This question involves the commonest languages still used in 2015.

Prof. John McWhorter and this answer argue different rates of language change, e.g. the language change from Old Norse to Icelandic2015 < the language change from Old English to English2015.

Are there or rankings any indices that compare such changes?

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    Why the downvotes? This is an excellent topic. If you the formulation isn't a fit for SE, modify it. – Adam Bittlingmayer Nov 27 '15 at 15:44
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    Google N-Gram Viewer can be used to this analysis for recent centuries, but it will take some work. In any case the results will depend on some subjective decisions of methodology. – Adam Bittlingmayer Nov 27 '15 at 15:47
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    @A.M.Bittlingmayer +1. Thank you for your support. The downvotes also disturb me. – AYX.CLDR Nov 27 '15 at 18:37
  • I'm not sure this would be at all meaningful as change can be highly contingent. The Tambora eruption wiped out a language (Tambora, non-Austronesian) in a day... a high rate of change; Hebrew was preserved as a liturgical language for centuries, a slow rate of change. A totally 'undisturbed' society may well have a slow rate of change, so the issue is about language-changing events: migration, invasion, war, social change... – Gaston Ümlaut Nov 27 '15 at 21:56
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    @Gaston Ümlaut I don't see how those two special cases invalidate the question, which I find very interesting. – David Garner Nov 30 '15 at 22:12

None known to me. But, by default, rate of change is just difference divided by time. Assuming we know the time for each language pair we care about, then the question is just how to measure the difference between languages, which is a more established field.

A key nuance of measuring differences between languages is that they can be directed - diff(b, a) is not necessarily the same as diff(a, b) because mutual intelligibility is assymetric, and that's a factor here because speakers of earlier stages of a language have no exposure to the future.

This also affects the benchmarks. If you had a way to time travel and test the ancient Angles on modern English, would your benchmark contain URLs and references to the World Cup, jazz hits, the Syrian war factions and electric cars? Or would you filter those out?

Some measures of language/dialect difference:

Vocabulary overlap

The size of the common vocabulary, or the set-theoretic-difference. Maybe stemmed or lemmatised, maybe frequency-weighted, maybe including the foreign loanwords that real people actually use in the real world.

Orthographic change

Given lists of cognates, take the edit distance. Maybe the changes affect many words but are predictable. Maybe the alphabet has changed, but some alphabet pairs are more 1:1 than others. Maybe it's the punctuation that has changed.

Mutual intelligibility

Unlike this above, this can actually cover semantic shift, but it's not very automatable or scalable or replicable.

The above are unsupervised approaches, but we could also build a representation using similar features for a supervised approach. So we input some inequalities - eg diff(Icelandic, Old Icelandic) < diff(English, Old English) - that we have decided are true, and then learn to predict it for arbitrary pairs.

Using a few rules and a dataset of language families and dates, we could generate many such inequalities reliably, eg diff(English, Middle English) < diff(English, Old English) or diff(Arabic, Hebrew) < diff(Arabic, Japanese).

There are many questions here, like how to weight changes in morphology that affect many words but are simple and consistent, and, last but not least, changes in syntax and grammar. Languages are in transition, often multiple forms are valid, while one may be more common. You need to find a comparable corpus for both languages, but again that is assymetric - there are modern Bibles, but you won't find today's newspaper or StackExchange comments in a language as written by the ancients.

All in all, rankings like this touch on so many language-specific issues - that ideally the implementer takes conscious but not ideological decisions on - that it either ends up misleading or contains so many caveats that the consumer is forced to actually understand those language-specific issues, at which point the ranking is unnecessary.

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