Prying Newton’s Grip on Military Thinking by using Pac Man: A Crowd-Sourcing Exercise (Part 3 of 5)by : Ben Zweibelson
This portion of this 5-part series introduces some unusual concepts such as topology, complexity theory, systems thinking, as well as postmodern theory to disrupt the dominant military frame for thinking and acting in warfare. Before we get into how Pac-Man (or Mrs. Pac-Man, my personal favorite from the 1980s) can help gobble up some of the limitations in how we conceptualize, articulate and render war fighting concepts, we need to clarify what a systematic war logic is, and how a systemic one differs in profound, foundational ways.
This brings into focus a significant tension in how modern militaries seek to approach different types of systems that exercise within security contexts that a military force is directed to address by their nation’s political and/or societal desires. For this systemic design discussion, two primary distinguishable patterns of logic that militaries generally employ to think and act for security affairs are presented below. They are ‘systematic logic’ and ‘systemic logic’. Systematic logic breaks things down for analysis and subsequent reassembly into the whole for formulaic, linear-causal activities that denote a stable and uniform context. Systemic logic requires consideration of larger systems ‘up and out’ through increasing abstraction, where framing the future is divergent (multiple possible but different futures) instead of convergent (a single end-state), and the systematic approach to ‘reverse-engineer’ from an established goal is avoided. Systemic design thinking attempts to generate and accommodate “multiple inequivalent descriptions” within a vastly complex context. The figure above shows the boundaries of systematic and systemic logic paired with military activities within each type of system setting.
Systemic logic differs from systematic logic in how a military force thinks and acts in complex warfare. Again, systematic logicfunctions with inputs linked to clear outputs, and where linear-causal relationships work mathematically (A plus B leads to C), even mechanically to sequence discrete and reducible activities across time and space to lead toward overarching objectives and goals. Thus, systematic thinking implies there is some direct, causal and ‘input-output’ correlated relationship that is quantifiable and suitable for analytic optimization within the system one is attempting to act within. Systematic logic is valuable for analytical optimization and yields clear, repeatable results in simplistic and complicated systems. This is where programmatic management functions best and is found in disciplines such as engineering where mathematical formulas are used to express natural science concepts (physics, chemistry). Systematic logic is highly successful in predicting behaviors and the dynamics of simple as well as complicated systems but becomes increasingly fragile within complex and chaotic systems.
Military organizations that over-invest in systematic logic are dependent upon doctrine, standardization of best practices, and employ elaborate campaign plans to stabilize and install a sense of order and predictability to what are often complex (or chaotic) adaptive systems. Modern military forces today tend to under-invest in systemic logic, where the disciplines of complexity theory, systems theory, military design, postmodern philosophy and military sociology are considered outliers, or in the case of postmodernism, decidedly off-limits for most institutions. When concepts or terminology are taken from any of these fields into modern military practice, they are rendered into systematic logic so that the systemic qualities are broken or discarded. Examples of this include how ‘synthesis’, ‘emergence’, ‘dynamic’, ‘non-linear’, ‘holistic’, or ‘problematize’ are misapplied frequently in military doctrine and theory through assimilation of these concepts into what is still an overarching systematic logic.
Today, the modern war paradigm maintains this epistemological framework in how it formulates decision-making, organization, administration as well as rationalizing how warfare must (and must not) be expressed. Yet within this dominant frame, the military as an institution created a scalable and uniform way to establish similar baselines for explicit knowledge across an organization or institution. This became the established military decision-making encapsulated in doctrine that direct how one will (and will not) think about warfare. Naveh et. al remark: “Just as literacy facilitates bureaucratic, administrative centralization, it also makes possible the codification and logical centralization of doctrine.” This codification thus cuts off any consideration of ideas outside or beyond the institutional limits of the modern war paradigm. Modern, industrialized (Western) militaries understand all strategic thought and action exclusively and at the expense of alternative modes of strategic thinking. Chia defines this with:
Planned change is usually associated with highly visible, ‘top-down’, and large-scale, system-wide initiatives involving significant disruptions such as structural reorganization, downsizing, a disruption of existing routines and/or an overall emphasis on the radical discontinuing of existing organizational practices…Much of the extant literature on the management of change continues to emphasize high-profile and often ‘heroic’ change initiatives as a modus operandi in achieving desired organizational outcomes; change is thought of as an exceptional event that must be made to happen through decisive intervention. Advocates of this ‘Planned’ approach to change insist that radical change cannot take place gradually or in a piecemeal manner, but must be rapid, disruptive, and even revolutionary in order for it to be effective. (Chia, “Reflections: In Praise of Silent Transformation- Allowing Change Through ‘Letting Happen,’” 11)
Chia and Holt find that “the more directly and deliberately a specific strategic change is single-mindedly sought the more likely it is that such calculated actions eventually work to undermine their own initial successes, often with devastating consequences.” The negatives of focusing direct, action-centered strategic change through deliberate (systematic) intervention as illustrated by modern military decision-making methodology may paradoxically exceed their apparent advantages when considered systemically. This requires not just a cataloging of a series of activities and tactical results in isolation, but a holistic and broad framing of system-wide change within areas that NATO or Joint Forces are focused for complex security challenges. In a critique of military technological overmatch against terror networks in Afghanistan and Iraq, Gorka remarks: “we are peerless in our capacity to apply kinetic force on target…But counting Reaper hits against jihadi high-value targets is just as bad a metric of victory today as counting Viet Cong body bags was during the Vietnam War.” Atran, in addressing revolutionary movements and their resistance to previously well-engineered, modern military solutions to security challenges, observes that contemporary terror networks such as the Islamic State are paradoxically able to exist and even thrive under conditions that used to entirely defeat and destroy previous adversaries:
During the surge of American troops in Iraq, up to three-fourths of the fighters were neutralized in al-Qaeda’s Iraqi affiliate, which would become ISIL, and an average of about a dozen high-value targets were eliminated monthly for 15 consecutive months, including its top leader, Abu Musab al-Zarqawi. Yet, the organization survivedand the group went on to thrive beyond all expectations amidst the chaos of Syria’s civil war and Iraq’s factional decomposition.
The desire to understand ‘change’ as exclusively nested in large-scale interventions is, according to Chia irresistible “because it is intimately linked to an inherent ‘heroism’ prevalent in the Western collective psyche” that is not limited to military and defense contexts; most all commercial, political, ideological, and academic communities view ‘change’ in this shared view. While the modern military institution continues to employ technical rationalism so that future wars might be better predicted, managed, controlled and dispatched using scientific principles and more efficient lethality, postmodernists disrupt this stance. Postmodernists posit that the appearance of objectivity in scientific texts is misleading, and “there is no methodology capable of achieving an unmediated, objective representation of the facts.” Exposing this radical perspective is just the first step in realizing alternative modes of thought and action.
‘Strategic indirection’ takes a paradoxical approach, thus threatening to upend many of the cherished beliefs of modern military organizations. This is where systemic thinking challenges systematic thinking and offers alternatives. Change becomes what Tsoukas and Chia describe as: “The reweaving of actors’ webs of beliefs and habits of action as a result of new experiences obtained through interactions…organization is an attempt to order the intrinsic flux of human action, to channel it towards certain ends, to give it a particular shape, through generalizing and institutionalizing particular meanings and rules.” Indirect strategy requires a different way of using war theories, complete with new mental models that break from existing (legacy) ones, where NATO or Joint Forces might construct entirely different decision-making methodologies that accomplish what their current decision-making methodologies seek in profoundly dissimilar ways. To do this, both institutions must consider alternative language and metaphoric devices to apply ‘strategic indirection’ towards military activities in security applications.
Strategic indirection shifts strategists toward a reversal where large-scale, high-profile, planned actions are not sought after for short-term effects or “quick wins” that appear to advance institutional self-relevant beliefs, values, and interests. In strategic indirection, an organization revises its appreciation “of the crucial role that such nuanced forms of responses and indeed non-action can play in shaping outcomes…[which] will help reorient and re-educate our attention toward the mundane and the everyday in accounting for success in human endeavors.” Modern military organizations should consider strategic action by “paradoxically [letting go] of the attempt to control and to predetermine outcomes. Managing change then consists not so much of willfully imposing our pre-designed order onto reality and forcibly making it conform to our will and fancy.” Instead, NATO and Joint Forces will want to resist this urge to confront reality with a strategic ‘head on’ mindset and as Chia advises, “let change happen of its own accord.” The key for complex military decision-making considerations now is precisely how one might go about accomplishing warfighter activities using this strategic shift to indirectness.
First, there must be a new emphasis on unintended consequences of localized, seemingly insignificant actions. Chia describes this with: “the key implication… is that successful outcomes can be attained without any intention on the part of actors and it is an acknowledgement of this possibility, rather than whether it is incremental or planned and large-scale that truly differentiates the Emergent approach from the Planned approach to change.” This is of paramount concern for NATO and Joint Forces in that currently, NATO-OPP, JPP and most analytical thinking on associated military activities continues to use the ‘modern’ style of thought that “accentuates a view of social reality as comprising discrete, static, and hence describable phenomena… according to this thought style, social phenomena such as ‘individuals’, ‘organizations’, ‘cultures’ and ‘societies’ are concrete and isolatable real entities or attributes which can be systematically described and explained, and therefore, meaningfully compared.” This is why nearly all analytical mapping of networks, groups or target ‘chains’ have tangible actors, groups or things inside each bubble or geometric shape depicted, and even the linkages are linear, causal and systematically (input leads to output) related to form a system. Although many sensitive activities are clandestine and might not be considered ‘high profile’ in execution, the term is used here in how an organization conceptualizes the role such a direct activity might have with expected (direct) effects upon the system targeted.
To move past the flat, 2D and systematic graphics from Parts 1 and 2 of this series (if you skipped reading those, this might not make as much sense- so please go back and look at the collection of military graphics that rely upon triangles, spheres, loops, linear-causal dynamics, cubes, rectangles and other modelings that reinforce a Newtonian styled, systematic logic for framing complex warfare. Pac-Man, depicted below, offers us a way to leap beyond this. Pac-Man’s board seems flat and just like all of these other examples initially; he cannot “jump around or over” the ghosts, as they all are stuck in this same flat 2D world. But there is more than meets the eye, and something going on that even as children when we played this, we might not have thought too much about why Pac-Man could magically travel from one side to the other of the board. How did those tunnels work?
In a two-dimensional world like Centipede or Donkey Kong, the player’s icon as well as all other things in the game can only interact in this same flattened, two-dimensional world. Yet in games like Pac-Man, the player can move ‘magically’ from one edge of the screen to the opposite one instantly by using one of the tunnels that link to the other side. A Möbius strip features this sort of non-orientable phenomena that will be expanded below. This seems confusing because most of the world (outside of some mathematicians, physicists and philosophers interested in topology) conceptualize reality in the traditional Newtonian styled worldview. Modern military doctrine explains entirely in two-dimensional, ‘Donkey Kong’ styled illustrations and graphics on every aspect of warfare conceptualization. Yet the often-overlooked topological ‘abnormality’ of those magical Pac-Man connected tunnels to opposing sides of the map offer a useful steppingstone out of the strictly two-dimensional, Newtonian styled conceptualization to different, novel ways to reimagine complex warfare.
Topology requires a little more explanation on how ‘surface’ is significant, so that militaries can begin to think about the metaphoric preferences in current doctrine and modeling (the space-cyber-SOF triad, centers of gravity, integrated deterrence, or ‘the gray zone’) and how they all adhere to what is still a Newtonian styled framing of warfare. A surface is a space where every isolatable point has a ‘neighborhood’ that appears to be a two-dimensional disc. If you take an orange or pumpkin and slice it right in half at the equator or anywhere else, you still will end up with a flat ‘disc’ shape. Some surfaces have boundaries, while others in topology do not. The earth is a sphere object and does not have any edge where an explorer might fall off, thus it is topologically a single surface ‘stretched’ into a topological sphere.
Topological objects that pair nicely with traditional military models and constructs do not involve much stretching at all, as they follow quite simple rules and are devoid of any of the curious properties of something like a Möbius strip. The triangle has a long and storied history in military affairs, from adorning shields of Medieval knights to the strategic framing of the circuitous trading of slaves, sugar and rum between West Africa, the West Indies, and the 17th-18th century northern colonies of British North America, to the nuclear triad underpinning American strategic deterrence throughout the second half of the 20th century into present day. From the most minute technical and tactical to the grand strategic, military forces and their political leaders conceptualize through models that are depicted in these clear, flat, and static geometric forms.
The rectangle can be made into a cylinder by connecting two sides together as shown below. The top and bottom of the cylinder are boundaries that would act as ‘edges’ that an explorer could fall off, if they were on the cylinder topography moving about. Topologists use mathematical formulas to ‘draw’ surfaces because beyond the simplistic, well-recognized shapes of triangles, cubes and rectangles, many objects that bend or even break dimensional properties are hard or impossible to ‘draw.’ One might consider that in military doctrine, every single conceptual model depicted is drawn in a flat, two-dimensional plane… meaning that anything in three, four or more dimensions must be simplified (or at times, over-simplified) to be depicted. The admitted vast complexity of modern warfare is unavoidably reduced toward conceptualization in a ‘Mario Brothers’ flattened world.
This figure helps demonstrate this with showing the mathematical framing on the left and how those shapes would be ‘drawn’ in illustrations on the right. The cylinder shape is quite easy to conceptualize and draw into two-dimensional space, despite it being a three-dimensional object. The torus or ‘donut shape’ in topography is also depicted below and features a slightly more complicated mathematical framing. A torus starts like a cylinder with the edges of two sides corresponding to one another glued together, yet the other two edges also must be stretched and glued together. Picturing this in the reader’s mind, the sphere must be warped so that the two long, circular edges at the top and bottom of the cylinder are glued together, forming a donut or what might seem like the inner tube to a bicycle tire. The mathematical formulas and topographical instructions from this point become increasingly difficult to visualize, and eventually they cannot be ‘drawn’ in two dimensions or even third dimensional spaces without sacrificing some essential properties.
Why might this be useful to modern military forces? When considering the thousands of years of military theories, methodologies, organizational forms, techniques, terminology and shared belief systems of different military groups, there are some significant patterns across cultures, societies and geographies concerning conceptual models that are either ascientific in origin (Augustine’s Holy Trinity as a triangle) or inspired more recently by natural science constructs. For instance, most every military task organization chart mirrors the ancient Greek treatment of how cities, families and organizations are arranged in centralized hierarchies, like tree branches stemming from a larger trunk.
Contemporary military strategies extend from a clear, linear-causal rationalization of ‘ends-ways-means’ that are regularly depicted formulaically in lines of effort, plunging forward in time toward predesigned objectives and goals frozen in an imagined future state. Newtonian laws of physics aid most everyone in regular daily activities such as throwing a ball, driving a car, or trying to intercept a dropped hot dog before the dog beats you to it. The question to ask military theorists and educators is whether all military doctrine and the theories, methods and techniques consisting within should be so utterly dependent upon simplistic two-dimensional rendered Cartesian and Newtonian constructs alone? Might the emerging complexities of cyberspace, space, and special operations-peculiar activities in competition, deterrence and different types of warfare require conceptualization beyond this ever-dominant Newtonian style for conceptualizing modern warfare?
The graphic above is, during lectures on this concept, I challenge the audience to use strips of paper provided to try to complete this challenge. You might wish to stop reading now and go cut a strip of paper and attempt this. [pause here if doing the exercise, or continue to scroll for the answer!]
For those of you that know the answer or figured it out (or not), the way to do this it to put a twist into the paper and connect it. I will put that graphic below the next paragraph so that readers that wish to do the exercise do not accidentally scroll into the answer!
A Möbius strip is the first useful example of a model that disrupts the cognitive limits of the Newtonian style, and thus might become a useful metaphoric device for various complex military topics. Möbius strips have already been widely used in many fields and disciplines beyond mathematics, working as a conceptual model or metaphoric device for understanding complex business relationships, in literature studies, political science and psychoanalysis, archeology and history, postmodern philosophy, and even gender studies. Many of these applications are metaphoric, where the qualities of the Möbius strip are reapplied toward non-mathematical, non-geometric contexts so that practioners of entirely different disciplines might gain new perspectives and inspiration. Military forces could do as these diverse communities and disciplines have, yet this would require a significant disruption of the pervasive Newtonian styling depicted across all modern military doctrine.
Before creating a Möbius strip, draw a centerline on both sides of the rectangle (long side). Then, using scissors to cut along that line, one can generate this surprising outcome. The Möbius strip can also be cut into six different mutually adjacent regions due to the Möbius strip not being an orientable plane (this goes off-topic a bit, so you can look up more on the Wiki page on Möbius strips for great summaries and graphics). This could offer military theorists a multitude of ways to conceptualize the complex interaction of military domains, different forms and functions of organized violence, the arrangement of actions and effects across various agencies and partners, or something entirely different that still adheres to the unique properties of the Möbius strip.
The Möbius strip could be an exceptional concept to apply toward military challenges through modeling, metaphoric device, or even methodological construction. It features the ability to move in a path that traces all boundary points in a single continuous curve, linking start point to end point, and able to infinitely continue in this sequence perpetually cycling between mirror flipped forms. Due to the Möbius strip’s unique properties, it also is an example of a chiral object that is distinguishable from its mirror image. The word chirality derives from the Greek word for ‘hand’, and if someone attempts to shake the right hand of another person with their left hand, they will directly experience how hands are chiral objects. This is another departure from the Newtonian styling of military models and concepts which all remain uniform, reversable, and proportionally equivalent such as in the earlier figures of spheres, cycles, lines and triangles.
Möbius strips abound, metaphorically, in modern society. The popular science fiction movie ‘The Matrix’, which draws from postmodern origins, provides a wonderful example of Möbius phenomena where the main characters that exist outside the simulated ‘Matrix’ digital world can hack into the system, entering the false digital reality where those that are conceptually ‘trapped’ engage in their lives. The heroes are physically at risk inside the simulation as computer agents attempt to ‘kill’ them inside, while other enemies and risks threaten their physical bodies as they lay vulnerable ‘outside’ in the actual Dystopian landscape that is reality. The conceptual struggles of Neo, the main protagonist, provide a telling example of a Möbius strip journey throughout the first movie as he questions which world is ‘real’ and who he is or is not.
How might Möbius strips replace the more rigid, simplistic Newtonian stylings for complex military affairs? Once a Möbius strip is formed, one can cut along the entire centerline and instead of producing two new and smaller Möbius strips as one would get with cutting a rectangle in half (longways), the result is one longer strip with two half-twists. Mathematically, in orientable planes such as a map of the United States or a square illustrated below, the ‘four color theorem’ proves that no more than four colors are required to color the regions of any map so that no two adjacent regions share the same color. Yet the Möbius strip violates this due to its unique properties. It breaks a host of ‘rules’ that Newtonian inspired constructs must follow, making these non-orientable objects worthy of consideration for complex military contexts. Why limit oneself to conceptualization of a rigid Newtonian stylization when so many other options and ways to break out of those conceptual barriers exist? Complex warfare ought not be conceptualized within such explicit, quantitative, and systematic representations. This refers to the metaphoric devices and does not imply that in a strict mathematical sense, a non-orientable surface is more complex than an orientable surface. For the purposes of conceptualizing warfare, only orientable, standard geometric constructs have been utilized for many centuries of military theory and practice.
This concludes Part 3 of this 5 Part series. This, part 1 & 2 and the very next section (posted each week) set up the position that existing campaign design at a war paradigmatic level is flawed, over-simplistic, dependent upon ‘pseudo-scientific’ conceptualizations lifted from natural sciences during the last 3 centuries of military professionalization, and much of how we conceptualize thoughts and action in time and space are fixated upon an illusion of an objective, mechanistic and reducible reality where sufficient time, resources and analysis ought to provide military forces with the ability to ‘win’. This may have been closer to some truth in past centuries, but in 2022 there is an extensive historical pattern of military failure to imagine, improvise, invent and reform beyond the accepted limits of our own institutional efforts to preserve, protect and ritualize.