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Manfred Mohr - Research in the Aesthetic Universe of the Cube

Lida von Mengden

Manfred Mohr positions his works on the interface between mathematical logic and aesthetics. Detached from materiality of any kind, they evolve the utopian dimension of a calculated world between configuration and disintegration, between construction and deconstruction. Do his works show images of hermetic worlds, exclusively bound by their own rules? Or are his computer-generated etudes on the great, quasi all-encompassing subject of the cube an attempt to aestheticise the utopia of a "pure" world of forms, based on the "purest" of all sciences - mathematics?

At the end of the 1960s, the artist was focusing on the notion of a new art for the technological era, and the concept of an art that was not determined by the emotions, but rationally. Influenced by Max Bense's writing on information aesthetics, which attempted to formalize the aesthetic content of an artwork on the basis of "aesthetic signs" and thus to open rational access to the understanding and production of art[1], Mohr radically questioned his own tachist notations influenced by Sonderborg. From then on, he saw action painting as overshaped by subjectivity, and sought possibilities of objectification. In an interim phase, which he referred to as Subjective Geometry[2], he continued to develop the emblematic aspects already to be found in art informel and thus invented his so-called imaginative pictograms (Mohr). Working from a combination of everyday symbols, electronic signs and mathematics formula, the artist set these Pop-like pictograms - simplified and monumentalised - on the picture surface using only black and white. From then on, increasing tendencies towards formalization emerged in his work. For example, he assembled a compendium of the signs that he had developed to date, publishing it as Artificiata in 1969. The breakthrough came in 1968, when he met the musician Pierre Barbaud, who was composing his first pieces of music using the computer. Mohr immediately recognized the potential of the machine for his own endeavor to produce "generative art"[3]. When, shortly after this, he was offered the chance opportunity to work in the Paris Institut Météreologique using a - room-sized - computer and a plotter, he immediately began to experiment. He wrote his own programs, testing the algorithms on the basis of the printed results, and altered them until they precisely represented his visual idea of a work. He referred to this approach as "one-to-one communication"[4] with the computer, and through it the machine became an instrument that he learnt to play, just as he had learnt to play the saxophone as a young man.
Although Mohr ultimately chose fine art after a career as a jazz musician, music remained a constant in his life. This is repeatedly indicated by short references in his texts and in conversations with him - such as the comment "all my works are inspired by music"[5] -, in which he associates his work with the computer and the works generated in this way with musical phenomena. But only in the most recent group of works, the subsets, does he refer explicitly to his musical 'roots' in Free Jazz, comparing the "seemingly contradictory chaotic visual conglomerate of forms" to a "jazzy contradiction based on fixed structures, ostensibly developed with complete freedom"[6], as if he had put his virtuosity to the test with this animation and could now improvise freely once again, using the computer as his instrument.

If one follows the computer animations subset.motion or space.color.motion /with their ever new constellations, one is drawn into an uninterrupted re-formation process of linear-geometric structures; the irregular linear grids and inset colour areas continually change their form, following their own rhythm, as if they were being subjected to a mysterious, indecipherable code. One is immersed in weird, indefinable depths - obeying a highly-complex perspective -, which topple back into the two-dimensional during this "change in perspective". A kind of technoid kaleidescope produces strange, apparently quite novel constellations, as if the previously unseen had been made visible. Although the viewer is unable to decipher a structural context, he becomes aware of the character of a system that unfolds from inner necessity. The question of 'beautiful' or 'ugly' appears obsolete, and the whole process becomes a work of art. subsets or space.color.motion present the perspective view of the 6-dimensional or 11-dimensional spaces of a rotating hypercube and mark the (temporary) end point of a long series of digital works by the artist. They represent the convincing result of almost 40 years of continuous intensive investigation into the sign-generating repertoire of line and cube. In this endeavor, Mohr has plumbed the possibilities offered by the computer with outstanding consistency, but has never allowed himself to be sidetracked to a gimmickry solely dependent on technology. From the beginning, he has maintained a sharp eye for both the distinctive qualities and the pitfalls involved in the employment of the machine. Fundamentally, his ideas have always centered on the artistic quality of the results. The parameters that were to become central in the later, generative works can already be found in the phase of "rationalizing the imagination"[7] in the Subjective Geometries: the dominance of the linear, the emphasis on individual signs and also on the empty spaces that connote both flat space and volumes, the arrangement of line structures, and - as from 1962 - the exclusive use of black and white. It was a "rigorous system of binary decisions" (Mohr), which became the foundation of his communication with computer and plotter.

Work with the Computer

From the word go, the artist was fascinated by the close relation to mathematics and the natural sciences that characterizes work with the computer, placing the production of art on an objective basis. Like no other, this medium offered the possibility of rational control over the artistic process. Mohr's criteria were logic, verifiability of the initial parameters and the results, precision, freedom from error and objectivity, and the computer fulfilled them all. The computing process took place via mathematical parameters, undisturbed by either subjectivity or emotionality. The computer thus offered ideal prerequisites with which to "overcome the limitations of the artist's personal traits" and to switch off "emotional clouding" (Mohr). In addition, the computing operations - in the case of complicated processes or large amounts of data as well - took place with amazing speed, meaning that it was possible to play through many configurations rapidly, assessing their aesthetic potential.
An essential precondition to the artist's generative works was the fact that he himself developed the algorithms. Only in this way was he able to use the enormous potential of the machine as an extension of human intelligence, as "visual high-speed thinking" and as "a heightening of our intellectual and visual experiences" (Mohr). Early on, Manfred Mohr became aware of the extent to which his work with the computer was influencing him. It compelled him to a "maniacal precision", which led to a clearer vision of his own way of thinking and intentions, thus promoting his creativity: "As it is possible to conceive the logic of a construction but not all its consequences, it is almost imperative to rely on a computer to show this large variety of possibilities; a procedure which may lead to different and perhaps more interesting answers, lying, of course, outside of normal behavior, but not outside of the imposed logic."[8] Following the scientific orientation in the early days of Computer Art, the artist not only published the results of his 'experimental set-ups', but also the mathematical programming formula in the relevant publications (for example in the magazine Computers and Automation). Up to the present day, he continues to explain his methods, so guaranteeing the verifiability of the process, as a principle of understanding.[9]
Like all early computer pioneers - such as Vera Molnar[10], Frieder Nake, Georg Nees, or Michael A. Noll - Mohr already employed random numbers in his first programmes, which intervened in certain decisions in the course of the programme[11]. Random processes or stochastic procedures lead to unpredictability in the results; in this way, it was possible for the artist to break up the determinist process of the algorithms. Mohr attaches importance to the fact that his random parameters, as mathematical chance, only disturb the algorithmic process in places where they cannot cause any fundamental structural alterations. This means, for example, that there is no uncontrolled 'disintegration'. By contrast to individual chance, the basic structure cannot be dismantled; it is only possible to determine changes in the directions of lines, or some selections made, for example when removing the edges of a cube. Despite these restrictions, chance plays the part of the true innovator, spurring the programme on like a "whip" (Mohr) and causing unpredictable numerical selections, inaccessible to the human imagination, which - in their turn -convey new impulses to the intuition. For this reason, Bense referred to chance as a guarantee of the "singularity of the mechanically generated aesthetic object"[12]. For despite the extraordinary wealth of constellations, random processors do not lead to simple repetitions, but to families of objects that display both identical and different characteristics. Fundamentally, Mohr accepts all the works configured after the 'end programme' as being of equal value, "as legitimate results"[13]. To date, he has generally published his work complexes as series on the basis of a selection of individual variants. Transferred onto canvas, they appear ennobled, confirming the traditional status of the original. Mohr's criteria for selection clearly demonstrate his preference for apparently technoid, implausible formations that question our aesthetic habits.

From "être graphique" to the 11-Dimensional Cube

Oriented on Max Bense's information aesthetics, Manfred Mohr has referred to semiotics as the "quintessence of his thinking"[14]. It is possible to view this as the reason for his efforts to find a semiotic basis for his artistic parameter. That is why he developed signs into "carriers of aesthetic information". Mohr is one of the few artists who never abandoned - even after the failing significance of semiotics within the scientific world - the semiotic rationale behind his art. On the contrary, by interpreting the aesthetic sign as the "Etre graphique" he created a stable foundation that remained valid for every extension of his sign repertoire. Etres graphiques are algorithmically generated signs; in Mohr's first phase they are precisely drawn linear geometries, whose formal independence guarantees them the character of an "iconic, self-reflecting sign"[15]. As abstract forms that can be detached, visually, from the logical content (of their origins)[16], they develop into the carriers of aesthetic information in the context of the work and its relation to the viewer.
One characteristic of the early algorithmic works is linearity, which also instruments the row structure, both qualities that reflect the typical calculating possibilities of computer technology at that time. Single elements are apparently isolated on the white surface, sometimes even when they are included in a flow of writing. Besides the primacy of a so-called 'linear iconicity' - which continues without interruption until the Etre graphique later becomes independent in Divisibility, Half-Planes and Laserglyphs - another fundamental feature becomes apparent: the neutral background is manifest as emptiness, evoking the notion of a non-space, pointing the viewer to the artificiality of the medium. In the early work UHF81 - which shows 64 such Etres graphiques, each enclosed in a circle - this missing space, with nothing in front or behind, is particularly noticeable due to the isolation of the technoid signs within the self-contained form of the circle.

Since 1973, Manfred Mohr has employed the cube as the original structure and repertoire for his development of signs. On this basis, he is in a position to systemise the Etres graphiques as image-constituting elements. Thus he has created for himself a metastructure or syntax that enables him to make a selection, according to specific rules, from a store of given signs - the edges of the cube or of its projection figure. Mohr has compared this basic structure to tonality in music; regardless of the complexity of the structure, mistakes in composition can be recognized immediately on this basis, just as when playing the piano. The artist's reasons for the selection of this particular figure for his sign repertoire point to the axiomatic: its immanent symmetry, its formal and structural stability, and - in terms of perceptual theory - its incisive Gestalt, which can tolerate manipulation for a long time. By selecting the cube, Mohr employs the figure among the five Platonic bodies that represents the earth. The artist subjects this particular body, which symbolisms the fixed or the unchangeable, to diverse strategies of decomposition, to deconstructions or constructions, the complexity of which is gradually increased and ultimately leads to the hypercube and into multi-dimensionality.
On the basis of the projection and rotation of the cube, Mohr develops graphic structures according to mathematical logics, using combinatory, statistical, additive or restrictive processes, growth programmes, etc.[17] No matter whether we are presented with the dissolution of an illusionary perspective representation of the cube in Cubic Limit I[18], or whether a form of graphic 'backbone' is drawn into the cube segments in the growth programmes, or the symmetry is broken by the rotations in the Four-Cuts, the linear is always dominant, evolving into the provider of further stimuli. As from 1976, the cube operations become more complicated; the artist increases the complexity of the structure by the mathematical-geometric introduction of a fourth dimension. In order to ensure that his visualization of such a complicated structure remains logical and aesthetically comprehensible, the artist invents methods with which he can depict randomly-defined diagonal paths through the hypercube, e.g. in the series Dimensions. Despite an enormous increase in complexity in the development of Mohr's oeuvre, and despite projections of geometrical space in multi-dimensional spatial depths - visualizations of the diagonal paths in 6- or 11-dimensional space, for example - the artist succeeds in maintaining the optical comprehensibility of these extraordinarily complex structures by introducing colour (as from 1999)[19].
Three aspects are decisive in terms of formal aesthetics: first, the increase in structural density does not correspond, by any means, to an increase in spatiality. Surprisingly, the configurations seem firmly bound to the two-dimensional surface. A convincing spatiality - even a certain plasticity of those elements which previously opposed any haptic quality - does not develop until colour is introduced as an aspect differentiating surfaces. Here, it may be fitting to point out "the computer's visual interface, the cathodic screen, becomes an important leveler of dimensions." [20]. Primarily, however, the non-space of the works must be ascribed to the graphic projection of the cube, to the strictly linear grid structure. As a quasi dematerialised sign, more of a mathematical-geometric figure of thought than a real cube, it transfers this special abstract quality to the elements generated together with it and their surroundings. When Mohr introduced rotation in the 1970s, he also influenced the space by means of motion. The linear signs began to float, apparently weightless, in an open space; a strangely place-less space, the ambiguity of which makes it difficult for the viewer to decipher the work incontestably as either flat surface or space and permits only rare perspective views or fold-over effects, when flatness appears to turn into spatiality.

The cube, or rather the square, not only developed into a paradigmatic figure for Mohr, but also for constructive-concrete art and Minimalism. It represents the search for the idea, the essence or the essential aspect of an artwork in 20th century art, a search which evolved into a condensing process. By using the cube and the square, the stereotypes of Modernism, Mohr consciously adopts his place within this tradition and thus accepts the meanings inscribed in it, such as a scientist age's faith in the unambiguous quality and comprehensibility of art conveyed by geometry, but he must also face up to its fundamental contradiction: "On the one hand, it [geometry] appears as a mimesis of technology, of the designability of universe, while on the other hand it becomes the refuge of a 'platonising' renaissance of aura."[21]

Mohr's art is often classified as Constructivism or Minimalism, and he has even reinforced such categorization himself. By turning to the essentialist language of the cube, Mohr certainly approached those trends consciously, and he tolerates the misunderstanding that his art is constructivist - among other things, to protect it from degradation as 'Computer Art'[22]. However, this formal proximity feigns something which it is not, or is only in part. For Manfred Mohr's style - the unmistakable, innovative quality of his art - is an inevitable product of the medium computer. Certain structural similarities in other artists' works point to stimulus from Mohr and indicate the innovative influence of his art. Even today, Mohr's approach may be regarded as seminal, as comparison with experimental computer works shows.[23] Pointedly expressed, Mohr's generative art can be seen as Constructivism developed to its logical conclusion. It employs the same parameters, e.g. constructive processes, rationality, the avoidance of a personal signature (neither subjectivity nor brushstroke) and orientation on industrial methods of production (precision), but draws the radical consequence and delegates the production process to a machine, which works with greater precision than a human being and guarantees reproducibility and variability. In Constructivism, the delegation of artistic production to an external instance was associated with a loss of control on the part of the artist and the 'eradication of aura' from the work of art. But it was precisely this new role of the artist as the giver of ideas and not as the doer which corresponded to the foundation of Concept Art; the idea of regarding the artistic concept as an artwork's essential aspect.[24] There is also correspondence with respect to the processual character of the artwork here. Both artistic tendencies regard different states of the artwork with respect to deviations in the realization of each individual work as part of their concept. Another common essential factor is the resulting degradation or rather relativisation of the individual work of art, the original, which is thus regarded as a section from a process.

When Manfred Mohr was asked about the advantages of computer-based work many years ago, he replied without hesitation: "precision"[25]. Today, in face of comprehensive social changes ensuing from the use of computers in all spheres of life and work - which lead to a more in almost all fields - we note a change of paradigms. The valid paradigm in 20th century art - that of the original - is being replaced by the paradigm of complexity. This is taking place in face of fundamental revaluation processes, which are no longer directed, reductively, towards the essential, but - as the world appears increasingly incomprehensible - focus on the complexity of constantly changing conditions. "In addition, it appears ... that the notion of the only 'correct' form, which enjoyed unrestricted validity in modernist art, is being replaced increasingly by aesthetics of complexity."[26]

Bearing in mind the artist's approach and all its stages, it is apparent that his artistic operations are fundamentally analytical in character. From the beginning, Mohr's interest was directed towards a structural examination of the formally inherent aesthetic potential of two-dimensional projections of the n-dimensional cube. He thus unfolded a tremendous wealth of ideas and designed a wide range of modi operandi in order to exhaust the immanent formal repertoire in its entirety, indicating a research concept that he owed - among other things - to his orientation on the science of information aesthetics, but also to the pretension to objectification expressed in the 1960s' mood of departure. Nonetheless, he determinedly continued this fundamental research in the world of geometric structures, pursuing - on the basis of a consistently binary language - the visualization of theoretical systems by exhausting the technological possibilities. Unimpressed by the ostracism of computer-based art or by its opposite - the exclusive use of computer effects in art, which usually no longer declare themselves as such today, but are devoted to the production of more perfect realities and pretensions of reality - Mohr continues to concentrate on a single paradigmatic object of research: for him, the cube becomes an example of the complexity of inherent geometric universes, comparable to an object of scientific examination. Its analysis ranges from a consideration of its macro-aesthetic state to investigation into its micro-aesthetic systematics. "In formal terms, my art is minimalist, but with respect to content, it is maximalist", as the artist once said, describing this paradox[27].

The scientific character of Mohr's brilliant computing and semiotic operations, transformed into the sphere of formal aesthetics, is also linked to the artist's genuine interest in the latest scientific insights, e.g. in the field of theoretical physics. He admits their stimulus when devising new pictorial systems, for example the concept of multi-dimensionality. In theoretical physics, the introduction of additional dimensions to our three-dimensional world - already suggested by Einstein's Theory of Relativity - is being discussed increasingly.[28] Mohr has created a mathematical-geometric model for additional dimensions with the hypercube, stimulated by the hypotheses of a 'multi-verse' and by String Theory. Such complex spatial volumes can only be calculated and ultimately visualized by means of algorithms, for sequences of figures whose configurations are never repeated only emerge through a continually operating process of generation; this is a pictorial world exceeding all human dimensions. It is no coincidence that Mohr's algorithms enabling the visualization of 6-dimensional spaces represent a suitable means to lend pictorial quality to the currently widespread notions of multi-dimensional worlds in quantum physics.

One can therefore refer to Mohr as an artist-researcher, certainly someone who is active in a hermetic space of logical-aesthetic operations, committed to the fundamentally autonomous character of his art. And yet the echo of his amazement at the world and the mechanisms by which it functions is precisely what alters the world of his imagination and his artistic universe. It is said that Kandinsky was so shaken by the possibility of splitting the atom that the world began to disintegrate before his eyes. But for Manfred Mohr the world opens up, unfolding together with previously unseen dimensions.
Today, in our highly technical society, we constantly encounter artificial substrates that pretend to be natural and offer an illusion of true reality, but there is no doubt in Mohr's case: his worlds are artificial and they display the fact openly.
And they leave no questions open, for one could never say of them, as Edgar Allen Poe said of the ideal landscape: "The original beauty is never as great as that which may be introduced". In Mohr's work nothing more can be introduced; the order is as precise as it is incontestable - despite all constructions and deconstructions, minimalisms and complexities - and that is why the question of beauty or ugliness is irrelevant.

[1] Bense refers to technology's comprehensive influence on people's awareness (compare Bense, Max: Aesthetica, Baden-Baden 1965, p. 126) and consequently demands the inclusion of the same rationality in the judgment and production of art; a turning away from subjectivity and emotionality. On this point, Lauren Sedofsky concludes: "Mohr found philosophical aesthetics that confirmed the technological sphere as our 'authentic reality', investigating theoretical physics, logic, linguistics and information theory at the interface of these disciplines and the avant-garde... Bense's 'projects' ['Projects of a Generative Aesthetics'] signalise the hour when the art object is mathematicized by manipulating signs according to the principles of a generative grammar.", Sedofsky, Lauren: Linienzüchter, in: cat. exhib. Manfred Mohr. Algorithmische Arbeiten, Josef Albers Museum, Bottrop 1998, p. 13 f.
[2] Compare cat. exhib. Manfred Mohr. Arbeiten 1966 -1980, Reuchlinhaus Pforzheim, 1988, p. 35.
[3] Mohr has referred to his works as "generative works" since 1969. In the chapter Projekte generativer Ästhetik Bense says the following: "By generative aesthetics, one should understand the sum of all operations, rules and theorems, the application of which to a number of material elements that can function as signs makes aesthetic states (distributions or forms) within them consciously and methodically creatable... At present there are four such possible abstract descriptions of aesthetic states (distributions or forms), which can be used for the production of aesthetic structures: the semiotic, which proceeds by classification, and the metric, statistic and topological, which are numerically and geometrically oriented." Bense 1965, p. 333.
[4] Manfred Mohr in conversation with the author, 10th October 2006.
[5] For example, in 1971 Mohr referred to himself in conversation with André Berne-Joffroy as a "musicien visuel, théorétique", compare cat. exhib. Manfred Mohr. Computer Graphics. Une ésthétique programmé, Musée d' Art Moderne de la Ville de Paris, 1971, p. 20.
[6] Manfred Mohr, quoted from: cat. exhib. Manfred Mohr, subsets (2003-2005), Galerie Wack Kaiserslautern/bitforms New York, 2005/06, no pag.
[7] Compare note 4.
[8] Mohr, Manfred, quoted from cat. exhib. Paris 1971, p. 38.
[9] Although he thus made his artistic concept generally accessible and verifiable in the codified form of the algorithm, his unusual artistic starting point - and 'his' random programmes - protected him from direct imitators. In recent years, Mohr has restricted himself to general descriptions of his methods in order to avoid plagiarism.
[10] Manfred Mohr is one of the few computer pioneers with training in art - like Vera Molnar, who also employed random programmes. Compare Barbara Nierhoff: Vera Molnar and the Computer - from the machine imaginaire to the 'machine réelle', in: cat. exhib. Vera Molnar. monotonie, symétrie, surprise, Kunsthalle Bremen, 2006, p. 10-23.
[11] In 1971, in Le Petit Livre de Nombres au Hasard, Mohr assembled the output of a random generator in sequences of columns.
[12] Bense 1965, p. 337.
[13] Manfred Mohr, quoted from cat. exhib. Manfred Mohr, Divisibility. Generative Works 1980-1981, Galerie Gilles Gheerbrant, Montréal 1981, no pag.
[14] ibid.
[15] ibid. In his aesthetic theory, Max Bense employed semiotics - originally developed by Charles Sanders Peirce - as a basis for the analysis of the artwork and its "aesthetic state". In the so-called 'triadic' semiotic relation between sign, signified and interpreter, in their relation to the object signs function as icon, index or symbol. The icon represents the object or has at least some traits in common with it. Compare Bense 1965, p. 306. [16] Compare Manfred Mohr, in: Algorithmus und Kunst. "Die präzisen Vergnügen". Texte und Bilder zur Ausstellung und Werkstattgespräch, eds. Nake, Frieder and Stoller, Diethelm, Galerie Meissner, Hamburg 1993, p. 38 (International Symposium INTERFACE II).
[17] Compare Mohr, Manfred, in: cat. exhib. Montréal 1981, no pag.
[18] The artist has calculated the immense number of possible combinations in this variant alone: overall, there are 4096 variants (compare cat. exhib. Manfred Mohr. Cubic Limit 1973-75, Galerie Weiller, Paris 1975, no pag.)
[19] An 11-dimensional hypercube consists of c. 42,000 cubes
[20] Compare Sedofsky 1998, p. 11.
[21] Janecke, Christian: Geometrisch Reduziertes im Sortiment der künstlerischen Moderne, in: cat. exhib. strictly geometrical?, Wilhelm-Hack-Museum, Ludwigshafen 2006, p. 12
[22] On the rejection of the computer, see: Taylor, Grant D.: The Machine that Made Science Art: The Troubled History of Computer Art 1963 -1989, Diss. University of Western Australia, Perth 2004, p. 50ff.
[23] In the early 1970s, Manfred Mohr was one of the most successful computer artists of his era. The critic Grace Hertlein referred to him as one of 'the best computer artists', 'highly intellectual and scientific'. Compare Taylor 2004, p. 125-127. In 1971, his works - referred to at the time as algorithmic works - were shown in the first individual exhibition of Computer Art world-wide at the Musée d'art Moderne in Paris, demonstrating the avant-garde status of his art and its unusual consistency and aesthetic quality. See also Ries, Marc: Medien und Abstraktion, in: cat. exhib. Abstraction Now, Künstlerhaus Wien, Graz 2004, p. 28 ff. and Carvalhais, Miguel: Code Acts, ibid., p. 46 ff.
[24] A well-known early example, before actual Concept Art, is Lazlo Maholy-Nagy's telephonic transmission of instructions for the production of an artwork during the 1930s.
[25] Quoted from Dworschak, Manfred: Manfred Mohr ist ein Purist unter den Computerkünstlern, in: Die Zeit, no. 42, 11th October 1996.
[26] Mengden, Lida von: Crossover und Komplexität: Paradigmenwechsel im 21. Jahrhundert, in: cat. exhib. Ludwigshafen 2006, p. 21; Compare Manovich, Lev: Abstraktion und Komplexität, in: cat. exhib. Graz 2004, p. 38-44.
[27] Mohr Manfred, in: cat. exhib. Montréal 1981, no pag.
[28] Compare Randall, Lisa: Theories of the Brane, in: Edge Foundation "The Third Culture", 2nd October 2003, quoted from http://www.edge.org: "In most versions of string theory the extra dimensions above the normal three are all wrapped up very tightly, so that each point in our ordinary space is like a tightly wrapped origami in six dimensions...If you look at a needle it looks like a one-dimensional line from a long distance, but really it's three-dimensional."