Statistical Universals of Language: Mathematical Chance vs. Human Choice

The book is a part of the Mathematics in Mind series. This series aims at bringing together mathematicians, philosophers and cognitive scientists to get wind of the nature of mathematics and statistics and the way they are learned from several indisplinary angles. It presents new insights into the nature of languages from a statistical point of view. The book makes the readers understand languages from the standpoint of a statistician. It makes one realize that the distinction between languages and Statistics is not always very significant. The book consists of twenty-two chapters. Several chapters have been clubbed together to give rise to seven parts. The first part of the book “Language as a complex system” comprises the first three chapters. The author has used the first chapter to clarify the aims, the structure, the position and the prospectus of the book. The first chapter “Introduction” talks about the observations and the findings of researchers who have meticulously sifted and analyzed the ingredients of languages. It brings to light that certain properties of languages are more statistical in nature than being mathematical. This observation has come about because of the abundant data available in several languages. Since these properties of languages are both statistical and universal in nature, the author has titled the book “Statistical universals of language. ” After explaining that a universal is a property which holds across every kind of natural language on Earth, the second chapter “Universals” explains and organizes the various approaches that have been taken concerning the notions of universals. The various layers of universals have also been explained. The chapter also includes discussions on stylized hypothesis and law. The third chapter and the first part of the book are titled the same. The third chapter is about the application of statistical methods to languages. It first explains the several terms that are used later in the text. These terms include the terms corpus, meaning, infinity, randomness, and power functions. The self-similar nature of a power function has been discussed in detail. The author explains the meaning of being self-similar via an elaborate exposition of the example of the famous fractal named Koch curve. Regarding the intriguing question of whether random text can duplicate the works of Shakespeare or that of Bertrand Russell (the author uses the example of Moby Dick), the author explains that, in the light of the Infinite Monkey Theorem, an infinite random text can produce any desired masterpiece of literature. The second part of the book “Property of population” comprises three chapters—chapters four through six. Chapter 4 “Relation between rank and frequency” is concerned with the analysis of words. The chapter explains the concepts of the frequency and the rank of a word in a language. The frequency of a word in a text is simply the number of occurrences of the word in th text. The chapter contains a detailed account of Zipf ’s law. The author illustrates Zipf ’s law by elucidating the rank-frequency of several words in Moby Dick. In it, the word “whale” appears 783 times and its rank is 38 as it is the 38th most frequently occurring word in the text. Similarly, the word “ship” appears 451 times and has rank 67. This law states that the rankfrequency relation for every text forms a power law with a slope of −1. In other words, if f is the frequency of a word and r is the rank, then