* manuscript of my paper at the Deleuze Conference 2013 in Lisabon, July 13th. With a few additional annotions. 

During this conference, we have heard many accounts and twists on a disturbing relation which Deleuze’s philosophy of capture, through the terms of what he calls the method of transcendental empiricism [1], appears to maintain with capitalism: Dorothea Olkovski even wanted the Deleuzean notion of the differential dy/dx to be understood as the very formula of ‘capitalism’ [2]. Let me suggest an abstract scheme, inspired by Deleuze’s  three synthesis of time from Difference and Repetition (1968) as a background, such that some room may be gained for considering.

Lets say, in very simple terms, that in early cosmologies, space is full with things, it is discrete, and time is compact and eternal – in the Timeaus, time is the image of eternity. In Deleuze, this corresponds to the first synthesis of time, that of habitus. In such a cosmology, logos is a kind of residue which conserves the possibilities of things as we understand them. A second synthesis of time emerges while these possibilities are gradually conceived as properties which are variable, combinable, and even producible: Memory now conserves the habitus of times past. With modernity, properties get primary before things, and space turns into an empty container of the ‘every thing’.  Time now appears as full of potentiality, and as differentiable.  The cosmos is now not an animal, but a system of dynamic balances. Logos, within this modern ‘cosmos’, is diagrammatic: it renders transparent the earth in its historical layers. It wants to conserve the richness of temporality in the processes which it maps and marks out. Universal is not anymore the proportionality of elements,  as fire is to air so is air to water, and as air is to water so is water to earth (Plato, Timeaus), universal is now the ‘property’ of being capable to transform energy form one form into another: work. Properties are generalized: temperature, weight, position, momentum. These are properties of energy and mass, the two only natural categories that are now continuously mapped into each other – by means of functions, not anymore by means of proportions. With this, we are not in a cosmos anymore, but in a thermodynamic universe. There is but one constancy for it: that the amount total of energy is what can neither be produced nor destroyed. From now on, logos conserves not anymore the possibilities that can be appropriated by technics, as in the first synthesis; it conserves the ‘natural’ oikos of the planet – ecology. The new concerns now are all about how populations can grow within the affluence of energy under the assumption of energy’s primary scarcity – we tend to forget about that, but Thomas Malthus calculated limits to growth as early as 1798.

With the third synthesis of time, the time of the future as Deleuze proclaims it, time is not full and differentiable, but empty. And space is not empty, but receptive – to nearly any ‘inscription’ at all. So what is full now, and differentiable, for Deleuze philosophy of the differential?  It is intellect, I would like to suggest. The troubling perspective Deleuze pursues thereby, and which stands behind much of the critique on his transcendental empiricism, is that in this perspective, reason and common sense are not the ‘most equally distributed’ things. Even worse – for Deleuze, to think means to create. It demands the sovereignty of masters – private thinkers, who dare to question established principles and to stage inconsistencies. The former he calls irony, and the latter humor [3]. The private thinker works with irony and humor, he steps out of the system, and hence does not work in the thermodynamic sense of mapping continuously, in one form or another, energy into matter, matter to matter, or energy to energy. Instead, the private thinker repeats. He doesn’t exploit differences, he raises their interplay to a higher power. To the nth degree. He does this by capture, not by description. He adds something. Time is not full in this third synthesis, it is empty – such that it can return. The eternal is still an image, in the Nietzschean-Deleuzean inversion of Platonism, yet not one which represents – it is an image which renders the present. Time is empty, space is receptive, the intellect is full and differentiable, and it acts upon time by capture.

The big question hence is: how can this ‘master-thinker of a time to come’ possibly raise a thing in its power for the benefit of all, and not simply of some?  After all, in order to repeat, she must inevitably corrupt the consistencies that host the daily comfort of the ‘non-private’ thinkers [4]. Let us remember, Deleuze wants his text to be understood as an apocalyptic text. It proclaims to step out of the comforts (and pains) provided by the three Kantian coherences: those of mankind, of God, or of the World [5].

It is well known how Deleuze justifies this stance through emphasis of learning [6] – learning means to risk one’s stable ground, and not everyone is disposed to do so in like manner. The deal of civilizations is that those who live on ‘grounds’ riskily can live from the produces of those who cultivate the grounds steadily. Potentially, this is not an unfair deal because she who learns produces the means to raise the welfare of all. Nevertheless, we can understand that from the agrarian point of view, which lives within sustainable cycles, cities are perceived as decadent, necessarily so, and in a literal sense: they produce cases that fall off from the natural cycles. There is inevitably something diabolic about any thing than merely can, but need not be the case. Universities, craft and manufacture, industry. Monuments. All of this burns energy in apparently disproportional manners – but as we also know, it produces medicine, engineering, and all the ‘comfort’ we call today the produces of capitalist logics.

However, within a thermodynamically entropic system, economy in the sense described – as a balance between city and rural areas across different temporalities – inevitably cannibalizes itself. Deleuze seems to tell us on the one hand that the only chance is to affirm such a relation, while at the same time, he advices us to parasite, to tap in and distort, to hitchhike the flows of transformations. To prevent them from growing into rigid structures. Yet, today as the fragility of the ecosphere and new responsibilities that come with the demographic constellations grow so omnipresent, this seems like an ethically irresponsible stance. Limits to growth are not an abstract consideration for most people today, they feel real and urgent. Limits of ‘dissipative’ systems are fuzzy, as we heard in that agitationally polemic talk by Dorothea Olkovski two evenings ago, they are diabolized as producing carambolage and disaster (as her images were to illustrate).

Against such a perspective, I would like to take Deleuzes insistence on decoupling form and content in all radicality, in the interest to relate entropy and economy differently. By differently, I mean non-thermodynamically.

Lets recapitulate to get started. For Deleuze, the flows of transformations   flow because they  form within a streaming milieu – Deleuze calls it sense, I referred to it as the differentiable fullness of all that can be the object of thought (intellect). Thought is capable of capturing content  from this streaming milieu by code, and of bounding it within formulaic structures – Deleuze’s categorially operative concepts. In these terms he describes the stratification of the earth, in “Geology of Morals” [7], as a kind of ‘substantiation’ of the liminal. For contemporary mentalities, his ‘substantiation’ may sound a lot like sophistry, because even though they are said to be material, they appear as peculiarly lofty and contingent. But there is a perspective which can complement his thoughts with a much more directly material notion of ‘substantiation’: there corresponds today, to the streaming milieu of intellectuality (sense, what can be thought), the streaming milieu of the sun within which the planet is bathing. Its light can be ‘captured’ by the ‘codings’ of semiconductors such that energy is produced and rendered harnessable. The openness of ‘all that can be  the object of thought’ corresponds here to an openness of ‘all the light that can be conserved as energy’. The decoupling of formula from the content expressed by D&G works not only in the fields of organic chemistry and particle physics, it also works with regard to ‘the nature’ of energy. It is crucial that in the case of photovoltaics, other than in any other case of energy harvest, the quantities gained are additional to that already stored within the ecosphere – the weather, the plants and animals, the earth. What we get thereby is an opening up of the thermodynamic closedness – however dissipative or fuzzy we might conceive of it. The amount total of energy in the universe may well be constant, yet that within the “nature” of the earth is not. There principally is to be taken into account an abundance of clean energy.

So in all preliminary brevity: how could we think now, under the assumption of principle abundance instead of scarcity, about the relation between economy and entropy in a Deleuzian way? Thought is for Deleuze, after all, “the dynamisms proper to philosophical systems”.

Entropy is, to quote from wikipedia.org “a measure of the number of specific ways in which a system may be arranged” [9].  – measure of a number, bear this in mind, for it is the inverse to the counting (numbering) of a magnitude [10]. Now, if entropy is taken as a thermodynamic quantity, formula and content are not treated as decoupled: a system is a system because it “works” and not because it “captures”. Entropy here is staged as a threat, and applied as a “measure of disorder”. The  maximum disorder that could be measured would be thermodynamic equilibrium. As a state of pure potentiality, with no regularity at all, such equilibrium would be the “death” of a system. It would be a static system, not one which transforms energy from one form into another.

So the question is, how could there possibly be an economy, a regularity of flows and exchanges, that corresponds to an affirmation, and not a diffamation of entropy ?  It is important to see: electricity from photovoltaics is energy not produced by work (the transformation of energy) but by capture through code. It may sound strange and somewhat amazing to view photovoltaics like that, but as a reality and fact, it doesn’t seem to be disputable. Only, weighting this phenomenon  as being of principle importance for how we think about the world – economy, politics, how we make sense of what we experience and engage in, this is much more critical.

An affirmation of entropy crucially depends upon a non-thermodynamic understanding of it. It is here where Deleuze’s static logical and ontological genesis is so helpful. We all know that thinking, for Deleuze is not about recognition, but about repetition. I would like to suggest that his  private thinker  is a thinker  within a non-thermodynamic,  yet entropic economy. He thinks privately because he wants to master entropy (the number of specific ways in which a system may be arranged). Entropy is his private ‘household’, his oikos. By decoupling the formulaic from the quantities expressed, such a private thinker proceeds probabilistically, not geometrically or mechanically. And he is a thinker and not a scientist because he measures his possibility space not in the terms of a combinatorial interplay of general forms – Platonic ideality, or geometric intuition. Instead, he knows how to deal with quantities that are strangely monstrous: they are discrete, and yet infinitary. Such are the instances of what I call liminitudinality. The framework to think about Deleuze’s categorial concepts is not that of formality, logics; it is that of quantity, algebra [11]. Deleuze foresees a universal method of classification, not a universal order of classification. His interest is not in a cosmo-logy, and neither in a techno-logy or an eco-logy, but in a literacy, in a cosmo-literacy. This is how I read it.

While logics of concepts insist on quantification (making existence and universality statements), an algebra of concepts is all about quantization, and how Deleuze treats it is as an ability. This cannot be done away with as a mere trick, Mathema literally means “that which is learnt”, and the mathematikos is someone “disposed to learn”. Deleuze shares this understanding with many philosophers of the past, certainly with Leibniz and Spinoza. For them, the openness of what can be learnt must constitute any notion of knowledge whose value is supposed to be determinable (quantifiable knowledge).

The famous inversion of Platonism does not concern an exchange of positions in the model-copy, being-appearance relation. This would concern ontology, and it is only derivative for Deleuze. Philosophical concepts for him are categorial, not classificatory. What is actually inverted is constitutional to classification: it is the role of numbers in Plato’s cosmology. In the Timeaus, numbers are of one kind. In Deleuze, they can be engendered in their kind. But lets give this a bit more space. In the Timeaus, numbers are the Soul of the Cosmos, they constitute the framework of the two spheres, of all that is (the universe) and all that is becoming (the world). What can be pondered through logos depends upon this framework of numerosity – the soul of the cosmos. It guarantees that one can learn to understand. For Plato as well as for Deleuze, the role of learning is primary to that of knowing. They are both dialecticians. The inversion consists in the methods according to which they conceive learning possible – here Deleuze replaces the role of mimesis with that of repetition.

With this, Deleuze affirms the developments in algebraic number theory, which begins not only to specify the universal nature of numbers into classes of wholes and fractions, positives and negatives, but which raises the more abstract issue of a peculiar disparity that is proper to all notions of wholeness.  If ‘fictitious’ numerical species like the infinitesimals and the imaginary units are “allowed” in calculation – and this is what boosted algebra in the 19th century, supported by all the novel applications in thermodynamics (real numbers) and electricity (complex numbers) – then the ‘nature’ of number can be engendered in its kind. Since the development of symbolic and universal algebra in the 19th century we are dealing with corpora of numbers (the German word is Zahlenkörper, field in English), which all incorporate one-of-a-kind ‘rationalities’ (i.e. arithmetics which instantiates locally, in one-of-a-kind ‘universes’). If numbers allow for learning, and can be engendered in their kind, then we ought to engender acts of thinking within thought. This is the formula not only of Deleuze, but also of other Algebraists like George Boole, Richard Dedekind, Charles S. Peirce, Louis Hjelmslev [12]:

“Penser c’est créer. Il n’y a pas d’autre creation. Mais créer, c’est dabor engendrer “penser” dans la pensée.”   

To think in this manner can no longer be mimesis. It is what Deleuze calls repetition. Raising a thing to its nth power.  In applied mathematics it is common to ‘formalize’ such ‘categorial universes’ in terms of power sets. They are called so because they embody a disparity which must be approached probabilistically [13]. Also for Deleuze, disparity is where the wild differences insist as the “differently different”, the “in-itself of difference”, or “the self-different which relates different to different by itself” [14]. Raising a thing to its nth power, this is not merely a metaphorical expression. Very literally, the degree of exponentiation governs directly the complexity of the terms in which a problem is treated: if we do not reduce to the least common exponent, although this is the easiest to calculate, if we instead build systems of partial equations of high degrees, the solution space thus rendered solvable can grow so vast that from the many solutions computable, we lack the criteria for determining which one of them is more necessary than another. Deleuze’s interest in probabilistics is not to reassure the expected, but to explore the unexpected.

So let me conclude: Thought, for Deleuze, is “the dynamisms proper to philosophical systems”. I would argue that he attempts to step out of the thermodynamical paradigm which sees in entropy only a measure of disorder. Instead he insists on an articulate-ability of systems, according to a mathesis universalis. “The adventurous character of ideas”, he sais, “conceived as differentials of thought, is still be be explored” – I hope it will be explored by private thinkers, who affirm entropy and develop new mastership through learning   that correspond to the factual potentiality of contemporary mathematics and the factual power of information technology. Such that an economy to come may soon be capable of relaxing the shocking improportionalities which currently unfold on local as well as on global scales.

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[1] Besides the more precise accounts given by Deleuze of this method in chapter four (CHAPTER IV IDEAS AND THE SYNTHESIS OF DIFFERENCE), the following passage from the introduction gives an accounts to what is at stake which may be easier to relate to: “Empiricism is a mysticism and a mathematicism of concepts, but precisely one which treats the concept as object of an encounter, as a here-and-now, or rather as an Erewhon from which emerge inexhaustibly ever new, differently distributed ‘heres’ and ‘nows’. Only an empiricist could say: concepts are indeed things, but things in their free and wild state, beyond ‘anthropological predicates’. I make, remake and unmake my concepts along a moving horizon, from an always decentred centre, from an always displaced periphery which repeats and differenciates them.” (Deleuze, Difference and Repetition p. xx/xxi).

[2] In her plenary talk to the 6th International Deleuze Conference in Lisboa, Portugal, July 12 2013.

[3] “There are two known ways to overturn moral law. One is by. ascending towards the principles: challenging the law as secondary, derived, borrowed or ‘general’; denouncing it as involving a second-hand principle which diverts an original force or usurps an original power. The other way, by contrast, is to overturn the law by descending towards the consequences, to which one submits with a too-perfect attention to detail. By adopting the law, a falsely submissive soul manages to evade it and to taste pleasures it was supposed to forbid. We can see this in demonstration by absurdity and working to rule, but also in some forms of masochistic behaviour which mock by submission. The first way of overturning the law is ironic, where irony appears as an art of principles, of ascent towards the principles and of overturning principles. The second is humour, which is an art of consequences and descents, of suspensions and falls. Must we understand that repetition appears in both this suspense and this ascent, as though existence recommenced and ‘reiterated’ itself once it is no longer constrained by laws? Repetition belongs to humour and irony; it is by nature transgression or exception, always revealing a singularity opposed to the particulars subsumed under laws, a universal opposed to the generalities which give rise to laws.” (Deleuze, Difference and Repetition p. 5).

[4] “The task of modern philosophy is to overcome the alternatives temporal/non-temporal, historical/eternal and particular/universal. Following Nietzsche we discover, as more profound than time and eternity, the untimely: philosophy is neither a philosophy of history, nor a philosophy of the eternal, but untimely, always and only untimely – that is to say, ‘acting counter to our time and thereby’ acting on our time and, let us hope, for the benefit of a time to come’.” (Deleuze, Difference and Repetition p. xxi).

[5] “Following Samuel Butler, we discover Erewhon, signifying at once the originary ‘nowhere’ and the displaced, disguised, modified and always re-created ‘here-and-now’. Neither empirical particularities nor abstract universals: a Cogito for a dissolved self. We believe in a world in which individuations are impersonal, and singularities are pre-individual: the splendour of the pronoun ‘one’ – whence the science-fiction aspect, which necessarily derives from this Erewhon. What this book should therefore have made apparent is the advent of a coherence which is no more our own, that of mankind, than that of God or the world. In this sense, it should have been an apocalyptic book (the third time in the series of times).” (Deleuze, Difference and Repetition p. xxi).

[6] cf. footnote 1.

[7] Deleuze and Guattari, Milles Plateau, ch. 3 p. 39-74 (english translation by Brian Massumi).

[8] Georges Bataille has also considered the role of the sun as a source of abundance in relation to energy – yet for him, the principle abundance was to be treated in the terms of excess, and was in need of being balanced through expenditure. Bataille’s achievement is to point out the urge for making the step from mechanical construction to thermodynamic balance when thinking about economy – yet this seems insufficient as I will argue in the remaining pages of this text. Cf. Georges Batailles, La part maudite (1946 and 1949), in engl. The Accursed Share (Volume 1: Consumption, trans. Robert Hurley (New York: Zone Books, 1991), and here especially his notion of a ‘general economy’ which he opposes to a ‘restricted economy’. He writes in the introduction: “An immense industrial network cannot be managed in the same way that one changes a tire […]. It expresses a circuit of cosmic energy on which it depends, which it cannot limit, and whose laws it cannot ignore without consequences. Woe to those who, to the very end, insist on regulating the movement that exceeds them with the narrow mind of the mechanic who changes a tire.” p.26). The step we are interested, with the notion of an entropic economy, differs from Bataille’s perspective in that we reject the laws that allow to govern thermodynamic system as an adequate framework for thinking about economy.

[9] accessed: July 11th 2013.

[10] magnitudes we ask ‘how much’, there is always a question of metrics involved and through that, of an assumed likeness in kind for all units that are identified through applying the same metrics; with number, on the other hand, we ask ‘how many’, and we count those units. For the idea that we measure a number such that it can count a magnitude – which is central for probabilistics and it’s treatment of so-called ‘random variables’ – this traditional relations gets confused (modulate-able) in very interesting and significant ways. As our treatment of this relation today tends to be almost entirely practical, I would like to recommend a somewhat ‘aged’ text by Augustus de Morgan as the most profound study on the involved philosophical issues in all their complexities I am currently aware of: Augustus de Morgan, The Connexion of Number and Magnitude: An Attempt to Explain the Fifth Book of Euclid, London, 1836.

[11] Quantity in symbolic algebra never means ‘number’ only – algebra is not arithmetics. It always involves the relation between number and magnitude, between counting and measuring. This is also why the notion of quantity in symbolic terms (achieved by Richard Dedekind and his ‘infinitary’ and ‘operational’ procedure of indexing one infinity with another infinity (the so-called Dedekind Cut)) provides the possibility for Riemann as well as for Grassmann to develop geometries, in the late 19th century, where universality does not exclude locality.

[12] It is one of the profound misunderstandings that in this statement, and likewise in the cases of the other mentioned algebraists, emphasis is place upon the first part – “penser c’est créer”. The role of creativity attributed to thought thereby is all too easily done away with as psychologistic or mystical; the emphasis for all of them lies, after all, on the second part, on how we can think about the engendering of thought within thought. This how is the crucial interest in Boole’s algebra of logics (not: algebraic logics!) in An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. Algebra for him is not at all what we today know as ‘Boolean algebra’ (cf. Theodore Hailperin, (1981). Boole’s algebra isn’t Boolean algebra. Mathematics Magazine 54 (4): 172–184. Reprinted in A Boole Anthology (2000), ed. James Gasser. Synthese Library volume 291, Spring-Verlag). For a very significant suggestion of how to apply Boole’s Algebra of Logic today in computation, compare Walter Carnielli “Polynomizing: Logic Inference in Polynomial Format and the Legacy of Boole” http://www.cle.unicamp.br/principal/grupoglta/Thematic-Consrel-FAPESP/Report-02-2007/C07.pdf (11.07.2013); with regard to Richard Dedekind, cf. his Was sind und was sollen Zahlen (1988). In the introduction he states forwardly: “My answer to the problems propounded in the title of this paper is, then, briefly this: numbers are free creations of the human mind; they serve as a means of apprehending more easily and more sharply the difference of things. It is only through the purely logical process of building up the science of numbers and by thus acquiring the continuous number domain that we are prepared accurately to investigate our notions of space and time by bringing them into relation with this number- domain created in our mind. If we scrutinize closely what is done in counting an aggregate or number of things, we are led to consider the ability of the mind to relate things to things, to let a thing correspond to a thing, or to represent a thing by a thing, an ability without which no thinking is possible. Upon this unique and therefore absolutely indispensable foundation […] must, in my judgement, the whole science of numbers be established.“; the role of creativity in Charles S. Peirce Semiotics I take to be widely known; in the case of Louis Hjelmslev, on the other hand, it is crucial that he names his ‘most general theory of langauge’ glossematics: a theory of ‘foreign words’. In the language he proposes to study, with his formulaic ‘theory’ (cf. his Prolegomena to a Theory of Language (1943[1969]), but more so in his posthumously published Résumé of a theory of language (1975), assumes to given nature of language at all, and instead takes all language (if it is to be theorized) as ‘foreign words’. The character of his ‘glosseme’ with the quantity notion in symbolic terms seems evident to me, especially since he draws many of his main ‘technical tools’ like variety, invariance, and so on from symbolic algebra.

[13] as the engl. wiki has it: “a class that contains (as elements) all the entities one wishes to consider in a given situation” – which plays, of course, very different roles in different paradigms, for example in set theory as opposed to category theory.

[14] Gilles Deleuze, Difference and Repetition, p.119.