Janusz Zagrodzki 


Connections between science and art become particularly apparent when artists refer to ontological concepts thus addressing problems which are typical of philosophy, psychology or natural sciences. Although for the scientist concerned with constructing organized systems of knowledge, success in any of these disciplines is based on logic and reasoning while art is the realm of fantasy limited exclusively by the expressive means at the artist’s disposal, in the empirical sphere it is possible for the artists to explore the fields hitherto reserved for the scientists. Reflection on structures and geometric relationships between individual shapes and cognitive curiosity focused on the work’s matter concern problems which are important for human knowledge across many overlapping fields of inquiry. Generally, scientific achievements should be explained and comprehended and artistic ones felt. On the one side, we have the rational search for the essence of knowledge, on the other – the play of imagination. But most of human conscious and subconscious activity integrates these two forms of creativity and occasionally even substitutes one for the other since both science based on the play of imagination and art totally subjected to conceptual premises are possible. The instruments the modern scientist and artist can operate are often so similar that assigning them to one or the other particular category is of secondary importance. Scientific discoveries pertaining to the structure of the universe, its micro- and macrospheres, often coincide with the explorations of the artists drawing analogous conclusions directly from the observation of nature.

The argument concerning the nature of the forces determining the laws of nature has divided the scientists almost from the emergence of science. The view assuming the constancy and immutability of reality was juxtaposed with its opposite pronouncing everything to be in flux and subject to change. Today, with still new evidence provided to support the theory of chaos, we tend to accept these two images of the universe simultaneously not to make them identical but to discover in each one the symptoms of some supreme order seen from different perspectives. Science tries to explain the causes of both immutability and volatility of the laws governing natural phenomena and uncover the principles underlying all metamorphoses. Thus the patterns informing natural phenomena possess their autonomous source which can be equally adequately described in the language of science and art.

It suffices to refer to the approaches of such masters of the avant-garde as Casimir Malevich and Władysław Strzemiński to realize how deeply art is indebted to the research work of the artists conducting their studies with truly scientific inquisitiveness. Strzemiński was absolutely convinced that “art which is modern in terms of its methods becomes similar to the ways in which science develops.” And through the abstracting of the “organic unity of forms whose organic nature makes them analogous to nature”, he was able to develop the model of objective unity and consequently his Unist paintings. The “form of the countenance of nature’s new majesty” uncovered by Malevich found its expression first in the black and then the white square. The tests concerned with the psychology of perception he conducted at the Department of Theory and Form of the State Institute of Artistic Culture (GINChUK) in Leningrad enabled Malevich to develop his “painting diagnostics” which would become the base of his “theory of the additional element”, the scientific foundation of the final phase of Suprematism.

Such fundamental concerns also informed the pursuits of Wacław Szpakowski who in his oeuvre developed a vision of the global image of infinity. He combined shapes found in nature into the arrangements of lines rhythmically changing their course and thus reconstructed the form of the real world. To him, the geometrical structures created over the period of over fifty years, between 1900 and 1954, were also sound recordings, the scores of the music he had found in nature. The series of drawings, each one comprising a single unicursal line, referred simultaneously to the spheres of man’s visual, aural and psychological experience and became Szpakowski’s book of the marvels of the world.


The first goal that Szpakowski set for himself was the science of perception and finding the method of imaging based on the ability to see, hear and even taste the forms, lines and signs existing in nature. The cyclical character of processes making up principal laws of nature, the existence of periodical repetitiveness, rhythms and symmetries of the perpetually renewing life provided models for the structures constructed in the manner analogous to the structures of actually existing physical bodies. Szpakowski began his study of nature from deciphering its most spectacular signals. In his diary, started when he was still a fifth form student in 1898-1899, he made detailed notes on hurricanes, cyclones, storms and tried to uncover their underlying regularities.

Szpakowski’s notebooks, kept from 1900, formed an integral part of his creative oeuvre, contain an enormous number of notes pertaining to almost all areas of life, art, and science. Diverse arrangements of geometrical lines are featured alongside notes on architecture, natural sciences, photography, and folk art. His reflections on styles, descriptions of landscapes and travel impressions are accompanied by drawings, diagrams and mathematical theorems. Szpakowski’s notebooks also contain musical notations of sounds produced by vibrating telegraph wires in various atmospheric conditions: storm and calm weather, rain and below zero temperatures; by stones pounding against each other. He analyzes the shapes of clouds and smoke. Among his inspirational figures, Szpakowski mentions the Greek mathematician Eudoxus of Cnidus (408-355 BC), a pioneer of mechanics, astronomy and geometry whom Benoit B. Mandelbrot, known for his contribution to fractal geometry and experimental mathematics, regards as the most creative of all ancient mathematicians. In comparison with Eudoxus, the famous Euclid (450-380 BC) was but an encyclopedist. The majority of books whose titles appear on Szpakowski’s reading list featured in his notebooks, the majority concern architecture but there are also many on aesthetics and art. Interestingly, among his many references Szpakowski mentions The Sense of Beauty, a seminal book by American philosopher George Santayana published in 1897 but little known in Poland. The author undertakes to explain the nature of beauty as arising from the intermingling of the viewer’s visual and aural experience with the object’s qualities. Santayana thus argues that beauty is not exclusively the property of the object but a human experience that is based on the senses and thus originates from a naturalistic psychology. Did Szpakowski have an opportunity to read the whole book? Did he just hear about it and reached for its final conclusion as corresponding to his own similar experience? These questions remain unanswered.

Many notes concern photography: times of exposure, characteristics of particular photographic materials (sensitivity to light and heat and other factors, grain), and his experiments to enhance contrasts or produce new effects through photographic techniques. Reflecting on history of architecture, Szpakowski discovered analogous solutions in nature and found them more suited to real needs. He regarded nature’s creations as far supreme in comparison to manmade and thus providing unsurpassable models for human endeavors. He tried to uncover and formulate the laws of geometry informing natural phenomena and regarded the principles of symmetry and repetition as governing both inanimate and animate nature. He derived the logic of life processes from cosmic rhythms, in particular those regulating the activity of the Sun, movements of planets, magnetism, and lunar cycles. To him, the mysterious code of nature regulating the rhythms of organisms, cells, particles and atoms, all systems that structure the order of life, constituted a fully harmonious system whose structural principles he tried to uncover and define.


Many aesthetic solutions can be found in nature which we take as the evidence of the universe’s underlying principles having a harmonic nature: for example, the circuital laws regulating the movement of water, sand, and air, wave formation, symmetry or self-similarity. In the theory of chaos and fractal geometry, the conception of determined randomness is an instrument to analyze the most complex natural phenomena. While regarding Szpakowski as a precursor of modern scientific discoveries would be an overstatement, his artistic instinct and perhaps also the ability mathematicians refer to as “geometric intuition” let him undertake an effort to decode the structure of the universe and give form to his own system of pursuing truth.

Patterns found in nature feature bands, spirals, patches and regular shapes multiplied or shifted along regularly arranged axes. A landscape is not a set of isolated forms: it has its specific geography and structure defined by numerical relations and so its representation inevitably resembles geometric diagrams or other mathematical concepts. The element which integrates the image is an arrangement of lines connecting individual shapes to form a logical and rhythmical system systems, a mental map of analyzed fragments. To Szpakowski, photography became a method of choice for studying natural processes. The initial goal was to document the landscapes illustrating the principle of the repetitiveness of forms. The image selected and fixed in the viewer’s eye contains but a portion of information sent from the observed object to the viewer. By manipulating the frame, focus and contrast, the observed conglomerate of forms may be processed to extract characteristic motifs producing the effect of broken lines. The human eye is more tolerant than the camera lenses and easily identifies the observed image with its drawn or mental image. This tolerance enables the artist to process signals coming from reality as perceived with the naked eye, directly from nature, and as fixed in its photographic image

The motif of mirror reflection is present in Szpakowski’s photographic notes almost from the beginning. As early as 1902, he creates his Self-Portrait in the Mirror which shows him with a camera. His well-known Multiple Self-Portrait (1912), in which he used two mirrors positioned at 90o angle, attracted international interest. The idea for the photograph, probably inspired by pictures taken by itinerant photographers setting their studios at village fairs in the late 19th-early 20th century, would be taken up by many artists. But Szpakowski’s photograph is very different from theirs. The multiplied images of self-absorbed artists feature in the oeuvres of Stanisław Ignacy Witkiewicz (ca. 1912) or Marcel Duchamp (1917). In contrast, Szpakowski makes eye contact with the viewer, invites him to enter the illusionist space. The Multiple Self-Portrait is a brilliant example of symmetrical system in which the mirror effect has been expanded by introducing an axis of rotation and thus automatically bringing in the element of time.


Many scholars regard the line as an abstract creation rarely found in nature, mostly in the form of soft edges with the only exception of the horizon. Szpakowski’s observations run counter this widespread opinion. The horizon is not the only linear element in nature. Tree trunks, plant stems, fir needles, reeds and their water reflections form diverse arrangements of parallel straight lines. Man, in his desire to control, organize and subjugate nature, also introduces arrangements of straight lines into the landscape. Poles, fences, planks and boards, connected with ropes, wires, bars, vertical, horizontal, oblique, spaced, bound or scattered – such elements create the organized matter of parallel and crossing lines thus integrating manmade and nature’s creations. The rhythmical lines of roads and furrows and geometric planes of fields and forests integrate this complex system into a unified, static and balanced linear structure.

To Szpakowski, style is “the way of employing form to suit the needs”, it is the sum of conventionalized forms dependent upon the mechanisms of perception of the lines possessing certain permanent characteristics. If differences between styles consists mainly in specific combinations of lines, then – according to Szpakowski – the source of style is human creative urge stimulated by impulses coming from nature. In his 1903 notebook, he writes: “[…] seeing the same objects over and over again, man casually gets familiar with their characteristic features and thus the images of these objects get fixed in his mind. These images often depart from reality… the model (nature) ≠ mental images ≠ created forms.” Interestingly, contemporary theories of visual perception emphasize that its development is influenced by one’ surroundings. Szpakowski’s notes from his trips across Latvia, Lithuania, Belarus and Russia as far as Archangelsk and the drawings and photographs he made during his voyages extract the shapes and their arrangements characteristic of a particular region. They carry the message that reality harbors within many unfamiliar and yet important aspects we usually do not notice.

Szpakowski’s effort to eliminate accidental arrangements and organize his drawings according to some common characteristics made him divide them into smaller groups. The majority were created during the period 1900-1914 that is when he was a student at the Department of Architecture at the Technical University in Riga and shortly after his graduation in 1912. In the 1920s and 1930s, Szpakowski often returned to these manual drawings adding some new ideas and organizing them according to his calculating system into closed series marked as: A, B, C, D, E, and F. The next stage in his research on the continuity of form was the study of spiral (series S) and the final one – the series of grids which he tried to connect to architecture. The final summery of his work on the infinity of line was the album compiled in the early 1950s featuring ninety-six drawings.


The visual aspect of discovering the lines existing in nature is not the only one informing Szpakowski’s notations. The material consistency of his drawings, their geometric, rhythmical structure almost automatically provokes associations with sound. The author of the drawings first had this kind of associations when he observed telegraph wires stretched between poles, their vibrations and sounds thus produced. He tried to convert these polyphonic sounds into music. And so, his drawings began to serve an additional function of recording these experiments. Szpakowski’s exceptional gift for integrating visual and aural impressions enabled him to develop the basis for composing homophonic music. The line’s breaks correspond to sounds rhythmically repeated at some regular time intervals. The pitch changes are encoded in the amplitude of the line’s deflection. Consequently, musical notation becomes an integral part of the drawings’ arrangement.

Form in music can be regarded as a continuous line rhythmically changing its course. Such line can be played and its unicursal nature can be interpreted as an unfolding sound. Theoretical premises of time and form in music and art reflect similar thinking. Abstract thinking makes it possible to move freely in the self-created universe of sounds. Thus interpreted notation becomes a musical score which may be read as sounds reflecting the mutability of the line’s course. The reverse process – that is converting sounds into a drawing – is likewise possible. The impression made by a visual form developed into a musical impression gives the chance to broaden human perception and stimulate perceptiveness.

Drawing lines may find its analogue in the articulation of sound creating in the boundless space the structure composed of superimposed forms of varied intensification: ordered and logical and at the same time open. Within this infinite stream, clearly defined sequences may be distinguished: they determine the final position of a given composition within the series as marked by the corresponding letter and number in the sequence. These tones are something between music and murmur: they are produced by superimposed sound waves or intertwining, rhythmically repeated sounds which, despite being immersed in a supreme continuum, retain their individual expression. Depending upon the line’s structural principle, its rhythm, turns, parameters and its point determinants, multiple sound registers may be revealed indicating various forms of movement, vibrations, ascending or descending currents, articulated with the calm, almost static course of straight lines. Exploring reality with all senses, especially sight and hearing, was fundamental to Szpakowski’s notation. He recreated the sound score of his drawings by pulling the strings of his violin. Zbigniew Bargielski has proposed a contemporary electronic form of interpreting the drawings as a form of musical notation.


The relationships between the form found in music and its reflection shaped by the artist have their continuation in the line’s optical life. Geometrically encoded patterns can unexpectedly change their arrangement, undergo transformation or animation and alter this seemingly immutable mathematic notation. Visual illusions alter the drawings’ form. The course of the line defines and reveals the rhythmical juxtapositions of squares and triangles and abruptly rising waves. Optical illusions affect subsequent transformations, most visibly reflected in the combinations of the simplest geometric systems. This method of making the message more dynamic is conformed by the calculations occasionally preserved on the margins of Szpakowski’s preliminary sketches.

All Szpakowski’s works have the same structure: the lines of uniform thickness of 1 millimeter are always spaced at the same interval of 4 millimeters. This imbues the drawings with similar characteristics and another uniting common feature is of course the line’s unicursal continuity. Szpakowski suggests the viewer should engage in the intimate act of discovering the continuity principle and encourages him to painstakingly follow the line’s course within the drawing, from its “beginning” to the “end”. This is the only way to understand the work’s message, experience its duration and “inner content”. It is the specific character of Szpakowski’s visual language that attracted the critics’ attention when his work was exhibited in Brussels and Ludwigshafen.

“Szpakowski’s focus on the viewer’s perception is unique, individual and astonishing. He cajoles the viewer to make his eye engage in continuity training… to get the thrill of the line’s geometrical adventures and delight in the pleasure of interpenetration. The relation is purely sensual, emotional, extraordinary. This is about something which has to be experienced in an entirely novel way” – wrote Marc Renwart.

“He was a quiet and taciturn and introvert thinker who would rarely open himself even to his own family. He did not demonstrate his rock-solid faith in his own abilities. It is rather difficult to explain verbally what is so arresting about this extremely simple art” – observed Frederik Hermans.

And Getulio Alviani ascertained: “Szpakowski’s oeuvre is absolutely timeless: suspended and aseptic, it could be the work of the Egyptians, the Greeks or the Mayas. It possesses the spirit and essentiality of some ancient scripture, its texts hidden behind its dry and discontinuous lines.”

Szpakowski possessed this very rare intellectual ability to grasp details and integrate them into a coherent whole. His system of recording and coordination would be unimaginable without his unique sharpness of vision and ability to extract the basic outline of space. His visual memory was so precise that he could easily retrieve any image of reality he had ever analyzed. Drawing the line and reading its course, its visual as well as sound form, became his principal goal. Studying natural phenomena, he always referred to sensory experience as the basic instrument for discovering new facts which still await scientific proof. The approach of contemporary technologists, marred with overreliance on instruments and gradually eliminating direct observation and testimony of the senses, was entirely alien to him. By integrating the psychological aspect, image and sound, he has created a universal notation suspended in the infinite duration of the endlessly repeated cycle of events.

First published in: Wacław Szpakowski 1883-1973. Nieskończoność linii, exhibition catalogue, Galeria Stara, Lublin, April-May 1998.