DeLanda: the mathematics of the virtual, okuma notları ec

INTENSIVE SCIENCE AND VIRTUAL PHILOSOPHY
The mathematics of the Virtual: manifolds, vector fields, transformation groups
ss: 9 – 41/56 okuma notları, ela çil, nisan 2007

Deleuze’ün felsefesinin dayandığı dönüşümler:

Actualization –Realization

Multiplicity –Essence

Morphogenetic process –Identity

Immanent to the material world –Factors that transcend the realm of matter and energy

Essences of processes –Essences of objects

Differential geometry –Analytical geometry
Gauss –Descartes
Reiman –Fermat, Einstein

kavramlar / teoriler:

The structure of spaces of possibilities
The regularities exhibited by morphogenetic processes

Manifold: variable number of dimensions and absence of a higher dimension imposing an extrinsic coordinate on the others. This defines a new state combined by many that does not need unity in order to form a system. Thus, an object’s instantaneous state becomes a single point, but the space that the object is embedded becomes more complex.

difference and repetition

the space of possible states

Models of physical processes:
1. the number of relevant ways in which an object can change,
2. relating those changes to one another using (differential calculus) while essences are traditionally singularities

State space

Progressive differentiation

Active transformation responses of the objects to events that occur to them.

Essences point to a clear and distinct nature, multiplicities point to a obscure and distinct nature. One of the metaphors used to define multiplicities is from biology: the process of a fertilized egg becoming a fully developed organism with tissues and organs. The other metaphor is from math (theory of groups): the property of invariance in transformations; and invariance is related with the degree of symmetry of a geometrical object. Some transformations may be symmetry breaking and these are called bifurcations.

According to Deleuze, multiplicities are concrete universals unlike essences which are abstract entities. The difference is the relationship among essences and among multiplicities: essences co-exist side-by-side sharply distinguished from one another, concrete universals should be thought as meshed together into a continuum.

Multiplicities give form to processes, not to final product.
A multiplicity is a nested set of vector fields related to each other by symmetry-breaking bifurcations, together with the distributions of attractors which define each of its embedded levels.

The distinction between metric and non-metric spaces

Topology: the geometry in which many discontinuous forms have blended into one continuous form.

Extensive and intensive physical properties

Virtuality

The four categories that should be avoided while thinking about the virtual:
Resemblance,
Identity
Analogy, and
Opposition /Contradiction