The Law All Languages Obey

  • By Michael Rivera
  • Posted 04.11.18
  • NOVA

Can a mathematical formula prove that dolphins have language?

Running Time: 02:36


The Law All Languages Obey

Published April 11, 2018

Onscreen: Can math reveal if animals have language?

Narrator: Consider ours for a moment.

In 1945, linguist George Zipf asked his students to plot out the frequency of each of the 264,430 words used in James Joyce’s Ulysses.

Laurance Dolye: He drew a straight line through it, and it had a 45-degree, minus-1 slope.

Narrator: Oddly, the most frequent word occurred exactly twice as often as the second most frequent word, three times as often as the third most frequent word, and so on down the line. In the logarithmic scale that mathematicians use, it looks like this.

Dolye: So he thought if that’s interesting, what if I take another book?

Narrator: Darwin’s Origin of Species.

Dolye: Same thing. “What if I take Chinese book?" Same thing.

Narrator: Turns out, every human language on the planet follows this rule, from Swahili to Arabic to Eskimo. It’s called Zipf’s law.

Brenda McCowan: What it suggests is that the structure of language is fundamentally the same. Across different languages.

Narrator: So what about animals? Brenda McCowan at UC Davis and Laurance Doyle at SETI (yes the Search for Extraterrestial Intelligence)—wanted to find out.

So they decided to analyze one of the most intelligent animals we know: dolphins. They communicate with an elaborate repertoire of whistles…

McCowan: We decided to start looking by categorizing whistles into types.

Dolye: Brenda McCowan had collected a bunch of signals and gotten their frequency of occurrence, and one morning, I got up, and decided, "Well, I wonder if this obeys Zipf's Law?"

Narrator: And wouldn’t you know…

Dolye: It obeyed Zipf’s law. So then I went and had a cup of tea, and then I went back and did it again, and it obeyed Zipf's Law.

McCowan: I was pretty excited. Because I mean it could have been anything. I mean, what's the probability that you're going to find something that is a negative one slope in another species? It’s not only exciting, but seems highly improbable.

Dolye: It’s one of those moments in science where you’re going wait a second, dolphins have a communication system with potential complexity as complex as humans. It doesn’t measure meaning, but it does measure what they could be saying.



Digital Producer
Michael Rivera
Michael Bicks & Anna Lee Strachan
© WGBH Educational Foundation 2018

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