Comment Not interesting yet. (Score 3, Informative) 43
It's possible that cetaceans have a true language. They certainly have something that seems to function the same as a "hello, I am (name)", where the name part differs between all cetaceans but the surrounding clicks are identical. The response clicks also include that same phrase which researchers think serves the purpose of a name.
But we've done structural analysis to death and, yes, all the results are interesting (it seems to have high information content, in the Shannon sense, seems to have some sort of structure, and seems to have intriguing early-language features), but so does the Voynich Manuscript and there's a 99.9% chance that the Voynich Manuscript is a fraud with absolutely no meaning whatsoever. Structure only tells you if something is worth a closer look and we have known for a long time that cetacean clicks were worth a closer look. Further structural work won't tell us anything we don't already know.
What we need is to have a long-term recording of activities and clicks/whistles, where the sounds are recorded from many different directions (because they can be highly directional) and where the recording positively identifies the source of each sound, what that source was doing at the time (plus what they'd been doing immediately prior and what they do next), along with what they're focused on and where the sounds were directed (if they were). This sort of analysis is where any new information can be found.
But we also need to look at lessons learned in primate research, linguistics, sociology and anthropology, to understand what ISN'T going to work, in terms of approaches. In all three cases, we've learned that you learn best immersively, not from a distance. If an approach has failed in EVERY OTHER SOCIAL SCIENCE, then assuming it is going to work in cetacean research is stupid. It might be the correct way to go, but assuming it is is the bit that is stupid. If things fail repeatedly, regardless of where they are applied, then there's a decent chance it is necessary to ask that maybe the stuff that keeps failing is defective.