Preliminary Problems in Constructing a Triolectic: Thoughts suggested following experiments in the use of “’pataposition” to render three-sided football in n-dimensional space.
The New Cross Triangle Psychogeographical Association (NXTPA), in collaboration with Strategic Optimism Football (SOF).
In the summer of 2015 CE, somewhere in a forest in Southern Lithuania, just a few miles from the exact geographical centre-point of Europe, a contingent of psychic workers undertook the construction of a triangular “supercollider” from the ’pataposition of three overlapping orthographic projections of the Kabbalist “Cube of Space”. Here they launched three simultaneous games of three-sided football into each other at high speed, the intense energies released in this “super-superposition” being sufficient to open up higher dimensional space, uncovering the deep triolectics at play within the science of exceptions. In doing so, the assembled situlogists successfully glimpsed the quantum hyperspace of psychogeographic gameplay, completing the first phase in what has been called the “Great Unworking”: Three-sided football’s attempt at the psychogeographical “unbinding” of Europe.
In 2012 CE the Luther Blissett Deptford League (LBDL) of three-sided football was established in London by former affiliates of the Workshop for Non-Linear Architecture (WNLA), commemorating the 50th anniversary of Asger Jorn’s preliminary codification of the game. At first the league had no players or teams, but slowly they began to drift in and, in late 2013, the addition of further players from the newly abolished University for Strategic Optimism (UfSO) enabled semi-regular fixtures to begin to take place. As a consequence of such regularity, the league gathered momentum, and, in summer 2014, it finally voted itself into existence, with players adopting a formalised structure of rules, teams, fixtures and the aggregation of results. The NXTPA’s delegate within Strategic Optimism Football (the team established from the auto-abolition of the UfSO) was one of two dissenting voices who opposed that decision, despite our own clear, if at the time inadvertent, culpability in facilitating this regularisation in the first place. Here we set out our reasoning for the first time.
Although we could not have known then how this formalisation would pan out, and were ultimately willing to cede to the experimental value it potentially unleashed, we now argue that the moment has come to introduce diversion. It is important, we propose, that even as the league propagates beyond the control of the psychogeographers whose dreams first animated it, it must cut lose from any attempts to rebind it once more into the binarisms of Euro-normativity. Encouraged by the early results from the Lithuanian experiments, we instead profess our intention to agitate in favour of the aforementioned Great Unworking.
Firstly, whilst not seeking to efface our own continuing active participation within the Luther Blissett Deptford League, we (super)position ourselves firmly against – but simultaneously both beyond and in complementary relation to it.
Lessons from Pinball
When discussing psychogeography and art in his Pour la forme (1959), Asger Jorn presents a diagram of a Galton Box, something like a pinball machine without the fun. Invented by the racist mathematician Sir Francis Galton, it demonstrates probabilistic distribution through use of a vertical board, spangled with multiple offset rows of pins, leading towards a number of gullies. Balls poured from the summit ricochet left and right, cascading through their pin labyrinth towards an eventual resting place in one of multiple conduits at the machine’s base. Despite – indeed through – the vagaries of chance, the collected balls will come to settle predictably, in a close approximation of a bell curve.
Jorn uses the Galton Box to argue that from pure chance arises pure predictability: the symmetry of the bell curve. From the perspective of probability, chance and determinism are thus shown to be two side of the same thing – apparently proving the validity of Hegel’s definition of chance, as taken up by Engels and then Breton. However, Jorn proposes that probability focuses too much on the abstracted outcome of chance as opposed to its experiential reality. Calculations of probability, which arise in and through the aggregation of results, focus only on ends and outcomes, in a manner hostile to genuinely experimental, unexpected and individuating events. It is not the perspective of each ball that concerns such calculations, merely the final distribution they give rise to. Indeed, in itself, no one ball’s path can be predicted, beyond a probability. The ball is a wave-function. Only when aggregated with the already measured fall of multiple other balls does its path become that of a particle, predictable.
In response, Jorn introduces a third pole to the dialectic. Opposed to the mono-perspectival science of probability (i.e. the synthesis of chance and determinism), which falsely universalises the position of the privileged European observer, he proposes something more akin to luck, which is a matter of superpositional, polyvariant perspectives. Considerations on whether an event is chance or necessity are tangential to whether it is lucky or unlucky, which is solely a matter of perspective: “unmeasured”, an event is at once both lucky and unlucky.
Here one finds the nascent form of what would become Jorn’s triolectics. Tangential to a dialectical contradiction of particular and universal, Jorn proposes another kind of universalism, a pataphyscial universalism – the equivalence of all particulars, in their particularity. Jorn’s slightly confusing augmentation of Marx’s method attempts, in short, to strip the teleology from dialectics by re-imagining the notion of superposition, beyond what Hegel had correctly identified as Euclid’s flawed formulation. Because for Jorn all conceptual syntheses can only be conceived of in opposition to another, third, superpositional possibility, arising from another direction or dimension, the primary effect is to puncture the notion of self-cancelling closure, reintroducing multiple perspectives as the condition of an open, creative future. It is what he elsewhere called the ‘transformative morphology of the unique’.[i]
Jorn argued that:
The social moralism of Surrealism transformed, so to speak, all of its faithful adherents into bell curves, because it had not understood what is important is […] the play of transmissions’.[ii]
We argue that in the form of a regularised, competitive league, the LBDL exhibits a stunning correlation with the Galton Box, as we shall now explain.
The Quantum Hexagram – Three-Sided Football as Micro, Meso and Macro
The six points of the unicursal hexagram signify the superposition of the micro, meso and macro scales. Against the dogmatists of quantum mechanics, Jorn – true to his hermetic training – similarly argued that principles operative on the suprasensible sub-atomic level, in fact self-replicate across all scales of reality. This is something, we hold, that our recent experiments in three-sided football strongly support.
We propose that three-sided football itself can be understood on multiple levels, the three primary ones, for our purposes here, being as follows:
Microcosm – the moment, or decision (the superpositional totality of an array of quantum triolectics in the body of the decider).
Mesocosm – the game, or situation (the superpositional totality of an array of triolectical decisions or moments on the field of play).
Macrocosm – The meta-game, or situlogy (the superpositional totality of all possible games upon the social field).
Each of these levels is fractal inherent within the others; a collapse or blockage in one can, we are proposing, quickly lead to a collapse or blockage in the others. This is what we will now explain.
Firstly, on the level of the moment:
In three-sided football, players are constantly faced with the reality of superposition at the level of gameplay. A player from team f perceives players from teams b and l – according to the theory of complementarity – as existing in a state of superposition, being simultaneously both opposition and ally (just as, indeed, player b does players l and f, and, player l does players f and b).
However, in making a pass, shot or manoeuvre – in short, a decision – player f potentially conducts an act of measurement, collapsing the superposition and rendering players b and l momentarily into the Aristotlean logic of definitively being either an opponent or an ally in that instant (in fact, some, such as D3FC have argued that even this very act of decision itself is nothing more than an artefact of the quantum nature of consciousness, which at its heart is structured around the similarly triadic relation of quantum chromodynamics).
The real consequence of such moments, however, cannot be known other than from the outside. This is to say that until such potential measurements are abstracted and themselves measured, at the higher level of the game, they remain superpositional. To put it simply, until the game is announced to be over, it remains open in its entirety, all remains in play, the consequences of each decision are not yet definitive, their full permutations are as yet unknowable and thus no true measurement has yet occurred. The game is like Schrödinger’s box, with the fate the cat with in it as yet undefined. Team f cannot say team b or l was definitively an ally or enemy other than from a perspective beyond the play of trajectories, i.e. only from the perspective in which all the balls have definitively come to rest – that is to say, when viewed from the outside as a complete game in its entirety.
As Jorn understood, one cannot at the same time look at what one looks with. Thus measurement or closure can only be conducted at a further level of abstraction, the path of any individual ball in Galton’s Box remains unknowable from its own perspective, only from the perspective of the outside observer, looking at the board as a whole, does it become predictable. Thus we are deferred from the microcosm to the mesocosm.
However, this same process in fact actually repeats on the meso level. If the game can be seen as the totality of each of the aforementioned microcosmic moments, each and every game, can itself likewise be seen as just part of the totality of the game of three-sided football as a whole, upon the social field.
Likewise, just as each particular game constitutes a myriad of moments that are superpositional until closed in measurement by ending the particular game of which they are part, so too, all such games are also superpositional until they are themselves measured, and thus ended. This measurement must, for the reasons mentioned above, likewise take place upon a higher level, which is to say, simply, that the full permutations and possibilities of any particular game themselves remain unknown and unknowable until such as time as the game itself is measured from the perspective of the totality of all such games.
The consequence of this is that, since this totality cannot be definitively ended while any such game remains in play, all such games, and the moments within them, cannot likewise be measured. All remains in a state of superposition. This is not an argument against abstraction per se; abstraction is the tool through which we can approach the totality. The mistake lies in thinking we can put it to bed.
However, it is also here is where the problem of the league system intervenes. As we have just seen, absent of definitive measurement, the meta-game of three-sided football in its totality – that is to say as the totality of all its possible games – is superpositional, open and in dynamic flux. This is because, as stated, the superpositional nature of each level is a consequence of all the others. Put in other words, the free condition of each is the free condition of all.
It is crucial to the superpositional nature of all three levels therefore, that games remain open and unmeasured at each of these three scales. If one makes a definitive measurement of one level, the superpositional nature of the others similarly collapses. What we are suggesting is that, for the successful implementation of triolectics upon the social scale, it is crucial that it remains superpositional on all levels. Once one introduces definitive measurement at any level, one produces the collapse into the familiar binarisms of Euro-normative thought.
Here is the rub. In a regularised league, within which one measures, records and aggregates results over time, one abstracts from the superposition between the levels of mesocosm and macrocosm, interjecting a form of measurement, but also thus a form of entropy. In definitively measuring a particular game – by granting it a consequential victory or defeat (as opposed to a merely nominal one, in which such distinctions are ultimately meaningless) – one introduces a definitive binary. This triggers a chain reaction bringing about the collapse of triolectical superpositions across all levels.
The binary of victory/defeat in turn correlates with a binary league position between the two poles of “top” and “bottom”, this then induces a form of false universality – a spectacular totality, if you will – abstracted from the particularity of the games one measures. This in turn definitively collapses the game’s superpositional nature at the level of the individual game’s superpositional passes, feints and tactical reversals, but also at the level of the game in its totality. The false universalism of the league comes to stand in for the absolute of three-sided football in its totality. It thus becomes abstracted from what can be called the experiment proper – the domain of the absolute – into a form of fixed, generalisable law, from which one in turn abstracts a universal, homogenous image of the game.
As Jorn noted in his introduction to triolectics (The Natural Order, 1962), any experiment in which the conditions are definitively regularised, and, as a consequence appear known in advance, can no longer accurately be called an experiment; its result becomes as predictable as the strictures of “Soviet” “Diamat” or the capitalist mantra “there is no alternative” . On this basis we argue that the current league system is thus fundamentally at odds with the very basis of triolectics itself.
What the league forgets that what is important is not the ‘final levelling out’, in Jorn’s words, but ‘the play of transmissions’. What is important is the superposition, not the measurement. Each game is a Galton Box, and the ball striking each pin is a pass. Until a final result is definitively measured, i.e. the ball comes to a rest at the end of the board, it splits both ways; it remains in a superpositional state – like the famous “double-slit” experiment, although this might better be understood as a “triple-slit experiment” – it remains open and in experimental flux. In measuring the result of a game for the purpose of league position, the game is rendered no longer as the play of transmissions, but rather only as the static ball at the bottom of its run, settled definitively into one of the gullies: it becomes a result, and thus transforms all its faithful adherents, in the end, into bell curves.
In aggregating such results, each game – rather than remaining in a state of superposition, in a state of play with all others – becomes on another, higher level, settled into a final resting place, so that the league itself functions precisely as the bell curve Jorn describes, ultimately becoming predictable. This is, indeed, something that has been noted by many players over the course of the league’s first season.
Naturally, there will be outlying games whose outlandish unfolding lands them far from the centre of the curve – just as there are outlying balls in Galton’s distribution. However, when aggregated, bundled with all the others as part of the league’s false universal, they remain equally predictable, and equally implicated in the collapse of triolectical superposition into the binary structure of “either-or” that defines traditional, two-sided, Aristotelian Association Football.
Binarism by the Backdoor
As stated, the consequences of this are not merely theoretical but have been consistently observed in practice. The direct result of a collapse into the renewed binarisms of either-or measurement (and an aggregation of results), is similarly a direct renewal of all those attendant binarisms that emerge from the binary nature of two-sided football.
Hence, with the introduction of the regularised and measured league system in 2014-15 CE, we have undoubtedly witnessed a renewal of the defeat or victory mentality, leading to heightened competitiveness. As a further direct consequence, we have also seen the return to some of the predictability offered by scientific method. Games have quite obviously begun to drift form what was ultimately experimental about them in Jorn’s understanding, becoming less interesting as a consequence. The binarisms of competition have invariably produced a binarism of tactics and gameplay, which has repeatedly led to two teams aligning against the third for the totality of a particular game (with an eye to ultimate league position), removing the self-organising dynamism of the triolectic function within the game itself, in which alliances shift regularly with each goal conceded. This leads to players abstracting organisational decisions to a higher power beyond themselves, even, in some cases, to demands for a referee’s intervention, and thus, a return of alienation. Therefore we see games tending towards a 10 vs 5 pattern, and as a consequence, a return to two-sided football by the back door. Binarisms reproduce binarism.
Furthermore, the collapse of the triolectic into duality has also seen a reversion to binaries on the higher social scale, what was above called the macrocosm. For instance, the game has begun to stratify once more along a binary of “ability” – between “weaker” and “stronger” players, “weaker” and “stronger” teams. In addition, and perhaps more urgently, it has also resulted in a reintroduction of the pronounced gender binaries of conventional two-sided football. It is certainly no coincidence that women players were, whilst in still in a minority, notable, frequent and valuable participants in the LBDL prior to its constitution as a system of aggregated measurement. Following the introduction of this system, the participation of women has observably been reduced to zero, whilst conversely, in other, irregular games, the gender composition has remained more diverse.
Both of these renewed binarisms also further add to the game’s predictability – producing ever more smooth bell curves for proponents of the league system to wave at one another. This shows us that a definitive system – one based in and upon measurement – tends not only towards definitive outcomes and forms, but ultimately towards specialisation. A kind of “priest class” emerges, those better able to master the intricacies of the game – owing to their specialist attention to its predictability and replicable nature. This leads in turn to a hierarchical organisation of the game, between those who pursue the “true faith”, and those heretics who dissent, or those who are otherwise excluded. Further, it reproduces a spatiotemporal specialisation, in which the game becomes concentrated within specific spatiotemporal enclaves. Specialisation flattens the multi-dimensional triolectic into the binary two-dimensionality of a spectacle.
It is no coincidence that the word league derives from an Ancient Roman system of measurement – originally the “leuga gallica” – developed as a tool of imperialist domination during the conquest and occupation of Gaul by the Roman Empire. Appropriating the Gauls’ more situlogical definition – which simply suggested the distance covered by walking for a period of time – the Romans standardised the measure. From these origins, the “league” was thus absorbed into what Jorn’s idiosyncratic psychogeography describes as the “Latin” mindset, with its inclination to unify and dominate.
Hence the particular is once again subsumed to a false universal, thus occluding it from a higher realisation in the equivalence of the absolute. One is cut short in the abstract, without pushing on, to the concrete. Results are bundled into fasci, with binary values replicated on all scales. Triolectical superposition collapses from the level of the individual pass, right up to the global totality of three-sided football as a whole. In short, this is a problem of accumulation. The accumulation of results, without some effective system of redistribution – in this instance the naturally redistributive triolectical relation – leads ultimately to the formation of a hierarchy, and thus, the reinstitution of the binarist and stratified relations of class society by the back door. It does so, just as did surely as the accumulation of grain in ancient Mesopotamia, or the accumulation of capital in 18th Century England.
Binary logic was favoured by philsophers from Aristotle onwards, precisely because it is a primary method of exclusion. A cannot be B, 0 cannot be 1. In triolectics A can also be B, 0 can also be 1. As a result of the reversion to binarism brought about by such accumulated measurement, three-sided football has also become exclusionary, across the three trimensions of revolutionary praxis: class, space and time.
As the demands of competition produce regularised teams, such games increasingly tend to exclude on the nature of class: by ability, gender, or number of players per team – hence total number of participants. Secondly, such games exclude on the basis of space: as games are no longer superpositional, they become geographically specific, those not able to access the vicinity of the “definitive” game are thus excluded – we might perhaps argue that this an extension of Eurocentrism, something echoed in the limitations of the World Cup format, when run along such binarist lines. Thirdly, games exclude on the basis of time: a collapse in superposition similarly reduces those who can contribute or participate to temporal vicinity, excluding those ‘too old’ or ‘too young’, the dead or those yet to be born. Again the effect is a homogenising exclusion, which places an abstract totality in place of the absolute.
Thus we reiterate our position against the league, as currently constituted, as a bundling of measurements. However, if we are not to replicate the very structures we have just identified, it is insufficient to simply oppose the league, to withdraw and just set ourselves against it. This would merely be to replicate the very binarism with which we accuse it. Instead, our position must become a superposition, we must also stand within it, beyond it, and in complementary relation to it.
To remain within the league structure, we develop the following medium term proposition: the remodelling of the results system itself into a triolectic. As a result, the binary linearity of the table would be overcome in a triangular relation of three forces, each simultaneously displacing the next in a self-organising triolectical dynamism. Following discussions with FIASCo and D3FC, we declare our intention to agitate in favour of a supplementary scoring system that equally rewards three complementary modes of game play. Thus, for example, a “blue” victory might be awarded for the team that concedes the least, as is currently the case, but at the same time, a “red” victory might be given to the team who scores the most, with a third “yellow” victory granted to the team for who there exists the smallest gap between the two former figures. All three conditions would thus be complementary, a team excelling at blue and red gameplay, would necessarily fail dismally on the yellow measure. Likewise, a team who pursued a strategy of a yellow and red victory, would also, necessarily, be defeated on the blue scale. Or perhaps these could operate, after Jorn, as measures of a teams relative preponderance to “unity”, “equivalence” and “variety”? Although it is likely that such measures would have unintended consequences – such as the specialisation of teams according to a preference for attack or defence – the permutations of such a system remain something to be more fully investigated through experimental means. Whilst we would, of course, have to await such practical results, such a system would, theoretically, reintroduce triolectics at the level of the league, but could not, still, be a substitute for a triolectics of the absolute however.
To rediscover a triolectics of the absolute requires we go beyond the league, but to remain in a complementary relation to it. As such this requires a further proposition. If the league system constitutes the interjection of binary measurement between the mesocosm and macrocosm, and thus in effect occluding the macrocosm from the perspective of all lesser scales – blocking an ascension to the concrete absolute with an abstract universal – we suggest that this might potentially be counteracted by superinducing another scale beyond the macrocosm, thus preventing measurement from reaching a final, definitive end, whilst actively mitigating against the tendency of accumulation.
In such a situation therefore, even if the league comes to dominate a chain of causality within the meta-game, this meta-game itself can be made simply one more superpositional equivalence within a further, higher level – that of the ’pata-game. Thus such a ’pata-game would bear the same relation to the meta-game, as the meta-game bears to each particular game. It would be the totality of all possible and impossible games of three-sided football. Thus, rather than seeking to dialectically supersede the league, it would instead suggest the supplementation of a complementary league, where what is valued is not the measurement of definitive accumulated results, but instead the absolute equivalence of each particular game, precisely in its particularity.
As can be seen from the above triagram, superinducing another, complementary, triolectic, supplementary to the first, results in the structure Microcosm-Macrocosm-’Patacosm and the structure Microcosm-Mesocosm-’Patacosm forming in a complementary and thus superpositional relation to one another. Not only does this facilitate the tripass of the binarist blockage activated by the measured league system, it likewise produces a supplementary “league” in which each game would, at least in theory be truly be superpositional upon all others – on all levels, macro, meso and micro. It becomes an imaginary solution in and for itself; games, fixtures, teams, venues and variations, all would become irregular, particular, complementary. Such a proposition rejects the unification of the game into a transcendental abstract in favour of a proliferation of potential, necessary and impossible varieties, of potential, necessary and impossible histories and, potential, necessary and impossible outcomes.
To this end we announce the formation of the “Great Unworking”, an anti-league of “unbinding”, whose aim must be to dispel the psychogeography of “Europe” as a binarist concept, that is to say structured upon inside/outside and the countless other dualisms emergent from the Cartesian-Capitalist worldview. It will seek to do so by applying triolectics at key pressure points upon the network of non-Euclidean leylines that structure the European field, both psychically and geographically. The meta-field of play for this task was cast between the three poles of Alytus, Silkeborg and Vienna, the ’pata-field is only just beginning to make itself known.
The implementation of the league experiment has not been a failure. It has enabled us to discover that binarism arises in measurement, as a form of exclusion, and that it is remarkably robust at self-replicating across multiple scales of reality. This is simultaneously worrying and encouraging: if the binary is so successful at self-replicating and expanding, might not the triolectic also be likewise? Might not the successful implementation of triolectics across multiple scales produce larger, self-replicating effects across myriad arenas as yet only dimly imagined? This question constitutes the terrain of the experiment with which we are now ultimately concerned.
Tae Ateh – Strategic Optimism Football (SOF)
Luther Blissett – The New Cross Triangle Psychogeographical Association (NXTPA)
Luther Blissett – The Academy of Practical Triolectics and Xenotopian Navigation (APTXN)
Luther Blissett – The Ex-Psychogeographers’ Nostalgia Therapy Alliance (XPNTA)
Luther Blissett – The Exarchia Square Triangle (North) Psychogeographical Association (XTNPA)
Ernest Hope – Association Psicogeografica Bucharesti (APB)
Karen Karnak – The International Federation of Independent Times (IFIT)
[i] Asger Jorn and Fabian Tompsett, Open Creation and Its Enemies: With Originality and Magnitude (on the System of Isou) (London: Unpopular Books, 1994), 32.
[ii] Jorn, Concerning Form (Silkeborg: Museum Jorn, 2012), 117.