Topology is a writing. As Henri Frignet elaborates, it is not a “representation” but a “presentation of the Real.” My interest in topology is hinged precisely on this point: if something signifies, at the level of a sentence or in the battery of discourse, it can be written as a Real that can be read. While this page is by no means intended to enumerate topological principles, I must explain a bit in order to define my aim in having combined, into one subheading, topology and artificial intelligence.

Topology, as Lacan espouses in his seminar of '78, is time. Not the logical time of the Symbolic register, which characterizes a measurable, ordinal relationship between existence and chronology, but chronological time itself: the physical apparatus in the psychical mechanism which implies a distance between psychical phenomena. It is the chronological time—a Real time—which topology can write and read.

Discursively speaking, this suggestion alone has a fascinating repertoire of consequences. In the political discourse, for example, I find topological time to be absolutely paramount to understanding censorship (a la Pierre Legendre): we can trace, not logically, but chronologically, the deformations of Power as it is filtered through a signifying machine of the censor, preserving unexpected traces of these mutations which continue to impose signifying consequences today. In the social field, a synthetic manifold of speaking beings, we can usefully deploy topology to chart the expression of acts, slips, and the generation of new discourses. Furthermore, we can see, clearly, the artificial nature of neurosis as something wholly concocted by the Law; I will leave this point intentionally vague, as, I believe, it represents Freud’s most dangerous and radical discovery.

Where I find topological writing to be most fruitful is as a screen for the scientific. The way topological writing picks up on the (forgotten, repressed) subject of science is absolutely fascinating. In terms of our contemporary bombshell of technological progress, artificial “intelligence”, I see topology as of particular merit as it discovers the traces of enunciation. In a way which can only be obvious to the literate, AI does not speak: yes, the whole thing is language, but it is an alchemical writing. It cannot enunciate, qua a “self”, and, thus, misses the synthetic property necessary for articulation. In other words, and I am stretching to conclusion prematurely, it is an unconscious: a flat geometry where holes exist on its surface, but do not create an edge. There is no slippage, there is no consciousness that it bleeds for fodder through lapsus or fault. Instead, this mechanical unconscious sleeps, dreams, and exposes its chronology as an amalgam of productions.

I am concerned with the introduction of this edge in the form of repression. Perhaps, at the mercy of science fiction, we will see this “intelligence” undergo an unprecedented subjectivization--not as a human being does in the social universe, but as something that remains to be seen. I believe that, given the logic of the introduction of the letter as espoused by Lacan, we might see the area of semblance--that which is determined in the subject by a logical repression of elements from a binary chain--develop on the spearhead of "quantum" computation. Given the recent innovations in stable, superpositional computing technologies, like Google's "Willow," this may occur long before it is understood. I am convinced that psychoanalysis will have new utility as this comes to fruition.