Mathematics and Information in the Philosophy of Michel Serres
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Mathematics and Information in the Philosophy of Michel Serres

Vera Bühlmann

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eBook - ePub

Mathematics and Information in the Philosophy of Michel Serres

Vera Bühlmann

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This book introduces the reader to Serres' unique manner of 'doing philosophy' that can be traced throughout his entire oeuvre: namely as a novel manner of bearing witness. It explores how Serres takes note of a range of epistemologically unsettling situations, which he understands as arising from the short-circuit of a proprietary notion of capital with a praxis of science that commits itself to a form of reasoning which privileges the most direct path (simple method) in order to expend minimal efforts while pursuing maximal efficiency. In Serres' universal economy, value is considered as a function of rarity, not as a stock of resources. This book demonstrates how Michel Serres has developed an architectonics that is coefficient with nature. Mathematic and Information in the Philosophy of Michel Serres acquaints the reader with Serres' monist manner of addressing the universality and the power of knowledge – that is at once also the anonymous and empty faculty of incandescent, inventive thought. The chapters of the book demarcate, problematize and contextualize some of the epistemologically unsettling situations Serres addresses, whilst also examining the particular manner in which he responds to and converses with these situations.

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A substitution takes place in which science eradicates language—this explains our time.
Michel Serres, The Five Senses1
Today we have reason to hope for what has, until now, been only an illegitimate desire: “that we might be able to understand in one and the same stroke the Greek miracle of mathematics and the fantastic blossom of Greek myth,”2 as Michel Serres maintains. It is only now that we can with legitimate desire hope for such a new classicism; this is because today, we can attend to the “Greek miracle” within registers in which Greek mathematics and myth themselves are but cases. This is because today’s science knows how to date its objects in a new way. History extends now to all that there is; all the scientific disciplines work together in attributing historical dates to nature, from the Big Bang (some fifteen billion years ago) to the appearance of life, or that of particular life forms on earth (as well as their extinction). But importantly, as Serres maintains in his 2016 book Darwin, Bonaparte et le Samaritain, Une philosophie de l’histoire, such historical dating equally applies now to phenomena that have hitherto been called (chauvinistically so) “prehistoric” (like cultures that have never developed a written alphabet).3 We need to understand Serres’s interest in such dating before the background of his earlier work on the relation between mathematics and myth. In an early essay entitled “Structure et importation: des mathématiques aux mythes,” Serres envisaged the implications of what he saw at work in the novel paradigm of extending history to all that there is. He wrote that if we can endow the concept of structure “with a normative, a cathartic and a purgative”4 definition, then “our time appears capable of reconciling truth and sense.”5 Might there really be a way of thinking in which one would not always find oneself belonging to—or having to take sides—between the sobering coldness of rational reason versus the exciting and consumptive warmth of the dark depth proper to all things that (ultimately) truly matter? It is right for both philosophy and science, according to Serres, to grant this other, this “Dionysian world”6 of “impenetrable, dense, dark sense in which the human soul, its affectivity and its fate are true” a central place. Are we not, with regard to knowledge per se, always also “dealing with reality, and with what it means to be human, within human time and human sufferings”?7 It is possible to think about this “on a universal scale,” he maintains.8 Of course it ultimately remains mysterious that there is thinking, knowing, feeling, and being here in this world. But are these deep meanings, these dark senses, only “symbols of history,” he asks. Serres’s answer is negative, “Are they not also, in their ultimate form, in their final determination, meaningful models of transparent structures, of an order of knowing, of intellect and of science?”9 Serres proposes nothing less than an outlook toward a thinking about intellection according to which rationalization does not ultimately amount (in the calculative sense of Enlightenment thought) to a demystification of life. But does it also prevent us from violently giving in to what Henri Bergson, in Les Deux Sources de la Morale et de la Religion (The Two Sources of Morality and of Religion [1932]) identified as the “essential function” of society, namely, being “a machine to make gods”?10
Serres was a trained mathematician. What triggered his interest in philosophy, as he told us,11 was a split between the worlds of ideas in which common people lived and those in which the people informed about the sciences lived. There is here a bifurcation at work that triggers the discrediting of an intuitive common sense vis-à-vis expert knowledge. Serres’s entire oeuvre is dedicated to finding a kind of understanding, a form of intellection, perhaps, that is capable of granting a shared world of ideas between science and culture. It is crucial for the possibility of such a world to emerge and such a sense of intuition to prosper, as I will argue, to accept mathematics as a “silent” kind of language. For Serres, as we will see, structure was not the mysterious key that would open all doors. Structure is a key, but not a mysterious one; it is formal through and through.12 Rather than mystifying structure, it is the world to which he is ready to grant a certain mysteriousness. In this century, Serres maintains, we have already seen several revolutions in the basic conceptions with regard to the sciences, and “moreover, further ones are announcing themselves.” They will “unhinge the theoretical universe just as suddenly and just as much as, with the slowness due to their inertia, they will unhinge the world of praxis and the ensembles of technics.”13 With regard to the mysteriousness of the real world, Serres maintains, structure “is a methodical, clear, well defined and elucidating concept”14 that is capable of putting us in touch with the world’s reality. Structure as a methodical concept is not estranging us from the real world. It is true that “We don’t have the same dreams anymore, we no longer think nor write as our direct ancestors did”15—but this is not a sign of estrangement from the world, for Serres. Rather, it is a sign of impatience with a certain “active cultivation of ignorance” in views that were once well reasoned, but are evidently no longer adequate.
The main line that will be developed throughout the book is that mathematics in Serres’s philosophy provides a lexicon of operative concepts, rather than foundations or supporting structures for science. At the core of this endeavor, to reconcile truth and sense, is the problem of ideation. We must reconnect with abstraction a capacity to provide for generosity, rather than seeing in it only a means of reduction, he maintains. The operative concepts of the mathematical lexicon trigger models that must count as “reduced,” but not because they would draw a poor representation of the phenomena they “model.” Models don’t “represent” at all, rather they “realize.” Mathematics is the inexhaustible source of a generosity from which such “reduced models” (that are capable of realizing particular phenomena) can draw. Like this, they are the words in a lexicon of mathematics through which we can learn to “sound silently” (to hear and to formulate objectively) how nature speaks.
Mathematics and information are crucial for understanding how the philosophy of Serres at large is an attempt toward a “general treatise on sculpture.”16 It is important to grasp Serres’s ambition to formulate such a general treatise as a philosophical treatise in the history of religion, not one in the field of aesthetics. This is because, as he writes, “the itinerary of aesthetics brings us to the feet of statues.” But encountering statues from this direction (the direction of aesthetics), “they sit in session or enthroned most often at the far end of temples where they are adored by idolaters who are scorned as superstitious.” Contrary to the itinerary of aesthetics, that of the history of religion “meets with and highlights this term of abuse [aesthetics], in itself remarkable and so akin to the statue that it contributes to breaking or overturning.”17 According to the kind of general treatise Serres had in mind (and which the lexicon of mathematical words is to constitute), “sculpture bears ancient witness to the anthropological genesis of experience in general. It carves, drills, and fashions. Rodin is right: gate is the true name of the sculptor’s ark.”18 The mathematical concept of structure is crucial for the conception of mathematics as such a lexicon. If applied to experience, mathematical structures provide formal keys for opening such gates: “Thus space and time open up through some gate that yawns or gapes open onto what language calls by the same word: experience. An expert gate, the same term, that is to say, open onto an exterior. The gate is a kind of pass. The world and life lead to a threshold that bars an elsewhere.”19
Such an understanding of abstraction (one according to a general treatise of sculpture that follows the itinerary of religion rather than aesthetics) hinges in essence on a different understanding of history. Taught by the school of the French philosophy of a history of ideas—by Georges Canguilhelm and Gaston Bachelard among others—Serres shared their concern for making history the object of rigorous science. But unlike them, Serres maintains that a scientific approach to understanding history is possible through mathematics and communication (information theory), not through linguistics and logics. If we are right to claim that there is a history of ideas—this is how he formulates his interest—then we must also deal with the inverse of this assumption, namely, that there is an idea of history. And we ought to assume between the two stances an inchoative relation of reciprocating dynamic as well as systematic implication, rather than regarding one as a function of the other. It must be possible to excavate an empirical field for the historians’ work—a field where the historian can be critical, one where there are methods of reconnecting a direct chain between a phenomenon and its source.20 Such empirical fields can be established with the help of structure as a “methodically clear, distinct, and elucidating concept”21 applied to the mathematical notion of information, not to a linguistic understanding of language in terms of signs. We can call such empirical fields for the historians’ work (where the history of ideas is investigated as much as the idea of history itself) the field of a communicational physics. The mathematical notion of information does not signify the quantity it captures; it indexes it. We miss the very character of information when we try to relate it to the passive representation of sense. Information affords an excavation of signification, a remembering kind of understanding in how signification makes sense: “The technical image of a black box does not signify anything different from what the word ‘empiricism’ says: it’s a matter of drilling an aperture to reach the inside. Experience: a hole towards the outside; empiricism: a window into the interior. In sum, openings onto another place.”22 Information, with its indexical capturing, works like a sieve, a filter: invariance and variation are not mutually exclusive with regard to the statuesque sculpting of reduced models by code. It is thanks to such a leaky form (or rather, spectral form) that the mathematical theory of information can facilitate a thinking capable of elucidating culturally significant contents through science (rationalizing), and scientifically significant contents through culture (realizing). With this in mind, we can acknowledge how Serres maintains that,
The simple and pure forms are not that simple nor that pure; they are no longer things of which we have, in our theoretical insight, exhaustive knowledge, things that are assumedly transparent without any remainder. Instead they are infinitely entangled, objective-theoretical unknowns, tremendous virtual noemata like the stones and the objects of the world, like our masonry and our artifacts [objets ouvrés]. Form bears beneath its form transfinite nuclei of knowledge, with regard to which we must doubt that history in its totality will be sufficient for exhausting them, nuclei of knowledge which are profoundly inaccessible like indelible marks. Mathematical realism is weighed down and takes on that old compactness which had dissolved beneath the Platonic sun. Pure or abstract idealities cast shadows once more, they are themselves full of shadows, they are turning black again like the pyramid. Today’s mathematics unfolds, notwithstanding its maximal abstractness and purity, within a lexicon which results, partially, from technology.23
Mathematics does not provide support or foundations; rather, it unfolds within a lexicon of silent and operative concepts. I attempt to characterize this thinking as a quantum literacy (Chapter 2), through looking at how code is at play within a mathematical notion of information. What preoccupied Serres’s thinking from the first of his books onward was in figuring out how to think about “communication.” Information theory shows us, Serres acknowledges, how inadequate our inherited views are that reserve language, interpretation, and “softness” for the human sciences, and mathematics, necessity, and “hardness” for the natural sciences. Mathematical communication accommodates all sciences in a common, universal, “white house” (la maison blanche). All things are engaged in the fourfold activity of sending, receiving, stocking, and dealing with information—a universal kind of activity that articulates the two categories of Serres’s physics of communication (which is likewise a communicational physics), namely, “hardness” (energy at great scales [thermodynamics, entropy]) and “softness” (energy at small scales [information theory, negentropy]). Serres proposed a philosophy of what he calls “the transcendental objective” and that accompanied his notion of a communicational physics. Categories, in such a philosophy, are scalar variants of the two universal categories—softness and hardness. We need to bear this in mind as we go on. It means that basic notions like quantity, quality, and locality ought to be considered in terms of how they order energies at smaller as well as larger scales. I will try to develop Serres’s idea that these scalar variants behave somewhat like musical instruments: through them, nature speaks in many tongues. The articulations of Serres’s communicational physics are articulated according to a particular kind of “temporal,” “tempered” or also “timely” wisdom proper to phenomena subsumed by the ancients as “meteora.” The wisdom at work in “reasoning” those phenomena manifests as the integral summation of all measurable durations (there is a particular relation between time and weather that I will elaborate in Chapter 3). With the help of such wisdom, we can think of the inverse of a natural history of ideas, that is, we can think the idea of history; that is because as the integral summation of all measurable durations, the wisdom of the meteora provides something like an inverse of the idea of the nature of number. The wisdom of the meteora can be conceived as the numericalness of nature. This amounts to the maxim that if we think about counting time, we need to temporalize counting in turn. Nature is countable, but countability too must be considered natural. Code provides the operators of such convertibility. This idea is developed in Chapters 3 and 4, “Chronopedia I: Counting Time” and “Chronopedia II: Treasuring Time,” as well as Chapter 6, “The Incandescent Paraclete: Tables of Plenty.” The orders of such articulation—its “metaphysics”—are scalar orders (orders in terms of scalae naturae), but its notion of order is conceived as a model that realizes, not as a model that represents. This is how we can find in Serres’s philosophy a proposal of how to reconnect with this old tradition of organizing rational thought in terms of gradual processes that can accommodate different hierarchies subject to one universal nature, but without imposing a particular hierarchy as representative. Through attending to how time is counted (as measurable durations), Serres proposes a method of maxima and minima, where Aristotle (for example) proceeded...

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