Posts Tagged ‘tetrapod limb’

What is Manuel Delanda trying to do in this reconstruction of Gilles Deleuze’s ontology? He is trying to provide an account of the interdisciplinary basis of Deleuzian philosophy, a philosophy that ranges from Lewis Carroll’s Alice in Wonderland to Henri Poincare’s topological geometry and beyond. Many things get lost along the way, like the problem of paradox and humor which is very important to Deleuze, but something else is gained—a kind of analytical clarity, which is contrary in some sense to Deleuze’s own rhetorical style. Regardless, what Delanda has done in this “already classic” book (back cover blurb) is to develop a notion of individuation, the virtual, and the actual that attempts a thoroughgoing displacement of Platonic and Aristotelian essentialism. Delanda tries to devalue the very idea of truth; importance and relevance are the key criteria for a Deleuzian epistemology; a problem is well-posed if it captures an objective distribution of the important and the unimportant, or more mathematically, of the singular and the ordinary (7).

Deleuze has a realist (not an actualist [33]) ontology: philosophers who grant reality full autonomy from the human mind, disregarding the difference between the observable and the unobservable, and the anthropocentrism this distinction implies (4). So one of the first implications of this is that Deleuze’s philosophy is not a story “about us”; it is about the world as assemblages, as nested spaces and times, as mutational transformations across timespace. Through a process ontology, Deleuze replaces the essences of entities with dynamical processes, some of which are material and energetic, but all of which remain immanent to the world of matter and energy (5).

            There is an objective illusion fostered by the concealment of process under product (68-9). Any area of the world which is in thermodynamic equilibrium is an area where intensive differences have cancelled themselves out, and hence an area which conceals the virtual without the need for human intervention. These areas of the world would constitute an objective illusion (74).

            In a Deleuzian ontology one must emphasize that the regularities displayed by the different possible trajectories in a given multiplicity are a consequence of the singularities that shape the vector field. Deleuze makes a sharp distinction between trajectories as they appear in the phase portrait of a system and the vector field (28-9). The vector field is the real source of the regularities or propensities in the population of possible histories (33). Unlike trajectories, a vector field is not composed of individuated states, but of instantaneous values for rates of change. Individually, these instantaneous rates have in fact no reality but collectively they do exhibit topological invariants (singularities). Ontologically, these invariants of a vector field are topological accidents, points in the field which happen to be stationary; Deleuze argues that these topological accidents should be given the ontological status of an event (a perfect storm? a scientific concept for this would be stochastic resonance). A key concept in the definition of a multiplicity is that of invariant, but invariances are always relative to some transformation. In other words, whenever we speak of the invariant properties of an entity we also need to describe an operator or group of operators capable of performing rotations, translations, projections, foldings, and a variety of other transformations on that entity. So the ontological content of the virtual must also be enriched with at least one operator. The quasi-cause is this operator and is defined not by its giving rise to multiplicities but by its capacity to affect them (84). The quasi-causal operator creates among the infinite series springing from each singularity “resonances or echoes”—the least corporeal of relations. A quasi-cause, or a relation of quasi-causality could be thought of in terms of the establishment of a communication channel between divergent trajectories that change the distribution of the singular and ordinary within a trajectory.

One of the chief targets of a Deleuzian ontology is essentialism. Essentialism can be understood as a theory of the genesis of form, a theory of morphogenesis, in which physical entities are viewed as more or less faithful realizations of ideal forms; essences act as originary, fully present models, eternally maintaining their identity, while particular entities are conceived as mere copies of these models; the essence of a thing is that which explains its identity, that is, those fundamental traits without which an object would not be what it is. “If such an essence is shared by many objects, then possession of a common essence would also explain the fact that these objects resemble each other and, indeed, that they form a distinct natural kind of things” (6-9).

            In Platonic essentialism or Aristotelian typological thinking, species were examples of “natural kinds”; animal/plant species provided the ideal model of what an abstract general entity was supposed to be. Contemporary evolutionary biologists such as Michael Ghiselin argue in contrast that species are not a higher ontological category. Essentialist and typological thought are rooted in the hierarchy of categories (each level of organism, species, genera representing a different ontological category). By contrast, contemporary science argues that the process of speciation is intensive in the sense that its description involves ideas of population and heterogeneity (in population thinking, using statistical analysis, the average is an abstraction and only the variation is real). For population thinkers genetic variation is the fuel of evolution: without adaptive differences between organisms natural selection would be incapable of yielding any improvements in the population (57-9). More, heterogeneity is the state we should expect to exist spontaneously under most circumstances; while in essentialist or typological thinking uniformity is the natural state and difference is what needs special explanation, for population thinkers it is difference that is unproblematic (71). The norm of reaction replaces the idea of degrees of perfection with relations between rates of change. The forms are thus statistical results of the population individuating itself through differential rates of change: “…the substitution of populations for types, and the substitution of rates or differential relations for degrees” (Deleuze, qtd. in Delanda 59-60). Thus, multiplicities replace essences; a species is defined by the morphogenetic process that gave rise to it; form-generating resources which are immanent to the material world (9). Unlike the a priori grasp of essences in human thought postulated by those who believe in such entities, there would be an empiricism of the virtual (85-6).

Emergent Intensity

Emergent Intensity

Deleuze replaces an essentialist morphogenesis with one based on the notion of intensive difference, which he differentiates from both qualitative difference and extensive difference. He conceives intensive difference not negatively, as lack of resemblance, but positively or productively, as that which drives a dynamical process. The best examples of intensive differences are the differences in temperature, pressure, speed, chemical concentration, color… (6).

            Intensive properties cannot be divided without involving a change in kind, a qualitative change (25). If a quantity of matter in a given state is divided into two equal parts, each part will have the same value of intensive properties as the original and half the value of the extensive properties (69). Intensive properties do not add up but rather average. This averaging operation is an objective operation, in the sense that placing into contact two bodies with different temperatures will trigger a spontaneous diffusion process equalizing the two intermediate values. Thus differences in thermodynamic intensities such as temperature are capable of driving an averaging process of equilibrium in a population of molecules. Unlike qualitative differences, differences in intensity can drive fluxes of matter or energy (69-70). Intensive differences such as temperature or pressure gradients within one body are productive, forming the basis of simple processes of individuation. Soap bubbles and salt crystals emerge from the spontaneous tendency of the molecular components to minimize a potential or intensive difference (70).

There are a large number of physical structures that form spontaneously as their components try to meet energetic requirements. These components may be constrained to seek a point of minimal free energy, like a soap bubble that acquires its spherical shape by minimizing surface tension, or a common salt crystal adopting the cube form by minimizing bonding energy. The point of minimal energy functions as a single point attractor (a singularity). Thus a topological form (a singular point [eg minimal energy] in a manifold) guides a process which results in many different physical forms. This is in contrast to a form of thought that posits the essence of sphericity (circle-ness) which then is realized in the world by soap bubbles. The topological form of singularities is mechanism independent, independent of their physical mechanisms (15).

            Mechanism independence (19-20) is a concrete universality, a concrete set of attractors-singularities (realized as tendencies in physical processes) linked together by bifurcations (realized as abrupt transitions in the tendencies of physical processes). Following Deleuze, Delanda also defines concrete universals as preindividual (before the individuated product) singularities and affects (74). The tetrapod limb would be a concrete universal: asymptotic singularity (a basin of attraction that is never fully actualized because of so many divergent final forms of it) and unactualized capacity (blocked or divergent series of bifurcations; an open set of potential combinations constantly mutating [79]) (77). The universality of a multiplicity is typically divergent: the different realizations of a multiplicity bear no resemblance whatsoever to it and there is in principle no end to the set of potential divergent forms it may adopt. Multiplicities give form to processes, not to products. This distinguishes the obscure yet distinct nature of multiplicities from the clear and distinct identity of essences. Finally, concrete universals are meshed together into a continuum often through feedback loop relations that resonate (the communication channel of a quasi-cause). (21). A continuous space progressively differentiates itself giving rise to discontinuous spaces.  The continuity of a multiplicity is not defined primarily by metric spaces, but by non-metric spaces (e.g. asymptotic closeness; asymptotic stability: small shocks may dislodge a trajectory from its attractor but as long as the shock is not too large to push it out of the basin of attraction the trajectory will return to the stable state defined by the attractor [29]) (22). The example of geometry (23-4): the metric space which we inhabit and that physicists study and measure was born from a nonmetric, topological continuum as the latter differentiated and acquired structure following a series of symmetry-breaking transitions (24).

            Given a cell with a specific history, and a certain inductive signal which can change its fate, the outcome of their interaction will depend on how many other attractors exist nearby in the state space of the network of genes within the cell. Far from directly determining the qualities of a differentiated cell, inductive signals trigger cells to switch from one attractor to another nearby one, guiding a process of qualitative differentiation which follows attractors as so many stepping-stones. This process of stimulus-independence is what defines the signature of the virtual: the traces which the virtual leaves in the intensive. 65

            The three ontological dimensions constituting Deleuzian thought—the virtual, the intensive, and the actual—can be understood in terms of individuals at different spatial scales populating the actual world embodied in discontinuous spatial or metric structures condensing out of a nonmetric, virtual continuum (61). As migration and folding (invagination) begin to yield finished anatomical structures nonmetric relations become progressively replaced by a less flexible set of metric ones (64). Thus, a relatively undifferentiated intensive space (defined by continuous intensive properties) progressively differentiates eventually giving rise to extensive structures (with definite metric properties) (25).

Tetrapod Limbs

Tetrapod Limbs

Multiplicities are obscure and distinct; the singularities that define a multiplicity come in sets, and they are structured through progressive differentiation (16). Singularities lead to an entirely different way of viewing the genesis of form (15). Singularities function as never-actualized (35) attractors for trajectories: a large number of different trajectories starting their evolution at very different places in the manifold may end up in the same final state (the attractor), as long as they all begin somewhere within the sphere of influence of the attractor (basin of attraction); singularities represent long-term tendencies of the system (14).

            A multiplicity is a nested set of vector fields related to each other by symmetry-breaking bifurcations (phase transitions), together with the distributions of attractors which define each of its embedded levels. Phase transitions are events which take place at critical values of some parameter switching a physical system from one state to another, like critical points of temp. at which water changes from ice to liquid, or from liquid to steam…the progressive differentiation of the spherical egg is achieved through a complex cascade of symmetry breaking phase transitions. Control parameters in a state space determine the strength of external perturbations to which the system may be subject. These control parameters display critical values, thresholds of intensity at which a bifurcation takes place, breaking the prior symmetry of the system (18-19).

This separates out the part of the model which carries info about the actual world (trajectories as series of possible states) from that part which is never actualized. What ontological status do such partially never actualized multiplicities have? Multiplicities have a real virtuality which forms a vital component of the objective world, virtuality is their mode of becoming. The virtual must be defined as strictly part of the real object (30). A space with multiple attractors breaks the links between necessity and determinism, giving a system a “choice” between different destinies and making the particular end state a system occupies a combination of determination and chance (35). The four elements of essentialist classificatory practices—resemblance, identity, analogy, and opposition—are displaced by real virtuality. 38 A nonlinear system with multiple attractors continues to display its virtuality even once the system has settled into one of its alternative stable states, because the other alternatives are there all the time, coexisting with the one that happens to be actualized. All one has to do to reveal their virtual presence is to give a large enough shock to the system to push it out of one basin of attraction and into another (75).

            In populations, the coupled rates of births, death, migration and resource availability correspond without resemblance to the differential relations that characterize a multiplicity. A given intensive process of individuation embodies a multiplicity, and the lack of similarity between the virtual and the intensive is explained in terms of the divergent character of this embodiment, that is, by the fact that several different processes may embody the same multiplicity (61).

            The assembly of multiplicities must yield individuals with the capacity to evolve; this process is characterized by intensive properties articulating heterogeneous elements, relating difference to difference (73). Contrast an assembly-line factory with the process taking place within and among living cells which results in the assembly of tissues and organs. The parts of an object put together in an assembly line are fully Euclidean, with rigid metric properties such as sizes, shapes and positions. This limits the kind of procedures possible for their assembly: rigidly channeled transport system, rigid motions to correctly position parts relative to one another. This rigidity also limits their capacity to affect and be affected and thus to mutate. Component parts used in biological assembly are defined less by rigid metric properties than by topological connectivity: the specific shape of a cell’s membrane is less important than its continuity and closure, and the specific lengths of a muscle less important that its attachment points. (Delanda uses topological resources to analyze certain recurrent or typical features of state spaces [14].) This allows component parts to be adaptive (to fold, stretch, or bend: topological connectivity). Components may float around and randomly collide, using a lock-and-key mechanism to find matching patterns without the need for exact positioning. All of this has consequences for the capacity to evolve through mutation and selection, the capacity to differentiate differences (73). In biological assembly mutations do not have to occur simultaneously in matching parts, channels, and procedures in order to yield a viable entity for natural selection. Thanks to diffusive transport, lock-and-key matching assembly, topological and adaptive parts, as well as stimulus independence, evolution has an open space in which to carry out its blind search for new forms (67). The finished product has some geometric properties and some intensive such as entropy or amount of energy; metric properties which expand the concept from structure to function; is characterized by qualities which are metrically indivisible like intensities (68).

Media Assemblages

Media Assemblages

             A multiplicity may be characterized by a fixed number of definite properties (extensive and qualitative) and yet possess an indefinite number of capacities (affordances) to affect and be affected by other multiplicities (71). Deleuze gives a two-fold definition of the virtual in terms of unactualized tendencies or singularities and unactualized capacities or affects (72). A multiplicity will exhibit a variety of capabilities to form assemblages with other individuals, organic and inorganic. The example that Delanda uses is the assemblage which a walking animal forms with a piece of solid ground (surface to walk on) and a gravitational field (endowing it with a given weight). The capacity to form an assemblage depends in part on the emergent properties of the interacting individuals (animal, ground, gravitational field), but is not reducible to them (72). Affects (capacities, affordances) are relational; what an individual affords another may depend on factors such as relative spatial scales; affordances are also symmetric involving both capacities to affect and be affected. (Keep in mind that classifying geometrical objects by their degrees of symmetry is a sharp departure from the traditional classification of geometrical figures by their essences. Groups are not classified by static properties but in terms of how they are affected (or not affected) by active transformations, by their response to events that occur to them. Degree of symmetry is not an intrinsic property of the entity being classified but always relative to a specific (group of) transformation(s) [17].) The interactions which organisms have with the organic and inorganic components of an ecosystem are typically of the intensive kind, an ecosystem being a complex assemblage of a large number of heterogeneous components: diverse reproductive communities of animals, plants and micro-organisms, a geographical site characterized by diverse topographical and geological features, and the ever diverse and changing weather patterns (73).

            One task of virtual  philosophy is to locate those areas of the world where the virtual is still expressed, and use the unactualized tendencies and capacities one discovers there as sources of insight into the nature of virtual multiplicities (returning to the interior of the tetrapod limb) (76-7).

We leave to another post the connection between this intensive ontology and a nonlinear history of institutions. Delanda takes this later question up in the conclusion to A Thousand Year of Nonlinear History. There he writes brilliantly of the BwO (body without organs, plane of consistency, qualitative multiplicity) through which intensive processes actualize various forms.

“Moreover, not only were there several particle accelerators mobilizing trigger flows of different kinds, there were coexisting motion of destratification of intermediate intensity which connected these flows, generating meshworks of different kinds: peasant and small-town markets; symbiotic nets of small producers engaged in volatile trade and import substitution; large cities and industrial hinterlands operating via economies of agglomeration; alpine regions elaborating industrial paradigms different from those of the coal conurbations, in which skills and crafts were meshed together instead of being replaced by routines and centralized machinery. What use is there in moving our level of description to the BwO if we are not going to take advantage of the heterogeneous mixtures of energy and genes, germs and words, which it allows us to conceive, a world in which geology, biology, and linguistics are not seen as three separate spheres, each more advanced or progressive than the previous one, but as three perfectly coexisting and interacting flows of energetic, replicative, and catalytic materials?” (267)

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