Zipf ’ S Law in Literature

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels. 1. INTRODUCTION The power law distribution of events introduced by the Italian economist Pareto [1], in the context of the wealth of nations and individuals, and restated by Zipf [2] concerning linguistics is perhaps the most ubiquitous law in nature. This power law statistics, which is a characteristic of fractal behaviour, is present in many different areas ranging from physics [3] and biology [4,5] to natural hazards [6,7,8], and from musical creative context [9] to economics [10]. Several applications in linguistics have already been done, but the literary aspects which have been analysed until now are all related to word formation within the literary texts [12,13]. To the best of our knowledge, no attempt has been made to verify the possibility of existence of a Zipf's law type within the literary context. By using the software WordSmith, from Oxford University Press, with electronic texts one is able to obtain the types/tokens ratio, types being the number of different words in a text and tokens, the total number of words in this text. Considering the fact that the types/tokens ratio will necessarily decrease as the tokens increase, we were led to think of a power law distribution, and therefore of relating this behaviour to Zipf's laws. Although the use of a rich vocabulary is not the sole indication of creativity in a writer, lexical wealth is certainly one characteristic to be expected in a literary writer of the stature of J. others. As a hypothesis, one would expect to find in literary texts a high rate of …