Beyond Ontology

Where are the abysses? But they are already swarming: through the lines of others' faces and in the depths of spaces, in reflections and in distortions, flowing over one another within the black holes through which subjectivity escapes. An abyss swarms because it is always consuming: it is the earth itself, an autopoeitic unity of timeless forces and endless devourings. The terrifying abyss of nonsense is fulfilled in the floating signifier -- not in the pure ‘being’ which speaks, but in the machinic mixture of surfaces and the self-destruction of the depths. Significations are yielded by dynamic enunciative assemblages, or precosmic abstract machines. Sense is so fragile: because it is founded upon nonsense. God, the world, and the self are all surface effects: they transcendently anchor sense, give a predetermined sense to themselves. They are their own guarantee--which is precisely why we have to trace beyond the surface.

Language does not possibilize itself: the world of incorporeal effects, or surface effects, makes language possible. This world is a distinction which allows speech: grounded only by pure events which wait upon us as we wait upon them, living only inside the language which expresses them. Secondarily only does language attract itself onto bodies as qualities. “Sense brings that which expresses it into existence, and from that point on is pure inherence, it brings itself to exist, within that which expresses it.” (166, 23rd series Logic of Sense) Sense is light, of the surface, a tracing between surfaces, an interface between subspaces, a biunivocalization: “Language is rendered possible by the frontier which separates it from things and from bodies, including those which speak.” (ibid.) Sense maps the fractal boundaries between the surface of the real and the virtual, and in this way functions as a primary transversal operator: affect, not the modes of existence of a body, but its nonsense: the black holes of sensation, the molecular flux of bodies and mixtures. A primary transcoding erupts: a hyper-organization becoming co-linearized, either in order words or DNA, which express the conditions of presentation-- the possibility of a saying or the annihilation of a representation.

But how is the surface organized, and how does the chaotic machinery of the depths work? The abyssal world of incorporeal effects can be seen to belong to another order of time: one of bodies, blockages, durations and causes -- the pure present, God; but there is another order, always already passed but always to come, the other time which is incorporeal, “the pure empty form of time,” stretching out infinitely in a straight line in either direction, the truth of time, which has unwound its circle and straightened itself up. This is the process of what Deleuze calls counter-actualizations: “Counter-actualization is nothing, it belongs to a buffoon when it operates alone and pretends to have the value of what could have happened. But, to be the mime of what effectively occurs, to double the actualization with a counter-actualization, the identification with a distance, like the true actor and dancer, is to give the truth of the event the only change of not being confused with its inevitable actualiztion.” (161 ibid) The time of the event, of the incorporeal affect, is the time of counter-actualization: taking the event and considering it at a distance, ‘making sense of it.’ So when the order of the surface is itself cracked, an 'inevitable' war machine arises to maintain order: but ought the surface be kept from breaking apart -- or should its fragmentation be accelerated?

Ethics is not only a science of brokenness, a toplogy of lack or fractions or strata... but a science of molecular integration, in short, of community. A first-order ethics presents an algebra of multipilicity and faciality simultaneously. Observer and observed find themselves, surprisingly, to be in the exact same position-- that is, of having to encounter the other. This is the profound reason an ethical algebra is attainable. The question is not: when ought we to extend the abyssal crack which is at once the subject, the marks and punishments upon the subject, and the whole depth of the social field? The question is much closer to asking: when does militant action possibilize itself? It is as when Deleuze asks: “How do we stay on the surface without staying on the shore?” (157 ibid.) While we forever try to prevent the crack from forming, we cannot subject any evolving process to axioms: we must accept the radical breaks of evolution while maintaining vigorously the position of life. We must recognize that mending a break is much more complex than cleaning a stain. In fact, healing is not where our attention is usually focused; it is at the margins where cracks erupt, “in people ready to destroy themselves,” who would prefer death to the false health of a broken society. Even more: without these cracks thought could not occur. “The eternal truth of the event is grasped only if the event is inscribed in the flesh.” (160 ibid)

So what is this double-abyss whereby we become but only through struggle, this “painful actualization”? But already more important is how to reverse it, how to counter-actualize it -- which means remaining at a distance. “It is to give to the crack the chance of flying over it’s own incorporeal surface area, without stopping, at the bursting within each body; it is, finally, to give us the chance to go farther than we would’ve believed possible to the extent that the pure event is each time imprisoned forever in its actualization, counter-actualization liberates it, always for other times.” When Dionysus speaks, he speaks from the undifferentiated ground of future generations. Alienation can be turned into revolutionary exploration. There is no nothing, no abyss, no undifferentiated ground: it is not a choice between full organization or chaos. Rather, there is a chaosmos: the abyss is swarming with difference. The ‘night where all cows are black’ is doubly a lie: if the bovine are not phosphorecscent, this is no fault of Being. We must trace the ‘other’ structure in order to go beyond phenomenology; but first, we must trace the ‘sense-structure,’ or power itself. We must trace a path beyond a grammar, beyond a pure logic of sense, to an ontology of nonsense. Language is an agrammatical, nonsyntactical, impersonal, pre-individual abstract machine. But language acts on bodies: it is only the affects and mixtures of bodies, the conjuration and coordination of surfaces, a splicing and fragmenting of structure and form. Language is thus always both at once, and sense is re-absorbed continually into the gaping depths... Self-destruction cannot always be counter-actualized: the only way nature operates is against itself. Anything is possible: not only that the contradictions are real, but that the real contradicitons are not merely for a laugh!

General Relativity and Self-Reference

Recent theories of galaxy-formation and cosmic evolution are inching closer to embracing the radical geometry of general relativity. In the decades since the publication of the Schwarzchild solutions to the Einstein field equations as given in his theory of general relativity, many physicists have staked and made their professional careers on the seemingly abstruse mathematical issues involved at the heart of the debate.

Scholars have been fascinated and even sometimes ‘consumed’ by the study of black holes and the associated conceptual complexities, perhaps especially the novel interpretations of non-linear geometry relating to the prediction of an extreme curvature of space and time. Initially a seemingly bizarre consequence of the field equations, it was perhaps all the more so due to the very unique conditions under which this “affine” torsion, or gravity vortex, ought to occur.

Since the days of those first thought-provoking theoretical intuitions, the body of scientific theory regarding black holes has grown enormously. We now believe that black holes are cosmic anchors at the center of most galaxies, curving the geometry of the universe at large, perhaps even “fracturing” it into infinite geodesic ‘slices.’ We are fairly certain that there is an awful lot of something providing an enormous amount of gravitational radiation.

We also now have a deeper understanding using differential geometry of the Newtonian assertion that gravity is acceleration. We are even beginning to look for gravitational waves, or ‘graviton’ particles, which amounts to something like looking for an accelerating shift in the geometry of spacetime.

Most of us know, but perhaps have not fully recognized the importance of the geometric innovation within Einstein’s thought in shifting from special to general relativity. The explanation of this shift can be summarized as follows: in special relativity, Einstein is still using a more or less linear geometry of curved space, which is called a Minkowski space.

With the shift to general relativity, Einstein has gone beyond curved Minkowski spaces to a new kind of 'self-constructing' space called a Lorentzian manifold, which possesses a radical non-linear geometry of momenta, whose curvature is defined by stress-energy tensors (or momentum.) Einstein had fully embraced an exotic auto-metric geometry where solutions of the system of equations are potential spatio-temporal geometries.

We began by considering black holes to be ‘marginal’ occurrences, but we are beginning towards a theory where they play a central role in the evolution of the cosmos. The lesson of the history of black holes is that autopoesis is an adequate paradigm at any scale, from the quantum to the cosmic to the social. Evolution is what the shift to ‘non-linear’ geometry in general relativity means: not only that spacetime has a curvature, but that this curvature has a curvature, that it can be fast or slow, self-destructing or evolving, divergent or harmonious, unified or fragmented, self-similar or infinitely differential, and arguably, even self-creating. Evolution is a cosmic principle that applies equally to tiny particles as to living creatures and galaxies.

But we must always remember that the relevance of evolution is political first. The history of the discovery of black holes reminds us of the importance of seemingly marginal occurrences. In other words, we ought to distinguish more clearly between the event of change and the process of change. Most will agree that the process of change and evolution is always in some sense amenable to observational modelling, because reality as such obeys only an internal and self-created measure, or law of motion. The event of change is, on the other hand, ontologically transversal -- a new space embedded within an old space.

It may also be helpful to think of this evolutionary ‘event’ as the shift between different spaces, or spaces moving at different speeds relative to one another. After all, even separated spaces can be made to intersect, and we can immerse a space within another space. So this is the cosmic situation: all spaces are interconnected, but all relationships are in flux. Knowledge, like life, is a rhizome, spreading out in all directions at once, ever-shifting, evolving and involving, gradually or quickly adapting to always-changing conditions.

The question of knowledge is always which situation it is deployed into, the transversal path it travels between spaces, or into an outer space from an inner space. What is important to recognize is that this fractal shift is nothing transcendental: it is a purely mathematical function. Consider a mapping f from a space A to a space B immersed within it.

f: A -> B

What is it that we should take the ‘->’ to represent? The '->' stands for an energy-transformation method, or transversal operation. In other words, '->' is any pairwise-matching rule that establishes a 'rhythm' between inter-facing geometries. We can understand this transformation in terms of Nash's work on immersion. Simply consider that for a given element x of an inner space, we are guaranteed some information-preserving mapping onto the outer space (into which the subspace is immersed)-- regardless of the global topogical structure or local geometrical structure of either of the spaces.

Now, most people know that Godel proved that a large class of deductive systems cannot find themseles consistent or complete. But we think it ought to be more widely known than it is that, since the publication of Spencer Brown's The Laws of Form, we can consider mathematics, logic, set theory and category theory, while essentially unfoundable, incomplete and inconsistent, they are such only insofar as they remain confined within their own non-self-referential containers and categorizations (even 'meta-mathematical' ones.) Yet Brown explains that this isn't bad news, but the best news: it was a clue that we can make use of a more fundamental pre-logic to recursively found mathematics itself. In fact such a 'calculus of self-reference' has been constructed, whose simple but somewhat non-intuitive rules allow us to inferentially derive logic, and even arithmetic and calculus, as well as set and category theory, and so on. In short, we can inscribe and prove even the most complicated results of some of the most advanced fields of mathematics using Brown's 'primary algebra' (or pa.)

In the pa, we begin with the void. It is an undistinguished space; we could argue there is no Universe because there has been no distinction made. Since all distinctions are made by an observer, the Universe is still a void while there is no observer present. Not a vacuum but vacuous: those things which may exist have not yet been told they may exist. Upon this void, let us suppose an observer arrives. Now we have a distinction: there are two spaces and thus a Universe, that is, we have made a mark, crossed a limit, traversed an interface via a singular point of local geometrical tension, which thereby accounts for the construction and subsequent immersion-into-itself of a complex topological space. We shall call such a separable or self-immersible space an observer space. Note the recursivity of this definition, for we are not concerned here with a projective geometry (though it is simple enough to derive it from the primary arithmetic) or even the seemingly critical question of vision; what we are rather interested in is the 'original' nomad transversal operator--the work of the observer-- which illuminates the heart of cognition, with the fact that the whole of mathematics (set theory, logic, arithmetic) can be derived from the primary arithmetic merely being the most clear example. Observation is the primary transversal operation.

Tranversal operators thus allow us to describe the evolving ex-tension of space from the involving in-tension of observation, from the functionalizing of the enunciatory-apparatus, or assemblage of presignifying intensities. Such an operator is a worker, and as such circumscribes and resonantes with the tension, or differential movement, between two spaces’ rules of measuring force. We could write: A(x) -> B(x), the particle x being the object-flow or subject-group. This can also be read as presenting the differential momenta between two non-linear dynamic systems. We can further decode this as a mapping which embeds or immerses an open space within itself, as in the conventional notation f(A)=B which often gets shortened even further A(B).

But the real question is this: where does the difference originate? Where did the tension come from in the first place? Not of course the tension within each space which forces every movement onto an observable path -- but rather the tension ‘between’ spaces observed in the transveral (function generating) operator ->. The transformation-operation encodes a transversal action across any spaces. Thus it describes the molecular evolution of a subject group, and not the position of a null transcendent absolute point of view, but precisely that of an engaged self-observing agency acting within time to fragment, tear apart, and finally dissociate a space entirely -- what eventually gets called 'working' -- in order to transform it into another.

Transversality

Wood Cells, Microscopy UK

"Transference and interpretation represent a symbolic mode of intervention, but we must remember that they are not something done by an individual or group that adopts the role of the 'analyst' for the purpose. The interpretation may well be given by the idiot of the ward if he is able to make his voice heard at the right time, the time when a particular signifier becomes active at the level of the structure as a whole, for instance in organizing a game of hop-scotch. One has to meet interpretation half-way."
Felix Guattari (Molecular Revolution 17)

The experience of awakening from a dream seems to present a veritable crossing-over: as from one world to another. The passage is (more precisely) from one logic to another, as well: as dream-subjects of 'the' dream-god, we constitute at once the substance of the dream-image and the form of the dreamer, in a simultaneous movement: when we dream we promise the coordination of distinct singularities. Object and subject should therefore not here be read as antithetical; in fact, they are recompositions of the very same (intensive) forces and (extensive) spaces.

We are already beginning to recognize the passage from dream to wakefulness is not a 'merely ontological' transition. The movement is properly metaphysical for we traverse a territory which is neither dream nor wakefulness. We can sense here the outlines of a single underlying prelogical layer of swirling primordial chaos and the subsequent arising of the impulse-to-order. What is the cause of the impulse?

The first articulation of the impulse is production--in the case of the pure biological, reproduction. The second articulation of the impulse is enunciation proper, an interpretation of any kind of production. Our axiom that practice precedes theory seems to support the following thesis: the primary impulses (production) guide the secondary impulses (interpretation.) It is all a question of the proper conditions for interpretation. And it is here we must not resort to logical or ontological dimensions, but a new kind of dimensionality, with a fractal structure which radically traverses and binds together all the various ontological bifurcations and refolds them into an assemblage (of production, enunciation.)

Guattari explains that transversality is a group phenomena: the spectral dynamic which propels the group forward. This is already the snare which has prevented transversality as such from being politicized: that those who 'transversalize' their group become subject-groups, with definite desires, aims, goals, in short, identities. Then they have already created virtual subjugated groups, and in fact risk decaying themselves into dependency upon a reified transversality, which is already an outdated and neurotic fetish.

Again: Guattari writes that transversality means the unconscious source of action in the group. There are no objective limits it cannot exceed, no ontological ruptures which a transversal mapping cannot reconstitute. Transversality carries the groups' desire. We cannot separate this from a political or ethical sense to transversality as well:

"It is my hypothesis that there is nothing inevitable about the bureaucratic self-multilation of a subject group, or its unconscious report to mechanisms that militate against its potential transversality. They depend, from the first moment, on an acceptance of the risk -- which accompanies the emergence of any phenomena of real meaning -- of having to confront irrationality, death, and the otherness of the other." (Guattari, Molecular Revolution 23)