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This article discusses a geographic phenomenon we consider centrally relevant to military strategy and planning at all scales, risk distance. Risk distance is the distance to the theoretical point in space and time beyond which it would be imprudent to continue an activity or to remain in a place. That dangerous point is what many in the military refer to as the ‘culminating point’.[i] When a commander calculates relevant distances to some likely confrontation in an armed struggle, the perceived costs and risks have an intimate relationship to the correlation of force at the points of potential contact. If, for instance, a point of intended future contact were so distant that a commander could expect to wield only inferior relative strength (at that contact point), he might be overreaching by forcing the contact, unless he at least assures that his force will have a safe escape. This question of the culminating point is central to rational strategy at every level, but has been short-changed in recent strategy literature. We emphasize it here, starting with a theoretical discussion of distance as the geographer knows it.
We take as axiomatic that competitive armed strength diminishes in accordance with the distance a force must travel away from its base or sanctuary. This ‘law’ is known in some circles as the Loss of Strength Gradient, a term proposed by economist Kenneth Boulding in 1962.[ii] A peace activist, Professor Boulding was nevertheless anti-communist enough that he wanted to enter the Cold War arms race debate in a reasoned way. It seems that to Professor Boulding it made a lot more sense to station forces in Europe than to increase the total amount of coercive force (especially nuclear) available to the United States. He believed that more ICBMs did not equal greater military advantage, a point he expressed in part through use of distance theory. The Loss of Strength Gradient is related to Professor Waldo Tobler’s ‘First Law of Geography’ that “everything is related to everything else, but near things are more related”; as well as to the observation called ‘distance decay’ that is widely referenced in geography and economics literature.[iii] The loss of strength (or influence) caused by increasing distance has a geographic consequence. Theoretically, there will exist places on the earth where opponents, although they may possess greatly unequal amounts of total coercive strength, will nevertheless have equal amounts of practicable coercive strength.
An economist, Professor Boulding demonstrated his thinking with charts. As depicted in Figure 1, Professor Boulding imagined the geographic world simplified as the limitless line A-B, with point A being one country and point B another in a world of only two countries. The line between points A and B represents the distance between the two countries.
Figure 1: The Loss of Strength Gradient in a single-line world.[iv]
Lines A-H and B-K represent each country’s amount of military coercive power. The slope of the lines H-L, H-E, or K-M represent the loss of effective military power as distance increases – the loss of strength gradient. Point D (between A and B) is derived as the geographic point in the world at which the two countries, although unequal in overall military capacity and capability, have equal strength. The graphic suggests (shown by line H-H’) that country A could achieve enough military power such that country B would have no place in the A-B world where B would enjoy military strength equal to that of A. However, part of Boulding’s suggestion, in an obvious simplification of the bi-polar US-Soviet confrontation, is also that a modest increase in coercive power on the part of B, the Soviets, could ameliorate or overcome even a great effort on the part of A, the United States, to increase its total and relative coercive power. An increase in coercive power by country B (represented by the line K-K’) might move the geographic point of equality to point D’ and so on logically. In his theoretical schematic, B could even move the geographic point of equal power closer to A in spite of A having increased its total power more than did B. With this observation about the relationship of force-to-distance in mind, Professor Boulding supposed that placing coercive force forward in Europe was a more reasonable way to favorably enhance relative US strength than an increase in total US power would be. Even this conclusion he clothed in disclaimers and exceptions.
In Figure 3 below, we re-make Boulding’s A-B single-line world into a globe, but continue to consider the strict competition of only the two countries A and B (we drop the allusion to the Cold War, now centering the two competitors on the poles), then the line of equal power (Circle D) makes a parallel around the world.[v] That parallel is closer to one pole than to the other, reflecting the greater total coercive force of A over B. In this simplified world, the surface area wherein B continues to enjoy greater strength appears in the shape of a beanie or simple yarmulke.
Figure 2: The Loss of Strength Gradient in a circular world.
Depicting the points of equal power and the areas of superiority would become quite an intellectual and artistic chore if we were to populate our imagined, spherical world with several countries of differing amounts of military power, each with varying national sizes and shapes. If we were to interpolate the idea further toward reality by including many dozens of countries, all conspiring alliances and constantly evolving in coercive power, the depiction would be nearly impossible to create. Perhaps because of that impossibility, writers on strategy who have gone about comparing countries’ military power tend to overlook the effect of distance entirely. They concentrate instead on direct factors of strength such as territorial space, population, economic performance, diplomatic acumen, technical innovation, cyber power, cultural influence and so on. None of the entries in a recent bibliography (prepared by the library of one of the US national strategy colleges) on the elements of national power discusses distance.[vi] This oblivion to the effect of distance on power does not, however, make the influence of distance go away.
All the above begs another question regarding the true measure of distance itself. Distance can be categorized as: Euclidean, cost or friction, and risk. Euclidean distance is unimpeded ‘normal’ mathematical or geometrical distance measured in established units such as meters or miles – sometimes said, ‘as the crow flies’. For most purposes, we measure cost distances as the time and money or other resources necessary to move people and things from one location to another. Risk distance, again, is the distance to a perceived, theoretical point in time and space beyond which it would be imprudent, irresponsible or self-destructive to proceed in some activity. For the most part, cost and risk distances are inversely related: Increases in a cost distance can shorten the predicted risk distance for military endeavor. For instance, a perceived point of unacceptable risk might be closer to home or sooner in time if extreme hot dry weather compelled a unit to carry more water than it would otherwise need. The higher cost distance (measured as an amount of needed water) shortens the perceived risk distance, that is, shortens the time or physical space beyond which it is not prudent to go.[vii] The careful military leader anticipates contacts, and, unless the mission involves some resigned contemplation of suicide, will make sure his line of withdrawal is secure in case he attacks or is attacked by a stronger force. Competent strategy implies the constant measurement of relative power, but with prudence to know that those measurements will often be wrong. Like so much else, this truth reigns in both the palpable world and the solipsistic one. The competitive leader wants to correctly interpret and shape physical reality in order to act prudently and to affect the perceptions and mindset of the opposing leader.
The perception in a leader’s mind regarding the where or when of his culminating point is obviously affected by geographic circumstances. Less obvious, or at least less discussed, are certain specific kinds of places and moments in time that most affect calculations of risk distance. Mountainous up-slopes are an example. During a pursuit in mountainous terrain, the fugitive usually knows which direction he will take when he gets to a junction of watercourses. His pursuer, on the other hand, is often obliged to make a blind decision as to which stream to follow. If for no other reason than this mundane fact of water and gravity, an advantage is given to uphill escape.[viii] Some human geographic phenomena have the same effect.[ix] An international border can act in a way similar to that of upslope terrain. The two phenomena (border and mountain) have a commonly measurable effect – they each can serve to shorten the pursuer’s risk distance more than they shorten that of a fugitive. With the international border the effect is not usually manifested directly in the perceptions of the small unit commander, but rather through a risk appreciation that is transmitted down from his leaders. For a squad in pursuit, an international boundary might be all but invisible, presenting little physical impediment to that squad’s continuation of its mission. The fact that it is an international boundary, however, creates a risk in the minds of superior leaders in the squad’s larger organization. Disciplined, the squad stops at the border – at what a more senior leader considers the culminating point. Sanctuaries of the FARC in Venezuela, or of the Taliban in Pakistan are common examples. Guerrillas often exploit administrative borders for the disparate advantages these geographic phenomena give to fugitive elements.
Renowned commanders and theorists counsel aggressive pursuit because an inferior force can be destroyed if it is unable to escape.[x] However, when a pursuing force presses beyond its risk distance, the pursued force may turn and counterattack, effect an ambush, or maneuver to cut off the pursuer from the erstwhile pursuer’s own line of withdrawal. Care regarding calculations of distance and strength (not just as to one-off pursuits in irregular war, but every kind and mix of military encounter) is a hallmark of great leaders.[xi] Our strategic conversation has to be taken beyond the effect that costs might have on a unit’s strength as distance increases, to the relative strengths of all forces, ours and our opponents’ over time. A discussion that took place in our office (apologies for not being able to cite a written reference) regarded the cost of an American soldier’s lunch in Arghandab. That meal might cost US taxpayers around $130.00, an expensive proposition over time. An ineffable rumor circulated that in getting that meal up from Karachi in ‘jingle trucks’, cash on delivery in Kandahar, $20 of the $130 easily might fall into Taliban hands in the form of willing and unwilling contributions along the way. Given all the relevant aspects of the human and physical geography, maybe it only took $10 to serve the Taliban fighter his lunch, money left over for a few rounds of ammunition. If the rumor were true, in a palpable sense, we were paying for both sides of the contest – an effect of dissimilar cost distances.
Informed by Boulding’s reminder of the obvious, we offer below a mapamundi that we are titling, The Access Environment (We include an appendix after the concluding paragraph of this article’s text that elaborates the strategic and cartographic rationales).[xii] We could have perhaps called it the ‘prudent risk map’ or ‘risk distances map’, or the ‘map of military culmination points and areas beyond them’. The map speaks for itself in great measure, showing that but for a minor percentage of the earth’s land surface, the impediments presented to the planner charged to contemplate the moving and sustaining of significant regular US military units are formidable. The map says, loudly, that while it might be difficult to predict where a US armored brigade will be sent into combat in the future, it is not hard to reasonably assert where it is unlikely to be sent except at great (probably imprudent) cost financially, diplomatically, or politically. The map suggests that, at this moment in history, by far the greater expanse of the earth’s land surface lies beyond the American military risk distance (at least if military were defined by the employment of an armored brigade). It would, in effect, be presumptively imprudent to send an armored brigade almost anywhere uninvited. If the reasons for going somewhere are great enough (newly perceived risks to the nation appear so great as to leave no option but to advance), then almost any costs will be born and hopefully some ameliorated. Today, however, (and posing the armored brigade as an appropriate standard unit for discussion) the following map makes an assertion, country-by-country, regarding how much of the world lies beyond the culminating point, that is, the world beyond which it would be imprudent to send an armored brigade in the absence of some new and startling knowledge.
Figure 6: The Access Environment
The Access Environment expresses strategic risk distance via three layers of phenomena that we believe will tend to influence some near-future (within twenty years?) American decision to send or maintain regular military units abroad. The first layer (which we depict in colors by country unit) is a set of basic geographic (human and physical) impediments. It may be that the physical distances are great, as they are, for instance, in the middle of Africa. It may be that the moral impediment is extreme, as regards, for instance, the territory of our neighbor Canada. The second layer of the map we call the impunity layer. It depicts foreign territorial spaces wherein some negative set of conditions or events exist which might create an effective quantity of American desire to visit with force, uninvited. We base this layer on the notion that someone somewhere will be trying to get away with something that Americans, as a country and represented by the US government, find impossible to tolerate. In other words, there exist and will exist, even in the near-term, some basic reasons for the United States government to decide to run additional risk, and to bear costs in terms of human life, moral authority, diplomatic leverage or simple logistical expenditure. The third map layer depicts invitational deployment. Given the nature of American diplomacy, the evolution of defense treaties and other accords, and a dynamic quantity of what other peoples perceive as American empathy for their concerns, there also exists the possibility that a genuine invitation would be extended for the presence of ostentatious American military might in the form of conventional units. We only find three places where this seems reasonably likely to happen or continue, and as to all three (Kuwait, South Korea, and Eastern Europe) our prediction is based on the fact that some level of conventional US ground force structure is already there.
There is a fourth current or set of phenomena that we do not depict as a layer on The Access Environment map, but which would nevertheless be a significant ingredient in a decision to send or not to send US military forces into foreign territory. That set of phenomena could be referred to as ‘national interests’, and here refers to a set of motivations held by US senior leaders, but not necessarily known to or even shared by the US public. These motivations might include selective or preferential economic advantages or politically influential emotive or ideological values. They might also include validly perceived threats that become known to leadership via professional intelligence, but which cannot be openly revealed. In any case, we are not able to create a cartographic layer showing the influence that all these kinds of ‘national interests’ have on the likelihood of US global military movement and placement. They are exactly those factors not suited to visual depiction. We mention them, however, as an unmapped influence in order to underline that almost any amount of risk might be accepted, run, overcome, or costs paid if the rewards seemed sufficient or if the predictable costs of not running the risk were deemed too great by national leadership. We also admit as how the elements of the four layers (three fairly easy to depict and one not) are separable only in theory. Their overlap and inter-relationship cannot be dismissed or drawn away, and without the dimension of ‘national interests’, it is impossible to comprehensively discuss a particular case. Nevertheless, the map reminds us not that distances are neither wholly determinant of our options nor determinant of the outcome of our endeavors, but that without an explicit, habitual calculation of distance we cannot reasonably compare relative military strength. We also cannot understand the culminating points of our various enterprises or how one affects another, and we will not do strategy well. Whatever levels of rectitude or existential imperative we might or might not be able to assign to the unmapped ‘national interests’, these latter will not be correctly framed without clarity regarding the other layers proffered here.
Risk distance is the relevant common denominator that allows a planner to compare the advantages and disadvantages produced by various seemingly disparate inputs, and it gives a strategic planner a tool for considering the effect that one seemingly detached military or non-military action (the employment of one or another element of national strategy) has on all others. In order to mount a bombing raid on Libya from a base in the United Kingdom, the distances might be far greater than the map might initially indicate if diplomatic relationships with France do not produce a right to overfly French territory on the way.[xiii] Diplomatic conditions with France might not put such a raid beyond the culminating point in the mind of a given American President, but they could certainly add cost distance. We could argue that the positioning of Outpost Keating in Afghanistan was beyond the prudent risk distance ab initio. It was operationally imprudent to place an outpost at the bottom of the valley near Kamdesh given the likelihood that the enemy could create a disadvantageous correlation of force that would compel our abandonment of the position.[xiv] We leave for a separate discussion at what point the compounding of imprudent tactical decisions constitutes imprudent strategy. We suggest, however, that if distance theory had been a staple in the diet of US military education – if Clausewitz’ culminating point were as favored a theme as ‘center of gravity’ – then the design and deployment of American military force in recent decades might have been more effective. Going forward, in order to build a more grounded strategic education, we think that historical investigations of risk distance would be a healthy start.[xv]
The Access Environment is a map of risk distances. We invite challenge to specific assertions, to which we are hardly wed.[xvi] We believe that risk distance is a valid and centrally useful concept not only at the global scale, but at all scales of military competition. A mapamundi divided by county-size (county, not country) territorial units would perhaps be more useful to special operating forces. We did not build The Access Environment map or our argument from any presumption of geographic determinism.[xvii] Rather, inseparably mixing physical and human geography, we find distance, as measured in costs and risk, to have a singularly influential impact on decision-making. Failure to correctly interpret distance is a great fouler of ill-conceived plans. Failure to address distance at all is a failure of strategic theory.
Layer I. Impedance: World territories colored according to overall impediment to the uninvited sending of coercive US military force.
Red. Utmost impediment, mostly intangible. These territorial spaces present a prohibitive risk to the United States (in terms of US domestic politics and diplomacy) ante the sending of coercive force into their territorial spaces without a genuine invitation. The criteria for this risk status are centered on respect that these countries have generated for their way of life, form of government and positive relationship with the people of the United States.
Orange. Extreme impediment, mostly physical. These territorial spaces also present a prohibitive risk to the United States for the sending of ostentatious coercive force into their territorial spaces. This risk is not generated because they meet all the sentimental criteria of those countries colored in red, but rather through the presentation of physical impediments, especially armed force available to the government of these countries, which can impose grievous physical costs on a foreign intervening or invading force.
Violet. High impediment, mostly intangible. These territorial spaces present great risk to the United States for the sending of coercive force into these spaces. They have generated some intangible risk in the form of respect for their way of life, form of government and positive relationship with the people of the United States (although perhaps not as much as those colored red), or the territorial space or government offers a specific geostrategic or economic advantage or utility especially prized by the US government (perhaps in spite of the country’s not generating a high degree of intangible risk).
Yellow. Moderate impediment, mostly physical. These territorial spaces present considerable risk to the United States for the sending of coercive force because of physical impediments such as size, remoteness, or extreme environmental conditions; or because the armed forces of these or neighboring countries can impose substantial physical costs on a foreign intervening or invading force.
Green. Low impediment. These territorial spaces present the least degree of risk to the United States for the sending of coercive force into them. The lack of risk in terms of US domestic politics or US global diplomacy may reflect their inadequate observance of basic human or civil rights or because their systems are so corrupt as to invalidate any reasonable assertion that the autochthonous governments can represent the people resident within their borders. These countries do not possess armed forces capable of presenting a significant risk to a deployment of US regular formations into their territorial space, nor do their physical geographies present a challenging impediment to military movement. Also, no third government has an alliance, protective or tutorial relationship with these places such as to present a consequential indirect risk.
Layer II. Impunity: World territories marked according to three reasonably envisioned categories of offending behavior.
Impunity menaced. ‘X’ marks. Reasonably, these territorial spaces might encompass sanctuaries for persons who will have created a reasonable fear in many US persons of impending traumatic harm to US persons or to nationals of countries closely allied to the United States.
Impunity for in flagrante. Slash lines. Reasonably, these territorial spaces might encompass sanctuaries for persons who will have perpetrated or abetted major, ongoing felonious violations of US law or violations of US citizens’ rights (illicit trade, computer hacking, kidnapping, piracy).
Impunity for immane behavior. Dot pattern. Reasonably, these territorial spaces might encompass sanctuaries for persons who will have perpetrated (or materially abetted) atrocities.
[Unlike the impedance layer, the impunity layer does contemplate and categorize reasons why the US government might determine to send coercive force into a territorial space, but the layer does not presuppose that the US government will send coercive force, only that a threshold degree of impunity might reasonably exist in a given territory. The timing of entry, amount or duration of uninvited force that might be sent is also not contemplated. In effect, perhaps, this layer offers a threshold set of national interests stated in terms of intolerable impunity.]
Layer III. Invitation and Invasion: Places to which regular US military forces (an armored brigade) might reasonably be invited correlate geographically with places where an invasion by the regulars of a third party might occur (although to us these invasions seem less likely than the invitations).
Invitation. Circles stars. Reasonably, the constituted and internationally recognized governments extant in these places might invite the United States to station heavy military formations within their territories.
Invasion. White arrows. It is feared (not unreasonably) by autochthonous analysts that an invasion by a neighboring country (to include the use of heavy military formations) could occur in these or nearby territories.
[The invitation part of this layer contemplates places that might extend to the United States a genuine invitation to canton heavy or conventional US formations (perhaps an armored brigade or equivalent, or more). Such an invitation, we presuppose, would be a result of fears not unreasonably held by a local government, along with the existence of a formal defense treaty between that government and the government of the United States. The invasion part of the layer contemplates locations where we believe that local populations might fear that an invasion of their, or a nearby, territory might be perpetrated and that such a perpetration would reasonably include heavy military formations.]
[i] The term ‘culminating point’ dates back at least to Carl von Clausewitz, the Napoleonic era, and classic strategy. See on this point, Karl von Clausewitz, On War, translated by O. J. Matthijs Jolles in Caleb Carr, The Book of War, New York: The Modern Library, 2000, pp. 838, 886; Howard, Michael and Paret, Peter, eds. Carl Von Clausewitz, On War, Princeton: Princeton University Press, 1976, pp. 528, 566;
[ii] Kenneth E. Boulding, Conflict and Defense: A General Theory. New York: Harper & Row, 1962, p. 162.
[iii] See, on this point, Waldo Tobler, “A computer movie simulating urban growth in the Detroit region,” Economic Geography, 46 (2) (1970): 234-240.
[iv] Kenneth E. Boulding, ibid, p. 162.
[v] This is adopted from Geoffrey Demarest, Risk Distance: The Loss of Strength Gradient and Colombia’s Geography of Impunity. University of Kansas, ProQuest, UMI Dissertations Publishing, 2013.
[vi] Ike Skelton Library, “Elements of National Power” (bibliography) Joint Forces Staff College Norfolk, VA, 2011, http://www.jfsc.ndu.edu/library/publications/bibliography/Elements_of_National_Power.pdf (accessed August, 2013). For the exception, see, K. Webb, “The Continued Importance of Geographic Distance and Boulding’s Loss of Strength Gradient,” Comparative Strategy, Volume 26, Issue 4, 2007.
[vii] Meanwhile, the likelihood of a deadly encounter with an armed enemy is itself a factor in the measurement of cost. (Moving within range of the enemy’s weapons, for instance, presents the potential for additional costs.) Thus the two, risk and cost, can be said to form what might be termed an endogeneity, that is, a cross-influencing relationship. The militarily relevant distance is the distance to the limit of prudence – to the ‘bridge too far’. On Operation Market Garden in WWII, see, Cornelius Ryan, A Bridge Too Far, New York: Simon and Schuster, 1974.
[viii] The assertion was inspired by Colombian terrain and the effect that Colombia’s innumerable slopes have had on smuggling success, landmine placement and the difficulty of military pursuits. “Every left-or-right dilemma presented to the pursuer shortens the distance to the pursuer’s culminating point (his prudent risk distance). With a little help from landmines and snipers, the fugitive can augment his enemy’s perception of the cost-distances, that is, greatly shorten his enemy’s risk distance.” Geoffrey Demarest, Winning Irregular War: Conflict Geography. Leavenworth, FMSO, 2014, p. 359.
[ix] As a matter of after-the-fact military critique, leaders are discredited who purportedly fail to press an opportunity to finish off a weaker force. Some will argue that Meade should have pursued Lee after Gettysburg. See, for instance, Center for Military History, American Military History, Washington, D.C.: United States Army, 1989, p. 254, http://www.history.army.mil/books/AMH/amh-toc.htm.
[x] Carl von Clausewitz, On War. Michael Howard and Peter Paret, eds. Princeton: Princeton University Press, 1976, p. 267; General Phillip Sheridan, according to Aradmin, “Civil War Cavalry Leaders Tribute Henry Rifle.” America Remembers, July 26, 2013. http://www.americaremembers.com/page/2/ ?taxonomy=product_type&term=simple
[xi] On this point we recommend James G. Reily, Middle Eastern Geographies of World War I, Fort Leavenworth: School of Advanced Military Studies, 2010 (monograph). Reily applies the Clausewitzian idea of ‘friction’ especially well, ibid, page 8. [Not ironically cost-distance is also called friction-distance]
[xii] The map itself was designed and created by Mr. Chuck Bartles.
[xiii] The reference is to Operation El Dorado Canyon, a raid on Libya in mid-April 1986. On this episode, see, for instance, Joseph T. Stanik, El Dorado Canyon: Reagan’s Undeclared War With Qaddafi, Annapolis: Naval Institute Press, 2003; Robert E. Venkus, Raid On Qaddafi. New York: St. Martin’s Press, 1992.
[xiv] On this episode, see, for instance, Jake Tapper, The Outpost: An Untold Story of American Valor, New York: Little, Brown and Company, 2012.
[xv] As a prompt for understanding risk distance and for the Marine in us all, note Presley O’Bannon’s exploits at Tripoli. The US Navy might move thousands of miles within prudent risk, but in order to be strategically effective, force had to be moved a few more miles – on land. On this episode, see, Richard Zacks, The Pirate Coast: Thomas Jefferson, the First Marines, and the Secret Mission of 1805, New York: Hyperion, 2005.
[xvi] None of our assertions are formed from any classified documents or other forms of classified input whatever. The Access Environment map is informed completely by unclassified, publicly available knowledge.
[xvii] Traditional military geography has concentrated almost exclusively on physical aspects of terrain. See, for instance, John M. Collins, Military Geography of Professionals and the Public. Washington D. C.: Potomac Books, 1998. We take the approach that it is only a didactic convenience to distinguish between human and physical geography; and that it is better to imagine geography as an interaction, not a separation of humans from their surroundings. As such, we tend to reject presentations that would divide ‘human terrain’ from physical terrain. Even in the militarily purest kind of combat, when a unit ‘takes a hill’, it takes the hill from someone or at someone’s expense.
[xviii] Please excuse our conflation of the electrical term ‘impedance’ in the layer title, along with its everyday cousin, ‘impediment’ in the color category subtitles. Webster’s Second Collegiate defines impedance as, “1. The total opposition offered by an electric current to the flow of an alternating current of a single frequency: it is a combination of resistance and reactance ....” We do not wish to carry the analogy with electricity any farther. The appeal of the term impedance over impediment is in its denotation of overall blockage to passage presented as a combination of both passive factors and active factors, which is measured according to area and density, and is generally asserted in relation to a single opposing phenomenon. In our map, impedance is synonymous with implied risk (also describable as perils or hazards) and possibly synonymous with other expressions of difficulty or potential cost. ‘Access denial’, for instance, connotes to us those measures and preparations that might be taken by an armed force to create a greater degree of overall challenge for going into a given space. It would be part of the impedance, other parts including physical geography, population, intangible factors occurring at home, and so on.