Here I am going to trace out what are the objects of concern for Deleuze according to De Landa in the first chapter of Intensive Science and Virtual Philosophy – “The Mathematics of the Virtual: Manifolds, vector fields and transformation groups“.
The object of concern is the multiplicity. It is developed in contrast to an object, we could call the metric object, familiar of philosophers and philosophers of science, which are clear and distinct and are defined and known by their essence. In contrast, multiplicities are obscure and distinct. They are defined not by an essence but by an progressively unfolding series. Hence, they are dynamic not static.
Metric objects, being clear and distinct, have extensive properties such as like length, area, colour. As properties of extent, they spread out from a centre, increasing (or decreasing by simple additions or subtractions of the same. (the extensive property ‘length’ of a pole is increased by adding more of the same property ‘length’ in the form of more pole). Multiplicities are defined by intensive properties, like heat, sound and energy. As properties of intensity they increase increase or decrease only with a change in the quality in the object in which it inheres (for examples see the bottom of this post).
When we comprehend metric objects we add one more dimension to that which they bear. In mathematics, we can think of comprehending or solving a line (with the single dimension of length) between two points by putting it on a plane (which has the dimensions of length and width), or perhaps comprehending a surface, such as the surface of the ocean by giving it a third dimension, its depth into the sea and a height into the sky.
Drawing this insight from mathematics to elsewhere, we can think of a collection of works of literature as a metric objects, cohering with and unity of its author, or a series of conflicts as a metric objects giving it a period of time or historical epoch (it is this account of extensive objects, as extending from a centre – an author – that Foucault writes about in ”Discourse on Language“. However, multiplicities are not metric, meaning that in comprehending them we do not, even must not, posit anything in addition.
Returning to mathematics, specifically differential geometry, the object of the manifold is such an object that allows us to comprehend it and work with it, not by adding any further dimensions, but by putting the axis on the surface itself.
“Gauss realised that the calculus, focusing as it does on infinitesimal points on the surface itself (that is, operating entirely with local information), allowed the study of the surface without any reference to a global embedding space. Basically, Gauss developed a method to implant the coordinate axes on the surface itself (that is, a method of “coordinatizing” the surface) and, once points had been translated into numbers, to use differential (not algebraic) equations to characterise their relations.” (De Landa 2002, p 11-12)
(This is what I deal with in the next post).
De Landa is already working to broaden the method beyond mathematics by adding in ‘operating entirely with local information’. That is, we can deal with our objects, such as cars or money, not through adding anything more than that which is given locally, in the context of their specific lives. The significance of this – what is given locally – will be written about in the next few posts. Understanding that what is given locally bears on ‘problems’ rather than simply accidental ‘solutions’, is a major point in Deleuze’s new empiricism. There is no outside to the analysis. This does not mean there is no framing, no metaphysics or assumptions. It is just that they are not outside the objects, our descriptions of them, or comprehension of them – they are not separate things.
At risk of distraction, I have a feeling that this might be what underlies Latour’s instance that all he does it serial description, but that to do good description one needs to me a good metaphysician (Harman review recording).
Examples of intensive objects:
You cannot increase the heat of water by adding more water of the same temperature, just like you cannot increase sound intensity by adding more sound waves. To increase the heat subsisting in water we must heat it, this necessarily changes the how the water behaves and at critical points changes it from solid to fluid or fluid to vapour. In the case of sound, the intensity or energy subsists in space as pressure. Changing the dimensions of this space, the positioning of the sources, is what effects the sound intensity.
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Manuel De Landa, Intensive Science & Virtual Philosophy (London and New York: Continuum International Publishing Group, 2005)
Michel Foucault, “Discourse On Language,” in Critical Theory Since 1965, ed. Adams Hazard and Leroy Searle (Tallahassee: University Press of Florida).
