Multiplicity

From Capitalism and Schizophrenia

“The word ‘multiplicity” … must be attached to the substantive form: multiplicity must not designate a combination of the many and the one, but rather an organization belonging to the many as such, which has no need whatsoever of unity in order to form a system” (DRC 230). "Multiplicities are defined by the outside: by the abstract line, the line of flight or deterritorialization according to which they change in nature and connect with other multiplicities" (ATPC 9-11).

Multiplicities cannot be counted or measured, they are unities in themselves, not in any supplementary dimension of perceived Unity (Many as One); and multiple in themselves, not as a number of singularities (Many Ones). A multiplicity consists of singularities that synthesize into a “whole” by relations of exteriority. This non-reductionistic holism can be understood through Manuel DeLanda:

“The reason why the properties of a whole cannot be reduced to those of its parts is that they are the result not of an aggregation of the components’ own properties but of the actual exercise of their capacities. These capacities do depend on a components’ properties but cannot be reduced to them since they involve reference to the properties of other interacting entities” (A New Philosophy of Science, Continuum 2006: 11)).

[edit] In the unconscious

The unconscious is composed of rhizomatic multiplicities rather than arborescent multiplicities. They are thus libidinal, unconscious, molecular and intensive. This way the do not divide without changing in nature. They move about in Brownian motion.

[edit] In mathematics

“The word multiplicity is a general term meaning 'the number of values for which a given condition holds.' For example, the term is used to refer to the value of the totient valence function or the number of times a given polynomial equation has a root at a given point.” (Weisstein, Eric W. "Multiplicity". From MathWorld--A Wolfram Web Resource.)