This is my image of what De Landa is saying on p 28 of “Intensive Science and Virtual Philosophy“. It is a way of working into a new form of thinking, of coordinating the surface, or conceptualising a situation.
1. We begin on a “manifold” or a framing for our analysis (the least dimensions/restrictions the better). Deleuze is much stronger on this. He writes, ‘However one sees it, we’re on the plane of immanence’ (Negotiations p 147).
2. We populate our framing with actual occurrences, for example experiences in fieldwork or experiments. (For positivists this is the end of the line, and possible why they wonder for what reason a philosopher would do fieldwork, because there is no philosophy in the field, no concepts. Concepts and the like are all in step one, and worked out or accepted in one’s method or framing.) But persevere, not yet committed to a world in which concepts are not generated in the field.
So here is the image a drew myself …

3. We allows these points, these actual occurrences to form trajectories. Maybe we call these standardisations such as tables, responses, sentences, narratives, images – all incomplete and partial, some more violent than others.
Perhaps this is where much social science ends up, with a discussion of these trajectories, and suggestions at their histories and futures, that is their determining structures. A well argued thesis, a good piece of research, in this case, is one that comes together as the explication of coherent trajectories. however, this is to go too fast. This is to mistake these trajectories as true representations of the real rather than expressions of the real. Rather than descriptions ‘true of’ a subject (relativism) or object (realism), these are descriptions are ‘true to’ an expressive reality.
4. So it is important we don’t rush. Here we refuse to accept these points as ‘data’ as populating, informing a trajectory. The points are actual occurrences but they are not data: fixed and bounded, static and discrete (extensive properties of metric objects). Instead, we treat the trajectories having intensities properties, as telling us how things change and move, how things become and respond, how things emerge in all kinds of ways. De Landa talks about doing this by undertaking the mathematical operation of “differentiation” (as opposed to the operations of addition and comparison which can be done to data).
Differentiation tells us the rate of change at each point. In maths these points are instantaneous rates of change, infinitesimally small (which I think offers some reassurance to our fieldwork experiences as infinitesimally small but still valuable). It is also important to note that differentiation takes places without needing extra dimensions of analysis, it is an operation where objects and framing are treated together.
5. After differentiation we no longer have points but vectors, to where and how fast things are changing. Letting these spread out over our manifold we can integrate them into many many more trajectories, ones that do not have any actualisations or points that have occurred, but we can say are possible. This manifold, now full of trajectories going this way and that, is the virtual.
the virtual is a space that is structured by singularities, points which are not on any trajectory but draw trajectories toward them. These singularities are not actual, they did not occur in the physical world, but they are real, they are objects that subsist in what occurs, they subsists as objects that shape the dynamics of the actual. The pattern or series of these singularities, which come together, is the multiplicity Deleuze talks about. These are the objects which we should hold as important in our analysis. They are not structures behind the things in the world, not the meanings or essences of objects. Multiplicities are real, structuring the flows of energy, that differentiate into all kinds of different objects. Multiplicities are problematic, they define and structure the space in which problems are defines and solutions become possible.



[...] “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). [...]
[...] Encounters, events, are these contradictory – incorporeal material – things. They are not clear and distinct objects (metric objects with extensive qualities) but obscure and distinct series of differentials. The being of the sensible is difference. To relate this to a previous post, encounters or events are the trajectories on the manifold. [...]