Regular Polygons

I have been wondering about spaces used in combat sports, almost all of which are formed by regular polygons: from the circle of sumo, to the square of boxing, to the octagon of mixed martial arts.

Regular polygons: circle, square, octagon

The circle is known in many cultures as the perfect shape or form: all lines of force radiate perfectly from the centre of the circle to its perimeter. In gladiatorial sports contested within a circle (which also include freestyle and Greco-Roman wrestling and various forms of animal combat) motion is continually assured by the degrees of freedom that this geometrical form allows; even when against the perimeter boundary there is plenty of room to maneuver.

The square competition area in organized boxing has existed at least since the institution of the London Prize Ring rules in 1743. Why the square (ironically referred to as a ring) instead of the circle for boxing? Is it because of the strong linear references characteristic of architectural forms in the modern age?

(As an aside, the circular area of competition in Greco-Roman and freestyle wrestling is inscribed on a square mat, which is then rolled up into a cylindrical form for storage. Similarly, the circular sumo dohyo is inscribed on a raised square platform, which presumably is meant to honour the historical traditions of the sport while fitting into the rational rectilinear spaces of modern Japanese arenas. Was this always the case for spectatorship of sumo?)

With the square, we cannot make the same claims to maneuverability mentioned earlier, despite its perfect symmetry on all axes that bisect the centre point. Lines of force are fairly constrained along horizontal and vertical dimensions, which leaves dead spots of motion in the corners — the last thing a boxer wants to do is get trapped in a corner with no line of flight to escape. This is not to say there is a dead spot in action; to the contrary, the constraint on motion often yields to a violent increase in action.

As for the octagon of mixed martial arts, it seems to exist primarily as a form of differentiation from other combat sports that serves an important role in the brand strategy of the Ultimate Fighting Championship organization. But beyond this pragmatic association, the octagon seems to offer us, by way of superficial observation, a hybrid of the two spaces mentioned already. Geometrically, this makes sense to us: a circle is nothing more than a regular polygon with an infinite number of sides, so the fact that the octagon doubles the number of sides of the square suggests that it will be more like the circle in the way it structures movement possibilities within.

Interior AnglesWe notice the difference particularly in the corners of each polygon: the interior angle of a boxing ring (black line) measures 90 degrees, while the interior angle of a mixed martial arts octagon (red line) measures 135 degrees, giving combatants in the latter space 45 more degrees of freedom to maneuver should they become trapped in a corner. What does this mean in terms of practical consequences? It suggests a competition with more mobility, more movement, and more action.

But we must qualify this last term: what do we mean by "action"?

In the glory days of prizefight boxing last century, action often meant a flurry of punch combinations being rained down on a boxer trapped against the ropes or in the corner; large, lumbering, powerful boxers, relics of the industrial age. Action today, by contrast, is far more about speed, with the goal being to sacrifice as little of the earlier gains made in power as possible. Thus, the newfound mobility offered by the octagon creates new kinds of strategic challenges as part of the action. How does one engage an opponent without sacrificing too much power in the more open space at the middle area of the octagon, or when retreat by the opponent is more easily possible, particularly in a lateral sense?

One-Eyed, One-Armed

Deleuze and Guattari, A Thousand Plateaus, p.424 (boldface emphasis added):

The State apparatus is thus animated by a curious rhythm, which is first of all a great mystery: that of the Binder-Gods or magic emperors, One-Eyed men emitting from their single eye signs that capture, tie knots at a distance. The jurist-kings, on the other hand, are One-Armed men who raise their single arm as an element of right and technology, the law and the tool. … This is not to say that one has exclusive right to signs, the other to tools. The fearsome emperor is already the master of large-scale works; the wise king takes up and transforms the entire regime of signs. What it means is that the combination, signs-tools, constitutes the differential trait of political sovereignty, or the complementarity of the State.

Courtesy of CBS

Can we not suggest that the two poles of sovereignty as they constitute the sporting Empire might be the sports-media production complex and the world anti-doping authorities? The first symbolically represented by the eye of CBS and the second by the juridical arm of Dick Pound?

Dick Pound

Spectacle and the cosmos of sign-constellations. Surveillance and the endocolonization of the body athletic. The first already the master of large scale works in terms of a massive, "networked" televisual production and distribution system rivaling the great aqueducts of Ancient Rome. The second taking up and transforming the regime of signs, for example by substituting the press conference for the podium ceremony as in the case of Beckie Scott, who was awarded a gold medal two years after the fact. One, an economy dependent on speed; the other, a nexus of power that seeks to curtail or limit speed.

Now, the interior of the running body becomes the smooth space within which this athletic war machine operates. What new methods, techniques, modalities, substances, agents might facilitate the quest for speed? The nomadic running-warrior continually seeks to find out and, consequently, its body must be striated, visioned, measured and administered by the State. In concert with the Newtonian physics that describe the earlier regime of disciplinary technologies, we now find biological, chemical and information systems subsumed under a contemporary regime of semiotic control: Nielsen ratings, steroid structures, world records, Q-scores, urine metabolites and markers, sponsorship contracts, masking agents, metres per second squared; all related on the one hand to global flows of capital and on the other to protein structures in the athletic body.

As an aside, the traditional nation-state plays a subordinated role in both of these poles of sovereignty. The media companies and their corporate sponsors are increasingly subject to the tides of global commerce and transnational capital, while becoming less beholden to national boundaries and laws. And WADA, which is a direct descendant of the International Olympic Committee, is today only tangentially accountable to its individual member nation-states. What complicates matters, however, is that most of the high-performance sport that attracts the interest of WADA (and to a lesser extent the sport-media complex) is still contested under the paradigm of nationalism.

Introduction to Rhythmanalysis

The following constitutes the conclusion of a paper I just presented in Copenhagen:

A central concern in Bale's analysis of high performance running is the space-time compression that occurs as technologized runners traverse standard spatial distances in ever-shorter temporal quantities. But we must draw a distinction between the imperatives of capital and those of the State (Deleuze & Guattari, ATP; Hardt & Negri, Empire). A world-class running athletes embodies a massive fixed capital investment that seeks maximal speed and the potential financial reward that entails, while the State seeks to maintain a perceived level of ethical integrity for its own spectacular purposes.

Bale's analysis refers to the acceleration of capital in its various forms and one of the ways in which the State seeks to control these bodies is by introducing a space-time dilation to offset the compression. The fully automated photo finish system essentially expands the final tenths of a second at the conclusion of a race so that the administrators may optically adjudicate the speeding bodies and determine a race victor. Similarly, where the wide space of the marathon creates permeability in the tight disciplinary enclosure normally understood with achievement sport, the State attempts to fortify the barriers between spectator and participant by using radio frequency transponder chips to compress the marathon sportscape.

Thus, the State, in the form of the International Association of Athletics Federations, is presented here as establishing countervailing impulses or rhythms of spatiotemporal compression or dilation in a controlling response to the unchecked immanence of high performance running bodies. Based in the tactile nature of networked electronic technologies this control may be described as panhaptic, which suggests that new tools are required to think beyond optical surveillance and conceptualize resistance to structures of authority, both within sporting cultures and in broader society.

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And I'd like to juxtapose this with a passage from Henri Lefebvre's Introduction to Rhythmanalysis (p.15, emphasis in original):

Everywhere where there is interaction between a place, a time, and an expenditure of energy, there is rhythm. Therefore:

a) repetition (of movements, gestures, action, situations, differences);

b) interferences of linear processes and cyclical processes;

c) birth, growth, peak, then decline and end.

Split Time

A reminder — With the introduction of RFID chips to the marathon sportscape, there is effected a doubling of time: the time measured by the master race clock (race time) and the database time recorded with the RFID device (chip time). While the IAAF recognizes chip timing as official in most cases, timing provided by a chip system is not accepted under any circumstances for the purposes of determining record performances. This makes the question of why the chip identity is so important even more crucial. Almost every technological innovation in sport is designed to enhance performance and/or improve archival measurement techniques, which cannot be said for the RFID chip, save for the (contentious) claim that it allows one to better measure personal best times.

No, this chip and its split, shadow time exists to striate a heretofore large, open smooth space — and to track objects through said space.

GVB and Holey Space

Deleuze and Guattari, A Thousand Plateaus, p.415:

Holey space itself communicates with smooth space and striated space. In effect, the machinic phylum or the metallic line passes through all of the assemblages: nothing is more deterritorialized than matter-movement. But it is not at all in the same way , and the two communications are not symmetrical. … Here, we would say that the phylum simultaneously has two different modes of liaison: it is always connected to nomad space, whereas it conjugates with sedentary space. On the side of the nomadic assemblages and war machines, it is a kind of rhizome, with its gaps, detours, subterranean passages, stems, openings, traits, holes, etc. On the other side, the sedentary assemblages and State apparatuses effect a capture of the phylum, put the traits of expression into a form or a code, make the holes resonate together, plug the lines of flight, subordinate the technological operation to the work model, impose upon the connections a whole regime of arborescent conjunctions.

While thus far I have suggested that Global Village Basketball constitutes a smooth space in contrast to the striated space of formal basketball governance, I have wondered several times to myself if in fact this project doesn't simply act as part of the apparatus of capture by a sporting Empire. Does the concept of "holey space" offer a way out of this conundrum? Doesn't GVB actually connect elements of the smooth (passages through cyberspace, non-choreographed performing bodies) with elements of the striated (fixed time frame, work model of score to unite all athletes)?

Unfortunately, in their discussion of space Deleuze and Guattari spend most of their efforts on the opposition between the smooth and the striated. While they acknowledge that these exist in admixture with one another, they don't discuss at any length how one changes to the other over time, or develop the idea of holey space to any great extent. But I will have to at least consider the possibility of GVB and holey space as facilitators of both connections and conjunctions in a sporting context.