This is the second in a series of extracts from Michel Serres: Figures of Thought that I will be posting in the run-up to the book’s publication around April 2020. The archive of all the extracts will be accessible here.
Serres’ algorithmic universal
In addition to the sharp contrast between Cartesian analysis and Leibnizian combination, there is also an illuminating set of differences between Cartesian and Leibnizian universals. We saw above that the Cartesian universal, along with that of the Classical age it epitomises, assumes that individual phenomena are instantiations of general, universal laws under which they can be losslessly subsumed and in terms of which alone they can be comprehended. The passage from the local to the universal is therefore, for the Cartesian, relatively straightforward: one must simply find and declare these laws, as illustrated in the case of the axioms of geometry. It will by now not come as a surprise to learn that Serres does not simply refute this Cartesian universal but opposes it by generalising it, re-framing it as one local variant or model of a broader, more complex structure.[1]
Whereas Descartes is a ‘monist’ when it comes to mathematical models, deriving his notion of the universal from the discipline of geometry alone and concomitantly considering geometry to be ‘the pole of the mathematical universe’ (SL 219).[2] Leibniz, by contrast, is a ‘pluralist’ (SL 230) who resists the umbilical approach of privileging any single model of mathematics over all others. Whereas Descartes’ strong adherence to a single model leads to dogmatism, the enormous plurality of possible relations between different models helps Leibniz to do justice to the infinite differentiation of the real: ‘to each labyrinth its own Ariadne’s thread’ (SL 119-20).[3]
The Leibnizian approach also has a way of relating the local to the global, but it is not through subsuming local phenomena under universal, static laws. Leibniz, and Serres after him, approach the universal through, and in, the singular. In order to understand this account of the universal we need to consider the algorithmic geometry that Serres contrasts to Descartes’ geometric paradigm. Algorithm occupies an important place in Serres’ thought. It plays a role not dissimilar to the ‘structure’ of Le Système, but acts less as a transcendental condition of isomorphism and more as a procedural operator that generates local instances of order without any necessary sense of a pre-existing grand unity.
In a further instance of ‘opposing by generalising’, Serres introduces the motif of algorithm by pluralising the origins of geometry. The story is most clearly told in Serres’ third book of foundations: Les Origines de la géométrie (1993), a title translated into English simply as Geometry. His main historical contention is that geometry in fact has two origins, one well known in ancient Greece originating with Thales and developing through Pythagoras, Euclid and Archimedes, and a more ancient, less well known origin in ancient Egypt and Babylon. These two origins of geometry provide two very different methods.
The Greek tradition of geometry, it will be remembered from the discussion of Descartes above, is declarative in its method. The method of algorithmic thought, by contrast, is procedural. For long centuries, in the Greek legacy algorithmic thought was obscured and eventually forgotten behind ‘the gigantic Greek construction’ of Euclidean geometry (EPF 223, 232-3; see also G 241/OG 136), until in the seventeenth century Pascal and Leibniz rekindled interest in this alternative way of reasoning with their calculus, Leibniz’s On the Combinatorial Art, harmonic triangle and invention of binary code, and Pascal’s triangle, calculating machines pioneered by both Pascal and Leibniz(EPF 229, see also PP 75). What all these have in common is that, rather than demonstrating from axioms, they calculate—or perform series of operations on—inputs in order to transform them into outputs or results. Serres describes this rediscovery of the procedural method, long buried under the Greek origin of geometry, in rapturous terms:
in this empty and new space, the entire classical age of the seventeenth century suddenly bursts forth and joyously leaps about. Like Pascal and others, Leibniz discovers America, I mean a new world in which, unlike the traditional one, everything is to be seen, found, constructed and populated, without institutional objects, without already occupied niches defended tooth and nail (G 136)
dans cet espace vide et neuf, tout l’âge classique fait irruption et gambade joyeusement. il Comme Pascal et d’autres, Leibniz découvre l’Amérique, je veux dire, un nouveau monde où, à la différence du traditionnel, tout est à voir, trouver, construire et peupler, sans obstacles institutionnels, sans niches déjà occupées défendues becs et ongles (OG 242)
From this point on, the two mathematics are locked in a bitter battle. On the one side geometry—pure, deductive, dealing in demonstrations—mocks the unworthy, everyday calculations of algorithmic thought. From the Greeks to Descartes , ‘the geometers constantly scorn these practices that are barely good enough for merchants and that, in the Middle Ages, were called logistics and algorism’ (EPF 232).[4] Leaving calculation to the guilds, geometry demonstrates from its lofty, abstract seat of superiority. On the other side, Pascal and Leibniz laud ‘local and rapid, subtle’ algorithms over ‘deductive, abstract and stiff’ demonstrations (EPF 232). For the declarative method, light is that which immediately brings absolute clarity. For the procedural method, the distinguishing quality of light is that it moves at great speed (PP 46; Pan 84-5; Ram 185; Her 86).
The final chapter in the story of algorithmic and geometric thinking sees the algorithm ‘fully triumphant’ (EPF 233) in the recent emergence, blossoming and dominance of the computer age. In 1936 Alan Turing invented the concept of a machine for simulating algorithms. Its input is a paper or cardboard strip of potentially limitless length, divided into cells each of which can either be blank or contain one symbol (for instance: 0 or 1). The machine can perform operations on the cells, such as replacing a blank cell with a 0 or a 1, or moving one cell to the left or right. Turing’s machine precipitated what Serres calls the ‘information revolution’ leading to the modern computer. This revolution is as significant for Serres’ thought as the Bourbakian formalisation of mathematics, such that in a 2003 interview with Peter Hallward he states ‘I am a child of Bourbaki and Turing’ (S&H 230). In the age of computers, long-exiled algorithmic thinking returns in triumph and ‘occupies the place and even threatens the abstract mathematics that came from the Greeks’ (Her 86).[5]
Serres’ account of the origins of geometry does not reject or even deconstruct the Platonic logos and the related Cartesian demand that knowledge be certain; it opposes it by generalising it. The Western tradition, he argues in L’Hermaphrodite, has laboured for two millennia under two related but distinct logoi. There is the Greek geometric logos, ‘formed by abstract and theoretical mathematics, deduced from principles and sculpted by non-contradiction into an axiomatic pyramid’ (Her 85).[6] The second logos dominant in Western history is of Judeo-Christian origin, ‘formed by Solomon’s principle, revisited at the beginning of John’s Gospel: nothing new under the sun; in the beginning were the Light and the Word’ (Her 85).[7] The problem with both these logoi, as far as Serres is concerned, is that they exclude all that is not in conformity with their axioms and principles, with their Light and Word. What algorithms offer us is a mathematics and a logos that are ‘more supple, more gluey [agglutinants] and positive’, proceeding not by division and exclusion but by federation and combination (Her 85).
Read in the context of Serres’ third, algorithmic logos, Derrida’s own critique of the Western logos in Of Grammatology and elsewhere appears as umbilical. Like Descartes, Derrida mistakes the species for the genus: he takes one possible logos (in fact he rolls the geometric and Judeo-Christian logoi into one), considers it as exhaustive of all possible logoi and, on that basis, proceeds to deconstruct it. Serres, by contrast, ‘opposes or generalises’ the Platonic logos by setting it in the context of an older, faster, subtler, more productive algorithmic logos. Where Derrida deconstructs, Serres opposes by generalising.
The local and the global
Finally in this chapter, Serres’ algorithmic approach also yields a new understanding of the relationship between the local and the global, the singular and the universal. Indeed, Serres affirms that an attempt to reconcile the universal and the singular has ‘always provided the horizon for my own work’ (S&H 230). One of the pioneers in this area is, once more, Leibniz, who ‘spent his entire life trying to unite a very abstract kind of work to a great monadic singularity, trying to grasp the latter by the former’ (S&H 230). Following the move we have seen performed a number of times already in this chapter, Serres’ approach to Descartes’ subsumption of particulars under universal laws is not to dismiss it out of hand but to oppose it by generalising it. Indeed, ‘[t]here is indeed a route from the local to the global, it is, precisely, the Cartesian route, with its chain of relations and proportions’, but ‘it is only one route among other possibilities’ (H5 71).[8]
Whereas declarative thought such as Descartes’s seeks to reach the global and the universal only in an axiomatic, determinate, and abstract way, Leibnizian procedural thought is incremental, possible, and concrete. Exploring each of these differences in turn will allow us to appreciate the unique contribution Serres’ thought can make to current debates. First, procedural thought approaches the global and the universal incrementally, not axiomatically. The philosophy of the prefix ‘pre-’ must establish its axioms from the outset, whereas the philosophy characterised by the prefix ‘pan-’ has freedom to move from example to example, gradually but inexorably establishing a larger and larger view of the complex relations linking all examples to each other. Procedural thought does not seek to accomplish everything in one abracadabresque axiomatic salto mortale, but advances little by little, ‘avails itself of procedures step by step and disperses itself into a thousand tiny problems’ (EPF 234).[9] The Cartesian method, by contrast, claims ‘to count on winning the whole war by a massive strategy of truth’ (SL 133) and, wanting everything, it risks finishing with nothing.
This does not prevent procedural thought from having universal scope, but it builds up its universality as it has need, as Serres illustrates with the example of jurisprudence:
Algorithmic reason can even evoke, in principle, a universal jurisprudence without any need for laws: indeed, it builds itself case by case and little by little, moving from the local the global, without invading the universe all at once, like law does.
la raison algorithmique peut même évoquer, en principe, une jurisprudence universelle sans qu’il soit besoin de lois : elle se construit en effet cas par cas et de proche en proche, en passant du local au global, sans envahir d’un coup l’univers comme le fait la loi. (EPF 218)
Our knowledge is neither that of gods nor of stones, Serres remarks, drawing attention to how the Cartesian two-speed gearbox of ‘truth’ and ‘falsehood’ and insistence on the criterion of certainty turn epistemology into what we might, following the pattern of onto-theology, call episto-theology. Leibniz, by contrast, locates human knowledge between the two extremes of this Cartesian radicalism, and his ars progrediendi (technique of moving forward) allows us to think in terms of degrees of truth and to advance gradually and progressively (SL 127-8). It can ‘supply useful tools’, even when it ‘offers no understanding of the whole object’ (EPF 230).[10] Purity and clarity are the terminus ad quem of Leibniz’s combinatory method; they are the terminus a quo of Descartes’ analysis.
Secondly, procedural thought is global and possible, not local and real. It is free of determinate content, and it prescribes operations, not magnitudes. The algorithmic order of the dictionary is practical, conventional and plural; the order of the declarative text is unitary, organised according to ‘temporal succession, announcement, suspense, movements of induction or deduction, the confrontation of dialogue’ (Pr xii-xiii).[11] The procedural text shows what it is possible to say, without saying anything in particular; the declarative text leaps from the local to the global by universalising its own approach in an umbilical gesture.
Thirdly, procedural thought is concrete, not abstract. It does not descend upon its object from the distant heights of universal axioms, but (as its etymology indicates) walks alongside it: ‘remaining close to its Latin root, the old French verb “procéder” signified walking one step at a time, but eventually designated an action and the method or “procedure” to execute it’ (Pr xii).[12] This may seem to be in contradiction with the previous point: how can procedural thought be both possible and concrete, whereas declarative thought is real but abstract? The answer lies in the difference between what we might call the architecture and the application of the two approaches. Procedural thought is global and possible in its architecture because it does not derive from any particular model; it is concrete in its application because it performs operations on particular objects, not on abstract models. Algorithmic thought works directly on the world itself, and seeks to ‘enter into the details of the singular’ (EPF 230). Declarative thought, by contrast, is real but abstract. It is real in its architecture in that it derives its approach from a determinate model of thinking, not from the possible combinations inherent in all modes of thinking. It is abstract in its application because it operates within the rarefied pomerium of pure extension, a space which exists only in the philosopher’s fancy.
As opposed to the Cartesian concept, procedural thought does not discount or smooth over any singularities, but includes ‘the connection, welcoming and inclusion of all the other places, however small they are’ (At 151).[13] The difference this makes is ‘gigantic’ (Pan 355). First of all, in not relying on a suite of concepts abstracted from singular or individual objects, it is radically non-dualist. Secondly, procedural thinking ‘restores dignity to the knowledge of description as well as of the individual’ (PP 46/T 43, translation altered);[14] the individual is no longer treated as inferior to the general, the singular to the universal, because there is no longer the dichotomy between singular and universal that geometric abstraction maintains. This algorithmic insistence on the dignity of singularity is a major influence on Serres’ view of his own thought: ‘My whole philosophy is there: there are no concepts; there are examples and events, that is all’ (Pan 84).[15]
On a number of occasions Serres illustrates the incremental and concrete aspects of the algorithmic approach to the universal with the example of the Google search algorithm. Rather than dropping the universal from the sky and crushing everything on which it lands, the search engine crawls painstakingly through concrete example after concrete example, finding a way of ‘weaving together’ local and global such that, in procedural thought ‘singularities trek towards the universal along algorithmic paths’ (EPF 256-7, see also ESP 84).[16] Before the rise of algorithmic search, if I wanted to learn about (to use the various examples Serres employs), the scorpion (Pan 84), the hip (PP 72-3), beauty (PP 45) or the circle (Pan 354-5), I would first have recourse to the concept, the abstract generality seeking to define the class of objects in question. In the umbrella-concept (concept-valise) of the circle, to all intents and purposes infinitely large, I could place all the round objects in the world. Now, however, a computer is able to present to me images of any and every type of round object. Now as a medical student I do not study ‘the hip’ as a generalised concept but an MRI of the left hip of an eighty-year old male; I study individual examples which, cumulatively, have generic reach (PP 72). With algorithmic thought, ‘individual singularity has become the centre of thought, taking the place of the concept’ (Pan 354-5),[17] and procedural thinking produces ‘a synthesis […] of the universal and the individual’ (EPF 239).[18]
Figure 1.13: The procedural universal emerges asymptotically from the expanding web of relations
Procedural thought thus avoids two equally undesirable extremes. On the one hand it resists the Cartesian temptation to ‘the aesthetic error of submitting everything to a law’, and on the other hand it avoids ‘the symmetrical error of being satisfied with fragments’ (CS 262/FS 239).[19] Both of these positions are not only mistaken but boring, and Serres prefers ‘a tension between the local and the global, the nearby and the far-off, the story and the rule, the uniqueness of the word and the unanalysable pluralism of the senses’ (CS 232/FS 239).[20] In this he is different from those other members of his generation, Derrida and Levinas prominent among them, who resist the subsumption of difference under unifying laws by stressing the incommensurability of singularities under the rubric ‘every other is wholly other’.[21]
One of the most enduring motifs of the complementarity of the local and the global in Serres’ work is drawn from a point in Leibniz’s Philosophische Schriften where he quotes Nolant de Fatouville’s Commedia dell’Arte play Arlequin, Empereur de la lune (Harlequin: Emperor of the Moon, 1693). Serres tells the story most fully in the Preface to The Troubadour of Knowledge. Upon returning from his journey to the moon, the multi-coloured Harlequin addresses a learned assembly eager to hear news of the strange world he has encountered, but the report they receive comes as a great disappointment. He tells his nonplussed audience that ‘everywhere everything is just as it is here, identical in every way to what one can see ordinarily on the terraqueous globe. Except that the degrees of grandeur and beauty change’ (TI 11/TK xiii),[22] or more succinctly that the lunar world, ‘is just like here, everywhere and always’, only ‘with varying degrees of size and perfection’ (SL 1).[23] What an anti-climax for those who were itching to hear of the exotic, the unheard-of, the Other.
As the scene continues, Harlequin is forced by his disgruntled audience to divest himself of his multi-coloured coat that, in its rich diversity of fabrics, seems to give the lie to his assertion of general uniformity He removes his outer coat only to disclose another multi-coloured garment underneath, which he in turn divests to reveal another and so on, peeling off layer after layer and eventually stripping down to his naked and tattooed body, ‘more a medley of colours than skin’ (TI 14/TK xv)[24] and no less variegated than his coats. Harlequin also reveals that he is androgynous, one who ‘mixes genders so that it is impossible to locate the vicinities, the places, or borders where the sexes stop and begin’ (TI 15/TK xvi).[25] In fact, he embodies the joining of a litany of dichotomies:
the right and the left, the high and the low, but also the angel and the beast, the vain, modest, or vengeful victor and the humble or repugnant victim, the inert and the living, the miserable and the very rich, the complete idiot and the vivacious fool, the genius and the imbecile, the master and the slave, the emperor and the clown (TK xvi)
la droite et la gauche, la haute et la basse, mais aussi l’ange et la bête, le vainqueur vaniteux, modeste ou vengeur et l’humble ou répugnante victime, l’inerte et le vivant, le misérable et le richissime, le plat sot et le fou vif, le génie et l’imbécile, le maître et l’esclave, l’empereur et le paillasse (TI 15)
After many of the audience have left in disappointment and consternation, and with the remainder talking with their backs to the now naked Harlequin, one of their number suddenly turns to look back and exclaims in amazement ‘Pierrot! Pierrot! […] Pierrot Lunaire!’ (TI 17/TK xvii). All-white, universal and blank Pierrot stands in the place of the multi-coloured, singular, chaotic and local Harlequin. The scene ends with the audience wondering ‘How can the thousand hues of an odd medley of colours be reduced to their white summation?’ (TI 17/TK xvii).[26]
Serres’ point is a chromatic one: blank, universal white is not composed of an absence of colour but of all local, determinate colours; the universal and global are arrived at not by jumping out of the local in a puff of abstraction, but by multiplying local instances and seeking carefully to relate them to each other. Harlequin and Pierrot are not enemies, and universality is not won at the cost of eliminating specificity but, on the contrary, by multiplying it. The global for Serres is incremental, asymptotically approached or, in the words of Marcel Hénaff, ‘the global does not pre-exist the local; it is the ensemble of their relations.’[27] For Serres we do not reach the global by abstracting from or transcending the local, but by multiplying ‘as much as possible singular cases, varieties and degrees, before we discover the invariant of the variation’ (SL 559).[28]
More than one commentator has taken issue with Serres’s reconciliation of Harlequin and Pierrot and his double affirmation of the global and the local. Peter Hallward, in his 2003 interview with Serres, identifies ‘two dominant tendencies in your philosophy, which I sometimes find difficult to reconcile’, namely a ‘“particularising” aspect, so to speak, which insists on the […] the irreducible labour of navigating a path between the various obstacles that we face in the “forest” of thought’ while ‘on the other hand, you often refer to holistic totalities that sometimes resemble absolute principles of sorts’ (S&H 231-2). This idea of there being two ultimately irreconcilable tendencies in Serres’ thought is taken up at greater length by N. Katherine Hayles, who argues that ‘[a]t times Serres seems to be tuned in to this world, emphasizing the fragmentary, turbulent nature of a universe in flux’ but ‘when he pushes toward a globalizing theory that would encompass this flux, he is in the paradoxical position of trying to extrapolate a general theory from paradigms that imply there are no general theories’. Her conclusion is that ‘different voices compete within the channel of Serres’ writing’, and he equivocates on the priority of the general and the fragmentary.[29] Bruno Latour voices similar doubts about the relationship between Serres’ insistence on synthesis and the disruption characteristic of Serresian figures like Hermes and the parasite (Ec 129-138, 158-163/C 86-92, 107-110).
Are these objections valid? What might we say in Serres’ defence? In her essay ‘Translating Ecocriticism’, Stephanie Posthumus rallies to Serres’ cause by arguing that Hayles’ and Latour’s objections are ‘rooted in a postmodernism that rejects any possible passage from the local to the global’.[30] This defence of Serres is fundamentally correct; these critiques seem to assume a Cartesian framework according to which universality must necessarily be in conflict with singularity, pluralism with monism, that generality must be violent in the Derridean sense and/or totalising in the Levinasian or Lyotardian sense, and that Pierrot must negate rather than fulfil Harlequin. What these critiques have not allowed themselves to contemplate is a ‘structure’ that is no straightforward synthesis of the ‘models’ it federates, or an algorithmic universal that emerges from among the concrete, the fragmentary and the singular, not to subsume or devalue them but to ‘crown’ them.
[1] This point is made in relation the universal in Marcel Hénaff, ‘Of Stones, Angels and Humans’ in Niran Abbas, Mapping Michel Serres (Ann Arbor: University of Michigan Press, 2005) 181-2.
[2] ‘le pôle de l’univers mathématique.’
[3] ‘à chaque labyrinthe son fil d’Ariane’.
[4] ‘les géomètres méprisent constamment ces pratiques tout justes bonnes pour les marchands et qu’on appelait au Moyen Age logistique et algorisme’.
[5] ‘occupe la place et menace même la mathématique abstraite issue des Grecs’.
[6] ‘formé par la mathématique abstraite et théorique, déduite de principes et sculptée en pyramide axiomatique par la non- contradiction’.
[7] ‘formé par le principe de Salomon, revu dans le début de l’Évangile selon saint Jean : rien de nouveau sous le Soleil ; au commencement la Lumière du Verbe’.
[8] ‘Du local au global il y a bien un chemin, le chemin cartésien justement, par chaîne de rapports et de proportions, mais ce n’est qu’un chemin parmi d’autres possibles’.
[9] ‘se sert de procédures pas à pas et se disperse en mille petits problèmes’.
[10] ‘Cette mathématique procédurale […] fournit des outils efficaces, même quand elle ne donne pas à comprendre la globalité de l’objet.’
[11] ‘suite temporelle, annonce, suspens, mouvement d’induction ou de déduction, affrontement d’un dialogue’.
[12] ‘proche de son ancêtre latin, le vieux verbe français “procéder” signifiait marcher pas à pas, mais a fini par désigner une action et la méthode ou “procédé” pour l’exécuter’.
[13] ‘passe […] par la connexion, l’accueil et l’inclusion de tous les autres [lieux], aussi petits soient-ils’.
[14] ‘redonne dignité aux savoirs de la description et de l’individuel’.
[15] ‘Toute ma philosophie est là : il n’y a pas de concepts, il y a des exemples et des événements, c’est tout’.
[16] ‘les singularités courent en randonnée vers l’universel, le long de chemins algorithmiques’.
[17] ‘c’est la singularité individuelle qui devient le centre de la pensée, prenant la place du concept’.
[18] ‘[u]n synthèse […] de l’universel et de l’individu’.
[19] ‘Connaissez l’erreur esthétique de tout soumettre à une loi […] Evitez l’erreur symétrique de vous complaire dans le fragment’.
[20] ‘une tension entre local et global, voisin et lointain, récit et règle, l’unicité du verbe et le pluralisme inanalysable des sens’.
[21] See, for example, Jacques Derrida, The Gift of Death, 2nd ed., and Literature in Secret (Chicago: University of Chicago Press, 2008) 82-117.
[22] ‘tout est partout comme ici, en tout identique à ce qu’on peut voir à l’ordinaire sur le globe terraqué. Sauf que changent les degrés, de grandeur et de beauté’.
[23] Quoted by Serres from Gottfried Wilhelm Leibniz, Die philosophischen Schriften von G. W. Lezbniz, ed. C. I. Gerhardt (7 vols.; Berlin, 1875-1880), VI, 548.
[24] ‘le bariolage bien plus que la peau’
[25] ‘L’androgyne nu mélange les genres sans qu’on puisse repérer les voisinages, lieux ou bords où s’arrêtent et commencent les sexes’.
[26] ‘Comment les mille couleurs du bariolage peuvent-elles se résoudre dans leur somme blanche ?’
[27] Marcel Hénaff, ‘Des pierres, des anges et des hommes. Michel Serres et la question de la ville globale’,
Horizons philosophiques. Le monde de Michel Serres, VIII:1 (1997) 83. CWs translation.
[28] ‘autant qu’il se peut les cas singuliers, les variétés et les degrés avant de découvrir l’invariant de la variation’.
[29] Hayles, ‘Two Voices’ 3.
[30] Stephanie Posthumus, ‘Translating Ecocriticism: Dialoguing with Michel Serres,’ Reconstruction: Studies in Contemporary Culture, Special Issue: Eco-Cultures: Culture Studies and the Environment. 7.2 (2007), online.
