If whales sang love sonnets or expositions on philosophy and mathematics to one another, would we know about it? I suppose that this is a signal processing problem: given what we know about whales’ listening and vocalization abilities, is there an upper bound to the complexity of what they could be saying to one another? Ditto for elephants.
I don’t know a heck of a lot about cetacean biology specifically, but I’ll take a crack at it:
There has been no evidence I’m aware of that demonstrates whales have the same type of complexity as human language, but there are still many mysteries about whale songs. Whale songs apparently do have some grammatical structure, but I’m a bit foggy on the details. They’re very interesting, and much work has been done over the past couple of decades, but not as much is known about whale songs and communication as is known about bird songs. One thing to keep in mind is that although whale songs do change over time, they tend to be rather similar in specific populations over years, so it’s not like they’re holding different conversations every day like people would.
People have tried to determine what signals the whales are sending to each other, but I don’t know what their success has been off the top of my head.
Here’s a little basic blurb on whale songs
This site may contain some reading you would want to persue
This site may also prove useful and has some links on the subject
Here’s an interesting site that may not answer any questions, but has recordings on it
While whales are quite intelligent, they are not nearly as intelligent as humans, so their communication is probably not as complex. But there’s a lot that isn’t known about this subject.
I dunno about the elephants.
IIRC, whales have a “vocabulary” of 16 sounds. Not much.
Also, the Early Wittgenstein said that even if we could understand what whales (he talked about lions, actually) were saying, then it would be totally meaningless. Our frames of reference are so different, there can be no common understanding. The Late Wittgenstein disageed with him though.
I saw a great cartoon that touches on this. It is at the Dolphin Language Research Facility. One researcher is coming in from the dolphin pool and says to another researcher, “They are making that funny ‘habla usted espanol’ noise again”
It’s pretty well established that birds and mammals DO communicate with other members of their species, through sounds and gestures. If you want to call this “language,” suit yourself. But the original poster makes a common mistake, by assuming that when animals communicate, they’re saying profound, important, interesting things to each other!
Remember the old Gary Larson cartoon about a scientist who’d found a way to translate dog language into English? He found that all dogs ever say is “Hey!” or “Hey, hey!”
Ever see Johnny Carson’s old sketch about a marine biologist who’d devised a computer that translated fish language into English? Turns out that all a shark can say is “I’m gonna bite your butt!”
Now, I love humpback whales. They’re awesome, beautiful animals. But they’re not much more intelligent than a cow. And their “songs” are simply long, complicated ways of saying either:
- “I’m horny- come mate with me”
or
- “This is MY territory, go away!”
Matter of fact, those two sentences make up 95% of ALL animal communication! Don’t give whales too much credit (they’re NOT discussing particle physics- they’re either looking to score, or looking for a fight).
I recall hearing a linguist once say that the unique thing about human languages is that they are “digital.” That is, we use sequenced words to break up an event, and use grammar to arrange the words. This is as opposed to body language or hand gestures, which are “analog” (“Hey you, come over here” I’m saying, without using words).
Based on this concept (which is more interesting than my synopsis), I’ve sometimes conjectured that whale songs are like language minus the essential ingredient of grammar. Which is to say, not a language at all. We need grammar to keep linguistic ideas from happening all at once.
Given the near-impossibility of accurately translating English to Chinese and vice versa, I’d say the disconnect with whales is easy to imagine. Rather, the whale POV is unimaginable, given that our close cousins the Han Chinese have such a different conceptual framework.
–Grump “talk about your ‘great walls’” y
I don’t know about “I’m horny- come mate with me” or “This is MY territory, go away!” making up 95% of all communication. I recently saw a really fascinating special on PBS where they attached this sophisticated super-deep diving camera to the back of one humpback whale in a pod of four or five, then watched the monitor as they dove thousands of feet straight down. At about 1300 feet or so, you could see one whale’s head turn around, actually look at the camera, (you could see it’s eye), then make some noises, after which the other whales also turned around and looked at the camera. I swear, it seemed like after a little conference, they decided to leave it alone and keep diving. If anyone knows where I can get a copy of this special, I’d love to see it again.
Also, don’t Orcas hunt in packs and display a clear intelligence / communication routine as they do? ie. wearing out the pray by surrounding it, steering it into deeper water, etc.?
From “Cosmos”, by Carl Sagan -
“A typical whale song lasts for perhaps 15 minutes; the longest, about an hour. Often it is repeated, identically, beat for beat, measure for measure, note for note. Occassionally a group of whales will leave their winter waters in the midst of a song and six months later return to continue at precisely the right note, as if there had been no interruption.”
Of course, the same could be said about your typical network-TV dialogue, never mind top 40 radio. 
Great feedback, gang! Following up one of the leads, I found the following abstract for Dudzinski, Kathleen. Communication and Behavior in the Atlantic Spotted Dolphin (Stenella frontalis): Relationships Between Vocal and Behavioral Activities. Dissertation. 1996:
So dolphins at least may have somewhat more complicated language than suggested by astorian (who was writing about whales, I hasten to add). Not quite partical physics though. 
TheeGrumpy: I’ve come across claimsthat whales possess grammar, although they have reportedly been met with some skepticism.
What if whale “songs” turn out to be more analogous to lyric-less music than to human language? This would greatly complicate the problem of translation, I would think. Music (without words) can be very complex and meaningful in its own way, but can we say that it’s truly translatable into language? Can Tchaikovsky’s Violin Concerto in D major be “translated” in English words, sentences and paragraphs? Or, seen the other way around, is it even possible to tell a knock-knock joke by playing the trombone?
Ahhh…but there are only ~44 English sounds. So if you consider that our vocabulary, our language is really not much more complex. It’s the way those 44 sounds are put together that makes our language. 16 sounds can be put together in a suprising number of ways. Sure, it might not yield an 80,000 word language, but it can still yield an infinite number of sentences, and could probably convey quite a lot of information. Maybe along the lines of a 3-4 year old’s vocab.
Jman
UPDATE on 19 year old thread.
2011 article sort of answers my question: Dolphin Studies Could Reveal Secrets of Extraterrestrial Intelligence | Space
- “It turns out that, according to information theory, dolphin communication is highly complex with many similarities with human languages, even if we don’t understand the words they are saying to one another.”
Also:
- Meanwhile, another feature of information theory, called Shannon entropy, can tell us how complex that communication is. …humans go up to about ninth order Shannon entropy… How do dolphins fare? “They have a conditional probability between signals that goes up to fourth order and probably higher, although we need more data,” said Doyle.
And here’s a 2020 article: http://cosmos.nautil.us/feature/54/listening-for-extraterrestrial-blah-blah
Zipf’s law applies to dolphins as well as humans: you can mathematically distinguish between a baby human babbling and an adult human communicating. Same for dolphins.
Humpback whales are being studied:
We found internal structure in dolphin communication as well. The big difference is that the dolphins have a core of about 50 signal types, whereas the humpbacks have hundreds. We are currently collecting data to determine what the highest-order entropy of the humpback whale communication system may be.
Dolphin political discussions must get quite heated.
I bet half of them claim to be the true heir to the French thone.
You made me spit out my tea 
The Hawaiian language only has about that many sounds, depending where you draw the line on differentiating between vowel sounds. (It uses only eight consonants.) Some more obscure languages have even fewer. You don’t really NEED that many sounds for a complex language.
That was a really old post you responded to. I’ll point out that after years and years of researching dolphins we can find nothing resembling a language at all, yet dolphins can communicate extremely complex information almost instantly. When you see the dolphin inmates putting on shows in groups of two or more they don’t have to have particular routines memorized, they can coordinate random instructions between themselves in a manner no human has been able to understand. Look for National Geographic articles on this topic, they are extremely revealing.
That’s not saying that their language is that complex, but only that based on the structure of the sounds they’re making, they could potentially encode that much information using them.
I’d be curious to hear how things like bird songs and the like come out on a similar analysis. That might give us some more perspective on it.
That’s right, but Hawaiian words are much longer. The state fish is called humuhumunukuapua’a.
It’s also a tasty drink…
https://drunkendiplomacy.com/blog/2016/11/25/humuhumunukunukuapuaa/