Zipf’s Principle of Least Effort

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. Also known as Zipf’s Law, Zipf’s Principle of Least Effort, and the path of least resistance.

The principle of least effort (PLE) was proposed in 1949 by Harvard linguist George Kingsley Zipf in Human Behavior and the Principle of Least Effort (see below). Zipf’s immediate area of interest was the statistical study of the frequency of word use, but his principle has also been applied in linguistics to such topics as lexical diffusion, language acquisition, and conversation analysis.

In addition, the principle of least effort has been used in a wide range of other disciplines, including psychology, sociology, economics, marketing, and information science.

Examples and Observations
Language Changes and the Principle of Least Effort
“One explanation for linguistic change is the principle of least effort. According to this principle, language changes because speakers are ‘sloppy’ and simplify their speech in various ways. Accordingly, abbreviated forms like math for mathematics and plane for airplane arise. Going to becomes gonna because the latter has two fewer phonemes to articulate. . . . On the morphological level, speakers use showed instead of shown as the past participle of show so that they will have one less irregular verb form to remember.

“The principle of least effort is an adequate explanation for many isolated changes, such as the reduction of God be with you to good-bye, and it probably plays an important role in most systemic changes, such as the loss of inflections in English.”
(C.M. Millward, A Biography of the English Language, 2nd ed. Harcourt Brace, 1996)

Writing Systems and the Principle of Least Effort
“The principal arguments advanced for the superiority of the alphabet over all other writing systems are so commonplace that they need not be repeated here in detail. They are utilitarian and economic in nature. The inventory of basic signs is small and can be easily learned, whereas it asks for substantial efforts to master a system with an inventory of thousands of elementary signs, like the Sumerian or Egyptian, which did what the Chinese, according to the evolutionary theory, should have done, namely give way to a system which can be handled with greater ease. This kind of thinking is reminiscent of Zipf’s (1949) Principle of Least Effort.”
(Florian Coulmas, “The Future of Chinese Characters.” The Influence of Language on Culture and Thought: Essays in Honor of Joshua A. Fishman’s Sixty-Fifth Birthday, ed. by Robert L. Cooper and Bernard Spolsky. Walter de Gruyter, 1991)

G.K. Zipf on the Principle of Least Effort
“In simple terms, the Principle of Least Effort means, for example, that a person in solving his immediate problems will view these against the background of his future problems, as estimated by himself. Moreover, he will strive to solve his problems in such a way as to minimize the total work that he must expend in solving both his immediate problems and his probable future problems. That, in turn, means that the person will strive to minimize the probable average rate of his work-expenditure (over time). And in so doing he will be minimizing his effort. . . . Least effort, therefore, is a variant of least work.”
(George Kingsley Zipf, Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. Addison-Wesley Press, 1949)

Applications of Zipf’s Law
“Zipf’s law is useful as a rough description of the frequency distribution of words in human languages: there are a few very common words, a middling number of medium frequency words, and many low-frequency words. [G.K.] Zipf saw in this a deep significance. According to his theory, both the speaker and the hearer are trying to minimize their effort. The speaker’s effort is conserved by having a small vocabulary of common words and the hearer’s effort is lessened by having a large vocabulary of individually rarer words (so that messages are less ambiguous). The maximally economical compromise between these competing needs is argued to be the kind of reciprocal relationship between frequency and rank that appears in the data supporting Zipf’s law.”
(Christopher D. Manning and Hinrich Schütze, Foundations of Statistical Natural Language Processing. The MIT Press, 1999)

“The PLE has been most recently applied as an explanation in the use of electronic resources, most notably Web sites (Adamic & Huberman, 2002; Huberman et al.

1998) and citations (White, 2001). In the future, it could be fruitfully used to study the tradeoff between the use of documentary sources (e.g. Web pages) and human sources (e.g. through email, listserves, and discussion groups); since both types of sources (documentary and human) are now located conveniently on our desktops, the question becomes: When will we choose one over the other, given that the difference in the effort has lessened?”
(Donald O. Case, “Principle of Least Effort.” Theories of Information Behavior, ed. by Karen E. Fisher, Sandra Erdelez, and Lynne [E.F.] McKechnie. Information Today, 2005)


Nordquist, Richard. “The Principle of Least Effort: Definition and Examples of Zipf’s Law.” ThoughtCo, Feb. 11, 2020,

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Urban Hierarchies and Anomalies

Settlements can be described as being part of the urban hierarchy. Where they stand on the hierarchy depends on many factors, the main ones being population, the number of services a settlement has and its sphere of influence. The best way to show the urban hierarchy is by using a pyramid, as shown in the diagram later.


The most obvious way of deciding where a settlement ranks on the urban hierarchy is by using the population of that settlement. The larger the population, the higher the settlement is placed on the hierarchy.

In the UK, the largest city in terms of population is London, which most people would agree is the most important settlement in the country and so deserves to be placed on the top of the urban hierarchy for the UK.

After that, the division between what is classified in each layer is a bit vague. Different sources will have different numbers for how many people are needed for a place to be called a city rather than a town for instance.

However, the most important thing to notice on the diagram is that as you go up the hierarchy, there becomes a lot less of that type of settlement. So, the diagram shows us that there are huge numbers of isolated farmhouses and hamlets. There are fewer villages and small towns and so on.

In the UK, many people would argue that only London should be placed in the highest rung of the triangle. However, some other large cities, such as Birmingham, Manchester, and Leeds are growing fast and may be considered to have reached the top level as well.

Urban Hierarchies

Services and Functions

Services are things such as retailers(shops), professionals (doctors, lawyers, etc), entertainment, government functions, and leisure. The theory goes that the larger a settlement is, and therefore the higher it is on the urban hierarchy, the more services and functions it will have.

In general, in the UK, this is the case. London is the settlement at the top of the urban hierarchy, and it has the greatest number of services and functions of any settlement in the country. For instance, it has the major international airports, it is the seat of our national government, it has the widest range of shops, including very special ones, and it has the most renowned professional services. This is because its population is large enough to support all of the services.

A small village may on the other hand only have the population to support a pub, post office, village store and perhaps a small garage.

Urban Hierarchies

Villages and other rural settlements have found over the last 20 years that it has been increasingly hard for services to remain viable in these settlements. Small post offices and banks have frequently been closed down, as there are simply not enough people using them to make them viable.

The number of services and functions that a town provides normally relates to the number of people living there.

There are, however, two noted anomalies. These are examples of settlements that do not conform to the general pattern, and they are explained below:

Anomaly A: A Tourist town: Towns, such as Brighton, Blackpool, and Eastbourne, that have grown due to the tourist industry, often have more services than their population suggests they should have. This is because many of their services are catering to the huge numbers of tourists who flood into the towns during the summer months. Hotels, guesthouses, restaurants, beach shops and ice cream stalls all are aimed to provide services for the tourists.

The extra tourist numbers swell the total population during the summer to a level that is more appropriate for the number of services provided.

Anomaly B: A Commuter Settlement: Many rural villages are becoming commuter centers, where people live, but work elsewhere. Many villages and towns around the London area fulfill this function.

Commuter settlements have a large resident population, but as very few of them actually work in the village, there is nobody to support any services. The commuters will do their shopping and banking in the city where they work. This means that these settlements will have fewer services than their population suggests they should have. Some commuter settlements are changing their services to cater to the different residents, with restaurants and cafes replacing the traditional village services.

Sphere of influence

The sphere of influence of a settlement describes the area that is served by a settlement, for a particular function. Its sphere of influence for different functions may cover vastly different areas. For instance, a supermarket may attract people from a 20-mile radius, whilst a leisure activity, such as going to the theatre may attract them from far further away.

The larger a settlement is the greater its sphere of influence is likely to be, as it has a wider range of services and functions to attract people to go there. This is shown in the diagram below. A small village may only have a village store selling daily newspapers and food such as bread and milk. People will only travel the shortest distance they need to buy these products. They are described as being convenience goods. In other words, something that you can buy easily and for the same price all over the place.

A larger town would have a wider sphere of influence because it would have shops and services that are more specialist, and so people would be willing to travel further to use them. An example might be a furniture shop. This sells comparison goods, in other words, products that you might shop around for before going ahead and buying something.

Urban Hierarchies

There are two major ideas to consider when looking at the sphere of influence of a shop of service. These are called the range and threshold population of a good.

The range of a good or service describes the maximum distance that someone would be willing to travel to obtain that good or service. A newspaper shop has a small range because people will not travel far to use them. A cinema has a much wider range as people are prepared to travel much further to go to it.

The threshold population of a good or service is the minimum number of people needed to allow that shop or service to be successful. The more specialist a shop is the larger its threshold population is.

A newsagent will have a small threshold, whereas a supermarket like Tesco needs a much larger population before it can consider opening a store.


Difference between Service and Function

As nouns the difference between function and service

is that function is what something does or is used for while service is an event in which an entity takes the responsibility that something desirable happens on the behalf of another entity or service can be service tree.

As verbs the difference between function and service

is that function is to have a function while service is to serve.

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Tourism: Its Spatial Affinity

Tourism and tourist show spatial affinity. Tourists tend to be attracted to some regions from antiquity.

There are four major sets of factors affecting spatial affinity:

  • Accommodation
  • Attractions
  • The economic impact of tourism
  • Tourists

Units of Consideration-Regions

  • Tourist Regions corresponding to administrative Units (Regions, Provinces, etc)
  • Tourist areas extracted and defined as special areas from the rest the non-tourist part of the country
  • Tourist regions which may cover the whole of the country but whose boundary do not correspond with the actual administrative organization


The distribution of accommodation is the most widely used measure in the tourist industry. Accommodation statistics tend to be used mainly to indicate spatial variations in the importance of tourism or to identify regions of different type of tourist activity.


To find appropriate explanations, one has to examine the complexities of tourist behavior, drawing power of major attractions, professional efforts by respective state governments, the approach of Central government towards states, the status of infrastructural networks including connectivity and overall socio-economic development.

Economic Impact of Tourism

Over the past six decades, a continued expansion can be observed in the tourism sector, becoming one of the largest and fastest-growing economic sectors in the world, according to the data provided by UNWTO (2016): almost 1.200 million international arrivals of tourists were observed in 2015, while this number was only 25 million in 1950. Although the American continent and the Asia-Pacific regions have registered higher growth rates in the last few years, Europe is still the continent accommodating the highest number of international travelers in the world. Two European countries (France and Spain) rank among the 4 largest destinations, from the point of view of both the number of visitors and the revenues generated by tourism.

Nevertheless, the importance of Europe in the context of global tourism is higher when we consider the number of international travelers (51% of the international arrivals worldwide) rather than the revenues obtained (36%). With much fewer travelers, the Asia-Pacific region (24% of the global volume of international arrivals) achieves a similar revenue compared to Europe (33%), while the American continent registers 24% of the global tourism revenues (receiving only 16% of the international travelers)


Tourists have a special spatial affinity for some places, for example, India has fascinated the travelers from the time immemorial. Perhaps the early travelers to India were the trading Persians. Evidence of caravans from Persia visiting India lies engraved in the inscriptions dating to the Persian King Darius. During the rule of Guptas, there was free access to the ports along with western coast~ seaborne commerce with Europe through Egypt was yet another reason for travel in and around the country. There was enough evidence of cultural exchanges between Persia and Chandra Gupta Maurya.




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The urban fabric is the physical form of towns and cities. Like textiles, urban fabric comes in many different types and weaves. 


Coarse grain urban fabric is like burlap: rough, large-scale weaves that are functional, but not usually comfortable. Such places consist of one of two things. Large blocks, predominated by big box stores and other car contract retail and corporate centers, or multi-block mega project dropped on a city without integrating the surrounding city or community.

Not only do coarse grain fabrics NOT give many opportunities for interconnecting; the fabric itself is usually inhospitable to interaction. Instead of asserting control over the street, such places turn inward, fortifying themselves against the perceived dangers of the outside. This begets yet more undesirability.

In this regard, coarse grain acts as a barrier for all but those who are there for a specific purpose. Just as we are not comfortable wearing a burlap shirt, we are not comfortable spending more time necessary in coarse-grained places.


On the other hand, there is fine-grained urban fabric. Like high count Egyptian cotton; fine-grain urban fabric can feel luxurious make people want to linger in or around it. The fine-grain urban fabric consists of several small blocks close together.

Within each block are several buildings, most with narrow frontages, frequent storefronts, and minimal setbacks from the street. Streets and opportunities to turn corners are frequent, and as a result, so are storefronts. This offers many opportunities for discovery and exploration. There are almost no vacant lots or surface parking. Also, as there are more intersections, traffic is slower and safer.

The fine-grained urban fabric is not imposed on a community like its coarse cousin. Rather, it evolves over time; responding to what came before, and adapting to what came afterward. This evolutionary process creates a place that is not frozen in the era when they were built but is dynamic and reflective of a neighborhood’s changing needs.

This creates an urban fabric that can seamlessly evolve over time from lightly developed residential areas to mixed-use retail to the dense urban core if that’s what the community desires. In this way, there are far more resilient than the mega-projects mentioned above who, when they lose a single-tenant, often fail.

Granularity of Economy

We can also talk about the granularity of an economy; an economy is fine-grained if it is made up of many small businesses and coarse-grained if it is made up of a few large businesses. (Of course, most economies are somewhere in between.)

Having a fine-grained economy made up of many small businesses is generally preferable over a coarse-grained economy made up of fewer businesses because it implies a more resilient economy (if one of the businesses fail, less is the effect on the overall economy) and more distributed wealth (the profit and ownership of the businesses are divided among many, rather than in the hands of a few.)

Cities are the physical manifestation of the economy and our built environment speaks volumes about our economy. It is easier to see this in smaller towns where the economic model is simplified; you can easily spot the difference between a small town dominated by a few large stores and a small town dominated by many smaller stores.

There is often a correlation between the environment that we physically see and interact with, and the underlying economics that built it.

Granularity of Cities

Older urban areas are typically very fine-grained.

While newer urban areas tend to typically be very coarse-grained.


The Benefits of Fine-Grained Urbanism

Fine-grained urbanism is preferable because it implies:

  1. Diverse ownership. Each individual lot typically has a different owner.

  2. Lower cost of entry. If we ignore the underlying price of land (small lots, in general, should be cheaper because you are buying less land), it takes less money to build a shop or a home on a small narrow lot, than building an entire apartment complex.

  3. More destinations within walking distance. An important part of good urbanism is fitting as much as possible within walking distance, so naturally, fitting more in gives you more choices to walk to.

  4. Greater resistance to bad buildings. Bad buildings can make less of an impact when they are limited in size.

Urban development should not be expensive by itself. The high cost of entry brought on by coarse-grained urbanism is leading to economic polarization where only those who already have money can invest and create more wealth, and everyone else is a mere consumer.

If we consider each building a destination, fine-grained urban areas are naturally more walkable because we have more destinations within walking distance than coarse-grained urban areas in general.

In contrast, with coarse-grained urbanism, we have one or two destinations taking up an entire block.

Fine-grained development also limits the impact of bad buildings. A property owner that builds a dull or ugly building, allows their building to become run down, or abandons it, negatively affects the streetscape. However, we can minimize the overall impact on the streetscape if the ugly or derelict building is just one of many along the block.


A fine-grained environment is a health environment from an economic and urbanist perspective. Large buildings are not bad, and the best cities I have visited have a diverse mixture. We should do our best to make our urban environment fine-grained — with development using as little land as possible. However, on the occasions when we do need to build large, we should do our best to make the result faux-grained.

Treat land is if it is the most precious resource your city has. Never wasteland or street space. Build real parks over greenspace. Create a place that is enjoyable and interesting — one that encourages entrepreneurship, where you can mostly depend on your own two feet for daily errands. That is how you create a successful city.

Link(s) and Source(s)



Strong Towns


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