2015 / Maciej Zdanowicz


1. The notion of a discursive geometry. The links of geometry with reality

In his considerations about the beginnings of art and prehistoric art, Wilhelm Worringer observes that the pursuit of a then-contemporary human beings to create geometrical patterns stems from the reactions to indefiniteness of natural phenomena. As Worringer defines it, the changeability of the conditions of nature triggers fear in aboriginal communities. Thus, the first creators begin to produce structured, which are characterised by stability and rationality in their form. As a result, the works of art are created which are in the opposition to ephemeral reality and identical with their creators’ intellectual structure. While perfecting the sense of observation and analysis, people notice specific regularities in their surroundings as well as the links occurring therein. Such capabilities are demonstrated in art, among other things, through developing a set of mathematical modi or by defining the proportions, the principles of a measurable anatomical structure of a human body. This forming of skills leads to a more profound reflexion upon the place where one is to live and function, the attempts of finding a transcendent dimension of the world. The possibility of a complex grasp of phenomena is demonstrated by the artists from the beginning of the 20th century. The abstraction based on the empirical investigation on one hand, and the intellectual reasoning on the other, leads to the development of a language of clean artistic forms. The creation is becoming an area for exploring the nature of perception, but also the goal in itself. Władysław Strzemiński understands the image as a creation parallel to the world of nature, with identical status, specific principles of creation and structure, just like any other element of the surroundings. In 1930, Theo van Doesburg proclaims the “Concrete Art Manifesto”, in which he calls for creation that will cease the imitation of nature. A similar opinion is expressed by Jean (Hans) Arp, who wrote in 1942: (…) we reject imitating nature, we do not want to recreate, but create, just like a plant which forms fruit (...).

More than a hundred years’ tradition of geometric art, significant achievements of the artists arising from constructivist trends of the first half of the 20th century as well as an intensive time of work and exchange finally results in exhaustion. At the dawn of the 21st century, this area is perceived as depleted, while the artistic and scientific milieus begin to depreciate this phenomenon, denouncing its narrow formalism and lack of communicativeness. It is the intention of the Discursive Geometry project to face this situation, since its assumption is to restore the relation with broadly-understood reality. This trend is emerging when the surroundings of artists as well as their working conditions are extremely complicated and rest upon multi-aspect relations. Wiesław Łuczaj writes:

Concrete art should be free from any symbolic relations with reality because the lines and colours are the concrete in themselves, whereas the Discursive Geometry depicts various relations with reality, such as, e.g. social behaviour of people, their participation in culture and art, our everyday life and other social relations, e.g. “references to the world of mass media, scientific references (such as references of art to mathematical systems, or post-humanistic reflexions on genes or artificial life) – relations to art and humanities (such as inspirations by music, architecture, written cultural documents or iconography).

Assuming that the contemporary reality is a space and time formed by a number of parallel discourses, the art is a tautology, one of the examples of such coordination. Thus, the language of geometry is again becoming the medium which is the means for interpreting reality and the expression of currently occurring changes. The way of representing such concepts is taking different form than in the past. The artists mainly make references here to separate messages, medial forms, they borrow the constructs of such utterances, they use quotes in an attempt to find their visual dimension. While noticing in the discussed trend the examples of attempts to transform and process the texts from a variety of sources, I set them within the area of transmedial practices. It is here where I ask the question about the themes evaluated within the Discursive Geometry, the issues discussed, the media which are the primary carriers for inspiration and the ownership thereof and finally – the principles of translation. This paper is the outcome of my preliminary studies on the discursiveness of geometry and it takes the contributory form, a basis for more profound analyses. The starting point for the initial considerations is the work of the artists directly cooperating with already-mentioned Wiesław Łuczaj, the animator of the movement being established and the custodian of exhibitions in scope of the discussed area.

2. The issue of transmediality

Contemporary art is the open field with tendencies of exploring, creating ever new relations which connect it to other fields of artistic creation as well as to any other area of human activity. All borders, both internal and external, are removed. Any attempts to defend the homogeneity and specificity of particular fields bring the opposite results, as they lead to and provoke the occurrence of a series of artistic practices, the essence of which may be described as transitive, as well as objects of art – medial hybrids which cannot be unequivocally categorised as a one, specific form of expression. The elements appearing here are mainly intermedia, mix-medial techniques, multimedia which utilise new technologies, and - as their components – performance activities, sound art, visual music, musical graphics, concrete poetry, sound poetry, but also assemblage, environment, site-specific, the art of installation, interactive realisations and many more. Marshall McLuhann states that such situation is caused by the fact of previous media being depleted.

I can trace back the sources of such transformations as early as to ancient times. I am referring here mainly to the notion of ekphrasis, a term derived from Greek, which literally means “direct description”. This term denotes a series of literary references to specific works of art. On one hand it is the above-mentioned description, and on the other - a proprietary interpretation of an object conceived earlier by another creator, fitted within a specific framework of a given literary form (epic, lyric, dramatic). This notion demonstrates strong connotations with the aesthetic category of mimesis, that is, the pursuit for imitating nature. As noted by Jacek Szerszenowicz, however, the difference between the terms is that the aforesaid mimesis corresponds to (…) the primal, pre-artistic reality.

Another basis for the scrutinised issue is also the concept of inseparability of all artistic fields, defined as the correspondence of arts. The collection of centuries-old considerations about the unity of all disciplines of art comprises numerous artistic reflexions and theoretical manifestos. It is, among other things, the formula “Ut picture poesis”, introduced by Horace and stating the opinion about the closeness of poetry and painting, as well as the belief about the parity of those two, seemingly distant, fields of creation. Similar substance is conveyed by other concepts which relate to other fields of art – “Ut pictura musica”, “Ut poesis musica”, etc. The terms of correspondence of arts itself (French ’correspondance des artes’) has been introduced by the poet and critic, Charles Baudelaire. The basis of the concept is the conviction that the source of symbiosis should be found not so much in their manifestations of art but rather in the human beings themselves, their extraordinarily sublime capability in scope of multi-sensual, complex reception of art. As a consequence, this belief has been developed in the studies and investigations in scope of the phenomenon of synesthesia and sensual synergy. Slightly earlier, Richard Wagner materialises the concept of a total work of art – Gesamtkunstwerk, which, as defined by the creator of this term – Karl Friedrich Trahndorf (1827) – is supposed to unify and bind within itself a variety of artistic forms. As understood by the above-mentioned composer, opera is such synthesis of sound, word, image and movement. These thoughts determine to a significant degree the exploration of the artists at the turn of the 19th and 20th century, leading to experiments and the emergence of progressive approaches at the peripheries of media, artistic disciplines.

Siglind Bruhn, a German musicologist, links the notion of ekphrasis to the area of artistic practices located between fine arts and music. She replaces the above-mentioned term with the notion of transmedialisation, borrowed from the reflexion and the studies on new media-related phenomena, in particular digital means of communication. The term of transmediality was introduced by Henry Jenkins, the author of the book ‘Convergence Culture: Where Old and New Media Collide’ (2006). The American theoretician focuses on permanently occurring processes of interchange and rotation of contents between various forms of broadcast, both the analogue and digital ones. In his understanding, the changes are maintained not only by the technologies and development in this industry, but also social and cultural behaviours and expectations of a contemporary human being. At this point, Tomasz Załuski presents a synonymous term of remediation, introduced by Jay David Bolter and Richard Grusin. This term indicates the capability of media to undergo transformation towards a different form of communication. The authors observe that particular media do not exist separately but determine one another, thus displaying the above capability. These statements develop the beliefs of McLuhann as regards the evolution of media forms, taking place both historically as well as on a daily basis:

(…) a characteristic fact for all media is that one medium is the “content” for any other medium. Speech is the content of a magazine as much as a written word is the content of printing and the printing – the content of a telegraph.

As regards the way of understanding the term of transmediality suggested by Siglind Bruhn, according to which it is the process of transferring certain structural properties and the content to another artistic medium, the notion which seems to be of significant importance is transposition. A synonymous term to it is transcription, which basically means translation process based upon the criterion of a strict adequacy as well as the principle of homology and analogy of linguistic forms. It is emphasised that with regard to the trasnmedialisation process it is crucial to convey not only the important content, but also certain formal properties.

3. Pictorial diagrams of statistical data

An important part of Wiesław Łuczaj’s work is the series of “Statistic Images”, realised continuously since 1999. The starting point for its creation is the statistic information regarding the contents of social life, contemporary social and cultural transformations, resulting from studies and surveys conducted in representative groups of adult inhabitants of Poland. The artist notices the changes after 19th century as well as the formation of mass societies. This fact has a considerable impact upon the understating of a human being – as an element of a greater community rather than a individual entity. Thus, the most frequent method of study and characterisation are the tools developed by sociologists and based on measurements and quantitative representation. Their results enable to outline the opinions, functioning models, transformation mechanisms and other elements that dominate in a given group. They are represented as numerical data assembled in a charts, but also in the form of geometrical diagrams and graphs. This type of visualisation is comparable with Wiesław Łuczaj’s working methods. Transposed numbers, translated into a plain, allow to obtain a shape proportional to their values. The picture constructed in such a way is becoming both an aesthetic object and a visual representation of a specific social issue.

4. Image as a topography – visualisations of spatial data

Another field explored by Łuczaj is visible in the undertaking called “Human Being as a Data Base”. Here, the artist addresses a specific person, perceiving him or her as a living archive, a collection of objective data. As a part of publicly conducted performances, he invites the inhabitants of Polish and foreign towns, asking them to mark a few significant points on the map which determine their lives. Such points, connected with lines, are both a visualisation of collected information and an intriguing linear structure. Łuczaj’s work fits into broadly understood mapping procedure, which consists in spatial demonstration of a content in relation to the assumed topography, which represents a specific place, geographical context, but also a virtual dimension, that is, architecture of Internet network, contents found therein, abstract space, maps of thoughts or so called mind mapping.

The strategy of mapping is also very characteristic of the artistic work of Joanna Zak, who is dedicated to record her own everyday activity as well as that of her family. Her work involves a meticulous recording of the route each person makes during a day. It mainly involves private space – the flat, presented as a grid, where each square symbolises one room: living room, child’s room, atelier, kitchen, hall, balcony, bathroom and toilet. The last field refers to an external space and the action of leaving the house. As she notes the directions of walking and time spent in particular rooms, Zak creates a simultaneous visualisation of everyday life activities, behaviours and cultural rituals. This picture is presented in the form of a diagram, a map, a stratifying structure of lines, dots and circles, while the scale is determined by time and the colour suggests activity of a single person. Dividing the composition into separate modules allows to introduce change, combine it with other works, to establish a multi-aspect game with the addressee. Through her practice, Joanna Zak fits into the area of reflexion regarding the condition of a contemporary woman. As she records her everyday route and creates a simplified evidence of her activity, she presents the role of a woman – mother, wife and artist. By analysing the links between specific items, e.g. the size of elements, differences in density of lines, the addressee is able to notice and guess the functions the artist performs most frequently as well as their extent.

Przemysław Suliga is an artist who uses small squares, typically of similar size, to prepare his works. He narrows the choice of colours to black and white, with an occasional introduction of a different colour. A dominant of scale, colour, and direction of arrangement is supposed to emphasise the visualised aspects and issues. An important reference to the artist’s practice are animal communities, their internal structure, hierarchy and the behaviours and mechanisms that take place therein. A single element symbolises a specific organism. The manner of their sequencing suggests their demonstrated, and element-specific phenomena. Suliga writes about his last series, titled “Adsorpcja – Synchronia – Struktura” (”Adsorption – Synchrony - Structure”):

In my work, absorption relates to the process of combining and binding the groups by the elements of a picture which are inspired by animals’ behaviour. Animals’ mutual absorption causes them forming pairs, groups or herd. The next word in the title is synchrony, which, according to my concept, is the phenomenon that demonstrates a swift transition of organisms in a given moment.

With his work, Suliga fits into the trend of post-humanistic reflexion. The artist reconstructs and presents the models of social organisation of animals. Also significant is the artist’s workshop and the method he uses. Initial photographs and scientific studies are subject to transposition, they are translated into a synthetic geometrical form by means of a computer software – an artificial intelligence simulator. The artist combines the inspirations induced by both natural environment and the technical one, created by people. This practice is similar to the methods the programmers use. The models of organisation observed in nature are becoming increasingly more often a basis for constructing IT systems, in particular developing the project of artificial intelligence. Thus, Suliga’s geometric picture – a single square module – a pixel, is developing into a metaphorical demonstration of this issue.

5. Visual transpositions of linguistic and digital systems

The works of an Austrian artist, Josef Lischinger, relate to the notion of language and extraverbal means of communication. The author aims to develop a message, a visual system that may be used as a means of communication. He is inspired by ancient, pre-alphabetic icon-based manuscripts. The process of achieving and developing the concept is manifested in the artist’s initial stage of work. The starting points for the synthetic geometrical compositions are the letters, typeface and colour, which - deconstructed and transformed – lose their original shape and change into a new, interesting form. In the subsequent realisations, an increasingly more consequent equivalence system is visible, a translation of language into a visual form. The compositional framework is outlined by a strip structure, a discipline of horizontal axes analogical to printed verses. Particular phones are represented as coloured rectangles, where the colour is linked with a specific letter. The works demonstrate a suggestive rhythmicity and relations between particular elements that are characteristic to a language.

An opportunity of a sound examination of Lischinger’s transposition system of a letter or a number into colour is provided by the series titled “Sudoku”, in which the artist makes a reference to this logic riddle. These are the pictures created on a grid of 81, small square cells of identical size. The arrangement is similar to a Sudoku board, and the method of applying particular colours is also borrowed from the game principles. The idea in the game is to complete each field with a number from one to nine in such a way that no number is repeated in any of vertical and horizontal columns. Lischinger assigns colours to specific numbers: 1 – red, 2 – mixed red and orange, 3 – orange, 4 – combination of orange and yellow, 6 – yellow mixed with green, 7 – green, 8 – combination of green and blue, 9 – blue. This arrangement suggests logic in considerations about colours, it is a specific colorimetric pattern. The transfer of colours into the picture is subject to above-mentioned clearly outlined rules. Subsequent solutions present new possible layouts and combinations. Lischinger’s concept also contains an element of interaction with recipients. Particular solutions of a colourful Sudoku represent three corresponding systems. This triptych is created by: “complete picture” being the vision of a completely solved visual puzzle, “riddle-picture”, where some cells are black and enable searching for own, correct solution, and, finally, the “key-picture” demonstrating the elements missing in the previous work. The empty space here is filled with white colour.

The interest in transposing numbers into visual form is demonstrated by yet another artist, Waldemar Bachmeier from Germany. His works consist of small, square canvases, covered by equally-sized, horizontal and colourful strips. The colours are selected from a palette of 49 hues which correspond to the numbers selected in Lotto lottery. This extremely simple concept of the creator is based on the visualisation of lottery results. Each painting has a title which includes the date and a sequence of numbers, which enables to understand the principles of translation. Considering the entire series and analyzing specific variations, it is possible to identify the pattern, a certain constancy is revealed despite a significant role of chance.

An example of the art based on mathematical system is the work of a German artist, Gerhard Hotter. The series of his paintings include an almost infinite string of transformations, combinatorics of artistic form, inspired by the sequences of Dudley Langford. In his studies, this Scottish mathematician analyses the issue of permutations and creating regularity-based strings of numbers. The essence of those studies comprises the calculations of the distance between the same numerical values in a given sequence, finding of a function that governs the sequence in the established system. As in the mathematical model, Hotter creates a set of smaller input forms – modules based on a square structure. The artist limits his choice of colours to two contrasting hues, which results in a system that resembles the form of a binary, zero-one, code. In this case, zero represents the background and one is the filled area. The further process consists in a scrupulous finding of the established order, the sequence of arranging particular elements in a larger, consistent pattern. To do it, Hotter uses computer software. A close proximity of each element results in their merger into new, geometric forms. The artist understands the adopted method of work as a universal one, which can be used for composing music or literary works of art.

Another artist who makes references to the architecture of information and aesthetics of mass media, is the French painter Jean-Francois Dubreuil. His work involves illustrating of journal publications and those of information magazines, including the most recognised and popular titles, such as “Le Monde”, „Le Figaro”, „Deutsche Zeitung”, „NY Times”. Dubreuil sets his work on principle of transposition, which he established himself and which refers to the structure of the visualised information. The artist maps the layout of a given page and then he classifies its content according to a type of medium and performed functions. Each group is attributed with a specific colour. Photographs and illustrations are represented by black, advertisements – by red, the grey colour represents the text, while other colours are selected according to specific factors and they result from a character of a given magazine and the significance of its content. The colour in paintings is presented in two ways. The first one is expressed by flat, uniform spots, whereas the other is presented as a coloured contour. The title of each painting contains information about its source, that is, title and the date of the original publication. A clear and simple principle of transposition allows not only to map the structure of contemporary information and freely available content but also to observe certain relations specific for present times, such as, among other things, the proportion between the visual and textual contents or between advertisements and news.

6. Geometrical ekphrases

Rita Ernst is an artist that creates paint layouts based on regular grids. She uses the elementary geometrical shapes, such as squares, rectangles, circles, vertical or horizontal lines, thereby achieving an impression of harmony and order. As she claims, the order and other classification systems have been the subject of interest to people since ancient times, because geometry gives the world the form and shape. The “excuse” to create particular paintings are the works of the most distinguished creators of the German modernistic architecture, such as, among other things, Eduard Ludwig, Mies van der Rohe, Walter Groupius. Rita Ernst is inspired by architectural plans, perspective projections of a given assumption. Her works are creative interpretations of the visualised concepts rather than their accurate projection. Her artistic method uses the principles of construction and functionality of building industry as the rules of forming the painting and outlining its role. The artist confronts the architectural and artistic understanding of harmony. From the architecture-related discourse, the artist shifts towards the discourse about painting. Very often, she displays her works in the buildings designed by the above-mentioned architects.

The works of a graphic designer Boris Muller are an example of blurring boundaries between the art and design. On one hand, it is an attractive and professionally formulated message, and an intriguing painting on the other. The artist has prepared the graphic design for the “Poetry on the Road 2006” festival. He creates his own visualisation system for poetry, which approaches the structure of word as a fundamental material of lyric. The process of transposition consists in attributing numbers to specific letters. Such numbers are arranged in extended sequences which apply to specific words and entire text structures. Using computer equipment that allows to perform quick and accurate calculations, the artist transforms a digit into a visual form, i.e. a circle. Also the entire composition is enclosed with a circular bracket. Depending on a numerical value of a given word, the designer obtains a series of size gradations, from tiny dots to monumental circles. Grey lines which connect specific elements indicate the correct sequence and their relation in the structure of a poem. The artist exposes the tools for mapping the structure of content on one hand, and on the other – statistical tools based on accurate measurements.

The scope of my artistic reflexion includes music and broadly understood sound. I refer both to specific works of art of classical music, in particular the contemporary one, as well as the sounds heard or recorded in a surrounding acoustic landscape. Geometric form is both a medium of expression as well as an essential equivalent of an audio event. Mathematicity and measurability of particular sound parameters acquires its objective, visual form, which has a regular shape. My method of transposing audio material into image consists in comparing the intensity of sound, that is, proportion between its loudness and the scale of a given element, correlating tone frequency to hue brightness and sound timbre to a colour associated with it. The sound sustain corresponds with a horizontal extension of the format of the composition or, the verse structure of a system, similar to a structure of a score. While analysing the music, I employ a clean art form. I refer to the principal property of art, which is its absolute character, no connotations whatsoever with reality and abstraction. As regards the attempts of visualising different acoustic landscapes, I use the photographs of a specific place. Overlaying the pictures, shifting and transparency cause details to vanish, thus creating an impression of unreality and allowing to achieve the effect of sustaining forms and movement.

7. Summary

In the examples of artistic realisations scrutinised above, I notice the pursuit of broadly understood attempts of visualising information derived from other fields of art or human activity. Quite often it involves using other types of media, means of communication, in particular digital media. The image is becoming a parallel carrier of the previously transformed data. In this respect, the art of the Discursive Geometry trend fits into a collective ritual of content consumption and it is the manifestation of mechanisms which are characteristic for contemporary societies. The language of geometry, previously associated with transcendent structure of reality and considered as an expression of struggling for utopian concepts, a perfect vision of the world and social order, is now a tool of diagnosis and it presents the fiasco of the modernism project as well as emphasises common dilemmas and disturbance.