Friction of distance is a core principle ofgeography that states thatmovement incurs some form ofcost, in the form ofphysical effort,energy, time, and/or the expenditure of otherresources, and that these costs are proportional to the distance traveled. This cost is thus a resistance against movement, analogous (but not directly related) to the effect offriction against movement inclassical mechanics.[1] The subsequent preference for minimizing distance and its cost underlies a vast array of geographic patterns fromeconomic agglomeration towildlife migration, as well as many of the theories and techniques ofspatial analysis, such asTobler's first law of geography,network routing, andcost distance analysis. To a large degree, friction of distance is the primary reason why geography is relevant to many aspects of the world, although its importance (and perhaps the importance of geography) has been decreasing with the development of transportation and communication technologies.[2][3]
It is not known who first coined the term "friction of distance," but the effect of distance-based costs on geographic activity and geographic patterns has been a core element of academic geography since its initial rise in the 19th Century.von Thünen's isolated state model of exurban land use (1826), possibly the earliest geographic theory, directly incorporated the cost of transportation of different agricultural products as one of the determinants for how far from a town each type of goods could be produced profitably.[4] The industrial location theory ofAlfred Weber (1909) and thecentral place theory ofWalter Christaller (1933)[5] were also basically optimizations of space to minimize travel costs.
By the 1920s, social scientists began to incorporate principles ofphysics (more precisely, some of its mathematical formalizations), such asgravity, specifically theinverse square law found inNewton's law of universal gravitation.[6] Geographers quickly identified a number of situations in which the interaction between places, whether migration between cities or the distribution of residences willing to patronize a shop, exhibited thisdistance decay due to the advantages of minimizing distance traveled.Gravity models and other Distance optimization models became widespread during thequantitative revolution of the 1950s and the subsequent rise ofspatial analysis. Gerald Carrothers (1956) was one of the first to explicitly use the analogy of "friction" to conceptualize the effect of distance, suggesting that these distance optimizations needed to acknowledge that the effect varies according to localized factors.[6]Ian McHarg, as published inDesign with Nature (1969), was among those who developed the multifaceted nature of distance costs, although he did not initially employ mathematical or computational methods to optimize them.[7]
In the era ofgeographic information systems, starting in the 1970s, many of the existing proximity models and new algorithms were automated as analysis tools, making them significantly easier to use by a wider set of professionals. These tools have tended to focus on problems that could be solveddeterministically, such asbuffers,Cost distance analysis,interpolation andnetwork routing. Other problems that apply the friction of distance are much more difficult (i.e.,NP-hard), such as thetraveling salesman problem andcluster analysis, and automated tools to solve them (usually usingheuristic algorithms such ask-means clustering) are less widely available, or only recently available, in GIS software.
As an illustration, picture a hiker standing on the side of an isolated wooded mountain, who wishes to travel to the other side of the mountain. There are essentially an infinite number of paths she could take to get there. Traveling directly over the mountain peak is "expensive," in that every ten meters spent climbing requires significant effort. Traveling ten meters cross country through the woods requires significantly more time and effort than traveling ten meters along a developed trail or through open meadow. Taking a level route along a road going around the mountain has a much lower cost (in both effort and time) for every ten meters, but the total cost accumulates over a much longer distance. In each case, the amount of time and/or effort required to travel ten meters is a measurement of the friction of distance. Determining the optimal route requires balancing these costs, and can be solved using the technique ofcost distance analysis.
In another, very common example, a person wants to drive from his home to the nearest hospital. Of the many (but finite) possible routes through the road network, the one with the shortest distance passes through residential neighborhoods with low speed limits and frequent stops. An alternative route follows a bypass highway around the neighborhoods, having a significantly longer distance, with much higher speed limits and infrequent stops. Thus, this alternative has a much lower unit friction of distance (in this case, time), but it accumulates over a greater distance, requiring calculations to determine the optimal (taking the least total travel time), perhaps using thenetwork analysis algorithms commonly found inweb maps such asGoogle Maps.
The costs that are proportional to distance can take a number of forms, each of which may or may not be relevant in a given geographic situation:
Some of these costs are easily quantifiable and measurable, such as transit time, fuel consumption, and construction costs, thus naturally lending themselves tooptimization algorithms. That said, there may be a significant amount of uncertainty in predicting them due to variability over time (e.g., travel time through a road network depending on changing traffic volume) or variability in individual situations (e.g., how fast a person wishes to drive). Other costs are much more difficult to measure due to their qualitative or subjective nature, such as political protest or ecological impact; these typically require the creation of "pseudo-measures" in the form ofindices orscales tooperationalize.[3]
All of these costs arefields in that they arespatially intensive (a "density" of cost per unit distance) and vary over space. Thecost field (often called acost surface) may be a continuous, smooth function or may have abrupt changes. This variability of cost occurs both in unconstrained (two- or three-dimensional) space, as well as in constrained networks, such as roads and cable telecommunications.
A large number of geographic theories,spatial analysis techniques, andGIS applications are directly based on the practical effects of friction of distance:
Historically, the friction of distance was very high for most types of movement, making long-distance movement and interaction relatively slow and rare (but not non-existent). The result was a strongly localizedhuman geography, manifested in aspects as varied aslanguage andeconomy. One of the most profound effects of the technological advances since 1800, including therailroad, theautomobile, and thetelephone, has been to drastically reduce the costs of moving people, goods, and information over long distances. This led to widespread diffusion and integration, ultimately resulting in many of the aspects ofglobalization.[12] The geographic effect of this diminishing friction of distance is calledtime-space convergence orcost-space convergence.[13]
Of these technologies,telecommunications, especially theInternet, has perhaps had the most profound effect. Although there are still distance-based costs of transmitting information, such as the laying of cable and the generation of electromagnetic signal energy (traditionally manifesting in ways such aslong-distance telephone charges), these are now so small for any meaningful unit of information that they are no longer managed in a distance-based form, but are bundled into fixed (not based on distance) service costs.[14] For example, some portion of the fee for mobile telephone service covers the higher costs of long-distance service, but the customer does not see it, and thus does not make communication decisions based on distance. The rise offree shipping has similar causes and effects on retail trade.
It has been argued that the virtual elimination of the friction of distance in many aspects of society has resulted in the "death of Geography," in which relative location is no longer relevant to many tasks in which it formerly played a crucial role.[15] It is now possible to conduct many interactions over global distances almost as easily as over local distances, includingretail trade,business-to-business services, and some types ofremote work. Thus, these services could be theoretically provided from anywhere with equal cost. TheCOVID-19 pandemic has tested and accelerated many of these trends.[16]
Conversely, others have seen a strengthening in the geographic effects of other aspects of life, or perhaps the increasing focus on them as traditional distance-based aspects have become less relevant.[17] This includes the lifestyle amenities of a place, such as local natural landscapes or urban nightlife that must be experienced in person (thus requiring physical travel and thus entailing the friction of distance). Also, many people prefer in-person interactions that could technically be conducted remotely, such as business meetings, education, tourism, and shopping, which should make distance-based effects relevant for the foreseeable future.[18] The contrasting trends of "frictional" and "frictionless" factors have necessitated a more nuanced analysis of geography than the traditional blanket statements of location always mattering, or the recent claims that location does not matter at all.[19]