1
The spatio-temporal extension of the world, its history and hi-stories, is constituted by the inversion (revolutio) of a double topology – an inversion that is determined from the outset.1 Any given moment of this history or these hi-stories is determined on the basis of a specific state or phase of this inversion. The double topology makes possible the emergence of two different topographies.
A topology is an axiomatic structure that organizes and orders the places and spaces in which we live and dwell. A topography is a landscape determined by a topology and comprised of such places and spaces.
The two topographies are 1. a poetic topology (PT), which determines the topography of intimacy, and 2. a mathematico-technological topology (MTT), which determines the topography of the world.
The two topologies have a polemical – and never neutral – relation to one another. Reconciling them is impossible. Together they form an absolute difference, which recurs in the initially concealed and then ever more manifest difference between intimacy and the world. The initial hiddenness of this difference is a specific moment of the inversion of the double topology.
During that phase of the double topology’s spatio-temporal inversion in which the PT takes precedence over the MTT, the latter is at the service of the former. The topography of the world is then structured according to the conditions of intimacy. Life is lived within a locally differentiated topography in which specific sites are assigned to economic and cultic practices. Though there may be a highly developed architectural tradition, the choice of such sites is still determined by a PT. Nature is the space in which the gods manifest themselves.
When the MTT comes to take precedence over the PT, however, the PT’s role in shaping the world is suppressed and intimacy is intensified. Locally differentiated topographies vanish: the world becomes placeless through the standardization of its space-time. A physical atopia ensues. Universal institutions begin to drive the world from its intimacy and to repress the intimate world. Economics becomes the sole principle of its organization. Local differences, such as those between peoples, nations and cultures, are increasingly brought into a state of con-formity.
This inversion of the PT and the MTT is regulated in accordance with the historical determination of the idea-matter-matrix (I-M-M), the source of production.2 The crucial point here is that the temporal course of history is bound up with the initially latent and then clearly manifest determinations of the MTT. It would have been impossible, for example, for the steam engine to have been invented after the jet engine. The steam engine and the jet engine are manifestations of different determining phases of the I-M-M.
The unity of the two topologies incorporates both the MTT and the PT: the universal of all universals, universality as such, consists in an ‘unprethinkable’ universal topology (UT), to borrow a term from Schelling. The UT is a pre-original, originary sense [voranfänglicher Ursinn], which is hyper-mathematically organized. All that is real is mathematically (re)constructible. The UT, however, is not itself real; it gives rise to [gibt] reality. The MTT and the PT are thus moments of the UT. They are integrated into the universal of all universals.
The notion of the mathematical (re)constructibility of the real is hyperbolic. It refers in the first instance to all that is objectified through the production process, i.e. to the world under the dominion of the MTT. What the PT produces is sense [Sinn]. This poetic sense withdraws from the realm of mathematical constructibility.3 It is not something real; it primarily determines an intimacy that withdraws from the real. Yet it can also serve to determine aspects of the real that, as real, are mathematically (re)constructible (such as the topography of a city as distinguished from another city or from nature).4
Both historical progress and the catastrophes of history are con-sequences of interferences between the two topologies. In its spatio-temporal extension, the MTT not only determines which technological inventions are more possible than others, but also which can be actualized within the mathematico-technological topography. The PT disrupts and delays the passage from the MTT to this topography. The more powerful MTT occasionally instrumentalizes the PT in the form of ideologies whose con-sequences are techno-genocides such as those of Auschwitz and Hiroshima. Ultimately, however, the relation is re-normalized and the interference disappears. It gives way to an order in which the two topologies, returning to their determinate relationship, regain a high level of stability. Anachronisms – artificial purities that cannot give rise to any new beginning – are integral to this state of normality. The key question for our time is whether this stable order can again be ruptured.
The inversion of the relation between the PT and the MTT constitutes a revolution, or rather, a linear series of revolutions. Yet the concept of revolution is ambiguous. As well as political revolutions, there are also ideological, scientific and technological revolutions. That these are not simply homonyms is shown by Marx in his description of the revolutionary – i.e. progressive – role of the bourgeoisie in the Communist Manifesto. Since the inversion is determined from the outset, it is in principle clearly perceptible.
1.1 The poetic topology
The PT can be summarized in the lines: ‘Well deserving [Voll Verdienst], yet poetically / Man dwells on this earth.’5 These are drawn from the draft of a late hymn of Hölderlin’s, beginning ‘In lovely blue …’ ‘Man’ thus lives in part according to the rules of the MTT, ‘yet’ first of all on the basis of the PT.
Poetry organizes the topography here, as can be seen in the example of Ancient Greece. When Socrates censures poetry in The Republic, it is because it is the educator of the Greeks.6 Philosophy contests this role. The PT thus comes under attack from the MTT very early on. Yet Plato’s own myths testify to how little the MTT is capable of inhibiting or prohibiting the PT. His thinking remains so possessed by poetry that in the Laws he even declares philosophy to be the true poetry.7
At first, then, the Platonic critique of pre-philosophical myths has little impact. Poetry continues to determine how life is lived, particularly via myths passed down through cults and cultic sites. Festivals punctuate the years in the different phases of life. Tragedy relates the hubris of human beings toward the gods. Comedy does not shrink from ironizing these very gods (consider Dionysus’s role in Aristophanes’ Frogs, for instance). The temple and the theatre form the centres of these small cities.
It is then no exaggeration to say that poetry and the poets fulfil a political function. Sappho, for example, wrote and performed her poems on the island of Lesbos for a thiasos, a community of young women with whom she lived.8 Here the topography of dwelling revolves around the site where the poet performs her songs with others.
Though the topography of dwelling changes with the Romans (their gladiatorial arenas, the forerunners of our football stadia, were unknown to the Greeks), myths and cults remain. Virgil’s Aeneid was not the only foundation myth on which the Romans drew. His Eclogues directly address the difference between the city and the country. Poetry speaks of this difference while also shaping it.
The PT plays a determining role in the Christian era. The Christian topography is a network of holy sites, spiritual places (e.g. Jerusalem, Bethlehem, Golgotha, ‘heaven and hell’), centres of power (the Vatican/St Peter’s) and paths that are still trodden by pilgrims today. In the towns and villages, churches not only function as landmarks; they also represent the divine. Cathedrals are the buildings of the Middle Ages. (It is only when the MTT takes precedence in the double topology that banks and office buildings start to become the tallest buildings in the city.)
In all of these periods, an important role is of course played by the public spaces of markets and ports – the topography’s transport hubs. But the topology of such spaces does not determine the universal world-form – it does not shape the universal public sphere. Life revolves around a series of narratives that link the intimate with the communal. The god plays an important role in the life of the individual and the cult.
Yet Hölderlin’s lines contain still more: ‘Poetically / Man dwells on this earth.’ Though the sense here is ambiguous, it is likely that the poet is not thinking of the planets but of the locally differentiated earth. ‘This earth’ is the earth here. Dwelling thus takes place on many different earths, whose topographies differ from one another. Even if Christianity makes a claim to universal truth, the globe is not a universal living space. The MTT, though present, remains latent beneath the meanings generated by the PT.
This remains the case up to the beginning of the modern era. At this point, the MTT begins to emerge from its latency. Technological developments give rise to criticism of the meanings produced by the PT. The erosion of religious meaning is accompanied by topographical changes. The universal space of the market becomes more important, while holy sites and paths begin to lose their significance.
The PT nonetheless still retains a role. Even in the period leading up to the Second World War, poets and writers (such as Stefan George and Ernst Jünger9) continue to occupy leading positions in the German culture industry. Myths remain politically relevant and come to be inscribed within ideologies and projects of imperial domination. The war and its crimes against humanity, however, form a demarcation line. In the wake of this singular shock to what is now one world, the PT is banished to a state of latency. In the universal topography, the poet becomes an anachronism. The MTT organizes the world.
This does not mean that it is now impossible for poetically charged places to exist. Even within the topography of the MTT, there remains an intimacy that makes distinctive places possible. This intimacy allows even the most placeless of spaces – such as car parks, airports and motorways – to become places. Lovers still associate their first and last meetings with specific sites. Roadside memorials serve to mark the loss. Yet these places have no reality.
1.2 The mathematico-technological topology
The MTT can be summarized by the following axiom from Spinoza’s Ethics: ‘From a given determinate cause there necessarily follows an effect; on the other hand, if there be no determinate cause, it is impossible that an effect should follow.’10 Everything takes place according to strictly determined relations of cause and effect. Every cause is already determined as an effect; every effect is already determining as a cause. The cause/effect is determined/determining. If everything takes place in this way, then everything is in principle mathematico-technologically (re)constructible.
The MTT determines the universal topography.11 The objects contained in this topography are absolutely possible and therefore necessary. Since the MTT is also co-determining of the topographies of intimacy (the poetic topographies), the objects of the latter are also subject to the conditions of possibility and necessity determined by the MTT. Nevertheless, the MTT cannot destroy the PT.12
The MTT is the condition of all possibilities. It contains all that exists and all that does not exist. What does not exist [was es nicht gibt] is not impossible. Possibilities are not to be distinguished from impossibilities but from other possibilities. Impossibilities can easily be shown to be contradictory. Impossibility in being, however – impossibility beyond contradiction – must be assigned to a distinctive topology. The topology of impossibility is the atopology of the UT.
The MTT is of universal significance; it is the ground of the universal. Dynamically organized universal structures and quantities are formed within it. These universal quantities – the universals – not only represent possibility; they are possibility itself, since they determine – i.e. de facto organize – the movement of things and people in a uniform and indifferent manner.13
The concept of possibility will inevitably have to be linked to that of necessity. This is because an absolute possibility is a necessity.
Actuality is an order of things that consists in the real differentiation of a finite but immense field of possibilities. This differentiation is determinate; it has a sense. The sense of actuality is never vague; it is always exact – too exact for the subject. The sense of history remains unknown to us because it is too subtle and refined. It is possible that more intelligent beings would be able to decipher it.
What from the perspective of the MTT has to be thought as absolute possibility manifests itself as the power of the productive universal – the universal constituted by the conjunction of technology, capital and the medium. All that is possible is actualized by this universal. There are no possibilities whose actualization is excluded within the TCM universal. For the subject, however, only that which is already passing over into the process of production appears possible. What remains unactualized cannot be characterized as possible. The MTT organizes the relation between possibility and actuality economically, i.e. in accordance with the conditions of measurable production.
Absolute possibility is necessity. Since the MTT determines absolute possibility, it is the ground of necessity. Indeed, a certain historical necessity manifests itself in the actuality of the TCM universal. This necessity is no fatum, no blind destiny. Were the subject able to comprehend all of the determining factors of her thought and actions, her history would come to form a static image. Everything has always already taken place. What will take place is already determined. Perceiving this is of course impossible. The subject can never become fully cognizant of her determined character.
While the PT generates differentiated topographies, the MTT produces a universal topography in which ‘non-places’14 play an increasingly significant role. Places that differ from one another on account of their individual meanings begin to vanish. Work and transit spaces become omnipresent. Virtual spaces also acquire greater importance, and already belong to the world-form. They extend the homogeneous space generated by the MTT.
Shopping malls, car parks, airports, hospitals, the internet, refugee camps, universities, government buildings, train stations, motorways, and so on form a global space in which the universal production process holds sway. This is a continuous space that, where possible, is no longer even to be interrupted by national borders. It is neutral, and prohibits any mark that would allow for an intimate relation.
By means of the virtual spaces of images, films and computer games, the continuity of this global space is extended into a sphere of production that only emerged in the last century. These virtual spaces also belong to the universal topography. We are more at home in them than in airport departure lounges, and we are more familiar with the universal topography of Springfield than with the topography of our home town, which does not differ in principle from the animated city.
The MTT is autonomous and illimitable. It is autonomous because it does not need anything in order to be. It is illimitable because there is no conceivable space-time in which it does not hold sway. Nonetheless, its actualization as a global universal topography is highly determinate [determiniert]. There can be no other world than this world. In principle, then, the future can be predicted. The unavoidable phases of instability and rupture have already been traversed, and the future – like the past – has now been normalized.
The PT is equally autonomous, yet limited, finite. Though it is intimately related to the solidity of bodies – to the earth – it does not need the MTT. Poetry is free. There are of course possible and actual space-times whose topographies are in no way determined by the PT. In its latent and unstable state, the latter might even collapse within the universal topography of the MTT. Yet from the ruins of the PT there would likely emerge certain traces capable of ensuring its persistence under the conditions of the MTT. Such traces would be visible to an intimate regard.
The MTT determines the transitory topography of the world; the PT determines the local topography of intimacy. They have so little to do with each other that the agent of the transitory topography unquestioningly assumes that its criteria have nothing to do with her intimacy. Even the most dynamic agents, such as those who operate in the economic sphere, negate the criteria of the transitory topography within their intimate relations. Real or not, love above all is no market.
The MTT and the PT thus constitute the preconditions of different topographies, insofar as they determine these topographies. A topography’s mode of determination is manifested in its particular form of production. Production, in turn, is actualized in the universal form of technology, capital and the medium. By means of these different topographies, the double topology determines the world-form that is technology.capital.medium.
The two topologies, however, are not everything. Something still withdraws. This does not mean that something else exists beyond them. What they do not incorporate – what is without them – is the metaphysical atopia of the impossible. This atopia is freedom – indeterminability as such. The impossible repudiates actuality: it is the unproductive beyond production, the atopia of disintegration. Beyond the double topology of being that transcends the real, the exigency of the philosophical, Neoplatonic alternative thus imposes itself: the One – the universal is freedom.
Notes
1 ‘Inversion’ here translates the German Umdrehung. Though the latter implies a turning over or upside-down, it is important to note that it can also refer to a rotation (in the sense of a motor turning over, for instance) – TR.
2 For Marx, ‘production’, i.e. ‘work upon the objective world’ is ‘active species-life [werktätiges Gattungsleben]’ (Karl Marx, Economic and Philosophic Manuscripts of 1844, in Collected Works, vol. 3 [Moscow: Progress Publishers, 1975], 277). By means of it, ‘nature appears as his [man’s] work and his reality.’ ‘In a world that he has created’ through production, what matters is then ‘objectification’. And ‘objectification’ always also means ‘self-objectification’. The question is then what areas of human activity this conception of production applies to. That it includes mental activity (insofar as this is oriented toward a product) is clear. Yet does mere movement already amount to production? If human beings and technology are equiprimordial – if the human being cannot be thought without technology – then we might think that any goal-oriented bodily movement is already technological. The product that arises through such movement is action. Marx developed this idea in his conception of reproduction as a ‘division of labor’. (This conception is clearly problematic, however, since movement here often differs greatly from forms of movement that, oriented by a specific goal, culminate in a definitive end point. The sexual act is marked by a significant teleological vagueness, which serves to distinguish it from the productive process. Sex is very often pursued for pleasure, at the additional and attendant risk of procreation.) In the present study, production refers to any determinate, goal-oriented movement. I do not wish to exclude the notion that animals also produce.
3 Poetic sense is wild, non-formalizable, and endlessly reinterpretable. This too leads to it being supplanted by mathematico-technological sense within the world. The normalization of all areas of life necessarily leads to the loss of poetry’s reality.
4 In what follows I shall generally avoid the concept of the ‘real’, but will be unable to dispense with it entirely. To what extent is sense real? Sense can constitute the ground of the real. The reality of the police, however, is different from the reality of a law. The latter can nonetheless be assessed through its general effects. The same cannot be said of the poem, which does not manifest itself in a worldly manner. Its meaning rather lies within the sphere of intimacy. But is the latter real in the same way as the Deutsche Bank? Does its sense not consist in being the other of this reality? Cf. here Markus Gabriel, Why the World Does Not Exist (Cambridge: Polity Press, 2015). Gabriel assumes the role of a spokesperson for ‘New Realism’ (5) and thereby finds himself in opposition to ‘constructivism’. He himself describes his philosophical position as a ‘form of pluralism’ (57). He argues that there are ‘many small worlds’ but no ‘one world to which they all belong’ (10). On my view, by contrast, there is both ‘one world’ and ‘many small worlds’. The question is then how ‘the one world’ relates to the ‘many small worlds’.
5 Friedrich Hölderlin, ‘In Lovely Blue’, in Hymns and Fragments, trans. Richard Sieburth (Princeton, NJ: Princeton University Press, 1984), 249.
6 It is significant that, at the beginning of the Republic, Sophocles is said to have spoken of his relief at having escaped the despotic clutches of Eros in his old age – a wise remark that he will revert to in his description of the tyrant ruled by Eros. Cf. Plato, Republic, in The Collected Dialogues of Plato, ed. Edith Hamilton and Huntington Cairns (New York: Pantheon Books, 1961), 329b/c, 574e. The characterization of Eros as a despot is a tragic topos, an element of the PT. Cf. Leo Strauss, ‘The Problem of Socrates: Five Lectures’, in The Rebirth of Classical Rationalism: An Introduction to the Thought of Leo Strauss, ed. Thomas L. Pangle (Chicago: University of Chicago Press, 1989), 171: ‘The great alternative to classical political philosophy is poetry.’
7 Plato, Laws, in The Collected Dialogues of Plato, ed. Edith Hamilton and Huntington Cairns (New York: Pantheon Books, 1961), 817a/b.
8 Cf. Sappho, Gedichte, ed. and trans. Andreas Bagordo (Düsseldorf: Walter de Gruyter, 2009), 11ff.
9 Cf. my Die Autorität des Zeugen: Ernst Jüngers politisches Werk (Berlin: Matthes & Seitz, 2009).
10 Baruch Spinoza, Ethics, in Spinoza: The Complete Works, ed. Michael L. Morgan, trans. Samuel Shirley (Indianapolis: Hackett, 2002), Part I, Axiom 3.
11 As Edmund Husserl once stated of mathematics: ‘Here we must note that the mathematician is not really the pure theoretician, but only the ingenious technician, the constructor, as it were, who, looking merely to formal interconnections, builds up his theory like a technical work of art. As the practical mechanic constructs machines without needing to have ultimate insight into the essence of nature and its laws, so the mathematician constructs theories of numbers, quantities, syllogisms, manifolds, without ultimate insight into the essence of theory in general, and that of the concepts and laws which are its conditions’ (Edmund Husserl, Logical Investigations, ed. Dermot Moran, trans. J. N. Findlay [Abingdon: Routledge, 2001], 159). It is no coincidence that Husserl draws an analogy between the ‘mechanic’ and the ‘mathematician’. Mathematics and technology together make up a specific domain of sense. The nature of the relation between mathematics and logic is a question that cannot be addressed here. Incidentally, however, Badiou states that ‘While mathematics thinks being qua being outside of all actualization, logic thinks the possible particular frameworks [cadres] of actualization, i.e. the localization of multiplicities’ (Alain Badiou, Le concept de modèle: Introduction à une épistémologie matérialiste des mathématiques [Paris: Fayard, 2007], 30). Badiou thus contradicts Husserl’s analogy between mathematics and technology. On the view I shall elaborate here, however, everything that is actualized is mathematically (re)constructible. We dwell, as it were, within mathematics (within the engineered world). Where the definition of mathematics is concerned, I am therefore closer to Husserl.
12 Here we touch upon a question that cannot be pursued further in the present study: the poetic sense of mathematics. Cf. Kurt Gödel, On Formally Undecidable Propositions of Principia Mathematica and Related Systems, trans. Bernard Meltzer (New York: Dover, 1992). If the axioms of mathematics remain incomplete, i.e. if they in no way follow from what they actualize, then even the origin of mathematics has a poetic significance. It too, however, is captured and absorbed by the MTT. In the world, Gödel’s undecidable propositions are entirely insignificant. They have not interrupted the productivity of scientific systems for the slightest second. That is of course no theoretical argument. But one would have to ask what status a theory can have that is disconnected, as it were, from the ontology of everyday life. Theoreticians love theory; and they radically overestimate what they love.
13 The concept of the ‘universal’ is rooted in a long-standing debate in the history of philosophy, which has its origins in the so-called medieval ‘problem of universals’ (cf. Kurt Flasch, Das philosophische Denken im Mittelalter: Von Augustin zu Machiavelli [Stuttgart: Reclam, 2013], 59–65). At issue in this debate is the relation between general concepts and individual entities. The positions that have emerged from it have been termed ‘realism’ and ‘nominalism’. Realism asserts the onto-logical independence of universals – in some cases, to such an extent that universals are held to exist even when there are no individual entities to which they apply. Nominalism asserts that universal concepts, inexistent in themselves, arise through mere linguistic convention. My position tends toward a moderate realism: universals exist, without being sensibly perceived, insofar as they manifest themselves in things.
14 Marc Augé, Non-Places: Introduction to an Anthropology of Supermodernity, trans. John Howe (London: Verso Books, 1995).