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At Travel.SE it was pointed out that in Georgia (the country), a visitor would have use of learning Georgian, Russian, and Armenian. That's three very different languages, with three quite different scripts, for such a small country! That prompts me the question:

In what country do we find the highest linguistic density? I don't know if this concept exists, but I mean the geographic derivative of the linguistic distance: e.g. a country where very different languages are natively spoken in a small area. Of course, this tends to infinity close to the language border, so let's stick to countries for now.

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If you want the smallest area containing the most languages which are the furthest apart on the language family tree, then perhaps Dagestan or Pakistan might be possible candidates I think. Then again there seems to be at least three factors in the equation so we might have to decide how best to weight them. –  hippietrail Nov 13 '12 at 9:35
    
I doubt you make use of Armenian in Georgia. –  Anixx Nov 13 '12 at 20:39
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Do you mean highest number of different languages speken by different people in the area or do you mean multilinguism, i.e. when the population as a whole uses several languages? –  Anixx Nov 13 '12 at 20:41
    
@Anixx: The city of Akhalkalaki (Ախալքալաք) is overwhelmingly Armenian (90%). Most signs are in Armenian or Cyrillic. Only official goverment signs are in Georgian. The same goes for most of the Samtskhe-Javakheti region (Սամցխե-Ջավախք). Here's some info on Wikipedia. –  hippietrail Nov 14 '12 at 9:41
    
I just read that Arnhemland in the remote north of Australia has a very high density not only of distinct languages but of entirely distinct language families. No statistics were quoted though as the article was intended for a lay audience. –  hippietrail Nov 22 '12 at 6:06
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3 Answers

Well Papua New Guinea famously has a lot of languages - 830 languages at the last count (and that's languages, not dialects!) However, I'm not sure about how different these languages are, but the numbers are huge and do come from a few different backgrounds. For example, English and Hiri Motu are pretty different languages.

If you take the land mass of PNG (452,860 km sq) and divide by the number of languages, according to ethnologue (830) you get a figure of approximately 546 km squared per language. The figure for Vanuatu would be approx. 107 km sp per language, indicating a higher density, but whether or not these languages vary as much as those of PNG, you'd have to consult the link given in jlovegren's answer.

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+1 Jared Diamond cites isolation and mountainous relief as a possible cause. –  Alain Pannetier Nov 13 '12 at 23:52
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Going by land area of the country, it'll be Vanuatu. Browse the statistics in the Ethnologue for more information.

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The Diversity index in the link looks similar to the statistic I asked for, and there Papua New Guinea (mentoined in Danger Fourpences answer) seems to have the highest score (table doesn't seem sortable though). –  gerrit Nov 13 '12 at 22:24
    
@gerrit Yes, that is correct. But PNG is about 40 times the land area of Vanuatu. –  jlovegren Nov 14 '12 at 1:45
    
Hmm, but if those are on islands spread out over a large oceanic area, I'm not sure if it fits with my idea of density. –  gerrit Nov 14 '12 at 9:45
    
As I mentioned, there are multiple factors so the weighting given to each factor will drastically affect the rankings, and I don't see any weighting specified. –  hippietrail Nov 14 '12 at 12:14
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If by "linguistic density", you mean the number of distinct languages spoken in an area divided by the size of the area, then Vanuatu would have the highest linguistic density for a country. Vanuatu has a total area of approximately 12,200 km² and is home to 108 known languages.

However, I'm not sure where the highest linguistic density would be found for types of geographic areas other than countries. Presumably, it would be some place else in the Pacific or perhaps sub-Saharan Africa or South Asia.

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I'm not sure what you mean. I see the point with Vanuatu. On the other hand, the islands compromising Vanuatu are spread out over a considerably larger area than 12,200 km². Still impressive, though. –  gerrit Nov 21 '12 at 13:56
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In point of fact, Vanuatu's total geographic area is 12,000 km². Its land area is 4,700 km². When you consider that all its languages are spoken on land (unless there is some hitherto unknown to science aquatic human species living in Vanuatu's waters and speaking one of its languages), its linguistic density is truly astounding. –  Rajan S. Nov 24 '12 at 19:15
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