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Crystal/

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Citation for published version (APA): Miller, C. F. B. (2020). Crystal/Cubism. In C. F. B. Miller, & G. Brockington (Eds.), Of : Essays in honour of Christopher Green (pp. 177-203). Paul Holberton Publishing.

Published in: Of Modernism

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Download date:03. Oct. 2021 !"#$%&' /!"#$%& !.'.#. &$(()*

To !nd the connection between the inner form (forme primitive) and the outer form (sécondaire) and to deduce the latter from the former, is an interesting and delicate point in crystallography. —G.W.F. Hegel1

In Léger and the Avant-garde (1976), Christopher Green coined the phrase ‘crystal Cubism’ to denote a trend that emerged in Parisian painting in the late , cognate with the wartime Call to Order:

The Cubist classicism which must have seemed imminent from 1916 on was now conclusively established, Léonce Rosenberg’s galerie de l’E"ort Moderne acting as its centre. A group had emerged. Amédée Ozenfant and Charles-Édouard Jeanneret were to look back on the Cubist ‘call to order’ under the title ‘Towards a crystalline state’ (Vers un cristal), and, because of the fact that the term ‘classical Cubism’ has already found for itself a !rm historical niche, this short-lived style with its accent on clarity, purity and structure might aptly be called ‘crystal Cubism’.2

The reference was to an essay, ‘Vers le cristal’, which I would translate as ‘Towards Crystal’, !rst published in July 1924 in the Purist magazine L’Esprit nouveau, then again in Ozenfant and Jeanneret’s 1925 collection, La Peinture Moderne.3 In previous texts the Purists had identi!ed the ‘!rst epoch’ of Cubism with the production of and Pablo from 1908 to 1912, and the ‘second epoch’ with the work of epigones such as Henri Hayden between 1912 and 1918.4 ‘Towards Crystal’ turned to a third, current phase, evident in the painting and of Braque, Picasso, , , Fernand Léger and . In the practices of these artists, Ozenfant and Jeanneret claimed to discover a ‘unitary motivating idea’ (une idée motrice unitaire), a ‘common conception’ that distinguished the ‘true Detail of !g. 55: , Three Women, Cubists’ from the Cubistic kitsch of advertising and design. This new, 1908

!"" authentic Cubism aspired to ‘a state of classi!cation, condensation, !rmness, rigour [fermeté], intensity, synthesis’, a trajectory they called the ‘tendency towards crystal’:

In nature, crystal is one of the phenomena that most moves us because it clearly demonstrates this tendency to apparent geometric organisation. Sometimes nature shows us the way in which its forms are constructed by the reciprocal play of internal and external forces. Crystal grows and stops growing according to the theoretical forms of geometry, and man takes pleasure in these arrangements because he !nds in them evidence [justi!cation] for the abstract conceptions of geometry: the spirit of man and nature !nd a common factor, common ground, in the crystal, in the cell, everywhere where order is perceptible to the point where it proves the laws for explaining nature, in whose legislation reason takes delight [que la raison s’est complue à édicter].5

In L’Esprit nouveau, Ozenfant and Jeanneret illustrated their postulates with two works each by Braque, Gris, Léger and Picasso, and three by Laurens. The list of ‘crystal’ Cubists expanded in La !"#$%&'(! Peinture moderne, to ‘Braque, Gris, Laurens, Léger, Lipchitz, Picasso, of etc’. Evidently, that et cetera included Ozenfant and Jeanneret themselves, as alongside four Picasso paintings and a sculpture by Lipchitz, they reproduced a by each of the authors.6 The 1925 Petit Larousse o"ered a working de!nition of ‘cristal’ in common parlance: ‘transparent mineral substance, taking naturally the form of a regular or symmetrical polyhedron’.7 That edition also featured ‘Cubisme’ for the !rst time: ‘Modern school of which emerged around 1910 with the intention of representing objects by synthesising them into geometric forms.’8 Synthesis and geometry: key terms in what follows. The Purists claimed to value crystal because it instantiated the ‘theoretical forms’ or ‘abstract conceptions’ of geometry, presenting a for the mathematization of the aesthetic. ‘The essential point’, wrote the Abbé René-Just Haüy, whose work at the end of the eighteenth century transformed mineral crystallography from speculative natural history into a modern mathematical science, ‘is that theory and crystallisation ultimately come together and !nd common ground’.9 Although scienti!c crystallography had undergone a revolution with the discovery of liquid crystals in 1888 and the development of X-ray di"raction from 1912, the Purists meant this

!"# 59. Pablo Picasso, Glass and Pipe, 1917. Reproduced in L’Esprit nouveau, Vol. 25, 1924

more traditional concept, analogous to what Michel Serres would ! . " . # $%&&'( have in mind when he later wrote that the ‘object of philosophy, of classical science, is the crystal and, in general, the stable solid, with clear outlines. The system is closed, it is in equilibrium.’10 Among the illustrations to ‘Vers le cristal’, perhaps the one that conformed most closely to Ozenfant and Jeanneret’s programme, was Picasso’s little Glass and Pipe (1917, !g. 59).11 The image subordinates its objects to elementary geometry. The table, central background !eld, pipe and glass are plane !gures, closed polygonal circuits, executed with a straight edge. By comparison with high analytic Cubism, the structural opposition between !gure and ground is stable (though the background and the table overlap, tilting towards ambiguity). With its sharp vertices and discrete elements, the Glass and Pipe seems to answer the Purist call for hardness and ‘classi!cation’. At the level of the picture’s irregular polygons, its ‘crystalline’ qualities are metaphorical at best. But in the glittering particles of sand that make up the ground, the pipe and the pro!le of the glass, there is probably quartz, a literal crystal.12 ‘Vers le cristal’ echoed Picasso’s !rst public statement, which he made in Spanish to before it was translated into English and published in May 1923 in the New York magazine, The . Rejecting the claim that Cubism was an ‘art of transition’, Picasso both likened Cubist painting to crystal, and asserted its autonomy at the level of the medium:

!"$ Cubism is not either a seed or a foetus, but an art dealing primarily with forms, and when a form is realized it is there to live its own life. A mineral substance, having geometric formation, is not made so for transitory purposes, it is to remain what it is and will always have its own form. […] Mathematics, trigonometry, chemistry, psychoanalysis, music, and whatnot, have been related to Cubism to give it an easier interpretation. All this has been pure literature, not to say nonsense, which brought bad results, blinding people with theories. Cubism has kept itself within the limits and limitations of painting, never pretending to go beyond it.13

Crystal here conveys the artwork’s ideal, ahistorical, autonomous being, which ‘will always have its own form’. Mineral geometry models the artwork’s supposed transcendence of temporality, a conventional modernist supposition.14 The telling paradox is that in

the same breath as a#rming the artwork’s autonomy from discourse, Picasso uses crystal to put Cubism into words. More than a few commentators have ignored Picasso’s warning against searching through scienti!c ‘contexts’ for Cubism’s meaning, !"#$%&'(! whether in fourth-dimensional mathematics, ether physics, general of relativity, or beyond.15 One or two exceptions aside, the science of crystals has been absent from the literature.16 Nevertheless, it is striking that whenever Cubism’s conventional metalanguage invokes planes, facets, arrises, striations, or even lattices, it rehearses the lexicon of crystallography. What follows will address the relation between Cubism and the discourse of crystals. This discourse inscribed Cubism’s horizon of expectations. In the !rst three decades of the last century, a mineral crystal aesthetics reticulated European art theory. The nineteenth-century genealogy of this aesthetics extended through Hegel to scienti!c crystallography. A diagram of this !eld will show points of intersection between crystallography and Cubism’s reception, and indicate the operation of the crystal metaphor in Cubist painting itself. My intention, however, is not to propose another set of ‘sources’ for Cubism. To the contrary, my line of inquiry will pivot from the science of crystals to a perceptual problematic at the interface between the corporeal observer and the graphic representation of polyhedral forms. From the encounter between mathematized objectivity and the contingency of subjective vision arises the motif of Cubism’s criticality – which is to say, its negativity.

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!#% To the extent that the Purists’ crystal artwork was an ‘act of pure creation’, it spoke to the post-Kantian assumptions of early Cubist criticism.17 Yet the valorization of polyhedral geometry implied a more ancient pedigree in Western idealism. In the Timaeus, Plato described how the divine Craftsman imposed order on the universe by marking out the elements ‘into shapes by means of forms and numbers’. The cosmos was thus composed of !ve regular solids: the tetrahedron for !re, the octahedron for air, the icosahedron for water, the cube for earth, and the dodecahedron for the universe as a whole.18 Again, whereas mimetic depiction was anathema to the ideal polis of the Republic, geometry represented ‘knowledge of the eternally real’, the ‘soul’s transport to the truth, […] productive of philosophical thought by directing upward that which we now wrongly direct downward’.19 Platonism had been an active factor in modernist aestheticism since the Symbolist !n de siècle.20 The crystal artwork itself emerged ! . " . # $%&&'( as an aesthetic paradigm from Symbolist poetics. André Gide’s 1892 essay, ‘The Treatise of Narcissus: Theory of the Symbol’, put it as follows:

The artwork is a crystal – a partial paradise where the Idea #ourishes in its superior purity; where, as in the lost Eden, the normal and necessary order has disposed all forms in a reciprocal and symmetrical dependency, where the pride of the word does not supplant Thought, – where sure and rhythmic phrases, where words, symbols yet, but pure symbols, are made transparent and revelatory.21

For Gide, the crystal artwork preceded discourse as an Adamic Idea, a naturally symmetrical symbol endowed with prelapsarian immediacy. For Ozenfant and Jeanneret crystal was likewise an ideal term, but also the telos of a system, the ‘unitary motivating idea’ for the Cubist project whose existence the authors were concerned to establish. As such it mimicked the function taken on elsewhere, in the postwar discourse around Cubism, by synthesis – a noun Ozenfant and Jeanneret presented as synonymous with crystal. The modernist Call to Order revived the rhetoric of synthesis with which and Neo- had designated ‘forms of aesthetic unity that stood over and above fragmented or merely aggregate kinds of quotidian experience’.22 This language survives today in the application of the term Synthetic Cubism to Cubist

!#! painting after , which restored contour after the high Cubist breakdown in the distinction between !gure and ground. Broadly speaking, synthesis in Cubist criticism connoted the dictionary de!nition: ‘the combination of immaterial or abstract things, or of elements into an ideal or abstract whole’.23 Merging, perhaps, with a certain Hegelianism in the circle around the Galerie de l’E"ort Moderne, Purist crystal was ‘synthetic’ to the extent that it claimed to resolve divisions between ‘internal and external forces’, ‘man’ and ‘nature’, abstract and concrete, form and matter, subject and object. In this respect, Purist crystal was an avatar of symbol, an ideal of positive sublation familiar from histories of aesthetic modernism.24 In modernist architectural theory, a full-blown aesthetics of crystal and glass had been taking shape since before the war. The Expressionist network around Paul Scheerbart, Bruno Taut and the Crystal Chain circle envisioned utopian fantasies about glass

architecture, while and theorists constructed a crystalline aesthetic that mediated between romantic utopianism and post-Cubist rationalism.25 For in 1919, architecture was ‘the crystalline expression of man’s noblest thoughts’.26 The !"#$%&'(! programme for a design for an artist’s house, commissioned by of Léonce Rosenberg from in 1923, stated that: ‘Your atelier must be like a glass cover or like an empty crystal. It must have an absolute purity, a constant light, a clear atmosphere.’27 In 1922, De Stijl held an at Léonce Rosenberg’s Galerie de l’E"ort Moderne, where among the exhibits was Mies van der Rohe’s model of a glass skyscraper. In ‘Vers le cristal’, Ozenfant and Jeanneret were positioning Cubist painting in a utopian subculture of architectonic crystallinity. Crystal was a major motif in early twentieth-century art history, too. Aloïs Riegl, in his Late Roman Art Industry (1901), viewed ‘crystalline’ beauty as typi!ed by ‘the strictest geometrical composition’. Such crystalline visual structure, ‘the !rst and most eternal law of inanimate matter’, approached ‘absolute beauty’.28 As his posthumously published Historical Grammar of the demonstrates, Riegl’s crystal aesthetic drew on the conventions of nineteenth-century crystallography:

Man creates inorganic motifs from the mineral mass known as dead matter. Nature has shaped this dead matter into crystals, bodies bounded by regular planar surfaces that conjoin at angles. The special

!#& property of the crystal is that its main body can be split along an ever- present, if only ideal, central axis into two equal halves, with each adjacent surface likewise being divisible into halves along its own central axis. The characteristics of crystallinity are thus (a) delimitation by regular surfaces conjoined at angles and (b) absolute stereometric and planimetric symmetry. In certain cases – in a regular polyhedron, for example – this symmetry can be multiplied on all sides: the dividing line need not !rst transect the linear central axis; rather, any line cut through the middle point will yield two congruent halves.29

Riegl’s crystallinity may have owed something to Hegel,30 but his understanding of inorganic, crystalline form was also in dialogue with later developments in German crystal science, which in the course of the nineteenth century had come to centre on axial symmetry.31 In Abstraction and Empathy (1908), Wilhelm Worringer took Riegl’s ‘crystalline’ for a key term in the ‘antithetic relation’ ! . " . # $%&&'( of his title:

Just as the urge to empathy as a pre-assumption of aesthetic experience !nds its grati!cation in the beauty of the organic, so the urge to abstraction !nds its beauty in the life-denying inorganic, in the crystalline or, in general terms, in all abstract law and necessity.32

Worringer’s antithesis between organic empathy and crystalline abstraction might be echoed in the distinction Picasso drew in 1923 between organic ‘seed’ or ‘foetus’ and mineral ‘geometric formation’. Picasso’s once and future dealer, Daniel-Henry Kahnweiler, was familiar with Worringer.33 For Heinrich Wöl%in, with whose work Kahnweiler was again conversant,34 crystallization was a metaphor for the historical formation of visual perception. ‘All artistic perception is bound up with certain decorative schemas’, stated the Principles of Art History (1915). ‘Visibility crystallises for the eye in certain forms. And each new form of crystallisation brings a new aspect of world content to light.’35 David Summers has argued that in Wöl%in’s notion of crystallisation, ‘decoration was not only geometric, but also stereometric, or three-dimensional’. At stake was ‘the geometric tradition of Western pictorial space’, which ‘may be considered in terms of a regular, crystalline structure: transversals are parallel to the base of a rectilinear picture format and to the plane of the

!#' picture surface itself, and perspectival orthogonals show continuous recession along a virtual plane, that is, into the picture space. Wöl%in’s “crystals”, in short, might be seen as endless narrative invention and variation on these themes’.36 As we shall see, we might read early Cubist practice as folding Wöl%in’s metaphor back on itself, with the ideal crystal schema opening onto a modern way of seeing that transgressed the limits of perspective as symbolic form.

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To ravel the clues in this ‘crystal ’ would seem to require a tolerance for zigzags.37 The Purists were not writing into a vacuum when they advocated a crystal Cubist aesthetic. Indeed, as I shall show, this aesthetic stretched back to Cubism’s very beginnings. Yet to grasp the dialectical kernel of this problem we must take a

detour through the and the of André Breton. Between 1932 and 1937, Breton referred repeatedly to the account of crystal given in the di#cult second section of G.W.F. Hegel’s Naturphilosophie, the Physik.38 The !rst citation occurred in Breton’s !"#$%&'(! public rebuttal of the criticisms addressed to Surrealism in February of 1932 by the essayist André Rolland de Renéville. Among others, Renéville had disparaged René Char, to whose defence Breton leapt by asserting that Char’s thought had in fact achieved ‘crystallisation, in the Hegelian sense of the “moment at which the mobile and restless activity of magnetism reaches complete repose”’, exhibiting a ‘transparency and hardness’ also manifest in his life.39 In the Philosophy of Nature, Hegel posited magnetism, with its dynamic of polar opposition, as the ‘dialectical activity’ that mediated between shapeless physical material and the shape (Gestalt) of the crystal. Crystal thus constituted a ‘totality’, the realization in nature of the dialectical Notion (Begri"). (‘The Notion is the principle of freedom, the power of substance self-realised. It is a systematic whole, in which each of its constituent functions is the very total which the notion is, and is put as indissolubly one with it. Thus in its self- identity it has original and complete determinateness.’)40 In the individual crystal, ‘the oppositions have been neutralised into the form of indi"erence; magnetism then expresses its di"erence as a determination of surface’.41 Hegel’s theorizing about the function of polarity in crystallization was consistent with the science of his day.42 The Philosophy of

!#( Nature’s crystal Gestalt corresponds to Serres’s ‘object of philosophy, of classical science’, the ‘stable solid, with clear outlines’, its system ‘in equilibrium’. With a non-contemporaneous, recondite &ourish, Breton deployed Hegelian crystal to code an ally’s virtues as a structure of neutralized polarities. Whether or not the poet subscribed to the philosopher’s century-old explanation of the physical world, our takeaway from this episode of intellectual posturing might be that the crystal metaphor, as Breton lifted it from the Philosophy of Nature, had the capacity to represent the materialization of the dialectic in a static Gestalt. In the words of Auguste Véra’s , which Breton consulted: ‘Ce qui n’était qu’une détermination immatérielle devient matériel et par là l’activité mobile et sans repos du magnétisme atteint à un repos complet.’ (‘What was only an immaterial determination becomes material and thus the mobile and restless activity of magnetism [which Hegel considered to be immaterial] attains a state of complete rest.’)43 ! . " . # $%&&'( In 1933, Breton used the crystal metaphor to !gure his strategy as co-editor of magazine, that ‘encyclopaedic’ attempt to subsume disciplinary distinctions between and sciences under a Surrealist rubric.44 In the December double issue, an anonymous editorial note – presumably authored by Breton – stated that despite its diverse content, each number of the magazine was a ‘homogeneous work’. Like the ‘hypothetical existence of the “nucleus”, from which the crystal can be reconstituted’, an ‘abstract’ editorial conception uni!ed the contributors’ ‘divergent approaches (artistic, literary, scienti!c)’:

But it is the crystal alone that we present. Since we are certain of its internal form (by appeal to approaches that seem to have a distinct view of it, albeit – almost necessarily – from a single angle), we have striven to deduce its external form – dimensions, shape, brilliance – with the sole concern of revealing objectively the connection between the two forms. […] Each overall publication published under the title Minotaure is justi!ed in our eyes insofar as we come through it to the determination, on the intellectual level, of an incontestable nerve centre [point névralgique] and attempt to constitute equilibrium on this point, that is to say the unity of di"erences, in order to give its new and authentic shape [!gure] to that thought which is always in the process of becoming.45

!#) To con!gure the relation between concept and content in Minotaure, Breton borrowed – tacitly this time – Hegel’s account of internal and external crystal form. The Zusatz (‘Addition’) to paragraph 315 of the Philosophy of Nature states: ‘as shape is the equilibrium of di"erences, crystal must contain a moment which represents an external relation, and which expresses its nature in the division of its mass’. Shape must both ‘di"erentiate itself’, and be ‘the unity of di"erences’. Thus in the crystal ‘there is an internal shape and an external shape, […] two totalities of form. This double geometry, this double formation constitutes, as it were, notion and reality, the soul and the body.’46 This double structure is important, not least because, as we shall see, it overlapped with Hegel’s account of the aesthetic symbol. Hegel was articulating the mode of speculative ideation, inaugurated by the Abbé René-Just Haüy (1743–1822), which

dominated French scienti!c thinking about crystals in the long nineteenth century. When Breton appealed to ‘the hypothetical existence of the “nucleus” [noyau], from which the crystal can be reconstituted’, he was adducing a concept that originated with !"#$%&'(! Haüy. Haüy’s initial question was this: why should the same mineral of substance take di"erent well-de!ned forms that would seem, at !rst glance, to bear no relation to each other? Observing two di"erent specimens of limestone spar, one a regular hexahedral prism, the other a rhomboid, we might be forgiven for believing that the two forms were ‘entirely foreign to each other’. On examination, however, ‘the meeting point which escapes us when we limit ourselves to the consideration of the exterior form, becomes perceptible as soon as we penetrate into the intimate mechanism of the structure’.47 With this approach, crystallography carried out the transition to the modern épistémè, by which scienti!c analysis came to relate ‘the visible to the invisible, to its deeper cause, as it were’, before moving ‘from that hidden architecture towards the more obvious signs displayed on the surfaces of bodies’.48 Haüy recounted how, if we cut the hexahedral prism along the natural joints of its layers, we would end up with a rhomboid ‘entirely similar’ to the aforementioned one. The process of ‘mechanical division’ along a crystal’s ‘arrises’ (arêtes) revealed the basic noyau – the kernel or nucleus – at its centre. Di"erent substances had di"erent nuclei, but if the substance was the same, the nucleus would be too, notwithstanding variations in

!#* secondary morphology. We should regard these nuclei, Haüy wrote, as ‘veritable primitive forms, on which all other forms depend’.49 Hegel refers directly to Haüy’s work:

To !nd the connection between the inner form (forme primitive) and the outer form (sécondaire) and to deduce the latter from the former, is an interesting and delicate point in crystallography. All observations must be carried out in accordance with a general principle of transformation. The outer crystallisation does not always accord with the inner; not all rhomboidal calcite has the same determination outwardly as inwardly, and yet there is a unity between the two formations. […] Haüy […] assumes the nucleus, lets the molécules intégrantes attach themselves to the surfaces of the nucleus in a kind of serial arrangement in which the outer shape depends on a decrease in the series of the base, but in such a way that the law of this serial arrangement is determined precisely by the pre-existent shape.50 ! . " . # $%&&'(

In Haüy’s theory, the ‘unity’ between the nucleus or primitive form and the secondary form depended on the arrangement of the submicroscopic molécules intégrantes (‘integrant molecules’) he hypothesized as the building-blocks of crystal structure. The molécules intégrantes took only three shapes: parallelepiped (a solid !gure whose faces are six parallelograms, of which opposite pairs are parallel – for example, the cube), triangular prism, or tetrahedron. The noyaux or formes primitives were limited to six: parallelepiped, octahedron, tetrahedron, hexagonal prism, dodecahedron with rhombic faces, or dodecahedron with triangular faces.51 From the nucleus, which Haüy imagined as a stack of contiguous molécules intégrantes, secondary form proceeded by regular ‘molecular decrements’. On each face of the nucleus, a recessive structure of deposition would build up a molecular pyramid. Interfacial coordination between these pyramids would in turn give rise to a new polyhedron, the secondary form.52 The illustration of iron pyrite given in the 1801 Traité de minéralogie – a ‘classic in the !eld’, whose atlas ‘counts among the most wonderful of the 19th century’– demonstrates how Haüy visualized crystal structure (!g. 60).53 In Haüy’s Fig. 75 we can see how the stacking of the cubic molécules intégrantes on the similarly cubic nucleus forms the pentagonal dodecahedron of the secondary form. In this instance, Haüy theorized that the decrements of the molecular

!#" 60. René-Just Haüy, plate from the Traité de minéralogie (1801). Reprinted in Haüy, Traité de critstallographie (: Bachelor and Huzard, 1822) !"#$%&'(! of layers followed a simple 2:1 ratio, and overall his theory of crystal formation prioritized mathematical elegance and simplicity over anything else.54 As one historian of crystallography has put it, for Haüy, ‘nature had formed crystalline matter in accordance with the principles of simple arithmetic and geometry; we should not attempt to complicate matters once these simple relationships had been established’.55 On the basis of his theory, the engravings in Haüy’s atlas obeyed the laws of descriptive geometry, a nascent branch of applied mathematics.56 An ideal ‘correspondence between theory and practice’ was at the heart of a crystallography which, in its own way, ‘symbolized that alliance of space geometry, crystallography and aesthetics, or more generally, that of mathematics and physics, that was bound to determine the future’.57 When the Purists wrote that crystal ‘grows and stops growing according to the theoretical forms of geometry, and man takes pleasure in these arrangements because he !nds in them evidence for the abstract conceptions of geometry’, they were registering Haüy’s legacy, rather than the then-incipient science of chemical bonding. Given his reading of Haüy, it is tempting to suppose that Hegel had in mind the pyramidal engravings of the Traité de minéralogie when,

!## in a celebrated passage of the Aesthetics, he described the Egyptian pyramids as ungeheure Kristalle: ‘gigantic crystals’.58 The double structure of early nineteenth-century crystal, with its inner and outer forms, its ‘soul’ and ‘body’ in Hegel’s phrasing, resembled a natural sign or, in Hegel’s terms, a symbol, which was ‘no purely arbitrary sign, but a sign which in its externality comprises in itself at the same time the content of the idea which it brings into appearance’.59 Content and form in Hegel’s symbol bore a relation comparable to the one between ‘primitive’ and ‘secondary’ forms in Haüy’s crystal, and indeed for the former the crystal-pyramid was ‘the simple prototype of symbolical art itself’ – the symbol of the symbol, the symbol of the very ‘beginning of art’.60 This ‘symbolic’ art, however, was a de!cient precursor of the ‘classical’ ideal, insofar as the originary crystal-pyramid had an absence at its centre, since death resided where, in Haüy’s terms, the noyau – the nucleus or kernel – would be. The pyramids, ‘though astonishing in themselves’, were ‘just simple ! . " . # $%&&'( crystals’ whose ‘kernel’ was a mere ‘departed spirit’.61 Characteristically, death was missing from André Breton’s application of Hegelian crystal to Surrealist symbolization, which culminated in the major statement, ‘La beauté sera convulsive’, !rst published in Minotaure in 1934.62 Returning to the problem Hegel addressed in the Philosophy of Nature, of the relationship between dialectical negativity and the static Gestalt, Breton wrote that convulsive beauty a#rmed ‘the reciprocal relations linking the object seen in its motion and in its repose’.63 He began by recalling his experience of crystal mimicry in the Grotto of the Fairies near Montpellier, where there was a mineral formation, known as ‘the imperial mantle’, which resembled a spectacular cloak – a simulacrum that recalled Breton’s invocation, in the 1933 text ‘The Automatic Message’, of crystal-scrying.64 However, Breton continues, ‘it is completely apart from these accidental !gurations that I am led to compose a eulogy to crystal’:

There could be no higher artistic teaching than that of the crystal. The work of art, just like any fragment of human life considered in its deepest meaning, seems to be devoid of value if it does not o"er the hardness, the rigidity, the regularity, the lustre on every interior and exterior facet, of the crystal. Please understand that this a$rmation is constantly and categorically opposed, for me, to everything that attempts, aesthetically or morally, to found formal beauty on a willed work of voluntary

!#$ perfection that humans must desire to do. On the contrary, I have never stopped advocating creation, spontaneous action, insofar as the crystal, nonperfectible by de!nition, is the perfect example of it. The house where I live, my life, what I write: I that all that might appear from far o" like these cubes of rock salt look close up.65

He then signposts the account of the crystal Gestalt given in the Philosophy of Nature.66 In that book, Hegel repeatedly compares crystallisation to art production. ‘The form disclosed in crystallisation,’ he writes, ‘stirs and moves in marvellous fashion, expressing itself in characteristic formations as an organic and organising impulse. These grow freely and independently; and anyone unused to the sight of these regular, ornamental shapes does not take them to be products of Nature, but attributes them rather to human art and e"ort.’67 As a

generator of ‘crystallised’ shape, nature is ‘like the artist’, but in an unconscious, immediate way: ‘That is, the Notion is not present as something conceived or imagined, while the thing stands over against the thinker and is fashioned by him; the Notion has not the !"#$%&'(! form of consciousness but is immediately in the element of being, not of detached from it.’68 By adopting crystallization as a metaphor for art production, Breton seems to espouse a quasi-romantic identi!cation with an unconsciously dialectical nature.

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According to one contemporaneous observer at least, scienti!c crystallography lay at the very ‘origin of Cubism’.69 In his gossipy 1926 volume, Evolution in , the of The Sunday Times, Frank Rutter, recalled being in Paris around 1908:

One day a painter I knew accompanied a friend of his, a student of science, to the Sorbonne and there heard a lecture on mineralogy. He returned from an improving afternoon with a new word – crystallisation. It was a magic word, destined to become a talisman of modern painting. […] A new theory of art was being constructed, based on the idea of the crystal as the primitive form of all things. […] A Primary Painter, I was told, would preserve sharpness in the edges of his planes and accentuate the angles of his volumes.70

!$% Rutter’s reference to primitive form bespeaks, in forgivably garbled fashion, the school of thought – familiar to us by now – that emerged with René-Just Haüy. Although the putative lecture attended by Rutter’s painter-friend took place almost a century after Haüy took the inaugural Chair of Mineralogy at the university in 1809, a 1908 Sorbonne mineralogy class may well have dealt with ‘primitive form’.71 In 1901, Frédéric Wallerant, Haüy’s successor at the Sorbonne between 1903 and 1933, vigorously defended Haüy’s ‘theory of primitive forms, which, with the law of symmetry and the law of rational indices, should serve as the basis of crystallography’.72 Wallerant’s 1909 textbook, Cristallographie, discussed primitive form in mineral crystals, with special stress on the planes and arrises (arêtes) of the ‘cubic particle’.73 In truth, however, by then forme primitive was an outmoded concept, having been supplanted in the mid-nineteenth century by the space lattice, the of corner points or nodes in the ‘unit cell’ of the crystal, which was the model for the mathematics of symmetry and ! . " . # $%&&'( ‘rational indices’ to which Wallerant referred, and is still in use today.74 Subsequently, the 1912 demonstration by X-ray di"raction of internal atomic regularity in crystals was the paradigm shift that ushered in the current era of crystallographic analysis, when it has become clear that most materials, including many biological ones, are crystalline to some degree.75 The modernist adventures of the crystal metaphor did not correspond to the canonical chronology of crystal science. In 1926, Rutter’s anecdotal history posed a version of the crystallographic forme primitive as formalism’s originary form. Picasso, he wrote, ‘is commonly given credit for having invented Cubism; but if I remember rightly, the Frenchman Georges Braque was !rst in the !eld with crystallisation, and the crystal theory certainly preceded Cubism’.76 What Braque was doing with his ‘crystallised’ of 1908, Picasso did with the body: ‘To restore the human form to its primary beauty and strength all that was necessary was to eliminate curved lines, and to reconstruct human faces and bodies in “primary forms,” i.e., octahedrons, dodecahedrons, six-sided prisms, or whatever geometrical !gure might be most suitable.’77 In this endeavour, Picasso was followed by Gleizes, Léger, Metzinger and others.78 The example Rutter gave was the painting, made by Picasso in summer 1909 at Horta de Ebro, bought by the collector Roger Dutilleul in 1910, and now lost, known as of a Woman in a Mantilla (!g. 61).79

!$! 61. Pablo Picasso, Head of a Woman in a Mantilla, 1909. Reproduced in , 1912, p. 33. Hal"one print. 19.3 x 15 cm. Musée d’Orsay, Paris, !"#$%&'(! of

We can see why Rutter and his unnamed Parisian interlocutors might have understood early Cubism as performing an identi!cation between painting and something like the so-called primitive forms of crystallography. One might plausibly infer from early Cubism generative (yet ideal) relations in the artwork between a polyhedral basic unit and a secondary array. Yet we need not endorse Rutter’s aetiology in order to grant that, at Horta, the !gurative world acquired a crystal habit, to use the mineralogical term for external crystal shape. In Picasso’s oeuvre the crystal metaphor clusters nowhere more densely than in what he did that summer. A charcoal study for the sequence to which Head of a Woman in a Mantilla

!$& belongs con!gures the chin, mentolabial furrow, lips, philtrum and nose, as a polyhedral aggregate in which the chin might be said to adopt the octahedral habit of, say, diamond or magnetite, and the nose the columnar, prismatic habit of calcite or selenite.80 Is it irrelevant to point out that the Ebro Basin is known for its selenite crystals? The crystalline aggregates from 1909, by turns cubic, lenticular, platy, prismatic, reticular, tabular, tetrahedral (to employ the vocabulary of mineralogy again), imply identity between !gure (often the female !gure known as by biographical criticism) and the geological environment, not least at the level of their earthy and stony hues. What is at issue in these images, however, is not this or that particular mineral referent, but rather the concept of crystal, and the metaphor of crystallization, where crystallization is a !gure for symbolization as such. I would suggest, in other words, that the crystal metaphor functions at Horta as a metaphor for metaphorization, as a !gure for image-making. ! . " . # $%&&'( Historiography has tended not to state the obvious about what Alfred Barr, in 1936, called – with scare-quotes to &ag the !gurative or received character of the term – early Cubism’s ‘“crystallized” form’.81 Nonetheless, as I noted at the outset, whenever criticism inscribes planes, facets, arrises, lattices or striations in Cubism, it shares its language with mineralogy. To my knowledge, the term facet arrived in the literature with the 1911 essay in which Ardengo So#ci eulogized the components of Braque’s still lifes as ‘objects in which crystal facets, re&ections of wood surfaces and inlaid work, and folded fabrics create a prismatic magic that recalls the solitary magic of alpine glaciers’.82 So#ci’s simile indicates the etymology of crystal. The Greek noun krustallos also signi!es ice, from the verb krustanein, meaning to freeze. In this regard, the Demoiselles d’, with its petrifying stares, is not only the origin-point, as Alfred Barr claimed, of the Cubist ‘plane’, but a freezing-point, crystallizing its own proscenium drapery in the rigid, frosted contours of the ice- curtain, through which, by the squatter’s temple, light seems to gleam like dawn through a glacier, rather than shimmering like candlelight on satin.83 The crystallized textile, which merges with the !gure at left, is a !gure for the crystallized canvas, for the crystallization of painting. The crystal metaphor continued to in&ect Cubism’s late twentieth- century historiography, sometimes obliquely. Searching for a noun with which to describe early Cubism’s sharp edges,

!$' !"#$%&'(! of

62. Pablo Picasso, Three settled on arris: ‘“the line, edge, or hip in which the two straight or Women, 1908. Oil on curved surfaces of a body, forming an exterior angle, meet” (Century canvas, 200 x 178 cm. 84 The State Hermitage Dictionary, 1889)’. The OED tells us that arris derives from the Museum, St Petersburg French arête (‘ridge’). Although the former has fallen into disuse, both arris and arête have been used as technical terms in geometry, meaning ‘the intersection of the faces of a polyhedron’, or ‘the line of intersection of the two planes which form a dihedral angle’.85 In this sense, the arête has a long history in Cubism’s reception.86 Again, since the late eighteenth-century origins of crystallography, arête has been the conventional word in French for a crystal edge.87 While Steinberg did not mention crystal in connection with the arris, gesturing instead at the more remote domains of classical

!$( architecture and heraldry, the rhetoric he applied to the ‘rocklike anatomic conglomerate’ of the 1908 Three Women (!g. 62) was both insistently geological, and pledged to the plane and the facet. Planes ‘gel into hardness, angular joints run between &attened surfaces, so that depicted form solidi!es everywhere in catastrophic abutments’. In Picasso’s ‘metaphorical idiom, the canvas terrain, come under pressure, reacts by contracting, buckling and folding; each plane brought up sharp to a sudden ridge, as though the faceting of the !gures registered an ongoing upheaval’. The artist, ‘one suspects, is here meditating yet another nativity story – the old miracle play about three-dimensional matter nascent in two. […] An irregular lattice of arrises emerges as the condition of three-dimensionality in symbolic form.’88 Steinberg was rephrasing, through the related !gure of metamorphic rock-formation, the crystallization metaphor for artistic production. From the corpus of Picasso’s practice at Horta del Ebro, T. J. ! . " . # $%&&'( Clark has isolated the ‘hard-edged, spotlit, reversible cube’ as the ‘governing !gure’ of early Cubism. The kind of ‘cube’ that appears on the forehead of the Woman with Pears (!g. 63) – the edge of a polyhedron at the seat of ideation – ‘can stand, in its absolute, interminable swapping of places between !gure and ground, concavity and convexity, for just the kind of work on illusionism that Picasso was doing in general throughout this whole period’.89 Might the ‘reversible cube’ function, Clark wonders, in such a way as ‘not to open onto paradox, but positively to produce its own determinate negation?’ The answer for Clark is no. Although early Cubism’s governing !gure pretends to the speculative moment of the Hegelian dialectic, seemingly thrusting towards a new totality, its reversibility is aporetic, undecidable. Cubism here performs at best a negative dialectic, or perhaps, in a di"erent register of valorization, a deconstruction. I would like to draw a diagonal line between Clark’s ‘reversible cube’, with its dialectical pretentions, and the crystal problematic in modern thought. The reversible cube entered scienti!c discourse as a privileged problem in the philosophy and psychology of perception, from the interface between the modern observer and crystallographic representation.90 The reversible or Necker cube is so-called after Louis-Albert Necker, the Professor of Mineralogy at Geneva who, in 1832, described an ‘observation of an optical nature’, which ‘has often occurred to me while examining !gures and engraved plates

!$) 63. Pablo Picasso, Woman with Pears, 1909. Oil on canvas, 92.1 x 70.8 cm. The , Florence, May Schoenborn Bequest !"#$%&'(! of

of crystalline forms: I mean a sudden and involuntary change in the apparent position of a crystal or solid represented in an engraved !gure’.91 In fact, although posterity has not transmitted it as such, the shape in question was a rhomboid (!g. 64).92 As Charles Wheatstone remarked in 1838, this ‘puzzling e"ect’ had long been familiar to students of certain diagrams in Euclid’s Elements, ‘which, when they were attentively looked at, changed in an arbitrary manner from one solid !gure to another, and would obstinately continue to present the converse !gures when the real !gures alone were wanted’.93 In this sense, reversibility represents a cognitive limit of the rationalization of space.

!$* 64. Necker’s rhomboid, from L.A. Necker, ‘Observations on some remarkable Optical Phenomena seen in Switzerland; and an Optical Phenomenon which occurs on viewing a Figure of a Crystal or geometrical solid’, The London and Edinburgh Philosophical Magazine and Journal of Science, Third Series, Vol. 1. no. 5, November 1832, pp. 329–37, p. 336. HathiTrust Digital Library, Digitized by Google, original from Harvard University

65. Mach card from William James, The Principles of Psychology (New York: H. Holt and Company, 1918), Vol. 2, p. 255, ! g. 72. HathiTrust Technically speaking, perceptual alternation in the ambiguous Digital Library, Digitized ! gure at the brow of the Woman with Pears involves & uctuations by Google, original from University of Michigan in perspective or , rather than ! gure-ground organization.94 Again, while both the Horta arris and the Necker rhomboid alternate between binary spatial interpretations, insofar as it & ips between convexity and concavity, the former has less in common with a transparent graphic diagram of a three-dimensional cube, than with other classic examples from the psychology of perception, such as the Beaunis cubes or the card illusion presented by Ernst Mach in his Analysis of Sensations. Indeed, the Mach card has entered Cubism’s historiography via the seldom-cited proposition that may have shared with Picasso the card illusion as it appeared in William James’s Principles of Psychology (! g. 65).95 Considerations of mechanical – biographical or iconographical – causation are super& uous here to the acknowledgement that Cubism addressed the same problems of visual ambiguity that have fascinated the psychology of perception since the nineteenth century.96 As is well known, this fascination was widespread in late nineteenth- and early twentieth-century European and North American popular culture.97 For my purposes, T. J. Clark’s reading of early Cubism becomes particularly suggestive at the point where

!$" phenomenal instability converges with something like dialectical negativity. As Necker before his crystal diagram, the embodied observer of the Woman with Pears’ crystalline habit faces a situation – an aesthetic experience – in which a single geometric pattern produces two opposed spatial perceptions. The one becomes the two. Although at !rst glance the static quality of images seems alien to negativity – dialectical contradiction’s ‘indwelling pulse of self-movement and liveliness’ – the crystalline stimulus generates reversibility, the alternation over time between antagonistic percepts.98 (At times Marx himself described the operation of the dialectic as an ‘oscillation’, a synonym for undecidability in the poststructuralist theory of the avant-garde.)99 Refusing resolution, early Cubism’s reversible crystallinity inveigled time into the image, dislocating any doctrine of the symbol as a synthetic unity that might transcend temporality. Crystallization at Horta both hailed and bade

farewell to the crystalline Idea.

▫ !"#$%&'(! In Aesthetic Theory, Theodor Adorno adopted crystallisation as a of privileged !gure for the formation of the modern artwork. A famous passage applies the metaphor to the (negative) dialectic in the artwork between autonomy and historicity:

The basic levels of experience that motivate art are related to those of the objective world from which they recoil. The unsolved antagonisms of reality return in artworks as immanent problems of form. This, not the insertion of objective elements, de!nes the relation of art to society. The complex of tensions in artworks crystallizes undisturbed in these problems of form and through emancipation from the external world’s factual façade converges with the real essence.100

The crystal metaphor in early Cubism precisely mobilized a ‘complex of tensions’ in form-perception. In their strangeness and reversibility, the crystalline assemblages of Horta enacted the immanent, unresolved negativity whose simultaneous autonomy from ‘reality’, and symbolization of the latter’s antagonistic ‘essence’, Adorno rendered as a crystallization. The artwork’s ‘immanent dynamic’, he wrote, ‘crystallises the dynamic external to it and indeed does so by virtue of its aporetic character’.101

!"# Early twentieth-century modernism in France inherited from the nineteenth century a concept of crystal as an ideal geometric structure, a closed system in equilibrium. In 1924 the Purists con!ated Cubism’s destiny with an image of crystal that recapitulated conventional assumptions about the synthetic qualities of the aesthetic symbol. In the 1930s, André Breton, with reference to Hegel, posed the dialectics of the Surrealist image as a crystallization. In fact, already in 1909, Picasso had elaborated with exceptional rigour the crystal metaphor for symbolization, in all its postromantic predicament. On the one hand, this reticular, prismatic, tabular, crystalline style dramatized a romantic identi"cation between subject and object, art and nature. On the other, this crystallization went so far as to stage its own immanent critique of idealist crystal, activating something like a dialectical negativity at the level of embodied perception, aesthetic experience, or the specular ground of metaphor itself. The crystallinity of early Cubism, then, encompassed ! . " . # $%&&'( both the positive, reconciliatory and the negative, disjunctive dynamics, whose contestation has animated dialectical thinking since .102

!"" !"#$%

1 G.W.F. Hegel, Hegel’s Philosophy of Nature, trans. A.V. Miller (: Clarendon Press, 1970), p. 177. 2 Christopher Green, Léger and the Avant-garde (New Haven and London: Yale University Press, 1976), pp. 130–31. There was a minor error in Green’s citation, which used an inde!nite article, where the original text was entitled ‘Vers le cristal’ (see below, n. 3). Green has recently revived the crystal metaphor to describe Cubist idealism as an aesthetic defence against the horrors of . See Christopher Green, Cubism and War: The Crystal in the Flame (: Fundació Museu de Barcelona, 2016), p. 9. 3 Amédée Ozenfant and Charles-Édouard Jeanneret, ‘Vers le cristal’, L’Esprit nouveau, no. 25, n.d. [July 1924], n.p.; ibid., La Peinture modern (Paris: Crès, 1925), pp. 135–45. Unless otherwise indicated, are my own. For publication dates of L’Esprit nouveau see the useful appendix to Jan de Heer, The Architectonic Colour: Polychromy in the Purist Architecture of (Rotterdam: 010 Publishers, 2009), p. 192. 4 Amédée Ozenfant and Charles-Édouard Jeanneret, ‘Le cubisme. Première époque. 1908–1910’, L’Esprit nouveau, no. 23, n.d., n.p (notwithstanding its title, this text dealt with Cubist painting between 1908 and 1912); ‘Le cubisme. Deuxième époque. 1912–1918’, L’Esprit nouveau, no. 24, n.d., n.p. 5 Ozenfant and Jeanneret, ‘Vers le cristal’, n.p. 6 See Ozenfant and Jeanneret, La Peinture moderne, pp. 142, 136. 7 Claude Augé (ed.), Nouveau Petit Larousse Illustré (Paris: Librairie Larousse, 1925), p. 254. Twenty-!rst century crystallography provides the following de!nitions: ‘a crystal structure is a regular arrangement of atoms or molecules’; or, ‘a crystal structure can be described as a 3-D lattice, decorated with atoms or molecules’. See Marc de Graef and Michael E. McHenry, Structure of Materials: Introduction to Crystallography, Di!raction and Symmetry (Cambridge: Cambridge University Press, 2012), pp. 49–50. 8 Ibid., p. 258. !"#$%&'(!

9 René Just Haüy, cited in Hélène Metzger, La Génèse de la Science des cristaux (Paris: Alcan, 1918),

of p. 195. 10 Michel Serres, Hermes V. Le Passage du nord-ouest (Paris: Minuit, 1980), p. 51. 11 Christian Zervos, Pablo Picasso, Vol. III (Paris: Cahiers d’Art, 1949), p. 120. 12 This is my presumption, based on the usual composition of sand, rather than technical analysis. 13 Alfred Barr, Picasso: Forty Years of his Art, Museum of Modern Art, New York, 1939, p. 12. 14 See Paul de Man, ‘The Rhetoric of Temporality’, in de Man, Blindness and Insight: Essays in the Rhetoric of Contemporary Criticism (Minneapolis: University of Minnesota Press, 1986), pp. 187–228; Rosalind Krauss, The Optical Unconscious (Cambridge MA: MIT Press, 1993). 15 On ether physics and the fourth dimension see Linda D?alrymple Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art (Cambridge MA: MIT Press, 2013). On Einstein, relativity and Cubism’s commentators see Henderson, ‘Four-Dimensional Space or Space-Time?: The Emergence of the Cubism-Relativity Myth in New York in the 1940s’, in Michele Emmer (ed.), The Visual Mind II (Cambridge, MA: MIT Press, 2005), pp. 349–97. 16 I am thinking of James Elkins, The Domain of Images (Ithaca and London: Cornell University Press, 1999), pp. 13–30; Spyros Papapetros, On the Animation of the Inorganic: Art, Architecture, and the Extension of Life (Chicago: Chicago University Press, 2012), pp. 161–210. 17 Ozenfant and Jeanneret, ‘Vers le cristal’, n.p. 18 See Plato, Timaeus, 53b–55c, in Plato, Timaeus. Critias. Cleitophon. Menexenus. Epistles., trans. R.G. Bury (Harvard: Harvard University Press, 1929). 19 Plato, Republic VII, 527b–c, in Plato, Republic, Vol. II, Bks. 6–10, ed. and trans. Chris Emlyn- Jones and William Preddy (Harvard: Harvard University Press, 2013). 20 On modernism and Plato see Mark A. Cheetham, The Rhetoric of Purity: Essentialist Theory and the Advent of Abstract Painting (Cambridge: Cambridge University Press, 1991). Cheetham does not deal with Cubism. 21 André Gide, ‘Le Traité de Narcisse. Théorie du symbole’, Entretiens, Vol. 4, no. 22, 1892, pp. 20–28, 26–27. 22 Jonathan Crary, Suspensions of Perception: Attention, Spectacle, and Modern Culture (Cambridge MA: MIT Press, 1999), p. 154. 23 See the entry for synthesis (6.a.) on www.oed.com. This entry was !rst composed in 1919. 24 On which see de Man, ‘The Rhetoric of Temporality’; Krauss, The Optical Unconscious.

!"" 25 See Detlef Mertins, ‘The Enticing and Threatening Face of Prehistory: Walter Benjamin and the Utopia of Glass’, Assemblage, no. 29, 1996, pp. 6–23. 26 Walter Gropius in an untitled pamphlet on the occasion of the Exhibition for Unknown Architects organized by the Arbeitsrat für Kunst in 1919, quoted in ibid., pp. 14–15. 27 Quoted in A. Elzas, ‘Theo Van Doesburg’, De 8 en Opbouw, no. 17, 17 August 1935, p. 174. Cited in Nancy Troy, The De Stijl Environment (Cambridge MA: MIT Press, 1983), p. 106. 28 Wilhelm Worringer, Abstraction and Empathy: A Contribution to the Psychology of Style, trans. Michael Bullock (Chicago: Elephant, 1997), pp. 94, 19. The citation is from Riegl’s description of the Arch of Constantine in his Late Roman Art Industry (1901). 29 Aloïs Riegl, Historical Grammar of the Visual Arts, trans. E. Jung (New York: Zone Books, 2004), p. 123. 30 Claude Gandelman, ‘ and the Theory of “Crystalline Beauty”’, Orbis Litterarum, Vol. 37, no. 2, 1982, pp. 122–33, 127. 31 On the concept of crystal symmetry in the nineteenth century see John G. Burke, Origins of the Science of Crystals (Berkeley and Los Angeles: University of California Press, 1966), pp. 147–76. 32 Worringer, Abstraction and Empathy, p. 4. 33 Yve-Alain Bois, ‘Kahnweiler’s Lesson’, Representations, no. 18, 1987, pp. 33–68, 34. 34 Ibid. 35 Heinrich Wöl!in, Principles of Art History: The Problem of the Development of Style in Early Modern Art, trans. Jonathan Blower (Los Angeles: Getty Research Institute, 2015), p. 310. 36 David Summers, ‘Heinrich Wöl!in’s “Kunstgeschichtliche Grundbegri"e”, 1915’, The Burlington Magazine, Vol. 151, no. 1276, 2009, pp. 476-79, 479. Summers points to the crystal metaphor’s ‘signi#cant ancestry’ in the writings of Kant and Schelling. In the Critique of Judgement §58, Kant gives a detailed account of crystallization according to the science of

his day, describing crystals – ‘extremely beautiful shapes such as it might take art all its time ! . " . # $%&&'( to devise’ – as ‘free formations of nature’, which exemplify the ‘ideality of purposiveness’ in natural beauty. This passage would resonate in Hegel’s writings on crystal. On the scienti#c context of Kant on crystal, see Hein van den Berg, Kant on Proper Science: Biology in the Critical Philosophy and the Opus Postumum (Amsterdam: Vrije Universiteit, 2011), pp. 127–30. 37 The phrase is André Breton’s, from the ‘Introduction to the Discourse on the Paucity of Reality’ (1927), in Breton, What is Surrealism? Selected Writings, ed. Franklin Rosemont (London: Pluto Press, 1978), pp. 17–28, 17. 38 On the Physik see John N. Findlay, ‘Hegel and the Philosophy of Physics’, in J. J. O’Malley et al. (eds.), The Legacy of Hegel (The Hague: Martinus Nijho", 1973), pp. 72–89. 39 André Breton, ‘Letter to André Rolland de Renéville’, trans. Mark Polizzotti, in Breton, Break of Day, trans. Mark Polizzotti and (Lincoln and London: University of Nebraska Press, 1999), pp. 72–77, 75–76. 40 G.W.F. Hegel, The Logic of Hegel, trans. William Wallace (Oxford: , 1892), p. 287. 41 Hegel, Hegel’s Philosophy of Nature, p. 175. 42 See M.J. Petry’s detailed notes in G.W.F. Hegel, Hegel’s Philosophy of Nature, ed. and trans. M.J. Petry (London: Allen & Unwin, 1970), pp. 329–30, n. 28. 43 G.W.F. Hegel, Philosophie de la nature de Hegel, trans. Auguste Véra (Paris: Librairie Philosophique de Ladrange, 1863), p. 609. 44 See the mission statement in the front matter of Minotaure, no. 1, 1933, which announced the magazine’s ‘encyclopaedic character’. 45 The text appears in the front matter of Minotaure, nos. 3–4, 1933. 46 Hegel, Philosophie de la nature de Hegel, p. 614. See André Breton, Oeuvres complètes, Vol. 2, ed. Marguerite Bonnet, with Philippe Bernier, Étienne-Alain Hubert and José Pierre (Paris: Éditions Gallimard, 1992), pp. 1709–10, n. 3. 47 René-Just Haüy, Exposition abrégée de la théorie sur la structure des crystaux (Paris: Imprimerie de Cercle Social, 1792), p. 5. 48 Michel Foucault, The Order of Things (London: Routledge, 2002), p. 249. See W.R. Albury and D.R. Oldroyd, ‘From Renaissance Mineral Studies to Historical Geology in the Light of Foucault’s The Order of Things’, The British Journal for the History of Science, Vol. 10, no. 3, November 1977, pp. 187–215, 196. 49 Haüy, Exposition abrégée, pp. 5–6. 50 Hegel, Hegel’s Philosophy of Nature, p. 177. 51 This was how Haüy framed the theory in the Traité de la minéralogie (Paris: Louise, 1801), Vol. 1, pp. 28–31. In his Essai d’une théorie sur la structure des cristaux (1784), he had viewed the molécule intégrante and the noyau as having the same shape in a given crystalline substance. See Seymour H. Mauskopf, ‘Crystals and Compounds: Molecular Structure and Composition

!"# in Nineteenth-Century French Science’, Transactions of the American Philosophical Society, Vol. 66, no. 3, 1976, pp. 1–82, 12. 52 Ibid. 53 Henk Kubbinga, ‘Crystallography from Haüy to Laue: Controversies on the Molecular and Atomistic Nature of Solids’, Acta Crystallographica, Vol. 68, 2012, pp. 3–29, 4. 54 Ibid. 55 John G. Burke, Origins of the Science of Crystals (Berkeley and Los Angeles: University of California Press, 1966), p. 92. 56 Kubbinga, ‘Crystallography from Haüy to Laue’, p. 4. 57 Ibid. 58 G.W.F. Hegel, Hegel’s Aesthetics: Lectures on Fine Art, Vol. 1, trans. T.M. Knox (Oxford: Clarendon Press, 1975), p. 356 (translation modi#ed). 59 Ibid., p. 305. 60 Ibid., pp. 356, 303. 61 G.W.F. Hegel, Hegel’s Aesthetics: Lectures on Fine Art, Vol. 2, trans. T.M. Knox (Oxford: Clarendon Press, 1975), p. 653. 62 André Breton, ‘La beauté sera convulsive’, Minotaure, no. 5, 1934, pp. 8–15; L’Amour fou (Paris: Gallimard, 1937), translated by Mary Ann Caws as Mad Love (Lincoln and London: University of Nebraska Press, 1987), p. 10. For an in$uential account of Bretonian Surrealism as working (unsuccessfully) to repress the death drive, see Hal Foster, Compulsive Beauty (Cambridge MA: MIT Press, 1993). 63 Breton, Mad Love, p. 10. 64 André Breton, ‘Le message automatique’, Minotaure, no. 3–4, 1933, pp. 55–65, 55–56.

65 Breton, Mad Love, p. 11. 66 ‘If the very place where the “#gure” – in the Hegelian sense of the material mechanism of individuality, beyond magnetism – attains its reality is above all the crystal, then in my view the place where it ideally loses this omnipotent reality is the coral, reintegrated as it should be in life, into the dazzling sparkle of the sea.’ Ibid., pp. 11–13. Here the relation between crystal and coral is analogous to the dialectic between art and life that typi#ed the historical

!"#$%&'(! avant-garde according to Peter Bürger. See Bürger, Theory of the Avant-garde, trans. Michael

Shaw (Minneapolis: University of Minnesota Press, 1984). For more on Breton’s Hegelianism, of see Jean-Michel Rabaté, ‘Breton’s Post-Hegelian Modernism’, in James E. Swearingen and Joanne Cutting- (eds.), Extreme Beauty: Aesthetics, Politics, Death (New York and London: Continuum, 2002), pp. 17–28. 67 Hegel, Hegel’s Philosophy of Nature, trans. Miller, p. 161. 68 Ibid., p. 293. 69 Frank Rutter, ‘The Origin of Cubism’, in Rutter, Evolution in Modern Art (London: George G. Harrap, 1926), pp. 80–106. 70 Ibid., p. 83. 71 For an account of the history of mineralogy at the Sorbonne, see Jean Wyart, ‘La Minéralogie à la Sorbonne’, Bulletin de Minéralogie, Vol. 102, no. 2, 1978, pp. 91–106. 72 Frédéric Wallerant, Étude sur la forme primitive des corps cristallisés et sur la symétrie apparente (Tours: Imprimerie Deslis Frères, 1901), p. 3. 73 Frédéric Wallerant, Cristallographie. Déformations des corps cristallisés, groupements, polymorphisme, isomorphisme (Paris: Librairie Polytechnique Ch. Béranger, 1909), pp. 85–86. 74 On the possible institutional reasons for the retardation of crystallographic science in France in the latter part of the nineteenth century, see Kubbinga, ‘Crystallography from Haüy to Laue’. On the space lattice and unit cell see de Graef and McHenry, Structure of Materials, pp. 52–61. The seven ‘primitive unit cells’ correspond to the seven three-dimensional crystal systems: triclinic, monoclinic, hexagonal, rhombohedral, orthorhombic, tetragonal, cubic. (Ibid., pp. 59–61.) 75 For overviews of the current state of crystallography see de Graef and McHenry, Structure of Materials; Christopher Hammond, The Basics of Crystallography and Di!raction (Oxford: Oxford University Press, 2015). 76 Rutter, Evolution in Modern Art, pp. 24–25. 77 Ibid., p. 86. 78 Ibid. 79 See Pierre Daix, Le Cubisme de Picasso (Neuchâtel: Ides et Calendes, 1979), cat. 293. 80 The is illustrated as Study (Nose and Mouth) in Je"rey Weiss, Picasso: The Cubist Portraits of Fernande Olivier (Princeton and Oxford: Press, 2003), Cat. 42, p. 87. For a guide to crystal habits, see Cornelis Klein, Minerals and Rocks (Hoboken, NJ: John Wiley & Sons, 2008), pp. 1–4.

!"! 81 Alfred Barr, Cubism and , Museum of Modern Art, New York, 1936, p. 31. 82 Ardengo So%ci, ‘Picasso e Braque’, La Voce [Florence], 24 August 1911; translated in Mark Antli" and Patricia Leighten (eds.), A Cubism Reader (Chicago: University of Chicago Press, 2008), pp. 128–40, 140. 83 Barr, Picasso: Forty Years of his Art, p. 60. 84 Leo Steinberg, ‘Resisting Cézanne: Picasso’s “Three Women”’, Art in America, Vol. 66, no. 6, November–December 1978, 115–33, 133 n. 36. 85 Pierce Morton, Geometry, Plane, Solid, and Spherical (London: Baldwin and Cradock, 1835), p. 126; E. Littré, Dictionnaire de la langue française (Paris: Librairie Hachette, 1900), p. 51. 86 Je"rey Weiss describes the 1909 Head of a Woman sculpture as ‘articulated through […] faceted forms that are composed of tilted planes and sharp edges, or “arrises” (arêtes), to borrow terminology from the author Maurice Gieure’. See Weiss, Picasso: The Cubist Portraits of Fernande Olivier, p. 16. Weiss is citing Maurice Gieure, Initiation à l’oeuvre de Picasso (Paris, 1951), pp. 151–55. 87 See Jean-Baptiste Romé de l’Isle, Cristallographie, ou description des formes propres à tous les corps du regne minéral (Paris: L’imprimerie de monsieur, 1783), p. 211; Auguste Bravais, Études cristallographiques (Paris: Imprimerie de Gauthier-Villars, 1866), p. 103. 88 Steinberg, ‘Resisting Cézanne’, pp. 127–28. 89 T.J. Clark, Farewell to an Idea: Episodes from a History of Modernism (New Haven: Yale University Press, 1999), p. 198. 90 The literature on reversibility is enormous. For a useful survey of the scienti#c fascination with reversible #gures, see Gerald M. Long and Thomas C. Toppino, ‘Enduring Interest in Perceptual Ambiguity: Alternating Views of Reversible Figures’, Psychological Bulletin, Vol. 130, 2004, pp. 748–68.

91 Louis-Albert Necker, ‘Observations on some remarkable phaenomena seen in Switzerland; ! . " . # $%&&'( and an optical phaenomenon which occurs on viewing a #gure of a crystal or geometrical solid’, London and Edinburgh Philosophical Magazine and Journal of Science, Vol. 1, no. 5, 1832, pp. 329–37, 336. 92 In Necker’s words: ‘The rhomboid AX is drawn so that the solid angle A should be seen the nearest to the spectator, and the solid angle X the furthest from him, and that the face ABCD should be the foremost, while the face XDC is behind. But in looking repeatedly at the same #gure, you will perceive that at times the apparent position of the rhomboid is so changed that the solid angle X will appear the nearest, and the solid angle A the furthest; and that the face ACDB will recede behind the face XDC, which will come forward; which e"ect gives the whole solid a quite contrary apparent inclination.’ Ibid. 93 Charles Wheatstone, ‘Contributions to the Physiology of Vision.– Part the First. On some remarkable, and hitherto unobserved, Phenomena of Binocular Vision’, Philosophical Transactions of the Royal Society of London 1838, Part 2, pp. 371–94, 381. 94 On this distinction see Long and Toppino, ‘Enduring Interest in Perceptual Ambiguity’, p. 749. 95 Marianne L. Teuber, ‘Gertrude Stein, William James, and Pablo Picasso’s Cubism’, in Wolfgang G. Bringmann et al. (eds.), A Pictorial History of Psychology (Carol Stream, IL: Quintessence Books, 1997), pp. 256–64. 96 Genealogically speaking, Cubist reversibility pertains to the epistemic conditions of subjective vision and attention that Jonathan Crary has delineated in Techniques of the Observer: On Vision and in the Nineteenth Century (Cambridge, MA: MIT Press, 1990), and Suspensions of Perception: Attention, Spectacle, and Modern Culture (Cambridge, MA: MIT Press, 1999). 97 For a survey see Laurent Mannoni et al., Eye, Lies and Illusions, Hayward Gallery, London, 2004. See also Dario Gamboni, Potential Images: Ambiguity and Indeterminacy in Modern Art (London: Reaktion, 2002), pp. 149–67. 98 G.W.F. Hegel, Hegel’s Science of Logic, trans. A.V. Miller (Oxford: Oxford University Press, 1969), p. 442. I use here the translation given in a helpful article by Thomas Weston, ‘Marx on the Dialectics of Elliptical Motion’, Historical Materialism, Vol. 20, no. 4, 2013, pp. 3–38, 12. 99 See ibid., p. 18. For oscillation as a deconstructive term, see for example, Rosalind Krauss, The Originality of the Avant-garde and Other Modernist Myths (Cambridge, MA: MIT Press, 1985), p. 62. 100 Theodor Adorno, Aesthetic Theory, trans. Robert Hullot-Kentor (London and New York: Continuum, 1997), p. 7. 101 Ibid., p. 301. 102 On this contestation see Gail Day, Dialectical Passions: Negation in Postwar Art Theory (New York: Columbia University Press, 2011), pp. 1–24.

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