Deleuze’s thinking expounds on Bergson’s adaptation of multiplicities in step with the catastrophe theory, chaos theory, dissipative systems theory, and quantum theory of his era. For Bergson, hybrid scientific/philosophical methodologies were not viable. He advocated tandem explorations, the two “halves” of the Absolute “to which science and metaphysics correspond” as a way to conceive the relations of parallel domains. The distinctive creative processes of these disciplines remain irreconcilable differences-in-kind, commonly manifesting in lived experience. Bergson: Science is abstract, philosophy is concrete. Deleuze and Guattari: Science thinks the function, philosophy the concept. Bergson’s Intuition is a method of division. It differentiates tendencies, forces. Division bifurcates. Bifurcations are integral to contingency and difference in systems logic.
The branching of a solution into multiple solutions as a system is varied. This bifurcating principle is also known as contingency. Bifurcations mark a point or an event at which a system divides into two alternative behaviours. Each trajectory is possible. The line of flight actually followed is often indeterminate. This is the site of a contingency, were it a positionable “thing.” It is at once a unity, a dualism and a multiplicity:
Bifurcations are the manifestation of an intrinsic differentiation between parts of the system itself and the system and its environment. […] The temporal description of such systems involves both deterministic processes (between bifurcations) and probabilistic processes (in the choice of branches). There is also a historical dimension involved […] Once we have dissipative structures we can speak of self-organisation.
Figure: In a dynamical system, a bifurcation is a period doubling, quadrupling, etc., that accompanies the onset of chaos. It represents the sudden appearance of a qualitatively different solution for a nonlinear system as some parameter is varied. The illustration above shows bifurcations (occurring at the location of the blue lines) of the logistic map as the parameter r is varied. Bifurcations come in four basic varieties: flip bifurcation, fold bifurcation, pitchfork bifurcation, and transcritical bifurcation.
A bifurcation, according to Prigogine and Stengers, exhibits determinacy and choice. It pertains to critical points, to singular intensities and their division into multiplicities. The scientific term, bifurcation, can be substituted for differentiation when exploring processes of thought or as Massumi explains affect:
Affect and intensity […] is akin to what is called a critical point, or bifurcation point, or singular point, in chaos theory and the theory of dissipative structures. This is the turning point at which a physical system paradoxically embodies multiple and normally mutually exclusive potentials…
The endless bifurcating division of progressive iterations, the making of multiplicities by continually differentiating binaries, by multiplying divisions of dualities – this is the ontological method of Bergson and Deleuze after him. Bifurcations diagram multiplicities, from monisms to dualisms, from differentiation to differenciation, creatively progressing. Manuel Delanda offers this account, which describes the additional technicality of control parameters, analogous to higher-level computer technologies that enable dynamic interaction. These protocols and variable control parameters are later discussed in detail in terms of media objects in the metaphorical state space of an in situ technology:
[…] for the purpose of defining an entity to replace essences, the aspect of state space that mattered was its singularities. One singularity (or set of singularities) may undergo a symmetry-breaking transition and be converted into another one. These transitions are called bifurcations and may be studied by adding to a particular state space one or more ‘control knobs’ (technically control parameters) which determine the strength of external shocks or perturbations to which the system being modeled may be subject.
Another useful example of bifurcation with respect to research in the neurological and cognitive sciences is Francesco Varela’s theory of the emergence of microidentities and microworlds. The ready-for-action neuronal clusters that produce microindentities, from moment to moment, are what he calls bifurcating “break- downs”. These critical events in which a path or microidentity is chosen are, by implication, creative:
On the basis of this fast dynamic, as in an evolutionary process, one neuronal ensemble (one cognitive subnetwork) finally becomes more prevalent and becomes the behavioral mode for the next cognitive moment. By “becomes more prevalent” I do not mean to say that this is a process of optimization: it resembles more a bifurcation or symmetry-breaking form of chaotic dynamics.
Varela’s “breakdown” is an event triggering diachronic emergence – a timeless interval of reserve potential that “restructures the virtual” (Protevi). Varela, with his deeply phenomenological leanings, and Deleuze and Guattari, with their nomadic surfaces, share a jagged cartography of concurrence. Their leanings vacillate (resonate) between difference and resemblance.