Distinguishing the General from the Generic / Pre-specificity / Projective Theory of Technology / Thinking as an Algebraic Mechanist

Articulating a thing entirely in its own terms Or: what can we understand by the notion of «engendering» ?

CONTENT

What is the subject of the generic?

Grammatizing symbolical domains

An abstract object’s integrity: political subjectivization
Beyond urban comfort, in a state of expulsion
Generic as an adverb, universality as an ouevre
Bodies of thinking live in algebraic universality

Characterizations of the subject of the generic

Characterization on a grammatical level
The man without quality (Robert Musil)
The city without identity (Rem Koolhaas)

Falling in love with the in-sinuousness proper to an economy of entropy

Primary abundance
Towards an information based architectonics
Within the Generic City: master, yet in ‘whose’ house?

Characterizations of the subject of the master

Attracted by the volatility of a flirt between the philosophical stances of ‘critical rationalism’ and ‘speculative realism’
Cosmic untendedness, prosaicness in verse
The proportionalization of infinity
Cosmo-politics, or putting to work a symbolist meter
Cosmo-literacy, or the alphabetization of the nature of number

Appropriating a body-to-think-in

The most common representation of the nature of numbers …
… and how it got into trouble that are not resolved until today
Algebraic operations, or how the nature of number can be brought to work

Masterpieces, and why there are so few of them

EigenArchitecture 

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this article is a draft version which will be published in: Ludger Hovestadt, Vera Bühlmann (Eds.), EigenArchitecture (ambra, Vienna forthcoming in Winter 2013).

You can download a .pdf version at academia.edu

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What is the subject of the generic?

Largely anyone who is interested in Computational Design today shares a tremendous fascination [1] about the somewhat dubious notion of *the generic*, and its promise of the ‘one-of-a-kind particularity’ of instances that can be computed. Much of the widespread attractivity of this promise is owed to the idea that such ‘one-of-a-kind particularity’ be neither example nor prototype, that its organization be not governed by a logics of rigid classification. Every generic instance counts as “typical” (not needing any surplus qualities to be specified) even though it may well be “singular”, the only one of its “kind”. In programming, the notion of the generic means to formulate functions that are of highest possible generality such that they apply to no specific structures of data, but to (virtually) any structure of data. More straightforwardly: in programming, the notion of a generic object suggests that its instances are a “this”, without being a “such”. Their ‘one-of-a-kind particularity’ can only be indexed, pointed to, it is a particularity which manifests never as corresponding to a certain genus, but only in terms of in-definite adequation within a scope of genericness that aspires to be universal (not classificatory), and which is being articulated by each particular manifestation of such an instance. The extra-ordinary – if not straight forwardly salvational – implication thereby is that with generic objects, articulation engenders universality. Generic objects promise, as objects with a non-transparent and apparently singular autonomy, to be shielded off from any attempt at appropriation by individually vested will, desire, interest, meaning. Instances that are realized from such a ‘generic object’ appear in a peculiarly innocent sense ‘genuine’.

The great fascination for such ‘genuinity’ today, as I understand it, is driven by a certain subversive pleasure geared against the exhaustive and demanding ‘political dynamics’ of what is usually referred to in Hegelian-Althusserlian-Lacanian terms of an economy of recognition.  It sets the political confines for most of the 20th century structuralist and post-structuralist discourses around a necessity to give difference and self-reference a primacy with regard to identity and representation. In all brevity, it is central for an economy of recognition that anything that can participate in and profit from it – anything that can find accommodation within the ‘modern’ nomos (political, as opposed to cosmological law) of a ‘modern’ oikos which is ‘mastered’ collectively (house-as-state) – needs to be mediated through language and concepts.

Such ‘mediation’ involves all the complex cultural issues related to questions like what is actually the ‘object’ described by linguistics (does language, if we could find its pure form, describe natural kinds?), is there a pure form to language at all, or is language as we speak on a daily basis ‘natural’ language – and if yes, are there many natures of language and what does such an assumption entail? and ought we regard language as a system, a structure, or what else? and is it possible at all to generalize from the diversity of languages actually spoken and written, and what does it entail to do so?

To make a long story (very) short, a peculiar in-seperability between interpretation and formalization has haunted notions of theory, objectivity, and subjectivity all throughout the 20th century. The respective discourses have grown quite removed, in all ‘critical’ negotiation, from what is perceived by many as ‘the real issues at stake’ (to improve and optimize the living conditions globally), and the voices raised are inevitably, it seems, also always acting tactically. But most of all, the idea of a position which could clarify permanently the confusions that spring and proliferate from linguistic attempts at clarification, appears to many, meanwhile, as raising the problems in inadequate terms [2]. Our relation to language simply remains as intimate as our relation to breathing.

Grammatizing symbolical domains

Now this is exactly what computational linguists like Noam Chomsky began to readily affirm – yes, he holds, language is so intimate to all of us that it makes sense to imagine it as a kind of a cultural ‘genome’ we are born with, just like we are born with a biological genome. Such a radical move, whose affirmation must count as a veritable philosophical capitulation!, was actually capable of moving beyond the preoccupation of ,critical‘ philosophy with the (politically all but innocent!) foundational issues about the nature and role of language for thought, specifically (ethnicism and racism), generally (socialism), or individually (capitalism). Instead, it was capable to modernize the interest in language itself by postulating a categorical break with the mimesis tradition altogether. No longer focusing on mimesis, and its questions of interpretation, truth, adequacy and so on, the interest now shifted to the pragmatism of sheer transformability. The so-called transformational or context-free ‘grammars’ and ‘vocabulary’ with which programming ‘languages’ work do not even claim to be ‘natural’; they are, to put it a bit provocatively, ‘genuinely engendered’. Let us look briefly at the development of two very strong paradigms in programming throughout the last decades. Early languages such as Fortan, Ada, or C started out with a procedural paradigm. The main interest was to make available for easy application, as a kind of toolbox of ‘instruments’ in coded ‘form’, the precise way of how a certain organizational procedure needs to be set up in order to function well. Every step of decision can thereby be ‘dispersed’ into constitutive procedures, and hence, an infinitesimal limberness can be introduced into organizational forms. The paradigm subsequent to this pursued a much less directly hands-on approach, and instead became more didactical. With languages like smalltalk, Java and C++, an Object-Oriented-paradigm followed the procedural one, and it strictly kept apart the levels of what (described by procedures) and how (the specification of this “what”). Through this distinction, negotiation began to be supplied by ‘computational augmentation’ about what is to be reached, and about how systems can be devised that allow to instantiate procedures (whats) in much wider variations. Object-oriented programming allows to device entire ‘libraries’ of ‘abstract objects’ that depend on no statically specified order and classification system. Yet such ‘abstract objects’ are not really ‘objects’, they incorporate entire ‘objectivities’ –  they allow for ‘one-of-a-kind particulars’ to ‘concretize’ singularly, and optimally be fitted according to the requirements of a task.

This is what we are talking about with the generic in computation: The ambition of programmers to develop informational ‘coatings’ as a kind of abstract packaging, as ‘symbolic cases’ that preserve and protect the ‘abstract object’s integrity’. All the potential functionalities offered by it ought to be provided in a most robust and compact ‘manner’, and for a largest possible variety of instances. Equipped with the techno-logical power of such ‘languages’, the subversive pleasure that seems to accompany the wide interest in Generic Design today lives on the one hand from a radical affirmation of those liberating and disciplinarizing constraints within an economy of recognition, which dictates that the nature of a thing is to be considered in the (politically sanctioned) terms in which it is actually addressed; yet it also lives from responding to this dictate by what I would call an ‘expansion in dimensionality’ by investing its energies into the ‘substantiation’ of speculative notions of reality: it sets up, by means of such genuinely engendered ‘languages’, symbolical domains which can accommodate the objects under investigation, in the terms that are sanctioned for describing them, but which open up further possibility spaces as well – which are governed ‘intra-specularly’.

An abstract object’s integrity: political subjectivization

But what kind of ‘integrity’ are we talking about here, when referring to an ‘abstract object’s integrity’? What kind of integrity is proper to symbolical domains that are governed ‘intra-speculatively’? Much of what this text will be dealing with concerns this question. Far from desiring to dis-enchant the wide fascination which surrounds emerging notions of the generic, this text will suggest to radicalize this fascination. Yet to ‘radicalize’ here, we will see, doesn’t mean to turn it ‘sharp’, as if into a weapon, or to device it specifically, as an instrument that could be serviced to a worthwhile cause. To radicalize a fascination is to radicalize what charms us, the ‘spells’ that take hold of us, and it is meant here in a sense as it literally applies to certain ideas about the nature of number, to which I will come back. In essence, it is about mathematical adjunction in field theory, which emerged out of algebraic considerations regarding the solvability of equations. For now we can say that to radicalize the notion of the generic involves affirming the symbolic nature of numbers [3]. And this entails, literally, to regard numbers in terms of finite, yet infinitely extendable ,corporeality‘ [4]. With the rise of abstract algebra in the 19th century, people were also speaking of providing domains of rationality for a certain (numerical) solution space (as instead of taking universal conditions of rationality for granted, as it is the habit in non-symbolic understanding of numbers) [5]. Put in general terms, corpus theory is central for establishing domains of unique factorization, that is, numerical domains where the arithmetic operations are well-defined for all elements of a corpus (i.e., not in general, but specifically). Thereby, arithmetics ceases to be in a non-problematic manner universally applicable. This, we regard as central to a different paradigm of programming which we would like to help growing stronger – not a procedural one, not an object-oriented one, but one we call pre-specific [6].

This entails several consequences for how we think about computability. Calculations cannot only be right or wrong, but they can also be set-up in a more or less adequate or inadequate manner. The solution spaces that are provided for calculations have different capacities. To put it quite provocatively:  Computing turns into an art (again), just like mechanics used to be an art (and not science) before industrialization. Even the expression to be industrious once meant to be apt and diligent, in terms of personal qualities one has acquired – very different from putting industriousness in the per se depriving terms of alienating submission to an orchestration that is strictly clocked by a responsibility external to oneself, as has become the predominant understanding today. The entailments for revitalizing this legacy of computing as an art are ambiguous, and they seem twofold: on the one hand its promise is to gain the possibility for a new criticality – yet on the other hand, this new criticality is one which is rooted in a kind of local universality. When we suggest to speak of an abstract object‘s integrity, this relates to the particular capacities provided by the solution space that is constituted by such an abstract objet.

But let us not discuss this further here in the rather technical terms of mathematics [7], and instead refer to the same issue – criticality in relation to a certain capacity and ability that is involved in partitioning, in identifying parts and wholes and their inter-dependencies – in the context of contemporary political theory. Within the ‘modern’ oikos, sheltered by a modern ‘nomos’ (a political, and not anymore a divine nomos), each ‘theme’ has to be treated as a ‘subject’ in order to find a platform for public address (newspaper, education, etc): what once enjoyed the generosity in how it was treated (or the silencing violence, or the doctrinary appropriation) attributable to common places (a ‘theme’ as a ‘topos’) now has to be accommodated within an overall organization, and that means, it’s treatment (discourse) has to be surveilled and negotiated. Such a ,subject‘, in a purely passive and non-political way, is an ,object‘ in the sense of the grammatical case of the accusative – the case of „that which is caused“, that which is „called to account“ and needs to be „accommodated in its proper place“ i.e., categorized [8]. A theme as  a ,subject‘ in that sense is what is put before public assembly, because its predication is yet to be clarified [9]. If we are to consider the integrity of those abstract objects which constitute the solution spaces in generic computations within a scale of adequacy, every common place interest (theme) turns into a ,subject-with-dispositions-and-capacities‘. The new criticality at stake, a criticality of finite synthesis, concerns the symbolic constitutions – and through that, the capacities of abstract objects – which are orientating power (public address and its surveillance) in discourse.

This same abstract issue [10] – the partitioning, the identification of parts and wholes and their inter-dependencies as problematical – features centrally for example in the contributions to contemporary political theory by Jacques Rancière. His notion of political subjectivation, which he developed in an essay entitled „Who is the Subject of the Rights of Man“ (2004), is very helpful for developing an idea about what such criticality entails. “Political subjects are surplus names,” he holds, “names that set out a question or a dispute (in French litige) about who is included in their count” [11]. For Rancière, the name of such a political subject cannot be proper names, nor the name of a general class (a noun). It is whatever and however may qualify such a noun: the adjective of the general class of humans. Thus, the name of such political subjects can only be ,generic‘, and as such it is, for him, the name of the ,demos’ [12]. Thus he refers to the ,demos‘ in an adjective sense, form Latin adjectivum, „that which is added to (the noun)“. It is in this adjectival sense that political subjects are surplus subjects for Rancière, a view which grants that giving a definition of the noun (humanity, in this case) is not necessary – it is barred from articulation and spelling out, it must be taken as a premise and treated approximately, just like the continuities of movements are treated in modern differential calculus [13]. Here is not the place to discuss Rancière‘s position in any adequate detail, yet it needs to be pointed out that our own proposition turns away from Rancière‘s at a certain point. By raising the issue of an abstract object‘s integrity, we propose to treat his notion of political subjects not in classificatory terms altogether, but in categorial terms. This means that we opt to regard political subjects, subjects named generically, as universal and adverbial (not as adjectival) [14]. We will come back to what this entails in more detail [15], for now let me simply point you to Michel Serres, who has most forcefully articulated such a perspective in his book The Natural Contract (1990): „My book argues that this Declaration [the Declaration of the Rights of Man and the Citizen from the French Revolution, and its update by the Declaration published by UNESCO after the second world war, (annotation by me, VB)] is not yet universal as long as it does not determine that all living beings and all inert objects, in short, all of Nature have in turn become legal subjects“ [16].

Let‘s remember, our interest is in a notion of criticality that need not sacrifice the infinite, in which thought plunges, in order to gain a notion of consistency. This means, we are looking for a notion of criticality which is not grounded in a general principle of sufficient reason, but one, we might say, that is governed in the way it is foundational for discourse, by a universal principle: that of finite synthesis [17]. How can we picture such governance? The topicality of a theme that comes to be of general interest cannot be treated as an ,objective fact‘ – precisely because as an ,objective fact‘, it is called into account. What I would like to suggest to see in act, in the expansion of the generic whose instances are viewed as pre-specific, is a universal corpo-reality, a corpo-reality of symbolical nature. Thanks to its symbolical nature, such corporeality is not ‘the one body of the collective’, as the political state-form may be interpreted, and it is not ,the one soul of the people‘ as Rancière‘s notion of the ,demos‘ seems to maintain. Nevertheless it is political. It binds, as symbolic corporeality, in lofty and contingent manner what Rancière conceives as dissensus: „This is what I call a dissensus: putting two worlds in one and the same world. A political subject, as I understand it, is a capacity for staging such scenes of dissensus” [18]. A dissensus for Rancière as for us, is not a conflict of interests, opinions, or values; it is, as he puts it, “a division put in the ‘common sense’: a dispute about what is given, about the frame within which we see something as given“ [19].

What names political subjectivity so understood must be generic, we agree with Rancière. But if we understand it as categorial, as an adverb of universality and not as an adjective of a particular natural class, it does not name mankind in terms of ,demos‘, it names ,nature‘ itself. The change is profound: both approaches opt for confounding the distinction between politics and nature, but Rancière‘s classificatory treatment of the generic name places us within a naturalness of politics, while the categorial treatment of it confronts us with a politicality of nature. Everything among which we live – facts and laws, artifacts and things, elements and climate, codes and rules – appear under their proper natality-aspect. Such a politicality of nature puts a dimensionality of genuineness in the place of points of origin and hereditary lineage. More precisely, it suggests to treat questions of origin and lineage by recourse to distributiveness. Such a dimensionality of distributed politicality adds the modality of probability to those of possibility and necessity, which govern in rationalist philosophy anything that extends in space and in time. Hence the political is not a sphere, both our views agree, rather it separates, as Rancière puts it, „the whole of the community from itself“ [20]. The political, for both views, shapes the gap between abstract literalness and the conditionality of possible verification of what is meant, by abstract literalness. Such a politics of difference is acted out, according to Rancière, by distinguishing two „counts of counting“ the community: „You can count the community as the sum of its parts—of its groups and of the qualifications that each of them bears“ – this way of counting is entirely rule-based and uninvolved, and it results in cold observation and surveillance according to a logics of classification (Rancière calls it ,police‘). A second way of counting, he puts as follows: „[Y]ou can count a supplement to the sum, a part of those who have no part, which separates the community from its parts, places, functions, and qualifications“ [21]. To Rancière, only this second ,counts of counting‘ is politics, and such counting is not uninvolved, it is acted out by political subjects, and it does not submit to rules in any mechanical manner [22]. It‘s procedures are infinitary, as opposed to the finitary way of counting by summation (that of his notion of ,police‘). His usage of ,counting‘ consciously evokes that mathematical practice in its irreducibly intertwined double sense of ,accounting‘ and ,governing‘. Such politicized counting, which affirms to count in infinitary values as supplements to each totalizing ,sum‘ follows in Rancière what might be called a materialist aesthetics of classification (not a formalist logics of classification). We can see now where the naturalization of politics happens in Rancière‘s position: his politics of difference is acted out in a two-fold manner, by ,the police‘ and by ,political subjects‘. Thereby, responsibility is delegated to one side only – that of political subjects, while ,the police‘ is treated almost like we treat the weather: as the quasi-material incarnation of necessities whose constraints are determined on a more abstract level (climate), but that we have to deal with for bringing both, rhythm and chaos, fertility and destruction, homogeneous and disrupted growth, prospering and corruption.

Beyond urban comfort, in a state of expulsion

In order to see more clearly what is at stake with a categorial treatment of what names political subjects, in distinction to a classificatory one, let us briefly consider what seems to be an important motive for Rancière and his classificatory treatment. Towards the end of his text he clearly states that he means intervening a certain contemporary tendency towards „erasure of the political in the couple of consensual policy and humanitarian police“ [23], a tendency which he sees threatening to turn what used to be political activity into „an anthropological or ontological destiny“ [24]. Political correctness, administrated by discourse,  perfidiously urges us to be ,passive‘ if we want to be politically ,active‘. His aesthetics of classification is geared against such false ,political correctness‘, which in effect hands over the legacy of political thought and action to some larger power which predicates us as Subjects of Rights. This ,larger power‘, obviously, manifests in the process of progressive raising of levels of welfare, which unfolds on a global scale, albeit in unequal manners and paces. Many call it simply ,capitalism‘. Rancière seems to ask, what if we dared to turn our backs to this urbanity which is spreading globally, propelled by its promise of quasi-salvational comforts, and which tends to erase all politics in the manner mentioned?  He does not seem to seek to somehow ,overturn‘ the system, nor to fight for more global justice, rather he seems to ask: Can there perhaps be an exodus, can we not learn to cultivate  differently the grounds on which we would happen to find ourselves, if we affirmed to live in a state of expulsion? Can we not begin to oppose the auto-logy of such destiny by producing the means we need, in order to remain active political subjects, through a kind of ,farming‘ that learns to root that for whose growth it cares, in – to use his own formulation of how political subjects ,count‘ – the infinity of a sublime object, the object of aesthetic judgement, which virtually supplements each sum? 

Rancière suggests a kind of aesthetical calculus rather than a logical one. It is aesthetical because its functions map procedures in a twofold manner, (1) by numbers that label the sums of infinite terms, (2) yet these labels are merely indexes, pointers [25]. Such an aesthetical calculus is ,genetic‘, it‘s function are productive, they do not merely represent a process, they initiate it‘s enactment. Such is the involvement and activity which Rancière holds necessary for counting as political subjects. It is not an activity which fights what is counted in a police manner, but one that has decoupled from such counting and instead regards it as a quasi-weather, as temporary states that are imposing certain conditions with which we have to deal, if we were to hold that it is not entirely unthinkable to begin again: by affirming to live in a state of expulsion from the secular urbanization of modernity, which used to be like a promised land but turned out to sentence its ,subjects‘ to the status of ,consumers‘, allowed of ,doing politics‘ in terms of ,correctness‘ which is policed by a kind of counting that builds on a logic of classification which deprives the individual of holding her aesthetic judgments as legitimate.

Generic as an adverb, universality as an ouevre

In all of this our own views would agree. But what is entailed now with opting for a categorical rather than a classificatory approach? How can we picture what a philosophical stance of ,critical rationality‘ would entail, a rationalism which is coupled with a notion of criticability that revolves around a symbolic understanding of numbers?  What would it entail to stick with Rancière‘s operative distinction of two „counts of counting“, while  transposing them onto a stage set such that the generic name acts as a universal name, adverbial not adjectival, a stage on which it articulates and spells out the oeuvre that produces nature? In all figurative brevity, it does not characterize life in such a state of expulsion as the life of farmers, but as that of gardeners. It is not the material grounds of a new existence, generic and singular (politics anchored in aesthetics) instead of comfortable and general (global urbanity) that needs to be cultivated, but the intellectual grounds of hetero-topia, common places (topoi) that are nowhere there, but nevertheless real. Heterotopia are the kind of sites that have consistency not despite but because they are distributed, they are „continents, cities, planets, universes“, as Michel Foucault imagines, that are engendered „in the heads of people from the in-between of their words, from within the deep layers of their stories and also from the place-less site of their dreams, the void in their hearts“ [26]. If heterotopia are nowhere there, this we take from Foucault‘s idea, it is because they are always already here – as utopian in the literal sense, a place which has no place, heterotopia spring forth from the non-places of the immediacy of a present we live through our bodies [27].

Thus we would suggest that the universality we see as being named by Rancière‘s notion of the political subject, once we think about it‘s generic name as adverbial rather than adjectival, instantiates as bodies-to-think-in. A particular body-to-think-in is one-of-a-kind, and its kind is what I mean with symbolic corporeality. We can look at the universal as an oeuvre, at work in the symbolic contracts that household the energy from it lives, as nature. Hence it is true that the symbolic is vested towards establishing consensus – for Rancière the negative of dissensus, and according to his dialectical thought the death of politics – but it does this as a means to make room for staging scenes of dissensus. The symbolic is neither political nor doctrinaire, it is operative, and only in a derivative sense is it functional. It is ‘at work’ indefinitely, never as a process which begins and ends. It creates the capacities proper to generic conditions of transformability, and it insists that these conditions be universal while at the same time having actuality only as local instantiations. We can see formula or equations as the symbolic ,form‘ such adverbial contracts take. What I would like to suggest is that they open up and cultivate an interval for the political subjectivization of any identity, just as Rancière claims it for what-is-being-named-by-the-demos (he speaks only of political “names” and political “subjects”, not of political “identities”). Nature‘s politicality-dimension constitutes, in its principle expropriation of particulars from their individual genuinity (generic means to expropriate all individuality from specificity), the non-possess-able disposition for staging scenes of dissensus.  Things have a genuinity, they have a nature, but it is symbolic and rooted in an elementary distributedness rather than in an individuality.

The unsettling aspect about understanding the symbolic in such terms is, of course, that it may be instrumentalized in both directions – politics and/or doctrine. There can almost be no better characterization than Rancière’s [28] own of what “kind” of subject is named thereby – cases whose kinship is unsettled: “Political names are litigious names”, he writes, “names whose extension and comprehension are uncertain and which open for that reason the space of a test or verification” [29]. For him, political names name political subjects in such a manner, and this is how they are capable of reorganizing “the frame within which we see something as given” [30].

I am aware that suggesting to see identity which can be expressed by a formula or equation in the same terms that Rancière finds for political subjects might strike one as a gross misunderstanding – isn‘t the solution space for a symbolic form determined in absolutely certain ways, not in uncertain ways? On which grounds can we speak of such a politicality dimension that belongs to nature, and of which we claim a universality that allows to characterize the abstract objects of symbolical computation in terms of their particular integrity? I briefly pointed to the importance of how we think about solution spaces when I introduced the notion of adjacency in mathematical corpus theory. Let us see in more detail how this is exactly what was at stake with the emergence of universal algebra throughout the 19th century, and how we are confronted today with its entailments.

Bodies of thinking live in algebraic universality

“Let us to try to make sense of the sentence—or develop the equation.” (Jacques Rancière)

Computing with the symbolic means of algebra has added a new dimension to mathematics: the input of certain values in a formula may not only turn out to be unsolvable, it may on the other hand also yield a solution space which is so vast in options that none of the possible solutions seem more necessary than any other. This was indeed the key critique on George Boole’s Algebra of Logics, which is illustratively expressed in an open critique letter by one of his contemporaries:

“The disadvantage of Professor Boole’s method is […] he takes a general indeterminate problem, applies to it particular assumptions not definitely stated in his book, but which may be shown, as I have done, to be implied in his method, and with these assumptions solves it; that is to say, he solves a particular determinate case of an indeterminate problem, while his book may mislead the reader by making him suppose that it is the general problem which is being treated of [emphasis mine, VB]. The question arises, Is the particular case thus solved a peculiarly valuable one, or one more worthy than any other of being solved? It is clearly not an assumption that must in all cases be true; nor is it one which, without knowing the connexion among the simple events, we can suppose more likely than any other to represent that connexion.” [31]

Boole’s methods were not shown to be faulty or inconsistent – the reason why they had been disliked or even spurned by so many was the immense depth of horizon his methods had opened up. Indeed, Hailperin has in a relatively recent paper explained how Boole’s ideas make sense only if we read them in relation to algebraic concepts like ring, module and domains, concepts that had, in his time, been far from digested and settled, not even on a methodological level, and certainly not on a philosophical level. I will come back to this in  a later part of the paper [32].

These preliminary indications are merely meant to induce some confidence in my postulation of the generic as constituting a kind of symbolic corporeality whose singular instances manifest as particular bodies-to-think-in, and in bearing with me a bit longer when speculating about what such a postulate might entail for thinking about computability. The most important aspect is that such bodies-to-think-in are collectively constituted – before they can be acquired individually. Yet this collective constitution is realized only through the individual acquisition of the bodies-to-think-in. The agility they are capable of relies upon individuals who learn to inhabit what has been collectively achieved. They turn lonely and clunky otherwise. We can think of such bodies-to-think-in perhaps best as literacies: we can see the canonical corpus of authoritative knowledge turning into bodies-to-think-in, animated and vibrantly present in manifold manner, according to the breath and articulacy in which these corpuses are inhabited. Such inhabitation, does it not point us towards the possibility of affirming mastery in a different manner than that of domination, dependency and exploit? Does it not announce a revival of other aspects proper to mastership, like generosity, care, and commitment? To inhabit politically such a canonical corpus requires the act of appropriation as we know it from learning-to-become-literate: not only in the sense of writing and reading correct sentences, but finding apt forms for one’s words, and apt expressions for one‘s thoughts.

Let us return from this preliminary remarks, and from viewing computability within the paradigms of programming, back to computational design more strictly. Here we can see in architecture for example, how the first wave of this fascination with the generic had raised an interest in form finding as opposed to giving form, or deciding about form. By now, this first wave has given way to an interest in developing the parametric conditions from which such forms can be found. Yet along with this comes a certain complication with regard to seeing in the ‘generic’ a kind of ‘genuinity’ that would liberate us from troubles associated with individual authorship and mastership: In the light of parametricism as a new paradigm in computational modeling it becomes much more transparent that indeed, the ‘one-of-a-kind particularity’ attributed to instances of such abstract objects is neither example nor prototype, but that there is a “suchness” to the “thisness” of their instantiations nevertheless, and that despite the engendering of its hylomorphic identity (its form and content) through mere tentativeness (purely indexical, without decision of how to interlink the dots into a figure), these instances are conditioned. Technically speaking, they are conditioned by a Master Model whose instance they are. Theoretically speaking, the form of ‘organization’ and ‘government’ proper to a Master Model (you can think of the intra-speculative domains mentioned above) may well be singular, yet they are not absolute – simply for the reason that there is an open range of manners in which each and every one of them could be set up. Or to put it differently: We may well be dealing with absolutes, when we deal with such ‘abstract objects’; yet they are absolutes whose symbolic nature tells us that there always are alternatives to be considered.

Characterizations of the subject of the generic

Characterization on a grammatical level

Against our suggestion to read the generic in an adverbial sense, the „grammatical common sense“ (if indeed there is such a thing) today maintains that the generic be the adjectival form for referring to a genus that can be represented by the formal notion of a class. There are many ways of how this could be explained [33], but the most important one seems to involve a strange ,metaphysical competitiveness‘ between the notions of genericness and universality. Traditionally, any one genus could never count as universal, because its rôle is descriptive and representational in relation to concrete things which in reality are always individual, and whose collective nature the genus is to determine.  Universality, on the other hand, has traditionally been attributed to categorial determination, of which it is clear that they are genuine abstractions (however we might think about the ‘nature’ of ‘abstraction’). No one would seek for ‘position in space’, or for ‘quality (per se)’ as a concrete instance of which we could say it exists! [34] Categories were held to be universal, and they were what concrete things would instantiate. This is how the universal comprehends, literally, that which is the property of all things.

It seems hardly an exaggeration to see in the conflation of this distinction, between classes and categories, the key aspiration for modernist political philosophy. In its striving to rid philosophy and science from metaphysics and theology, it seeked to overcome orders of supposedly natural kinds and their rigid class distinctions. The challenge was, and still is today, to find a way of ‘attaching’ the universality proper to categories of abstract criteria to the notion of class which can be formed according to concrete marks of distinction. The quest for a universal subject, a universal object, or even a notion of universal reality, must try – if it wants to be critical and not dogmatic – to identify a notion of universal class. A universal class would be a class which acts genuinely without self-interest, and in the interest of all. Or to put it differently, more adequate but also more difficult: the universal _class would be the class where self-interested action coincides with the needs of humanity as a whole [35].

The man without quality (Robert Musil)

Robert Musil has famously written a novel of a man whom he portrayed in the light of such an essential abstinence from desiring individual property, as the man who aspires to be, tautologically, nothing but a man (Der Mann ohne Eigenschaften, 1930-32). The novel accounts the struggles its protagonist has to take upon himself: as a character with a life of his own, Ulrich is faced with this task as a sheer impossibility. He tries to find meaning for his life under the condition of resigning from any possibilities offered to him by the particular class to which he happens to belong – in his case as an intellectual, a mathematician by education, that of the Bourgeoisie. In vain attempts to reconcile “soul and exactitude”, his vocation and his profession, he searches for a place and role purely within the ‘universal class of mankind’ – that is, by refusing to accept any privileges that might be granted to him on the basis of his particular individuality-within-the-actuality-of-the-social. Musil’s novel is appreciated widely for its capacity to express and thematize in most subtle and differentiated ways a widely shared mood of the Zeitgeist of his time, and counts today as one of the most influential books of the 20th century.

The city without identity (Rem Koolhaas)

More recently, the architect Rem Koolhaas has taken up this Musil’ian theme, yet now in relation to cities instead of an individual person. The Generic City gives the portrait of a city in the light of having done with all that Musil’s protagonist still tries, in vain, to reconcile for himself – in short: identity, property, history, the entire inheritance from a pre-modern era with which an individual has been equipped ‘to-begin-and-continue-with-itself’, in short, to lead a proper life. The Generic City confronts us with an account of the peculiar realism of the generic, there is neither identity nor history nor property in the Generic City. Consequentially, the Generic City establishes its order in purely infrastructural, systematic and continuous terms. There is singularity in the Generic City as he portrays it, yet it is a singularity which is liberated from the standardized. Rather than incorporating a cosmic, cosmological or otherwise transcendent order, the Generic City provides settlement within what Koolhaas in all consequentiality calls Junkspace: pre-empted from ever manifesting something of substance – something that would have to be conceived of in how it maintains its own finite continuation – such space is only there to ultimately be disposed of. All reason for categorization is annihilated in it. In Junkspace, order must not be wrested from chaos. Instead, one-of-a-kind-particularity (which he calls ‘the picturesque’) is wrested from the homogenized.

Unsurprisingly, the reception of Koolhaas’ portrait of the Generic City is quite different from that of Musil’s theme-opening novel. Bluntly speaking, it tends to be perceived as a bothering impertinence. Its clinical viewpoint and the somewhat drastic (and also, arguably, resigned sarcastic) tonality is often taken for the cynicism of a global architect who portrays, with a certain braveness, it must be admitted, a threatening development which he contributes to and lives from: the drastic homogenization of our living environments. For many people it seems clear, that the homogenization he portrays is an effect of the expansion of capitalist economy and a respectively darwinian survival of the fittest dynamics that goes along with it. To such an understanding, Koolhaas’ suggestion to relate these effects of homogeneity to the strengthening expansion of the generic must appear monstrous. Large portions of the aggressions Koolhaas attracts are surely because he seems to ridicule hopes that feed from the believe that there must be a way to purify the generic from the exploitative dynamics of capitalism, and to find in it, finally, a long-seeked means to realize the core values of socialist and modern politics.

But where am I speaking from, when daring to refer so distantly and seemingly uninvolved to this thematic locus of vibrant emotion (and activism)? Before turning to my staging of that conceptual persona which, as I would like to convince you, ought to complement that of the Generic, namely the concept of the Master, it seems adequate to make a few short statements about this.

Falling in love with the in-sinuousness proper to an entropic economy 

Primary abundance

I am speaking from a point of view which credits a development with principle importance in a manner that is not usually shared today, even though as a phenomena, it is almost permanently in the media – yet as an observation only, without instigating the least dissensus so far. The phenomenon I mean is this: our planet is literally bathing in the solar stream, with 10’000 times as much energy to be potentially harvested from its light particles as all of humanity is currently using worldwide, each day, streaming by, each day, continuously so. For the first time ever, we can encapsulate and integrate, within the planet’s eco-sphere, energy that is additional to that which is already stored in it‘s manifest natural body, in the weather, in plants and animals, in stone and earth. It may sound strange and somewhat amazing to view photovoltaics like that, but as a phenomenon it doesn’t seem to be disputable, really. Yet weighting this phenomenon as being of principle importance for how we think about our habitat and anything that derives from such thinking – economy, politics, how we make sense of what we experience and engage in, this is much more critical. Because it means to attempt ‘generalizations’ that were based on what this ‘phenomenon’ implies.

What would that mean in the first place, attempting to ‘generalize’ on the grounds of regarding the planet’s location in the universe not in terms of its position within the interplay of cosmic forces, as in astronomy and geometry, but in terms of the planet’s active energetization? I put ‘generalize’ and ‘phenomenon’ in quotation marks. Why? Because this ‘fact’ is an ‘artifact’. It didn’t come about (in a naive sense) naturally, it became a fact only on the decisive grounds of human intellectuality. Photovoltaics is technics at the (yet) most sophisticated level. And to generalize usually means to delineate classes such that they are capable of representing as adequately as possible, in mimetical terms, a certain common nature among different things as they are given. Yet in the case of the earth, viewed in such terms, we have a singular situation. Attending to how we might ‘address’ the planet’s situation in the universe in terms of its energetization inverses our well-tested and refined language games around localizability. The principle of locality in time and space – the principle that each thing has its place – needs to be replaced with a principle of circumlocution. The point is that which is being given, not that from which we can deduce is given in an immediate sense. It is not enough to consider circum-stances as characterizing location, more radically: we owe our location to the circum-giving (das Umgeben, in German) of rambling tails (the wave ranges of cosmic streams). Under such conditions – let us call them adverbial –  quantization precedes localization, just like it is the case in quantum electro-dynamics, which also views light as particles [36]. In all consequence, attempting to ‘generalize’ from the implications of photovoltaics irrevocably urges us to distinguish between ‘generalization’ and ‘abstraction’ much more strictly. The implications of such generalization are abstract at first, they affect our notions of universality, but they also reach back to what we hold as general, the empirically based and classified descriptions of things. Attempting to generalize from the planet’s situation within the solar stream comes close to a modulation of cosmological stability. To put it as pragmatical as possible: it suggests that we should count on a primary abundance of (clean) energy, and with that, an abundance of water and food; furthermore, bringing all materials that are rare and scarce into a regenerative cycle were not anymore a principle problem, because the main obstacle to recycling are energy-budget calculations, which depend upon the principle scarcity of resources. In less pragmatical and more theoretical terms: Such an inversion turns the earth not only into an object, but also into a subject. This falling together inevitably collapses the critical distance which is so necessary for thinking considerately – which literally means through observing the stars, from com- „with“ + sidus (genitive sideris) „constellation“ –  and not furiously and impetuously. This was the the key motive for Gilles Deleuze, with his difficult attempt at inverting, philosophically, the entire legacy of platonism, which he stated in strikingly clear terms: „[i]t is not the slumber of reason that engenders monsters, but vigilant and insomniac rationality“ [37]. If it wouldn’t sound so dramatical, it would seem adequate to say, instead of speaking about the possibility to ‘generalize’ from this ‘phenomenon’, that to assume the very possibility to do so entails assuming the possibility of engendering the earth in its kind.

This is a hyperbolical way to put it, and I am aware of the polemical nature of that. To contextualize this, I would like to come back now to what the perspective of universalizing the Subjects of Human Rights entails in more detail. Let‘s attend more closely to the position of Michel Serres already mentioned earlier [38]. To illustrate more concretely what motivates such overstatement – that we are engendering the earth in its kind – we can take up helpful terms he has coined. He names ‘collectivity’ the new object-subject distribution, and places in its range of responsibility what he calls world objects: “By world-objects I mean tools with a dimension that is commensurable with one of the dimensions of the world. A satellite for speed, an atomic bomb for energy, the Internet for space, and nuclear waste for time […] these are four examples of world-objects.” The turn in the language game of localizability for him means that “we become the victims of our victories, the passivity of our activities. The global object becomes subject because it reacts to our actions like a partner.” [39]

Hence, attempting to generalize from the planet’s situation within the solar stream in terms of its energetization and circumgivenness (instead of position and locality) comes close to a modulation of cosmological stability, and this, perhaps, with a momentum no less severe than that of the secularization of cosmology which had accompanied modernity. There is little reason to doubt that we can continue to count on what we believe to ‘know’ – all the technical and scientific artifacts certainly bear witness to that; yet we might have to reconsider how we can account for the stability which is captured in what counts as knowledge. If our thinking about the earth means to engender it in its kind, the earth – of which we are, intimately, a constitutive part – is the ‘whole’ which comprehends all that can be articulated, and all that can be substantiated in formally corporeal terms (symbolical artifacts) as well as in materially corporeal terms (manifest artifacts). Taking the implications of mastering photovoltaics serious means to articulate the ‘identity’ of the earth not in its general or correct terms, but in any terms that can be substantiated. And it also means that all the terms that can be substantiated are terms that properly characterize its kind.

Modern science has assumed a natural homogeneity as characterizing all things natural, in terms of which it attempted to classify scientifically all things on equal basis, dynamic yet universally coordinated, within dimensions whose interplay apply uniform and globally. Michel Serres has named them as the “dimensions of the world” – speed, energy, space, time. The principle which modernity has found for applying in identifying the individuality of all things in this manner, as constituted not by natural kinds but by a universal nature, was “work”: transforming energy from one form into another. The architectonics of such systematicity rests on the assumption that the amount total of energy within the cosmos be finite. Only on the basis of this assumption can we learn to understand forms of individual becoming purely on the basis what a thing is doing, literally, through understanding the transformations of energy and matter. What we see questioned with the principle of primary abundance is not this axiom, but the adequacy of the modern (thermodynamical) stance to treat world and universe alike. There seems to be no reason to reconsider that the amount total of energy within the universe be stable, and that energy is what can neither be produced nor decay. It is the equivalence between cosmos and universe which appears as inadequate from the energy perspective of primary abundance. In concrete terms: the amount total may well be finite and stable within the universe, yet that which is integrated and encapsulated within the ecosphere of the planet earth is not. The criticality we are looking for, one that were not based on a principle of sufficient reason but on one of finite synthesis, needs to live up this change in perspective.

Towards an information based architectonics

Michel Serres has recently suggested not only that [40], but how the two physical categories of mass and energy – those that are derived from the principle of work – could be complemented with a third component that is orthogonal to the latter two: information.

“I do not know any living being, cell, tissue, organ, individual, or perhaps even species, of which we cannot say that they store information, that they treat (or process) information, that they emit it and they receive information. […] I know of no object in the world, atom, crystal, mountain, planet, star, galaxy, of which one could not say again that it stores information, it treats (or processes) information, it emits and it receives information. So there’s this quadruple characteristic in common between all the objects of the world, living or inert.” [41]

Between all things in the world, he suggests, what is common is a fourfold activity – to store, to treat, to emit and to receive information. While work, the transformations between energy and matter, was the emancipatory principle that allowed to overcome pre-modern doctrines of natural order by demarcating a strict separation between culture and nature, mind and matter, spirituality and reason, the introduction of information severely complicates things. While work as a category operates on the level of representing a generality (the class of all things in sofar as they are natural (or technical, in the sense of scientifically natural, as they do work), the fourfold activities operate on the level of actualizing abstractions. The cosmos (world, manifestations of things) does not represent a universal order (forms, templates, types etc). In fact, the universal cannot be represented because it is pure and infinite activity: storing, treating, emitting, receiving. The so induced notion of universality cannot be represented by concepts, it acts. Within the quantum clouds of probability distributions it keeps predicating potentially, and can only be actualized when articulated (factorized and complemented with coefficients) within a formula, and expressed as a case of the symbolically established solutions space. Information (what is distributed and integrated in this acting) is like the photons from the solar stream: an elementarity of abounding and discrete packages of powerful indefiniteness. It comes in abounding and indefinite streams. Articulating it in the terms of an alphabet excites its indefiniteness to take on the characteristics of what we might call an imaginary magnitude, corresponding to how the number which counts (and through that, governs and accounts) the possibility space is indexed, and indexically labeled. Such indexing articulation raises the indefiniteness of information into lofty probability distributions of local density (amplitudes) and local plenty (probability amplitudes). As long as information is not thus excited and raised, it is indefinite just like the photons of solar radiation are indefinite as long as they don’t incite, through inter-action, state changes within the relative stability of chemical bonds.

In all consequence, the relation that can be maintained to the universal, so conceived, varies locally and depends upon the capacities and abilities that can be mobilized for articulating the terms of a formula which render solvable functional mappings. As long as the virtuality of the universal is not actualized, it remains pure indefinite elementarity, an elementarity we could call ideal because it is of no substance. Such virtuality of the universal is a kind of ideality that belongs to all things. In order to turn substantial, it depends upon being actualized, and such actualization, I would suggest, is achievable in acts of learning. Learning, literally, is an act of appropriation: it means mastering a subject matter, and it is through such mastering that the virtual can be actualized and rendered manifest. It is not the formula which incorporate the universal in any schematic sense; the formula, in their apparent schematicness, depend upon animation through the learnedness according to which the partitioning differentiation of the activity it constitutes, as a matheme, is modulated. To conceive of formula as mathemes in its Gk meaning from mathema, for “that which is learnt”, has been the custom for many philosophers throughout antiquity to enlightenment, and has been revived very prominently in the 20th century by Martin Heidegger in Die Frage nach dem Ding (1950), and also a.o. by Jacques Lacan, Gilles Deleuze, Alain Badiou. From our point of view with regard to primary abundance, what all of them are concerned with (in very different ways!) is that the universal – if it is in-act (ontologies of the event) – is literally entropic, from the Greek term entropia, from en for “in” and trope for “a turning, a figure of speech”. The universal is that which keeps turning within figures of speech.

With this, we can now summarize our proposition of an entropic economy: It is not against entropy, but thanks to it that we can maintain a locally variable relation to the universal, and substantiate figures of speech by treating them as abstractions, not as generalizations, and by striving to formalize them into the constitution of a possible matheme. From the point of view of mathemes, the relation we can maintain to the universal is locally variable, and it is subject to an ‘economy’ which is both, collectively and individually based, and whose ,stocks‘ are those accumulated through learning, and whose exchanges are rated by the appreciation of mastership. In all dramatic exaggeration: surplus names can be rated in terms of any scale, from completely worthless to sublime dearness. The subjects that are mastered, by learning, are political subjects in Rancière’s sense which I have introduced earlier. They are subjects whose names to not represent definite collectivities. It is in this sense that their names are abstract, not general.  They are “surplus names, names that set out a question or a dispute about what is included in their count.” The predicates whose activity is being governed by such counting are, due to the virtuality of their universality, open predicates: they do reign by (arithmetic) means of summation, division, etc, yet what they sum up is symbolically constituted, and because of that, can never be exhaustively totalized as a finite sum. They are predicates which open up a dispute about what they exactly entail and whom they concern in which cases. They are capable of introducing an interval which makes possible political subjectivization into any status quo. “Political names are litigious names,” Rancière points out, “names whose extension and comprehension are uncertain and which open for that reason the space of a test or verification. Political subjects build such cases of verification. They put to test the power of political names, their extension and comprehension” [42]. It is such putting-to-test that formula, conceived as mathemes that are allowed to calculate with what has been learnt, are engaged in. What has been learnt can also be taught. If we cease to represent the universal, and instead relate to it by means of actualization, what opens up is the perspective of an economy in which all acts of appropriation are contributing to – not depriving – the prosperity of the universal. What comes within reach to be thought is an economy where privation increases the wealth of that which belongs to all. If an individual learns to know, through acquiring mastership, developing it as a proper ability and demonstrating that and how it can virtually be learnt by anyone, it differentiates and proliferates the richness of the universal.

From the adverbial and categorial point of view to universality, the commonness of the common nature of things is the result of inception, rather than the result of conception. With regard to political subjects (in the extended sense proposed in this text, not in Rancière‘s original sense), abstraction precedes the concrete existence of that which presents itself to us in regularities. That which appears recurrently as cases follows a categorial order before it can be tested inductively, empirically. Abstractions are for learning, generalizations are for testing and settling the learnt such that it can be treated as a case, as a “such” and not only as a “this”.

Contrary to pursuing a prosaic disenchantment of the fascination with the generic, I hope to have been able to express why I think it only now begins to get truly interesting: the generic introduces a possible understanding of mastership which, seemingly paradoxically, builds on the premise of expropriation.  It introduces an understanding of masterhip where the –ship, the affix demarcating „a state, condition of being“ is primary to the individuality which actualize and acquire this state – the masters.

Within the Generic City: Master, yet in ‘whose’ house?

By coining the striking word of mankind as having to come to terms with ‘not being the master in his own house’, Psychoanalysis has suggested that we ought to understand ourselves through roots within the unconscious as a peculiarly expropriated groundedness of what can be understood and known. Psychoanalysis has rendered explicit a veritable negative form of architectonic thought which operates by working through an element of collectivity that remains unavailable for all attempts of taking control. Jean-François Lyotard has modulated this language game by making the point that notions of humanity need to be rooted in an element of what he calls ‘the inhuman’, a constitutive part of us which we do not control. It may be birth, infancy, the law, god, or the unconscious. Jacques Rancière has taken up this consideration in his reflections about Who is the Subject of the Rights of Man to which I have made reference several times: “Absolute evil begins with the attempt to tame the Untamable, to deny the situation of the hostage, to dismiss our dependency on the power of the Inhuman, in order to build a world that we could master entirely”, he writes, and continues: „Such a dream of absolute freedom would have been the dream of the Enlightenment and of Revolutionary emancipation. It would still be at work in contemporary dreams of perfect communication and transparency“ [43]. Important is that such inhumanity is the irreducible otherness, the part of the untamable of which human being is both, host and hostage, Gastgeber and Gast, as a relation we might perhaps call ‘co-existence’ or ‘genuine mutuality’ [44]. Along the lines introduced in this text, I would say it is the infinitary surplus that needs to be taken into account where ever we are working with summations, checks and balances.

The grand project of an architectonics of reason, whether in positive or in negative terms, even if it were to inverse the problematics of mastership into non-mastership – into purely activity that doesn’t require mastership at all, but that unfolds auto-logically and auto-matically – meets its limits and turns stale and oppressive in the reduction of its own categories to representable schematisms. A schematism cannot engage critically with its own constitution intra-specularly. Our interest in a next paradigm for programming languages, a pre-specific one after the procedural and the object-oriented ones, derives from the unease in observing that these limits are indeed being met today.

Programming languages, as I have argued earlier on, have entirely broken with the mimetical paradigm of language – their grammars are engendered, their structures are governed self-reliantly, symbolically, within the confines of certain arbitrarily set determinations of usefulness. Without an understanding of mastership, all engagement with intra-specularity would mean to subject ones own critical engagement to the governance of these arbitrary determinations. In other words, if the generic makes a worthwhile point in suggesting to trust in a ‘groundedness’ of knowledge that roots within an elementarity of distributedness, where all particular instances are expropriated from their individual specificity, such trust would mean – in programming more generally – to subject readily to the abstractly synthesized and arbitrary Master Language, or to Master Models in object-oriented computing more specifically. The problem thereby is not that these synthesized Masters are synthesized; and neither that their ‘nature’ is induced according to the orientation on a certain ambition. The problem is that the synthesized Masters tend to appear as quasi-naturalized, while in fact they are synthesized by acts of learning and on the basis of acquired mastership. The problem, hence, is that they ought to be esteemed and treated accordingly – that is, the categories with which they operate ought to be understood as characterizing ‘political subjects’, not the subjects of ‘natural kinds’. The criticality with which they need to be met is not one principled by criteria indicating when reason is sufficient, but by criteria which index the capacities that constitute acts of finite synthesis.

Thus, instead of referring to this dimension of expropriation as an expansion of the Unconscious, the Law, Provenance, or Divine Chance into and within the scope of what can be computed, I prefer to call literacy this abstract ‘where’ where ‘what can be engendered through learning’ is rooted and grounded. We need not make any appropriative claims about the untame-ability and insistentiality that animates literacy, if we relate to it as a kind of body-to-think-in which indeed is generic, and hosts us before it can be inhabited individually, while it’s existence depends, at the same time, on actually being acquired and inhabited by individuals. We can now see, in literacies, that which incorporates „loftily“ what I have earlier suggested to understand as the politicality-aspect of nature. I have characterized it as a dimensionality constituted purely by distributivity, and as complementing the modalities of the necessary and the possible with a further aspect, that of the probable. Expropriation and mastership maintain a kinship relation that might appear surprising [45]. Yet at the same time we all know well, how in order to communicate – whether in spoken words (speech), written phrases (discourse) or symbolic terms (algebraic code in IT and IT based CT) – we depend on means and constraints from which we may well choose, but to which we have to submit first, in order to be able to choose. As long as we don’t master articulation and expression, argumentation and composition, signal interpretation and interface decodings, the less schematic and more interesting ones of them appear to us not as wrong, but as empty, superfluous, often confusing, insufficient, not entirely adequate, et cetera. It sounds quite paradoxical, but we feel comfortable, individually, within this generic dimensionality (our literacies) proportional to how well we are able to ‘master’, individually, these collectively constituted and governed capacities. [46]

Characterizations of the subject of the master

Attracted by the volatility of a flirt between the philosophical stances of ‘critical rationalism’ and ‘speculative realism’

So let us get back then to characterizations of the second conceptual persona that features centrally in this text, next to that of the Generic: the Master. While many contemporary intellectuals seem prepared to submit, with all due acrimoniousness, the rich legacy in architectonic inception to forms of often all-too unimaginative and uninspired scientism [47], a young French philosopher is currently raising hopes for the possibility of philosophy to actually continue its legacy of architectonic inception. Quentin Meillassoux is central to an emerging school of so-called ‘speculative realism’, or sometimes ‘speculative materialism’, a vibrant field of intellectual thought and debate which is characterized through its re-activation of metaphysical and ontological themes, while at the same time being very active in strictly programmatical and political terms as well. Furthermore, the people associated with this community are closely watching the recent technological changes, and they often take certain aspects from what they can observe as their starting point. All of this is interesting enough for our context of computability, information, and architecture. Yet what I would like to focus on here, in order to bring out as clearly as I can the distinction between what I suggest to call ,critical rationalism‘ and ,speculative realism‘, is not this larger context around Quentin Meillassoux in general, but a particular book he recently wrote on Stéphane Mallarmé’s poem The Throw of the Dice (Un coup de dés jamais n’abolira le hasard, 1897). This book, entitled Le Nombre et la Sirène. Un Déchiffrage du Coup (2011) is equally brilliant as it is unsettling with regards to our interest in computability. The main protagonist in the poem is the Master, in the double sense of a particular authority and yet also (like it is the case for most fictional characters) in a generic sense. We encounter the Master on a boat in the midst of a stormy and wild sea, holding dices in his fist and pointing his hand into the air. The poem never resolves what the Master actually does or intends to do with the dices, whether he wants to throw them in order to learn about his near destiny, whether he beliefs that he can intervene the ‘fulfillment’ of what appears to be his ‘predicament’. Are the dices a sign of the master’s despondence, his impotence to continue being what he is, a master, vis-à-vis the powers of cosmic chance that science has just began to affirm in the stochastic methods introduced by Laplace and others? Does the calculation with probability mark the ultimate end to any form of mastership, and instead enforce a more humble stance for man in a cosmos whose nature is determined indirectly, on the level of a second derivative, as a paradoxical determination of being indetermined?

Most of the interpretations somehow unfold along these lines [48]. The brilliance of Meillassoux’s reading lies in opening up, quite inversely to these readings, a novel possibility of how the poem can be interpreted as presenting an instance of actual, successful mastership. Meillassoux presents nothing less than an understanding of the Master in an entirely original way, which relies neither on annihilating chance nor on desiring to control it, and the calculations that are possible with it, objectively. We could easily call what Meillassoux reveals in Mallarmé’s poem a symbolist way of engaging with the theme of mastership – yet this, at first sight at least, comes close to saying nothing much surprising. And yet, the theme of symbolism as Mallarmé renders it present in the poem, and which is worked out by Meillassoux, not only affects severely what is more commonly associated with symbolism in art, it also affects the notion of symbolisms in mathematics – the entire legacy of developing, trusting and departing from what can be learnt through working out resolutions to formula. The clue in Meillassoux’s reading – as I would put it – is to have Mallarmé engender a one-of-a-kind corpus of numbers whose ‘nature’ is universal, while at the same time being singular. Meillassoux speaks differently about this, he does not mention the context of corpus theory in mathematics at all, for him it is all about  the unique event of depositing the number that can be no other (on the side of Mallarmé) and someone (him, Quentin Meillassoux) finding it. Already before Meillassoux, many interpreters have seeked to find a clue, and to be able to prove the hermetic nature of the poem as a treasure which were capable to conserve something inarticulate yet essential, by seeking to demonstrate how their clue fits the structure of the poem like a key fits the keyhole. What distinguishes Meillassoux’s reading from any such attempt is that he finds the clue he needs not in some exteriority to the poem, but only because he engenders it himself, immanently, by working-through and appropriating the materiality of the text, intimately and from within the poem, literally by not much else than counting, speculating reasoning, and by providing the grounds for his reasoning in clear and distinct form. And yet it would be mistaken to assume that at stake in Meillassoux‘s reading is a notion of mastership which relates to a Cartesian subject, which knows how to master an object in all critical distance and pious devotion (after all, for Descartes it is God gifting us individually with ideas [49]). Rather, at stake in Meillassoux‘s reading is a notion of mastership based on what I would call insistentially shared intellectual intimacy. The mastership which Meillassoux portrays in Mallarmés poem, I would like to suggest, is mastership in succeeding to invoke acts of learning against the sheer improbability that characterizes learning. In such a situation, all clearly set identity distinctions between author, reader, and the protagonist character are raised into a lofty cloud where the outcome, after settling back to ‘commonness’ again (which we could call existential extimacy) after such exposure into the insistential intimacy of such learning, is profoundly uncertain. This is ever more remarkable, I think, if we consider that our present, in the beginning 21st millennium, marks a moment when all hopes that count as reasonable with regard to the relation between chance and calcuation go towards controlling chance through calculus, under the positivist restraint that such calculation needs to be combined with the provisional empirical precision and explication that characterizes the least degree of speculation. Against this critical divide between induction (empirical) and legitimate generalization (formal and deductive), Meillassoux affirms the move to symbolically encapsulate both, and work empirically within the abstract ‘indexicality’ of the poem’s ‘material’ [50]. I call it indexicality and materiality of the text because the stance of such ‘encapsulation’ means to depart not from clearly bound dimensions, but from a state of mixture involving the semantics, the harmonic and graphical meter, the broader historical-political-cultural context as well as the history of the legacy he continues (poetry), and all hermeneutic aspects one can think of; having all the distinctions that grow out of these classical dimensions, he takes the liberty of putting them into a cloud of probabilistic relationality from which he then sets out to extract his own reading, where all classical stances that could be taken as a ‘ground’, end up to be slightly shifted, revolved, rearranged in a manner that is consistent within itself, yet which lacks objective necessity in the consistency it arranges. Indeed the main hypothesis he puts forward is that Mallarmé‘s project was not to represent the divine but to dissolve it, through his own poetic oeuvre [51]. It is this contingent character of his reading, coupled with fine exactness and formal rigor, which gives the set up for what I would call ‘the improbability of learning’ which I see staged in Meillassoux‘s reading. Every act of learning, I would like to argue, confronts us with just such a ‘confused’ and ‘over-saturated’ situation. To deal with such confusion through trust, until one has developed a ‘stable ground’ or ‘consistency’ which one can master in a relaxed (not in any particular and strict way dependent) manner, is the ‘spiritual’ character of learning – in all ambiguity this entails.

I must say that this emphasis on seeing a notion of mastership introduced, through Meillassoux’s reading of Mallarmé’s poem, which sets upon the fundamental improbability of learning, is not (not directly, at least) the way Meillassoux himself wants to guide the outlook that departs from his reading. For him, this point of view would be much too prosaic. In his eyes, the genius of Mallarmé (and that of himself) is – explicitly and literally so – programmatically spiritual in nature, not ‘technically’ spiritual as I would prefer to have it with my emphasis on learning and literacy. The great passion which I wish to point to as being involved in any act of teaching/learning plays a crucial role for Meillassoux as well, he is very attentive to it, yet to him it does not characterize learning in general, he sees in it a singular moment which grows so powerful in this focalization as a singular moment that he recognizes in it an act of divine nature. I will not attend much here to the aspects of Meillassoux’s book where he draws quite daring consequences from this, suggesting to see in the poem a veritable liturgy which is capable of hosting and bringing comfort and orientation to a community-to-come, open to anyone who is willing to participate in performing the sacred rituals of what he calls “Mallarmé’s secular religion” [52].

Cosmic untendedness, prosaicness in verse

But let me sketch a bit the larger context within which Meillassoux is inspired to such ideas. For it is a context which bears close familiarity to the contemporary situation in architecture, vis-a-vis the power of computing. So what was at stake more generally with the question of meter in poetry, and the rise of free verse?

Since antiquity, poetry was always credited a certain dignity, as rightfully deserving a peculiar kind of spiritual trust. Different from other manners of expression through language, a poet did not lecture a doctrine, and did not speak in the name of an authority. And yet, there was a peculiar necessity attached to poetry because any appreciation of excellence, as a poet, was tied to the poet’s strict subjection to a metrical law that is larger and more binding than his will: A poet strictly had to subject his verses to the conservative constraints of poetic meter [53]. If a poet could lend his voice to evocate a thing with elegance, and without doing it violence, that is through masterfully playing within these constraints, there could be attached, to that which is voiced poetically, a certain divine autonomy or gift. Like this, whatever was articulated poetically could be articulated only indirectly, and thus remains divine in nature. The Oeuvre of a poet was to express this divine insight. Like this, it is not appropriated by the verse that composes it, and what is more, the meter that renders the verse voicable allows the listeners/readers to participate in the appreciation of such divine nature. There was in this sense, of a peculiarly poetic and strangely singular kind, a necessity involved in the creative vocations of addressing that which cannot be voiced directly. Due to this necessity, poets were held to deserve a particular kind of spiritual trust. Before the background of this legacy, the rise of so-called free verse in 19th century poetry mirrored a profound crisis of cosmic untendedness which has its roots in a larger context, and which resulted from the strict separation of science from religion during enlightenment [54]. For poetry, the indirect manners of linking the sounds not only grammatically correct, but also figuratively coherent through rhythm, rhyme, alliteration patterns and the like on a structural level, began to turn prosaic as the custom of fixed meter became secularized. Allegorically speaking, within the Cartesian coordinated space of representation, connecting points to the continuity of a line can count as no more but a simulated continuity. It is in a similar sense that also the poetic line (verse) literally began to turn prosaic [55]. It is difficult to thematize this today, but of such awkwardness was the secularization that took possession of the ancient legacy of creative speech! It’s old and trusted sense of necessity was threatened, naturally, from the arbitrary decisions that ordered the lines of free verse. At the time when Mallarmé was writing, that very spirit of modern prosaicness had set out to modernize even poetry, while nevertheless remaining keen in attempting to maintain a distinction between poetry and prose. Like the other symbolist poets, Mallarmé was outraged about the entailments of this development [56]. Yet different from other poets, Mallarmé never seems to have released his outrage through taking sides, programmatically, either for the conservatives or the modernizers. This is precisely why his poems have been interpreted in the 20th century mainly along the lines of necessary acceptance of the impossibility of mastership (and authorship) in the exposure to stormy cosmic untendedness. His character of the Master is read with admiration as bearing up bravely in a spirit of affirmed vain against his own awareness of his ultimate impotence.

It is before this background that the recent reading of Mallarmé by Meillassoux touches such a sensitive zone. It opens up the perspective that the symbolist answer to these developments might not merely be read in terms of a bourgeois sublimation as a proclaimed continuation of the spirit of fine arts – bourgeois because in poetry, separated from its dignity, there is nothing really at stake anymore, except the gain in private pleasure. Symbolization appears, with Meillassoux’s reading, as something more than merely the crafty and artsy coating in codes and educatory puzzling of a truth which is as inevitable as it is bare of offering true delight. Let us attend now more closely to how symbolism is being substantiated by Meillassoux’s reading.

Let’s have a brief but somewhat closer look at what Meillassoux does. His claim is to see in Mallarmé a true symbolist-master, because he sees him as having engendered his own numerical corpus, i.e. a symbolical nature of numbers, from ,placing‘ in the manner of a distribution (hidden in the seemingly arbitrary meter of the poem) the one number which cannot be another: 707 [57]. The entire analysis of Meillassoux revolves around determining the ,identity‘ of this number – as the being of chance (l‘être du hasard) which consists in making itself infinite [58]. Meillassoux‘s thesis is that from this one number, the sum of all the words in the poem, Mallarmé has extracted the meter in which he wrote the poem – and which Meillassoux explicates as ‘the clue’ he finds from the experience of what I have called the insistential intimacy ‘within’ the poem’s proper interiority, by working through its material. The meter Meillassoux hence postulates is not, like the arbitrary structures of prose and free verse, fully contingent without any ‘generically necessary’ motivation. Why? Because rooted within the necessities constitutive for a  symbolic corpus is an entire algebraically-constrained scope of articulate-ability [59]. This scope of articulate-ability is capable of rooting, within his engendered numerical corpus, a metric of poetical structure under the strict governance of what counts how: it is a metric which is both open for some interpretative instantiation, but which also embodies as a certain trans-personal, not strictly willfully postulated, necessity. For Meillassoux, it is the being of chance. So let’s see how the meter which Meillassoux extracts from the sum of the poem‘s words, is not simply a representation of the meter Mallarmé has worked in, but truly an extraction. That is, the result of an algebraic-symbolic procedure. And let us see what is meant by this ‘numerical corpus’.

Because his procedure is itself masterfully artistic, and it would be silly to summarize it here, it must be sufficient to indicate in inverse terms how Meillassoux proceeds: he looks for the summation of the numbers cast by the dice throw, based on Mallarmé‘s line which says that „Toute Pensée émet un Coup de Dés“ [Every Thought engenders a Dice Throw]. If the clue to the poem lies in identifying the number which could not be any other, so Meillassoux, then it‘s „meaning“ must be to achieve the inevitable engendering of this number (in German I would say „ins Werk setzen“ – tentatively to be translated as „to put in place and action“) a thought of such nature, and this in a manner such that it unfolds by necessity when being read within the oeuvre. Hence, the identity of this number which Meillassoux is looking for cannot be given as a representation, it must be ,placed‘ operatively. As he puts it: „il y a une façon triviale, mais par là même précise, de comprendre cette phrase. Au lieu de dire qu’il s’agit dans cet énoncé d ‘affirmer, de façon assez vague et plutôt banale, que toute pensée est un pari, nous pouvons 1’ interpréter ainsi : toute pensée, dans la mesure où elle est fomulée dans un langage, produit une série de nombres aléatoires liés aux composantes de langage nécessaires pour la formuler. Notre phrase conclusive contient en effet, comme toute phrase, un certain nombre de lettres, de syllabes, de mots, de substantifs, etc. Ces nombres sont « engendrés »  par la pensée qui s ‘y trouve formulée, mais ils n’ont par eux-mêmes aucun sens – et en particulier aucun sens lié à la pensée enjeu“ [60].

In short, Meillassoux substantiates his hypothesis such that the final code consists of the cyphers 7 – 0 – 7, and he legitimates the entire argumentative path that leads him to this number by showing that it – if written as 707 – is indeed the number that counts all the words in the poem.

The proportionalization of infinity

So if we explicate this procedure inversely, it strikingly resembles what any statistician does on an ordinary basis: he determines the ‘indexical magnitude’ (often called random or chance variable) in which the possibility space ‘consists’. All he needs for that is a code, e.g. the alphabetical code, or the morse code, or any physically metrical measure expressed in digital code [61]. The creativity of Meillassoux lies, among many other aspects, in looking out for what might count as such a code for ,probabilizing‘ Mallarmée‘s poem. For example, based on some contingent yet well-reasoned speculation, he ascribes a specific importance to the numbers 5 and 7, links those to the stellar constellation of which Mallarmé says, in one line, that the final sum of the number-that-cannot-be-another is expressed in. An excerpt of how he plausibilizes this:

„Or nous savons […] que l’auteur du Coup de dés tenait les étoiles en leur dissémination pure comme un symbole céleste du Hasard. Découper par le regard une constellation dans cette splendeur dépourvue de sens, c’est accomplir un acte tout à fait analogue à l’acte poétique selon Mallarmé. Car ce poète s’attache à faire scintiller les mots, forgés et disséminés par le hasard de la langue, par l’usage d ‘une syntaxe déroutante en laquelle chaque vocable semble isolé par une « lacune » de tous les autres, comme décontextualisé: ce qui lui permet de rayonner d’une lumière qu’on ne lui avait jamais connut“ [62].

Although he does not mention it, Meillassoux is pondering one of the favorite themes in thinking about proportionality – the golden ratio. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to their maximum – this is exactly what Meillassoux‘s reading will postulate [63]  (without stating it explicitely). The golden ratio has inspired people throughout many centuries precisely because it provides maxiumum stability for maximally different ,components‘ within a strictly proportional framework. This is why Le Corbusier has famously integrated the golden ratio into his architectural measuring system which he called The Modulor, and which he ,rooted‘ in a certain partitioning scheme of the human body. But different than Le Corbusier, Meillassoux suggests to root his ,poetic modulor‘ not in the profane human body but in the numerical corpus of divine chance. Like this, Meillassoux takes the non-initiate reader through a fabulous and aw-inspiring journey to how he ends up with the number 707 which – in the finale of this speculative trip through possible codes – turns out to be, and I am sorry for the prosaicness in putting it that way, the chance variable we know from ordinary statistics, the sum of all the counted words.The number-that-cannot-be-another facilitates to carry out probabilistic analysis on Mallarmé‘s text. Even in statistics, a random variable is not a variable strictly speaking, for it has no fixed value. In other words, it is not a magnitude of which we could ask metrical questions like how much. What it does is labeling a number which counts a magnitude that is unknown. Like this, a chance number (I would prefer to call it ‘indexical magnitude’) can incorporate a possibility space, and allow to experiment with it in probabilistic terms, by partitioning it into a set of events which can be combined in their interplay. More concretely, Meillassoux experiments with adjoining (metaphorical, non-mathematical) „domains of rationality“ for his hypotheses, that is in his case, certain alphabets like stellar constellations, or the musical scale of C major which facilitates his way to decipher the number indexed by particlular words in particular constellations, like car si. From these distributions patterns and regularities he seeks to extract a certain meter – and this means, in his case, nothing less than a proportionality of numerical infinity. –

We can put this aspired context of an agnostic-spirituality-turned-into-a-civic-religion to the side, and consider simply in terms of method how Meillassoux proceeds in order to determine the unknown indexical magnitude (chance variable). His procedure might best be called ‘hypothetico-inductively’, and because of its performed creativity, it can surely count as truly instructive for anyone working with statistical procedures. How Meillassoux proceeds is extremely interesting, which is only more impressive if we consider that on the formal level, it corresponds to ordinary standards in how probabilistic analysis works. Except that in scientific contexts, speculation and creativity in the determination of the chance variable is, of course, much less desired and appreciated. But there as in the case of Meillassoux, the metrics (proportionality) ‘induced’ can be tested ‘empirically’ on the formal level (in the case of Meillassoux that of the poem), until a model is found which doesn’t leave any inconsistencies that could not be integrated meaningfully into that model. With this model, he then works hermeneutically for making sense of it, providing its legitimation on numerical basis. This is how the rôle of the meter with which he works is not not entirely arbitrary, but also not in any coercive way necessary. There might be other models of meter for measuring another chance variable on the basis of which one could carry out numerical analysis, and which would very likely be capable of ‘substantiating’ very different overall readings. This does not weaken the brilliance of Meillassoux’ own reading, in my opinion. But it does introduce complications for the performative-lithurgic role he attaches to his reading. While I obviously do not share this programmatic stance, I very much share the interest in seeing a novel understanding of mastership, rooted in symbolization within probability space.

Cosmo-politics, or putting to work a symbolist meter

This novel understanding of mastership is rooted in a slight shift in perspective, which allows Meillassoux to look at Mallarmé’s poem in this way: he does not read the poem in terms of how it articulates the nature of chance directly, but in terms of how it articulates the nature of chance through articulating the nature of number. Rhetorically, this is how he can begin his book with a powerful statement like “Let’s get to the point directly”(p. 9). The point he wants to get at directly, this is the nature of number. Yet, we must remember, according to Meillassoux this nature is engendered in the poem. So there can be no mentioning of “directness” in any strict sense. Directness, this is what we can pursue if we presume a nature of number, not if we attempt to evocate such nature in a poetically particular manner. The power of the opening of Meillassoux’s book is a rhetorical trick which envelops in a veiling manner all implications that point in this direction. For him, as he makes clear later on, Mallarmé’s act of articulating poetically the nature of number is an absolute and singular act, this is what moves him to see in the poet author a figure no less eminent than that of Jesus Christ – the way he sees it, Mallarmé literally incorporates, in his oeuvre, the possibility of a new poetic meter to come. According to Meillassoux, Mallarmé is a figure as eminent as Christ because as the latter sacrifices his body, Mallarmé sacrifices the Corpus of his Oeuvre – the living ‘substance’ of what makes him a master, by giving over the reception of it to the unlikeliness that is proper to anything which is governed by chance.

This is how Meillassoux wants to read this engagement with the ‘indexical magnitude’ of a ‘chance variable’ within the Christian theme of transsubstantiation. Within this Eucharist tradition, the sacrifice of Jesus Christ’s body was ‘necessary’ to evocate the unity of a community to come – anyone who believes in the actuality and truth of this happening was welcome within the community, whose unity grounds on no other inclusion/exclusion criteria but the appreciation of this ‘act’ and its particular theological interpretation. Re-enacting it brought absolution and purification of the members from their sins, and from their distinctions among each other, and constitutes the ‘force’ capable of strengthening the Holy Communion. Meillassoux reads Mallarmé’s act (of sacrificing the corpus of his oeuvre to the unlikely reception in the unlikely event that someone actually bears witness to his act, and proclaims its significance widely) in strict parallel to this tradition. He imagines also a people to come, to be united through re-enacting the liturgy of Mallarmé’s poetic oeuvre as a means to strengthen such a coming sense of community. Such union, Meillassoux imagines as a truly post-modern communion, that is, a people who complement a secularized politics with a poetic religion. The daring cultural historical symmetry evoked thereby is that of modernity in the position of the old Testament, and the problem of how to continue modernity (which is our problem today) in the position of the New Testament. In his poetically grounded cosmo-politics, Mallarmé is stigmatized by Meillassoux as the only one and true Master, who has managed to gain victory over chance (which reigns within science and thereby unsettles the very values that are foundational of modernity, e.g. individual identity, self-governing subjects, scientific progress through steady refinements in approaching the realization of an ideal and universal (all-inclusive) order, etc). Meillassoux, in his reading, reveals his own communal identity as that of those who know how to bear testimony to Mallarmé’s symbolist and graceful gift to humanity – the act of his sacrifice.

Cosmo-literacy, or the alphabetization of the nature of number

If we relate this interpretation to its recent reception, it may on the one hand strike one as unbearably uncomfortable, to the degree that one feels tempted to call it silly. Yet on the other hand, one cannot help but admire the conclusiveness in actually working with the text material as it is there, in the verses of the poem and the reality of the contextual questions raised, and this makes it equally much an irresistible attraction. Indeed, it is long since a voice in philosophy has dared to articulate such claims on such speculative yet precise grounds! But then again, such intimacy of philosophical thought with what we might call religious energies is straightforwardly inevitable if one seeks to resist the submission of philosophy under the ultimate governance of scientifically-declared legitimization – that is, to free it from all forms of inspiration and spirituality. What Meillassoux does, and what can be decoupled from his mission, I think, is exposing a notion of method that proceeds by scientific standards, yet hands it over to the field of aesthetics and art. From this perspective, and in order to appreciate the originality of Meillassoux‘s reading, one does not have to follow him in the mission he attaches to it. Mallarmé’s poetic articulation of the nature of number, if we read it not as a poetic dedication in the form of a song of praise or an ode to this nature, but along with Meillassoux in a quantitatively symbolist manner, points the way of how we might consider symbolization as a means for learning how to articulate numbers and develop mastership in dealing with the indexically and symbolically given ‘magnitudes’. Such mastership grounds in learning how chance variables can be counted, literally in the sense of ordered enumeration (discretizing and grammatizing) but also more comprehensively in the sense of governing.  

If we affirm that modernity has disenthralled us from all hopes in Aristotelian-minded symbolization, as the articulation of the Voice of Being [64], we might also affirm in Mallarmé’s poetic articulation of the nature of number a continuation in the spirit of Aristotle. Since Pythagoras, and especially since Plato’s Timeaus, the widely spread idea about the nature of number is that the very ‘framework’ of a Cosmos which we can hope to understand by reason, consists in numbers. The numbers are the soul of the cosmos, which the Platonic Demiurg has mingled and mixed, cut into two to connect end with end, such that an inner circle comprehends all material becoming, while an outer circle comprehends all ideal being. Numbers make up the Auxiliary Structure for a Cosmo-logy, they are the necessary Coefficients in any formal term. Numbers are what is capable of holding, literally, a logical cosmos in order – we come back to this in more detail in the following paragraphs. Suffice it to say for here, that from such a perspective, Meillassoux’s reading of Mallarmé’s poem would suggest nothing less than that the nature of number at stake is one which can now be alphabetized. If the natural numbers are what is capable of holding, literally, a logical cosmos in a universal order, by deriving criteria for consistency from the assumption of primary ‘fullness’ or ‘perfection’, the symbolical nature(s) of number need to find criteria for consistency by dealing with ‘primary abundance’. Dealing with primary abundance would mean that no order of consistency (logical order), no such and such ‘fullness’,  can ever comprehend all that might, virtually, be possible.

Is not this a reading whose relations to poetry feel almost banal? While ancient meter was capable of liberating logics from directly stating truth and thus made room for poetic articulation which may count as divine because it is neither comprehensively necessary nor arbitrarily contingent, the meter engendered by Mallarmée (and any meter that can be engendered in the same manner) makes room for cosmo-literal articulations of ideas that might characterize a world to come.

But, we might ask, does the assumption of such a quantitatively symbolist manner of poetic articulation not indeed confront us, as Meillassoux seems to hold, with a sheer impassability (German Ungangbarkeit)? To count as poetic (and not political) articulation it would be essential for such a symbolist manner not to treat this nature which it articulates (that of number) in a violent manner. It must affirm this nature’s dignity, i.e. as inexhaustible by the reasoning of finite synthesis or speculation – while nevertheless setting out to articulate it as a means to communicate that which does not avail to appropriation by reason. In short, it must respect its ‘integrity’ and ‘identity’ neither on the transcendent grounds of sufficient reason, nor on symbolist grounds of infinite speculation (as Meillassoux proposes), but on symbolical grounds of finite synthesis. Such respect would be the core aspect of a truth notion that were worthy to be called that of a critical rationalism.

Appropriating a body-to-think-in

One of the arguably most influential documents of the history of Western Culture – Plato’s dialog Timaeus – tells, in the form of a myth, the coming into being of the cosmos such that we can conceive of it logically. The cosmos turns into the subject of knowledge in Timeaus account, and he conceives of it as a symbolical body – the cosmic animal – whose corporeality he conceived, somewhat surprisingly perhaps, already 2500 years ago as being constituted by numbers. In Plato’s cosmical animal, there is but one nature of numbers. Today, with Universal Algebra, we have as many natures of numbers as we can symbolize consistently into structures. We call them by the names of Rings, Fields (Zahlenkörper), Modules and the like. They work with Matrices and ‘animate’ relations  – animate because vectors are lines that embody direction, they have a ‘motive force’ or ‘cause’ immanently to the relation they incorporate. We call algebraic structures Universals, in the plural, and each of them has ‘one-of-a-kind’ scopes of how their organization may be articulated. Much of our technics today is ordinarily dealing with such abstract structures. At the same time, philosophers and mathematicians are initiating veritable battles around how these structures are to be rooted and identified (the so-called Foundational Crisis, and more recently, the struggle between set-theory and category-theory for primacy in settling or overcoming the issue of foundations).

Let me perhaps indicate initially where I intend to lead this line of thought. What I would like to consider is viewing what we readily call ‘a symbolical corpus’ outside the confines of representational speculation, reflexion and mimesis, and instead in terms of indexical speculation, reflexion and mimesis. Such an indexical turn would entail to relate to the symbolical corpus‘s of mathematics not as we relate to a constellational order of the Heavens, but as we relate to our bodies. Our bodies too do not fully avail to reason, and they constrain our sensual and motoric capacities. Might not the notion of ‘a body’ be a better word than the notion of ‘a house’ for picturing what the philosophical tradition has strived to conceive as the Architectonics of Reason? A body-to-think in, with proper constraints of intellectually sensual (intuition) and intellectually motoric (literacy) capacities? Is it possible that we are so much accustomed to an understanding of numbers as giving us the one and only framework within which things can be rationalized and appear consistent, that the assumption of treating them as ‘bodies-to-think-in’ sounds too frighteningly strange? Even if one might feel spontaneously compelled to agree, the question that motivates such a daring shift in perspective has been up and on the table for more than a century:

How might we come to terms with universal algebra, its symbolic corporeality by probabilistic methods, and the generic instances that are articulated out of it?

The most common representation of the nature of numbers …

To put it in words we all remember from schooldays: we take the positive integers as the proper class of natural numbers [65]; we know we can symmetrically mirror them to negativity – for the sake of speculative analysis; and we remember that the boundedness among the integers can be ‘spelt out’ into ratios (the rational numbers) – if only we put the integers into mutual relations. Of course we also don’t forget the irrationals, those numbers which yield an indefinite value when they are put into a ‘ratio‘. Despite their name, they are not too troubling anymore. There are sophisticated limiting and bounding processes with logarithms and series such that the counting in of irrationality seems like a reasonable and respectful tribute to be paid to the vastness of real numerical nature. An illustrative picture for this concatenated and comprehensive nature of numbers is the continuous number line. With its totality, including rationals and irrationals alike, we associate today the domain of the real numbers. To put it straightforwardly: the real numbers contain all that can possibly be marked out by reason, as rational or irrational, and hence understood about numbers’ nature.

… and how it got into troubles that are not resolved until today

This was still the firm belief of one of the founding fathers of a logical calculus, Gottlob Frege (1848-1925) when he assumed – not unlike a prosaic double of Plato – the existence of a transcendent realm where the class of natural numbers rest as ‘objects’, eternally and ideally, and given directly to human reason without requiring the mediation through the senses [66].  With his text The Foundations of Arithmetics–A Logico-Mathematical Enquiry Into the Concept of Number (1884) we have another strong story about the nature of numbers by one of Mallarmé’s (1842-1898) own contemporaries. While Mallarmé (according to our discussion above) has taken the Platonic numerical ideality and turned it into a probabilistic one, Frege took it and turned into a logical one.  Only three years after Frege, also Edmund Husserl wrote a treaty entitled The Concept of Number (1887). He published an own book entitled Philosophy of Arithmetics (1891) only 4 years later. While Frege meant to engage strictly logical issues into such elementary consideration with the intent to purify reasoning, at least ideally, Husserl instead meant to complement logical issues with psychological issues – which he hoped to be capable of treating with equal rigor as is possible for logical issues. We cannot go into this theme with much breath here, but let me briefly recapitulate the larger context and how it relates to our two Conceptual Persona, the Generic and the Master, and the possibility to see, in what they open up in their interplay, the birth of bodies-to-think-in that are collective before they can be appropriated individually, and whose nature is engendered together with the symbolical corpus of numbers according to which they are organized.

First, let us take this background as an indication that indeed something larger than a poet’s personal resignation vis-à-vis the rise of free verse must have been at stake in the 19th century. This seems all the more justified if we remember that the mathematician George Boole (1815-1864), whom I have already mentioned earlier for having been accused of proceeding in a strikingly similar manner as Meillassoux does in his reading of Mallarmé – namely of “bringing forward definite solutions from treating indefinite problems symbolically” [67]  – preceded all of these investigations on the nature of number by a few decades. His main work was entitled in all due provocation: An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities (1854). To view Mallarmé in this context adds a lot of plausibility to Meillassoux’s shift in perspective, namely that the poem is not directly about the nature of chance, but about that of number. But not only this. It also tells us something important about our context and interest in computability, design, and the Generic today – it allows us to see the force of what Rancière calls dissensus at work in all that can be computed: dissensus is “not a conflict of interests, opinions, or values” but “a division put in the ‘common sense’: a dispute about what is given, about the frame within which we see something as given” [68].  While on the level of generic instances, those one-of-a-kind-particulars that can be instantiated and modulated within the framework of a master model, we might only negotiate “conflicts of interests, opinions, or values”; what is at stake with a criticality on the level of the master models is indeed dissensus as “a division put in the ‘common sense’: a dispute about what is given, about the frame within which we see something as given”. This is why we ought to treat the instances of generic computing as pre-specific rather than as typical (i.e. to view them as generic in an adjectival, not in an adverbial sense), and the respective master models as what they are: models that owe everything to mastership, and not to some generic“nature”. But lets look more closely at how this background in number theory relates to computation.

Algebraic operations, or how the nature of number can be brought to work

As sketched above, the understanding of the nature of numbers has indeed been bracketed and marked as ‘something to be put in question’ throughout the 19th century. Yet this was not, however, a result of pure intellectual curiosity and ideological speculation, but by the facticity of technical eminence: The taming of electricity equally rests upon calculating with a domain of numbers that does not fit within the continuity (represented as the real number line) within which all that can be called natural about numbers ought to be accommodated. Calculations that regarded waves and currents had to be rooted in a numerical domain that is organized by a peculiar unit, of which it is indeterminate what magnitude (which physical quantity) it allows to measure. Descartes had suggested to call this unit ‘imaginary’, only to discard it as irrelevant and purely speculative – the imaginary unit is that of the square root of minus one. The ‘impossibility’ it manifests is obvious: surely everyone remembers from somewhere that arithmetically, the multiplication of a negative number with itself must yield a positive result. Hence, it ought be categorically impossible, or at least sophistically meaningless, i.e. without any real consequences, to extract a root from a negative quantity. And yet, it does yield consequences, and not only that, it yields consequences in reliable and modulate-able manner: as Israel Kleiner accounts, in his book A History of Abstract Algebra, mathematicians have “given meaning to the ‘meaningless’ by thinking the ‘unthinkable’, namely that square roots of negative numbers could be manipulated in a meaningful way to yield significant results” [69].

All of electronic technics, including information technology and quantum mechanics, rests on the application of this particular numerical domain – whose magnitudinal referent is symbolically determinable, while remaining physically (and philosophically) “unthinkable”, “meaningless”. To put it more simply, it remains unclear of what such a ‘how much’ can be determined. The imaginary unit allows to measure whatever is indexed within the systematicity of a symbolism, and this makes it so peculiarly “unnatural”. Unnatural, that is, unless one were to assume a nature of such a symbolism whose magnitude is only indexically given. And this is exactly what was at stake throughout the 19th century as the development of abstract algebra prospered more and more. The disputes indeed centered around whether we ought to assume different natures of numbers – a variety of different numerical Genus’ – and if yes, how many.

The nature of number might not be one: Alfred North Whitehead attempted to gather all these developments in a first systematic study under the troubling caption of Universal Algebra in 1899. It was a work that cleared the view on these developments [70] and stated as straightforwardly as groundbreakingly: the problem at stake is the relation between mathematics and logics. To get clear on what we are talking about – why was this groundbreaking? While logics promises to give adequate classification of the nature of things (or in the modern paradigm: the determination of objectivity), such adequacy has rested for Plato (as well as again later, for the moderns) on the assumption of finitude on the empirical side of science. If we start out from things as they are manifest corporeally, in terms of magnitudes that can be measured, we can depart from very basic (and through that very secure) assumptions, and reach gradually more and more abstract heights through speculative generalizations. Such is the trust in scientific method by the moderns in a kind of science that lets itself be guided by the logics of finitude, as opposed to spiritual doctrines which all involve infinity. It rests on the assumption that the nature of number is one and that number is universal. From this nature, hence, it ought to be possible that one can extract universal principles that are capable of treating all things equally, and therefore justly. Such universality was seen by Frege and Husserl, and many others at the time (and still today), in arithmetics. The suggestion of Boole, on the other hand, was to ascribe the status of universality to Algebra instead of Arithmetics. This opens up the notion of the universal to infinitary determination. Algebra has been understood, always, as the art of determining unknown quantities through procedures of articulating the proportionate terms that in their interplay make up a formula; with the elevation of its status beyond its merely representational character (what Meillassoux calls “the correlational” [71]), the meaning of ‘unknown’ opens up the modern tradition of keeping the scientific and the artistic, in its entanglement with some sort of spirituality, strictly apart. It  releases instead a nature of the technical – the means for artifice – in an unbounded condition between mastership and schematical repetition, in which all questions of legitimacy are once again unsettled.

The consequences of affirming the infinitary methods are such that we cannot maintain any longer in an unproblematical manner that the universal – that which is to be regarded as the property of all things – accommodates naturally the categories we apply, even in the natural science, as they too, meanwhile, fall within the domain of techno-logy. Affirming to work with infinitary methods entails dealing with an inverse situation: the categories we apply, in science as elsewhere, determine what can be treated as universal. In all radicality, this amounts to saying that universality appears as a kind of wealth, it means that the universal can prosper or decay. It means that there is an economical dynamics constitutive for what counts as universal; it means that that which can be the property of all things can be more or less prosperous and that this prosperity depends upon the capacities of intellectuality.

This might seem a little like sophistry, admittedly so. And indeed, this criticism has accompanied the disputes around the nature of number from early on. Rafael Bombelli, who contributed much to the development of a calculus of this peculiarly imaginary numerical domain (constituted by the imaginary unit), wrote already in the 16th century: the development of such a calculus “was a wild thought in the judgment of many; and I too was for a long time of the same opinion. The whole matter seemed to rest on sophistry rather than on truth. Yet I sought so long until I actually proved this to be the case.” [72] The calculus he developed worked with articulated formulations of the One according to rules such as (+√−1)(+√−1) = −1 and (+√−1)(−√−1) = 1. These rules allow to define, mathematically, addition and multiplication; yet these definitions do not apply to all numbers in general, but only to numbers that are members of numerical domains that form corpus‘s, and which are specified according to their immanent partitionability and organization.

This is the level of abstraction proper to algebraic number theory and all mathematics and logics that work algebraically; today this entails nearly all of applied mathematics. The philosophical problems entailed thereby had been systematically put into its proper relations by Alfred North Whitehead in the above mentioned book called Universal Algebra [73]. Let me add, perhaps, that the relevance for keeping track of developments on such an abstract level, which urges us to assume a symbolically (not naturally) determinate ‘nature’ of numbers is crucial for developing an understanding of what we are actually doing, when we work with universal code in computation. Anything that we regard on the level of its electric materiality must count as a manifestation of such symbolically engendered ‘nature’ [74]. Its ‘nature’ can be determined based on probabilistic measurements – measurements which we carry out today, usually without much consideration, in terms of ‘information’. It is before this background that Michel Serres urged intellectuals across all disciplines, in his lecture form 2007, to engage with the fact that the storage, treating (processing), emission and reception of information is the “quadruple characteristic in common between all the objects of the world, living or inert” [75].

Masterpieces, and why there are so few of them

So we can see how much this peculiar procedure which Meillassoux ‘detected’ in Mallarmé’s poem is indeed a procedure which is intimately affin to what preoccupied anyone who followed the development and the rise of universal algebra. Mallarmé, with his desire to link abstraction directly to poetic texture, and his poetic interest in evoking through words rather than describing with words (which became famous as the mark of symbolism in art) certainly was following all of this. It seems more than likely that with his fascination for ‘absolute truth’ he attempted to draw the consequences from what he saw happening to the idea of the universal. He hoped to be able to continue the cultural legacy he was ambitious to contribute to, poetic verse and the dignity it had always been attributed, by reconsidering, poetically, all these issues around the nature(s) of number, the nature(s) of counting, and the modalities of mastership in relation to both.

Meillassoux’ reading is original in the way he found to quantitatively engage with the symbolist tradition in poetry. It stresses the interest in attending to the powers of symbolization in terms that are not strictly ‘linguistic’, thereby reducing reality to language and relations of reference and interpretation. Instead, he draws our attention to terms in algebra that are best called ‘formulaic’. What it stresses is not only the ‘nature of number’ as problematic, as something that needs re-conception, but also the ‘nature of formulas’. It is in this vein that another document form the early 20th century is important to consider: Gertrude Stein’s lecture What are masterpieces and why are there so few of them (1936). In an inverse manner to what we have discussed so far, she does not so much attend to clarifying the “belonging” or “authorization” of the voice with which the figure of the master articulates his evocations. Instead she draws attention to the articulated evocations themselves. Stein insists on the reality of masterpieces, in all their problematicity. For her, a masterpiece bears testimony to the fact of acts of engendering. She sees them motivated out of a principle unsettledness of any identity issue, the identity of the master as well as the identity of the subject matter a master masters.

„It is not extremely difficult not to have identity” she says, “but it is extremely difficult the knowing not having identity. One might say it is impossible but that it is not impossible is proved by the existence of masterpieces which are just that. They are knowing that there is no identity and producing while identity is not. That is what a masterpiece is.“ [76]

EigenArchitecture

Like Stein, we want to hold on to the idea that articulations of things entirely in their own terms is not an absolute impossibility, although it certainly seems a paradoxically tautologous idea. Yet this is one of the core interests behind what we wish to thematize in this book as EigenArchitecture. We are interested in a literacy that arises out of such an algebraic, formulaic and apparently tautological notion of identity, a literacy which cultivates the infinitary articulateability of the One (identity). If we affirm infinitary methods in computation, the terms that express an identity are not nominal terms, but poly-nominal terms. And polynomial terms, unlike nominal terms, are capable of settling their clauses in amphibolic multiplicitous structures. Every polynomial term involves variable values and constant values, of which the latter can be ‘spelt’ by attaching them to designate-able and balance-able constellations of coefficients. In other words, they participate in a quantity which is yet to be determined. Polynomials name terms whose literalness needs to be characterized. They are quantitative, yet the quantity they comprehend is not a fixed value, but a genuinely relational value. They comprehend ever so much – tantum – as the term is rendered capable of bounding within the constellation of amphibolic multiplicities that makes up the system of formula in which polynomial terms feature. Properly speaking, the determinability of this ever so much is adjoined to the terms. It is in this manner that we can speak of articulating a thing entirely in its own terms. In qualitative terms, however, such articulation of course depends upon how developed and differentiated the literacy and mastership is, of the person who articulates.

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Footnotes

[1]  this expression is deliberately “exported” here from religious vocabulary, where Mysterium Tremendum et Fascinosum is used to attribute holiness to God. It is an ambiguous expression which acknowledges the finitude of man’s capacities to understand. It makes reference to something which is fascinating and yet at the same time profoundly unsettling, because it promises a kind of automatic comfort, belonging and beauty, in which every one is welcome, while also confronting us with man’s helplessness and insignificance in the face of divine inviolability.

[2]  Especially the diverse attempts of a post-critical return to philosophy as a rational and metaphysical enterprise, which are referred to as marking a ,speculative turn‘ in recent philosophy, associated with philosophers such as Quentin Meillassoux, Ray Brassier, Graham Harman.

[3]  An example of such extensions of numerical corporeality are the complex numbers, which are composed by adding the imaginary unit √ -1 to the real numbers.

[4]  Field theory is more adequately, albeit in English less often, called theory of numerical corpus. This is consistent with the French expression for fields, which is corps, as well as the German one, Körper.

[5]  To provide domains of rationality for a certain (numerical) solution space makes sure that the roots of a polynomial with coefficients raised to their n-th power can be expressed in terms of radicals according to an integral domain governed by the principle of unique factorization. Especially Leopold Kronecker preferred to speak of domains of rationality, in distinction to the main inventor of corpus theory, Richard Dedekind. Instead of domains of rationality, Dedekind thought about the possibility to extend a numerical corpus in terms of prime ideals. The two stances can be seen to represent two epistemological vectors of induction (primary in Kronecker‘s empirically grounded approach), and the strange mixture which Charles Sanders Peirce – another key figure in the rise of universal algebra in the latter half of the 19th century – attempted to define as abduction which establishes the conditions of deduction (Dedekind‘s approach grounded in abstraction).

[6]  Cf for a discussion of the Dedekind approach to ground corpus theory in acts of abstraction in relation to an understanding of computation and calculability: Vera Bühlmann, „Continuing the Dedekind Legacy Today, Some Ideas Towards Architectonic Computability“, paper delivered at the Turing 2012 Conference in Manila, Philippines, March 2012. Available online: www.monasandnomos.org/2012/12/05/computing-within-the-open-totality-of-anything-that-can-be-the-object-of-thought-continuing-the-dedekind-legacy/

[7] For whoever is interested to follow this line of thought towards a criticality that is local and universal, we can recommend the superb book by Jules Vuillemin, La Philosophie de l‘Algèbre (PUF 1962), and here especially the chapter IV „La Théorie de Galois“ (pp.222-300) in relation to adjacency in mathematics, its relation to the notion of groups, and its overall entailments for the Kantian and post-Kantian notions of criticality.

[8]  the accusative is the grammatical case whose primary function is to express destination or goal of motion, from Latin (casus) accusativus “(case) of accusing,” from accusatus, past participle of accusare. Latin accusare means “to call to account,” from ad– “against” (see ad-) + causari “give as a cause or motive,” from causa “reason” (www.etymonline.org).

[9] from Greek kategoria “accusation, prediction, category,” verbal noun from kategorein “to speak against; to accuse, assert, predicate” (www.etymonline.org).

[10]  The way Rancière approaches and unfolds his political arguments, which center around a foundation of politics in aesthetic judgements, involves to follow him on an unusually high and demanding level of abstraction. Indeed, this is often one of the key points for which he is criticized – it raises people‘s suspicion because it is not easy to follow (in understanding, not in action!). Contrary to this view, his engagement with abstraction is precisely what exposes him for us within the current landscape of political theory and philosophy – which is to a large amount straightforwardly programmatical, if not outrightly polemical, by not demanding the reader to understand the abstractions at work in it. This is unfortunate because it cannot facilitate a problematical engagement with the proposed arguments, but rather demands devoted followership – the creation of ,movements‘, by being promised (by the authority of expertise that is declared too difficult for the common person to understand, and hence needs to be presented in trivialized and infantilized manners) to „stand on the right side of history“. Cf for example Slavoj Zizek, Die bösen Geister des himmlischen Bereichs. Der linke Kampf um das 21. Jahrhundert, Fischer 2011.

[11]  Jacques Rancière, „Who is the Subject of the Rights of Man“, The South Atlantic Quarterly, Volume 103, Number 2/3, Spring/Summer 2004, pp. 297-310, here p. 303.

[12]  Jacques Rancière, ibid. p. 306.

[13]  Leibniz‘ dictum was, famously, that nature makes no jumps – the assumption of uniform continuity in natural processes has been central for applying the then new infinitesimal methods in modern science. It is needed to support all epistemological positions that consider themselves analytical-empirical. It seems to us that Rancière is opting for a similar framework as this one between movement-continuity (infinitesimal calculus in science) for his context, that of political acting-human (aesthetic judgements in politics).

[14]  If you are slightly irritated by this counter-positioning and ask yourself, why should ,universal‘ not also be an adjective – an adjective of all that is – you are hitting the crucial point: by seeing it that way, as an adjective, you would consider all that is in terms of a given set, class, kind, totality. With due respect to the distinctions between these terms, in all cases the notion of the universal would be a descriptive notion. And all conceptual dynamics involving an idea of ,surplus‘ must need be treated in the stigmatizing terms of accumulation on one side, correlated with deprivation and exploit on another side. This all is well known. Our interest in Rancière‘s notion of political subjects as surplus subjects comes from his rebut of such a notion of surplus. By taking recourse to aesthetics as that which he holds capable of ,rooting‘ a political subject, he proposes to ground politics in manner that involves rationality and the sublime in a manner in which the latter is not treated as a finite stock and resource, but as an infinite source of dignity. Such a notion of surplus shifts the problematics from issues of just distribution and optimal rationalization of stocks to the more abstract issues of partitioning and manners of counting that depend upon the decisions involved in partitioning, prior to the finitude of anything materially manifest and given. So in his case, reading ,demos‘ as an adjective for the human, he turns ,demos‘ into something like a political soul, a divine reality that lives in the people, and is only derivatively there for an individual to participate in – never to own or have. Opting in favor of a categorial approach against a classificatory one, even a generative one in the manner of Rancière, means to invert the outlook he presents: it is not by barring ,the noun‘ from being articulated and spelled out that we can avoid the deadening reification of settling with representations of identities – but by excessive articulation and spelling out of ,the noun in its actions‘, this inverted view holds. To our mind, the activity of the political subject depends upon a categorial view that bears in mind that categories are operative and abstract, in infinite mode, one that never arrests and mistakes them for describing general states. It means, in short, to treat it as adverbial, not as adjectival. Or to put it in metaphorical terms, Being friendly is not easy, and, annoyingly so, it gets the more difficult the more clarified and defined our understanding of ,friendliness‘ is. Clarification depends upon schemata, and directly opposes richness and wealth of understanding when the levels of abstraction, on which the schemata are operative in providing clarification, are conflated into the representational plane of a general concept. Abstract concepts are actualized within the bounds of finite corporeality, hence what qualifies them seems best to be treated adverbially, as adverbs describe the circumstances of activities, events, happenings, enacted properties and relations.

[15]  cf. pp. xx in this article.

[16]  Michel Serres, „Revisiting the Natural Contract“, a lecture held at the Institute of the Humanities at Simon Fraser University (Canada) on May 4, 2006 (translated by Anne-Marie Feenberg-Dibon). Online: www.ctheory.net/articles.aspx?id=515 .

[17]  For a contemporary contextualization of this idea cf an article by Sjoerd van Tuinen, „Difference and Speculation: Heidegger, Meillassoux and Deleuze on Sufficient Reason“, forthcoming in: Beaulieu, Alain & Kazarian, Edward & Sushytska, Julia (eds.), Deleuze and Metaphysics, Lanham, MD: Lexington Books 2013.

[18]  Jacques Rancière, ibid. p. 304.

[19]  Jacques Rancière, ibid.

[20]  Jacques Rancière, ibid. p. 305

[21]  Jacques Rancière, ibid.

[22]  cf footnote 10. This is what distinguishes Rancière‘s approach from those which demand followership by faithful devotion (of the illiterate) rather than critical subscription (by the literate), with the effect that his arguments hardly lend themselves for creating a movement that is to realize a political program.

[23]  Jacques Rancière, ibid. p. 309.

[24]  Jacques Rancière, ibid.

[25]  It is important to see the difference of an aesthetical calculus to phenomenology and semiology – both of these attempt to supplement calculus with either a general theory of signs, or with perception. An aesthetical calculus, on the other hand, does not keep a notion of calculus as distinct from one such supposedly more general theory. It stresses that the notion of calculus cannot remain untouched, if we want to avoid sacrificing the openness of the infinite. Thus, I describe it‘s labels in the conventions of symbolisms, as indexes and pointers (codes), and not as signs etc.

[26]  Michel Foucault, Les Hétérotopies, Radio France, 7 décembre 1966, here cited from the Suhrkamp edition 2013, p. 39.

[27]  cf Michel Foucault, Le Corps utopique, Radio France, 21 décember 1966, here cited ibid., pp. 55-65.

[28]  although he would, by what I can understand from his own programmatically political commitments – which he keeps respectfully separate from his philosophically political commitments, as I have argued before (fn. 10) – not at all agree with my proposed application of his concept in the context proposed here.

[29]  Jacques Rancière, ibid. p.304

[30]  Jacques Rancière, ibid.

[31]   letter by Henry Wilbraham, published in The Philosophical Magazine, supplement to vol. vii, June 1854, cited in: Rod Grow “George Boole and the Development of Probability Theory”, p. 8. available as a preprint version online (http://mathsci.ucd.ie/~rodgow/boole1.pdf). Cf also: „Boolean Algebra is not Boole’s Algebra“, by Theodore Hailperin, Mathematics Magazine Vol. 54, No. 4 (Sep., 1981), pp. 172-184, as well as Walter Carnielli, “Polynomizing: Logic Inference in Polynomial Format and the Legacy of Boole” available online (www.cle.unicamp.br/principal/grupoglta/Thematic-Consrel-FAPESP/Report-02-2007/C07.pdf) and Stanley Burris, “The Laws of Boole’s Thought”, available online as a preprint (http://www.math.uwaterloo.ca/~snburris/htdocs/MYWORKS/PREPRINTS/aboole.pdf).

[32]  cf in this article pp.35ff.

[33]  There is, for example, an extremely interesting history regarding the status of grammatical cases. All throughout the centuries, the disputes of the grammarians centered around how cases can be accounted for: cases express all kinds of relations – there are languages still today which know more than 20 distinct cases that differentiate the most common ones, that of nominative, dative, genitive and accusative – and the question of how we can account for them involves assumptions about causality. There are two main positions for which different schools have opted: a casus is what is fallen off something, literally. That‘s how it is caused. The common sense today seems to hold that the case of nominative is somehow different form all the other cases, and that the latter are indeed what falls off from the nominative – a view which puts the noun in a grammatically central position. Yet since the earliest grammaticians, another view held that the nominative case is like all the others, and that they mark the imprints of activities that are happening with some degree of regularity. Activities that happen in repetitive manners. According to this view, verbs in infinitive form are marked out as central for identifying syntactical units in language, not nouns. It is easily transparent how two views entail profound metaphysical implications. Cf. the classic book by Heinrich Hübschmann, Zur Casuslehre (1874), and Louis Hjelmslev, La Catégorie des Cas, Wilhelm Fink Verlag, München 1972.

[34]  this is of course not really true; in fact, what characterizes late scholastic philosophy is precisely a forceful dispute around the claim, raised by some scholars, that we ought to assume a reality distinct from that of concrete particular or individual things, and proper purely to the universal. It was called the problem of universals, and to liberate thought from the kind of dogmatism that could be attached to such a reality notion was surely one of the great moving forces behind the break of renaissance. Universals constitute every notion of ‘pure reason’ – against which Descartes brought forward new analytical method linked to an attitude of ‘fundamental skepticism’, and with which Kant, a bit later on, seeked to reconcile with the Cartesian ‘method of doubt’ a certain legitimacy for speculation in his Critique of Pure Reason (1781).

[35]  What haunts modernity, and thereby hinders it to continue with itself in its own terms, is the idea of a natural reality, one that were capable of hosting a notion of universal commonality. Still today we can read much of contemporary political philosophy with the lens of how a universal subjectivity might be conceived – from this point of view, even very contemporary contributions to the political discourse root back rather directly to Hegel’s suggestion to understand Bureaucracy as such a universal class which serves all, without self-interest, and to the Marxian totalization of this idea by seeing in the universal class the Proletariat: from Laclau and Mouffe’s dialectical affirmation of the political as a condition of competing hegemoniality to Hardt and Negri’s Multitude as the political subject of the New World Order they postulate, Badiou’s and Zizek’s ideas about how to conceive, in secular terms, of an abstract Persona whose voice is to matter most (Zizek’s lacanian-hegelian Master Discourse; and Badiou’s set-theoretically constituted mathematical ontology) to Agamben and Virno’s interest in personifying abstractly the (Marxian) concept of a General Intellect.

[36]  Cf. Richard Feynman, QED – The Strange Theory of Light and Matter, Princeton University Press 1985.

[37]  Deleuze, Gilles & Guattari, Félix, Anti-Oedipus. Capitalism and Schizophrenia, transl. Robert Hurley, Mark Seem, and Helen R. Lane, London/NY: Continuum, 2003, p. 112.

[38]  cf in this article p.8.

[39]  Michel Serres, lecture to the Institute of the Humanities at Simon Fraser University (Canada) on May 4, 2006, entitled Revisiting The Natural Contract, on http://www.ctheory.net/articles.aspx?id=515; cf also Michel Serres, Le contrat naturel. Paris, Bourin (1990).

[40]  The aspect that there is a third component is a key motive of cybernetics, and has perhaps most prominently been articulated by Norbert Wiener: “information is not energy nor matter” – without being able to suggest a different architectonics that could accommodate all three of them. Michel Serres approach here is the first that aspires to do so.

[41]  Michel Serres, „Les nouvelles technologies: révolution culturelle et cognitive“, lecture held on december  11 2007, at the occasion of the 40th anniversary INRIA, a public institution for research devoted to the sciences of computation (science du numérique) in France. Online: https://interstices.info/jcms/jalios_5127/accueil .

[42]  Jacques Rancière, ibid. p.304

[43]  Jacques Rancière, ibid. p.307

[44]  Hans-Dieter Bahr has developed this theme towards a veritable reconception of philosophy, which he calls Xenosphie. Cf. Hans-Dieter Bahr, Die Anwesenheit des Gastes. Entwurf einer Xenosophie, Bautz Verlag, Nordhausen 2012.

[45]  A recent discourse where thought is devoted to this kinship between expropriation and mastership, via the question of whether and how sexuality can be understood as the being of symbolic relations, i.e. the being of relation-in-general, was published in two booklets, one by Jean-Luc Nancy, L’“il y a” du rapport sexuel (edition Galilée 2001), and one by Alain Badiou and Barbara Cassin, Il n’y a pas de rapport sexuel. Deux leçons sur «L’Etourdit» de Lacan, Fayard 2010.

[46]  Judith Butler makes a similar argument about language as the dimension in which we are all equally dispossessed, in her essay entitled “Giving an Account of Oneself” (Diacritics 31.4. : 22 – 40). Her argument, I would suggest, can be expanded and generalized along the lines I propose here.

[47]  For any esteem of intellectuality as something that has been achieved by civilization, it is, for example, a sheer disaster that so much of research all across the social science and engineering disciplines today, is evaluated, funded and discussed along the simple and reductive line of CO2 reduction.

[48]  The “death of the author” which was proclaimed a.o. Roland Barthes, Maurice Blanchot, Jacques Derrida, a claim which is dedicatedly rooted in particular readings of Mallarmé’s great character of our poem, the master.

[49]  Cf. Jules Vuillemin, La Philosophie de l‘Algèbre, Presses Universitaire de France 1962, especially the concluding chapter „La Mathématique Universelle“, pp. 465-518.

[50]  in his earlier book After Finitude, an Essay on the Necessity of Contingency (Continuum, London 2008 [originally in French, Après La Finitude, 2006]), Meillassoux has reflected on what such an ‘encapsulating move’ entails in relation to the philosophical tradition, and has introduced the notion of ‘correlationalism’ for referring to all stances that embrace a transcendental position. He has suggested to call ‘realism’ any stance that negates correlationalism. With due distance to the euphoric reception of this proposal (but also with some sympathy) Alberto Toscano has discussed the (also politically) problematic aspects about such an ambiguously ‘generous’ generalization: „Gegen Spekulation oder eine Kritik der Kritik der Kritik“, in Armen Avanessian (Ed.), Realismus Jetzt, Merve Berlin 2013, pp.57-75.

[51]  „Nous avons développé abstraitement l’hypothèse qui nous a paru correspondre, dans le Coup de dés, au projet de Mallarmé depuis 1895 – celui d’une diffusion, plutôt que d’une représentation, du divin par l’OEuvre.“ Quentin Meillassoux, Le Nombre et la sirène. Un déchiffrage du Coup de dés de Mallarmé, Fayard, Paris 2011, p.89.

[52]  „La modernité avait donc triomphé, et nous ne le savions pas. La passion mise, tout au long du XIXème siècle, à arracher le messianisme de sa condition chrétienne, à réinventer une religion civique délivrée du dogme, une politique émancipatrice extérieure à l’ancien Salut; […] Mallarmé nous aurait appris que la modernité avait en effet produit un prophète, mais effacé ; un messie, mais par hypothèse ; un Christ, mais constellatoire. Il aurait architecturé un fabuleux cristal d’inconsistance contenant en son coeur, visible par transparence, le geste de sirène, impossible et vif, qui l’avait engendré, et l’engendre toujours. Et le poète aurait ainsi diffusé le « sacre » de sa propre Fiction auprès de chaque lecteur acceptant de se nourrir de 1′ hostie mentale de ses Pages fragmentées. Le tout selon un athéisme exact, pour lequel le divin n’ est rien au-delà du Soi s ‘articulant au Hasard même.“ Quentin Meillassoux, ibid. 2011, p.128; cf. also pp. 78ff.

[53]  the role of meter in poetry can be paralleled with the role of modularity in the architectural order of columns.

[54]  this same crisis famously provoked Kant to face the problem of philosophy being left with grounding reason within the sole alternative of either scepticism or dogmatism, an alternative which he seeked to overcome with his notion of critique as a means to de-throne the centrality of whatever notion of ‘pure reason’. Cf for a broader discussion again Jules Vuillemin, ibid.

[55]  In the same manner, it is this cosmic untendedness which liberated architecture to concentrate on the vectors of how to build institutions as a form of political ‘tendedness’ on the one hand, and on that of radically subjecting the building practices to procedures of technological industrialization – a vector which itself found an institutional form in the Polytechnical Universities that were founded in the late 18th and all throughout the 19th century. The secularization movement in post-revolutionary Europe was carried by this momentum of modernization, and it affected also the fine arts. The mechanists were considered artists before this, as the French expression of industry as “Arts et Métier” still illustrates.

[56]  cf. Jacques Rancière, Mallarmé, the Politics of the Siren, Continuum, London 2011 (originally in French, 1996).

[57]  the whole argument is summarized in the chapter entitled „Sommes“ (Summations), Meillassoux ibid. 2011, pp.47ff.

[58]  Significantly, the subtitle of the German translation of Meillassoux’s book, „déchiffrage“ is translated as „Verrätselung“, not as „Entzifferung“, as the engl. translation has it (decipherment). In engl. „Verrätselung“ could perhaps best be expressed as „dis-ciphering“.  It strikingly makes Meillassoux‘s point explicit: that Mallarmé‘s ouvre seeks to dissolve, rather than to represent or even resolve, the nature of the divine. Cf. fn. 51.

[59]  It needs to be pointed out again that Meillassoux himself is not speaking with reference to the mathematical theory of numerical corpus; interested as he is in dis-ciphering (cf. fn. 58) the notion of number, in order to dissolve what it renders present, he speaks of the identity of his number 707, of the particular being of this number (which he identifies as the incarnation of an altogether new notion of number, namely number-as-chance).

[60]  Meillassoux ibid. 2011, p. 32.

[61]  Whoever is interested in the backgrounds of communicational coding theory, and the role of entropy measure and chance variables therein, is recommended to look at the classic paper for communication theory by Claude E. Shannon, „The Mathematical Theory of Communication“ (1948), where he describes the two modes of coding that are still central today, in the distinction they have introduced, so-called channel coding and source-coding.

[62]  Meillassoux ibid. 2011, p.30.

[63]  in the second part of the book, entitled „Fixer l‘infini“, pp. 61ff.

[64]  Univocity is the crucial assumption in Aristotelian metaphysics. It demarcates where Aristotle departs from his teacher Plato, for whom the cosmic assumption (especially in the Timeaus) is a principle of Analogy and Proportionality. The book which Alain Badiou (as whose faithful disciple Meillassoux identifies himself) wrote on Gilles Deleuze, entitled The Clamour of Being, clearly itemizes these sentiments in a straightforward polemic (University of Minnesota Press 1999, originally in French in 1996).

[65]  starting from 2. Even within a nature of number so conceived, the integration of the 0 for nothing and the 1 for entity remain a crucial obstacle for any exhaustively explanatory consensus.

[66]  for him, the explanation why humans have been capable of “inventing” mathematics as the core power of reason, is that these idealized natural numbers are “reason’s nearest kin”. “Frege’s central claim in the Grundlagen was that in arithmetics we are not concerned with objects which we come to know as something alien from without through the medium of the senses” writes Michael D. Potter in his book Reason’s nearest kin. Philosophies of Arithmetics from Kant to Carnap (Oxford UP 1996), “but with objects given directly to our reason and, as its nearest kin, utterly transparent to it.” (p. 79).

[67]  cf. in this article p.13.

[68]  Jacques Rancière, ibid. p. 304. Cf. in this article pp. 6ff.

[69]

 Israel Kleiner, A History of Abstract Algebra, Birkhäuser Basel 2007, p.8.[70]  It is clear that Frege’s suggestion regarding the transcendent one nature of number, as well as that of Husserl regarding a psychologically differentiated one nature of number, both aspire to ward off what Whitehead faced boldly – the universality of algebra (not of arithmetics), and with that, the nature of number as subject to categorial determinability.

[71]  Quentin Meillassoux, After Finitude, an Essay on the Necessity of Contingency, Continuum, London 2008 [originally in French, Après La Finitude, 2006].

[72]  Israel Kleiner, ibid, p.8.

[73]   a book which he wrote before he set out, together with Bertrand Russell, to once and for all clarify the troubles in their seminal work Principia Mathematica (1910-13). Whiteheads subsequent turn away, after the acknowledged failure of the approach proposed in the Principia, from analytical philosophy and towards a new kind of metaphysics in Process and Reality (1929) must surely be understood in terms of his awareness of the profundity of the problems involved.

[74]  I think it is hardly an exaggeration to say that this lies at the heart of the new attention philosophy started to attribute to a primacy of Difference beneath all possible notions of Identity, from Kirkegaard and Hegel via Nietzsche to Heidegger, Derrida, Deleuze and Lacan.

[75]  Serres, ibid. 2007.

[76]  Gertrude Stein, What are Masterpieces and why are there so few of them? Conference Press, Los Angeles 1940. Available online: http://gaslight.mtroyal.ca/masterpieces.htm.

4 thoughts on “Articulating a thing entirely in its own terms Or: what can we understand by the notion of «engendering» ?

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