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Whale Songs Follow the Same Mathematical Rule as Human Language

Whale song, though technically not a language, is organized in a familiar pattern.

Mihai Andrei
February 10, 2025 @ 4:49 pm

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In the early 1970s, engineers listening for Russian submarines started detecting strange underwater signals. Using hydrophones (underwater microphones), they repeatedly picked up rhythmic, varying sounds. It turned out they were listening to complex vocalizations produced by humpback whales.

Humpback whale songs are among the most sophisticated in the animal kingdom and an outstanding example of non-human culture. Now, researchers have demonstrated that these vocal sequences exhibit structural similarities to human language. While we don’t yet understand their meaning, whales appear to organize their sounds in a way that mirrors our own communication patterns.

humpback whale just under the water surface
Image credits: Animalia.

Languages all around the world follow a similar statistical pattern known as a Zipfian distribution. In simple terms, a small number of words (such as “the” or “is”) are used very frequently, while most words are used far less often. This occurs because efficient communication prioritizes brevity for common words while reserving longer, more complex words for clarity in rarer cases.

This distribution follows a consistent rule: the most frequently used word appears about twice as often as the second most common word, three times as often as the third, four times as often as the fourth, and so on. Remarkably, this pattern holds across spoken, written, and signed languages.

Researchers led by Ellen Garland from the University of St. Andrews hypothesized that humpback whales might exhibit a similar pattern. Since both humans and whales learn their vocalizations socially, the researchers suspected their songs might follow the same underlying principles.

Two species, one structure

To test this idea, the team analyzed eight years of humpback whale song data and compared it to how human infants learn speech. They found that recurring elements in whale songs follow a Zipfian distribution, much like human language.

“This work shows how learning and cultural transmission can shape the structure of communication systems: we may find similar statistical structure wherever complex sequential behavior is transmitted culturally,” says Professor Inbal Arnon from the Hebrew University.

“It raises the intriguing possibility that humpback whales, like human babies, may learn their song by tracking transitional probabilities between sound elements, and using dips in those probabilities as a cue to segment the song.”

It’s already remarkable that two unrelated species like humans and humpback whales have such a similar sound structure in their language. The discovery is even more striking considering that humpback whale songs are not technically a language.

“Revealing this hidden language-like structure in whale song was unexpected, but it strongly suggests this cultural behaviour holds crucial insight into the evolution of complex communication across the animal kingdom,” said co-author Ellen Garland. “Whale song is not a language; it lacks semantic meaning. It may be more reminiscent of human music, which also has this statistical structure, but lacks the expressive meaning found in language.”

“Whether the units we detected using the infant-inspired method are salient to the whales themselves remains an open question.”

Could language evolution be convergent?

Spectrogram of humpback whale vocalizations
Spectrogram of humpback whale vocalizations. Image via Wiki Commons.

“These findings challenge long-held assumptions about the uniqueness of human language, uncovering deep commonalities between evolutionarily distant species. It suggests that our understanding of the evolution of language can benefit not only from looking at our closest primate relatives, but also at cases of convergent evolution elsewhere in nature,” adds Simon Kirby, one of the study co-authors.

“Looking beyond the way language is used to express meaning; we should consider how language is learned and transmitted culturally over multiple generations.”

By looking beyond the meaning of language and focusing on how it is learned and transmitted across generations, researchers may uncover universal principles of communication that span across species.

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