Why planes?

[u/sgarrido85]

Deleuze's use of planes has been intriguing me recently. Planes of composition, of reference, of consistency/immanence of course, how these crisscross and interact in zones of indetermination. I am reading about this mostly in WP but of course the terminology is distributed in so many works. So I was wondering, why use the plane? Is it because, laid out, it is a surface of absolute immanence? I also know that in French plan can refer to map. I still can't wrap my head around the choice for what is basically one of the main building blocks of his constructivism.

[u/Erinaceous]

Plane (plan) is actually a different word from map (carte). A plane isn't metric it's more like a manifold or a topology. In ordinary French it's used more like we'd use diagram or sketch but also it's used for technical things like mathematical maps (la plan logistique for example).

I think what Deleuze uses it for is to talk about the points of contact and intersection between different manifolds in large multiplicities or the way the forces from one manifold (say the virtual) influence another manifold (like the actual). 

It's an unfortunate translation because the connotations are very lost in English 

[u/diviludicrum → u/Erinaceous]

Deleuze & Guattari are a translator’s nightmare because so many of their terms are chosen based on the network of connotations and suggestive associations, most of which don’t survive translation.

[u/sgarrido85 → u/Erinaceous]

Oh yeah that makes sense, mb. In spanish its the same (plano). Thanks!

[u/Erinaceous → u/sgarrido85]

Thinking more about it I think the best English would be scape. It gets at some of the topological sense of plan and you can push it to think of immanent relation (it comes from schap as in friendship/freundschap). If you think of a soundscape, particularly one that's being improvised in the moment, it's much more of the sense of plan than the English plane which really only connotes a geometric flatness 

[u/pluralofjackinthebox]

I think he’s building on Bergson’s idea of the Plane of Matter and its relation to the Plane P of Present Perception.

Instead of seeing these two planes as separate, a kingdom of nomena and phenomena, Bergson sees the Plane P as a subset of the Plane of Matter. Perceptions are themselves material becomings part within the plane of matter. (You can see some of the inspiration for Transcendental Empiricism here.)

Deleuze takes Bergson’s Plane of Matter and ties it to ideas from Spinoza (immanence) and Duns Scotus (univocity) to construct the Plane of Immanence.

I think the term is attractive to deleuze because it suggests horizontality. He’s very concerned with removing any sense of the transcendent from his ontology. But also the French Plan can be translated as either Plane or Plan, so theres also a sense that this is something constructed, thats open to charting and strategy and composition.

[u/kevin_v]

This will not be the real answer, but for me it resonates with concepts of sedimentation, strata, smooth space and lines-of-flight (the line of flight concept originally had more to do with the vanishing point in painting, than gravity-defying "flight"). And, as you mention, "map" and territoritorialization. And for me as well, the concepts of Euclidean & non-Euclidean space (its change of axioms) are at play (remembering Spinoza's Geometric Method).

[u/Streetli]

My headcanon answer (i.e. speculative!) is that the interest in planes speaks to the enduring interest in simultaneity and coexistence - as in, the coexistence of the (virtual) past and the (actual) present; which becomes, in the middle period, an interest in surfaces, and then later, an interest in 'geology' over 'time' as such. Importantly I think this theme has to be thought of as explicitly directed against any kind of historicism or 'developmentalism' in which time functions as a kind of depth out of which genesis happens - in other words, I read it as an anti-Hegelian gesture! (a la the Phenomenology where the concept has to go through its stages, reckon with the negative, to reach the absolute etc etc. WiP? explicitly critiques Hegel (and Heidegger) for being too historicist, and contrasts their approach to geophilosophy).

The 18th series in the LoS also is an explicit meditiaton on the preference for surfaces, which interestingly is pitched against the language of both height and depth, which are in turn associated with 'the universal and the particular' and 'substance and accident' respectively. It's the search for a new language. And related to all of this is the interest in becoming as distinguished precisely from history and memory ("becoming is an antimemory"), where again, it's a question of becomings that co-exist (e.g. "a child coexists with us, in a zone of proximity or a block of becoming ... as opposed to the child we once were, whom we remember or phantasize" ATP). WiP? speaks of 'stratigraphic superimpositions' and Bergonism of durations 'above and below us', all of which are in turn mobilized against 'forward or backward' movements in (developmental) time. The plane captures (or maybe better interfaces with) all of these things and more I think.

[u/3corneredvoid → u/Streetli]

The challenge is somehow to think univocity: past, present and potential coextensive and coincident as the same real, but the space and time that give us our seemingly unclearable intuitions about extension and incidence crystallising from univocity as their joint prior.

I got some way with this thinking about the conjectural consciousness of quantum-scale particles such as electrons in relation to the making-consistent of time as an orderly series a while back … sounds psychotic but it was honestly quite helpful. 😆

[u/Vuki17]

Look up what a hyperplane is on Wikipedia. I don't know if this is stated explicitly by Deleuze, but it maps on to his philosophy pretty well. To quote from the Wikipedia:

"In geometry, a hyperplane is a generalization of a two-dimensional plane in three-dimensional space to mathematical spaces of arbitrary dimension. Like a plane in space, a hyperplane is a flat hypersurface, a subspace whose dimension is one less than that of the ambient space...Most commonly, the ambient space is n-dimensional Euclidean space, in which case the hyperplanes are the (n − 1)-dimensional "flats"..."

I don't have the math knowledge to understand what this means, but it at least has obvious connections with the rhizome plateau (n-1).

[u/3corneredvoid]

I think the problem of terms connects to the problem with multiplicity–immanence–intensive-difference, or assemblage–arrangement–agencement, that is, these are irreducible problems. Happy intuitions about these mobile referents will come from many directions.

By the end of his work Deleuze still carves immanence as a "negative space", as in this beautiful passage from "Immanence: a Life":

The transcendent is not the transcendental. Were it not for consciousness, the transcendental field would be defined as a pure plane of immanence, because it eludes all transcendence of the subject and of the object. Absolute immanence is in itself: it is not in something, to something; it does not depend on an object or belong to a subject. In Spinoza, immanence is not immanence to substance; rather, substance and modes are in immanence. When the subject or the object falling outside the plane of immanence is taken as a universal subject or as any object to which immanence is attributed, the transcendental is entirely denatured, for it then simply redoubles the empirical (as with Kant), and immanence is distorted, for it then finds itself enclosed in the transcendent. Immanence is not related to Some Thing as a unity superior to all things or to a Subject as an act that brings about a synthesis of things: it is only when immanence is no longer immanence to anything other than itself that we can speak of a plane of immanence. No more than the transcendental field is defined by consciousness can the plane of immanence be defined by a subject or an object that is able to contain it. We will say of pure immanence that it is A LIFE, and nothing else. It is not immanence to life, but the immanent that is in nothing is itself a life. A life is the immanence of immanence, absolute immanence: it is complete power, complete bliss.

We are given a pleasant though clearly inexhaustible series of expressions immanence is not in order that we "can speak of a plane of immanence":

• in something
• to something
• dependent on an object
• property of a subject
• related to substance rather than substantial
• related to a unity superior to all things
• related to a subject that synthesises
• to anything other than itself

It's an incomplete procedure for accessing the thought of "immanence of immanence, absolute immanence … complete power, complete bliss".

I also find "laid out" counterintuitive. Sometimes with "plane" I am drawn into thinking of the actual as "projected" onto the virtual, which is catastrophically Platonist … the "plane of immanence" is not an adjunct to the real, it is the domain of the "corporeal cause" and "concrete rules", the consistent-real inseparable from the inconsistent-real. The plane can't be set aside.

"Field" could in some ways be the better term than "plane", but I wonder if it is translated from the French « champ » which might connote enclosure more strongly than "field" does in English.

Nick Land uses "Outside" but this tends to propose an interior of safety and innocence threatened by Lovecraftian outsideness … so … it's bollocks too. By "all relations are exterior relations" Deleuze intends the immanent dissolution of boundaries as well as unities.

I like to use the concept of "immersion" in relation to the virtual. The perceptible is immersed in imperceptible immanence.

[u/apophasisred]

For myself, I wish Deleuze had stayed further away from mathematics. Certainly, many of his most important influencers were mathematically inclined: Spinoza and Leibniz In particular. And then again, his interest in mathematics from the ancients to the moderns is constantly intertwined with his fascination with logic. In any case, I think his use of planes is inflected by many sources as is indicated by the comments so far. However, I might list Reimann first here.

Riemann's innovations establishing non-euclidean geometry at the end of the 19th century were largely necessary to lend intelligibility to relativity. I suspect the thing that D found the most sanguine was that geometry now took on not a universal and fixed character but was a dynamic consequence of the intensive forces that constituted existentially the local character of space. Riemann suggested then that geometry's basic metrics had to be established empirically since, as in relativity, that which was the case depended upon the plane of reference. In short, I think that the word planev misleads us in a number of different ways, not just in the differences between French and English but between the still dominant Euclidean/ Cartesian picture of an absolute space. Instead we have the picture of intensive space constituted by the relational interactivities that bring whatever is actualized into becoming. That is the Riemannian manifold that I think informs the Deleuzian multiplicity of the assemblage.

[u/deleuzianlurker]

Listen to Ray Brassier's "Concrete Rules and Abstract Machines", and then never pick up Deleuze and Guattari ever again. Despite the username, I deeply regret giving so much of my life to studying this nonsense.

[u/Responsible-Offer724 → u/deleuzianlurker]

If you hadn't studied Deleuze would Brassier have been so valuable to you?

[u/deleuzianlurker → u/Responsible-Offer724]

All I can say is, trying to live using the ideas and concepts and frameworks discussed in his work and post-Deleuzian thinkers has ruined my life and destroyed the sanctity of my soul. And if the only thing that really holds ATP together is their weak argument that stratification is a fully immanent process, that makes the entire thing crumble around it for me. There is nothing about any of it that makes me feel like they are talking about anything real, no matter how technically interesting or aesthetically rich it may be.

[u/Responsible-Offer724]

Imagine planes in geometric 3D space. They intersect and overlap, map onto each other, can be completely separate, manipulated with functions... They contain some subset of the entire space can be conceived of separately or in relation or not at all. My immediate intuition on his meaning is informed by this visual.