TENET describes the attempt to create a movement of resistance that is not registered by the big Other. No archives, only minimal information (a word and a gesture), loose ends are « tied up ». The structure of knowledge (cognitive map) is supplemented by a structure of feeling (But what does your heart tell you? »), and finally by a speculative decision (« I am the Protagonist »).
The film turns on the ontological parallax between the perspectives of Neil (Spinozist) and the Protagonist (Hegelian).
In TENET the apprenticeship of time follows the sequence laid down by Zizek in SEX AND THE FAILED ABSOLUTE in his explication of Lacan’s topology: the Moebius strip, the Cross-cap, the Klein Bottle.
The first step, which will become clear only later, is when our nameless Protagonist is taken out of his life, he is « vanished ». At this stage he has not yet decided that he is the Protagonist, so let us call him Prot.
Prot is inducted by a mysterious master, who recruits him, and gives him just the bare minimum of knowledge: a word (« tenet ») and a gesture (hands interlocking fingers) and the information that there is a Cold War (physics pun, where « cold » refers to entropy).
This master institutes a process of anamnesis, only inverted, of remembering a future that hasn’t happened yet. Even the word « tenet » is a piece of that future. Prot will later come to conclude that he will have been recruited by his future self by way of temporal inversion.
Thus begins Prot’s induction out of linear ideology and into the real world of temporal complexity. He does not know it yet, but he is being incorporated into a series of loops, of Moebius strips constituting his own timeline.
After encountering a series of inverted objects Prot finds himself in a struggle against inverted humans, and by means of a « Turnstile », a technology of inversion, proceeds to invert himself, travels back in time, and then de-inverts himself.
This is his first conscious experience of a temporal Moebius strip.
Prot has begun to learn dialectical (« nonlinear ») thinking and can thus work effectively in a « temporal pincer », that makes use of two simultaneous but inverted with respect to each other, Moebius strips.
This is his first conscious experience of a temporal cross-cap.
Whereas the Moebius strip permits him an awareness of the identity of opposites that remain antagonistic (fight scene with himself), the Cross-cap converges on a point of suture that is in danger of being de-sutured by the Algorithm to create a negentropic apocalypse.
The « bad » future, despite inventing the technology of inversion, seems to think in linear terms: create a massive inversion that eliminates the past, accomplish this by means of a few Moebius strips. This technological future is not capable of thinking dialectically in terms of cross-cap temporal pincers. This is its weakness.
The passage to the further stage of the apprenticeship comes about when Prot realises that he is not the pawn of some mysterious Other, but that he is working for himself (in his speculative identity of positing his presuppositions). The cause is simply the effect of its effects.
This is his first conscious experience of the Klein Bottle.
The space of thinking requires us to move outside the linear, in whatever direction, to the unorientable. To maintain this unorientability a different type of abstraction than the algorithm is needed.
This abstraction that comes to us from our future is called « tenet ».