für Johannes Sistermanns, **Ma Un Ma **SoundPlastic Exhibition /

WP Festival Donaueschinger Musiktage 26.10.2016

http://www.sistermanns.eu/#page/home

The subject is immense,

requiring every order of knowledge and endless information.

Besides, when such a complex whole is in question,

the difficulty of reconstructing the past,

even the recent past,

is altogether comparable to that of constructing the future,

even the near future;

or rather, they are the same difficulty.

The prophet is in the same boat as the historian.

Let us leave them there.

Paul Valéry

** **

** **

**Kapitale Körper, sonderbares Universum**

**0**

Alles was wir wissen

vom Körper der Chiffre

ist dass er intakt

und über Entsprechungen im Allgemeinen

organisiert ist.

Der Körper einer Chiffre ist monetär und vergnügt,

und stets vermögend genug, um Kredit zu geben.

** **

Der Körper einer Chiffre ist ganz,

weil er aufrichtig unwahrscheinlich ist.

Er ist von Zufälligkeit und erfasst damit

ein Außen in seiner jeweils unvergleichlichen Charakteristik:

nichts herauszustellen.

**I**

Wo überhaupt nichts ausgestellt wird

wird es möglich das Tönen der Welt

in seiner Neuigkeit zu empfangen.

Das Mögliche resultiert aus dem Zirkeln,

wobei die Wendungen erschließen was erreicht werden kann,

mit dem ungerichteten Festhalten an “Vielem”.

**II**

Nichts zeigt sich

in den Körpern von Chiffren

die tönen und fest werden während sie

sich in Worte, Zahlen und Formen wenden

in einer Schrift die keine Nacktheit kennt,

einer malerischer Schrift.

Solche Schriftlichkeit ex-skribiert

was weder konstant noch variable ist

sondern elektrisch und sich anbietet,

mit Sorgsamkeit und Begehren Spannung zu erhalten:

als kapitaler Körper, eine Sonderbarkeit des Universums.

**III**

** **

Neuigkeiten der Welt

erschließen sich als genuine Botschaften.

Sie sind leer von allem was in ihren Wendungen rotieren

und sich drehen könnte.

Sie haben nichts zu sagen,

sind zirkulär aber voll.

Wie ein Spektrum von weißem Licht,

der Totalität von jeglicher Farbigkeit,

einer Summe die nie aufhört zu summieren.

**IV**

** **

Nichts drückt sich aus in malerischer Schrift.

** **

Malerische Schrift

ist Möglichkeit ohne Macht.

Sie ist weder kräftig noch gewaltsam.

Sie ist fähig in verträglicher Manier zu handeln,

durchlässigkeit zu erzeugen,

und eine Scheidung von Ton und Lärm zu erlassen

die weder ausgrenzt noch einschließt sondern beides gleichzeitig tut.

Malerische Schriftlichkeit

maximiert Verbindlichkeit.

Wo nichts ausgewiesen wird

eignen sich genuine Botschaften das Vermögen an

jenen Wert zu investieren

den sie zu ex-skribieren vermögen.

** **

**V**

** **

Das Klingen von genuinen Botschaften

bringt eine Klarheit, die üppiger Brillanz entspringt

und die nur insofern Einsicht bereitet,

als dass das, was von ihr herausgestellt wird,

mit Garantie

vor dunklem Grund aufscheint.

Es ist die Klarheit einer Krypta

dessen brillante Einsicht

auf obskure Weise im weißen Spektrum verbleibt,

der Totalität von jeglicher Farbe die nie fertig wird zu summieren

was sich beugt und zurückwendet

was mit einer gewissen Regelmäßigkeit

frequentiert.

** **

**VI**

** **

Die Klarheit einer Krypta

birgt nicht eine bestimmte Form

sondern jegliche Form überhaupt.

Sie ermöglicht keine Reflektion

es sei denn man begegnet ihrem Begehren ergründet zu werden.

In diesem Fall nährt sie ein Licht das Licht ist

nicht weil es scheint sondern weil es strahlt und entflammbar ist.

Das Aufleuchten dieses Lichts

ist nicht nur vollkommen unwahrscheinlich,

fremdartig und unheimlich,

sondern auch so delikat und verletzlich

dass jede Begegnung nur darin stattfinden kann,

es in einer Weise zu bewahren

von der für niemanden gewiss ist

wie sie charakterisiert und mitgeteilt werden kann.

Die Begriffe dieser malerischen Schriftlichkeit

vermögen das delikate Artikulieren von Aufgeregtheit

und kommen ohne Bloßstellung und Obszönität aus.

Sie entspannen und sie üben sich in der chiffrierten Formalität einer unwahrscheinlichen Zeitform – jener Zeit, die eine kryptographische Gegenwart zu stiften vermag.

**VII**

Die Körper von genuinen Botschaften

sind gesetzlich indem sie in aktiver Weise

nichts bewirken.

** **

Alles was sie je tun

ist den Rest von dem aufsummieren,

was sie zu fassen vermögen.

Sie sind von natürlicher Öffentlichkeit.

**VIII**

** **

Das Mögliche resultiert aus dem Zirkeln

während Wendungen anbahnen was getan werden kann

um aus dem Halten von Vielheit zu schöpfen.

Virtuosität hängt von einer Metrik ab die danach strebt,

kapitale Körper zu ermessen

indem sie das Zirkulieren von überhaupt nichts verzeichnet.

Überhaupt nichts, das sich regelmäßig

und immer wieder mit neuen Gesichtszügen vorstellt

welche sich für andere kapitale Körper stets als anziehend und aufregend erweisen. Das Universum ist so prallvoll mit sich selbst

dass es überquellt.

Seine Eigenartigkeit und seine Selbstvertrautheit

hören nie auf originell zu sein. Stets wieder wird es geboren

in jenen kapitalen Körpern

die am sonderbaren Eigenwert der Dinge festhalten

– von dem eine Ordnung über Generationen hinweg

kontinuierlich lernt, wie sich etwas achten und ermessen lässt.

Alles was wir wissen

vom Körper einer Chiffre

ist dass er intakt ist.

**IX**

Die Krypta

in deren Begriffen der Körper einer Chiffre sich vergegenwärtigt

als “eine ganze Summe” gemünzt

in was auch immer als solide gelten mag

– spektral aber gut etabliert,

fremd aber intakt.

**X**

** **

Ein solides Sekret kristallisiert vergnügt

indem es hinausreicht, über die bewahrenden Grenzen

seiner eigenen Intaktheit. Es ist verbunden

mit einer Art von Vernunft,

dessen Rationalität nie auszählt und Geltung beansprucht

ohne sich zu verpflichten, dem Reellen

denjenigen Preis zurückzubezahlen, den sie ihm schuldet.

Und den zu kennen nie jemand beanspruchen kann.

]]>*abstract*

My paper will relate Serres’ personification of Sisyphus to the naive and intuitive notion that the role of „information“ be a kind of „elementary patch“—not really an element and not really a particle either, more like a mixture of both, pieces of an enormous puzzle perhaps—patches which one can expect to fit together neatly and smoothly and with no need to apply force, if only enough care is invested in figuring out how the patches must be arranged so as to continue and complement each other. These patches of information are to show the way things fall into place „just as they ought to,“ naturally. It is the very vulnerability of this intuitive idea that Serres’ re-reading of Sisyphus is capable of appreciating. All existentialist praise of Sisyphus has neglected, Serres maintains, that there can be no reckoning about Sisyphus without his host; and his host, so Serres tells us, is the stone. The object that determines Sisyphus as a subject. Sisyphus is not the modern hero, a hero whitewashed, and emancipated, from power and ambition. He is not the hero who, stripped from the burden of ever effecting anything at all, exists face-to-face with pure necessity and can therefore guard, in the manner of a bureaucrat, a notion of righteousness that rests in the sheer repetition of routine. The myth’s character does not become a modern hero because he has been punished and corrected by the Gods for the cunning, ruse and mischief, with which Sisyphus had challenged them in ever new attempts to reconcile transcendence and immanence; he is not a post-Christian crucified, without resurrection, he is not a modern savior. To Serres, Sisyphus is the personification of someone who values the object as the reception of news, neither good nor corrupt, simply as the appearance of something extrinsic to the heretofore manifest wholeness of the web of relations. Sisyphus plays a central role in Serres’ novel humanism, because he renders novelty communicable. This communication is the contribution of the excluded third to the bipolar idea of communication between sender and receiver, between origin and destination, between source and reception.

SISYPHUS. HIS PRISMATIC COMMUNICATION AND HIS DEALINGS WITH WHAT IS PUZZLING

**Sisyphus**

„From the darkness of times, out of the hollows of the underworld, from an abyss of pain, a report recurs that some thing will keep returning here—and all we do is talk about the man who keeps taking it away from there, we Narcisses’.”(Michel Serres,The Five Senses)

Sisyphus, the story of the *ruse-ful human* who played his games with the will of the Gods, and who was punished, eventually, by Thanatos – God of death and the afterlife – with a sentence that predicates Sisyphus to roll uphill a heavy stone, only to pick it up the next day where he had, already, the day before. For centuries Sisyphus has been received as a figure expressing the fall of mankind, the expulsion of humanity, due to the human striving for mastership; in the modern era of the 19^{th} century, Sisyphus turned into the epitome for a tragic humanism, a non-narcissistic and non-anthropocentric attitude where human nature resides in orienting thought entirely face-to-face with pure necessity, and to think of oneself thereby as guarding a notion of *righteousness* that rests in the sheer repetition of a routine, without *wanting* anything at all. Serres gives a novel turn to this genealogy, and maintains that Sisyphus tale teaches us about how non-anthropocentric thought can constitute a novel humanism: Sisyphus stands for a human subject that subjects not to history, nor to something transcendent, but to the object. He stands for a subject whose work is genuinely *humane* to the degree to which it is pointless in ever concluding something – not as the acceptance of tragedy, but as the reception of a report that initiates the possibility for knowledge.

The legend of Sisyphus actually reports that something *will keep returning*, “here”. The object is what is being *re-ported*– an object with no other reference than an indexical one, “here”, here some thing keeps returning. What? *That* is the puzzle. But there is a secular aspect to the Sisyphus tale. It is that this sort of “puzzling” is no longer to be an *apocalyptic* puzzling, one for which at the end of time there would be revelation, one where revelation, true insight, would demarcate – indeed, *bring* *about* – an end to time as it passes. It is an objective puzzle, and the object is what we subject to. And by subjecting to the object, the object – itself indeterminate but determinable – is being constituted. To such a notion of the object, there is a direction, a goal, an *objective*. What is puzzling about it is that *where* this direction, this objective, is *heading* to – it is this *objective place * that is at stake in Sisyphus’ puzzling dealings. To Serres, it is the place of hominiscence, the place where the nature of humanness originates from. It is a place that is indeterminate not despite but *because* it is determinable in myriads of ways and manners: it is the entropic place from which order, as the negative to entropy (negentropy) is being *wrested* as time *passes on*.

To Serres, Sisyphus is the personification – a mask of generic humaneness – of someone who values *the object as the reception of news*. Such news are neither good nor corrupt, what they “bring” is simply a report of, or the appearance of, something extrinsic to the heretofore manifest wholeness of the web of reasonable relations. A report as every invention brings about, makes appear, something new – Renaissance perspective, infinitesimal calculus, thermodynamic apparatus’ like the steam engine, they have all endowed the domain of what can objectively referred to with aspects that had been dubbed “mystic”, “exclusive”, “alchemic” and the like before. Sisyphus plays a central role in Serres’ novel humanism, and, I will try to argue, this is not because he were *gifted with inventiveness* but because he renders novelty and inventiveness *communicable*. This communication is the contribution of the excluded third to the bipolar idea of communication between sender and receiver, between origin and destination, between source and reception.

*Hors-Là: how to address the vicarious space of conductivity ?*

Guy de Maupassant has invented a character called Horla, which the protagonist in his short story keeps encountering in a peculiar kind of shadow. Horla is a phantom that is transparent (passive, lets shine through) but not without an irreducible lucidity of its own. It sits in front of the mirror and it catches, before the mirror can actually do so, the images the mirror is about to reflect. Michel Serres, the polymath writer who has been pursuing, for more than five decades, the project of a natural philosophy of communication, writes about this peculiar character:

“What a strange shadow: it is and is not, present and absent, here and elsewhere, the middle which ought to be excluded but cannot, hence contradictory. This is why he [Maupassant] calls him Horla”.

^{[1]}

*Horla,* this is, to Michel Serres, the character of a kind of spectrality that actively sums up all projections that could possibly be reflected, in a kind of summation whose total is indefinite, and because of that, determinable. What is at stake with this proposal by Serres?

Let us approach indirectly. There are phenomena that are to be considered as *genuinely simulacral but nevertheless real*, as Mark Hansen has beautifully put it in a talk on his project of a speculative phenomenology.[2] The question he raised thereby is of interest to media theory at large: how to *address* philosophically the particular kind of “spectrality” at work in communication media, and how to address the *rendering of appearances* (that technical spectra afford in quantum physics-based science, chemistry for example or electro-engineering)? The predominant question with regard to quantum physics is that of location and the point of view of the observer. But in order to address the active role of those spectra, as a kind of impersonal agency, we will have to complement that question with one that asks about how to think of the *temporality* involved in such observations. For such observations are, in a strict sense of the term, *mediagenic: *they are observations engendered by mediation, by resorting to a middle ground “that ought to be excluded but cannot”[3].

While there clearly is an emerging common sense with regard to the importance of attending to the temporality dimension at work in quantum-physical “positivity” (the “eventfulness” of probability spaces, the “massive activity” in particle physics (radioactivity) and in chemistry (molecular bondages), there are many proposals of how to do so. – Serres interest in Maupassant’s character Horla lies in that it impersonates *cryptographically* the source of a peculiar kind of originality. It is an originality that affords tracing back lineages and hence gives birth to continuity, but the afforded tracing is not one that heads for a beginning that would reside in some transcendent beyond. It affords a kind of tracing within a space that opens up from and co-extends with just such tracing. It is a kind of originality, hence, of which we might feel inclined to call it *vicious,* because by all apparent evidence it appears to be circular (just consider the vocabulary of quantum physics: radiating activity, returning frequencies, extension in phases etc). We must also consider that the agency at work in this self-referentiality indeed is attributed, by Maupassant and also by Serres, “character”. We seem to have good reason, hence, for rejecting to even consider such a space *as* a space (one that springs from circular tracings and that is to coextend with the lineages that are thereby being traced): both notions, that of “character” as well as that of “vice” (in “vicious”) are words with primarily moral connotations.[4]

Surely, the positivity at stake in quantum physical phenomena cannot be grounded, ultimately, in moral categories: this would indeed force philosophy to sacrifice its own knowledge of how to articulate and maintain space for hesitation, by demanding accounts that are considerate and capable of withstanding scrutiny, accounts which demand intersubjective, methodical evaluation and argument rather than subjection to absolute authority. Is Serres indeed, with his proposal to conceive a space that were capable of accommodating this fabulous character, Horla, with this peculiar, paradoxical “transparent lucidity,” suggesting that philosophy make this sacrifice?

The notion of the *vicious circle in reasoning* was given the general sense of “a situation in which action and reaction intensify one another,” according to the etymological dictionary, by 1839.[5] An agency that were caught up within such a space of vicious circularity would inevitably be a dangerous agency, a corrupting one, a pretentious one, one that mocks any idea of perfection – from which all moral notions of justness, righteousness, balanced valency etc are inevitably being derived. Lets pause and remember: how can phenomena that are genuinely simulacral but nevertheless real possibly be approached by philosophy in a gesture of reclamation rather than capitulation, this was our starting point. And how can Serres’ proposal of a space called *hors-là*, (out, there) possibly be of service to this?

The space which is at stake here is mediated by *Horla the fabulous phantom*. By attributing this character to technical spectra, Serres indeed affirms that the quantum space of *a physics of light* is a space where intensification is triggered, where interferences show up and cannot be entirely reduced, where the directed beams of reflection are thwarted and go in all directions, diffractively. It is a noisy, a querulous space, but it is also a rational space (quantum physics does support a certain kind of mathematics). Yet it is that of a rationality within which no one particular order can be purified (quantum physics involves probabilistics and complex numbers, numbers whose rationality is constituted by imaginary units). A particular order, out of this pool of what we could call *abundant orderality*, can only be exposed before the noisy background of all of this exposed order’s “others”, all those other possible orders with which the one exposed has originally been mixed up and from which it has set itself apart. And it is exactly this crystallizing kind of separation process from within an entropic orderality of mingled bodies that Serres’ proposal of a space called hors-là serves to address. How so? By rendering this mingled bodies *measurable*, in maps drawn by ciphered graphisms (cryptography and topology)[6]. Like this, what appears within moralist terms as the space of * vicious circularity* thereby turns into the space of

[…]

**Technicity rather than logistics: the vicarious space of an electric circuitry**

The space indexed by Horla needs no longer be regarded as the corrupt space of a vicious circularity: it can be addressed critically as a vicarious space of an electric circuitry. Originality in terms of such a space, *hors-là*, provides for an *in* that ‘indexes’ an *out* without making positive statements, epistemological or ontological, about this *in* or this *out*. This space itself, the space of a physics of communication, is neither *out* nor *in*, neither *here* nor *beyond*, neither *past* nor *future*, neither *physical* (in the classical, pre-quantum sense) nor *metaphysical* (in the classical or the modern sense): it is the *vicarious* space that is, continually but diffractively and intermittantly, *being sourced through indexing *an out in an in. *Hors, là. Out there, here*. The positivity of quantum physics can only be addressed in a vicarious domain of a representation where the reference relation is indefinitely intermitted by substitutes. Substitutes that supply places from indexing what has not been indexed before: the space of this vicarious domain co-extends with the tracings of its own point zero, its own mathematical, metrical “originality”. * *

Of just such strange “nature” is the quasi-physical domain that communication channels have been establishing, for real and this for nearly a century now: channels are literally technical spectra, they render apparent a certain generic order which can be observed only before a “plentiful background” of noise (entropy), rather than one of an empty tabula rasa. Serres illustrates this idea of a plentiful background with the color spectrum, where white light stands for such a “plenty” because it expresses any color at all, and this in a material, physical manner: “white light” is, ultimately, radiating nuclear activity of quantum-physical mass. Within such “materiality”, channels are established for ‘surfing’ on top of the singled out frequencies, but nevertheless *amidst* the massive agitation of what is technically called *Brownian motion*. The space of such generic and entropic materiality must be considered as having as many formats of coordination as it has channels: a communicational web, a ‘pan-centric’ (rather than centralized or de-centralized) network. This is what Serres proposes to address as hors-là, a space of conductivity sourced from indexing.

It is a *vicarious* space of substitutional operators, a space hence bare of signification, sense, and undetermined with regard to meaning. Not because it would be empty in the sense of “lack “as a substantive, but in that of “lacking” as a kind of *frequentative* preposition: the zero neutrality of white light *lacks* in that it *leaks*, in the same sense as spectra *lack *in that they* leak, *and such leaking is accessible only through measuring its *frequent happening* (a frequency). The formality in this vicarious space that is one of communicative conductivity is spectral, it lacks in that it leaks. White light is percolating not because it lacks color, but because it is “abundantly full” of color. This vicarious space is a space where points are indexes that *point actively*, points that are literally *pointers*.

Let us come back now to our initial concern, namely that of raising the question of temporality for phenomena that are genuinely simulacral, rendered and merely apparent, but that must, nevertheless, count as real. We can see now how channels, within such a vicarious, indexical space of electro-magnetic conductivity must be considered as countering the *reversible time of classical physics* as well as the *irreversible passing of time in thermodynamics *(and in dialectical history)!

Communicational channels provide for passage that “goes, within time, upstream,” and that establishes spaces of relative and locally sustainable reversibility as particular temporary “niveaus” or “plateaus”: the generative exposition of a temporal order before a noisy background of abundant orderality (the entropic stream of time that passes, the 2^{nd} Law of thermodynamics).[9]

Serres has another legend to illustrate that what is at stake hereby is a novel notion of *vulnerability*. I would like to conclude with merely reading the beginning passage to you. It is from his *Second Book on Foundations, *called* Statues*.

*Sphinx and Oedipus*

The sphinx– What animal stands on four feet at dawn, Oedipus, man who is passing by and who will die if he doesn’t reply or find the answer to the riddle?Oedipus– Doubtless man, who before walking or standing crawls, a small child, on four legs like an animal. A childish answer. But before man, the animal itself, quadruped like you. Although you lie down in the avenues or before the temples, showing your king’s face or your young woman’s chest or even spreading your bird’s wings, your four legs are obvious to see, oh wildcat. Man and brute mixed can remain quadruped.The sphinx– What animal stands on two feet at noon, beneath the shadowless sun?Oedipus– Man, of course, a biped like me, adult, standing, a walker, wandering, with a mobile niche, or like you, with a king’s face and queen’s breasts […]

The sphinx– What animal stands on three feet when night falls?Oedipus– The man, again and always, who leans on a staff of old age when fatigue and age arise. Every animal that walks, to the best of my knowledge, does so on an even number of legs, therefore no beast, no monster, oh sphinx, could live on three feet. The non-living, the dead, the inert are necessary for that. Only the object, the thing in equilibrium can stand in front of or after the animal and the man, static tripods, pyramids or tetrahedrons with triangular sides, the results of human labor. They can be called statues since they stay up all by themselves: your shadowless questions only bear on statues or equilibria. […]

The sphinx– Oh, Oedipus, do you know why you’re risking death?Oedipus– Yes, I’ve known for a little while now; the decipherers of riddles, my fathers, believed themselves to have gotten out of the difficulty for having heard me answer ‘man’ to your questions. They didn’t even consider the fact that we were risking our lives, the both of us. If I don’t answer or am mistaken you’ll kill me; if I say the truth you’ll die. We’re having a dialog on pain of death. What are we gambling, as though at the dawn of history? Our lives. If I die you’ll sacrifice a man; if you die I’ll sacrifice a mixed body of man and animal: here’s the first progress.The sphinx– New and unexpected Oedipus among the diviners of riddles of ordinary mothers and fathers, why don’t we take up the question again?Oedipus– It consists precisely in mixing animal and man. Your riddle resembles your body. It’s always necessary to guess the man concealed behind the animal.The sphinx– Give me some time, Oedipus, before my death.Oedipus– Forget that man that crawls as a quadruped during his childhood, soon to be standing, senile so quickly. Why not say he’s still on four feet when the embalmers lay him out on the alabaster table shaped like a stretched-out lion to empty him of his entrails and organs? What can he be compared to in his mummy wraps? What dull foolishness!The sphinx– Recount again and take your time; save me.Oedipus– Here’s the time: this day in which the sun rises, like a godsend, running to its zenith and falling to the western horizon, which everyone takes to be a short life, mysteriously measures our entire history and gives the laws of hominization.[…]

Michel Serres,

Statues, Second Book on Foundations, Bloomsbury 2016 [1987].

[1] Serres, *Atlas*, Merve, Berlin 2005 [1994], 59.

[2] This text is based on the response I was invited to give to Mark Hanson’s keynote lecture „“Entangled in Media, Towards a Speculative Phenomenology of Microtemporal Operations” at the Philosophy After Nature Conference in Utrecht, September 2014.

[3] Serres, *Atlas*, 59.

[4] According to etymonline.com, “vicious” means “unwholesome, impure, of the nature of vice, wicked, corrupting, pernicious, harmful,” when applied to a text “erroneous, corrupt,” from Anglo-French vicious, Old French vicios “wicked, cunning, underhand; defective, illegal,” from Latin vitiosus (Medieval Latin vicious) “faulty, full of faults, defective, corrupt; wicked, depraved,” from vitium “fault”.

[6] This is really the overall theme of Serres book *Atlas – *he discusses how we can exercise a kind of map making for the globalizing world, where maps do not depict territorial order but communicative order. Such map making combines „prophecy with geometry“: it demands that calculations based on stochastic integrals, statistical mappings and probabilistic predictions be graphed out, and treated in geometric and constructive terms as well, no longer exclusively in analytical and deductive manners.

[7] This is the core theme of Serres book *Le Parasite *(1980), where he discredits the idea of a restoration of a balance as the ideal successfulness of communication, and instead begins to theorize a natural economic order that is genuinely communicative, where the sun must count as the ultimate capital. Capital, then, can no longer be thought of as the exploitative accumulation and concentration of resources. It must be addressed as the primary source of all kinds of banks of energy-information that nature organizes in. It is a very early view of a world naturally globalized through communication, an idea Serres picks up, in its ethical implications, in *Le Contrat Naturel *(1990).

[9] This is, very generally, the theme in Serres’, *L’Incandescent,* Paris, Le Pommier 2003, where he introduces the concept of „Exodarwinism“ to refer to such temporality.

“A computational approach enables architecture to be embedded with an extraordinary degree of information.“

(Michael Hansmeyer: www.michaelhansmeyer.com)

I would like to discuss three of Michael Hansmeyer’s recent experiments in computational architecture (*Platonic Solids* (2009), *Subdivided Columns* (2010), *Digital Grotesque* (together with Benjamin Dillenburger 2013)) in relation to what Peter Eisenman has recently foregrounded, in a conversation on the foundations of digital architecture: Architecture ought to find ways of coping with such miraculous deeds as “saving a void from the negative by making it positive,” or doubling and dividing volumes (cubes).^{[1]} In this formulation, Eisenman was explaining how in his Biology Center in Frankfurt, Germany (1987) he was trying to rid the architectonics of this project from any figure/ground dialectics. His interest was to “use a computer as a modeling tool capable of drafting predefined forms in endless sequences based on logical statements in code”^{[2]}. With regard to this, I want to suggest, Hansmeyer’s own experiments provide an inverse approach to the same interest (overcoming structuralist figure/ground dialectics as well as the poststructuralist infinitary rendering of it): Where Eisenman works by sequencing predefined forms (form as logical statement), through considering form as symbolically coated by code (symbolical in the mathematical sense of the word), Hansmeyer explores how we can consider form not as logical but as entropic (generic) statement, and, in its coded ‘coat’, as a means for algebraic ‘sourcing’ of ‘poly-tomic elementariness’ (*poly-tomos*, Greek for that which can be divided in many ways). His quest is one for form made up of symbolically coated atomicity or in-divisibility (*a-tomos*, Greek for that which cannot be divided), for which it indeed makes sense to say, as he does, that architecture “can be embedded with an enormous amount of information”[3]. This text elaborates on how we can think of ‘form’, with Hansmeyer’s experiments, as the ‘contractual form’ of ‘symbolic solids’. Like geometrical forms, they too regulate relationships rationally; but the can do so with larger or lesser capacity for dealing with the co-existence of ‘aspects that don’t seem to add up’ in unambiguous manner. I thereby suggest to refer to Eisenman’s ‘foundations’ as ‘architectonic plots’.[4]

Operations involving negativity, voidness, formality and elementariness are related to a set of classical problems in mathematics—among them doubling the cube, angle trisection, and squaring a circle— that has arguably propelled the development of mathematics as the ‘technics/art of thinking’ at large[5]: These apparently very specific geometrical problems are actually ‘genuinely’ abstract, or in other words ‘purely mathematical’, in the sense that they do not lend themselves handy for immediate application to a specific situation at hand. They make things appear *more* instead of *less* complicated and unsettled, at least initially; hence their treatment has often raised mistrust.^{[6]} But on the other hand, the iterative and many-versed treatments have also driven the progressive movement towards mastering more and more abstract manners of counting and measuring, which is evidently indispensible for the invention of novel technical instruments and procedures.^{[7]} These geometrical problems involve constructions that keep the study of form and its relation to number apart. They refuse to conflate exactitude (geometry) and rigor (rationality), they oblige us to treat meaning and measurement, attribution and assessment with regard to the constructed object, separately. How? By involving mechanical operations with symbolized ‘units’ whose intuitive ‘reference’ to graspable things escapes exact comprehension *in principle*: zero, negative entities (negative numbers), the root of a negative number (imaginary numbers), a bounded infinity (via the distinction between cardinality and ordinality) or the particle of a partitioned one (irrational numbers).^{[8]} These symbols, hence, must count as algebraic, pure place-holders, notational substitute-characters one relies upon for reasons that cannot void themselves of their constitutive speculativeness,^{[9]} because what these ‘superior’ symbols claim to stand in for counts, according to all established common sense and knowledge, at best as genuinely unsettled: mathematical symbols are in pact with the (mathematical) irrational.

We can see better now the philosophical relevance of what is at stake with the ‘foundations’ of digital architecture, or, respectively, its ‘architectonic plots’. One may ask, however, what is supposed to distinguish the works of architecture from those of the mechanical arts^{[10]} —which were indeed referred to as ‘arts’ for precisely the reason that they could deal with the infinite in indefinite manner. In any case, such ‘foundations’ touch upon the nature of the sacred, its relation not only with art but also with the problem of violence and the practices of sacrifice and exclusion, and through that with the anthropologically invariant role of myth for the constitution of a collective ‘we’.^{[11]} This is indeed why I want to speak of Eisenman’s ‘foundations’ for architecture in the sense Aristotle began to use the term ‘plot’ in his poetics as the dramatically versed “arrangement of events that happen in a story”, which I read essentially as a theory of how to dramatize myth in a symbolical as-if domain of the quasi, where the irrationality (infinitaryness) of real deeds are symbolized by substitute characters (e.g. acts, actors, characters, performance).^{[12]} This distinction is also what relates the topos of the ‘work’ to that of ‘art’, and with George Bataille to the idea of a general economy of the sacred as the infinite work, with Maurice Blanchot to the idea that literature, by speaking about what cannot be said, is the work of death, and with Jean-Luc Nancy to a decoupling of communication from work, as the im-possible constitution of the in-operative community.^{[13]}

As a manner of decoupling this architectonic plot from all tentative immediacy, I suggest to view ‘the building’ as ‘the plot of dramatizing architectonic articulation’, and the arrangement of events it is to accommodate as the dramatic prism through which we can regard a building as an actual and active form of thinking. A prism in optics is a diligently cut and polished solid figure, which breaks the rays of light that shine through it according to particular patterns—hence a prism affords perspective and method, yet in a manner in which precision and rigor are kept apart. A building then is a form of thinking because it resolves a particular ‘insight’ as a spectrum—hence a mediated ‘in-sight’. Of such a mediated insight, we can think of as a ‘theoretical promise’: theoretical because what is at stake in such a promise becomes fixed only as the promise is being referred to as a building’s singularly dramatized, yet generic, plot. The architect does not properly speaking *realize* such a promise, I would suggest, she *dramatizes* it. The building’s plot, in that sense, becomes positively in-definite rather than positively in-finite (as mythical divinization or theological revelation would suggest). Being a ‘natural’ myth (rather than the mythological story of a tradition), in that it embraces means of ‘superior’ mathematics, such a ‘building as theoretical promise’ is inevitably in pact with an anonymous, impersonal agency. Yet it is not the agency of a tool (like the computer, a ruler or a compass), it is the agency at work in mathematics as the art of learning. A building’s plot engenders a presence (is a ‘natural’ myth), and hence is actual, precisely because its rational accounts cannot exhaustively legitimate what it promises to manifest.

Architectural disposition in planning (ichnographia, scenographia, orthographia)^{[14]} then depends not alone on intention and design (on the side of the architect as cognitive subject) nor on objective requirement (on the side of a building as object of cognition), but also on a kind of mastership that belongs to the object, that relates to what I called ‘the impersonal agency’ that is at work in architectonically active form (form of thinking as the theoretical promise that articulates formulations, indefinitely so, of what can be learnt). It is this mastership of objectivities with which an architect ‘partners’ when she formulates the promise a building is going to manifest; the architectonic qualities can no longer refer to an essentialist reference of ‘the beautiful’, ‘the adequate’, or ‘the useful’ immediately, but only in a manner that contracts the abstract identity of such quality symbolically.

This has two important aspects:

- With regard to itself, such contractual quality is
*always*perfect, fulfilled, yet in a speculative manner void of reason because algebraic symbols are self-referential in the sense that they refer to one and the same cipher (the total of a cipher’s notational symbols must always make up zero (‘cipher’ is a word for nothing, zero)). Like all speculation, algebraic symbols proceed circuitously: they build on what is assumed to be given, then they support explanations for the givenness of what has been assumed to be there in the first place. - With regard to the real stakes that belong to the abstract identity of such quality, that is being contracted in the formulation of a promise, such quality is
*never*perfect or fulfilled—because it is the very character of a promise to be overdetermined with possible meaning, to build upon polytomic elements, and, we might add to highlight the role of sophistication (and sophistry): to sparkle in its formulations with more or less objective brilliance or mastership.

So how can we look within this context at Michael Hansmeyer’s experiments in computational architecture?[15] His interest is “to embed an extraordinary degree of information,” as he puts it^{[16]}. As long as ‘form’ is taken as equivalent to ‘pre-determined logical statement’, such an interest appears vain, and the involved computation reduces to sophistry. What I would like to suggest is that all three of Hansmeyer’s works explore how an architect can ‘partner’ with this ‘impersonal agency’ that is at work in active forms of thinking. Furthermore, all three works explore and seek getting used to the formality of symbolic self-referentiality that is not only ‘tauto-logical’ (and reproduces variations of the same), but rather invariantly ‘tauto-nomical’ because it regards the elementariness of form in a quasi-atomist manner; ‘quasi’ because it explores the symbolic polytomy of the atoms in relation to the code in which they are computed. Each work attributes symbolically an un-reasoned, (entropically ichnographic) elementariness to an architectonic form of thinking (in Hansmeyer’s work: platonic solids, columns, grotto), upon which it operates and from which it engenders a symbolical solid: the fully rational (operation of subdivision) and practical (aesthetic articulation) manifestation of beauty as a promise.

*Platonic Solids* (2009) attends to the most primitive forms, the platonic solids, and repeatedly employs one single operation – the division of a form’s faces into smaller faces – until a symbolic form is articulated in »agreeable« manner.

*Subdivided Columns* (2010) focuses on the Doric Column and subdivides it iteratively eight times according to its own order, thereby producing 5,8 million faces. One such pre-specific typicality of this order is elected here and plotted into a cardboard model (1 mm sheets).

* *

*The Digital Grotesque* (2013, [together with Benjamin Dillenburger]) is a walkable room produced by 3-D printing. A simple input form is recursively refined and enriched, culminating in a geometric mesh of 260 million individually specified facets. Every detail of the architecture in this project is generated through customized algorithms, without any manual intervention. And yet it is not only that during the computation every point (spatial or temporal) is latently connected to all the other points; rather, each one actively reflects them all at once at every instant, and this in an individual manner that in each case responds to and communicates with all the others – the actuality of this happening, this is what the architects settle.

^{[1]} „The Foundations of Digital Architecture: Peter Eisenman,“ in conversation with Gregg Lynn on the opening day of the *Archaeology of the Digital* exhibition at the Canadian Center for Architecture (CCA). Available online: https://www.youtube.com/watch?v=hKCrepgOix4

^{[2]} as the project’s presentation at the Canadian Center for Architecture (CCA) puts it: http://www.cca.qc.ca/en/collection/2061-the-heart-of-the-biozentrum.

[3] Michael Hansmeyer: www.michaelhansmeyer.com

[4] This means creating a conceptual hybrid between architecture theory (Vitruv’s triplet of addressing ‚disposition’: ichnography, scenography, orthography) and and drama theory (Aristotle, *De Poetica* (335 BCE)).

[5] *Mathematics* literally means all that pertains to *mathema*, Greek for ‘learning’.

^{[6]} The French Academy of Science, for instance, has declared right after the French Revolution that work on these problems by mathematicians will no longer be considered as legitimate contributions to the corpus of academic knowledge (by argument of being a waste of the nation’s intellectual resources). “The Academy took this year the decision to never again consider a solution for the problems of doubling the cube, trisection of an angle, squaring the circle and of a machine of claimed perpetual movement. Such sort of researches has the downfall that it is costly, it ruins more than one family, and often, specialists in mechanics, who could have rendered great services, and used for this purpose their fortune, their time and their genius.“ Cited in: American Mathematical Society, *The Millennium Prize Problems*, published with the Clay Mathematics Institute, Cambridge Massachusetts, 2006. (http://www.claymath.org/library/monographs/MPPc.pdf). Indeed, solutions to these purely abstract problems have often been brought forward in suggested “demonstrations” (in the axiomatic sense of formal proofs) of the existence of an infinite magnitude (like “God”), cf. Hudry, Françoise (ed.), *Le Livre des XXIV Philosophes* (Latin text and French translation), Millon, Grenoble, 1989.

^{[7]} Methodically speaking, the point of mistrust towards manners of treating these problems is that suggesting resolutions to these purely mathematical problems is not rooted in “elementary” mathematics (the Euclidean elements), but involve what is somewhat helplessly called “superior” mathematics—which means that any resolution to these problems manifests in constructions (axiomatic demonstrations of theorems) that cannot be achieved and reproduced with compass and ruler alone. This „superiority“ is an ambiguous term, as in the Greek (Platonic) origin, the term was used in reversed manner and attributed to geometry for precisely the reason that it did not involve numbers, and hence proposed a way to bypass the problems of incommensurability that arise for example from demonstrations dealing with the irrational diagonal of a square. Eg. cf. John Tabak: *Geometry: the language of space and form*, Facts on File Math Library, New York 2004.

^{[8]} While in Antiquity, mathematicians and mechanical artists didn’t have the symbolic notations we have today, the Hippocrates’ and Archimedes’ of former times did have technical devices (like spirals, feeding from what we today call “angular momentum”) that operate on the same physical principles we have learnt to index by symbolical notation only much later. This is for example the strong emphasis underlying Michel Serres’ suggestion to relate Lucretius’ clinamen to contemporary physics: Archimedes’ mathematics, which underlies and gives coherence to Lucretius poem (according to Serres) translated into hydraulic mechanics; it is the blindness of modern science to conceive of mechanics as static, and fluid mechanics as a derivative thereof. “We mix experiment with equations. And we accompany the protocol, step by step, with formalism and with metrics: Without this continual proximity, no experimentation, no law. The Greeks would, I believe, have been strongly repulsed by this mixture. They did not have, as we do, a unitary mathematical physics. Theirs was double. They produced rigorous formal systems *and *dissertations upon nature like two separate linguistic families, like two disjunct wholes. And, since they are often signed with completely different proper names., no one dares to think that they are structurally isomorphic.” Michel Serres, *The Birth of Physics*, Transl. by Jack Hawkes, Clinamen Press, London 2000, p. 13. That nature and mathematics are indeed to be regarded as disjunct, and that they ought to be reasoned as isomorphic, is Serres key point also in *The Natural Contract* (1990): the real and the rational are to be considered equipollent (equality in force, power or validity); one cannot be subjected to the other, this in-subordinatory relation is the Natural Contract is supposed to formulate.

^{[9]} cf. Alfred North Whitehead, *Treatise on Universal Algebra with applications*, Cambridge University Press, Cambridge 1910. In relation to this cf. also Michel Serres: „At the beginning of the seventeenth century, when what we came to call the applied sciences first made their appearance, a theory spreads that one can find in several authors, although none of them is its sole source, which *seeks *to account for a harmony that is not self-evident. This discourse may be found in the work of Leibniz, Descartes, Pascal, Fontenelle and so on, but even before them in Galileo, and perhaps in a number of alchemists. What spreads is the idea that nature is written in mathematical language. Language here is too strong or too weak a word. ln fact mathematics is not a language: rather, nature is coded. The inventions of the time do not boast of having wrested nature’s linguistic secret from it, but of having found the key to the cypher. Nature is hidden behind a cypher. Mathematics is a code, and since it is nor arbitrary, it is rather a cypher, Now, since this idea in fact constitutes the invention or the discovery, nature is hidden twice. First under the cypher. Then under a dexterity, a modesty, a subtlery, which prevents our reading the cypher even from an open book. Nature hides under a cypher. Experimentation, invention, consist in making it appear.” Serres, *Birth of Physics*, ibid., p. 140.

^{[10]} It is interesting to remember that for Vitruv, the subject matter of architecture included (1) buildings, (2) machinery, and (3) clocks (gnomons). Vitruvius: *De architectura libri decem*, book one.

^{[11]} Cf. especially René Girard, *I See Satan Fall Like Lightning*. Maryknoll: Orbis Books, 2001; Georges Bataille,*Theory of Religion*, MIT Press, Cambridge MA 1992, also Jean-Luc Nancy, “Myth Interrupted” in *The Inoperative Community*, University of Minnesota Press, Minneapolis 1991, p. 43-70; for a more generally historical documentation cf. Robert Hamerton-Kelly (Ed.), *Violent Origins: Walter Burkert, Rene Girard, and Jonathan Z. Smith on Ritual Killing and Cultural Formation*, Palo Alto, California: Stanford University Press 1988.

^{[12]} ‘Action’ derives from the Latin translation of the Greek term *energeia* (and not *dynamis*) for a reason: *energeia* meant activity in infinitive mode, and it was reserved by Aristotle for the prime mover because it denoted what exceeds rational grasping via the sequencing of this infinitive activity into finite elements of processes cf. Ludger Jansen, *Tun und Können. Ein systematischer Kommentar zu Aristoteles’ Theorie der Vermögen im neunten Buch der Metaphysik*, Springer, Wiesbaden 2016 [2002].

^{[13]} Georges Bataille, *The Accursed Share (v**ol. 1 & 2*)*,* MIT Press, Cambridge MA 1993; Maurice Blanchot, The Infinite Conversation, University of Minnesota Press, Minneapolis, 1969, and *The Unavowable Community*, Station Hill Press, Barrytown, 2006 [1983], Maurice Blanchot, “Literature and the Right to Death” in *The Work of Fire*, transl. by C. Mandel, Standford: Stanford University Press 1995; Jean-Luc Nancy, *The Inoperative Community*, University of Minnesota Press, Minneapolis 1991.

^{[14]} Vitruv, ibid., book one.

[15] Cf. the captions to the images in this text.

^{[16]} http://www.michael-hansmeyer.com/#2

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author’s manuscript.

In his *Ten Books on Architecture*, the Roman architect Vitruvius gathered all the existent knowledge on architecture in one comprehensive treaty including the building of temples, of course, but also the construction of clocks (gnomon, sun-dials) and the fabrication of machinery. The dedicated aim of gathering all the distributed knowledge in architecture has been to generalize from local customs and the ethical/religious meanings attributed to the built works, and to propose rules and conceptual distinctions for addressing and critically evaluating „the establishment of public order“^{[1]} in a manner that can preserve the built environment’s „worth“. Vitruv proposed three categories – *utilitas*, *firmitas*, and *venustas* –, and introduced six elementary concepts by which an architectural object can be qualified according to these categories.^{[2]} None of these concepts is self-standing, like a separate metrics, but rather must be brought to work together by the architect in singular manners; the planning of this interplay – this is the work in which an architect can be more or less professed. Vitruvius’ conceptual apparatus is to provide critical assessment of such professionalism, such that the „worth“ of architecture can be preserved over generations and regions. It includes practical aspects as well as theoretical ones, which he distinguished as *fabrica* and *ratiocination*. The six elementary concepts are (1) *ordinatio: *centering in selecting one module from which the metrical unit for the overall taxation is to be derived in order to the establish a singular work’s „ordination“ by articulating and proportioning the members of the work; this idea of ordination is analogous to Vitruv’s suggestion that rather than ideas of the magnitudes and scales impersonated by a particular God, the human body can be referent to proportionate metrics in architecture;, (2) *dispositio: *regarding the conception and disposition of all the work’s elements in plans, (3) *eurythmia: *the well-proportioned overall appearance of the work, (4) *symmetria: *for the harmony of the order with regard to the module from which its metrics is derived, (5) *decor* or *propriety*: for customization of the work according to established customs, and (6) *distributio* (in Greek *oikonomia*): for a distribution of building materials and expenses adequate to the wealth and status of the customer.

The generalization from local customs and the ethical/religious meanings attempted by Vitruv is so interesting because it proceeds in a manner of which I claim here that it *parallels *rather than imitates or reproduces philosophical methods of generalization and classification. Against this postulate of parallelism (—> *equation*), there is a long tradition of Vitruv’s reception; according to this reception, architecture, especially the public order it articulates in cities, was thought of as realizing an ideal of a cosmic order in the here and now of the world. The predominant critique on Vitruv since the Renaissance is that his proposed methods operate with proportion, without ever specifying the attributes of the proportions with precise ratios.^{[3]} If, however, we return to his interest in the preservation of architecture’s worth not through the discourse of aesthetics, regarding architecture as an art, but through an approach informed by physical conservation, Vitruv’s apparent failure reveals itself as its very mark of distinction and excellence: whatever the value this worth preserves may be – beauty, harmony, the good, etc – such an approach at systematization lives from *not* specifying the nature of this value in any determinate manner (—> negentropy, —> invariance). The preservation of this value would be achievable only as a state of entropy, in which all of its articulations would be equally „likely“ – meaning in the architectonic context which is concerned with criteria of adequacy rather than of happening – equally „adequatable“. Such an entropic state provides an atomism of value like the thermodynamic state of entropy (of the universe) provides an axiomatism of forces. We can think of the disposition of a work, its plan-ability, as such an entropic state, and we can call this ‘architectonic disposition’, picking up on Alberti and Serlio, an architectonic model. According to Vitruv, the elements of this disposition – quasi its vertices – must comprehend the full combinatorial space of the totality of possibilities the six elementary concepts are capable of determining. “Planning” or “design” – to use todays concepts – can be read as a reduction of the combinatorial potentiabilities, by configuring the potential elements in an objective way.^{[4]} Vitruv foresees three dimensions of conception which we know today as ground plan, elevation and perspective. He calls these three dimensions of conception *orthographia* (the natural, potential elements, in renaissance: elevation), *ichnographia* (the contraction of the potentiabilities of these elements, in renaissance: floorplan) and *scenographia* (the operation of contracting, in renaissance: perspective or 3 dimensional plan).

If Vitruv’s triad of architectonic disposition could be demonstrated in a generalized form, then his architectural theory might lend itself for developing an information architectonics. It might provide orientation in how to generalize again from the numerous spreading out of disciplines that fall victim to increasing local seclusion, hermeticism, and what could be called a certain banality of highly technical specialization without systemic overview. Might the conceptual apparatus that constitutes architecture as a *profession* (rather than as an art or as a science) provide a model of how to preserve the „worth“ of the public order that is embodied in knowledge? This, of course, is but a biased and speculative outlook. But here are some indexes of how such a re-interpretation of architectonic disposition could be started.

The notion of architectonic disposition has recently been picked up by Michel Serres, who argues exactly along these lines. Ichnography, scaenography, orthography are terms that allow him to theorize a notion of system which contracts the first and the second laws of thermodynamics: its invariant conservation (1st Law) *and* its drift towards dissolution (2nd law). „Physics describes a system,“ he argues, „but not one that is hierarchic, deductive, or tightly ordered, as in the series of the Stoics: it is a set, a general equilibrium, a balance sheet that takes account of the stochastic“^{[5]}, as he puts it in *The Birth of Physics *(1977), where he develops his notion of the *foedera naturae*, the natural contract, in distinction to what he calls the *foedera fati*, the contract of destiny. Serres interest in the contract, here and in other texts, must be understood as translating the dimension of architectonic „orthography.“ Like this, one can decipher the same notion of system, always contracted to mathematical models and never self-evident, which he explored perhaps most prominently in his book *Le Système de Leibniz et ses Modèles Mathématiques* (1968). The introduction here is entitled „Ensembles théorique“ and Serres begins with the subchapter „Scénographie, Ichnographie.“ Scholars interested in Leibniz share a kind of embarassment, he begins. It concerns the irreconcilability of Leibniz’s rigorously systematic thought, while this very systematicity doesn’t cease to refuse itself to rigorous understanding. Leibniz presents his reader, as Serres puts it,

„a potential ordonnance which lets itself be divined and which refuses itself ceaselessly, a vague idea of a perceived coherence seen a thousand times in the mode of cavalier, and which hides its géometral, the sense of progressing in a labyrinth of which one holds the thread but has no map. Offered perspectives, multiplied points of view, infinitely iterated possibilities: it never seems that one could actually arrive at the exhaustive limits of a synoptic, spread out, complete and actual plan“.

^{[6]}

Serres here argues for a notion of the system which comprehends and organizes all that obeys the principle of identity, yet as an invariant of which he assumes nothing else except that it be capable of absorbing and integrating all the variations that can actually be attributed to it; one can refer to such a notion of system only via mathematical models, he maintains. Such models are not addressed as representing a reality (or ideality), they must be fashioned in profile to each other rather than to a frame of reference. Their profiles are to be worked out under the criteria of isomorphism (equality with regard to their formality) between all of them, rather than correlation (linear hierarchies of consequentiality) or representation between model and modeled reality. In Serres’ notion of a mathematical system „there is a plurality of possible paths of deduction;“[7] it is thus a notion of system which is „an irreversible order,“ which „like a ladder“ is made up of a plurality of „orders, derived from an infinitely replicated infinity of infinities (par „infinité d’ infinités infiniment répliquée’)“.[8] Within such a sheaf of orders, „my enunciations are universal and they conserve the analogy [a „discrete multiplicity“, which Serres contrasts with a function as „a continued variation“]“[9]. This is why mathematical modeling of the system, conceived as a ladder where different orders, each infinite, are leading from one to the other, progresses indefinitely. Its steps are governed by „laws of binding one–multiple, finite– infinite, which are of value in multivalent manner for perception, liberty, knowing, creativity, remembering etc, which all are at work also in the mathematical model.“ Hence, to Serres it is not mathematics which governs all these aspects of reality (perception, liberty, consciousness, creation, remembering etc) rather, he assumes, „there is no relation of cause and effect here, there is a parallelism of structure“. Serres’ notion of a system which contracts the invariant conservation (1st law, orthographia) *and* its drift towards dissolution (2nd law, ichnographia) is alway integrated, bound together (scenographia) mathematically, in models. The system, thereby, is never represented by its models. The relation between them is a contract that formulates their mutually implicative cordiality, the orthographic politeness that makes up the *foedera naturae*, the Natural Contract: „the model of the system, this is the system of the model“.

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^{[1]} cf. the preface by Vitruv, dedicated to his Ceasar.

^{[2]} I understand these concepts as elementary in a quasi-material, quasi-pre-socratic sense: all of them factor in all of the architectonic work, like the material elements in the Timeaus factor in all of the sensible bodies (all things are made up fire, water, earth and air, and between them we can assume the lawfulness of a proportionality: fire is to earth as air is to water).

^{[3]} Günther Fischer, *Vitruv NEU, oder was ist Architektur?* Birkhäuser, Basel 2009.

^{[4]} One can say that Vitruvius introduced models in „space“, the renaissance, with Alberti, introduced the models we are used to today (lineamenta), as models of motion in „time“, and that in today’s discrete (digital) geometric paradigm we are discovering models in „life“ (—> *invariance*)

^{[5]} Michel Serres, *The Birth of Physics*, Clinamen Press, Manchester 2000, p. 128.

^{[6]} Michel Serres, *Le Système de Leibniz et ses Modè**les Math**é**matiques* (1968), here cited from the kindle edition, position 162. My own translation, from French: „[…] une ordonnance potentielle qui se laisse toujours entrevoir et qui sans cesse se refuse, l’ idée vague d’ une cohérence perçu mille fois en vue cavalière et qui dérobe son géometral, la sensation de progresser dans un labyrinthe dont il tiendrait le fil sans en avoir la carte. Perspectives offertes, points the vue multipliés, possibilitiées infiniment itérées: il ne parait jamais qu’on puisse parvenir aux limites exhaustives d’un plan synoptique, étalé, complet, actuel.“

[7] ibid., position 190.

[8] ibid., position 487.

[9] ibid., position 492.

]]>author’s manuscript.

The mathematical notion of the equation is first documented in the 16th century, when it seems to have been introduced as what we would today call a *terminus technicus* for organizing the practice of equalizing mathematical expressions. It seems to have been introduced to European Renaissance science and philosophy together with algebra: an *equation *is the *mathematical form* for rationalizing and reasoning identity. The term “algebra” comes from Arabic *al-dschabr* for the „the fitting together of broken parts“, and its first appearance is usually referenced to the title of the Persian scholar al-Chwarizmi’s book *Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-ʾl-muqābala* (*The Compendious Book on Calculation by Completion and Balancing*). Two things are important to point out right ahead: the mathematical term of an equation references a mathematical form for stating identity, and it does so precisely by *not* assuming identity to be given as a whole. In this regard, it crucially differs from the identity notion in philosophy – it helps to reason and rationalize identity, but in the original sense of Greek *mathema*, literally “that which can be learnt”, and *mathematics* for “all that pertains to what can be learnt”. Through this emphasis on learning (rather than knowing), and hence on mathematics as an *art*, the equational notion of identity is always already in pact with the mathematical irrational (the infinitary). It remains indetermined with regard to the whether identity as a postulated principle is to be regarded as a logical device, or whether it there is to be assumed a substantial reality of this principle in nature that can empirically be studied in physics[1] (–> invariance). This indeterminedness is indeed the key aspect which Michel Serres attributes to algebra for the advent of modern science and its paradigm of experimentation at large: Experimentation, invention, consist in making the cypher under which nature hides appear, he maintains. “At the beginning of the seventeenth century, when what we came to call the applied sciences first made their appearance, a theory spreads that one can find in several authors, although none of them is its sole source, which seeks to account for a harmony that is not self-evident.” Rather than looking at conceptual identity as the provider for self-evident harmony to look for in nature, what begins to spread, since Galileo and certainly with Descartes, Leibniz, Pascale, Fontenelle, is “the idea that nature is written in mathematical language.” But Serres immediately points to the insufficiency of the term language here; he points out the constitutive role of algebra for the role of mathematics in experimentation, and specifies that “[l]n fact mathematics is not a language: rather, nature is coded. The inventions of the time do not boast of having wrested nature’s linguistic secret from it, but of having found the key to the cypher. Nature is hidden behind a cypher. Mathematics is a code, and since it is not arbitrary, it is rather a cypher.” Serres’ speaking of cypher here is to be taken in mathematical sense: cypher is a term for how, in mathematical notation, *naught* can be expressed. It literally meant zero, from the Arabic term *ṣifr*, for zero. A cipher constitutes a code that affords encryption and decryption such that once the operations have been performed, the “text” or “message” – nature, in Serres’ cited passage – that it envelops, has not been affected by these operations. Algebra, as the art of speculative completion and balancing, experimentally searches for the code *without having it to start with*: the equational notion of identity hence is capable of organizing the practice of equalizing mathematical expressions in experimental manner. “Now, since this idea [that the harmony to be seeked is not self-evident but depends upon experiment, VB] in fact constitutes the invention or the discovery,” Serres continues, “nature is hidden twice. First under the cypher. Then under a dexterity, a modesty, a subtlery, which prevents our reading the cypher even from an open book. Nature hides under a cypher. Experimentation, invention, consist in making it appear.”[2

This emphasis on an equational identity notion, whose determination correlates with its articulation in the characters of a cipher and by the rules of a code, bears two great promises: (1) it affords a thinking that is capable to leaving its object – that which it envelops in code and makes appear – unaffected, and thus gives new support to a scientific notion of objectitivity; (2) this thinking proceeds algorithmically, formally, and hence can be externalized into mechanism that can perform it decoupled from a human cogito, but at the same time this does not liberate thought from mastership and literacy, for “reading” this cypher behind which “nature hides” crucially depends upon dexterity, modesty, and subtlery. In other words: a reasoning that can be externalized into a mechanism, and hence render obvious a not self-evident harmony (an interplay of parts that function well, work together fittingly, etc), must be considered strictly decoupled from any notion of truth. Equational identity is genuinely abstract. The *Introduction to Mathematics* written by Alfred North Whitehead is an exemplary text elaborating on the notion and role of mathematical abstractness.[3] How this role can be played today by a mathematical notion of information remains a largely open issue to this day. [4]

This article indexes Alfred North Whitehead’s *Treaties on Universal Algebra* from 1898 as the moment in which algebraic abstractness begins to find a novel embodiment in “information”.[5] It will trace some of the “genetical” heritage of mathematical abstraction whose lineages conflue here.[6] Until the late 19th century, algebra was used almost synonymously with a theory of equations, and its symbolical notion was thought to encode quantity in its classical double-articulation as magnitude (metrical, answering to *how much*?, presupposing a notion of unit) and multitude (countable, answering to* how many*? presupposing a notion of number). When Alfred North Whitehead wrote his* Treaties*, this had changed: with Cantor’s countable infinities (among many other factors that had been contributed, to name only a few of the most important names, by William Rowan Hamilton, Richard Dedekind, George Boole, Hermann Günther Grassmann,), the classical distinction between multitude and magnitude gave way to a more abstract distinction between ordinality (answering *to the howmaniest?*) and cardinality (*how many*?).[7] The generalized quantity notion was now that of ‘sets’; the status of mathematics with regard to philosophy and the natural sciences, but also with regard to linguistic form (structuralism) and literary form (e.g. in Wittgenstein’s notion of ‘natural language’ as ‘mathematical prose’) was profoundly unsettled thereby. This is what it means to say that mathematics is no longer concerned with quantity, but with symbolical systematiciy. When Whitehead wrote his *Treatise on Universal Algebra,* algebra needed to be addressed by means of what he suggested to think of as „a comparative study,” because it had given rise to “various Systems of Symbolic Reasoning“.[8] And those *Systems of Symbolic Reasoning*, as Whitehead calls them, had been looked upon „with some suspicion“ by mathematicians and logicians alike – as Whitehead puts it: „Symbolic Logic has been disowned by many logicians on the plea that its interest is mathematical, and by many mathematicians on the plea that its interest is logical“.[9]

The practice of equalizing mathematical expressions, which gave rise to the notion of equation, meant that arithmetics could not only be done with numbers (*arithmos*) understood in an Aristotelian sense (as ontological science), but with what we could call ‘lettered/characterized numbers’ that entailed an intermediary symbolical-notational formality (codes or poly-tomistic alphabets, elements that are not non-divisible, atomic, but partitionable in many ways). The decisive aspect is not that letters of the alphabet were newly used in mathematics[10]; it is that alphabetic letters began to be used for the notation of numbers *in a manner that changed the concept of number*: numbers, now, could be articulated as an interplay between variable parts and constant parts. This was not the case in antiquity. Here, numbers were always determinate numbers of things, while the algebraic concept of number works upon what is a ‘given’ only in the form of a metrical measurement point. Eventually, this novel manner of thinking about numbers gave rise to sophisticated procedures of estimation like stochastic interpolation and extrapolation. Mathematics thereby came to be seen as an activity, an intellectual and practical art, and the resulting geometry was referred to not as ‘elementary’ (*stochastiké*, in the tradition of Euclid’s Elements), but as ‘analytical’, ‘specious’, and eventually as ‘population based’ (modern stochastics, probabilistics).[11] The notion of a mathematical *object* was called by the early algebraists *la cosa,* the unknown – or not exhaustively known – ‘thing’.[12]

This novel notion of the object triggered in philosophy (and in politics) the inception of concepts of *sufficient reason* on the one hand, and of *absolutism*, literally meaning “unrestricted; complete, perfect”; also “not relative to something else,”[13] on the other hand. Not relative to something else meant for mathematics that the role of proportion (A is to B as C is to D) as the classical paradigm for analysis (literally the dissolving, from Greek –*lysis*, for “a loosening, setting free, releasing, dissolution,” from *lyein* “to unfasten, loose, loosen, untie” what is analog, from Greek *analogon*, from *ana* “up to” and *logos* “account, ratio”) was generalized, and thereby also relativized; proportion was now addressed as ‘proportionality’, and reason was now relative to conditions of possibility and the inclinations of dispositions. The practices of equalizing mathematical expressions unfolds in this generalized role of proportion as proportionality, and the notion of ‘equation’, with the symbolic forms of organizing these practices can be understood as the technical term to express this relativization of the analogical structure of proportion. It introduced a novel art, the *ars combinatoria*, and the practice of algebraically equalizing mathematical expressions culminated with Newton’s and Leibniz’ infinitesimal calculus as a novel *mathesis* *universalis* (a universal method) which triggered a fierce dispute in the 18^{th} century between philosophical Rationalism (baroqu’ish and ‘orthodox’ in spirit) and Empiricism (reformationist and ‘modernist’ in spirit). Immanuel Kant’s notion of the transcendental, together with his program of critique for philosophy, eventually relaxed the disputes (temporarily)[14]. Algebra, as the theory of equations, was now to provide insights not about the nature of elements immediately, but in rules that can be deduced from Natural Laws that reign in physics. Mechanics came to be seen as a particular case of a more general physics, including dynamics and soon thereafter also thermodynamics. It was now the formulation of these laws (no longer that of mechanical principles) that was to be stated in the form of equations, accessible critically through empirical experiment coupled with exact conceptual reasoning, and hence decoupled from an affirmation of any metaphysical (and theological) assumptions in particular.[15] [16]

[–> negentropy; –> invariance].

**************************************

[1] Cf. Jacques Monod, *Chance and Necessity, **An Essay on the Natural Philosophy of Modern Biology*,

Vintage Books, New York 1972 [1970].

[2] Serres, *Birth of Physics*, ibid., p. 140.

[3] For an extensive discussion of mathematic’s abstractness cf. Alfred North Whitehead: *An* *Introduction to Mathematics, *Williams and Norgate, London 1917*, *especially the first chapter „The abstract Nature of Mathematics“.

[4] Michel Serres, “Les nouvelles technologies : révolution culturelle et cognitive”, Conférence de Michel Serres lors du 40è anniversaire de l’INRIA en 2007, available online: https://www.youtube.com/watch?v=ZCBB0QEmT5g; cf. also the manuscript “Information and Thinking” of his lecture at the Philosophy after Nature Conference 2014 in Utrecht, forthcoming in the conference’s proceedings edited by Rosi Braidotti and Rick Dolphjin.

[5] Alfred North Whitehead, *Treatise on Universal Algebra with applications*, Cambridge University Press, Cambridge 1910.

[6] A remarkable study on the Cogito in terms of a materialist genetic heritage is: Anne Crahay, *Michel Serres. La Mutation du Cogito. Genèse du Transcendental Objectif*, De Boeck, Brussels 1988.

[7] cf. Sören Stenlund, *The Origin of Symbolic Mathematics and the End of the Science of Quantity*, Upsala University Press 2014 (available online: http://www.divaportal.org/smash/get/diva2:709492/FULLTEXT01.pdf)

[8] ibid. vi.

[9] ibid.. Cf. also the discussion of how Universal Algebra proceeded and evolved until the 1960ies by George Grätzer: *Universal Algebra*, The University Series in Higher Mathematics, D. van Nostrand Company Inc., Princeton 1968; as well as for a discussion of the subject’s developments since the 1950ies until 2012: Fernando Zalamea, Synthetic Philosophy of Contemporary Mathematics, transl. by Zachary Luke Fraser, Urbanomics 2012; also cf. the appreciation and critique by Giuseppe Longo, “Synthetic Philosophy of Mathematics and Natural Sciences. Conceptual analyses from a Grothendieckian Perspective. Reflections on “Synthetic Philosophy of Contemporary Mathematics” by Fernando Zalameo, available online at Giuseppe Longo’s institutional page CNRS, Collège de France et Ecole Normale Supérieure, Paris: http://www.di.ens.fr/users/longo/files/PhilosophyAndCognition/Review-Zalamea-Grothendieck.pdf

[10] Indeed, the separation of a particular notational system for mathematics is a rather recent development compared to the history of mathematics; it is a bifurcation after many centuries of using one and the same script for linguistic as well as mathematical articulations. Cf. Gerd Schubring, “From Pebbles to Digital Signs: The Joint Origin of Signs for Numbers and for Scripture, Their Intercultural Standardization and Their Renewed Conjunction in the Digital Era” in Vera Bühlmann, Ludger Hovestadt, *Symbolizing Existence, Metalithicum III*, Birkhäuser, Vienna, 2016 (in press).

[11] Cf. Rosa Massa Esteve, “Symbolic language in early modern mathematics: The Algebra of Pierre Hérigone (1580–1643)“, *Historia Mathematica***, **Elsevier, Volume 35, Issue 4, November 2008, 285–301.

[12] Jules Vuillemin gives a fabulous account of these complex interrelations in his seminal book *La Philosophie de l’Algèbre, **Tome I : Recherches sur quelques concepts et méthodes de l’Algèbre moderne* (Paris: 1962).

[13] cf. www.etymonline.com; also the article by Wilhelm G. Jacobs, „Das Absolute“, in: Hans Jörg Sandkühler (Ed.), Enzyklopädie Philosophie, Felix Meiner Verlag, Hamburg 2010, p. 13-17.

[14] It seems not entirely implausible, at least, to think about the early 20th century foundational crisis as a continuation of just these disputes on higher levels of abstraction. For a largely unbiased account and a serious and open-minded suggestion of how to approach the dilemma, cf. Hermann Weyl, *The Continuum: A Critical Examination of the Foundation of Analysis, *(1918).

[15] Due to its brevity, this summary follows the lineage in the critical tradition what has turned out as the predominant one, linking 20st century analytical as well as continental philosophy; it thereby understates the ideas of Leibniz, Lambert, and others, who maintained that algebra, by its calculatory and symbolic methods, could actually be seen as opening up the closedness of classical logics in the Aristotelian tradition, thereby introducing an *ars inveniendi*, an *art of invention *into logics – an approach that was still pursued by figures as eminent for the 19th century development of algebra as Charles Sanders Peirce (abduction) or Richard Dedekind (abstraction as a creative act). Against these ideas, Kant famously stated: „Die Logik ist […] keine allgemeine Erfindungskunst und kein Organon der Wahrheit; – keine Algebra, mit deren Hülfe sich verborgene Wahrheiten entdecken ließen“ (Immanuel Kant, Logik. Ein Handbuch zu Vorlesungen (1800), Friedrich Nicolovius: Königsberg; Akademie-Ausgabe, Bd. 9, 1–150, A 17, here cited in: Volker Peckhaus, „Die Aktualität der Logik als Organon“, in: Günter Abel (Ed.), *Kreativität : XX. Deutscher Kongress für Philosophie, 26.-30. September 2005 an der Technischen Universität Berlin : Kolloquienbeiträge*, Hamburg: Felix Meiner Verlag, 2006. For an introduction of the conflicts the unsettled status of algebra triggered in the empirical sciences themselves, cf Elisabeth Stengers’ *Cosmopolitics I*, University of Minnesota Press 2010 [2003], especially book II *The Invention of Mechanics, Power and Reason,* p. 68ff, therein „The Lagrangian Event“ (112ff.) and „Abstract Measurement: Putting Things to Work“ (129ff.).

[16] Cf. the seminal study on the implications of this for axiomatics by Robert Blanché, *L’Axiomatique*, Presses Universitaires de France, Paris 1980 [1955]; there is an English edition of this book by Geoffrey Keene, Monographs in modern logic, The Free Press of Glencoe, New York 1962, but it excludes the crucial two chapters with which Blanché ends his study, discussing the implications for science and for philosophy. Cf. on the genealogy of philosophical notions of necessity and contingency, and the relatively recent upheavels with regard to this genealogy, als Jules Vuillemin’s studies *Necessity or Contingency. The Master Argument*, distributed for Center for the Study of Language and Information by The University of Chicago Press, Chicago 1996; and *What Are Philosophical Systems*, Cambridge University Press, Cambridge 2009.

author’s manuscript.

The main inclination this article will try to develop concerns a danger that Michel Serres has stated as follows: not to confuse invariance and identity.[1] Jacques Monod, to whom Serres refers with this statement, has pointed out the source of this likely confusion with regard to what he calls the “quantic revolution”[2]: “The principle of identity does not belong, as a postulate, in classical physics. There it is employed only as a logical device, nothing requiring that it be taken to correspond to a substantial reality.”[3] After the quantic revolution, however, the principle of identity ceases to be a merely logical device; in quantum physics, one of its

“root assumptions is the

absoluteidentity of two atoms found in the same quantum state.[4] Whence also the absolute, non-perfectible representational value quantum theory assigns to atomic and molecular symmetries. And so today it seems that the principle of identity can no longer be confined to the status simply of a rule of logical derivation: it must be accepted as expressing, at least on the quantic scale, a substantial reality.”[5]

But isn’t the notion of identity, at least in its philosophical scope, always already entangled with notions of substance, and hasn’t it been one of the most valuable achievements of 20^{th} century philosophical discourse to argue that talk of identity, at least with regard to cultural issues, be unnecessary, that its substantiality is always already discursively constituted and that we can learn from science that to speak of identity means evoking a logical abstraction, at odds with any realist position, and ought better be addressed in terms of a notion of materiality that must be forged situatively. A notion of materiality that is obliged to take into account a very large number of factors, to a degree of complexity about which we can only learn from “real” bodies of all kinds, organic and/or chemical, with regard to their environmental niches (in “culture” as well as in “nature”) and the evolutionary interplay among such niches (in the earth and environmental sciences as well as in history and politics), rather than from ideally constructed typologies, morphologies, ideologies. Must it not be regarded as an ethical obligation to commit ourselves to a derivative, differential and functional view on sexuation (ontologies: genderedness, queerness, nomadicity, “bodies-that-matter”) rather than a structural or homeostatic, symmetry based and equational view rooted in identity (metaphysics: principles, laws, axioms, elements, atoms)?[6] Hasn’t this been the great emancipation of the last few decades? It certainly has. And it is at the core of the confusion of which Serres warns us, between invariance and identity. In such a confusion, this term, *invariance*, would indeed overcloud once again whatever brightness with regard to the future, that the painfully wrought emphasis on difference over identity and the ethical practices of counterbalancing and weighting up of normativity and standardization with esteem for singularity in its own rights, might invite us to hope for. But Serres’ warning of confusion not only points to the fragility of how we value the emancipatory worth of such critique; it also entails that we come to terms with a notion of substantial and absolute identity.[7]

“A blue alga, an infusorian, an octopus, and a human being-what had they in common? With the discovery of the cell and the advent of cellular theory a new unity could be seen under this diversity. But it was some time before advances in biochemistry, mainly during the second quarter of this century, revealed the pro- found and strict oneness, on the microscopic level, of the whole of the living world.”[8]

This oneness is the subject of Serres’ ciphered atomism, [9] of the entropic cataract of atoms falling, as particles of regularity in declination – clinamen, an angularity – through the void, conjugating into local turbulence, where and by which “atoms meet”[10]; his notion of the atom is the minimal condition to explain how turbulence forms, “appearing stochastically in laminar flow” [11] the substance of chance, the cataract. His notion of the atom encrypts the magnitude of a substantial notion of chance as the universal principle (Zufall), in which pockets of negentropy capture local and temporary order: “Systems of conservation for chance, systems which orientate and control themselves, packed to their limits with negentropy. Enzyme catalysis, a capacity for discrimatory selection.” [12] Can ontogenetic life (specious life forms) be compatible with the second law of thermodynamics (the drift towards maximum entropy, the disintegration of all forms of organization into its atomization where each particle of formality is of equal probability), apparently compatible only with phylogenetic life (the common origin of all individuals), he asks? And he maintains yes, it can: “the conceptual pair information-entropy reduces to a level of the objective, calculable, positive, the old metaphysical twin notions of chance and necessity”.[13] Because the role of information as a currency in the economic calculations of the thermodynamic balance sheets (information is not gratuitious, every observation has its price, –> *negentropy, *and –> *Maxwell’s Demon*), we find afforded by the pair information-entropy *a physical theory of heritage. *

The question that can be foregrounded by a discussion of the term “invariance” concerns how substantial identity, absolute because governed by chance, might possibly be distinguished in quantitative terms. What Michel Serres and Jacques Monod, building on the information theory in the tradition of Oswald Wiener, Léo Szilard, Léon Brillouin, suggest (–> *negentropy*), is that such identity can be quanitzed as binding amounts of information capable of preserving a certain structure across variable transformations: Monod’s invariance can be understood as an “invariance content” (quantized specie-iality) that is “equal to the amount of information which, transmitted from one generation to the next, assures the preservation of the specific structural standard”.^{[14]} Invariance is reserved for a quantity that establishes a niveau of information or negentropy^{[15]} (bound information). What is hence established, from invariant content, is what Monod calls “teleonomic information”. Teleonomy refers to probabilistic calculations on the combinatorial total of transfers that can apply, in conformity with the laws of conservation, to an invariant amount of information.^{[16]} It is Monod’s great achievement to have distinguished (1) an *operable definition of chance *as the* unknown *(due to the imperfect experiment, while not knowing all the initial conditions, the cost of observations), chance at work in logical/formal terms in stochastical statistics, and (2) an *essential* definition of chance, by attributing chance a substantial and absolute identity.[17] We can easily associate the operable chance with entropy as an operational measure in thermodynamics, and essential chance with the principle assumption that the amount total of energy in the universe be finite and invariant. The latter cannot be counted, it can only be coded and like the identity of all life forms in terms of DNA, it can be deciphered through translating between manners of coding.

There is a universal nature (substantial identity) that pertains to all things, and this universal nature is what Jacques Monods suggests to address in terms of an object’s “strangeness”.^{[18]} One confuses invariance with identity whenever one reads Monod’s use of “strange” in his discussion of “strange objects” as an adjective, Serres elaborates; “strange does not qualify a substantive”, rather “strange” operates as a quantifier, not as a qualifier. The molecular theory of the genetic code is “a physical theory of heritage” that complements the Darwinian evolutionary view. A physical theory of inheritance is a basis that quantifies substantives in terms of different niveaus of negentropy (as amounts of chance, that can be deciphered from the mutually implicative relation between invariant and teleonomic information). With his notion of the *strange object*, Monod suggests a notion of the object that neither contradicts the principles of physics (2^{nd} law of thermodynamics, one universality) nor those of Darwinian biology (natural selection in evolution, pluralist universality of natural kinds). Hence ontogenetic and phylogenetic life are both compatible with thermodynamics. But the central assumption thereby is that invariance genetically, chemically, and physically precedes teleonomy: “the *Genomenon* is the secret code of the *Phaenomenon*”, as Serres puts it.^{[19]} The “strange object” is one which neither presupposes a distinction between natural and artificial, things endowed with a purpose (project) and things natural (without purpose), nor one between animate and inert. It is crucial for understanding Monod’s primacy of code to emphasize that what is all-too-often short-circuited as “the code of life”, to Monod is a relation between code and its secret (life) that is one of mutual *independence*, one regarding the phenomenon of life (not life itself) and one entirely chance-bound in the substantial definition of the term:

“[…] between the occurrences that can provoke or permit an error in the

replicationof the genetic message and its functional consequences there is also a complete independence. The functional effect depends upon the structure, upon the actual role of the modified protein, upon the interactions it ensures, upon the reactions it catalyzes – all things which have nothing to do with the mutational event itself nor with its immediate or remote causes, regardless of the nature, whether deterministic or not, of those causes.”^{[20]}

In order to illustrate this postulated independence between the code itself and its articulated manifestations, Monod discusses the coincidence of genuinely heterogenous sequences via the example of a worker fixing a roof, letting go of his instrument accidentially, and a passerby who is in no way related to the worker on the roof but who is hit by the falling instrument and killed thereby. If one were to assume that there be a larger logics that homogenizes these two heterogenous series, one would indeed have to assume that the passerby was fatefully predicated to die like this from the very beginning of his existence; against the assumption of such fatalism, Monod stresses his two definitions of chance, as (1) operable and (2) substantial. While the genetic text itself is a closed and finite system (with its residual alphabet of amino acids and nucleotides), the source of the biospheres incredible variety results from errors in the transcription of the code’s sequences. For this transcription process it is crucial that one always has to consider *pairs* of nucleotides (literally *that which is with a nucleus*), one cannot do with singularized and original ones. These pairs – and this is the essential role invariant amounts of information need to play, counterbalancing the structural teleonomy of bound information – must be deciphered in a double sense. This is how Serres can say: “nature is hidden twice. First, under the cypher. Then under a dexterity, a modesty, a subtlety, which prevents our reading the cypher even from an open book. Nature hides under a hidden cypher. Experimentation, intervention, consist in making it appear.“[21]

*****************************************

[1] Michel Serres, „Leben, Information, und der zweite Hauptsatz der Thermodynamik“, in *Hermes III Übersetzung*, Merve, Berlin 1992 [1974], S. 53-96.

[2] Algebra, which used to be regarded in the 17^{th}/18^{th} century the *theory of equations*, has transformed by the early 20^{th} century into what was now called *Quantics, *the theory of “algebraic forms” also called “residual forms”. Residual forms are forms that “define” by *conserving something indefinite throughout transformations*, while it is the transformations themselves that they regulate their formality, their morphisms (not the nature of any sort of content, as in the hylemorphic tradition). With the seminal work of Emmy Noether and others on reformulating the Laws of Thermodynamics as *Laws of Conservation*, Quantics turned into* a general theory of invariances. *Cf. Yvette Kosmann-Schwarzback, *The Noether Theorems. Invariance and Conservation Laws in the Twentieth Century*, transl. by Bertram E. Schwarzbach, Sources and Studies in the History of Mathematics and Physical Sciences, Springer 2011; as well as Jean-Marc Levy-Leblond and Françoise Balibar, *Quantics: Rudiments of Quantum Physics,* North Holland, 1990.

[3] Jacques Monod, *Chance and Necessity, **An Essay on the Natural Philosophy of Modern Biology*,

Vintage Books, New York 1972 [1970], p. 101.

[4] The author here refers his reader to V. Weisskopf, in “Symmetry and function in biological systems at the macromolecular level,” Nobel Symposium No. 11, ed. Engstrom and Strandberg, New York (1969), p. 28.

[5] Monod, *Chance and Necessity*, p. 101.

[6] cf. especially Donna Haraway, *SF, Speculative Fabulation and String Figures,* edited in: 100 Notes, 100 Thoughts: Documenta Series 099, Hatje Cantz 2012.

[7] We might say, invariance applies “only” to the quantum domain; but what might appear at first like a hygienic “restriction” of the upheavals that announce themselves to one domain in particular is in fact its total expansion. Not only particle physics, but also all of chemistry and molecular biology, as well as the mathematical quantity of information (through its operationalization in terms of entropy and negentropy) *involves* the “indefinite scalarity”^{[7]} of the “quantic revolution”. Any notion of a situatively, differentially forgeable, embodied materiality today, hence, will find itself affected by it. Karen Barad has made a strong case pointing in this direction, cf. her *Meeting the Universe Halfways*, Duke University Press, 2007.

[8] Monod, *Chance and Necessity*, ibid., p. 102.

[9] cf especially Michel Serres, *The Birth of Physics*, Manchester: Clinamen Press 2000.

[10] ibid., p. 6.

[11] ibid., p. 6.

[12] Serres, „Leben, Information und der zweite Hauptsatz der Thermodynamik,” ibid. p. 63.

[13] ibid. p. 62.

[14] Monod, *Chance and Necessity*, ibid., p. 13.

[15] Serres, „Leben, Information und der zweite Hauptsatz der Thermodynamik,” ibid. p. 57.

[16] Monod, *Chance and Necessity*, ibid., p. 14.

[17] This is his commitment to Léon Brillouin’s emphasis on the substantiality of code in information theory, which led him to distinguish negative and positive information alongside the distinction between negative and positive entropy. Cf. his seminal book *Science and Information Theory*, New York: Academic Press, 1956. Serres discusses this commitment at length in “Leben, Information und der zweiter Hauptsatz der Thermodynamik”, ibid.

[18] cf the introductory chapter in Monod’s *Chance and Necessity,* „Strange Objects“, p. 3-22.

[19] Serres, „Leben, Information, Zweiter Hauptsatz der Thermodynamik“, ibid., p. 59.

[20] Monod, *Chance and Necessity,* p. 114.

[21] Serres, *The Birth of Physics*, p. 140. Serres further developed this idea of a ciphered atomism in his more recent book *L’Incandescent*, Paris, Le Pommier 2003.

*by Vera Bühlmann*

author’s manuscript.

In this article, I would like to discuss one of the key moments of reference in 20^{th} century information science, which arose from thermodynamics and which in fact links the latter to the former in many important aspects. Maxwell’s famous thought experiment explores how to think of heat, if we can conceive of it neither as a force nor in (metaphysical) substantial terms (–> negentropy). Before discussing how the stakes were formulated in this thought-experiment, and how these same stakes were re-articulated in famous discussions of it, it is important to understand that here, we have the beginning of a certain coinage of thinking about chance in purely operational terms: one which attributes probability to humanly imperfect faculties that need not, in principle, be taken into account if operations in the natural sciences be carried out by a “pure” agency like the particular intelligence which Maxwell set out to design in his thought experience. This very background links the concept discussed in this brief article to the discussions about artificial intelligence at large, also beyond the elected aspects that will be discussed here.[1]

James Clark Maxwell responded to the problem of thermodynamics’ irreversibility with a thought experiment designed to resolve the subjectivity which apparently inheres to experimental science when it involves heat balances (through probability). If heat is apparently not to be held identical with energy (irreversibility, 2^{nd} law) nor approached in metaphysical terms as a new kind of substance, then we can think of heat as the motion of molecules in populations, Maxwell maintained. Individually, so he formulated the belief of many of his contemporaries, the molecules must obey Newton’s Laws: Every action, every collision, must be measurable and calculable in theory. This assumption led him to invent a scenario that involves a perfect observer, one whose faculties were not to be flawed like the human imperfect ones, in short, a cognitive agency freed from all subjectivity, probability, and hence whose reasoning would be freed from irreversibility. Maxwell set up the ideally perfect experiment where the observer is to be capable of purifying the science of heat from the factual irreversibility at work in it (–> negentropy). For this observer, thermodynamics would be as determined and without need for the assumption of a final cause or any other agency that acts in non-reasonable manner from a distance, as Newtonian physics is.[2]

When Leó Szilárd attended to Maxwell’s thought experiment, he hoped to dissipate the rather metaphysical discussions that had emerged and gave rise to both animist as well as vitalist discussions of the possibility of a “perpetual movement” which Maxwell’s agency – if considered a legitimate concepts – would render real.[3] Instead he re-considered Maxwell’s purely mechanical agency at stake in computational terms and equipped it with the capacity to memorize and evaluate all the observations it makes, and hence be capable of making up for the inevitable expenditure of energy through understanding how it could be balanced again.[4] The core assumption of Szilárd[5] was that even this perfect observer’s faculties of observation would have to be accounted for in terms of measurement and calculation else – if observation is not formalized – the thought experiment’s value for justifying a classical notion of experimental science is nullified at once (since by definition such observation would transcend the conditions of experimentation). In order to account for the demon’s observation in those terms, Szilárd introduced “information” and “memory” into the set-up (although Szilárd did not speak of “information” properly, he spoke of the results of measurements which needed to be memorized in whatever “form”)[6]. He effectively transformed Maxwell’s original conception of a demon, acting mechanically like a thermostat, into a *deus ex machina*, an artificially intelligent being that can remember whatever experiences it makes while measuring.

But there were problems with faculties perfected in Szilárd’s manner as well: Once we assume that a system needs to be quantized in order to be measured and hence remembered, we are dealing with the unknown quantities of microscopic variables that “make it possible for the system to take a large variety of quantized structures”: stochastic definitions (Laplacean determinism) apply only to lower frequencies like those of a thermostat (in essence the kind of intelligence Maxwell conceived of), but not to higher frequencies like those of an oscillator (the re-devolpment of Maxwell’s intelligence by Szilárd); higher frequencies display no stochastic distributions; position and magnitude of the waves cannot be at once observed and hence such observation involves probabilities. Even if the perfect agent would apply his perfect faculties by measuring (objectively), it’s assumption would not lend itself to stigmatize probabilities to the side of subjectivity against a supposedly stochastic distribution of objective nature.

Probability enters the picture of Laplacean determinism in that the movement of molecules has to be measured and calculated *in populations (rather than individually)*. This implies a foregrounding of a certain role of code in this measuring and calculating.[7] The methods of probabilistics differ from those of stochastics with regard to this role of encryption. From this perspective, entropy is a term to measure the dissipation of heat by means of encrypting “a large amount”– large enough to count the totality of possible transformation in an ideal state in which every next step is equally likely (entropy). The core assumption of thermodynamics is that the amount total of energy in the universe be invariant, that nothing can be added or subtracted to it (First Law of Thermodynamics). Entropy is the name for that number, and its extension (largeness of this number) is subjected to encryption in algebraic code (–> equation). Like this, to think of energy in terms of entropy does not depend upon a semantic or substantial interpretation of energy, and it does not need to know just how much energy there really is in the universe (–> invariance). Every system that real (empirical) science can identify is *one that factors in* in this only cryptographically knowable invariant amount total of energy in the universe.

Léon Brillouin, building upon the work of Szilárd, went a step further. Familiar with Turing’s[8] and Shannon’s[9] and Wiener’s[10] work on a mathematical notion of information and their dispute with regard to whether information can be measured in terms of the experimental entropy notion applied to physical systems (Shannon), or whether it needs to be accounted for in Schrödinger’s terms of negentropy import in biological systems[11], Brillouin foregrounded the role of “code” in such “intelligent” computation and applied a *double* notion of negentropy and entropy – one to energy, one to information, under the assumption that both be linked by code: free (entropic) information to him is the maximum amount of apriori cases formulated in a code. The apriori cases can be computed by combinatorics, and each of them must be regarded as equally likely to happen in entropic information. Bound (negentropic) information is empirically measured information (in experiments with any particular manifestation of such a code). This transcendental in the measurement of information allows for thinking of information as a kind of currency that through circulating is capable of transforming energy into information and vice-versa. This is how Brillouin could affirm the ultimate failure of Maxwell’s thought experiment: Not even an observation can be obtained gratuitiously, he maintained, and all information has its price.

The implications of such an economy, one that transforms information into energy and vice versa, has only rarely been explored so far. It is mainly pursued in the work of Michel Serres, which I want to point to in conclusion to this article. Thus we want to ask with Michel Serres: “What does this demand for an absolutely exact measurement mean?” He resumes:

“In a famous theorem, Brillouin proofed that a perfect experiment can absolutely not be realized, because it would produce an infinitely large amount of information and, in addition to this, an infinitely large amount of negentropy would have to be expended. […] the classical physicist believed that he could go to the very limits, and observe what would happen if all mistakes in observation could be reduced to zero; today we know that this margin is impossible, because the costs for this observation would rise to infinity. Absolute determinism is a dream, for perfect precision with regard to the initial conditions cannot be achieved. In other words, this demand [for the perfect experiment, VB] exceeds the limits of a possible experiment, it transcends its own postulates. It is possible to proof that one can never know exactly all the parameters of an experiment. There remains a rest of chance, a remainder of the unknown […].[12]

The consequences Michel Serres draws from the failure are as original as daring: chance is to be regarded as the object of science, he maintains, not nature! Michel Serres sees in information theory a philosophy of physics that is inherent to the domain of physics. It is remarkable, he points out, that Brillouin titled his book *La Science et La **théorie de l’information. *This book contains, so Serres, an epistemology of the concept and the praxis of experimentation, formulated in the language of physics, exhaustively descriptive, quantified, normalized and constitutive. This epistemology is at once one of natural laws, precise and approximational insight, hence all of classical philosophy, as well as, in the theory of code, language, script and translation it contains, this epistemology is all of modern philosophy as well. “Philosophers ought no longer search for an epistemology of experimental reason, nor write schoolbooks about it; it exists already.” [13] The theory of information is the philosophy of nature inherent to physics precisely in that it acknowledges this remainder of chance, which insists in all that can be known as substantial to any concept of understanding and knowledge. It is this remainder upon which Serres’ “logiciel intramatériel” operates. The subjectivity or agency of this logiciel constitutes “l’objective transcendentale”, a transcendental objectivity whose forms of intuition are not, as in Kant, constituted by physics notions of time and space, but by Brillouin’s “a priori probabilities” – the maximum and finite (albeit, depending on the code at stake, very large) number of equally likely cases which the combinatorics of a code may compute. To Brillouin and to Serres, the codes in terms of which information can be measured – as the currency that circulates in energetic expenditure – are to be regarded as different levels of negentropy in a manner analog to the energy levels in quantum mechanics, where bound particles can take on only certain discrete values of energy (rather than any energy, as is the view for particles in classical mechanics). Codes, as levels of negentropy, provide the sufficient reason for a certain disposition of knowing or “architectonic speculation” (–> *architectonic disposition*).

[1] The point I want to highlight is that against all enthusiasms of this outlook (non-anthropocentric cognition and reason) stands a certain complication in how we think of chance: from a quantum-science point of view, there appears the need to complement the operational definition with one that considers also a certain “substantiality” of chance itself – not in order to relativize the objectivist paradigm of science, but quite contrarily, in order to maintain its centrality for a non-dogmatic, scientific understanding of knowledge (–> invariance).

[2] “A being whose faculties are so sharpened that he can follow ever molecule in is course, and would be able to do what is at present impossible to us. […] Let us suppose that a vessel is divided into two portions, A and B by a division in which there is a small hole, and that a being who can see the individual molecules opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will, thus without expenditure of work raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics,” cited in Leon Brillouin, (J. H. Jeans, “Dynamical Theory of Gases”, 3^{rd} ed. p. 183, Cambridge UP New York, 1921)

[3] second perpetual motion of a second kind …

[4] As Gleick points out, Szilouin thereby anticipated Turings famous thought experiment by some years.

[5] In his 1928 Habilitation entitled *Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen.*

[6] cf. gleick

[7] The systems of real physics can count as universal only in the mediate sense that they obey the laws of thermodynamics. But the entropic, thermodynamic universe itself cannot be thought of as a physical system properly, because the universe’s entropy itself is an assumed ideality – an ideality which is to serve as a support to the experimental paradigm of science, with the least possible semantical (biased) import.

[8] Turing…

[9] Shannon, Claude E., “A Mathematical Theory of Communication”, *Bell System Technical Journal* 27 (3): 379–423 (1948);

[10] Norbert Wiener: *Cybernetics: Or Control and Communication in the Animal and the Machine*, 1948

[11] Shannon discusses the term negative entropy, but considers its distinction negligible for information as a mathematical quantity notion. It was Norbert Wiener, who via the work by John von Neumann, Alan Turing, Claude Shannon and Leo Szilard maintained against Shannon that negentropy is in fact crucial, rather than negligible for a mathematical theory of information; it is largely due to this dispute that until today, different notions of mathematical information are in usage: (1) information as a measure for order in terms of entropy, and (2) information as a measure for order as negentropy; while both speak of information as a measure, and hence capable of establishing order, the two concepts of order are actually inverse to each other: order as negentropy means minimal entropy (maximal amount of bound energy, minimal of free or available energy in Schrödinger’s terms), while order as entropy means minimal negentropy (maximal amount of free and available energy, minimal amount of bound energy in Schrödingers terms). Much confusion in the understanding of “information” arises from this still today.

[12] Michel Serres, my own translation … from the German version:

[13] Michel Serres, my own translation … from the German version:

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“Thought interfers with the probability of events, and, in the long run, therefore, with entropy”.^{[1]} The term “negentropy” is born from this very situation. It was introduced by Schrödinger to distinguish biological systems from physical systems, and then generalized by Léon Brillouin into the domain of information theory. The perspective from which it will be discussed here situates the term in a certain problematics: the central paradigm of empirical experiments for science, and how the algebraic encryption of quanta in quantum physics interfer which non-probabilistic practices of measuring and counting in this paradigm. It is only by means of computations performed upon cyphers, the mathematical way of articulating *naught*, *nothing*, and the equational manners of balancing and completing by involving an encrypted negativity to all countable and measurable positivity, that probabilistic procedures are applicable: for it, the amount total of possible cases that are said to happen with probabilistically determinable likeliness must be finite and countable. Negentropy, in accordance with this, means negative entropy; it quantifies and makes countable the symmetrical negative of what the term entropy quantifies and makes countable. And entropy was introduced by Robert Clausius in want of “a word for measuring a quantity that is related to energy, but that is not energy”.^{[2]}

The problem that triggered postulations of an interference between thought and this particular quantity, entropy, must be understood before the background of the modern assumption that thought cannot affect the nature of its object, that it only affects the subjective understanding of this nature. While subjectivity depends upon will or intent, natural forces are working determinably and gratuitously. We can formulate the analog of this situation in terms of thermodynamics, insofar as the conversion of heat into energy, or energy into work, leaves the amount of heat (in this analogy playing the corresponding role to the nature of thought’s object) unaffected: the total heat in a system remains constant, it merely passes from a hotter body to a colder one. At the same time, the 2^{nd} law of thermodynamics states that we cannot maintain an identity between heat and energy: “No matter how much energy a closed system contains, when everything is the same temperature, no work can be done. It is the unavailability of this energy that Clausius wanted to measure”.^{[3]} If heat is regarded as the manifestation of energy in a system, what is needed is a distinction between energy that is available for work, and energy that is not: the total amount of heat in a system may be constant, but it cannot be transmitted (from a warmer to a colder body) *without some work being executed*. Thus, the work done by natural forces in the thermodynamic setup cannot be regarded, after all, as “gratuitous” in the same manner as it is classical physics. Thermodynamic processes introduce a certain irreversibility into how we think of the conversion of energy from one form to another – “Time flows on and never comes back”, thus Leon Brillouin 1948 – which in the classical formulation of natural laws does not exist. When the modern paradigm for experimental science builds on the assumption that thought leaves the natural object it tries to conceive untouched, we can see now that it is exactly this assumption which appeared to break down – if physical processes involve a certain irreversibility, then the thinking that guides experiments plays in a manner that cannot so easily be disregarded.^{[4]} In thermodynamic processes, energy is not lost, but it dissolves, it becomes “useless”. This is the so-called “expense problem” related to the irreversibility that applies to thermodynamics: the amount total of entropy (unavailability of energy for work) in all physical systems that can be studied empirically, experimentally, necessarily seems to increase. There is hence a source of disorder that applies to systems which “seemed strangely unphysical,” that even “implied that a part of the equation must be something like knowledge, or intelligence, or judgement” as James Gleick puts it in his recent study *Information: A Theory, A History, A Fl**oo**d* (2011). He continues: “Dissipated energy is energy *we* [emphasis added] cannot lay hold of and direct at pleasure, such as the confused agitation of molecules which we call heat”.^{[5]} Heat, it began to be clear, cannot be regarded as a force nor as a substance, it was not equivalent to energy. In the course of these developments, order – as the epitome of objectivity – acquired a certain amount of subjectivity; it entailed the eye of an observer: “It seemed impossible to talk about order or disorder without involving an agent or an observer – without talking about the mind.” The above used formulation, “necessarily seems to increase” expresses the controversiality of the 2^{nd} law as a law properly: it is based entirely on observation. Its philosophical or even cosmological implications, if it indeed is a “law”, are immense: it introduces the inevitable (however distant) doomedness of all life on earth. Lord Kelvin was not the only well established scientist who began to consider the consequences of the Universe’s “heat death”, as this doomedness was often referred to, for science. Resolutions to this problem began to be discussed in terms of the possibility of a perennial kind of motion that began to be linked up with an interest in “A perfect experiment” as one that is liberated from reasoning biased by the imperfect human faculties and their limitations (—> Maxwell’s Demon), and that arguably still haunts todays discourse on Artificial Intelligence. ^{[6]}

Let us jump now to the introduction of the negative entropy term. Erwin Schrödinger introduced it in *What is Life? Mind and Matter* (1944) as a term that allows to expand the thermodynamic view from physics to biology, and thus also to relativize the implications of the physical view on the entropic universe. His point of departure is that animate systems are capable of metabolizing – of binding and incorporating temporarily – a kind of energy which he called ‘free’ in the sense of ‘available’, or ‘unbound’. Negentropy came to mean for Schrödinger a term that allows for quantifying life (but is not life) similar to how for Clausius, entropy had come to mean a term that allows to quantify energy, (without being energy). What used to be the energy-expense problem of work for Maxwell turned henceforth into a veritable economy in terms of import and export at work in the biosphere-world of thermodynamics – organisms import negentropy (quanta of life), as Schrödinger put it, and the more they do so the more they rid themselves of entropy (quanta of physical entropy now conceived as disorder, vis-à-vis an organisms temporary order/organization). The biological paradigm hence seems to contradict the 2^{nd} law of thermodynamics, and instead suggest that the metabolisms that make up the biosphere were in fact capable of decreasing rather than increasing the universe’s entropy (the amount of work unavailable in the thermodynamic universe). The competing paradigms contrast like this: While thermodynamic physics relates the notion of the universal to the universe (as, ultimately, one generic nature), biology relates universality to the specific natures of life forms. The physicalist notion of entropy, which in physics started out as denoting not *the absence of order* but *the virtual presence of order in any of its possible variations*, appeared, from the light of how biology’s operational term of negative entropy can quantify life, as the relative absence of possible variations of order, or as the relative absence of order, or, in short, as “disorder”.

It is this dilemmatic impasse between a certain monism and its pluralist counterpoint that the introduction of “information” into the thinking about thermodynamic processes managed to abstract from, and to open up. I can only point briefly here to how this converting between information and energy works.^{[7]} My core reference is the quantum physicist Léon Brillouin’s adoption of Schrödinger’s term of negative entropy in a manner that adds an algebraically quantized (cryptographic, –> equation) notion of information to this competition (between physics and biology). Brillouin conceived of information as a kind of currency that circulates in energetic expenditure (the import and export between systems), such that “all these [macrological, quantum physical, VB] unknown quantities make it possible for the system to take a large variety of quantized structures, the so-called Planck’s complexions.” ^{[8]} With this, he began to postulate information science as the proper domain for quantizing how physical entropy (the virtual presence of any-order) and biological entropy (the absence of order, disorder) relate to one another without subjecting one to the other. Familiar with Turing’s^{[9]} and Shannon’s^{[10]} and Wiener’s^{[11]} work on a mathematical notion of information and their dispute with regard to whether information can be measured in terms of the experimental entropy notion applied to physical systems (Shannon), or whether it needs to be accounted for in Schrödinger’s terms of negentropy import in biological systems^{[12]}, Brillouin foregrounded the role of “code” in such “intelligent” computation and applied a *double* notion of negentropy and entropy – one to energy, one to information, under the assumption that both be linked by code: free (entropic) information to him is the maximum amount of apriori cases formulated in a code (any finite system of ordered elements like the morse code, or the Roman Alphabet, the Periodic Table in Chemistry or the DNA in molecular biology); the apriori cases can be computed by combinatorics, and in entropic information each of them must be regarded as equally likely to be actualized. Bound (negentropic) information is empirically measured information (in experiments with any particular manifestation of such a code). This inclination in the measurement of information allows for thinking of information as a kind of currency – an operator capable of establishing general equivalence, equivalence between observation and object – that circulates in the physical expenditure of energy in executed work as well as in the economy of import and export in a biological systems’s metabolism. “We cannot get anything for nothing, not even an observation”, Dennis Gabor famously maintained.^{[13]} This very important law is a direct result of our general principle of negentropy of information, Brillouin elaborates, and “[I]t is very surprising that such a general law escaped attention until very recently”.^{[14]} The acquisition of information in measurement not only has a price, it also yields something: an increase in operational power; an idea that lends itself to develop a theory of how to quantize and hence quantify in like manner to energy (Clausius) and life (Schrödinger) something like “power of abstraction” (–> invariance). It is this very idea, that information and energy articulate each other in an evolutionary dynamics and in mutually reciprocal manner, that the assumption of a perennial motion is no longer needed in order to proceed with the experimental paradigm in science. With Brillouin’s quantum-cryptographical theory of information, information can be transformed into energy (as electric current), and the other way around (through studying distributions of heat).

^{[1]} David L. Watson in his 1930 article entitled “Entropy and Organization” in *Science*, 29 August 1930: 220-222, cited in James Gleick, *Information: A History, a Theory, a Flood*, Harper Collins, 2011, here from the kindle edition: Position 4306.

^{[2]} James Gleick, ibid., Position 4313.

^{[3]} ibid., position 4323.

^{[4]} Cf. Léon Brillouin, *Science and Information Theory,* Dover, New York 2013 [1956], here referred to in the kindle edition, position 2766. In the measurement of any physical system, there are macroscopic and microscopic variables to be taken into account. The former refer to those quantities that can be measured in the laboratory, but they do not suffice to define completely the state of a system under consideration. Once a system is also considered in quantum-terms of its radiation and absorption, there is an enormously large number of microscopic variables to be taken into account as well – and these, one is unable to measure with accuracy as they regard positions and velocities of all the individual atoms, quantum states of these atoms or of the molecular structures, etc. “Radiation is emitted when a physical system looses energy,” Brillouin explains, “and absorbed when the system gains energy,” ibid., position 2776.

^{[5]} Gleick, *Information*, ibid., position 4355.

^{[6]} “ In other words, as Serres asks, can we maintain that the second law of thermodynamics, which states the necessary increase in entropic energy, is itself universal – even though it is only a “Law” based on experience? His answer is: “Yes, but not quite in the manner of Newton. It [the second law] is it [universal], if I may say so, in non-continuous manner, from region to region. There are archipels, here and there, between them, islands of negentropy. In the limit case we have to deal with an antinomy in the Kantian sense, when one assumes for that instance the universe as being either open or closed. In any case, it is universal in its negation or better: in that which it excludes: perennial motion.” Michel Serres, „Leben, Information, und der zweite Hauptsatz der Thermodynamik“, in *Hermes III **Ü**bersetzung*, Merve, Berlin 1992 [1974], S. 53-96, here p. 80. My own translation.

^{[7]} Cf. Brillouin, ibid., for an extensive and detailed discussion.

^{[8]} Brillouin, ibid.:“There is no continuity at the atomic level but only discrete stable (or metastable) structures, and the atomic system suddenly jumps form one structure to another one, while absorbing or emitting energy. Each of these discrete configurations of the quantized physical system was called a “complexion” by Planck.” Position 2762.

^{[9]} Allan M. Turing, „The Chemical Basis of Morphogenesis“. In: Philosophical Transactions of the Royal Society of London, series B. 237, Nr. 641, 1952, S. 37–72; and „On Computable Numbers, with an Application to the Entscheidungsproblem“. In: Proceedings of the London Mathematical Society. 42, 1937, S. 230–265.

^{[10]} Shannon, Claude E., “A Mathematical Theory of Communication”, *Bell System Technical Journal* 27 (3): 379–423 (1948).

^{[11]} Norbert Wiener, *Cybernetics: Or Control and Communication in the Animal and the Machine*, MIT Press, Cambridge MA, 1948.

^{[12]} Shannon discusses the term negative entropy, but considers its distinction negligible for information as a mathematical quantity notion. It was Norbert Wiener, who via the work by John von Neumann, Alan Turing, Claude Shannon and Leo Szilard maintained against Shannon that negentropy is in fact crucial, rather than negligible for a mathematical theory of information; it is largely due to this dispute that until today, different notions of mathematical information are in usage: (1) information as a measure for order in terms of entropy, and (2) information as a measure for order as negentropy; while both speak of information as a measure, and hence capable of establishing order, the two concepts of order are actually inverse to each other: order as negentropy means minimal entropy (maximal amount of bound energy, minimal of free or available energy in Schrödinger’s terms), while order as entropy means minimal negentropy (maximal amount of free and available energy, minimal amount of bound energy in Schrödingers terms). Much confusion in the understanding of “information” arises from this still today. Cf. James Gleick, ibid., around position 3956, although, it must be criticized, Gleick doesn’t seem to be aware of the implications of the issue at stake

^{[13]} Dennis Gabor, MIT Lectures, 1951 cited in Brillouin, ibid., position 3805.

^{[14]} Brillouin, ibid., position 3805.

Can we accommodate the urban in the City?

How can we come to terms with the theorem central to information science, that information cannot be acquired without paying a price, that the nature of information is negentropic (Leon Brillouin, Michel Serres) ? What does that imply for understanding the cultural role of “communication” ?

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**abstract**

Philosophy has to reconsider how it addresses the world, Michel Serres maintains in his “materialism of the incandescent void” (*L’ Incandescent*, 2003). This, for him, is an issue of metaphysics: the world, as we ought to address it, is a world that actively knows. The metaphysics Serres advocates revolves around a principle of invariance, it operates with “white concepts” (concepts considered as spectra rather than form), it draws upon an anonymous, impersonal agency at work in “knowing”, and it addresses the world by a six-fold proper name: *Pantope* (all of its places), *Panchrone* (all of its durations), *Panurge* (not demiurge, the public worker, but the universal worker), *Panglosse* (all of the spoken tongues), *Pangnose* (all of knowledge), *Panthrope* (all sexes, instead of only man as in ‘anthropos’). This talk provides a tentative introduction to Serres’ architectonics, and it suggests addressing his materialism of the incandescent void as a materialism of identity that articulates itself in the language of a mathematical realism: mathematics does not provide support or foundations, it provides a lexicon, according to Serres. I will attempt to speculatively develop this thinking further towards what it might mean to become literate in a kind of writing that is, irreducibly so, a “quantum writing”.

**CONTENTS**

**1 The quickness of a magnanimous universe**

**2 Impersonal agency**

**3 Invariance: Genericness as entropy**

**4 Genuine and immanent to the All of Time: Le “ logiciel intramateriel”**

**5 White Metaphysics: How old does the world think it is? **

**6 Materialism of identity **

**7 (Pan’s) Glossematics: entropic economy**

**8 Quanta of agedness: from heat to incandescence, from storage to bank account**

**9 Quantum writing: the priority of substitutes to things themselves**

**Incandescent materialism, literacy in quantum writing**

»It will do the practical man little good to say that only a metaphysician would ask such questions. The historical fact is that numerous impractical men not only asked these questions but struggled for centuries to answer them, and their successes and failures are responsible for much by which the practical man regulates his life in spite of his impatience with all metaphysics.«

– Eric Temple Bell,

The Magic of Numbers;22.»In other words, while most of us can imagine what we owe to our parents as a kind of debt, few of us can imagine being able to actually pay it-or even that such a debt ever should be paid. Yet if it can’t be paid, in what sense is it a

debtat all? And if it is not a debt, what is it?«– David Graeber,

The First 5000 Years of Debt;92

**1 The quickness of a magnanimous universe**

Michel Serres, who introduced this concept central to my talk, ‘* the incandescent’*, thinks of himself as a materialist thinker and as a mystic of mathematics[1]. We should bear this in mind when attending to the one formula that perhaps orientates his thinking as a writer and philosopher at large: to him,

**2 Impersonal Agency**

An equation so articulated, in terms of equipollence, must hence be attributed a ‘status’ of its own. For Michel Serres, * this status is metaphysical*,[3] it can be addressed with what he calls

The term gnomon is of neutral gender, Serres tells us. It used to designate in Greek,

“[…] the axis of a sun dial’s disk, and it signified ‘that which comprehends, decides, judges, distinguishes, interprets, yes, that which knows (

connaître)[…] Intercepting the light of the sun, its shadow inscribes on the disk certain events of the sky and the earth, the solstice, the equinox, and the latitude of a location. It works automatically. Automatic means: without intervention of subjective and cognitive intention.”[7]

The gnomon works a bit like a stylos, a writing tool, Serres continues, but there is no hand that holds it. And further: “The things of the world give themselves to be seen by an object that displays them. One thing, the gnomon, intervenes in the world and the latter reads in itself the writing that it traces.”[8]

Generic identity, restless unsettlement, anonymous agency, the auto-logos of a world that reads within itself in an active manner that is called “connaîrtre”, “knowing” – does this not announce * the very end of metaphysics*? How can such a philosophy possibly remain committed to a

We have to consider what it entails for Serres to say * “information theory is the philosophy of physics”.*[9]

**3 Invariance: Genericness as entropy**

** **In his text “Life, Information, and the Second Law of Thermodynamics”, Serres maintains that it has been a mistake of information theory before Léon Brillouin, to make the principle that reigns thermodynamics also its own. The principle that reigns thermodynamic entropy is that of “telenomy” – a nomos, a lawfulness, that acts from a distant point at the end of time. Serres * contrasts “telenomy” *with another principle, that of

It is crucial to grasp what is at stake thereby. Without going very far into technical details, let us just remember that * entropy in thermodynamics is an ideal state attributed to a “system” of which is assumed that it be infinite (the universe)*. But “an infinite” is not countable, and hence cannot be regarded as a “system” – not without making some further assumption as to a limiting function that cuts trough this infinite. In thermodynamics, the operationalization of this idea assumes that the amount total of energy in the universe be 1) finite and undecided, and 2) invariant. Its magnitude can neither increase nor decrease. Entropy, here, is a descriptive term for the state in which such a system’s

Now to the crux of the story. We have seen the ideal condition, but of course in practice, the laws of thermodynamic are applied to *sub*systems and the metastable balances they maintain among each other. And here, in order to allow for their description, the principle of invariance is usually translated into rules that render constancy. But there is a crucial mathematical distinction between invariance and constancy: invariance does not require any apriori specification of that peculiar quantity, whereas with constancy, such specification is required. If we speak of invariance, we argue with * algebraic elements*, in terms of

The implications are weighty: with * invariance, we always think in terms of greatest possible preservation (of immanent transversality)*, while with

So how does the notion of invariance play in here? * It brackets the question of the “free energy’s reservoirs” finitude* and treats its quantity algebraically as invariant, meaning at once in-determined (not subjected to ordering-relations) but determinable.[11] With a mathematical understanding of invariance, we can link identity and genericness on the scale of the universal instead of opposing the two on the scale the empirical.

**4 Genuine and Immanent to the All of Time: Le “ logiciel intramatériel”**

* Universal invariance*, in Serres’ metaphysics, is neither biological nor physical nor chemical, it is

* Brillouin generalized Schrödinger’s notion of negative entropy from thermodynamics more strictly, and applied it to information science.* Instead of making use of this distinction (entropy/negentropy) with regard to energy, where it amounts to deciding about

But, from a philosophical point of view, does this generalization not suggest that Brillouin thereby * voided the original commitment of entropy-theory to realism, and delivered it to a frame of linguistic transcendentality ?* With Serres, we would be mistaken to think so. Communication, for him, means to trace back the thermodynamic force, heat, to its quantum physical ‘condition of possibility’: ‘communication’, for him, means

There is, hence, a materialist point of view from which an apparently animistic statement like “the world inscribes itself upon itself”, and “deciphers from itself what it itself has encrypted” * does not amount to a dualist metaphysics where a distinction between subject and object is always already presupposed*. It does, however, introduce a transcendentality. But

“as an objective support for an information to be received, conserved, emitted.”[17]

The Cogito of the objects, a cogito that is distributed throughout all the things in the world, is * also* a

“This type of intra-material software conditions our cognitive performance, as if it were a kind of transcendental objective. […]”[18]

Serres *nomos* that acts from a distance, his ‘transcendental objective’ (goal, telos), now depends upon being, itself, * instructed*. The

The gnomon * takes stock of measured temporality*, but not in the sense of keeping track of history. It does not take stock of temporality in a sense that would seek to

Hence, mathematics provides first of all * entries to a novel kind of lexicon, it is not a support or a guard rail.[21]* Its concepts are “invariant forms”, spectrums, they are “the any form in general” as Serres specifies.[22] The impersonal

**5 White Metaphysics: Who does the World think it is? **

** **With this * banking of unbound quanta of temporality*, Serres’ metaphysics operates with a notion of “neutrality”. We have to understand the full implication of Serres’ replacement of telenomy with invariance, and of his “objective Cogito” and “neutral Logos”. It is not merely a slippery metaphor, when Serres reverts here to finance: Thinking of equations in terms of equipollence (equality in force, power,

These elements are not “neutral” in the sense of normal, stripped from all properties other than a general base.* Rather, they are “neutral” because the axiomatics – the systems of valuation – that build on them have to account for all of the properties that might be attributed to the world*. Without any rest.[24] They are elements of an ‘omnipotent neutrality’ – and they cannot be taken for granted (they are what needs to be ‘achieved’ via a materialism of identity/equations of equipollence) whereas Value, as the invariant (un-ordered, material) amount total of such omnipotent neutrality, can (this is what ‘Metaphysics of Value’ means).

If the entropic universe is a universe in which all things are at once nothing-at-all and anything-at-all, then the Cogito at work in universal reason can no longer feel entitled to address the world in any immediate way. There is a chapter in *L’Incandescent* entitled “Accès à l’Universel”, which begins by maintaining that, hence, we have to * reconsider how we address the world*. In it, Serres complements the

But how can augmentation mean something else than generalization, advances on an orderly and logical ladder whose steps are deductions? If Serres’ philosophy is a realism, and not an idealism, as he claims, then there must be an other way to think about “augmentation”. But if things in their universal genericness are nothing-at-all in a manner in which they can be anything-at-all, then surely this “augmentation” cannot be concerned with the universal nature of things either, or can it?

One way out would be to assume that this metaphysical status of value, and the Nature of Economy at stake, is a transcendent – fatalist – * Government of Pure Capital, of competition between General Equivalence that has lost all reason*. But this is irreconcilable with the emphasis Serres gives to his materialism as one that

But first, how can we think about augmentation? We must turn again to this notion of * equipollence between Rationality and Reality* at this point, and ask about that peculiar status of such equations. It is metaphysical, we saw, but in which sense? –

The status of an equation is metaphysical insofar as Serres’ metaphysics affirms * a principle Law that reigns the universe, the Law of Chance* (the physical nature of the universe is entropic). The ‘status’ of an equation, hence, is universal insofar as it

* To augment means to proceed on the entropic ladder of neutralization,* because steps that identify a common factor (rather than settling on a common denominator) render in multiplicitous manner how a bondage can be decoupled, and hence guarantee the articulation of contracts

**6 Materialism of Identity **

Generic identity is metaphysical and universal for Serres in the sense that * to be *is not just

Thus, much of what is needed, for making sense of Michel Serres proposal, can be collected in the question of how we think of the status of a formula. Does it really * state* identity? does it

A formula, for Serres * dis-ciphers identity rather than re-solving it*, to borrow a term I take from the German translation of Quentin Meillassoux’s book on Mallarmé

But what exactly should be attractive about this idea of * dis-ciphering*? It is from such transcriptions, that render identity in re-solutions, that Serres’ universality can be one that expands – despite it being, from the very beginning, itself and only itself, as all that it generically is .

* Dis-ciphering and transcription* is how Serres’ entropic ladder of augmentation works. They are what Brillouin’s principle of negentropy, when applied to information (rather than to energy) afford: here, Brillouin’s

The truly metaphysical question now is whether there is an ultimate limit to the entropic ladder: “__Does there exist a boundary stone, a__* bottom limit for this de-differenciation into neutrality*?”[28] For Serres, the prefix

With this idea Serres is actually very much in tune with rising interests in the philosophy of mathematics. Fernando Zalameo has, in a recent book entitled * Synthetic philosophy, Contemporary Mathematics*, urgently called for a philosophy that engages with the levels of abstraction that ‘real’ mathematicians work with since the introduction of the group concept, and especially since the 50ies of the 20

**7 (Pan’s) Glossematics: Entropic Economy**

In other words, what we have to consider is the decoupling of code from signification. We have to consider * the a-signifying character of mathematical notation*, in the sense of a notation that is decoupled from the substance/content it forms/expresses. I am reverting thereby to Louis

To maintain this indefiniteness is what the algebraic treatment of “an unknown” as an unknown in both axial aspects, the * quantitative* ones as well as the

Serres’ notion of the incandescent void dis-solves the thermodynamic model to the level of quantum physics, where, in other words, this “unanalyzed, amorphous continuum” is subject to a kind of quantization who’s “quanta” are undecided as to whether they must count as discrete or continuous, wave or particle, magnitude or code. Or rather, for which we always have to take both aspects into our accounts. The most important implication of this is that * the entropy notion change*s: while Hjelmslevian purport manifests as the spectrum itself, immediately so, superimposed on which the different languages organize zones in variable manner,

Serres * Cogito, the agency at work when concepts that are white spectrums are dealt with*, produces a Logos (all that can be articulated with the lexicon of white concepts) that cannot do without a metaphysics, without categorical registers of how that which is universal in all things can be ‘identified’.

“I call it [the world, VB]

Pantope[all of the places, VB],Panchrone[all of the durations, VB],Panurge[not demiurge, the public worker, but the universal worker, VB],Panglosse[all of the languages, VB],Pangnose[all of knowledge, VB],Panthrope[all of the sexes, “men and female six times integrated”, instead of anthrope, VB].”[36]

** **

**8 Quanta of Agedness: From Heat to Incandescence, from Storage to Bank Account**

Serres references the notion of the incandescent to * Georges-Louis Leclerc, Comte de Buffon*, a French naturalist, mathematician, cosmologist, and author of d’Alembert and Diderot’s encyclopedia in the 18

“Buffon takes the incandescence of balls of earths containing iron, then lets them cool down in order to calculate the age of the planet according to a reduced model. Neither Newton nor his universe of forces had memory; Buffon’s burning bowles of earths accumulate energy under the form of heat and they function, accordingly, like bank accounts that use up their money when they cool down; here we have a new clock. It counts not points in reversible time à la Newton, and as my watch indicates, but an irreversible and entropic time of the usage of the wheelwork, that is, the time of its aging.” [37]

It is this notion of * an aging of the earth* that is central to Serres. It is a notion which has experienced a powerful evolution since Buffon, and which perhaps

How matter comes to matter is thereby brought in a * mutually implicative relation* with with how time comes to act as time.

Like Nietzsche’s, his thought as well is preoccupied with how * to deliver the human from the spirit of revenge*. But he rejects the latters doctrine of the eternal recurrence of the same, he replaces Nietzsches dynamical model with a quantum physical one in which everything that happens happens within the active transversality immanent to an All of time.

Nietzsches unsettling dictum was that all meaning originates in promise and derives from a relation of debt, from which it ‘naturally’ evolves according to the favors and privileges in how the settlement of this debt is negotiated. The agency at work in such promise is handed over by Serres from subjects to objects. The transformation of Nietzsche’s dictum hence reads as follows:

“All things, in principle, conduct themselves like memories. The universe banks accounts. All things are number, the memory of the world conserves traces.”[38]

‘Agedness’ is what the universe banks and accounts. * The traffic that circulates* in this universes’ immanent transversality – within an All of Time – is addressed by Serres as

Serres Universal Nature of Economy, hence, banks on * an abundant past* rather than on

“[…]My brain, speaking only of it instead of many other things to which the same would equally apply, is composed of ancient parts, reptilian, and others as new as those evolved with the chimpanzees or bonobos, and then furthermore with parts that are incomparably much more recent. […] Similarly, my DNA appeared, of course, with the conjunction of my parents who stitched it together like one stiches together different maps, but in its own structure, it is more than 3 milliards of years old; even older still, the atoms that compose it and me go back to the fabrication of hydrogen and carbon from the galactic energy of the universe.”[41]

When Serres speaks of a “Real Age” that is common to *“*old men and the newly borne, grandchildren and grandmothers, animals and plants, friends and enemies, to all that are carrying DNA”, he gives us a model of * how to hold on to the idea of generational descent in terms of dia-sequentiality, i.e. without submitting to the linear branching of the tree as a law of con-sequentiality*. Before Time, all, at any instant, is equal, as he says, an equality that is contracted “in two fractions: one minimal, the individual age, the other much larger”, universal belonging. Serres

**9 Quantum writing: the priority of substitutes to things themselves**

Serres universe is not * an empty container, an impure vacuum or, a “storage-memory” or the sterile template-matrix of a “pre-figured data bank”. *It is a universe that is temporal before it is spatial, but this time is not properly processual: a process

“The womb of a pregnant woman knows a billion different biochemical reactions per second; while I am writing this, my organism produces almost as many. Like a cornucopia [das

Füllhorn, VB], the non-denumerable pours out of an instant. […] Our organisms carry, we will know it in the future, dozens of clocks, cardiatic, digestive, nervous or molecular, all of them tumbled up by the time difference towards the end of a long distance flight. How can we think the instant and duration without making reference to this internal unease, circulatory, existential, whose appearance indicates an organic knot through which our relation to time is constructed, or to our relation to the sum of durations these clocks indicate […] ?”[42]

* Universal time is the non-denumerable, the uncountable sum of all real durations*, and as such it is always in a state of unease – like our organic time after a long distance flight. It is uncountable unless via its organization of how matter matters in how temporality acts as temporality, and this organization involves not only causes and consequences, but also the codes that establish the latter two.

“Things do not reduce to causes, they also carry codes. They act ones upon others, certainly, but they also signal among themselves”.[43] (60)

Serres doesn’t think a materiality of memory that is general, as Bergson arguably does, but one that is generic and atomist. Time, then, doesn’t * flow* like a river, it

“All things, in principle, conduct themselves like memories. The universe banks accounts. All things are number, the memory of the world conserves traces.”[44]

When Serres maintains that “all things are number” he is not saying that all things are unitary identities. They are number because signals are signals (and not signs) in sofar as their recording happens in terms of numerical chiffres (figures). * Numbers are crucial for maintaining an a-signifying notion of code*, they allow Reality to figure in Rationality. Code can be a-signifying only insofar as it is always both, alphabetical (a finite set of elements) and numerical (units of infinity). In that precise sense, code is alpha-numerical: a logics of the alphabet, that on its own hurries forth straight to Omega (the ultimate destination, the locus of action in the principle of telenomy) is transversed in code by the numerical figuration of the Alpha. Within alpha-numerical code, if you say A you must not necessarily say B, to put it bluntly. The linear transport according to order relations is always intercepted –

Within communication so conceived, * the Alphabetical’s ideal completion*, Omega, turns into

With Serres’ white metaphysics, the algebraic group of all concepts of which each encompasses lucidity like spectra do, * quantum writing *no longer conserves the gospel of a beginning and an end of time; instead it conserve the secret key that belongs to no-one-in particular and every-one-in-principle

In terms of generic identity’s “Real Age,” all things are equal: entropic noise. But insofar as they are addressed through quantum-writing that grants them this entropic reality, all the things of the world have inscribed in themselves the protocols of an ‘ad-tribution of value’ that knows * no partition key or distribution scheme that would originate in a beyond of the obligations that contract them.* Quantum writing articulates these obligations. The obligations of an equation in terms of equipollence between Rationality and Reality do not use up deposits, and thereby, inevitably, foreclose a future in some of its openness. They descend into durations, unlock the depth of an instant, and thereby create novel deposits. The promises with which the articulations of obligations fly are propelled by

[1] as he called himself in a recent conversation (https://www.youtube.com/watch?v=1qFdYgjWg9s)

[2] eg. cf. the Natural Contract, p.24, 90

[3] cf. *L’Incandescent*, p. 101ff.. The promise of this metaphysics is not sterile and cold truth, but the excitement of vulnerability, quickness and liveliness: „Les concepts blancs forment un groupe plutôt qu’une simple classe: Ils procèdent les uns des autres. Cherchez la liberté, vous connaîtrez; cherchez la connaissance et vous inventerez, cherchez le savoir et l’invention ensemble et vous ne pourrez pas ne pas aimer.“ He goes as far as to answer his own question „A quoi sert la Metaphysique?“ with „incarnation“ of a generic ‚body’ that is born from any body’s body. It is crucial for understanding why his book is a book on humanism. Metaphysics is indispensible for „rester humain, et ne pas en mourir“ (106).

[4] If quantum theory is right to maintain that light is, after all, a particle, and that matter comes to matter from how the light’s radioactivity deals with charges of electricity; cf. Feynman, *QED, The Strange Theory of Light and Matter*.

[5] Karen Barad

[6] Serres, L’Incandescent, p. 61

[7] “De genre neutre, le terme gnomon qui désignait, en langue grecque, l’axe du cadran solaire, signifiait ‘ce qui comprend, décide, juge, distinguw, interpète, out, ce qui connaiît’ […] Interceptant la lumière du soleil, son ombre écrit, sur le cadran lui même, quelques évévements du ciel et de la terre, le solstice, l’équinoxe et la latitude du lieu. Il marche automatiquement. Automatique veut dire: sans intervention de l’intention, subjective et cognitive.” ibid p. 61

[8] Ibid.

[9] Serres, Leben, Information Zweiter Hauptsatz der Thermodynamik“, Hermes III

[10] L’Incandescent: “Comme un transcendental temporel, certaines conditions du connaître datent de centaines de millions d’années.” p. 62

[11] Michel Serres, “Motoren. Vorüberlegungen zu einer allgemeinen Theorie der Systeme”, in: Hermes IV. Verteilung. Merve, Berlin 1992, pp. 43–91.

[12] Michel Serres, “Verrat: Thanatokratie,” in Hermes III: Übersetzung, trans. Michael Bischoff (Berlin: Merve Verlag, 1992 [1974]).

[13] cf. l’interférance, 106. Invariance “[…] is the transcendental space of all and any communication”.

[14] Serres, Leben, Information Zweiter Hauptsatz der Thermodynamik“, Hermes III

[15] cf. Giuseppe Longo’s discussion on the concept of invariance in his article: „Synthetic Philosophy of Mathematics and Natural Sciences“ (http://www.di.ens.fr/users/longo/files/PhilosophyAndCognition/Review-Zalamea-Grothendieck.pdf)

[16] cf. Anne Crahay, *Michel Serres, la mutation du cogito: Genèse du transcendantal objectif* (1993)

[17] Serres, L’Interférence, p. 106.

[18] l’Incandescent, 61

[19] Serres, “Was Thales am Fusse der Pyramiden gesehen hat,” 214.

[20] This fourfold activity is Serres „Quadruple universal“, an activity (rather than a property) in which all things being, alive or inert, participate. „Information and thinking“ (lecture manusript at Philosophy after Nature conference in Utrecht, 2014).

[21] Serres, Hermès I, Communication, p. 10: „La mathématique n’est plus un support, ou un garde-fou, elle est un dictionnaire.“

[22] (interference 110).

[23] “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 constitute an infinitely entangled, objective-theoretical unknown, tremendous virtual noemata like the stones and the objects of the world, like our masonry and our artifacts. Form bears beneath its form * transfinite nuclei of knowledge*, with regard to which we must worry that history in its totality will not be sufficient for exhausting them, nuclei of knowledge which are profoundly inaccessible and which pose themselves as problems.

[24] cf. The Natural Contract. Whenever one side of the equipollence (between Rationality or Reality) dominates the other, it produces pollution. p. xxx

[25] Serres, Interview de Michel Serres sur l’autorité, https://www.youtube.com/watch?v=GeJgTmZ9EBc

[26] Cf, the beginning of La Communication, Hermes I

[27] cf. Serres, Genesis.

[28] L’Incandescent, p. 103

[29] ibid. p. 101

[30] Cf. Hermes, The Nord-West Passage

[31] Serres, Genesis

[32] Hjelmslev, Prolegomena, p. 52

[33] This is indeed, I think, why Hjelmslev was so much concerned with pointing out that his approach to language is one that * affords a science of language*, that its interest concerns

[34] Identity, for Serres, is a question of „appartenance“, belonging, affiliation, German Zugehörigkeit. cf. the chapter „L’Identité, les Appartenance“, p. 113ff.

[35] cf. Serres, Revisiting the Natural Contract (http://www.ctheory.net/articles.aspx?id=515)

[36] L’Incandescent, p. 184; But even if the world can be addresses as a legal subject, it’s “panonyme” is still haunted by all that pertains to it: * panic* – which in its Greek sense means ‘all that pertains to Pan, the god of woods and fields, the source of mysterious sounds that caused contagious, groundless fear in herds, crowds, or in people in lonely spots’.

[37] “Buffon porte à l’incandescence des boules de terre mêlée de fer, puis les laisse refroidir, pour calculer l’âge de la planète selon ces modèles reduits. Newton ni son univers the force n’ont du memoir; les boules brûlantes de Buffon accumulent l’énergie sous forme de chaleur et fonctinonent donc comme des comptes en banque dépensant leur monnaie en refroidissement; voila une nouvelle horloge. Elle compte non point the temps réversible à la Newton qu’indique ma montra, mais le temps irréversible et entropique de l’usure de ses rouages, donc de son vieillissement.” (51).

[38] “Toutes choses, en principe, se comportent comme des mémoires. L’Univers banque des comptes. Toutes choses sont nombres, le monde mémoire conserve des traces.” (53).

[39] Cf. my argument on Serres reading of Balzac’s La Belle Noiseuse in: „“Ichnography”—The Nude and Its Model. The Alphabetic Absolute and Storytelling in the Grammatical Case of the Cryptographic Locative” Bühlmann et.al.,Coding as Literacy 2015 (https://monasandnomos.org/2015/04/03/ichnography-the-nude-and-its-model-the-alphabetic-absolute-and-storytelling-in-the-grammatical-case-of-the-cryptographic-locative/)

[40] “nous voilé tous presque aussi vieux que la Terre” (21).

[41] “Mais mon cerveau, pour ne parler que de lui, se compose de parties anciennes, a la manière reptilienne, d’autres aussi nouvelles que celles que développèrent chimpanzés ou bonobos, enfin d’autres encore, incomparablement plus récentes. […] De même, mon ADN apparut, certes, avec la conjonction de mes parents qui le bâtirent comme on bat des cartes, mais dans sa structures propre, il a plus de trois milliards d’années; plus ancien encore, les atomes qui le et me composent remontent à la fabrication de l’hydrogène et du carbone par l’énergie galactique de l’Univers.”

[42] “le ventre d’une femme enceinte connait un million de réactions biochimiques à la seconde; pendent que j’écris ce mot, mon organisme en produit presque autant. Comme d’une corne d’abondance [Füllhorn], l’innombrable jaillit [hochsprudeln] de l’instance. […]Notre organisme comporte, nous le savons désormais, des dizaine d’horloges**,** cardiaque, digestives, nerveuses ou moléculaires, toutes bouleversées par le décalage horaire à la fin d’un long vol en travers des longitudes. Comment penser l’instant et la durée sans nous référer à ces malaises interne, circulatoire, existentiel, don’t l’apparition indique le noeud organique ou se construit notre rapport au temps ou à la sommes des durées qu’indiquent lesdites horloges […]?”

[43] “Les choses ne se réduisent point à des causes, mais posent aussi des codes. Elles agissent les unes sur les authre, certes, mais encore se font signe entre elles.” (60)

[44] “Toutes choses, en principe, se comportent comme des mémoires. L’Univers banque des comptes. Toutes choses sont nombres, le monde mémoire conserve des traces.” (53).

[45] Serres, *Les Nouvelles du Monde* (1997)

[46] cf the chapter „Un aveu d’identité: tout inné, tout acquis“ in L’Incandescent, p. 120ff. where it reads: „Il n’y a pas de discussion ni de contradiction ni même de proportion entre l’acquis et l’inné, entre les deux cartes [d’ identité] dont je parle: tout inné, tout acquis, cette étrange addition forme l’homme“; and further: „En mon corps, mon âme et mon entendement-palimpseste, mille textes et dessins se donnent rendez-vous, pesamment surchargés, oubliés prestement, mémorisés, se chevauchant, effacés sans cesse et cependant toujours repeints et récits en sillons remodelés. Toute chose écrits sur cette absence; ou: personne plus les autres; voilà le moi. Ego nemo et alii.“

]]>– David Graeber,

The First 5000 Years of Debt;92