Mathematics is the language of the universe and we can apply it in various fields. Statistics, as one of its branches, is instrumental in understanding the concepts through collected data.
When these data show certain results, they can take the form of a formula or a law. In linguistics, one such law is called “Zipf’s Law”, also known as “the Zipfian Distribution” or “the principle of least effort”.
It is a statistical principle often observed in various fields, including linguistics, economics and information science. Named after the linguist George Zipf, it describes the uneven distribution of elements in a given set, where a few elements are significantly more common than the majority, which are quite rare.
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In linguistics, Zipf’s law refers to the keyword density/frequency of word usage in a natural language. It states that in a large corpus of text, such as a book or collection of documents, the most frequently used word (the first ranked word) will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, and so on. This creates a ranking where the frequency of words follows a power law distribution.
For example, in English, the most common word is “the”, followed by “of”, “and”, “to” and so on. These extremely common words are often called “stop words” because they occur so frequently that they don’t contribute significantly to the meaning of a text.
It can also be applied to other phenomena beyond language, such as the distribution of income in a population, the popularity of websites or the frequency of terms in a search engine query. It illustrates how a small number of elements dominate, while the majority are much less common.
It is a valuable concept in data analysis because it can help identify patterns of inequality and concentration in different data sets. It has applications in fields such as natural language processing, information retrieval and economics.
Going back to the law, one of its fascinating aspects is the phenomenon of the “long tail”, which makes sense. While a language may have a core vocabulary of a few thousand commonly used words, there’s a long tail of rare words that make up the rest of the language. These uncommon words may be field-specific technical terms or simply less common words that add nuance to communication. They can also pose challenges for language models and statistical analysis.
Here is the frequency of some words in this article made via wordcounter.net
However, despite the long tail of rare words, the language continues to evolve with the introduction of new words. As culture, technology and society change, new words emerge to reflect changes in human experience.
In our daily lives, we benefit from this law because it has implications for the predictability of words in language processing. Because of the high frequency of certain words, predictive text algorithms often give priority to suggesting these common words as we type. That’s why your smartphone keyboard might suggest “the” or “and” before other less common words. This is the result of Natural Language Processing (NLP).
I’ve also read that some linguists suggest that Zipf’s law might be a result of the way languages evolve. This is interesting and has given me food for thought. Frequent use of certain words can lead to shorter forms over time. This is apparently known as “lexical reduction”, where commonly used words tend to become shorter and easier to pronounce.
Literary scholars often use Zipf’s law to analyse texts. It can help identify unique features of a writer’s style, such as vocabulary richness or the use of rare words. I suspect it’s also used to decipher the cryptic messages in some criminal cases.
Another detail is that although Zipf’s law applies to many languages, the specific words that are most frequent can of course vary. For example, in some languages function words such as pronouns and prepositions are highly frequent, while in others content words such as nouns and verbs dominate.
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