Aside from English, they're all closely related languages (Hindi, Marathi, Gujarati). I wouldn't really expect knowing related languages to give the same payoff as say knowing languages from different groups or families of languages.
((Japanese, Mandarin, Cantonese),
(Hindi, Marathi, Gujarati),
(English, French, Italian, German, Dutch, Latin))
Are you saying that knowing one from each set is more beneficial than knowing three from any one set?
http://upload.wikimedia.org/wikipedia/commons/4/4f/IndoEurop...
There are subdivisions like Germanic and Romance in the language family which do seem sufficiently far apart. However, there are quite a few subdivisions that seem very closely related.
I wonder if there is a way to draw entirely new subdivisions based on benefits of knowing languages from each subdivision.
Also, intuitively, what you say about knowing unrelated languages makes sense. I am curious however, if you had some deeper insight or knowledge into why (if true) this might be?
http://en.wikipedia.org/wiki/Language_isolate
http://en.wikipedia.org/wiki/Japonic_languages
Also from http://en.wikipedia.org/wiki/Japanese_language: "During the Heian period (794–1185), Chinese had a considerable influence on the vocabulary and phonology of Old Japanese."
I think that qualifies as somewhat related?
The same goes for the influence of Chinese on Japanese, only more so: Chinese and Japanese aren't remotely related.
As far as Japanese being an isolate, please keep in mind that the Ryukyuan languages are practically dead and all the other Japonic language are long since dead. There's some _very_ scant evidence that it might be part of the hypothetical Altaic group of languages, but the evidence is weak at best, and only marginally more plausible than the Nostratic hypothesis.