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# Distance Decay

When gas prices go up, do you find the prospect of a long-distance road trip less attractive? It costs more to get where you want to go, even though the distance and amount of time it takes haven't changed. Imagine if there were no gasoline to be had, and you were limited to a bicycle or even your own two feet to get to the beach, 300 miles away. That would take days or weeks, depending on how rugged the terrain was, what physical shape you were in, what happened along the way, and other factors.

How you interact with destinations such as the beach is influenced by a phenomenon known as distance decay, an essential effect of the friction of distance. To figure out what this means, let's get going.

## Distance Decay Definition

Don't be confused: nothing is decaying here!

Distance Decay: The effects caused by interaction between two places decrease as the distance between them increases. Interactions include flows of people, goods, services, ideas, money, and so forth.

## Distance Decay and Friction of Distance

Distance decay is an effect of the friction of distance, a fundamental process in geography. Waldo Tobler's First Law of Geography says it most simply:

Everything is related to everything else, but near things are more related than distant things.1

The friction of distance is derived from the inverse square law, rooted in physics. Many equations describing spatial activities in the quantitative social sciences (e.g., in economics, and spatial analysis in geography) are derived from it. The law states that as distance increases, the effect of two things on each other decreases as the inverse of the square of the distance. If they are twice as far from each other, they exert one-quarter of the attraction, etc.

People tend to be bound by the friction of distance because of a wide range of costs imposed by traveling from point A (origin) to point B (destination) and, usually, back. These costs are all commonsense; as we highlighted in the introduction, we choose where we go based on specific variables.

### Choice of Destination

Suppose a variable such as fuel cost rises, then we would say that the friction of distance increases. We still have to go to work and back; we might eventually choose to work somewhere closer if the friction of distance continues to grow. We might decide to carpool or take public transportation if it is available. However, we might reconsider going shopping at a more distant destination over somewhere closer until fuel costs drop and friction of distance decreases.

A migrant who does not plan to return to their place of origin may consider the overall attractiveness of several destinations balanced against the relative costs of getting there. The friction of distance dictates that the closer people are to a migration destination, the more likely they are to migrate there, and vice versa.

### Travel Costs

Travel takes energy. This means fuel for the transport we are using. Even if we are walking, it means cost in terms of calories needed. Farther destinations cost more to get to, though the mode of transport and how many other people go with us can radically change costs and change the friction of distance. Additional costs that affect friction of distance are involved with everything from the type of terrain to weather to risks such as dangerous traffic and many others. Migrants may face costs such as violence, exploitation, imprisonment, challenging physical geography, and other factors, in addition to what they have to pay on every leg of the journey.

Fig. 1 - Mountain ranges (such as the Colorado Rockies, pictured) are an example of a terrain feature that increases the friction of distance through the difficulty of road maintenance and environmental risks such as storms

### Traffic Costs

The more people going to the same destination at the same time along the same route, the longer it takes once traffic starts to get congested. At airports, this can be expressed by delayed flights and holding patterns; on highways, this means slowdowns and gridlock. Fuel costs and other costs associated with losses incurred by delays can be factored in here.

### Construction and Maintenance Costs

Water, air, and land are pretty distinct in terms of the different costs they impose on the construction and maintenance of the devices used to transport people, goods, and messages, across or through them, as well as the upkeep of the routes themselves.

For transportation of people and goods, a river needs to have its channel kept open, and a sea needs to have a system of tracking vessels and hazards such as storms. Airspace requires careful attention to the weather as well as a tracking system. Land surfaces, however, require the building and maintenance of a network of transportation routes. All of these can increase or decrease the friction of distance.

For the transport of information (including money), fiber-optic cables, cell towers, and satellites are increasingly reducing the friction of distance.

## Geography of Distance Decay

Because of the process of friction of distance, a pattern of distance decay is built into the structure of space. You can see it in the landscape. This is because people are spatial beings who make rational decisions about travel, just like you do.

Planners and others involved with constructing the spaces we inhabit recognize that the mass movements of people, called flows, are predictable. They use a gravity model of spatial attraction (another concept borrowed from Newtonian physics) wherein it is recognized that more massive places such as cities exert more influence on less massive places and vice versa. "Mass" is not measured in molecules but in numbers of people (as an analogy only).

Fig. 2 - In State College, PA, restaurants, bars, and shops cluster on South Allen Street, serving the tens of thousands of pedestrians at Penn State University a stone's throw away (behind the photographer). Distance decay effects begin to be felt a few blocks outside the picture.

You can see this happening in an urban setting. Urban models such as the Multiple-Nuclei Model recognize that similar economic activities group together to reduce the distance decay effect. For example, a university district includes many thousands of students who may not have vehicles and have limited time between classes. The service economy recognizes this, and you can see it in the landscape with commercial strips adjoining campus crowded with fast-food restaurants, coffee shops, and other services students want. Distance decay comes into play as you walk away from campus: the farther you get, the fewer services are offered. Eventually, you pass a point where walking there is not feasible between classes and the commercial pedestrian landscape changes to one geared toward people with vehicles.

In AP Human Geography, you may be asked to relate, differentiate, and provide examples of distance decay, the friction of distance, flows, time-space convergence, spatial patterns, scale, and other general concepts, particularly as they can be applied to the gravity model, central place theory, urban models, and various types of diffusion and migration.

## Difference between Distance Decay and Time Space Compression

Time-space compression (not to be confused with time-space convergence) is a result of the reduced friction of distance caused by the interactions in capitalism that speed everything up. The term suggests that time and space are squished together, which is indeed what happens in capitalist globalization, as first suggested by Karl Marx. Prominent UK geographer David Harvey discovered time-space compression.

Capitalism is all about competition, meaning products are more competitive the faster they can move. Communication speeds up; money changes hands faster...the result is that geographic spaces are brought closer together, not physically but through how long it takes for people and communication to travel between them. This has other effects, such as homogenization: places start to look like other places, and people begin to lose accents and other cultural characteristics that evolved when the friction of distance was much more significant.

In effect, time-space compression is distance decay as created by economic globalization.

The Quantitative Revolution introduced equations and mathematical modeling to geography in the 1950s. Complex maps of commuter, consumer, and migrant flows derived from distance decay models were based on regression analysis and other tools that aided urban planners and governments in decision-making. Thanks to computers and GIS, advanced quantitative social science models with many variables have become possible.

## Examples of Distance Decay

We mentioned above how you can see distance decay in action around a university. Here are some more places where distance decay can be seen in the landscape.

### CBDs

Because the central business district of any big city is essentially a pedestrian landscape, it experiences strong effects of distance decay. In the first place, agglomeration, the economic phenomenon whereby large firms situate close to each other because of their interconnecting functions, is partly a means of avoiding distance decay. Have you noticed how the height of buildings and the number of pedestrians drop sharply as you leave the CBD? People need to be able to move between skyscrapers quickly and efficiently. You may even see elevated walkways connecting buildings, which is a way to reduce the distance decay effect further.

### The Metropolitan Area

In an automobile landscape, distance decay is visible over great distances. It has been analyzed and applied in models that maximize efficiency in transportation related to the journey-to-work (commute) and in terms of real estate development, where builders understand that people balance the need to reduce the friction of distance with a desire to live in the suburbs. When you look at a map of a large metro area, you can see distance decay at work: the farther from the center, the more spread out the roads, the buildings, and the people.

Fig. 3 - Houston at night: the distance decay effect is visible in the decreasing amount of human settlement with increasing distance from the CBD (at the center)

### Language

A typical example of the effects of distance decay on cultural diffusion can be seen in how languages change the farther they are away from their hearth. Specific factors that influence this include less contact with people in the hearth and more contact with local influences such as other languages and specific cultural conditions not present in the hearth.

### The End of Distance Decay?

As we mentioned, the friction of distance in terms of communications has effectively been reduced to zero: space no longer matters. Or does it? Will CBDs cease to exist because companies go entirely online? Will more and more places look the same thanks to instantaneous communication and quicker transportation times?

Maybe not. Places may seek to look different and be different to avoid becoming just like everywhere else. Travelers often look for local restaurants and unique experiences, not the same things they can find at home or anywhere else. Only time (and space) will tell.

## Distance Decay - Key takeaways

• Distance decay is an effect of the friction of distance
• The friction of distance increases or decreases depending on numerous cost factors involved with the interaction between places or between people and places
• Distance decay can be seen in urban landscapes where economically-competitive activities need to be located close to large numbers of people
• Distance decay influences cultural diffusion such that the effects of a culture are felt less the farther one is from a cultural hearth (e.g., of a language)

## References

1. Tobler, W. 'A computer movie simulating urban growth in the Detroit region.' Economic Geography Vol. 46 Supplement. 1970.

Distance decay is caused by the friction of distance.

Distance decay effects increase as distance from a cultural hearth increases.

You can calculate distance decay using the law of inverse squares.

Distance decay effects dictate that given the choice between equal destinations, a migrant will go to the one that is closest.

The gravity model states that areas of greater "mass", meaning a greater force of economic attraction, will exert force on areas of lesser mass.

## Final Distance Decay Quiz

Question

What does the First Law of Geography state?

"Everything is related to everything else, but near things are more related than distant things."

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Question

"Decay" in distance decay means

Loss of effect

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Question

If fuel costs double, assume the cost of a private commute by automobile doubles. What methods can a commuter use to keep the cost of their commute the same and not increase the friction of distance?

-Carpool. Two commuters divide the fuel cost of a single vehicle

-Move half the distance to the workplace

-Find a new job location that is twice as close as the old job

-Get a car with twice the fuel efficiency

-A combination of the above factors

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Question

The following is not a cost factor influencing a migrant's choice of destination:

They are all cost factors

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Question

The type of distance decay associated with global capitalism is called:

Time-space compression

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Question

In terms of friction of distance, a hurricane is to a ship as a ______ is to an 18-wheeler.

snowstorm

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Question

The term for when "everything looks the same" is:

homogenization

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