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Further Along the Möbius : Using a Klein Bottle Concept to Consider Complex Warfare Differently
by : Ben ZweibelsonOriginal post can be found here: https://benzweibelson.medium.com/further-along-the-möbius-using-a-klein-bottle-concept-to-consider-complex-warfare-differently-e1a5c91ce092
The first part of this 5 part series is linked below, and readers ought to check that out first before venturing further, as I set up why Pac-Man is the metaphoric device here for breaking out of static, simplistic, Newtonian styled models and constructs for conceptualizing warfare.
Again, metaphoric devices are what individuals, groups and societies employ underneath all language so that terminology reflects into a rationalization of accepted theories, beliefs, and conceptual models that contribute to the formation of decision-making methodologies used to engage in complex reality. This constitutes a social paradigm, and critical examination of the metaphoric devices as well as the conceptual models used can help any organization or person think differently when a paradigm is failing them in reality. Below, the Klein bottle construct is demonstrated on the left with the topological instructions as well as an approximation in two-dimensional space of what a Klein bottle looks like. On the right, the original Möbius strip configuration of the earlier figures is doubled, just as a Klein bottle can be produced by gluing together two Möbius strips together in topological space.
Metaphorically (again, not mathematically analogous), militaries could combine two Möbius strip adaptations to further deepen a myriad of possible configurations on complex warfare. The many paradoxes of complex warfare such as how progress in eliminating terror group leadership would, often unavoidably, generate surges in societal resistance against ‘occupiers’ and ‘infidels’ in Iraq, Syria, and Afghanistan. In another ‘Klein bottle’ example from Afghanistan, a military unit sought to improve a mountain village by digging a well close to town so that the local women did not need to walk an hour a day to collect water. The unit celebrated their humanitarian project, but soon found the well destroyed and suspected that, obviously of course, enemy Taliban were responsible. Later, that unit learned that the women of that town sabotaged the well because those long walks were their only reprieve to socialize and get out of the house. Military units search for schools to build, wells to dig and enemies to kill, without often realizing that their own efforts ‘pour back into itself’ and create some of the very problems they are seeking to solve. The popular military expression of ‘a self-licking ice cream cone’ works here and illuminates Klein bottle properties.
Above, the ‘air-land-sea’ and ‘cyber-space & SOF’ dynamic of a single Möbius strip is paired in the same non-orientable topology of a Klein bottle with another Möbius strip security metaphoric device. Here, the ‘spectrum of warfare’ original Newtonian styled construct is reimagined in a Möbius fashion where activities below the threshold for open warfare interacts with declared or undeclared hostilities. In earlier metaphoric efforts, the original ‘spectrum of warfare’ optical, visible light spectrum entertained a ‘gray zone’ which also used the metaphoric device of visualization, cones and rods of human perception to explain complex security contexts. The Möbius strip changes that, while the Klein bottle depicted above and in greater detail below takes that even further.
The above figure must be conceptualized not in a Newtonian stylization where spheres and arrows interact in linear-causal, formulaic, and mechanistic fashion, but reimagined through the non-orientable topology of a Klein bottle. The doubling of a Möbius strip may be useful as a metaphoric device so that, as depicted above, the two strips can introduce multiple complex security phenomena that are otherwise oversimplified in Newtonian military doctrine such as the cube example from Joint Planning Publication 5–0. Above, the tensions between the traditional physical domains of air-land-sea and corresponding primary military services and geographically oriented commands that focus upon these interact with the cyberspace, space, and special operations ‘domains/entities/effects’ that are different, yet increasingly significant in explaining contemporary security challenges. In parallel depiction, a second Möbius strip functions within this Klein bottle where cooperation, competition, deterrence, and recognized hostilities (organized violence) moves back and forth, reconceptualizing all the above security concepts into ‘one topological surface’, stretched and morphed so that it can pour back into itself; security affairs across humanity need not be arrangedexclusively in a flattened ‘Mario Bros’ imagined world bound in Newtonian certitude.
With Klein bottles, “the outside world has been turned inside’, in that the paradoxical, non-linear, and emergent phenomena of complex reality to include security affairs is no longer over-simplified into categorization buckets such as how the military currently deconstructs complex warfare objectively into reductionist models prolific across modern doctrine and training.
Klein bottles, as non-orientable surfaces, lack edges or bounds. The bottle dissolves the distinction between inside and outside, as everything that contains the Klein bottle is also contained by it; a paradox but also a fascinating way to incorporate complexity theory into military thinking, if only to disrupt and perhaps dislodge the dominance of Newtonian rationale on war. There are many ways to play with these ideas that ‘the Klein bottle is in the world, but, at the same time, the world resides within the Klein bottle’ where the traditional military domains of ‘air-land-sea’ are themselves contained within the vastness of space, while cyberspace is contained within each of these physical (and in space’s consideration, ‘supra-physical’) domains… yet warfare can exercise entirely inside of cyberspace while directly impacting the physical reality of humanity in profound, even devastating ways that arguably compare to the horrors of many physical acts of warfare.
Metaphorically, Klein bottles might better adapt to the paradoxical experience of time and space, history and social construction of reality, and how humans live both in an objective, tangible physical reality while also existing in a shared, conceptualized and highly subjective ‘second order of complexity’ that denotes human existence. Donas, in adapting Klein bottles to a political science and psychoanalytical approach explains:
The Klein Bottle/Surface has no in-and-out frontier, it is shaped as a tridimensional moving field, it flows within itself in a rhythm of pulses. It entangles the individual with the multiple, the width of its borders reaches out toward alterity, but it returns to itself in a never-ending reentry loop. We can also use it as a representation of time and history, the movement of a surface toward becoming in the present that emerges from the landmarks of what has been lived, only to flow again and reenter in the timeline of the past.
Complex warfare, articulated to military forces using non-orientable objects as metaphoric devices could offer far more latitude in how complexity theory, systems theory, social paradigm theory and postmodern concepts that are significant yet largely discounted in modern military doctrine, theory, education, and practice might be assimilated into how and why security forces understand conflict in novel, unrealized ways. This does require significant revision, reframing and retirement of nearly all modern military doctrine, complete with reconceptualization of the primary military theories, models, methodologies and the very terminology that largely converge toward a shared Newtonian fetishization of understanding complex warfare.
This additional illustration shows a Mobius-like iterative loop between the traditional physical domains of nation-state warfare with the foreign policy and diplomacy options where recognized, formal wars are declared, executed, and resolved. From the 17th Century through much of the 20th Century, arguably this dynamic represents a systemic pattern (advocates of Carl Von Clausewitz subscribe to such a natural order of reality and warfare therein).
While competition, deterrence and diplomacy coincide with the Westphalian order of warfare between nations and predates the 17th Century in many earlier yet similar forms, this iterative cycle illustrated here takes on new prominence from post-1945 through the collapse of the Berlin Wall and the end of the Soviet Union. The Cold War, as a bipolar nuclear superpower balancing act, would best illustrate a Mobius loop between these two topological regions where limited conflicts, proxy wars, and other forms of competition, deterrence and diplomacy prevented any large-scale conflict as well as nuclear escalation. With the 1990s acting as a period of downsizing of military forces, a refocus on humanitarian and peacekeeping efforts, and a global reordering with a unipolar single nuclear superpower, there were no rival nations for the United States to extend the Cold War construct with. This coincided with the arrival of cyberspace, the rise of the Information Age and an increasingly hyperconnected, interactive and socially dynamic global commons. Space would slowly see the rise of commercial access and influence, with national space programs becoming cooperative, collaborative, but also more dependent upon commercial entities. Non-state actors would in the 1990s gain national ‘instrument of power’ equivalent abilities, even if temporary, where entities such as drug and criminal cartels, proxy state actors and terrorist groups as well as individual super-enabled persons could threaten or rival a national IOP capability/effect in ways never before seen. Computer hackers represent a prominent example of this, with single operators as ‘lone wolves’ increasingly able to act with devastating consequences.
This last graphic takes many of the concepts offered in parts 1–5 of this series and generates a working example model for how military campaign design, targeting relationships, and strategic planning might be re-conceptualized using Möbius strips, Klein bottles, and complexity theory instead of a strictly linear-causal, mechanistic and systematic form that exemplifies how Newtonian styled military doctrine and planning currently is depicted and understood.
