Please read the texts that define the fifth dit-mansion w, subjective initiation and objective initiation [1] and then examine the following figure which maps w as the combinatorial ground of spatiality:

The figure presents two logical modes of w. Let’s call them the prior mode (the first w-axis at the top) and the posterior mode (the second w-axis below it) since they respectively take place prior and posterior to the generation of the Master-Signifier S₁.

In the prior mode of w, S(Ⱥ) provides the ground zero of signification (w=0), objet a is the negative magnitude that draws the bow, as it were (w=-1), and S₁ is the unary result of the objective initiation (w=1). The negativity of objet a marks the inward horizon of desire in the prior mode.

Another name for objective initiation is de-separation [2] which is akin to but more elementary than the analytic discourse. Both de-separation and the analytic discourse generate the Master-Signifier S₁ but they follow different routes: Analytic discourse addresses the divided subject $ by donning the semblance of objet a and keeping the knowledge S₂ in brackets, whereas de-separation combines the semblance of objet a directly with the truth of the lack in the Other S(Ⱥ). In any case, the prior mode shows how a Master-Signifier is born.

In the posterior mode of w, the subject $ marks an empty point of reference (w=0), S₁ is the signifier that represents the subject for other signifiers (w=1), S₂ is the signifying chain or knowledge for which the subject gets represented (w=2), and objet a is an excess that remains from the subject’s representation (w=3). The excess of objet a marks the outward horizon of desire in the posterior mode.

The inward and outward horizons of objet a in the prior and posterior modes together compose the extimacy of desire.

The four symbols in the posterior mode are ordered exactly in the way they line up in Lacan’s four discourses. The subjective initiation may alternately refer to the operation of hysteric’s discourse (emphasizing ‘subjective’), master’s discourse (emphasizing ‘initiation’) or capitalist discourse (hysterical master who conceals ‘initiation’ behind ‘subjective’).

Once we acknowledge the extimate horizon of desire that links w=3 back to w=-1 via objet a, the four symbols get connected in a loop, and consequently all four discourses can take place in the posterior mode.

The posterior mode of w also provides the combinatorial ground of spatiality [3]. Examine how each of the four symbols is associated with a space-time coordinate:

1) The Master-Signifier S₁ is elevated and raised like a flag to establish political hegemony, so it is associated with height: y coordinate.

2) The knowledge S₂ is widely disseminated on the bandwidth of an information channel and it’s warranted by an unknown x, so it is associated with width: x coordinate.

3) The objet a evokes desire and thereby bestows a depth to the subject’s life-world, so it’s associated with depth: z coordinate.

4) The subjective aspect of space-time is its temporality, so $ is associated with time: t coordinate.

Now it’s obvious why the prior mode and the posterior mode differ precisely at w=0: The subject $ stands for symbolic temporality, whereas the lack in the Other S(Ⱥ) stands for real temporality, in other words, S(Ⱥ) stands for w itself.

Using the coordinate associations above, let us articulate the fundamental fantasy of mathematics embodied in the following formula:

y = f(x)

It’s the impossible fantasy of deriving the Master-Signifier S₁ (y) from the knowledge S₂ (x); in other words, it’s the fantasy of becoming an informed master.

(Turkish)

Işık Barış Fidaner is a computer scientist with a PhD from Boğaziçi University, İstanbul. Admin of Yersiz Şeyler, Editor of Žižekian Analysis, Curator of Görce Writings. Twitter: @BarisFidaner

Notes:

[1] See “Fifth dit-mansion: w”, “Subjective Initiation and Objective Initiation”

[2] See “Beyond the Sexual ‘Relationship’”

[3] The combinatorial provides a real ground for spatiality, not merely a symbolic ground. See “Symbolic Ground and Real Ground”