deleuze, the fold leibniz and the baroque

5/27/2018 Deleuze, The Fold Leibniz and the Baroque

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T H E F O L DLei bn i z and the aroqueGilles Deleuz e

Forew ord and translation by Tom Conley

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Contents

www.continuumbooks.comFirst published in Great Britain 1993 by The Athlone Press,Reprinted 2001Reprinted 2003, by ContinuumThis edition, 2006a ) The Regents of the University of Minnesota 1993First published in France asLe ph: Leibniz e t he baroque( i i ) Les Editions de Minuit, ParisBritish Library Cataloguing in Publication DataA catalogue record for this book is available f rom the B ritish libraryISBN 0 8264 9076XAll rights reserved. No part of this publication may be reproduced,stored in a retrieval system, or transmitted in any form or by anymeans, electronic, mechanical, photocopying or otherwise, withoutprior permission in writing from the publisher.

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Translator's foreword: A plea for LeibnizxI The oldhe pleats of matterThe fold that goes to infinity The Baroque home the lowerfloor: matter, elastic forces, springs Organism and plasticforces Organic folds Why another floor is needed, aproblem of the animal soul The elevation of reasonablesouls, and its organic and inorganic consequences he folds in the soul5Inflection Singularities Baroque mathematics and varia-tion: the irrational number, the differential quotient, thefamily of curvatures The new status of the object Perspectivism: variation and point of view The new statusof the subject From inflection to inclusion The subdivision The monad, the world, and the condition of closure3 What is Baroque?0The room without windows The inside and the outside, thehigh and the low Heidegger, MaHarm and the fold

Baroque light The search for a concept The six estheticqualities of the Baroque Modern or abstract art: textures andfolded forms nclusionsufficient reason7Events or predicates The four classes of beings, the genres ofpredicates, the nature of subjects, the modes of inclusions, thecase of infinity, the corresponding principles Leibniz's


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CONTENTSONTENTSmannerism The predicate is not an attribute The fivecriteria of substance Styles and depth The play ofprinciples5 Incompossiblity indviduality liberty 67Incompossibility or the divergence of series The Baroquenarrative Preindividual and individual singularities Theplay of the Baroque world Optimism, the world's misery,and Mannerism The question of human liberty Aphenomenology of motifs Inclusion of the predicate andthe living present Leibniz and Bergson: movement as ithappens Baroque damnation6Wat isaneven?86Whitehead the successor Extension, intensity, the indivi-dual Prehensions and monads Eternal objects Theconcert Modern Leibnizianism: suppression of the conditionof closure, and the neo-BaroqueH HavngaBody9Percepioninthe fods 9The requirement of having a body First stage of deduction:from the world to perception in the monad Minuteperceptions: the ordinary and the remarkable Differentialrelations Recapitulation of singularities Psychic mechan-ism and hallucinatory perception Dusts and folds in the soul Second stage: from perception to the organic body Whatdoes perception look like? Organs and vibrations: thephysical mechanism of excitation Pleats of matter Thestatus of calculus8 The two floorsThe two halves: the ones and the others, the 'each' andevery M athematics of halves The role of the extrema Virtual-present, possible-real : the event Leibniz and H usserl :the theory of appurtenances Body and soul: appurtenanceinverted, provisional appurtenances Domination andvinculum The three species of monads: dominant, domi-nated, defective Crowds, organisms, and heaps Force Private and public Where does the fold go?

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Thenewharmny 39Baroque clothing and matter clothed The fold to infinity:painting, sculpture, architecture, and theatre The unity ofthe arts T he world as a cone: a l legory, emblem, and device Leibniz s concettism Music or higher unity Harmonics: themonad as number Theory of accords The two aspects ofharmony: spontaneity and concertation Harmony, melody,and Baroque music

Notes 15 9Index 193

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Translator s forewordA plea for Leibniz

Soon after finishing what would bear the title of The Art of the West anesthetic history of the High Middle Ages, Henri Focillon theorized theexperience of his research in Vie des formes 1Reflecting on the emergenceof the Rom anesque and Gothic styles, Focil lon confronts di lemmas facingall historians of the Middle Ages and ancien regime. How do styles develop,and why do they differ so markedly? Do they succeed one another orshare pertinent traits? Do esthetic styles convey, in a broader sense, thenotion of particular 'manners of thinking'? Can styles be periodized and,if so, what are the ideological motivations betraying the historicalschemes that also tend to produce them?In the context of French literary and esthestic history in the aftermathof the First World War, Focillon departs from traditions of esthetic andliterary botany that date to Sainte-Beuve and Auguste Comte. For them,tables, categories, genealogical trees, and lines of phyla could map outgreat mnemonic systems. They would soon program the ways the Frenchnation would construct its patrimony. Students of these para digms wouldforever recall the grids, fill them with appropriate facts and traits, andthus be 'informed' by schemes of knowledge. To the contrary, Focillonnotes that the Romanesque and Gothic, two dominant and contrastivestyles, often inflect each other. They crisscross and sometimes fold vastlydifferent sensibilities into each other. The historian is obliged toinvestigate how the two worlds work through each other at differentspeeds and, in turn, how they chart various trajectories on the surface ofthe European continent.

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TRANSLATOR S FOREWORDRANSLATOR S FOREW ORDIn V ie des formes, Focillon rethought the logic of evolution that hadbeen bequeathed to the twentieth century. On the one hand, aremarkably firm tradition of inquiry, observation, and historicizationcame with positivism. Yet, on the other, the really creative positivists ofthe nineteenth century Ba lzac, Hugo, and Proust built works whosemass, fragmentary totality, and changing effects impugned the tabledsymmetries that their scientific counterparts had invented. The history ofthe Romanesque and Gothic appeared, in the eyes of Focillon, no lessmassive in its overall effects than the poems and novels of nineteenth-century literary masters.At certain points, Focillon s overview of the Middle Ages resembles amix of technical history and organic chemistry. Forms move back andforth, disappear, recur, or bring out new shapes when they aresuperimposed or interconnected. Gothic maidens at Reims indeed smilewhere Romanesque peasants at Vezelay had been staring, exorbitantlyand aghast, at the onslaught of the Second Coming. Both stylesexperience a Baroque phase. Romanesque buildings, and sculptures ontympana and capitals, with their solemn aura, share features that can beidentified best by categories whose descriptives belong to a later period. In a similar vein, the textured effects of 'irreality' in the flamboyant in thefifteenth century tend to narrate the entire history of the adventure of theogive, and flow into the life of culture in general.Through the theory gained from his observations, in Vie des formesFocillon calls into question the rationale of periodization. With figuresborrowed from biology, he bends many of the schematic lines ofpositivistic forebears. At the same time, adapting Wilhelm Worringer'snotion of the 'Gothic' as what signifies a will for movement runningthrough the entire Middle Ages, Focillon assails the gap that existed, inthe entre-deux-guerres, between French and G erman culture. He writes of ahistory of art composed of differently paced but intermingling phases. An'experimental' beginning seeks solutions to problems that a 'classical'moment discovers and exploits. A 'radiating' rayonnant) period refinesthe solutions of the former to a degree of preciosity, while a 'Baroque'phase at once sum s up, turns upon, contorts, and narrates the formulas ofall the others.

The Baroque thus does not comprise what we associate with Bernini,Borromini, or Le Brun. The Baroque state reveals identical traits existingas constants within the most diverse environments and periods of time.Baroque was not reserved exclusively for the Europe of the last three

centuries any more than classicism was the unique privilege ofMediterranean culture.' 'Baroque' designates a trope that comes fromthe renewed origins of art and has stylistic evidence that prevails inculture in general. Under its rubric are placed the proliferation of mysticalexperience, the birth of the novel, intense taste for life that grows andpullulates, and a fragility of infinitely varied patterns of movement. Itcould be located in the protracted fascination we experience in watchingwaves heave, tumble, and atomize when they crack along an unfoldingline being traced along the expanse of a shoreline; in following the curlsand wisps of color that move on the surface and in the infinite depths of atile of marble; or, as Proust described, when we follow the ramifying anddilating branches of leaves piled in the concavity of the amber depths of acup of tea.Gilles Deleuze appears to share these same sensations in his dazzlingreading of Leibniz. The Fold tells indirectly of the reincarnation of theFranco-German philosopher through the Baroque, as understood byFocillon in its broadest and most influential way, that radiates throughdifferent histories, cultures, and worlds of knowledge. Deleuze's workmay be the first and most daring venture to take the Baroque, in thespecific figure of the fold, through the history of art, science, costume,mathematics, lyric, and philosophy. The Fold might also stand as one ofthe most personal, sensuous, and original of all of Deleuze's writings. Atthe same time its breadth might also strike readers as difficult and opaque.At first glance, the book is disarming. The implied reader is taken to be asfamiliar as the author is with atomic theory, differential calculus, classicaland contemporary painting and music, and with the history of logic. Yetthe pleasure Deleuze affords comes with the confidence he invests in thereader: the work is composed a s if spoken to a friend relaxing on a sofa bya w indow of a sm all apartment, on a second or third floor, that overlooksa large city. Without pretension Deleuze speaks of marvelously difficultequations in differential calculus, biological and fractal models, of theperformance of the music of Pierre Boulez, and of esthetic history. Thebook s tone flatters us at the same time it dismantles without posture orgrandiloquence some of the most shopworn beliefs we have inheritedabout the texture of our physical world. In what remains of this preface Ishould like to touch on what Deleuze appears to be doing with Leibniz,and how his affiliation with the philosopher affects what we discernabout contemporary issues.

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TRANSLATOR S FOREWORDRANSLATOR S FOREWORDDeleuze argues that while the Baroque has been a disputed term in thefine arts, esthetic history, and music, it has not been associated witheither a philosophy or a philosopher apt or complex enough to embodyand theorize its principles. For Deleuze, Leibniz happens to be thephilosopher of the Baroque. Leibniz is so contemporary that the ensembleof his research on science and mathematics, or his treatments ofcontradiction, belief, music, and theology help to explain or unfold what we know about the world at the end of the twentieth century.

The experience of the Baroque entails that of the fold. Leibniz is thefirst great philosopher and mathematician of the pleat, of curves andtwisting surfaces. He rethinks the phenomenon of 'point of view,' ofperspective, of conic sections, and of city planning. Included in thecategory of things folded are draperies, tresses, tessellated fabrics, ornatecostumes; dermal surfaces of the body that unfold in the embryo andcrease themselves at death; domestic architecture that bends upper andlower levels together while floating in the cosmos; novels that invaginatetheir narratives or develop infinite possibilities of serial form harmonicsthat orchestrate vastly different rhythms and tempos; philosophies thatresolve Cartesian distinctions of mind and body through physical means without recourse to occasionalism or parallelism grasped as foldings;styles and iconographies of painting that hide shapely figures in rufflesand billows of fabric, or that lead the eye to confuse different orders ofspace and surface.Now in The A rt of the West, Focillon remarks that the age of the'Baroque Gothic' witnessed the birth of the mystical experience. It ischaracterized, as other thinkers have since shown in greater detail, by anindividual's account of his or her voyage to and from an ineffablyuniversal event, which set the body in a trance, and which has left marks,scars, or other physical evidence that confirm the individual's tale ofpassage. The mystical venture convinces because no language can besaid to represent what it means. It is tantamount, in part, to whatDeleuze, by means of Leibniz, Henri Michaux, and Gaetau Clerambault,might call an event: it may not have an empirical or historical basis, but ithappens to be the virtual sensation of a somatic moment of totalizationand dispersion. In the novel or poetry, it can be felt as a seriality ofepiphany. Its scientific analogies might include the thoughts of infinitythat come with the view of the world in which all of its visible objects aremoving aggregates of infinite numbers of atoms and molecules. In thevision of Alfred North Whitehead, a philosopher inspired by Leibniz, an

event can be seen in the duration that produces the site of a pyramid, anavalanche of snow, or the jagged edge of rifts in a block of ice. ForDeleuze, an event unfolds from the union of our perception and theduration of a fan of the kind Mallarme describes in his occasional verse that unites and disperses a word (an even t and an object (an eventailwhen it swirls the atmosphere.

These rarefied areas of sensation constitute a mystical and mathemat-ical dimension of the Baroque. Leibniz, declares Deleuze, stands as thefirst philosopher able to deal with the experience of events and the worldof atomic dynamics. Deleuze himself appears to be mystical insofar asmuch of The Fold especially in the arguments that develop fromsufficient reason, incompossibility, perception, and the apportioning ofspace (in chapters 4 through 8) develops through absolute identity withLeibniz. A reader often notices an indirect discourse that melds with themovement of the New Essays on Human Understanding or the correspon-dence with Arnauld. Deleuze, whose voice translates better than any theexperience of contemporary time, is harm onized with that of the Franco-German philosopher at the threshold of the Enlightenment. As we listento Deleuze, in the intimacy of the Baroque home in which The Foldappears to be taking place (figure 1 in the first chapter), we perceivephilosophical and ethical dilemmas on the horizon of our lives.Reincarnation of Leibniz follows a pattern of force. Deleuze has oftenidentified with philosophers of the past not always the m ost renowned in order to confront political and ethical issues of the present. When hewrote on Nietzsche in the early 1960s, Deleuze was Nietzsche: helaunched a transvaluation of a culture, mired in existentialism, that hadnot completely assimilated the effects of its colonial history. He thenbecame Spinoza and Bergson at a time when intellectuals collectivelycried for a 'return' to Freud. To extend and modify the canon ofphilosophical writing, he wrote on Kafka, Melville, and, later, FrancisBacon. Yet Leibniz has always been a powerful force in all of Deleuze'swriting, and at this stage of the philosopher's career The Fold comes as nosurprise. The earlier writings (especially Logique du sens often mentionLeibniz with admiration, or use the Monadologie to recall the complexityof scientific theory in the ancien regime, but they never develop intoidentification with Leibniz's signature.A truism of French intellectual history states that for national andphilosophical reasons every postwar thinker, from Jean Hippolyte toJacques Derrida, must contend with Hegel. Deleuze had resisted the


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TRANSLATOR S FOREWORDRANSLATOR S FOREWORDtotalizing effects of the dialectic by aligning himself at once w ith Cartesianand left-wing political traditions. He made moves that showed how, byway of Spinoza, a more complex, fragmented, and prismatic philosophyantedated Hegel and could not be supplanted by systematic dialectics. Inthis light the study of Leibniz implies that an extraordinarily delicatefiligree of concepts, winding through organic and inorganic worlds, has tobe retrieved. Leibniz is thus also a philosopher of habitat and ecology. Hismyriad connections and series of concepts are not held in a prescribedorder or a unifying system. Multiplicity and variety of inflections produce'events,' or vibrations, 'with an infinity of harmonics or submultiples.'Movement of a concept that has bearing upon a subject's impressions ofthe physical world does not elevate according to a spiral plan, whichbelongs to philosophy, but radiates or ramifies everywhere in thegeography of experience, such that we can imagine movement of lightand sound, together, as folds of ethereal matter that waft and waver.An exquisitely sensuous view of the world is obtained through thecurved shapes that Leibniz creates with calculus, and from manifestationsof folds that we follow in modern art and poetry. Deleuze implies that if achronology of the history of philosophy is mapped over the kinds ofvibrations and events developed from the Gothic period until now,something goes awry. Leibniz is not merely a chapter in the history ofmathematics, cognition, or logic. The relation of monadic thinking to oursense of the world cannot be discounted; the movement of his reasoningshares many common traits with what theorists of science, musicians,and artists are now making of habitat.Leibniz, he implies, develops a philosophy that bridges the pre-Socratics, Lucretius, and neo-Einsteinian thinkers. In light of earlier work(Proust et les signes) and his most recent writing (Qu est-ce que la philosophie?with Felix Guattari), The Fold joins philosophy to the ecology ofhypothetical experience. In his study of In Search of Lost Time. Deleuzenoted that Proust's mission bore a Platonic label. The quest would restoreart and lead to an enduring and redemptive idea. But what the text seeksto redeem is riddled from within by a stylistic practice that scatterseverything that would comprise a 'whole' or a 'unity.' Yet since the workis finished in its incompletion, 'there must be a unity which is the unity ofthat multiple piece, of that multiplicity, as in all of those fragments.' 6Deleuze's stress on the partitive shows how Proust's great project of atotal novel betrays a 'communication that would not be posited as aprinciple, but would result from the play of [textual] machines and their

detached pieces, of their unconnected parts' (196). It is Leibniz whoinspires this observation, since the seventeenth-century philosopher 'firstposed the problem of communication resulting from closed units or fromwhat cannot be attached' (196). By means of Leibniz's innovation, whichmarks the limits of communication, the subject is enveloped in thepredicate, just as Proust's intention is folded into his effect. Inclusion ofthe subject in the predicate implies that the world makes up a chaoticcosmos or chaosmos. By way o f Leibniz's logic, Deleuze is able to conceiveof artworks composed of units that are neither logical nor organic, 'that is,neither based upon pieces as a long unity or a fragmented totality; norformed or prefigured by those units in the course of a logical developmentor of an organic evolution' (191). As in Focillon's vision of a 'life of forms'that mixes biological and serial figures in its description of the Baroquephase, or in the giddy effects of partial things in the novel that betrayProust's intentions, a hierarchy of organic and inorganic things no longerholds. 'Life' is invested into brute matter insofar as it, too, is perpetuallymoving, metamorphosing, or emigrating from one condition to another.

All of a sudden, by way of the relation of atomic theory to that of themonad, an ideology of hierarchies of life begins to totter. When organicand inorganic materials are differentiated not by a wall but by way of avector (early in chapter 1). There ensues an ethical problem about howwe are to apprehend the world. That humans stand as triumphantsubjects among inert objects no longer holds. They no longer own thingsas they had in the world of possessive individualism. Now it must beasked how humans select and designate what they call 'living' or 'inert.'If organic life cannot be easily demarcated from inorganic matter, itbehoves subjects to look at all matter from a different angle. Leibnizpoints toward an ethics that appends the science of ecology. In his turn,Deleuze suggests that an at once abstract and tactile sense of matter mustfigure at the crux of any social practice.In more recent work that follows the implications of The Fold, Deleuze(and Felix Guattari) promote conceptual activity that will move in thedirection of a 'geophilosophy.' Entailed is a revolution of 'absolutedeterritorialization.' 7 The authors do mean that philosophy advocates thecollapse of national boundaries or a return to diversities of economic orethnic worlds, but that the totalitarian aspect of liberal democracy(spurred by the demise of the Soviet Union and the prospect of theEuropean Economic Community) has to be atomized, at least in onestage, by the labor of conceptual thinking. They suggest that philosophy

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TRANSLATOR S FOREWORDRANSLATOR S FOREWORDcan acquire agency by the use of a monadic sensibility when it addressesissues of habitat and thinking.In Qu'est-ce que la philosophie, a geopolitics of deterritorialization isadvanced. The authors speculate that Greek philosophy is something thatoriginates with migrants who arrive on the Aegean peninsula and,through their example, initiate a collective sense of immanence. Ulysses,not Robinson Crusoe, is the ruseful plebian, the everyman who inhabitsurban space, and who gives rise to a conceptual process in which areplanted the seeds of its own demise. When it commodifies concepts,marketing seeks to co-opt philosophy. Deterritorialization, and itsobverse, reterritorialization, implicitly tie monadic thinking to the art ofdisplacement an d transformation.' A stick is, in its turn, a deterritorializedbranch' (p. 66). Those who conceive of organic and inorganic matter fromthis point of view tend to be geophilosophers. Their activity 'slides' on thesurface of the world, as on a wave. A 'surfer,' the geophilosopher movesalong the crest of turbulence, on the shoulders of waves that envelopmind, energy, and matter, and that diffuse them into the atmosphere.

Allusive as the politics of geophilosophy may be, some of its clearestmanifestations are found at the end of The Fold. In the final chapter,Deleuze ties Leibniz's concept of 'new harmony' to Baroque andcontemporary music. 8He picks up, however, the strands of his discussionon the Baroque home that he had elaborated in the first and thirdchapters. By virtue of the radiation of musical waves that move in andabout monads, the world is made up of 'divergent series,' and thusresembles an infinity of pleats and creases of unified and dispersed matter.All of a sudden the distinctions that were used to elaborate Leibniz'svision of space in which the monad is composed of two 'floors,'including first, an upper, private, intimate area (that would be a stage fora chamber ensemble) and, second, a lower, public level where massescirculate are no longer sustained. The sentences break off from themusic of monadic harmony and decor; they turn to issues of habitat.The last question that Deleuze poses involves what it means to live inthe world. Our experience of a shrinking globe inflects the vision of themonad, since compressions of time and space modify 'the difference ofinside and outside and of public and private' (p. 137). Thus, contempor-ary artists and musicians in the line of Leibniz transform monadology intonomadology . They are emigrant thinkers who deterritorialize acceptednotions of space. Like the shift of the opposition of organic and inorganicmatter into tonal flow and flux, the movement from an order of ethereal

and private space over a teeming public world (or 'fishbowl') indicateshow the geophilosophy will operate. The two worlds must fold into eachother. The political implication is that the 'upper floor' of the first worldmust refuse a distinction with second, third, or fourth worlds by (a)rethinking the difference of organic and inorganic forms and (b) byreducing the speed of its movement to harmonize with that of the 'lower'world.

Leibniz had mediated what historians study in terms of socialcontradiction of the ancien regime with an activity that 'folds, unfolds,and refolds' matter, space and time. Contemporary artists, alsogeophilosophers and students of revolutions, are impelled to work inthe same fashion. Their activity accounts for the shrinkage of the world,its increased organic mass, and consequent impoverishment of biologicalvariety. Forms, like modes of folding, disappear. The political strategy ofThe Fold continually bends our dilemmas back onto Leibniz's fascinationwith infinite and curvilinear forms. Leibniz opens a window onto ourworld: Deleuze appears to use Leibniz's concept of harmonics to advocatethe possibility of infinity to be thought within the restricted limits of ourhabitat. A process without spatial development is implied by the non-Hegelian tenor of the last clause in the book: plier, diplier, replier. ThusDeleuze argues for rediscovery of other styles (manieTes) of folding thespace of life. If philosophy can theorize the shrinking limits in which welive, Leibniz exemplifies a system that does not flatten nature to a conceptor world-picture. The searing irony is that Leibniz refuses simplificationso at the very time his work indicates how the technology of capitalismcan be developed. 9By counterexample, the infinity of the fold locateswhere and how the world has since become compressed. Now if the foldtraverses all matter, its movement allows us to conceive ways ofinhabiting the world with tactical resourcefulness. Its very abstraction for what indeed is the fold? allows for elaboration of sensibilities notunder the yoke of liberal democracy.It may be that Deleuze's imagination of the fold harbors an impracticaland unfounded optimism in respect to what can be conceived in ourhistory of accelerated compression of time and space. The politics of thefold would seem to be so chimerical that Deleuze and Guattari could belikened to two 'spiritual automata,' Quixote and Sancho, who venture inan intimate infinity of philosophical space far from the stress that humanlife and social contradiction impose on the globe. It is licit to wonder if thework withdraws into an interdisciplinary monad.


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Seen thus, The Fold and Qu'est-ce que la philosophie would behypothetical approaches to problems population, habitat, displacement,geocide that require urgent and practical commitment. Habitat, it mustbe countered, includes conceptual virtue. And since they beg reaction ofthis kind, these works can also be said to orient philosophy to the futureof the planet in ways that pragmatic means have yet to conceptualize. Infact, The Fold finds the clearest expression of its politics in the ways tha t autopian thought and by utopia can be meant Leibniz's fancifully lucidinvention of the monad joins the labors of philosophy.Leibniz is political because he is utopian. His theories of curvature,movement, and point of view cannot be localized. Deleuze and Guattarinote that a 'utopia is not separated from infinite movement: Utopiadesignates absolute deterritorialization, yet always at the critical pointwhere the latter is attached to the relatively present milieu, and especiallywith forces that are the fab ric of this milieu.' 1 The pleats and hems of theideal Baroque home thus do not merely refer to a 'nowhere,' as ifprompting a mirror-reading of Samuel Butler's Erewhon, but also to a'now-here' that is present whenever and wherever the concept of itsspace is taken up.In this sense Leibniz's theories are not specifically 'objects' but, inDeleuze's lexicon, Baroque territories. They pertain to a nature endowedwith forces that Leibniz describes by tracking the motion of infinitefolding, or by investigation of the caverns and crannies of porous shapesopened in the twists of stone, fossils, and metamorphic rocks. These areterritories of contemplation for the mind, but they are not to be abusedwhile it 'lives and thinks in a state of self-contained reflection' (p. 99). Asimilar politics emerges from Deleuze's comparison of Descartes's andLeibniz's views on extension. For the former, the material world can bemapped out from the axis of the thinking subject, in rectilinear fashion,and can be divided into discrete units. The resulting geography resemblesthe order and process of the quincunx, a two-dimensional system ofgridding and squaring that places a center (the ego) at the intersection ofthe diagonals of a surrounding square. When the self moves into space, ittransforms one of the corners of the square or rectangle of its peripheryinto the site of a new center, around which new extremities areestablished, and so forth, until space is conquered." For the latter,neither the self nor the world can work so schematically. Everywhere thesubject swirls in the midst of forces they exert stress that defines theindividual body, its elasticity, and its bending motions in volumes that

produce movement in and of extension. The subject lives and reinacts itsown embryonic development as a play of folds (endo-, meso-, andectoderm) rather than as a battleground pitting the self against the world.By way of Leibniz's critique of Cartesian space the author pleads for tactof body and environment.

The Fold makes its sensibility manifest through its turns of style. Thesentences are simple, and the transparency of their expression oftenbeguiling. They are built less from the verb or the tension of the subjectand predicate than along the path of its logical 'seams' on the edges orpleats of each sentence. Many start with what appear to be conversationalmodes, with c est, c est bien, ce n est plus, c est que , or c' est qu'il y a. ... Thesebeginnings promise less than the philosophically charged incipit, es gibt, orthe French i y a, 'there is,' 'what is ... is the fact that,' etc., that tend toidentify the writer with a hidden authority invested with the power tojudge and control those who read or listen. Deleuze employs c est as aconnector, as a unit that can link concepts into serial chains that attach toany number o f other sentences. The construction stages the process alsodear to Leibniz that conflates subject and predicate. Cast thus, Deleuze'ssentences articulate the problem of inclusion and connection of differentlexical constructions. Vocables and phrastic units are apt to ramify. Theconcept itself 'becomes a subject' in conformity with each level ofgrammatical parts and wholes. Leibniz's logic marks a break, Deleuzeargues (in 'Sufficient Reason,' chapter 4), with the classical conception ofthe subject as a rational being. By using terms linked by the copula to be,and by varying on c est, Deleuze does not shirk responsibility for eleganceof argument or stylistic clarity: following Leibniz, he summons thedistinction of subject and predicate that grounds Cartesian reason. Thecontinuity of style in The Fold keeps the one either subject or predicate from being an attribute of the other.

At the same time, transparency is gained in the apparent simplicity ofthe sentence. Different and simultaneous movements of logic and styledevelop within the syntax of each phrastic unit. In this sense, Focillon'sdescription of Baroque 'syntax' in medieval art is not without parallel tothe style of either Leibniz or Deleuze. Baroque forms, notes the arthistorian, 'live with passionate intensity a life that is entirely their own.... They break apart even as they grow; they tend to invade space inevery direction, to perforate it, to become as one with all itspossibilities: 12 Deleuze's style promotes confusion of form and sign, butparadoxically, in ways such that the overall effect does not draw attention

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TRANSLATOR S FOREWORDRANSLATOR S FOREWORDto itself. The sentence signifies its content, but the content is seriated toconform to the rhythm of the argument.With some exception, Deleuze's sentences tend to be short, simple,and pellucid. In their concatenation, they break open and recombine,inviting the reader to isolate given clauses and reconnect them, toproduce mobile effects where verbal groups jump into or recur in otherclauses. The implied movement mimes what the author finds in the playof fixity and passage in Leibniz's taste for simultaneous mobility andclosure of concepts. Once again, the manner confirms what Deleuzeobserves about the sufficiency of Leibnizian reason: an 'extraordinaryphilosophical activity which consists of the creation of principles,' wherethere are 'two poles, one toward which all principles are foldingthemselves together, the other toward which they are all unfolding, inthe opposite way.' The double movement betrays what Deleuze calls 'theextreme taste for principles,' far from favouring division into compart-ments, that 'presides over the passage of beings, of things, and of conceptsunder all kinds of mobile partitions' (p. 58).The geometrical shapes of Deleuze's sentences reproduce the serialitiesof which he writes. Leibniz manifests a vision of the world withconsequences that exceed the correlation of philosophy with thebeginnings of industrial technology. At the beginning of the eighteenthcentury, the idea of a stamp (or an impression promoting the effect ofindividual style) 'imposed a law of constancy on the production ofobjects. With the fold a fluctuation or deviation from a norm replaces thepermanence of a law, when the object assumes its place in a continuumof variation.' The object acquires a new status when it refers no longer toa spatial conception of molding, but a 'temporal modulation' or a'continuous variation of matter' (chapter 2). The object is not withdrawnfrom the mold that forms it. A 'continuous temporal molding' ofserialized objects replaces a paradigm of spatiality by another, of temporalorder. So, too, is the tenor of Deleuze's style. Deleuze notices thatLeibniz's mathematics of continuity and modulation change utterly ourideas about the object and event, but all the while they conform to anorder of preformation.

Deleuze's diction tends to replicate this standard for transformation.The sentences do not reflect a law, but vary on their implicit norm. Theyare declarative; often composed of two or three independent clausesconnected by a colon or conjunctions; unlike a classical concept, they donot seek to recall the origin of a signatory stamp. Attention is shunted

away from their composition to the logical process that makes theirlinkage appear as an unfolding of ideas and shapes. Modulation thereforebecomes a criterion of style. Consequently, the verbal material does notset forth to tell a narrative, based on Aristotelian poetics (exposition,movement toward a 'plot-point,' and resolution), that would tend toreach a kernel truth in the story of Leibniz and the Baroque. Nor doesDeleuze, as might Jacques Derrida, construct an elaborate system oftextual defense that produces a surface of tantalizing involutions, orexpressions of foreplay, which defer a gripping conclusion that inverts ortwists the exposition. Instead, each chapter establishes a modulated flow,as it were, of concept-sentence-units, which flatten illusion that generallyaccompanies the rhetoric of argument or narrative. The chapters can beread in any order; their conclusions are enveloped everywhere in the'machinic' manner of the text.

The French edition is composed of long paragraphs that envelop thethemes listed serially in the table of contents. Mos t of the material follows but not always the order he places under each chapter-heading. Thelogic of the argumentation is carefully outlined. If the table of contents isnot studied beforehand, the organization of materials can appear dense orchaotic. To attenuate that im pression, I have taken the liberty of insertingbreaks in the text that roughly follow the themes listed in the summary. Ihave also divided many of the paragraphs into smaller units. Whereas thespecialist of philosophy may have no difficulty following the developmentof Deleuze's reasoning, readers of different backgrounds may find theadded space helpful for pause and reflection. Otherwise, I have stayed asclose as possible to the order and rhythm of the arguments.Wherever possible, I have quoted English translations of Leibniz fromstandard and available editions. The way that the German, French, andEnglish editions of Leibniz are used in The Fold is outlined in the Prefaceto the Notes.For this translation I wish to thank Biodun Iginla, of the University ofMinnesota Press, who encouraged its undertaking; Brian Massumi for hismagnificent example of A Thousand Plateaus and timely advice about thisproject; Ann Klefstad and Mary Byers for their alert reading andemendations; John Aubrey, of the Newberry Library, who solved manybibliographical riddles. Their assistance has been invaluable. Theblemishes the reader will find are solely the fault of the translator.


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1The pleats of matter

The Baroque refers not to an essence but rather to an operative function,to a trait. It endlessly produces folds. It does not invent things: there areall kinds of folds coming from the East, Greek, Roman, Romanesque,Gothic, Classical folds. ... Yet the Baroque trait twists and turns its folds,pushing them to infinity, fold over fold, one upon the other. TheBaroque fold unfurls all the way to infinity. First, the Baroquedifferentiates its folds in two ways, by moving along two infinities, asif infinity were composed of two stages or floors: the pleats of matter, andthe folds in the soul. Below, ma tter is amassed accord ing to a first type offold, and then organized according to a second type, to the extent its partconstitutes organs that are 'differently folded and more or lessdeveloped.' Above, the soul sings of the glory of God inasmuch as itfollows its own folds, but without succeeding in entirely developingthem, since 'this communication stretches out indefinitely.' A labyrinthis said, etymologically, to be multiple because it contains many folds. Themultiple is not only what has many parts but also what is folded in manyways. A labyrinth corresponds exactly to each level: the continuouslabyrinth in matter and its parts, the labyrinth of freedom in the soul andits predicates. If Descartes did not know how to get through thelabyrinth, it was because he sought its secret of continuity in rectilineartracks, and the secret of liberty in a rectitude of the soul. He knew theinclension of the soul as little as he did the curvature of matter. A'cryptographer' is needed, someone who can at once account for natureand decipher the soul, who can peer into the crannies of matter and readinto the folds of the soul.'

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dosed pr ivate room,d e c o r a t e d w i t h a d r a p e r yd i v e r s i f i e d b y f o l d s

c o m m o n r o o m s , w i thsevera l smal l open-Inge the f i ve senses

THE FOLD

Clearly the two levels are connected (this being why continuity risesup into the soul). There are souls down below, sensitive, animal; andthere even exists a lower level in the souls. The pleats of matter surroundand envelop them. When we learn that souls cannot be furnished withwindows opening onto the outside, we must first, at the very least,include souls upstairs, reasonable ones, who have ascended to the otherlevel ('elevation'). It is the upper floor that has no windows. It is a darkroom or chamber decorated only with a stretched canvas 'diversified byfolds,' as if it were a living dermis. Placed on the opaque canvas, thesefolds, cords, or springs represent an innate form of knowledge, but whensolicited by matter they move into action. Matter triggers 'vibrations oroscillations' at the lower extremity of the cords, through the intermediaryof 'some little openings' that exist on the low er level. Leibniz constructs agreat Baroque montage that moves between the lower floor, pierced withwindows, and the upper floor, blind and closed, but on the other handresonating as if it were a musical salon translating the visible movementsbelow into sounds up above. It could be argued that this text does not express Leibniz's thought, butinstead the maximum degree of its possible conciliation with Locke. Thetext also fashions a way of representing what Leibniz will always affirm: acorrespondence and even a communication between the two levels,between the two labyrinths, between the pleats of matter and the folds inthe soul. A fold between the two folds? And the same image, that of veinsin marble, is applied to the two under different conditions. Sometimes theveins are the pleats of matter that surround living beings held in the mass,such that the marble tile resembles a rippling lake that teems with fish.Sometimes the veins are innate ideas in the soul, like twisted figures orpowerful statues caught in the block of marble. Matter is marbled, of twodifferent styles.

WOlfflin noted that the Baroque is marked by a certain number ofmaterial traits: horizontal widening of the lower floor, flattening of thepediment, low and curved stairs that push into space; matter handled inmasses or aggregates, with the rounding of angles and avoidance ofperpendiculars; the circular acanthus replacing the jagged acanthus, useof limestone to produce spongy, cavernous shapes, or to constitute avortical form always put in motion by renewed turbulence, which endsonly in the manner of a horse's mane or the foam of a wave; matter tendsto spill over in space, to be reconciled with fluidity at the sam e time fluidsthemselves are divided into masses.

4

THE PLEATS OF MATTER

The B aroque H ouse (an a l legory)

Huygens develops a Baroque mathematical physics whose goal iscurvilinearity. With Leibniz the curvature of the universe is prolongedaccording to three other fundamental notions: the fluidity of matter, theelasticity of bodies, and motivating spirit as a mechanism. First, matterwould clearly not be extended following a twisting line. Rather, it wouldfollow a tangent.' But the universe appears compressed by an active forcethat endows matter with a curvilinear or spinning movement, followingan arc that ultimately has no tangent. And the infinite division of mattercauses compressive force to return all portions of matter to thesurrounding areas, to the neighbouring parts that bathe and penetratethe given body, and that determine its curvature. Dividing endlessly, theparts of matter form little vortices in a maelstrom, and in these are foundeven more vortices, even smaller, and even more are spinning in theconcave intervals of the whirls that touch one another.

Matter thus offers an infinitely porous, spongy, or cavernous texturewithout emptiness, caverns endlessly contained in other caverns: nomatter how small, each body contains a world pierced with irregularpassages, surrounded and penetrated by an increasingly vaporous fluid,the totality of the universe resembling a 'pond of matter in which thereexist different flows and waves.' 8 From this, however, we would notconclude, in the second place, that even the most refined matter isperfectly fluid and thus loses its texture (according to a th esis that Leibnizimputes to Descartes). Descartes's error probably concerns what is to befound in different areas. He believed that the real distinction between

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THE FOLD THE PLEATS OF MATTER

parts entailed separability. What specifically defines an absolute fluid isthe absence of coherence or cohesion; that is, the separability of parts,which in fact applies only to a passive and abstract matter. 9According toLeibniz, two parts of really distinct matter can be inseparable, as shownnot only by the action of surrounding forces that determine thecurvilinear movement of a body but also by the pressure of surroundingforces that determine its hardness (coherence, cohesion) or theinseparability of its parts. Thus it must be stated that a body has a degreeof hardness as well as a degree of fluidity, or that it is essentially elastic,the elastic force of bodies being the expression of the active compressiveforce exerted on matter. When a boat reaches a certain speed a wavebecomes as hard as a wall of marble. The atomistic hypothesis of anabsolute hardness and the Cartesian hypothesis of an absolute fluidity arejoined all the more because they share the error that posits separableminima, either in the form of finite bodies or in infinity in the form ofpoints (the Cartesian line as a site of its points, the analytical punctualequation).That is what Leibniz explains in an extraordinary piece of writing: aflexible or an elastic body still has cohering parts that form a fold, suchthat they are not separated into parts of parts but are rather divided toinfinity in smaller and smaller folds that always retain a certain cohesion.Thus a continuous labyrinth is not a line dissolving into independentpoints, as flowing sand might dissolve into grains, but resembles a sheet ofpaper divided into infinite folds or separated into bending movements,each one determined by the consistent or conspiring surroundings. 'Thedivision of the continuous must not be taken as of sand dividing intograins, but as that of a sheet of paper or of a tunic in folds, in such a waythat an infinite number of folds can be produced, some smaller thanothers, but without the body ever dissolving into points or minima." Afold is always folded within a fold, like a cavern in a cavern. The unit ofmatter, the smallest element of the labyrinth, is the fold, not the pointwhich is never a pa rt, but a simple extremity of the line. That is why partsof matter are masses or aggregates, as a correlative to elastic compressiveforce. Unfolding is thus not the contrary of folding, but follows the fold upto the following fold. Particles are 'turned into folds,' that a 'contraryeffort changes over and again.'" Folds of winds, of waters, of fire andearth, and subterranean folds of veins of ore in a mine. In a system ofcomplex interactions, the solid pleats of 'natural geography' refer to theeffect first of fire, and then of waters and winds on the earth; and the

veins of metal in mines resemble the curves of conical forms, sometimesending in a circle or an ellipse, sometimes stretching into a h yperbola or aparabola. I The model for the sciences of matter is the 'origami,' as theJapanese philosopher might say, or the art of folding paper.Two consequences result that provide a sense of the affinity of matterwith life and organisms. To be sure, organic folds have their ownspecificity, as fossils demonstrate. But on the one hand, the division ofparts in matter does not go without a decomposition of bendingmovement or of flexions. We see this in the development of the egg,where numerical division is only the condition of morphogenic move-ments, and of invagination as a pleating. On the other hand, theformation of the organism would remain an improbable mystery, or amiracle, even if matter were to divide infinitely into independent points.But it becomes increasingly probable and natural when an infinity ofindeterminate states is given (already folded over each other), each ofwhich includes a cohesion at its level, somewhat like the improbability offorming a word by chance with separate letters, but with far morelikelihood with syllables or inflections.' 3In the third place, it is evident that motivating force becomes themechanism of matter. If the world is infinitely cavernous, if worlds existin the tiniest bodies, it is because everywhere there can be found 'a spiritin matter,' which attests not only to the infinite division of parts but alsoto progressivity in the gain and loss of movement all the whileconservation of force is realized. The matter-fold is a matter-time; itscharacteristics resemble the continuous discharge of an 'infinity of wind-muskets.' 4 And there still we can imagine the affinity of matter for lifeinsofar as a muscular conception of matter inspires force in all things. Byinvoking the propagation of light and the 'expulsion into luminosity,' bymaking an elastic, inflammable, and explosive spirit from animal spirits,Leibniz turns his back on Cartesianism. He renews the tradition of VanHelmont and is inspired by Boyle's experimentation. 5 In short, to theextent that folding is not opposed to unfolding, such is also the case in thepairs tension-release and contraction-dilation (but not condensation-rarefaction, which would imply a void).The lower level or floor is thus also composed of organic matter. Anorganism is defined by endogenous folds, while inorganic matter hasexogenous folds that are always determined from without or by the

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THE FOLD

surrounding environment. Thus, in the case of living beings, an innerformative fold is transformed through evolution, with the organism'sdevelopment. Whence the necessity of a preformation. Organic matter isnot, however, different from inorganic matter (here, the distinction of afirst and a second matter is irrelevant). Whether organic or inorganic,matter is all one; but active forces are not the only ones exerted upon it.To be sure, these are perfectly material or mechanical forces, whereindeed souls cannot be made to intervene: for the moment, vitalism is astrict organicism. Material forces, which account for the organic fold,have only to be distinguished from the preceding forces, and be added toit; they must suffice, where they are exerted, to transform raw matter intoorganic matter. In contrast to compressive or elastic forces, Leibniz callsthem 'plastic forces.' They organize masses but, although the latterprepare organisms or make them possible by means of motivating drive, itis impossible to go from masses to organisms, since organs are alwaysbased on these plastic forces that preform them, and are distinguishedfrom forces of mass, to the point where every organ is born from apreexisting organ. 8Even fossils in matter are not explained by ourfaculty of imagination; when, for example, we see that the head of Christwe fancy in the spots on a wall refers to plastic forces that wind throughorganisms that already exist.

If plastic forces can be distinguished, it is not because living matterexceeds mechanical processes, but because mechanisms are not sufficientto be machines. A mechanism is faulty not for being too artificial toaccount for living matter, but for not being mechanical enough, for notbeing adequately machined. Our mechanisms are in fact organized intoparts that are not in themselves machines, while the organism is infinitelymachined, a machine whose every part or piece is a machine, but only'transformed by different folds that it receives."' Plastic forces are thusmore machinelike than they are mechanical, and they allow for thedefinition of Baroque machines. It might be claimed that mechanisms ofinorganic nature already stretch to infinity because the motivating force isof an already infinite composition, or that the fold always refers to otherfolds. But it requires that each time, an external determination, or thedirect action of the surroundings, is needed in order to pass from one levelto another; without this we would have to stop, as with our mechanisms.The living organism, on the contrary, by virtue of preformation has aninternal destiny that makes it move from fold to fold, or that makesmachines from machines all the way to infinity. We might say that

8


between organic and inorganic things there exists a difference of vector,the latter going toward increasingly greater masses in which statisticalmechanisms are operating, the former toward increasingly smaller,polarized masses in which the force of an individuating machinery, aninternal individuation, is applied. Is this Leibniz's premonition of severalaspects that will come true only much later? 8No doubt, for Leibniz,internal individuation will only be explained at the level of souls: organicinteriority is only derivative, and has but one container of coherence orcohesion (not of inherence or of 'inhesion'). It is an interiority of space,and not yet of motion; also, an internalization of the outside, aninvagination of the outside that could not occur all alone if no trueinteriorities did not exist elsewhere. It remains the case that the organicbody thus confers an interior on matter, by which the principle ofindividuation is applied to it: whence the figure of the leaves of a tree,two never being exactly alike because of their veins or folds.Folding-unfolding no longer simply means tension-release, contraction-dilation, but enveloping-developing, involution-evolution. The organismis defined by its ability to fold its own parts and to unfold them, not toinfinity, but to a degree of development assigned to each species. Thus anorganism is enveloped by organisms, one within another (interlocking ofgerminal matter), like Russian dolls. The first fly contains the seeds of allflies to come, each being called in its turn to unfold its own parts at theright time. And when an organism dies, it does not really vanish, but foldsin upon itself, abruptly involuting into the again newly dormant seed byskipping all intermediate stages. The simplest way of stating the point isby saying that to unfold is to increase, to grow; whereas to fold is todiminish, to reduce, 'to withdraw into the recesses of a world.' 9Yet asimple metric change would not account for the difference between theorganic and the inorganic, the machine and its motive force. It would failto show that movement does not simply go from one greater or smallerpart to another, but from fold to fold. When a part of a machine is still amachine, the smaller unit is not the same as the whole. When Leibnizinvokes Harlequin's layers of clothing, he means that his underwear isnot the same as his outer garments. That is why metamorphosis or'metaschematism' pertains to more than mere change of dimension:every animal is double but as a heterogenous or heteromorphiccreature, just as the butterfly is folded into the caterpillar that will soonunfold. The double will even be simultaneous to the degree that the ovuleis not a mere envelope but furnishes one part whose other is in the male

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element.In fact, it is the inorganic that repeats itself, with a differenceof proximate dimension, since it is always an exterior site which entersthe body; the organism , in contrast, envelops an interior site that containsnecessarily other species of organisms, those tha t envelop in their turn theinterior sites containing yet other organisms: 'Each portion of matter maybe conceived as a garden full of plants, and as a pond full of fish. Butevery branch of each plant, every member of each animal, and every dropof their liquid parts is in itself likewise a similar garden or pond.' IThusthe inorganic fold happens to be simple and direct, while the organic foldis always composite, alternating, indirect (mediated by an interior site). 22

Matter is folded twice, once under elastic forces, a second time underplastic forces, but one is not able to move from the first to the second.Thus the universe is neither a great living being, nor is it in itself anAnimal: Leibniz rejects this hypothesis as much as he rejects that of auniversal Spirit. Organisms retain an irreducible individuality, andorganic descendants retain an irreducible plurality. It remains that thetwo kinds of force, two kinds of folds masses and organisms are strictlycoextensive. There are no fewer living beings than parts of inorganicmatter. 23 Clearly an exterior site is not a living being; rather, it is a lake, apond, or a fish hatchery. Here the figure of the lake or pond acquires anew meaning, since the pond and the marble tile no longer refer toelastic waves that swim through them like inorganic folds, but to fish thatinhabit them like organic folds. And in life itself the inner sites containedare even more hatcheries full of other fish: a 'swarm.' Inorganic folds ofsites move between two o rganic folds. For Leibniz, as for the Baroque, theprinciples of reason are veritable cries: Not everything is fish, but fish areteeming everywhere. ... Universality does not exist, but living things areubiquitous.It might be said that the theory of preformation and duplication, asobservations made through the microscope confirm, has long beenabandoned. The meaning of development or evolution has turned topsy-turvy, since it now designates epigenesis the appearance of organs andorganisms neither preformed nor closed one within the other, but formedfrom something else that does not resemble them: the organ does notarch back to a preexisting organ, but to a much more general and lessdifferentiated design. 4Development does not go from smaller to greaterthings through growth or augmentation, but from the general to thespecial, through differentiations of an initially undifferentiated fieldeither under the action of exterior surroundings or under the influence of

internal forces that are directive, directional, but that remain neitherconstitutive nor preformative. However, insofar as preformism exceedssimple metric variations, it tends to be aligned with an epigenesis to theextent epigenesis is forced to hold to a kind of virtual or potentialpreformation. The essential is elsewhere; basically, two conceptions sharethe common trait of conceiving the organism as a fold, an originaryfolding or creasing (and biology has never rejected this determination ofliving matter, as shown nowadays with the fundamental pleating ofglobular protein). Preformism is the form in which this truth of theseventeenth century is perceived through the first microscopes. It ishardly surprising that from then on the same problems are found in thesense of epigenesis and preformation.

Thus can all types of folding be called modifications or degrees ofdevelopment of a same Animal in itself? Or are there types of irreduciblefoldings, as Leibniz believes in a preformist perspective, and as Cuvier andBaer also contend from an epigenic standpoint? 25 Certainly a greatopposition subsists between the two points of view. With epigenesis theorganic fold is produced, is unearthed, or is pushed up from a relativelysmooth and consistent surface. (How could a redoubling, an invagination,or an intubation be prefigured?) Now with preformism an organic foldalways ensues from another fold, at least on the inside from a same typeof organization: every fold originates from a fold, plica ex plica. I fHeideggerian terms can be used, we can say that the fold of epigenesis isan Einfalt, or that it is the differentiation of an undifferentiated, but thatthe fold from preformation is a Zweifalt, not a fold in two since everyfold can only be thus but a 'fold-of-two,' an entre-deux, something'between' in the sense that a difference is being differentiated. From thispoint of view we cannot be sure if preformism does not have a future.

Masses and organisms, masses and living beings thus fill the lower level.Why then is another storey needed, since sensitive or animal souls arealready there, inseparable from organic bodies? Each soul even seems aptto be localized in its body, this time as a 'point' in a droplet, that subsistsin a part of the droplet when the latter is divided or diminished involume: thus, in death the soul remains right where it was, in a part ofthe body, however reduced it may be. 26 Leibniz states that the point ofview is in the body. 27 Surely everything in the body works like amachine, in accord with plastic forces that are material, but these forcesexplain everything except for the variable degrees of unity to which they

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bring the masses they are organizing (a plant, a worm, a vertebrate ...).Plastic forces of matter act on masses, but they submit them to real unitiesthat they take for granted. They make an organic synthesis, but assumethe soul as the uni ty o f syn thes is , or as the 'immaterial principle of life.'Only there does an animism find a connection with organicism, from thestandpoint of pure unity or of union, independently of all causal action. 28It remains that organisms would not on their account have the causalpower to be folded to infinity, and of surviving in ashes, without theunity-souls from which they are inseparable, and which are inseparablefrom them. Here is the great difference that makes Leibniz break awayfrom Malebranche: not only is there a preformation of bodies, but also apreexistence of souls in fertile seeds. 29 Life is not only everywhere, butsouls are everywhere in matter. Thus, when an organism is called tounfold its own parts, its animal or sensitive soul is opened onto an entiretheater in which it perceives or feels according to its unity, independentlyof its organism, yet inseparable from it.But and here is the whole problem what happens with bodies, fromthe time of Adam's seed that envelops them, that are destined to becomehumans? Juridically, one might say that they carry in a nutshell 'a sort ofsealed act' that marks their fate. And when the hour comes for them tounfold their parts, to attain a degree of organic development proper toman, or to form cerebral folds, at the same time their animal soulbecomes reasonable by gaining a greater degree of unity (mind): 'Theorganized body would receive at the same time the disposition of thehuman body, and its soul would be raised to the stage of a reasonablesoul, but I cannot decide here if it occurs through an ordinary process oran extraordinary work of God.' 3 Then in every event this becoming is anelevation, an exaltation: a change of theater, of rule, of level or of floors.The theater of matter gives way to that of spirits or of God. In the Baroquethe soul entertains a complex relation with the body. Forever indissoci-able from the bo dy, it discovers a vertiginous animality that gets it tangledin the pleats of matter, but also an organic or cerebral humanity (thedegree of development) that allows it to rise up, and that will make itascend over all other folds.The reasonable soul is free, like a Cartesian diver, to fall back down atdeath and to climb up again at the last judgment. As Leibniz notes, thetension is between the collapse and the elevation or ascension that indifferent spots is breaching the organized masses. We move from funerary

12


figures of the Basilica of Saint Laurence to the figures on the ceiling ofSaint Ignatius. It might be claimed that physical gravity and religiouselevation are quite different and do not pertain to the same world.However, these are two vectors that are allotted as such in the distinctionof the two levels or floors of a single and same w orld, or of the single andsame house. It is because the body and the soul have no point in beinginseparable, for they are not in the least really distinct (we have alreadyseen it for the parts of matter). From this moment on any localization ofthe soul in an area of the body, no matter how tiny it may be, amountsrather to a projection from the top to the bottom, a projection of the soulfocalizing on a 'point' of the body, in conformity with Desargues'sgeometry, that develops from a Baroque perspective. In short, theprimary reason for an upper floor is the following: there are souls on thelower floor, some of whom are chosen to become reasonable, thus tochange their levels.

Movement, then, cannot be stopped. The reciprocation of theLeibnizian principle holds not only for reasonable souls but also foranimal or sensible souls themselves: if two really distinct things can beinseparable, two inseparable things can be really distinct, and belong totwo levels, the localization of the one in the other amounting to aprojection upon a point ('I do not think that we can consider souls asbeing in points, perhaps we might say ... that they are in a place througha connection'). As degrees of unity, animal souls are already on the otherfloor, everything being accomplished mechanically in the animal itself atthe lower level. Plastic or machinic forces are part of the 'derivativeforces' defined in respect to the matter that they organize. But souls, onthe contrary, are 'primitive forces' or immaterial principles of life that aredefined only in respect to the inside, in the self, and 'through analogywith the mind.' We can nonetheless remember that these animal souls,with their subjugated organism, exist everywhere in inorganic matter.Thus in its turn inorganic matter reverts to souls whose site is elsewhere,higher up and that is only projected upon it. In all probability a body however small follows a curvilinear trajectory only under the impulsionof the second species of derivative forces, compressive or elastic forcesthat determine the curve through the mechanical action of thesurrounding bodies on the outside: isolated, the body would follow thestraight tangent. But still, mechanical laws or extrinsic determinations(collisions) explain everything except the unity of a concrete movement,no matter how irregular or variable it may be. Unity of movement is an

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THE FOLDaffair of the soul, and almost of a conscience, as Bergson will laterdiscover. Just as the totality of matter arches back to a curving that can nolonger be determined from the outside, the curvilinear course followed bya given body under the impetus of the outside goes back to a 'higher,'internal and individuating, unity on the other floor, that contains the'law of curvilinearity,' the law of folds or ch anges of direction. 31 The samemovement is always determined from the outside, through collisions,insofar as it is related to derivative force, but unified from the inside, tothe degree it is related to primitive force. In the first relation, the curve isaccidental and derived from the straight line, but in the second it isprimary, such that the motive force sometimes is mechanically explainedthrough the action of a subtle surrounding, and sometimes is understoodfrom the inside as the interior of the body, 'the cause of movement that isalready in the body,' and that only awaits the suppression of an obstaclefrom the outside. 32Hence the need for a second floor is everywhere affirmed to be strictlymetaphysical. The soul itself is what constitutes the other floor or theinside up above, where there are no windows to allow entry of influencefrom without. Even in a physical sense we are moving across outermaterial pleats to inner animated, spontaneous folds. These are what wemust now examine, in their nature and in their development. Everythingmoves as if the pleats of matter possessed no reason in themselves. It isbecause the Fold is always between two folds, and because the between-two-folds seems to move about everywhere: Is it between inorganicbodies and organisms, between organisms and animal souls, betweenanimal souls and reasonable souls, between bodies and souls in general?

The folds in the soul

Inflection is the ideal genetic element of the variable curve or fold.Inflection is the authentic atom, the elastic point. That is what Kleeextracts as the genetic element of the active, spontaneous line. It testifiesto his affinity for the Baroque and for Leibniz, and opposes him toKandinsky, a Cartesian, for whom angles are firm, for whom the point isfirm, set in motion by an exterior force. For Klee, however, the point as a'nonconceptual concept of noncontradiction' moves along an inflection.It is the point of inflection itself, where the tangent crosses the curve.That is the point-fold. Klee begins w ith a succession of three figures.' Thefirst draws the inflection. The second shows that no exact and unmixedfigure can exist. As Leibniz stated, there can never be 'a straight linewithout curves intermingled,' nor any 'curve of a certain finite natureunmixed with some other, and in small parts as well as large,' such thatone 'will never be able to fix upon a certain precise surface in a body asone might if there were atoms.' The third marks the convex side withshadow, and thus disengages concavity and the axis of its curve, that nowand again changes sides from the point of inflection.Bernard Cache defines inflection or the point of inflection as anintrinsic singularity. Contrary to 'extrema' (extrinsic singularities,maximum and minimum), it does not refer to coordinates: it is neitherhigh nor low, neither right nor left, neither regression nor progression. Itcorresponds to what Leibniz calls an 'ambiguous sign.' It is weightless;even the vectors of concavity still have nothing to do with a vector ofgravity since the axes of the curve that they are determining oscillatearound it. Thus inflection is the pure Event of the line or of the point,

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Gothic scans ion: gothic a rch and re turn

Vpoint of returnothic arch

THE FOLD THE FOLDS IN THE SOUL

the Virtual, ideality par excellence. It will take place following the axes ofthe coordinates, but for now it is not yet in the world: it is the Worlditself, or rather its beginning, as Klee used to say, 'a site of cosmogenesis,''a nondimensional point' 'between dimensions.' An event that wouldawait an event? That is how the inflection already moves through virtualtransformations, that is (for Cache), three transformations. 3The first are vectorial, or operate by symmetry, with an orthogonal ortangent plane of reflection. They work according to optical laws,transforming inflection at a turning point, in an ogive, or pointed arch.The ogive expresses the form of a moving body that espouses theconfiguration of lines of flowing liquid, and the return, the profile of thedepth of a valley when waters are brought together following the line of asingle course.The second set of transformations is projective: such transformationsconvey the projection, on external space, of internal spaces defined by'hidden parameters' and variables or singularities of potential. ReneThorn's transformations refer in this sense to a morphology of livingmatter, providing seven elementary events: the fold; the crease; thedovetail; the butterfly; the hyperbolic, elliptical, and parabolic umbilicus. 4Finally, the inflection in itself cannot be separated from an infinitevariation or an infinitely variable curve. Such is Koch's curve, obtained

by means of rounding angles, according to Baroque requirements, bymaking them proliferate according to a law of homothesis. 3 The curvepasses through an infinite number of angular points and never admits atangent at any of these points. It envelops an infinitely cavernous orporous world, constituting more than a line and less than a surface(Mandelbrot's fractal dimension as a fractional or irrational number, anondimension, an interdimension). 6Nonethelesss homothesis causesvariation to coincide with a ch ange of scale, as in the case of the length ofa geographical gradient. Everything changes when fluctuation is made tointervene in the place of internal homothesis. It is no longer possible todetermine an angular point between two others, no matter how close oneis to the other; but there remains the latitude to always add a detour bymaking each interval the site of a new folding. That is how we go fromfold to fold and not from point to point, and how every contour is blurredto give definition to the formal powers of the raw material, which rise tothe surface and are put forward as so many detours and supplementaryfolds. Transformation of inflection can no longer allow for eithersymmetry or the favored plane of projection. It becomes vortical and isproduced later; deferred, rather than prolonged or proliferating: the line

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effectively folds into a spiral in order to defer inflection in a movementsuspended between sky and earth, which either moves away from orindefinitely approaches the center of a curve and at each instant 'risesskyward or risks falling upon us.' 7 But the vertical spiral neither retainsnor defers inflection without also promoting it and making it irresistible,in a transversal sense: a turbulence that is never produced on its own,whose spiral follows a fractal mode by which new turbulences areinserted between the initial ones. 8 Growing from other turbulences, inthe erasure of contour, turbulence ends only in watery froth or in aflowing mane. Inflection itself becomes vortical, and at the same time itsvariation opens onto fluctuation, it becomes fluctuation.The definition of Baroque ma thematics is born with Leibniz. The ob ject ofthe discipline is a 'new affection' of variable sizes, which is v ariation itself.To be sure, in a fractional number or even in an algebraic formula,variability is not considered as such, since each of the terms has or musthave a particular value. The sam e no longer holds either for the irrationalnumber and corresponding serial calculus, or for the differential quotientand differential calculus, in which variation becomes presently infinite.The irrational number is the common limit of two convergent series, ofwhich one has no maximum and the other no minimum. The differentialquotient is the common limit of the relation between two quantities thatare vanishing. But we can remark that in both cases the presence of acurved element acts as a cause. The irrational number implies the descentof a circular arc on the straight line of rational points, and exposes thelatter as a false infinity, a simple undefinite that includes an infinity oflacunae; that is why the continuous is a labyrinth that cannot berepresented by a straight line. The straight line always has to beintermingled with curved lines.

C

Between the two points A and B no matter in what proximity they maybe there always remains the possibility for carrying out the rightisosceles triangle, whose hypotenuse goes from A to B, and whose

summit, C, determines a circle that crosses the straight line between Aand B. The arc of the circle resembles a branch of inflection, an element ofthe labyrinth, that from an irrational number, at the meeting of thecurved and straight lines, produces a point-fold. It is identical in the caseof the differential quotient, with the point-fold A that retains the relation

ce

when these two magnitudes vanish (that, too, is the relation between aradius and a tangent that fits the angle in C). 9 In short, there will alwaysbe an inflection that makes a fold from variation, and that brings the foldor the variation to infinity. The fold is Power, as we see in the irrationalnumber that appears by way of an extraction from a root, and in thedifferential quotient that appears by way of the relation of a magnitudeand a pow er, as a condition o f variation. Force itself is an act, an act of thefold.When mathematics assumes variation as its objective, the notion offunction tends to be extracted, but the notion of objective also changesand becomes functional. In some especially important mathematicalwritings, Leibniz posits the idea of families of curves depending upon oneor several parameters: 'Instead of seeking the unique straight tangent in aunique point for a given curve, we can go about seeking the tangentcurve in an infinity of points with an infinity of curves; the curve is nottouched, it is touching, the tangent no longer either straight, unique, ortouching, but now being curvilinear, an infinite, touched family' (theproblem of the inverse of tangents). IThere exists thus a series of curves

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that not only imply constant parameters for each and every curve, but thereduction of variables to a 'single and unique variability' of the touchingor tangent curve: the fold. The goal is no longer defined by an essentialform, but reaches a pure functionality, as if declining a family of curves,framed by parameters, inseparable from a series of possible declensions orfrom a surface of variable curvature that it is itself describing.This new object we can call objectile. As Bernard Cache has demonstrated,this is a very modern conception of the technological object: it refersneither to the beginnings of the industrial era nor to the idea of thestandard that still upheld a semblance of essence and imposed a law ofconstancy ('the object produced by and for the masses'), but to ourcurrent state of things, where fluctuation of the norm replaces thepermanence of a law; where the object assumes a place in a continuumby variation; where industrial automation or serial machineries replacestamped forms. The new status of the object no longer refers its conditionto a spatial mold in other words, to a relation of form-matter but to atemporal modulation that implies as much the beginnings of acontinuous variation of matter as a continuous development of form.In modulation 'a pause never intervenes for withdrawal from the moldbecause the circulation of the source of energy amounts to a permanentwithdrawal; a modulator is a continuous temporal mold ... Moldingamounts to modulating in a definitive way; modulating is molding in acontinuous and perpetually variable fashion."' Can we not affirm thatmodulation is what Leibniz is defining when he states that the law ofseries posits curves as 'the trace of the same line' in a continuousmovement, continually touched by the curve of their convergence? His isnot only a temporal but also a qualitative conception of the object, to theextent that sounds and colors are flexible and taken in modulation. Theobject here is manneristic, not essentializing: it becomes an event.If the status of the object is profoundly changed, so also is that of thesubject. We move from inflection or from variable curvature to vectors ofcurvature that go in the direction of concavity. Moving from a branchingof inflection, we distinguish a point that is no longer what runs alonginflection, nor is it the point of inflection itself; it is the one in which thelines perpendicular to tangents meet in a state of variation. It is notexactly a point but a place, a position, a site, a 'linear focus,' a lineemanating from lines. To the degree it represents variation or inflection, it

THE FOLDS IN THE SOUL

can be called poin t o f v iew. Such is the basis of perspectivism, which doesnot mean a dependence in respect to a pregiven or defined subject; to thecontrary, a subject will be what comes to the point of view, or rather whatremains in the point of view. That is why the transformation of the objectrefers to a correlative transformation of the subject: the subject is not asubject but, as Whitehead says, a 'superject.' Just as the object becomesobjectile, the subject becomes a superject. A needed relation existsbetween variation and point of view: not simply because of the variety ofpoints of view (thou gh, as we shall observe, such a va riety does exist), butin the first place because every point of view is a point of view onvariation. The point of view is not what varies with the subject, at least inthe first instance; it is, to the contrary, the condition in which an eventualsubject apprehends a variation (metamorphosis), or: something = x(anamorphosis). For Leibniz, for Nietzsche, for William and HenryJames, and for Whitehead as well, perspectivism amounts to a relativism,but not the relativism we take for granted. It is not a variation of truthaccording to the subject, but the condition in which the truth of avariation appears to the subject. This is the very idea of Baroqueperspective.It might, however, be claimed that point of view explodes with theproximity of concavity: does there not exist a contradiction betweencontinuity of infinite variation and the discontinuity of viewpoint? Is thisnot the same contradiction between the law of continuity and theprinciple of indiscernibles that many authors (following Kant) denouncein Leibniz? The question is moot if, from the outset, we try to notcombine continuity and contiguity.' 3Although they are not contiguous,singularities, or unique points, belong fully to continuousness. Points ofinflection make up a first kind of singularity in space, and constituteenvelopes in accord with indivisible relations of distance. But neither onenor the other contradicts the continuous. There are as many points ofview whose distance in each case is indivisible as inflections ininflection, whose length increases. Continuity is made up no less ofdistances between points of view than of the length of an infinity ofcorresponding curves. Perspectivism is clearly a pluralism, but it thusimplies by its name distance and not discontinuity (certainly no void is


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THE FOLDHE FOLDS IN THE SOULgiven between two points of view). Leibniz can define extension (extensio)as 'continuous repetition' of the situs or position - that is, of point o f view:not that extension is therefore the attribute of point of view, but that theattribute of space (spatium), an order of distances between points of view,is what makes this repetition possible."Point of view on a variation now replaces the center of a figure or aconfiguration. The most famous example is that of conic sections, where

the point of the cone is the point of view to which the circle, the ellipse,the parabola, and the hyperbola are related as so many variants thatfollow the incline of the section that is planned ('scenographies'). Allthese figures become so many ways by which a 'flat projection' ismapped out. And this projection is not exactly the circle, which it wouldbe only under the privilege of an old conception of perspective. Rather,it is the objectile that now declines or describes relations of curves: thoseof the second degree, in which the circle plays a role. This objectile orprojection resembles an unfolding. But unfolding is no more thecontrary of foldings than an invariant would be the contrary ofvariation. It is an invariant of transformation. Leibniz will designate itby an 'ambiguous sign." 5 It is effectively enveloped in variation, just asvariation is enveloped in point of view. It does not exist outside ofvariation, just as variation does not exist outside of point of view. That iswhy, at the basis of this new theory of conic sections, Desargues calledthe relation or the law enveloped by a variation 'involution' (forexample, a triangle that is supposed to turn around an axis, thedispositions of the points defined on the axis by the projection of threesummits and by the prolongation of the three sides)."

Michel Serres has analyzed superlatively both the consequences andthe presuppositions of the new theory of conic sections: in a world ofinfinity, or of variable curvature that has lost notion of a center, hestresses the importance of setting point of view in the place of the missing

center; of the new optical model of perception, and of geometry inperception, that casts aside tactile notions, contact and figure, in favor ofan 'architecture of vision'; of the status of the object, which now existsonly through its metamorphoses or in the declension of its profiles; ofperspectivism as a truth of relativity (and not a relativity of what is true).In each area point of view is a variation or a power of arranging cases, acondition for the manifestation of reality: thus the alternating series ofconics, beginning with the summit of the cone (a finite point, an infinitestraight line, a finite circle, an infinite parabola, a finite ellipse, an infinitehyperbola), or rather the series of powers to the second degree from theapex of the arithmetical triangle, and for every area the need to assign thepoint of view without which truth could not be proven, that is, to arrangeseries of variations or determine each case. 17In all these areas Leibnizconstructs the 'table' of cases that refers to point of view as jurisprudenceor the art of judgment. It comprises the need to find the correct point ofview - or rather, the best - without which disorder or even chaos wouldreign. When we mentioned Henry James it was with respect to Leibniz'sidea about po int of view as the secret of things, as focus, cryptography , oreven as the determination of the indeterminate by means of ambiguoussigns: what I am telling to you, what you are also thinking about, do youagree to tell him about it, provided that we know what to expect of it.about her, and that we also agree about who he is and who she is? As in aBaroque anamorphosis, only point of view provides us with answers andcases.We have gone from variable curvature to the origin of curvature (fromthe concave side), from variation to point of view, from the fold toenvelopment, in a word, from inflection to inclusion. The transitioncannot be discerned, somewhat like a right angle that is not measured bya great arc but by a tiny arc situated close to the summit: it is at thesummit 'that the angle or the inclination of the two lines is found.' 18 W ewould nonetheless hesitate to say that visibility is located in point ofview. We would need a more natural intuition to allow for this passage tothe limit. Thus it is a very simple intuition: Why would something befolded, if it were not to be enveloped, wrapped, or put into somethingelse? It appears that here the envelope acquires its ultimate or perhapsfinal meaning: it is no longer an envelope of coherence or cohesion, likean egg, in the 'reciprocal envelopment' of organic parts. Nor even amathematical envelope of adherence or adhesion, where a fold still

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envelops other folds, as in the enveloping envelope that touches aninfinity of curves in an infinity of points. It is an envelope of inherence orof unilateral 'inhesion': inclusion or inherence is the f inal cause of the fold,such that we move indiscernibly from the latter to the former. Betweenthe two, a gap is opened which makes the envelope the reason for thefold: what is folded is the included, the inherent. It can be stated thatwhat is folded is only virtual and currently exists only in an envelope, insomething that envelops it.From no w on it is not exac tly point of view that includes; or at least, itdoes so only as an agent, but not of a final cause or a finished act(entelechia). Inclusion or inherence has a condition of closure orenve lopment , which Leibniz puts forward in his famous formula, 'nowindows,' and

deleuze, the fold leibniz and the baroque

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