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This question is similar to this one; the difference is that I'd like to find out about quantitative measurements that are not based solely on the vocabulary.

Are there any such objective quantitative measurements in existence? The Levenshtein distance mentioned in the top answer to the other question seems to be vocabulary based; if two languages with the same vocabulary differ grammatically then Levenshtein distance wouldn't measure that.

I wonder whether a comprehensive linguistic distance was ever proposed.

I think such measurement is possible. Here's one possibility: consider an autoencoder trained to translate between the given languages. An auto-encoder, as any neural network (NN), has a definite size: the number of nodes. And, because it translates between the given languages, the NN encapsulates the difference between languages.

Now the numerical distance between languages can be based on the smallest possible size among all the auto-encoders translating between those languages. One could measure that by training a bunch of NNs of different depths and sizes, qualifying their accuracy, and defining a the distance between languages as the smallest size among all the qualified auto-encoders between them.

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