There’s a good article on the OP’s topic from Nov 2020 by Kershenbaum et al entitled, “Shannon entropy as a robust estimator of Zipf’s Law in animal vocal communication repertoires”, which unfortunately is over my head. One of the building blocks of information theory is Shannon entropy: the intuition is that unexpected sounds convey more information than expected ones. From Wiki:
The core idea of information theory is that the “informational value” of a communicated message depends on the degree to which the content of the message is surprising. If a highly likely event occurs, the message carries very little information. On the other hand, if a highly unlikely event occurs, the message is much more informative. For instance, the knowledge that some particular number will not be the winning number of a lottery provides very little information, because any particular chosen number will almost certainly not win. However, knowledge that a particular number will win a lottery has high informational value because it communicates the outcome of a very low probability event.
Kershenbaum et al note that efforts to assess animal language complexity struggle with small datasets outside the human domain. They outline 3 recommended testing methodologies depending upon whether the communication is high or low entropy and whether it appears to have a high or low vocabulary. Their introduction characterizes the existing scientific consensus (notwithstanding my previous post on the CETI Project (note pun: SETI - CETI)) . Emphasis added:
All animal species have evolved communication systems to suit their ecological requirements, but these systems vary greatly in their complexity, and the volume of information that can be transmitted, received and interpreted. Humans appear to be an extreme case, with the capability of conveying essentially unlimited information in our language, while relying on a finite set of signal elements. Non-human animals, on the other hand, are generally thought not to possess any true language (Cheney & Seyfarth, 1998; Fitch, 2005)… Comparative studies between human language and non-human animal communication systems continue to be important for identifying the conserved features of these systems and explaining any differences that emerged (Fitch, 2005).
Cheney & Seyfarth’s paper is entitled, “Why Animals Don’t Have Language”. It emphasizes ape studies, though it covers a few dolphin ones as well. They argue that while some species use labels, there’s little evidence for creating new calls and new labels for novel objects. Similarly, while they can be taught sentences, they don’t spontaneously create new sentences on their own. I suspect that this sort of thinking is what TriPolar’s National Geographic article was alluding to. I speculate that CETI got funding because larger whales haven’t been subjected to these sorts of inquiries to the extent that dolphins have.
The Kershenbaum paper uses datasets from 11 species including humans, orangutans, baboons, orcas, bats, and mockingbirds. It wasn’t a comprehensive study: it didn’t include dolphins, gorillas, or chimpanzees. I struggle to interpret figure 8 but AFAICT bats are language geniuses based upon their entropy. Humans cover the k=~-1 range, as do a few species of birds depending upon the metric. But again, I don’t quite grasp this paper. (Also, I haven’t figured out how to post an image here- I tried.)
I’ll observe that just as language is not universal among primates, it’s conceivable that it could exist among some whale species and not others.