Actually, information theory would argue that if the more compactness was
driven by having less information due to a low transmission speed/bandwidth,
then you would likely have more ambiguity (i.e. less information on the
receiving side) not less.
Also, there have been numerous studies comparing spoken and sign languages
in terms of sentence structure. The most interesting ones (for both spoken
and sign) are the ones dealing with languages that are invented by small
groups who haven't been previously exposed to other languages.
Unfortunately, I don't have access to specific references currently.
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