Matt Segall has in a pluralistic spirit posted a counter-rumination to my preceding ruminations, so I am cross-posting my comment here.

Deleuze and Guattari are not proposing a new Grand Narrative, but just one possible micro-story. Another story of movement may be more to your taste. Deleuze claims that the notion of movement has changed from that produced by the application of an external force. “All the new sports – surfing, windsurfing, hang-gliding – take the form of entering into an existing wave.There’s no longer an origin a starting point, but a sort of putting-into-orbit” (NEGOTIATIONS, 121). So I think you can have your orbit and your horizon too. The movement is noetic, this is why Deleuze and Guattari talk about the “eyes of the mind”, and so finds its place in the noosphere. I think the “bad” verticality is the move away from the Earth, considered as a Cavern of Illusion, but the getting into orbit story shows that verticality is not an essence to be universally proscribed. Also the text talks about running to the horizon AND coming back, so there is a notion of gravity, one could call it “horizontal gravity”. Deleuze and Guattari are in favour of multiple dimensions, what they call “n minus one” dimensions. What is subtracted is not necessarily verticality in a literal sense but a dimension dominating all the others, in whatever direction. So the transcendental sphere, as a multiple dimensioned mega-hyper-sphere, is a good image of that. If you look at the movements described in LOGIC OF SENSE and also in the CINEMA books you have lots of descriptions of intensities as rising and falling, so intensive verticality is OK for Deleuze. Don’t forget that Deleuze has two time axes that intersect perpendicularly in his diagrams, virtual time or AION and actualised time or CHRONOS, so the image of the cross is not absent from Deleuze’s imagination of the cosmos (despite what many think).

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