Least effort and the origins of scaling in human language pnas. Zipfs principle of least effort thomas pynchon wiki. Zipfs law of abbreviation and the principle of least effort. Hence, all tests should focus on the particular power law stated in eq. In this article, the early hypothesis of zipf of a principle of least effort. Least effort and the origins of scaling in human language ncbi.
Also known as zipfs law, zipfs principle of least effort, and the path of least resistance. That is, the second most frequent word is used only half as often as the. This study investigated the influence of the principle of least effort ple introduced by zipf in his 1949 work, human behavior and the principle of least effort. The best known effort to create such a hierarchy is the ranksize rule developed by g. Zipf 1949 discovered a general principle of human behavior, which was named principle of least effort. This work provides a mathematical tool to derive zipf pareto laws directly from the idea that living systems always follow the rule of least effort in their. Language users optimise a miniature lexicon for efficient communication, cognition, vol. Zipfs law and the frequency of characters or words. Prp1p2 n where pr the population of the rth city, p1 the population of the largest city, and r the size rank of the rth city in the set. However, many workers believe that zipfs law is a manifestation of a fundamental but poorly understood law. Pdf evidence for the truth in george kingsley zipfs principle of least effort can.
Gencay, ramazan 2010, an introduction to textual econometrics, in ullah, aman. Zipfs law then emerges for logarithmic signal cost distributions, which is the. Reviews george kingsley zipf, human behavior and the. Zipfs law is an empirical law, formulated using mathematical statistics, named after the linguist george kingsley zipf, who first proposed it zipfs law states that given a large sample of words used, the frequency of any word is inversely proportional to its rank in the frequency table. Pdf the principle of least effort and zipf distribution. True reason for zipfs law in language sciencedirect. The principle of least effort is a broad theory that covers diverse fields from evolutionary biology. Zipf coined the expression, principle of least effort to describe this relationship. The principle of least effort within the hierarchy of.
Language users optimise a miniature lexicon for efficient communication. This law describes surprisingly diverse natural and social phenomena, including percolation. Because so many realworld processes behave this way, the pareto principle tells us that, as a rule of thumb, its worth assuming that 20%. I optimal for listener if all pieces of information correspond to different words or morphemes.
For example, zipf s distribution of word frequencies can result from a principle of least effort 7,8 in the evolution of language, or even from random sequences of letters and spaces 9. In particular, it shows that the distribution of dsc members by company, very closely follows a zipf distribution, where the number of dsc members, for a given company, is proportional to rs, where r is the company rank, and s 0. At its most basic, the zipfs formula is as follows. A simple and efficient test for zipfs law sciencedirect. The model incorporates the principle of least effort in communications, minimizing a combination of the informationtheoretic communication. Many languages, such as english, french, spanish, have been found to exhibit some universal characteristics called zipfs law,,which read as p r. Let us make an observation on the zipf law, as it is known today. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. The frequency distribution of words has been a key object of study in statistical linguistics for the past 70 years. In 1949 he published human behavior and the principle of least effort. In other words one either resists or goes with the flow, depending on what one can put in and what it. This article first shows that human language has a highly complex, reliable structure in the frequency distribution over and above this classic law, although prior data visualization. Human behaviour and the principle of leasteffort addisonwesley, cambridge, ma, 1949. It is a discrete form of the continuous pareto distribution from which we get the pareto principle.
George kingsley zipf who wrote human behaviour and the principle of least effort. In the book human behaviour and the principle of least effort, g. Jan 25, 2016 this study investigated the influence of the principle of least effort ple introduced by zipf in his 1949 work, human behavior and the principle of least effort. In an ordered set of cities representing a given country, the product of. George kingsley zipfs grandfather was frederick sebastian zipf, who was born in tauberbischofsheim, germany. Zipfs law simple english wikipedia, the free encyclopedia. Zipfs law states that the relative frequency of a word is inversely proportional to its rank. Zipf s law of abbreviation and the principle of least effort citation for published version. Why zipfs law explains so many big data and physics.
Deriving zipf law principle of least effort vs maximum efficiency. Accordingly, many mechanisms are put forward to explain the emergence of the zipfs law, such as the rich gets richer, the selforganized criticality, markov processes, aggregation of interacting individuals, optimization designs and the least effort principle. Zipf s law synonyms, zipf s law pronunciation, zipf s law translation, english dictionary definition of zipf s law. Zipf based number generation matlab answers matlab. Human behavior and the principle of least effort by zipf, george kingsley. The principle of least effort is the theory that the one single primary principle in any human action, including verbal communication, is the expenditure of the least amount of effort to accomplish a task. We then discuss the correlation between three widely considered distributions. The chunk as the period of the functions length and. The principle of least argues that people will act by way of minimizing their potential average workload. Balancing signal usage cost and communication efficiency. Accordingly, many mechanisms are put forward to explain the emergence of the zipf s law, such as the rich gets richer, the selforganized criticality, markov processes, aggregation of interacting individuals, optimization designs and the least effort principle. Explanation and exact formula of zipfs law evaluated from rankshare combinatorics a shyklo abstract this work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. Jun 06, 2012 prof george kingsley zipf was a professor of linguistics and a long time faculty member of harvard.
Zipfslaw zipfs explanation was his principle of least effort. Li 1992 shows that just random typing of letters including a space will generate words. In such a theory, the principle of economy plays an important balancing role. The principle of least effort ple was proposed in 1949 by harvard linguist george. Language users optimise a miniature lexicon for efficient communication the linguist. Request pdf zipfs law of abbreviation and the principle of least effort. Zipfs law definition of zipfs law by the free dictionary.
Zipfs law and the pareto distribution differ from one another in. Zipf s law has been here derived from first principles. Power laws, pareto distributions and zipfs law many of the things that scientists measure have a typical size or. In 1949 george zipf, a harvard linguistics professor, published human behaviour and the principle of least effort.
Aug 11, 2015 with zipfs law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders. Zipfs law from a fisher variationalprinciple sciencedirect. In this article, the early hypothesis of zipf of a principle of least effort for explaining the law. Oct 07, 2007 the unprincipled principle of least effort. That is, whenever we need an entity to communicate, on the premise of being able to make our idea understood, most of us would prefer to use a short one. Zipf distribution is related to the zeta distribution, but is. To my knowledge the actual expression principle of least effort wasnt used by zipf until the 1949 book. Pdf human behaviour and the principle of least effort.
George kingsley zipf argues that the law is valid because the least effort principle in human behavior 2. Zipfs law because they think that linguists have established it to be a linguistic law, and linguists believe in it because they, on their part, think that mathematicians have established it to be a mathematical law. I human behavior and the principle of least effort addisonwesley, 1949 cambridge, ma2 i bonus. The principle of least effort is analogous to the path of least resistance. Explanation and exact formula of zipfs law evaluated from. Figure 1 shows how zipfs law is apparent in data on city populations in three high income, three lower income, and three historical economies. Human behavior and the principle of least effort addisonwesley, cambridge, ma, 1949. So word number n has a frequency proportional to 1n thus the most frequent word will occur about. Zipfs law is a law about the frequency distribution of words in a language or in a collection that is large enough so that it is representative of the language. Human behaviour and the principle of least effort by. An introduction to human ecology george kingsley zipf addisonwesley press, 1949 human ecology 573 pages. Prof george kingsley zipf was a professor of linguistics and a long time faculty member of harvard.
However, many workers believe that zipfs law is a manifestation of a fundamental but poorly understood law of nature whose investigation can. The principle was studied by linguist george kingsley zipf, author of this classic treatment of the subject. A common representation of empirical data is the socalled rankplot or zipf plot,, where the jth element of the system is represented by its size, length or frequency k j against. Minimum cost and the emergence of the zipfmandelbrot law core. George kingsley zipf, human behavior and the principle of least effort.
The thesis is an investigation of the principle of least effort zipf 1949 1972. A mechanism for zipfs law we have failed to demonstrate unambiguously that zipfs law is on a par with newtons law of gravity or any of the other laws of nature. Zipf s law in three domains by showing that, in each of them, the existence of a latent variable leads to a broad range of frequencies. We address several of these here, and attempt to explain their origins in terms of simple principles of language use, including, but going beyond, zipfs own principle of least effort. It presents a formula for rankshare distribution and illustrates that zipfs law, is descended. The influence of the ple was measured by examining articles across various disciplines published between 1950 and 20 that cited zipfs original work. Internet, obtained on cdrom in pdf or in form of printed copies. Human behaviour and the principle of least effort by george. The zipf family relatives owned and ran the local brewery, brauerei zipf.
Pdf this work provides a mathematical tool to derive zipf pareto laws directly from the idea that living systems always follow the rule of least. Zipfs law of abbreviation and the principle of least. There is more than a power law in zipf scientific reports. Furthermore, we demonstrate that data with both a varying number of dimensions, and fixed but high dimension, leads to zipf s law under very mild conditions. It is closely related to many other similar principles. Concept that an entity, organization, or system tries either to change its environment to suit its needs, or to change itself to suit the demands of the environment whichever is easier in terms of effort and cost. I believe it to be related in some deep sense to maupertuis principle of least action which states that in attaining a given state, any physical system seeks to minimize the. The principle of least effort is a broad theory that covers diverse fields from evolutionary biology to webpage design. Also known as zipf s law, zipf s principle of least effort, and the path of least resistance.
Since the principle is also functional, the thesis adopts a functional theory of language as. What became known as zipfs law inversely relates the size of an occurrence of an event to its rank. Deriving zipf law principle of least effort vs maximum. Balance between speakers desire for a small vocabulary and hearers desire for a large one. Since the principle is also functional, the thesis adopts a functional theory of language as its theoretical framework, i. Remember, for some countries, the population data is missing in some given years. A recent research shows that simultaneous minimization in the effort of both hearer and speaker based on the gametheoretic evolution will lead to zipfs law in the transition between referentially.
Owing to the cooperation of zipfs eldest son, this paper contains invaluable sources for the historical investigation and a biography of g. Ihuman behavior and the principle of least effort addisonwesley, 1949 cambridge, ma3 ibonus. Frequency is plotted as a function of frequency rank for the terms in the collection. The emergence of zipfs law jeremiah dittmar august 10, 2011 abstract zipfs law characterizes city populations as obeying a distributional power law and is supposedly one of the most robust regularities in economics. In the literature, zipfs law is often illustrated by plotting city rank r against city size s. Zipfs law states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table. At one level it reads like the man has discovered a very good hammer, more of a sonic screw driver, and in over 540 pages he proceeds to demonstrate that everything is a nail.
We notice, following zipf 1949 in human behavior and the principle of leasteffort that writing and speech are an optimal compression. Theory of zipfs law and beyond lecture notes in economics and mathematical systems 632, springer, heidelberg, germany, 2010. As the principle of least effort is proposed by zipf, it is also called zipfs law. It postulates that animals, people, and even welldesigned machines will naturally choose the path of least resistance or effort. Ferrer i cancho and sole then combine the listeners and speakers efforts within. I encoding is simple but decoding is hard i zipf uses the analogy of tools.
Zipfs law arises naturally when there are underlying. This distribution approximately follows a simple mathematical form known as zipfs law. So, looking at the zipf distribution, it turns out to be an easy one to deal with, sort of. True reason for zipfs law in language article pdf available in physica a. A pattern of distribution in certain data sets, notably words in a linguistic corpus, by which the frequency of an item is inversely proportional to its.
He was a roman catholic, and, according to a family tradition, sang in his church choir. Frederick sebastian zipf came to america from tauberbischofsheim about. Zipfs law 1,2,3, usually written as where x is size, k is rank, and x m is the maximum size in a set of n objects, is widely assumed to be ubiquitous for systems where objects grow in size or. Zipfs law holds for phrases, not words scientific reports. Zipf famously discussed a number of patterns in the distributions of linguistic units, such as words and phonemes, in texts.
Pdf some reasons for using zipfs law in the analysis of. Influence of the principle of least effort across disciplines. Sa typical value around which individual measurements are centred. Zipfs law was popularized by george zipf, a linguist at harvard university. The line is the distribution predicted by zipf s law weighted least squares fit.
The principle of least effort within the hierarchy of linguistic. A simple example would be the heights of human beings. A simple and efficient test along that line is presented in the next section. To illustrate zipfs law let us suppose we have a collection and let there be. You may need to select for a while for a good data set. He theorized that the distribution of word use was due to the tendency to communicate efficiently with least effort and this theory is known as zipf s law. Let us start by considering a basic form of zipfs law. For example, zipfs distribution of word frequencies can result from a principle of least effort 7,8 in the evolution of language, or even from random sequences of letters and spaces 9. No doubt, though grs use of things zipfian raises some interesting questions on the books chronology. This paper documents, to the contrary, that zipfs law only emerged in. Zipfs law and the pareto distribution differ from one another in the way the cumulative distribution is plotted. In some cases, the literature associates zipfs law with the case where. But more interesting to me when i actually read this book is the very bizarre drift of zipfs thought.
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