Lectures / Thinking as an Algebraic Mechanist

MANUSCRIPT // The Sun and its Inverse: Reclaiming the Role of the Mathematical in Understanding Media [and the Technics of Digital Communication] with Michel Serres

My paper at the conference THE ULTIMATE CAPITAL IS THE SUN // METABOLISM IN CONTEMPORARY ART, POLITICS, PHILOSOPHY AND SCIENCE (http://theultimatecapital.org) organized by Matteo Pasquellini, Elena Agudio, Dorothee Albrecht, Bonaventure Ndikung and Eylem Sengezer at Akademie der Künste in Berlin, October 25/26 2014.


While listening to the other papers on neuroscience, the contemporary attention on the brain in philosophy, and the way these are linked up with the quest for a contemporary politics, I cannot help thinking that the brain begins to play a role very much the same as the cosmos used to play. All throughout the centuries, until Enlightenment, worldly order was conceived as a miniature of the cosmic order. And now – perhaps – the brain enters the scene as the authoritative medium between the two. The gesture with which it does this appears still as undecided to me – it is unclear whether it seeks to provide the modern anthropocentric view with a positive, scientific notion of the human in general, or whether it really wants to turn back, as Michel Serres does, to how we can avoid making the basic modern equation which identifies notions of generality with universality. Is the brain seen as a miniature cosmic universality – or is it supposed to the material basis of studying non-hermeneutically a general nature of human beings, this, it seems to me, is the big question. Of course the universal is about a common nature, a nature common to all that is, and before the modern generalization of it in the anthropocentrist world view, this nature was distributed unevenly according to the natural kinds. What is at stake is very simply this: the universality Serres seeks to reanimate is one towards which knowledge can prosper, one that is not granted naturally, effortlessly, as a common denominator – a common sense organ or a common faculty – like the modern generalized version is. For Serres, the faculties are common because they are objectified – with computers, each one of us has St-Denis head in his hands, the objectified totality of all the cognitive faculties. The challenge for neurophilosophy seems to be at this point where to go – does it see in the objectified faculties an emerging subjectivity of humanity as a collective, a new subject about to accelerate and propel the heliocentric revolution where all thought revolves around the sun? Like the Singularity people maintain around Kurzeil and his University for Global Change? Because Serres own stance is radically different. The objectified faculties cannot be humanities common nature, it cannot be the human subject in general. Rather, we must make sense of what it is that we carry on our necks where our heads used to be. And this, for Serres, is the link to the cosmic. We all carry incandescent lights. In the universe of which astrophysics tells us, all emerges out of cosmic dust. The incandescent lights on our heads are like those nebula, they are gatherings of „cognitive“ dust, out of which anything might form. We have to turn away from the heliocentric model for philosophy and adopt a geocentric one again – but, and this is crucial, symbolically so. Serres theory of the quasi-object, which is at the same time, a theory of the quasi subject, explains this as follows:

„Ball isn’t played alone. Those who do, those who hog the ball, are bad players and are soon excluded from the game. They are said to be selfish. The collective game doesn’t need persons, people out for themselves. Let us consider the one who holds it. If he makes it move around him, he is awkward, a bad player. The ball isn’t there for the body; the exact contrary is true: the body is the object of the ball; the subject moves around this sun. Skill with the ball is recognized in the player who follows the ball and serves it instead of making it follow him and using it. It is the subject of the body, subject of bodies, and like a subject of subjects. Playing is nothing else but making oneself the attribute of the ball as a substance. The laws are written for it, defined relative to it, and we bend to these laws. Skill with the ball supposes a Ptolemaic revolution of which few theoreticians are capable, since they are accustomed to being subjects in a Copernican world where objects are slaves.“ (parasite, 225)

Ok, maybe we can come back to this link between brain science and cosmic philosophy in the discussion afterwards. Lets get started after this warmup.

From mediation within history to communication across historicities (The Great Story)

That the Universe not only comprehends space but also unfolds in time – indeed, that the Universe has a history – with this, we can perhaps say, began what we call today Enlightenment. The cosmos can now be addressed in the speculative terms of a calculatable nature. Immanuel Kant has translated cosmological physics into philosophy, as generalized Historicity. In his 1755 text Universal Natural History and Theory of the Heavens, or an Essay on the Constitution and the Mechanical Origin of the Entire Structure of the Universe Based on Newtonian Principles he accounts for the same situation that Pierre Simon Laplace’s Celestial Mechanics will boldly formulate a little while later: Historicity understood in cosmological terms, after Newton, comes to be seen as equivalent to the paradoxical idea of a Deterministic Chaos or a Cosmic Order in the state of its dis-solution, with a reference point in degree zero, so to speak. Cosmology is now scientific, and everything begins to gravitate around „development“. In today’s science of the cosmos, it is still the Laplacean/Kantian formulation of the nature of stars and suns in nebula of cosmic dust – nuclei of atoms pulverized in the mills of spinning cosmic time – that aggregate and eventually, when a particular mixture happens to have gathered, acquire an incandescent light that begins to shine as the nuclei synthesize, acquire atomic weight, and accrete dust and thereby grow in mass, or in other words, solidify. This is how nebula of cosmic dust give birth to suns, whose activity of nucleosynthesis radiates from the center and gives birth to planets, thereby engendering all the physical and chemical elements from stellar dynamics out of the Universes’ Nature that unfolds from local abundances of elements and isotopic signatures, as the astrochemists call it, that are distributed within each galaxy.

But in addition to the 18th century view, Serres maintains, we now ought to read this cosmic origination as a process of communication across historicities rather than as a one history: stellar bodies all emit, receive, store, and exchange radiant energy – in Serres philosophy, radiant energy is the „content“ of information, circulating in how all things physical „articulate“ themselves in the language of mathematics. His is neither a dualist position nor is it a monist one, it is one of absolute difference, as I will argue. Yet such difference, to him, is not what exists or is given, it is what insists in the very attempts to pinpoint it – be it as separateness or as oneness. Absolute difference is the genuine unlikeliness between the Rational and the Real, as he puts it in The Natural Contract, or between Intellect and the Universe. The form of an equation cannot only be considered as the representation of identity. We can also look at it in inverse terms as the expression of absolute difference. Let us see how Serres’ characterization of the Sun as ultimate capital can help us to make sense of this „inversion“.

All thinking is exposed to the black background of Non-Knowledge

In his recent lecture at the Philosophy After Nature conference in Utrecht a few weeks ago, Serres explained:

Philosophy loves light and has turned it into the model of excellent knowledge, especially the splash of daytime sunshine. Sparkling with truth, light is supposed to chase away the darkness of obscurantism. That is an absurd and rather counter-intuitive idea, as we all know that any candle, as weakly as it may shine, immediately pushes back the shadow of the night, while no one has ever seen darkness overcome any source of light. This ideology is terrifying, because if we turn the day into the champion of knowledge, we are left with only one unique and totalitarian truth, as hard and unsubtle as the sun at high noon, the star that astrophysics has eventually confined to the minor rank of the yellow dwarf. I say no to this tyranny, no to the yellow dwarfs. […]

We associate the cosmos with an order, an orderly arrangement, as the Greek origin of the term suggests. Now we have to learn, contemporary astrophysics and astrochemistry tell us, that   in the cosmos, nothing is solid. For Serres this means that finally, philosophy can attend to it again! It is the dissolution of solidity – or genuine obscurity, to put it drastically! – that keeps all that is (the Universe) actively together.

In fact, thinking is much less like the day than like the night  where every star shines like a diamond, where every galaxy flows like a river of pearls, where every planet, like a mirror, reflects the light it receives. Thus authentic knowledge overflows with results and intuitions; it sets up multiple reference points grouped into constellations with forms that are as disparate as those of scholarly disciplines. Thus knowledge finds temporary truths whose luxuriously colored sparkle flickers and changes with the duration of the Great Story. The only lights that do not tremble emanate from planets without an original brilliance and that, as I said, behave like mirrors. Magnificent, but modest enough to be reduced to the punctual […] great in size but wavering in doubt and questioning, those truth-stars stand out against the enormous black background of non-knowledge, that is empty without limitations  or full of yet unexplored galaxies: things still to be understood and to be grasped.

It is with words so drastic that Michel Serres demarcates his own position vis-a-vis heliocentric cosmology and its translation into philosophy, where the new emphasis on the historical nature of order – and the possibility of deliberate programmatic development – gave rise to philosophical and scientific determinism. For Kant, such a determinism condenses in his philosophical apriorism: Criticality with regard to the inevitable antinomies and paralogies of pure, speculative reasoning promises that all reasoning can be cleansed by from the obscurantism that results from idiosyncratic thought, such that the apparently inevitable counterpart to the symbolic, namely the diabolic, the evil of misunderstanding and dissensus, might be, more and more, disempowered. The assumption of a generic human nature is crucial for the modern translation of cosmology into cosmopolitics. More than 200 years later, Serres urges, we have to turn back to the cosmos with our logics, to the idiosyncrasies it nourishes, we have to learn to think what it means to go „from rotational revolution to an expanding Universe“. He begins his so entitled paragraph as follows:

„To the Platonic ideology of a single sun-struck truth, Immanuel Kant added an image of such a high degree of narcissism, that it should have worried the wise. Brightly positioned on those days at the center of the world, the sun became, in his philosophy, the very subject of knowledge: the Sun-Ego (roi-soleil), in a word. One can barely resist the impulse to burst out laughing at the sight of such a paranoid scheme whose lack of modesty ends up putting each one of us on the throne of a king. Let’s say no to the dwarf who believes himself to be the tyrant of knowledge. This self-revolving world, that may have once been revolutionary, now seems all too narrow-. A laughable scheme it is too, as astrophysics introduced us to a trillion galaxies, blue supergiants, black holes and other singularities in great numbers, inhabiting a universe, deprived of a center or endowed with multiple centers, decorated with precious gems, as Verne would have it. Visible only at times and at night. To account for Kant, in my view,  those suns, in their own way, know and see.“

Yellow Dwarf is an expression in astrophysics which refers to a classificatory norm   regarding the extension and quantity of brightness of stars – it covers stars during what we could call an „adult life“, after they have accreted their mass and settled within the galactical gravitational balance, and yet before they will, eventually and slowly expand   only to fall apart and disintegrate into cosmic dust. Serres alludes with this to the centrality of the status of Coming of Age (Mündigkeit) in Kants philosophy – it is the hinge which puts, according to modern cosmopolitics, „each one of us on the throne of a king“. Anthropology, as the basis for an entirely science based cosmopolitics grounds knowledge in a   general human nature, subjected to a   general form that disciplinarizes pure reason, such that its speculative postulates can be criticized on grounds that are, by declaration, indisputable.

Competing about what can afford a general nature of reason: geometry of arithmetics?

Serres’ polemic against this primacy of the general is not an idle one. This new program for a human rather than a cosmic order was no longer compatible with the ancient understanding of Mathematics as the art of learning. It marks the beginning of a long story of arbitrarily limiting the open and infinite vastness of what can be rendered intelligible by mathematics. If there is a natural, and entirely general, principle of reason, then there must be a logical, systematically determinate, technics of learning – not an art, which has always one foot in the element of the infinite, and remains, hence, depended upon the grace of spirituality. The offers on the table to free individual reasoning from having to be possessed and gifted with spirit on which not everyone may count equally   were twofold: a pure intuition, propagated by Kant, as an organ of common sense; or a pure intelligence, as propagated by Laplace, as a disembodied demon, a daimonion, not, perhaps, so much unlike the voice of conscience.

Serres urges us to consider that neither one of them are adequate. If nothing that is of cosmic order is solid, because the universe comprehends order as well as disorder, we are ill counseled by both. For him, as he puts it, „intelligence is immanent to the world, and probably co-extensive with the universe“. This, again, is our inverted equation from the beginning – an equation which expresses radical difference rather than identity. I will come back to this.

What we can see between the Kantian and the Laplacian options is a competition between geometry and arithmetics with regard to which one of them can affording a general nature of reason, and hence, a purely symbolic order from which all opportunities for dissensus are – objectively so, with no subjective deliberation involved – sorted out, or to use a perhaps overtly strong term: exorcised. Yet I use it deliberately, in order to point out how much this question was entangled with questions of good and bad, and ultimately, of salvation.[1] A short episode to illustrate what I mean: In his classic textbook The Development of Mathematics (1950), E.T. Bell describes how abstract, symbolical Algebra appeared like an ‘undiscovered continent’ on the horizon.  Those who pushed the application of the symbolic methods of reasoning without dedicated political or economical commitment were ‘adventurers’, whom Bell calls ‘illegitimate Kings’ striving for ‘profit’: masses of young mathematicians were recruited, he writes, who mistake the kingdom of quanticsfor the democracy of mathematics. Quantics was the name of the branch which studied algebraic forms, before it turned into a general theory of invariances. Leading Algebraists were accused of mobilizing ‘totalitarian’ regimes of calculation, by recruiting mathematicians for theory without applications and use. If we recall the decision communicated by the French Academy of Science shortly after the French revolution, that the classical mathematical problems like squaring a circle, doubling a cube or trisecting an angle should no longer be credited within institutional science because they consume the publicly owned workforce of mathematicians for metaphysical interests, it seems understandable that the attractivity of studying algebraic forms for its own sake, was perceived as an offense or even deceit of enlightenment values. In effect, it was stigmatized a political threat. Only gradually, with the practical usefulness of allowing those obscure, genuinely abstract and conventional symbols that boosted algebra in the 19th century, and with the inventive success in technological mastership that resulted from calculating with such symbols, were more and more methods of symbolic reasoning legitimized.

Eventually the millennia old divine analogy between cosmos and geometry   gave way to an adapted one, no less divine,   between the human reason and arithmetics. It was no longer geometrical elements   but   natural numbers that are considered as the building blocks upon which science may found universal order. This is how Gottlob Frege could eventually state in his famous Foundations of Arithmetics: A Logico-Mathematical Enquiry into the Concept of Number (1884): „[i]n arithmetic, we are not concerned with objects which we come to know as something alien from without through the medium of the senses, but with objects given directly to our reason and, in its nearest kin, utterly transparent to it.“[2] For the entire program of logicism – that is, for the philosophical doctrine that arithmetics be part of logics –, culminating in Turing Computability – this idea is key: arithmetical reasoning does not depend upon Kantian forms of intuition, or anything like it. And due to this, it was to provide a frame of reference freed from any empirical complexity, a givenness of mathematical objectivity directly to our reason.

But Frege’s Natural Numbers had to be accommodated within an ideality of sorts: „A third realm must be recognized“ besides Ideas and Things, Frege wrote and continued: „Anything belonging to this realm has it in common with ideas that it cannot be perceived by the senses, but has it in common with things that it does not need an owner so as to belong to the contents of consciousness.“[3] – Where Kant had placed his transcendental subject, Frege introduced a domain of objective ideality, as a third that is capable to mediate between the empirical and the rational. It is not difficult to see here a further articulation of the Laplacian demon: an abstract priviledged site, occupied by the uninvolved third.

Michel Serres’ concern with framing media in the terms of a logic of the parasite is directed against this postulated thirdness of a transparent and objective realm. Intellect for him is no less mathematical, and no less algorithmical even, but it is immanent to and co-extensive with a universe that has a nature, and that expands. He refers to the Universe not despite but because he sees in it „a bordering of order and disorder.“ Disorder, noise, belongs to this universe as order does – it is the condition sine qua non for the universe to have a nature, to live through the births and the deaths of its galaxies.

Michel Serres opposes the alternative between geometry and arithmetics, and opts for the anarchic third – in this context, algebra. Calculations, he urges, do not render results that are necessary in any mandatory sense; rather, they multiply the vastness and contingency of computable results. Computation is neither arithmetic nor geometrical, even if in its applications, it is. But computation, Serres stresses vehemently, is algebraic. Its forms are symbolical, i.e. discrete and articulate – they are polynomial – and they do something different from geometrical forms: namely – they conserve, they do not outline and define. Algebraic forms conserve the possibilities of transformation of a given quantity. They say nothing about the essence of the quantity at stake. Algebra places intellection within a Universe of Discourse whose statements are algebraic. In this universe, all questions pertaining to essentiality or Being are bracketed out: For the algebraist – and in this he is diametrically inverted to the logicist – numbers don’t naturally have content. This stance is at odds with both options for establishing a notion of generally valid reason: the Kantian one of pure intuition as well as the Laplacean/Logicist one of a pure intelligence. From the point of view of algebra, numbers are encryptions, they establish a choreography in the void, and are genuinely symbolic. They count a nature of which they respect that it remains, ultimately, arcane. All   the art of counting can hope to achieve   is to preserve what it counts indirectly, by not trying to outline its boundaries, by   not   defining it. From the algebraist’s point of view, the art of counting is to be infinitely considerate of the arcane obscurity pertaining to that which is counted. Numbers are for algebraists, what Serres characterizes as „substitutes“ in the chapters that are decisive for his theme of the sun as the ultimate capital, they are „jokers“: theories, insofar as they area mathematically formalized, work

„[…] in the realm of general equivalence. It is outside the true, outside the false; it indicates contents that are jokers. La cosa, as the Italian algebraists of the Renaissance used to say, la cosa, the thing said to be unknown, the unknown = x, multivalent, of which it can always be said that it takes all values.“[4]


What I am currently very much interested in is how these distinctions play a role in contemporary computing, and information based empirical science such as climatology or cognitive science. It is clear that „numbers“, their „nature“ and their geometric vs arithmetic treatment and so on, are no longer the language game in which things are expressed. The language apparently much more capable is that of frequencies, signals, impulses, phases, phase spaces, spectrums. It is the language of quantum science. And it is the language of communication and information technology. But at its core is, now as ever, how we measure and count quantities. If science and philosophy is not about adequating the real and the rational in an identity, but about expressing their radical difference by articulating each in their algebraic, symbolic form   in an equation that states their equipollence rather than represents their equivalence, then the primary concern becomes, indeed, a question of surplus value of code. I cannot develop this here, but let us see, as a final episode, how Michel Serres embraces this algebraic view.

„Given be the universe of discourse“, he maintains, and „this universe can be organized according to the distribution of jokers.“ He goes on to imagine two extreme cases, one in which no jokers are there to organize the universe, and one in which there are arbitrarily many. A discourse with no joker reduces beyond monosemy to identity: „Thus the universe in question is undervalued by a = a“. If on the other hand you increase the number of jokers according to which you seek to investigate the organization of the universe of discourse to the maximum, „polysemy overtakes the space with multivalence and equivocity.“ Near the end of a given universe of discourse is the world of dreams, he maintains, „completely filled with polyvalence“. More drastically, and straightforward to the point we need to get at: „At the limits of the dream, at the limits of the universe, the discourse composed exclusively of jokers is money. When there are only jokers, that’s capital, a bank account, the general equivalent. They overvalue the world.“ If a universe of discourse needs to include all that can be the object of thought, it is „a curious universe, though a logical one“. It is one „where dreams adhere to finance, where gold is near dreams.“[5]

[1] For Serres, the situation is simple: we cannot purify the symbolic form the diabolic, order and disorder are both universal. But we can strengthen the relation of equipollence between the real and rational. For whenever one of them overpowers and subjects the other, violence takes over. (Natural Contract)

[2] Gottlob Frege, The Foundations of Arithmetic, transl. by J. L. Austin, 2nd editio, Blackwell, Oxford 1953 [1884] §105

[3] Gottlob Frege, “Thought,” translated by Peter Geach and R. H. Stoothoff in The Frege Reader, edited by Michael Beaney (Oxford: Blackwell Publishers, 1997), pp. 325-345, 337. In the German original, Frege speaks of an empire, not a realm as the translator in the cited version has decided. This is an important aspect, even though there is of course no straight link with the subsequent evolution of this concept in the German political context in the first half of the 20th century. But in any case, it is widely acknowledged that the political notion of the Drittes Reich was essentially driven by some intramundane and non-psychological myth of salvation. The original passage goes like this: „Ein drittes Reich muß anerkannt werden. Was zu diesem gehört, stimmt mit den Vorstellungen darin überein, daß es nicht mit den Sinnen wahrgenommen werden kann, mit den Dingen aber darin, daß es keines Trägers bedarf, zu dessen Bewußtseinsinhalte es gehört.“ Gottlob Frege, „Der Gedanke. Eine logische Untersuchung“. In: Beiträge zur Philosophie des deutschen Idealismus, 2. (1918/19), S. 69; Dirk Koob: Sozialkapital zur Sprache gebracht. Göttingen 2007, S. 133.

[4] Serres, parasite p. 163

[5] Serres: „As for the distribution of jokers in the universe of discourse: the identity principle and the principle of indiscernables are undervalued, and the circulation of money, right near dreams, is overvalued.“

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s