating the Levenshtein edit distance can then be used as data for plotting a graph, giving both a numeric and visual indication of distance. Of course, this method does force you to reduce language to a scoring system, which, you could argue, leaves room for an uncomfortable amount of speculation.

Here's an example, from a quick google image search: Here's an example, from a quick google image search

And a wikipedia article: https://en.wikipedia.org/wiki/Levenshtein_distance

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    Levenstein distance is not enough anymore. "Dynamic programming" (awful name btw) alignment algorithms are much better. That means that you do a phonetic alignment and score the edit distance on phonetic grounds. While levenstein will treat /p/ and /b/ as a missmatch, a phonetic alignment algorithm will give them a good score, because the interchange of /p/ and /b/ is a very common sound change. If you're interested have a look at this algorithm webdocs.cs.ualberta.ca/~kondrak – Midas Feb 15 '17 at 20:09

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