The words “city”, “radish” or “mitochondria” do not appear in the same proportions when you look at a large set of texts in French. Nothing surprising, certain terms are commonly used, others are more sought after, even rare or specialized. More surprising, when we classify the words of a book, for example, according to their frequency of occurrence, we see that the first appears twice as much as the second, three times more than the third, ten times more than the tenth, etc. We obtain what we call the “Zipf law”, which belongs to the family of power laws. This empirical rule is found in a large number of languages.
If the emergence of this structure is not fully understood, a hypothesis suggests a link with the fact that languages are transmitted cultural features. Indeed, it seems easier for babies to learn a language if they can intuitively predict what sound or word is likely to be pronounced after another. But what about animals for whom vocalizations are also the result of a cultural transmission? Do we find the law of Zipf? Ellen Garland, from St Andrews University, in the United Kingdom, and her colleagues were interested in the chair of humpback whales.
In some animals, vocalizations are instinctive and are therefore not the fruit of learning. This is the case for example for dog barking. But in other species, the little ones reproduce the song by listening to their elders. We find this cultural transmission, especially in certain singing birds or in the humpback whale.
In these cetaceans, only males repetitively vocalize songs, the structure of which is very complex. Sound units (or “notes”) are assembled in “sentences” repeated several times, which forms a “theme”. And finally, several “themes” are chained and make up a “song”. A song lasts about twenty minutes and can be repeated for hours or even days. The role of the song remains mysterious, even if specialists think that it would be used to attract a partner.
Within a population of humpback whales, there is a great uniformity of the songs. However, the latter are not immutable, they are constantly evolving during a season and can, in a few years, change completely. In contrast to this long -term development, in the South Pacific, specialists have also observed “revolutions” where a song is notably replaced by another, introduced by a neighboring population.
The richness of structures and the complex dynamics of songs raise many questions, in particular on their learning. How do whales integrate song? Studies carried out during one of these revolutions, with the transition from one song to another, have confirmed that the song was based on a cultural transmission. This led Ellen Garland to hypothesize that these songs must present statistical structures similar to the law of Zipf.
To prove it, the first difficulty was to find a method to segment the song of whales. In a human language, the task is simple because the words are well identified. But how do a human baby segmented a flood of words in practice? He learns to delimit the words based on probabilistic reasons. Within a word, sounds are very often associated, on the other hand from one word to another, the succession of sounds sometimes marks ruptures, the probability falls suddenly. Ellen Garland and her colleagues exploited this idea to segment the song of marine mammals. They worked with records of songs collected for eight years with a single population of humpback whales.
By analyzing the frequency of appearance of the various isolated segments (which represent a sequence of notes), the researchers recognized the law of Zipf. And they also found that another ZIPF law was at work. This stipulates that the most frequent words are also the shortest. This law is found in other animal species and is justified by a selective adaptation which favors effective communication with information compression. If the signal to prevent a “danger” was very long, the alert would arrive too late.
The researchers checked that their result was not an artifact linked to their way of segmenting the song of the humpback whales. To rule out this risk, they analyzed the songs using two other cutting procedures. The results were the same.
The search for statistical structures in various animal communications, especially among singing birds (such as the familiar Roselin or the Mandarin diamond), has already been carried out in the past. And teams had then found a so-called “zipf-mandelbrot” law, which has an additional parameter and is thus more flexible than the law of Zipf. Moreover, the analysis of “notes” in the song of the whales had then led to a law of Zipf-Mandelbrot. Segments as defined in this new study therefore have a different structure and closer to what is observed in human languages. It is possible that the application of this technique to the song of singing birds also leads to a zipf law.
The law of zipf applied to human languages has this specificity that segments are words that carry meaning. In addition, even in artificial languages, like Esperanto, we find this statistical rule. The analysis of the Voynich manuscript, a book of the Middle Ages written in an unknown language that resists cryptanalysts, shows that these texts follow the law of Zipf. This suggests that they are written in a real language and are not just random charabia.
Ellen Garland and her colleagues, however, insist on this fact: the highlighting of the law of Zipf in the song of cetaceans does not allow us to conclude that it is a language whose segments would be carrying a specific meaning. “These discoveries question theories on the singularity of human language, by highlighting common points between two very distant species,” notes Simon Kirby, of the University of Edinburgh. This strengthens the idea that learning plays a key role in the emergence of this statistical structure. “This study shows how learning and cultural transmission can model the structure of communication systems. We could therefore find similar statistical structures wherever a complex and sequential behavior is culturally transmitted, ”concludes Inbal Arnon, researcher at the Hebrew University of Jerusalem.
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