57/ Affect Theory Conference: Worldings / Tensions / Futures MMXV

Affect Theory Conference: Worldings / Tensions / Futures
Stream #19 - Querying Fluidities: an affective aesthetics of space / touch / habit

Affective Warping of Manifolds: No Movement, No Brain
Andrej Radman

It would no longer involve raising to infinity or finitude but an unlimited finity, thereby evoking every situation of force in which a finite number of components yields a practically unlimited diversity of combinations. It would be neither the fold nor the unfold that would constitute the active mechanism, but something like the Superfold [...]. And is this unlimited finity or superfold not what Nietzsche had already designated with the name of eternal return? The forces within man enter into a relation with forces from the outside [...].[1] (Deleuze: Foucault)

Introduction
The presentation will consist of two parts which mirror the title and subtitle of the conference. The first part will position the discipline of architecture in relation to the Affect Theory. The second part will propose that the so-called perceptual illusions are not illusions. They are locally generated geometro-dynamical effects expressed as warping of manifolds due to lack of cohomological critical sets across scales. Surely a mouthful like that would qualify as the WTF.

1 Affect Theory and Architecture

1.1 Environmentalism
To embrace radical empiricism is to see cognition as belonging to the same world as that of its ‘objects’.[2] There is no need to postulate the existence of a more fundamental realm. There is no ultimate foundation but the immanence of powers, relations, and bodily compositions. Natura naturans (the engendering) and natura naturata (the engendered) are inseparable. As we shall see, for Gibson (J.J. not W) the formula is neither ‘mentalism’ nor conditioned-response behaviourism, but ‘environmentalism’.[3]

1.2 Radical Empiricism
The first step to break out of the correlationist loop is to acknowledge that - with or without us - matter does matter.[4] This is the crux of the Affective Turn. While affections (i.e. feelings) are endogenous, affect is impersonal, pre-individual and unmediated (exogenous). Paradoxically, feelings are states produced by thought, but thoughts are actually produced by affects. As William James surmised, it is crying that makes us sad and not the other way around. “We were virtual knowers [...] long before we were certified to have been actual knowers, by the percept's retroactive validating power.”[5]

1.3 Umwelt
For this reason architects ought to focus on affect (affordance), rather than on meaning (sign). In contrast to (the discursive) signification, expression is singularly determined (i.e. univocal). In other words, architecture is effective not because of its predicates, but rather for that absolutely singular event of its relationality that remains irreducible to determination. Consequently, the built environment (i.e. milieu) affects without determining any meanings a priori. It neither demands nor precludes any consensus.

1.4 Niche Constructionism
In this we side with the architecture theorist Jeffrey Kipnis who insists on the cleavage between engineering and architecture, i.e. between the subjugating effect of the former (engineering) and the liberating affect of the latter (architecture).[6] While engineering – as science or technology – delivers the greatest good for most people by reducing difference, architecture – conceived as art – offers emancipatory potential by creating new existential niches, i.e. new affects. The goal-oriented human action cannot be used as the design criterion because the freedom of action is never a de facto established condition, it is always a virtuality.[7]

1.5 Psychotropism
Architects, we thus want to claim, produce nothing but affordances or the way of affecting.[8] If to think differently one has to feel differently, and if the sole purpose of design is to change us, then architecture is a ‘psychotropic practice’ that modulates and compels routines of experience. Psychotropy is Daniel Smail’s version of what another brilliant Daniel (i.e. Daniel Stern) called the modulation of ‘affective tonality’.[9] It includes the mood-shaping of others (tele-tropy), things we do to ourselves (auto-tropy) and things we ingest (associated milieu?).[10] In the words of Smail:

The mood-altering practices, behaviors, and institutions generated by human culture are what I refer to, collectively, as psychotropic mechanisms. Psychotropic is a strong word but not wholly inapt, for these mechanisms have neurochemical effects that are not all that dissimilar from those produced by the drugs normally called psychotropic or psychoactive.[11]

1.6 Prometheanism
Smail refers to Christianity to exemplify the difference between tele- and auto-tropic practices. Christianity with its tele-tropic practices, such as liturgy and confession, is famously hostile to a range of (‘sinful’) auto-tropic practices, such as masturbation and alcohol consumption.[12] It could be argued that psychotropy is one of the fundamental conditions of modernity. Smail associates it with the advent of civilisation which “brought with it an economy and a political system organized increasingly around the delivery of sets of practices, institutions, and goods that alter or subvert human body chemistry. This is what gives civilizations their color and texture.”[13]

1.7 Neo-Vitalism
The reference to the so-called secondary qualities, namely colour and texture, is not coincidental and will be addressed below. Suffice it to say, for now, that the neo-rationalist division of the current speculative realist discourse (i.e. Brassier and Meillassoux, pace neo-vitalists) is eager to either eliminate these qualities from consideration altogether, or reverse the famous Lefebvrian dictum and turn the texture back into a text.[14] As far as we are concerned, any attempt to do so would be to commit the fallacy of what Whitehead called the bifurcation of nature; and to regress to representationalism.

1.8 Neo-Lamarckianism
As Catherine Malabou argues, the recent interest in the brain is not to be dismissed as neuro-reductionism.[15] Rather, it is the locus of the most promising research trajectory that places biology and history (i.e. nature and culture) on the same footing. Only humans are biologically compelled to modify and redesign their environment in an innovative and historical manner.[16] The (Neo)Lamarckian nature of cultural evolution (a.k.a. Baldwian evolution as acceleration) exposes the vulnerability of exclusively Darwinian explanations. Passive adaptation (i.e. ‘evo’) is complemented by active modulation (hence ‘evo-devo’). Geno-reductionists were eager to postulate that our behaviour was shaped by genes but could offer only vague ideas about how they actually did so. It has now become undeniable that the environment shapes the phenotypical expression of genes.[17]

1.9 Epigeneticism
The ecological school of perception was ahead of the Epigenetic curve: “ask not what’s inside your head, but what your head’s inside of.”[18] Epigenesis, let us remind ourselves briefly, is a theory of development in which forms are influenced and modified by environmental factors.[19] No wonder that it should appeal to architects (as niche constructionists) who could be said to sculpt brains by way of sculpting neither the genetic, nor the epigenetic, but the epi-phylo-genetic.[20]

1.10 Enactivism
The distinction comes from the philosopher of technology Bernard Stiegler who urges us to rethink the long-lasting legacy of privileging episteme over tekhne.[21] The ‘what’ (tekhne) invents the ‘who’ (the human) at the same time that it is invented by it. Strictly speaking, architecture as a sedimented epi-genetic mnemonic device has an even higher order of autonomy, which makes it epi-phylo-genetic.[22] If epigenetics is the concept of non-genetic heritability (such as language acquisition), then epi-phylo-genetic means that the rhetoric of “we build our cities and in return they build us” is to be taken literally.[23] Stiegler explains:

Epiphylogenetics [...] designates the appearance of a new relation between the organism and its environment, which is also a new state of matter. If the individual is organic organized matter, then its relation to its environment (to matter in general, organic or inorganic) [...] is mediated by the organized but inorganic matter of the organon, the tool with its instructive role [...]. It is in this sense that the what invents the who just as much as it is invented by it.[24]

1.11 Ethology
It is time for the discipline to awaken from the slumber of anthropocentrism and shake off the baggage of old dichotomies. Deleuze and Guattari propose that we drop anthropomorphism for geomorphism.[25] In the same vein, Keith Ansell-Pearson calls for a major reconfiguration of ethology (to become a theory of capacity): “Behaviour can no longer be localised in individuals conceived as preformed homunculi, but has to be treated epigenetically as a function of complex network systems which cut across individuals and which traverse phyletic lineages and organismic boundaries.”[26] Put simply, relation comes before that which it places in relation.[27]

1.12 Pragmatism
The ecological (immanent) approach must not rely on representation, which typically comes in the form of a model. The goal is not to understand how to construct a model of the world but how to use the world as its own model. James’ fellow pragmatist C.S. Peirce recognised the limit of the if/then logic (of induction and deduction) and argued for the what/if logic of abduction. This form of material inference proceeds from effect to cause, from observation to explaining hypothesis (Shaviro’s speculative extrapolation).[28] Famously, ecological perception takes relations to be as real as objects (relata). Furthermore, relations (as higher order facts or invariants) are not only real, they can also be directly perceived. It is a reality that is subject to scrutiny, i.e. indefinite differentiation. It unfolds in experience, but does not sit behind experience.

For example, take three static images of a frame within a frame defined not by outlines but by two superimposed textured surfaces (patterned, as they usually are in the environment). Let us now imagine that the surfaces start looming (as a result of forward locomotion), as revealed by the continuous transformation of the pattern (self-induced optical flow) within and without the inner frame: 

(Source: Carello and Turvey, The Ecological Approach to Perception)

a) If the rate of change of the inner and outer patterns is the same,
    the frames are flush (co-planear);
b) If the rate of change of the inner pattern is faster,
    it is a protruding obstacle (in front);
c) If the rate of change of the inner pattern is slower, it is a recessed opening
    (behind) which affords ‘walk-through-ability’.

1.13 Immanence 
The senses cooperate and fold upon each other, intensively cross-referencing disparate planes of experience. They are neither separate nor discrete. Nor are action and perception, movement and image. In Gesture and Speech, André Leroi-Gourhan shows that encephalisation “begins from the feet” more than from the head, since the brain ‘profits’ from locomotion but does not provoke it.[29] The necessary connection between experience and environment requires a continuum-thinking that is attuned to transformations of states (field of rapidities and slownesses) rather than identification of objects (figure-ground).[30] We ought to stop treating systems as isolated first (structure) and as interacting second (agency). In other words, we ought to think transversally (i.e. immanently).

Let us now turn to the second part.

2 Warping: WTF

2.1 Transversality
In their paper “Symmetry and Symmetry-Breaking in Thermodynamic and Epistemic Engines” the ecological psychologists Kugler and Shaw propose a different strategy based on the non-linear coupling of the thermodynamic laws.[31] We shall deal with the concept of symmetry (breaking) below, but let us first describe the other terms. ‘Engine’ stands for any system that supplies dynamics for another system (abstract machine). Traditionally, physics is taken to be the study of thermodynamic engines, while psychology is the study of its epistemic counterparts. Biology was meant to suture the gap between the systems with and without complex interiors.[32] The First and Second Laws are in effect the nomoi of repetition and difference, respectively.[33]

2.2 Superfold
The confinement of the same scale (either mi-mi or ma-ma) has inevitably lead to the paradox of mind/body dualism which has in turn fuelled various reductionist strategies. The revelation that linearity is but a rare case of nonlinearity has given birth to the eco-system, the cross-scale science par excellence (Superfold as irreducible complexity). The transversal coupling remains reversible across the same scale (symmetry-preserving), but crucially, it is irreversible across different scales (symmetry-breaking). The former can be summed up in the famous mereological maxim: the whole is the sum of its parts. The latter is eco-logical and does not offer such reassurance. In Superfolding, the synthesis is not the analysis in reverse.

2.3 Ecosophy
In ecology the whole is more or less than the sum of its parts (neg-entropy).[34] This is what Spinoza meant by “we don’t know (a priori) what a body can do.”[35] For any two (or more) interacting systems, there is a subset of solutions that can be used to understand the outcomes of their dynamical relationship. The ‘critical set’ that specifies shared symmetries between the respective systems of organisms and their environments is called affordance (higher order invariant), which is akin to the Deleuzian affect. Affect, it is important to remember, always cuts both ways. It is shorthand for the capacity to affect and be affected (relational ontology).

2.4 Metamodelling 
Thanks to Felix Klein we can define the whole of geometry as the study of invariants of a particular transformation group.[36] An invariant is exactly what it sounds like: a magnitude that does not change under the action of the transformation group.[37] Klein went on to classify all the known geometries and realised that they formed a ‘hierarchy’. In this hierarchy, as one progresses from Euclidean geometry, fewer and fewer properties remain invariant (and groups include more and more transformations), while, as one regresses, the geometric spaces become increasingly less bland or more detailed (striated).

Take a square for example. We are not going to define it in terms of the if/then propositional knowledge (essentialist ‘whatness’): “If it has four sides then it is a square (3 triangle, etc).” Instead, we will follow the what/if logic to (abductively) determine what happens if we manipulate it, in other words, what are its capacities. The cartography of invariants under transformation (that which is preserved in the face of change) will render visible the ‘hierarchy’ of different geometries (from the striated Euclidian to the smooth topological, including everything in-between):

Klein's Erlangen Programme: Different geometries as subgroups, classified by invariants under transformation.

2.5 Multiplicity
The Erlangen Programme showed that all geometry could be treated in the same way and that seemingly disparate geometries (racing car/horse) were in fact expressions of the same underlying principles. As such, it fits the Deluzian One=All formula of multiplicities that do not succumb to unities or totalities. The nesting of geometries is quintessential for the project of transcendental empiricism which is at cross purposes both with the naïve empiricism (positivism) and transcendental idealism. “The essential thing, from the point of view of empiricism, is the noun multiplicity, which designates a set of lines or dimensions which are irreducible to one another”, as Deleuze explains, “Every ‘thing’ is made up in this way.”[38] DeLanda offers the following genealogy of the (most) important Deluzian concept:

Although the creators of these classifications saw in them a purely logical construction [...] Deleuze views them as morphogenetic, as if metric spaces were literally born from non-metric ones through a loss of symmetry [...]. While in cardinal series judgments of exact numerical identity of two series can be made, in ordinal series only rigorous judgments of greater or lesser differences can be made. Deleuze, whose ambition was always to create the first philosophical system based exclusively on positive differences, made a great deal out of this link.[39]

2.6 Ontotopology
Where does it all leave us in terms of architecture? To adopt a topological approach to architecture and urbanism, we suggest, is to think in terms of capacities (to affect and be affected), rather than mere (intrinsic) properties.[40] As Gregory Bateson maintained, capacity is always relational: “It makes no sense whatsoever to try to understand the anatomy of half a chicken.”[41] While meaning is traditionally defined in terms of an organism’s perception governed by ‘intentionality’, affect is a-personal, pre-subjective, extra-propositional and sub-representational, i.e. immanent.[42] Experience is not an event ‘in’ the mind. Rather, the mind emerges from an interaction with the environment (ontotopology). Architects ought to know better; the so-called perceptual illusions are not illusions, but locally generated (geometro-dynamical) effects. Or as Deleuze would have it, things are powers, not forms.

Geometro-dynamical Effect: Manifested as warping of manifolds due to lack of cohomological critical sets across scales

Let us conclude by considering a well-known ‘optical illusion’, not as a self-induced effect on the part of the observer, but as the observer’s state-space which gets literally warped by what it detects. Kugler and Shaw explain:

By tracking the equidistant, parallel lines depicted by the trivial gradient sets of a flat space (B) to the left (A) and to the right (C), we see what failure of our nervous systems to solve the cohomology problem means perceptually.

2.7 Mereotopology
What cohomology actually measures, at its most elementary, is the failure of local solutions to glue together to form a global (cross-scale) solution. [43] It is the impossibility of patching the locally consistent data into a consistent whole. Simpler still, it is the impossibility of totalisation. Cross-scale science or what we referred to as ‘Superfold’ provides a frame-free means for explaining the (felt or perceived) discrepancies between local and nonlocal constraints. Kugler and Shaw continue:

The information for change in curvature of the lines is due to the failure of gradient sets (A), (B), and (C) to share a common homological solution. Hence the pair of lines conforms locally to the direction and distance metrics of the manifold to which they are most proximal. Our state space as observers is being warped by what it detects rather than causing the effect itself. The critical set properties [affordances/affects] have as much reality status as any other physical property, and more than most. Hence the lines are indeed curved, and they are not illusions! [emphasis added][44]

2.8 Logos Spermatikos
It was the Stoics who first proposed that things themselves are bearers of ideal events which do not exactly coincide with their properties. Any (actual) incarnation may in fact be seen as a (provisional) ‘solution’ to the problem posed by the virtual the same way that the eye is the solution to the problem of light. This is what makes the virtual problematic rather than ideal. However, this logic must not be reduced to the mannequin opposition between the quantitative actual and qualitative virtual. The difference between the difference in degree and the difference in kind is not reducible to either: “Between the two are all the degrees of difference - beneath the two lies the entire nature of difference in other words, the intensive.”[45] And indeed, for Deleuze it is the intensive nature of difference which binds the virtual and actual, the ideal and sensible, and provides the catalyst for individuation. Connected by an intensive process, the molecular and molar are irreducible to one another.

2.9 Conclusion
The geometro-dynamical effect is the Stoic incorporeal effect of the material cause which in turn operates as a quasi-cause.[46] It is of the same ilk as the process by which mass singularities curve space-time. The major difference is that such effects may be induced through neuro-perceptual fields into the engines of thought and experience. These pockets of inconsistency, Kugler and Shaw insist, are like local inertial frames. They show up as nonlinearities (not “perceptual errors”) at the more exacting level of systems integration.[47] Hence we do see the “illusions”, yet we do not see them as being consistent over local frames. The failure of homologies to mesh across scales (harlequin’s cloak) is unsurprising since the molar products have fewer degrees of freedom (i.e. less symmetry) than the molecular flows.

However, if we accept as really real only that which is cohomologically systematic (i.e. linear) across our experience, perhaps the fault lies more with our all-too-Phenomenological notion of experience than with the reality.

It is not a matter of judgement but of sensibility.[48]


Notes:

[1] Gilles Deleuze, Foucault, trans. Seán Hand (Minneapolis: University of Minnesota, [1986] 1988), p. 131.

[2] Harry Heft, Ecological Psychology in Context: James Gibson, Roger Barker, and the Legacy of William James's Radical Empiricism (Mahwah, NJ: L. Erlbaum, 2001), p. 73.

[3] James Jerome Gibson, The Ecological Approach to Visual Perception (New Jersey: Lawrence Erlbaum Associates, [1979] 1986), p. 2.

[4] Correlationism marks a self-reflexive loop (marked by finitude) where nothing can be independent of thought.

[5] William James, Essays in Radical Empiricism (New York: Cosimo, [1912] 2008), p. 32.

[6] Jeffrey Kipnis, et al (2015) “2015 Grad Thesis Prep Symposium” in SCI-Arc Media Archive. Southern California Institute of Architecture, http://sma.sciarc.edu/video/2015-grad-thesis-prep-symposium/. (accessed May 4, 2015).

[7] Robin Evans, “Interference” in Translation from Drawing to Buildings (London: AA Documents 2, 2003), pp. 16-17.

[8] James Jerome Gibson, The Ecological Approach to Visual Perception (New Jersey: Lawrence Erlbaum Associates, [1979] 1986), p. 127.

[9] Daniel N. Stern, The Interpersonal World of the Infant: a view from psychoanalysis and developmental psychology (New York: H. Karnac, 1985). Cf. Daniel Smail: On Deep History and the Brain (Berkeley: University of California Press, 2008).

[10] There is not only the exterior milieu and the organic interior milieu, Deleuze and Guattari suggest, but also the annexed or associated milieu, whereby sources of energy different to the material that will make up the interior are annexed to the organism. See: Gilles Deleuze and Félix Guattari, A Thousand Plateaus (London, New York: Continuum [1980] 2004), p. 51.

[11] Daniel Smail: On Deep History and the Brain, p. 161.

[12] Daniel Smail: On Deep History and the Brain, pp. 177-178.

[13] Daniel Smail: On Deep History and the Brain, p. 162.

[14] Steven Shaviro, Universe of Things: On Speculative Realism (Minneapolis: University of Minnesota Press, 2014), pp. 65-84. Cf. Henri Lefebvre, The Production of Space, trans. Donald Nicholson-Smith (Oxford: Blackwell, [1974] 1991), p. 222. “The actions of social practice are expressible but not explicable through discourse; they are, precisely, acted - and not read.”

[15] Catherine Malabou, “Anthropocene, a new history?”, https://www.youtube.com/watch?v=eDdTqr-5APg. (accessed September 30, 2015).

[16] Kwinter Sanford Kwinter, “Neuroecology: Notes Toward a Synthesis” in The Psychopathologies of Cognitive Capitalism: Part Two, ed. Warren Neidich (Berlin: Archive Books, 2014), pp. 313-333.

[17] Bruce Wexler, B. (2013), “Neuroplasticity, Culture and Society” in The Psychopathologies of Cognitive Capitalism: Part one, eds. De Boever and Neidich (Berlin: Archive Books, 2013), pp. 185–218.

[18] William M. Mace, “James J. Gibson's Strategy for Perceiving: Ask Not What's Inside Your Head, but What Your Head's Inside of” in Perceiving, acting and knowing; Toward an ecological psychology, ed. Robert Shaw and John Bransford (Hillsdale, NJ: L. Erlbaum Associates, 1977), pp. 43-65.

[19] Biologist Conrad Waddington (1905-1975) is often credited with coining the term epigenetics in 1942 as “the branch of biology which studies the causal interactions between genes and their products, which bring the phenotype into being.” The extent to which we are pre-programmed versus environmentally shaped awaits universal consensus. The field of epigenetics has emerged to bridge the gap between nature and nurture.

[20] Harry Francis Mallgrave, “Embodied Simulation” Sculpting the Architectural Mind: Neuroscience and the Education of Architect, https://www.youtube.com/watch?v=jbCIJ5ZQ6pA (accessed September 30, 2015).

[21] Bernard Stiegler, Technics and Time 1: The Fault of Epimetheus (Stanford, California: Stanford UP, 1998).

[22] Bernard Stiegler, “Who? What? The Invention of the Human” in Technics and Time, 1: The Fault of Epimetheus (Stanford, CA: Stanford University Press 1998), pp. 134-179.

[23] Ontogeny: development (developmental and organismic scales). Phylogeny: descent and branching (reproductive and evolutionary scales).

[24] Bernard Stiegler, "Who? What? The Invention of the Human," in Technics and Time, 1: The Fault of Epimetheus (Stanford, CA: Stanford University Press 1998), p. 177.

[25] Deleuze and Guattari oppose the Ecumenon or the abstract machine as it composes a stratum to the Planomenon of the plane of consistency (49-50; 56; 73). Although the Ecumenon composes the ‘unity of composition’ of a stratum by establishing “the identity of [exterior] molecular materials, [interior] substantial elements, and formal relations [limits or membranes]”, it is never unitary, but is broken by the diversity of epistrata and parastrata. See: Gilles Deleuze and Félix Guattari, A Thousand Plateaus (London, New York: Continuum [1980] 2004), pp. 49-50; 56; 73.

[26] These developments call for a major reconfiguration of ethology (as a theory of capacity). See: Keith Ansell-Pearson, Germinal Life: the Difference and Repetition of Deleuze (London: Routledge, 1999), p.171.

[27] Gilles Deleuze and Félix Guattari, A Thousand Plateaus (London, New York: Continuum [1980] 2004), p. 350.

[28] Charles S. Peirce, “Abduction and induction” in Philosophical writings of Peirce, ed. by J. Buchler (New York, NY: Dover [1903] 1955), pp. 302- 305. See also: Reza Negarestani,“Frontiers of Manipulation,” Speculations on Anonymous Materials Symposium (2014), http://www.youtube.com/watch?v=Fg0lMebGt9I. (accessed September 30, 2015).

[29] Encephalisation marks the massive expansion of brain (i.e., humanisation). See: André Leroi-Gourhan, Gesture and Speech (Cambridge, MA: MIT, [1964] 1993), p. 229.

[30] Lars Spuybroek, The Architecture of Continuity; Essays and Conversations (Rotterdam: NAi Uitgevers, 2008).

[31] Non-local generic (First Law) and local epigenetic (Second Law). See: Peter N. Kugler and Robert Shaw, “Symmetry and Symmetry-Breaking in Thermodynamic and Epistemic Engines: A Coupling of First and Second Laws”, Synergetics of Cognition, eds. H. Haken and M. Stadler (Heidelberg: Springer-Verlag Berlin, 1990), pp. 296-331. The first law of thermodynamics is that of “conservation of matter and energy,” which states that matter and energy cannot be created or destroyed. Matter and energy can be transformed, and energy can be converted from one form into another, but the total of the equivalent amounts of both must always remain constant. The second law of thermodynamics states that energy of all sorts tends to change itself spontaneously into a more dispersed, random, or less organised, forms (entropy).

[32] Deleuze opposes nomos, as distribution (smooth space), to logos, as law (striated space).

[33] By complex interiors we mean systems with intentional dynamics, i.e. with an operator by which local applications of the Second Law must be cohomologically conditioned by nonlocal constraints which preserve the integrity of the First Law.

[34] Whereas the Second Law has been viewed as a destructive agency that tears down order, a new view of the Second Law has emerged recently that views it as an active participant in constructive processes. Systems open to the import of high grade energy (replenishing processes) and the export of low grade energy (dissipative processes) can develop new symmetries that lead to new intentions exhibited as attractor states. The new attractors emerge out of the competition between the dissipative and escapement processes. The attractors are invariant solutions (symmetries) that relate the micro states of a system to macro states.

[35] Gilles Deleuze and Félix Guattari, A Thousand Plateaus (London, New York: Continuum [1980] 2004), p. 283.

[36] Claire F. Michaels and Claudia Carello: Direct Perception (Englewood Cliffs, NJ: Prentice-Hall, 1981), pp. 31-36.

[37] For some concrete examples of invariants (attractors as long term tendencies of systems), we can list the structural ones such as gravity and horizon; or transformational invariants such as seasons, diurnal cycle, etc.

[38] Gilles Deleuze and Claire Parnet, "Preface to the English Edition" in Dialogues (New York: Columbia UP, [1977] 1987), p. xii.

[39] Manuel DeLanda, “Materiality: Anexact and Intense” in NOX Machining Architecture, ed. Andrew Benjamin and Lars Spuybroek (London: Thames & Hudson, 2004), p.373.

[40] Manuel DeLanda, A New Philosophy of Society Assemblage Theory and Social Complexity (London: Continuum, 2009).

[41] This understanding of life is bound up with Deleuze’s analysis of sensation. Sensation is produced when the forces which flow over the body (at the nonorganic level) encounter an external force. For Deleuze, sensation exceeds the bounds of the organic body because it is registered at a level prior to the organization of the organic body and its organs. Sensation is not representational.

[42] Gregory Bateson, “Lecture on Epistemology”, http://www.archive.org/details/GregoryBatesonOnEpistemology (accessed September 30, 2015).

[43] The problem is how do modular quantities, when distributed under only local constraints, fit together globally over the manifold that they attempt to cover (e.g. tessellation).

[44] A solution to the cohomology problem requires that all of the available degrees of freedom in the space (or, space-time) be used up by the tessellation of cohomological modules. When this is so, then the entire causal efficacy of physical pseudo-forces or mental pseudo-forces is naturally assimilated into the curvature of the most fundamental space. Any leftover “force” effects must be residuals of the cohomological process, and will present themselves as nonlinearities. If the process continues sufficiently deep into the micro-scale, regions near chaos are entered and, perhaps, crossed. When this happens the old homologies of the base-space dissolve and new singularities emerge to reorganize the space into a higher-order.

[45] Gilles Deleuze, Difference and Repetition (New York: Columbia UP,[1968] 1994), p. 239.

[46] Deleuze acknowledges the Stoic influence both in his early The Logic of Sense (1969) and later in A Thousand Plateaus (1980), co-written with Guattari. The concept of quasi-cause (dark precursor) prevents regression into simple reductionism. It designates the pure agency of transcendental causality. The difference in itself relates heterogeneities.

[47] They are wrongly assumed to be self-induced alterations in one’s “mental” state space, either as neurogenic anomalies or cognitive “errors” that distort perception of the world.

[48] Gilles Deleuze, Gilles, Nietzsche and Philosophy, trans. Hugh Tomlinson (New York: Columbia University Press, [1962] 1983), p. 94. See also: Andrej Radman, “Sensibility is Ground Zero: On Inclusive Disjunction and Politics of Defatalization” in This Deleuzian Century: Art, Activism, Society, eds. R. Braidotti and R. Dolphijn, Leiden & Boston: Brill/Rodopi, pp. 57-86.