THE LETTER 58 Spring 2015, Pages 31-58

This paper explores the various meanings attached to Lacan’s famous graph
of desire. The graph represents the relations between desire and the law, the
signifier, the subject and the code. In addition, the relations between desire
and the desire of the Other and among desire, jouissance, and the drive are
examined. It is proposed that the graph is constructed as an ascending and
descending structure of facilitations, punctuations and limitations, of circular
repetitions and lines that escape them. Beyond the drive, the subject asks
‘What do I want from the Other and what does the Other want from me?’
These questions are anything but rhetorical, as no matter what we do, we will
never find complete answers to them, mainly because the answers are hidden
in the questions. In other words, desire is essentially related to the loop
between desire and the desire of the Other. We learn from Lacan that desire is
unconscious and inseparable from the law. He also claims that, although impossible
to fully capture — the Other lacks the signifiers to represent desire —
desire can be represented with the help of mathematical graph theory. Graph
theory allows the placing of many Lacanian concepts in one picture, such as
phantasy, the ideal ego, the ego ideal, the formula for the drive, the signifier
of a lack in the Other, the signifying chain, the treasury of signifiers. The most
difficult part of the graph to represent is the ‘beyond’ of castration, the nonexistence
of the phallus and the unthinkable Being of the subject (of the Real
and the Other jouissance) that is missing within the Other and the battery of
signifiers.
Keywords: desire, graph of desire, topology, castration, jouissance
Graph theory and the Königsberg Bridge Problem
Graph theory is a branch of mathematics that uses mathematical structures to
model pair-wise relations between objects. A ‘graph’ is then created from ‘vertices’
or ‘nodes’ and lines called ‘edges’ that connect them. In the graph of desire the
vertices or nodes are represented by the circles that contain symbolic formulae.
While we understand that the term matheme was not introduced by Lacan until…