I'm curious as to whether anyone has attempted to come up with a quantitative measure of information conveyed by written words, symbols or graphs, and particularly curious if anyone has studied Japanese kanji or Chinese hanzi in this context.
It's often said that Chinese and Japanese are more "information dense" in their written languages, which seems intuitively true given that tweets in Japanese, Chinese and Korean average out as much shorter than other Western languages. But I don't know of any attempt to put actual numbers to the amount of information that can be conveyed by logographs in Japanese and Chinese (I'm not discussing Korean as I have no knowledge of the language.)
Intuitively this seems like a near impossible task, given the amount of ambiguity in, for example, the character:
Which in Japanese can mean "above", "up", "elder", "before", "previous", "based on", "since" and so on, depending on the context. Some of these meanings are shared with Chinese, where it can also mean "to attend a class", "to climb up" or "to go up".
Nonetheless, I wonder if anyone has ever attempted such a quantification for Chinese/Japanese, or indeed in any written language. I haven't managed to find any studies through Google Scholar or through quick googling.