Manfred Mohr: algorithmic man

by Frieder Nake

There is hardly an artist who has been more supportive than Manfred Mohr in helping art critics and historians classify his work. He defines his work phases, produces series of pictures from computer programs, gives descriptions of the algorithmic decisions of his production, and produces well-designed catalogues.
For many years, well-known art critics, theoreticians, art dealers, and artists have commented on Mohr's êtres graphiques in exhibition catalogues.
Will I be able to add substantially to those authors' insight? This is quite doubtful, and the attempt could easily be disastrous. Yet I am excited by the chance - it doesn't happen every day that a computer scientist is given the opportunity to express his thoughts in an art catalogue.
Towards the end of this essay, I will return to the cultural situation which makes this possible, even demands it. In the catalogue of the exhibition "Algorithmic Works" (Spring 1998, Bottrop), Manfred Mohr says about the pictures of his work phase Half-Planes: "These shapes ... tell stories of an inconceivable, yet computable 6-D space." This statement invites one to look into it more carefully.

Conceivable. Computable
So they tell stories, these images. One should think of them as a series on large white walls. They constitute a unity. In isolation they are but instances, aspects, or examples of some work. But once we take hold of theme and context, i.e. "six-dimensional space and hypercube" in our case, and view the ensemble as one, we get an inkling of the narration which will thus open us up to contemplation. Inconceivable, says Mohr, this space is, but yet computable. In one short expression the theme of the artist shows up! I want to elaborate on this.
Inconceivable but computable! A stupendous remark. Isn't the computable exactly that which we could hardly conceive better or more precisely? What can remain mysterious and inconceivable from a phenomenon that was made computable? Anything that is made computable can be produced by a machine. Machine-made entities are totally controlled. All mystery has been lost. Pure syntax dominates. Isn't that so? And yet - Manfred Mohr is right in his remark on the inconceivability of six-dimensional space and hypercube. The reason is that we have no trouble conceiving it in our mind, even if we have great problems trying to do the same with our senses and bodies. Even worse: multidimensional space is one of the great inventions by mathematicians. Considered ontologically, space exists only in the mind. All attempts to experience higher dimensional space bodily, to wonder around in it, are nonsense and rubbish.
The space we think of here - space created by thought, as David Hilbert might say - is nothing but a schematic continuation of attempts to precisely describe the three dimensions of our experiential world, and prepare it for computing. We can easily grasp width, length, and height because our body and its senses allow us to go left and right, back and forth, up and down. We do this continuously from the first minute of our lives onwards. We do it to such a degree that we dream of it.
The concept of a Cartesian space formalizes such conditions. When Descartes invented it, he soon discovered a strong analogy between measuring in geometry and counting in arithmetic. This analogy is based on the invention of the coordinate system. It renders shapes into numbers and mathematical functions. Quality becomes quantity. The hand, which now still caresses a form, will become a series of fingers that count and soon manipulate nothing but symbols. How daring and clear!
Once mathematics has advanced so far as to describe precisely each point in three-dimensional space of bodily experience by three numbers, there is no reason not to take a vector of four numbers as the representation of a point in four-dimensional space - this space suddenly appearing in that same act. Five numbers, of course, represent points of five-dimensional space, six numbers those in six dimensional space, and n numbers stand for points in n dimensions.
These spaces of higher dimensions are postulates, thought products, inventions, gedanken experiments for computations. This total precision of thought corresponds to total estrangement from sensual experience. Neither the eye, nor any other sense, can comprehend anything. Inconceivable for our senses, but computable for our mind: such are the conditions of higher dimensions, be they four, six, or even more.
The step into this world, so alien for most living humans, is adventurously grandiose. However, I do not see any predominance of mind over senses justified by it. Nor of the other way around, senses over mind. Both, mind and senses, belong to us, to our human capabilities. The popular question of predominance, posed from afar by mathematics, really shows the pitiful and narrow-mindedness of the one who asks it.

In space
For many years now, Manfred Mohr has studied the hypercube in six dimensions. None of us could ever escape to the sixth dimension. Manfred Mohr, however, most likely is among those few people who, by prolonged and intensive activities, have acquired a deep intuition of the conditions in that space. We may, indeed, gain an insight from the mental eye in cases where the body eye loses all sight. We all know explanations that start from the bodily experience and, by analogy, lead us from two and three into four and more dimensions.⁽¹⁾ Such mental journeys are required here. Manfred Mohr has followed them so far and so often that he can show in pictures some of the things he may have seen there with his eyes shut. His pictures tell stories from that cold - as some claim it is - world of mathematics. True, many will experience the geometric line constructions for which Manfred Mohr is known as brittle and austere but also as many faceted and surprising. They appear brittle only insofar as they represent something that is not familiar to most of us. Even though my job with this text cannot be an essay in art history, it needs to be said that Mohr's congruence with many 20th century artists is obvious. Superficially, his canvasses show lines and areas and colors, and don't reveal anything at first sight unless a context is established. Only context enables us to make sense out of our sensory perceptions. In the case of Manfred Mohr this context is the hypercube. It has become something like the artist's aesthetic homeplace.
Mohr's works during thirty creative years on their surface present forms of strictly straight lines in black and grey on a white or, sometimes, grey background. He radically gave up color in order to explore different kinds of relations. We may compare Mohr's creative work between 1970 and 2000 to that of Josef Albers. Albers himself characterized his art as research into the interactions of color. Mohr's would by comparison be research into the interaction of straight lines, i.e. of a particular kind of form. These expeditions into form lead to a point where the internal logic of the work determines its external shape. The frequently square frame of many modern pictures dissolves into bizarre boundaries. The work becomes a sign of itself - an index with the strictest ties to its origin.
Manfred Mohr himself, as well as Mihai Nadin and others, have pointed to the roots of his thinking as being in the neighborhood of Max Bense (1910-1990) and the Stuttgart School. This may mean a lot of different things. Mohr has repeatedly emphasized two aspects. First, he puts forward the idea of generative art. Bense introduced it in a short text in 1965 to praise Georg Nees and the appearance of computer art.
Generative art would be Manfred Mohr's term of choice as compared to computer art, an expression he despises, but which has become prevalent. Second, the semiotic interpretation of art is important. It will be our topic in the following paragraphs.

Work and work of art
The artist creates works - to emphasize this, only works. Other interested parties, perhaps, turn a work into a work of art. The artist does not create art, but reasons for art. Possibly, his work could become art. The artist is an enabler, not an ultimate accomplisher. Even today, however, one still reads the contrary. But artists refute this by not answering the question about which message we should be able to detect in their pictures. Manfred Mohr is one of them. In his well-arranged New York studio he creates systems.
Whenever something occurs, it must have a departure and an arrival. The occurrence connects departure and arrival. A relation between the two is established.
The occurrence of art is such a relation between artist and observer. The artist constructs order, the observer destructs it. The departure may be given precisely, says Manfred Mohr; not so the arrival. His intent, in any case, is to precisely describe his productive steps. One has to wait and see what occurs after this. How and what we see is up to us.
When we start talking about what we see, it will be loud and there will be many voices and a great disorder, and it is quite all right that way, for, as previously said, the arrival could hardly be different. The artist is an enabler of arrivals comparable to those in an airport or a central station when the plane has landed or the train has arrived, and when all the people waiting for the arrival, all of a sudden burst into a chaos of voices and moods. The precisely describable departure of the plane or train is reason for the great mess of the arrival.
All the artist's aspirations and intentions, however, are directed towards art, even though he creates only works whose transformation into works of art remains the job of others - of critics, museums, publishers, book sellers, customers, visitors, the public in all its tremendous variety. The artist puts all his hopes into the recognition of his work as a work of art. Rarely ever will he be happy with the role of a Sunday painter. But despite all his efforts, the art in his work is a matter of finding its place in art history; it is not a matter of inherent order. The works' inscribed order is reason for its inscription into the world of art. It is true though that things don't develop in society in such a cleanly separated way. But for descriptive purposes this seems okay.
The occurrence of art is a relation of departure and arrival, and thus a relation of communication. As such it is semiotically conceivable.

Art creates signs
We say: art creates signs. This happens, when and if artist and observer are put into a relation. The sign is, within limits, the describable aspect of this relation.
Charles Sanders Peirce (1839 - 1914) conceived of the sign as a relation by which a representamen stands for an object by virtue of an interpretant. The two functions of designation and interpretation are integrated into the sign. The act of creating a designating material (representamen) for a designated entity (object) in the sign is met by the act of interpreting the relation of designator and designatum by its meaning (interpretant). Creation of a sign and interpretation of a sign are tightly interwoven. Only in analyzing the sign can they be separated. In actuality, one does not occur without the other. With the sign, we arrive at a concept of the oscillation between designation and denotation, between form and content.
Peirce's triadic concept of sign has a marvelous feature: it is recursive. We discover, when we try to describe more explicitly the mysterious interpretant of a sign, that it is itself a sign. Only in terms of a sign are we able to express the interpretant. That same step from sign to interpretant to sign is repeated in an infinite chain of interpretants. It represents our never ending search for meaning, our compulsion to interpret. The multitude of layers of a work shows up in such chains when we conceive of the work as a sign. The interpretant emerges from an act of interpretation. It may also be introduced by an act of intention. Interpretation is an act by the observer, intention is an act by the artist.
On behalf of the observer, the sign relation is established by encountering a material perceivable thing. The observer takes that thing as a representamen that he immediately associates with a meaning. Thus he creates an interpretant which more or less exactly evokes the hidden object.
On behalf of the artist, the sign relation is established by encountering an ideal conceivable intent. The artist takes that intent as an interpretant that he gradually expresses as a shape. Thus he creates a representamen which more or less convincingly designates the intended object.
Either way, we discuss the representamen rather pointedly in terms of matter and corporeal conditions whereas we discuss the interpretant in terms of mind and relational conditions - i.e. in terms of signs. We are, perhaps, only now in a position to fully appreciate Peirce's suggestion of an implicitly recursive concept of sign. Only today with the advent of the digital technique and the digital media signs themselves have been subjected to a mechanical process. The computer - the digital medium - epitomizes recursivity as an artifact. The recursivity has become mechanized. We will take a closer look at Manfred Mohr's intricate signs.

Algorithmic signs
Writing about Mohr's pictures entails writing about signs. I assume this happens because of the immediate impression generated by the powerful structures of black lines on a white wall. Any observer who has not barricaded himself behind his judgments of taste will experience this. When he asks himself "What is this?", the immediate answer is: "signs".
But when he does so, he inadvertently equates "sign" with "representamen", the part thus becoming a whole. The black bars on white, in all their silent power, however, become signs only when they function in designative and interpretative situations. Manfred Mohr comes to our aid with a concise explanation of the hypercube in six dimensions, of its diagonals, and of paths along the edges of the hypercube leading from start to end of such a diagonal. The crooked lines on the two-dimensional picture plane are projections of the edges of the hypercube from six-dimensional space. It seems quite easy and obvious to identify the objects and representamens of the sign in Mohr's pictures. But sometimes, their interpretation still requires an effort.
Without reference to higher-dimensional space, hardly anyone will be able to detect the designated objects. Even then it is no easy task to identify the individual straight line with the proper dimension and orientation of the edge from which it originates.
Precisely here is where the art shows up! For what can be said at all can be said clearly (Wittgenstein): this is representamen and object and the algorithm of projection between the two, in our case. But something exists beyond. It shows in ever new and different ways: the interpretant.
If we enter a more detailed analysis of Mohr's signs following the trichotomies defined by Peirce and refined by the Stuttgart group, a multitude appears. In the syntactic dimension, signs are differentiated as line quality, singularity, and generality. All three may beautifully be linked to aspects of the algorithmic origin of the pictures. These equally and clearly possess indexicality and iconicity (in the semantic dimension). Symbolic features can also be identified in relation to the object. In the pragmatic dimension of the interpetant, we look out for aspects of rheme, dicent, and argument. Rheme is the individual line or angle; dicent is the individual picture, which asserts its algorithmic origin; finally, argument is the entire series which the picture belongs to and whose combinatorial completeness Manfred Mohr is always interested in. He enters into the six-dimensional hypercube in his quest for a level of complexity. This makes combination and selection a challenging affair and wraps that which is to be shown into aesthetic ambivalence. Mohr is way too much an artist, I want to add, to let us get away easily. All the visual events in his pictures are tied to the structure of the abstract thing "hypercube". He thinks of it as a ghost flitting around all of the pictures, whose presence we vaguely suspect. In each individual picture, he permits a view of parts, subgroups, and substructures. The effect is that of hiding something.

The work as a class
We arrive at the secretless secret of Mohr's art: at the algorithmic origin of the arrangements of lines. We have studied their subject matter, the multidimensional hypercube. We have dealt with their semiotic features. Both are combined by the construction of the algorithm. This construction is often taken as the most important characteristic. Not rightly so, Manfred Mohr often tells us. But still, rightly, I want to argue against this.
The signs he establishes in his works, the representamens he creates for his object, are what matters. They constitute his works. Our artist would be hard-pressed if he had to create all that without help from the computer. Viewed from the process of production, the algorithmic dimension is the most important one, indeed. But viewed from intention and result, it no longer is. We cannot describe the departure of a work more precisely than by an algorithm.
The brittle variety, the surprising power of expression, the immediate sign quality of Manfred Mohr's works are strongly bound together by algorithms. Those algorithms determine the entire class of the pictures of one work phase. This artist creates works as classes. His series are not variation as finger exercise, but combination as mind effort. The individual picture is part of a compound unity, implicitly or explicitly. The compound unity is a mental string which exists in the algorithm in crystal clear form - a precise enjoyment, in Max Bense's words.
For Manfred Mohr, the computer is not a casual instrument. It is rather the necessary medium making possible the narration that the artist initiates with the algorithm. The artist as algorithmic man, as narrator of a new kind, delivers news from a world much familiar to mathematicians but totally alien and unfamiliar to the rest of us.

The return of color
Form. Algorithm. And color? Yes - color! It is almost forty years since Manfred Mohr decided not to use color any more. But now, in the year 2000, it re-appears in his pictures. Brittle. Stark. Disconcerting. Sure: algorithmic. He himself would, as always, explain it to us most clearly and convincingly. As I understand it, the situation is this.
We stick to the six-dimensional hypercube. We stick to its 32 internal diagonals and to the paths along edges from the starting point to the end point of a diagonal. There are 720 such paths per diagonal. The new pictures don't just consist of such edge-paths. Continuing algorithmic research into the black line, those paths are now used to define colored areas. The areas are generated in the following way. Two edge-paths get related to each other by their six edges. Vertices of corresponding edges are connected by straight lines. Quadrilaterals are thus defined which are then colored and projected onto the picture plane. Into this strict process a random element is injected with the choice of four paths of edges (out of the set of 23040 possible ones). (We could describe the generation of the colored areas more abstractly by taking an equivalent graph instead of the hypercube as the start.)
Colors are selected from a palette precalculated by the artist. He maintains a loose connection to the earliest phase of generative art in the mid-sixties: the colors of a palette are randomly selected; if the result doesn't meet the artist's taste, he discards the palette and has the machine recalculate it. The overall color style is his very personal decision. It relates to the quality of representamens in the same way as line widths did in the past. Taken together, connectedness, neighborhoods, repetitions, similarities, and shock value of the colored areas, however, are the results of the algorithmic process. They appear exactly as they must because of the algorithm. The artist provides for their possibility by defining the algorithm. He gains a distance from his work whose visual appearance, often enough, comes as a shock to himself. Algorithmics may contain elements of cruelty.
Mohr's work exists in a double way. It is an individual perceivable, corporeal materialization in its own right. At the same time, it is an instance of an algorithmically (i.e. computable) defined class. This class is the immediate work of the artist. We, as observers, get to see the class mediated only by its instances. They are, in turn, accessible to the artist only through the medium of the computer running under control of the algorithm.

Duplication
Algorithmic art thus connects an observer's perception with an artist's creation, connects arrival with departure, by way of the dialectics of the individual and the general. In the digital world, things always exist double: at the computer periphery, they are accessible by our senses; in the computer memory, they are accessible by the processor. We can explain the digital principle very well with this idea of duplication.
Manfred Mohr is one of those few who have, for a long time, had an inkling of this. He has through his systematic work turned that inkling into experience. Without mercy, he forces us into it in his new colored pictures. The algorithm treats form and color exactly the way it has to and it couldn't behave any differently since it doesn't know anything except through codes and numbers. We, however, experience form and color the way we want and can, locked as we are, into our habits, preferences, prejudices, bad tastes, fashions, moods, situations, and contexts.
The artist creates reasons and occasions. We perform the rest, and we marvel or are frightened. Openness and infinity of the mental space, closeness and limitation of the bodily space. Danger and security. Manfred Mohr: algorithmic man.
The logically enforced - or should we say: the algorithmically determined - may give rise to a rating of ugliness in an observer's aesthetic judgment. This may be how the duplication appears. The aesthetics is to be found in the narration offered - in the algorithm's content, and the picture's form. The hidden meaning has to be felt as the innate connections of the colored areas in their six-dimensional context. It is based on a computable structure that appears disturbed and alienated in the picture. A grand confrontation with the bounds of perception and the boundlessness of mind.

Third culture
A last remark shall be added. C.P. Snow's slogan of the two cultures has come up again. It plays some role in the current cultural discourse.⁽²⁾ In his Rede lecture in 1959, Snow had pointed out a gap of ignorance between the literary and the scientific intelligence, or between the humanities and the sciences. The western cultures were really split into two, not communicating with each other and interpreting reality - as nature and society - in totally different ways. Snow's lecture sparked a lively discussion without a definitive outcome. In 1963, he commented on this himself and expressed his hope of a third culture uniting the best aspects of hermeneutic-critical and constructive-formal intelligence. His original purpose was to seek a better balance between the rich and the poor countries.
Digitization and mechanization of mental labor slowly appeared on the scene. Nowadays, they shed a different light on Snow's thesis. It is less political. Today the digital principle is a common fact. With the World Wide Web and with ubiquitous computing it has become an everyday cultural fact. There is much indication that a new type of intelligent behavior is required in order to understand, live with and master the algorithmic approach to reality and the duplication ingrained into a semiotization of reality.
An intelligence is required that feels comfortable in both of Snow's cultures, and that is capable of hermeneutic as well as constructive expression. An algorithmic-semiotic intelligence! An intelligence beyond the realm of things, comfortable in the fluidity of sign processes. An intelligence that should not get hooked on the superfluous essay but on creating works that enable: works as algorithmic classes. Departures and arrivals. An intelligence that emerges from semiotic reflections after the assault of Western civilization and its break at the wall of the Pacific (Lyotard). Algorithmic artists like Manfred Mohr will no doubt belong to its pioneers.

Concluding I would like to add that this text was inspired by discussions with the artist during some wonderful summer days in New York City 2001. I would like to thank him kindly.