John Johnston in his book The Allure of Machinic Life: Cybernetics, Artificial Life, and the New AI will compare the work of nonlinear dynamics and its notion of a chaotic attractor as exhibiting the precise attributes of what Deleuze and Guattari call an abstract machine, which inhabits equally the realms of matter-energy and abstract mathematical function (1), quoting D&G in A Thousand Plateaus:
The abstract machine in itself is destratified, deterritorialized; it has no form of its own (much less substance) and makes no distinction within itself between content and expression, even though outside itself it presides over that distinction and distributes it in strata, domains, territories. An abstract machine in itself is not physical or corporeal, any more than it is semiotic; it is diagrammatic (it knows nothing of the distinction between the artificial and the natural either). It operates by matter, not by substance; by function, not by form. Substances and forms are of expression “or” content. But functions are not yet “semiotically” formed, and matters are not yet “physically” formed. The abstract machine is pure Matter-Function – a diagram independent of the forms and substances, expressions and contents it will distribute. (A Thousand Plateaus, p. 141)
After a lengthy discussion on chaos theory he will make a comparison between the primordial and dynamic quality of an abstract machine, which is what D&G are trying to elucidate, showing that it cannot be conveyed in the language of a “thing” and its “representation.” If both thing and representation could change in a dynamic relationship of reciprocal determination, then perhaps the “diagrammatic” quality of the abstract machine could be conveyed. Viewed as a type of abstract machine, however, the peculiar qualities of the chaotic attractor begin to make a unique kind of sense. As both an array of forces and a mapping of their vectors, the chaotic attractor is what deterritorializes the assemblage, both pulling it into a state of chaotic unpredictability and pointing to a new mathematical coding that allows this process to be measured. Rather than view the attractor as a kind of Platonic form that exists independently of its instantiation in a particular nonlinear dynamical system which is how attractors are sometimes viewed we should say, as D&G say of the abstract machine, that it “plays a piloting role” (142): it neither preexists nor represents the real, but constructs it and holds it in place. (Johnston, p. 153)
As Johnston explicates – in using experimental data in a manner not to confirm what is already known but to measure the rate of its destruction, Shaw (the nonlinear dynamics theoretician) becomes a kind of probe head, the human part of a machinic assemblage that functions like a dynamic feedforward device, relentlessly pushing into the unknown (or at least the unpredictable future) all while insistently measuring the rate of that advance. What is affirmed and confirmed for both physics and philosophy, and against their prior and respective idealizations is that processes of dynamic change follow the irreversible arrow of time. (Johnston, p. 154)
(As a side note I began thinking of Dark Matter and Dark Energy. Do not these mathematical objects that are neither matter nor energy in the sense of the term we know in the positive matter of the phenomenal universe represent such notions as abstract machines with the properties of such strange attractors? Many scientists believe that Dark Matter and Dark Energy make up 95% of the known universe, yet they are not yet detectable by our scientific instruments and apparatuses. They are mathematical objects that explain the missing information in the system we know as the universe. This notion of the abstract machine and chaotic attractor acting as a blueprint or diagram that is neither form nor substance, yet constructs and holds the universe of phenomenal matter and energy in place seems uncannily similar. Obviously trying to analogize from such notions is not the best policy. Yet, it makes you wonder.)
“The abstract machine is pure Matter-Function – a diagram independent of the forms and substances, expressions and contents it will distribute. – Deleuze & Guattari”
1. John Johnston. The Allure of Machinic Life: Cybernetics, Artificial Life, and the New AI (pp. 152-153). Kindle Edition.