Algebraic Concepts Characterized / Architectonic Articulations / Pre-specificity / Projective Theory of Technology / Thinking as an Algebraic Mechanist / Uncategorized

Invariance

by Vera Bühlmann

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 absolute identity 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 20th 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 (2nd 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 replication of 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 17th/18th century the theory of equations, has transformed by the early 20th 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.

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