Spatial and Combinatorial — Işık Barış Fidaner

Let me begin by taking the Deleuzian concept pair, actual-virtual, and propose an alternative concept pair, spatial-combinatorial: Actuality is spatial because it takes place in spaces, whereas virtuality is combinatorial because it consists of combinations of possibilities (“clouds” as Deleuze calls them) [1]. Now we can associate this pair with another pair from thermodynamics, macrostate-microstate: Macrostates include physical properties like temperature, pressure etc. assigned to spatial regions of a system, whereas microstates include possible combinations or arrangements of molecules in a system. This also aligns with Deleuze-Guattari’s molar-molecular. This brings us to a more general concept pair of physics, Energy-Entropy: Energy is defined through the spatial macrostate, whereas Entropy is defined through the combinatorial microstates. Thus we have redefined the Deleuzian actual-virtual in thermodynamic terms [2].

Intuitively, entropy is a loss of useful energy. The first law of thermodynamics states that the total energy is always conserved. However, useful energy is only a part of the total energy: Energy of a spatial system is useful insofar as it can be converted to other spatial forms. But some of the total energy is always inevitably and irreversibly lost: It gets off to the combinatorial realm. This loss of useful energy gives an intuitive description of entropy, which, according to the second law of thermodynamics, always increases.

So we can associate our concept pair, energy-entropy, with an intuitive concept pair, useful-useless: The word “energy” mainly signifies the useful part of the total energy, whereas “entropy” signifies the useless part of the total energy. Energy that remains spatial is useful energy, whereas energy that becomes combinatorial is useless entropy. This is a quite general conception that can basically be associated with the pairs, positive-negative, life-death. Thus Energy and Entropy are akin to Freud’s Eros and Thanatos [3]. And Lacan’s saying “Every drive is virtually a death drive” means that the phenomenon of Energy emerges from Entropy, i.e. macrostates emerge from microstates, actuality from virtuality (note the word “virtually”), the spatial from the combinatorial, the useful from the useless.

This is a parallax of two perspectives: The useful emerges from a gesture of dismissing the useless, whereas the useless is an “indivisible remainder” (Žižek) that is dialectically related to the useful. I recently expressed this parallax by associating Decryption with an aggressive perversity that is useful to a symbolic authority, and Decipherment with a sexual hysteria that appears useless but redefines use by its real authorization [4]. These two perspectives Decryption-Decipherment roughly correspond to Deleuze-Guattari’s concept pairs, territorialization-deterritorialization, paranoia-schizophrenia.

In the discussion above, we merely described entropy intuitively as “a loss of useful energy”, but we haven’t yet given it a proper definition. After realizing that macrostates emerge from microstates, we can define entropy as a measure of information: Entropy is related to the number of possible microstates; it’s the information necessary to reconstruct the microstate. Entropy as information can be associated with the equivocity of signifiers in psychoanalysis [5]. Since the equivocity in language expresses jouissance, we reach at another intuitive concept pair, pleasure-jouissance: Pleasure is useful energy, whereas jouissance is the loss of pleasure in useless entropy.

Pleasure is the part of jouissance that can be captured and assigned to spatial zones in bodies and systems by willful authorization [6] whereas jouissance itself remains to be the infinity of the combinatorial [7] whose manifestations can be found in the unconscious desires of the bodies and the failures, bugs, glitches of the systems.

(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] Virtuality is told to be something beyond the existing possibilities. But what is beyond a limit is defined by the limit itself, and “behind the curtain of phenomena, there is only what we put there.” (Hegel)

[2] The proper opposite of the spatial is not the temporal. It is the combinatorial. The temporal is the form that the combinatorial takes when it is bounded by the spatial. Spatiality and combinatoriality also correspond to Žižekian-Lacanian All and non-All.

[3] Goodstein’s States of Matter begins with these sentences: “Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. Perhaps it will be wise to approach the subject cautiously.” Another reason to associate entropy with death drive.

[4] See “Decryption and Decipherment”

[5] Univocity, on the other hand, is spatial. In a space everything has univocal coordinates. A coordinator’s job is to spatialize the combinatorial to attain univocity. Like Fredric Jameson’s “cognitive mapping”. The word “analytic” in analytic geometry signifies this univocity.

[6] For body, system, will, authority, see “What Makes a Symbolic Order?”

[7] Jacques-Alain Miller uses the term “combinative” in his otherwise mostly spatial approach to topology in Lacan: Topologically Speaking. He attempts to reconcile these two terms with the oxymoron “space of combinatives”. This reminds one of another oxymoron, “combinatorial space” in mathematics.