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Art, nature and new geometry

• Ξαγοράρης, Παντελής

During the pre-Socrates antiquity, the philosophical and scientific research was closely related to the artistic one, and the arts —in general— were developing under a penetrating spirit of control that was aiming to conform to some measure, to a “potential symmetry” with emphasis —according to the Platonic perception— on the relationship of Beauty to Science and to the archetypal, ideal and specific forms of knowledge that limits the extremeties of subjectivity.Plato is known to consider the knowledge as more important than the poetic urge, and to believe that the artist must reach the depths of his work and exert control over it, thus approaching the highest level of knowledge where his foresight is used to express his inner vision poetically through words.Pythagoras, who taught that the number is the substance of beings, invented the numerical system of musical harmonies that has formed the theoretical background of the music later used by Pythagoreans —after Aristoxenus of Taranto— as a means for the inner change of man.Classic Greek art had been deeply influenced by that spirit and other more general conceptions referring to the creation of the universe through total harmony, as well as by a ‘Pythagorism’ of numbers that was seeking aesthetic pleasure through the devout scrutiny of “the perfection of numbers”.As it has been shown by several studies, the European art during various historic periods —from the renaissance (L. da Vinci, A. Durer, L. Paccioli among others) to the impressionists and cubists (G. Seu- bat, P. Cezanne, J. Gris, etc.) has been influenced by the same ideas, mainly through the conscious effort to introduce mathematical elements into the art works under various interpretations (mystic, aesthetic, rational, etc.), and also into their analysis and assessement applying certain geometric systems (golden section, etc.).Several theoretical works by pioneers of cubism and abstract art describe quite clearly a close relation to similar Platonic concepts such as the submission of the material means to the dictations of the idea as expressed by the object, and the appraisal of the art work based not upon imitation, but on the use of rhythm and harmony as criteria that lead to beauty.The effort to formulate various visual systems using objective criteria, and the comprehention of the importance carried by the epistemological analysis of the art object, can be found in theoretical essays by artists like W. Kandinsky, P. Klee, K. Malevitch, etc., whilst the notion of the abstract geometric structure is consciously materialised in the work of artists like P. Mondrian, M. Bill, R. Lohse, etc.It is artists related to the Bauhaus, influenced by the development of science and technology, whose writings mostly offered important comments on visual systems, cultivating the notion of the artistic creation which is closely associated to logical thoughts and arguments seeking to humanize technology.These concepts lead to the more recent logic that refers to a system of symbolic codes and inter-relations permiting a transfer from one proposal to another: relations of ‘union’, ‘section’, ‘order’, or “differentiation”, and “transition”.The structural approach in the study of the arts (P. Francastel) relates to the corresponding analysis by J. Piaget on the structural development of the perceptive organization, and on the definition of the shape as a set of structured characteristics being inherent in a perceptive action —conceptual, motional, etc.The structure is generally defined as a system of transformations governed by specific formation laws founded axiomatically on the concepts of the various parts and of the whole. An indispensable condition for the existence and the formulation of a structure is the presence of opposing elements (straight line and curve, convex and concave, warm and cool colours, etc.) with active contradictory properties of similarity and non-similarity in their multiple aspects.One of the first mathematical structures is the concept of groups —introduced by E. Galois and found in almost all fields of mathematics and other sciences— which results from a logical-mathematical subtraction and has been successfully applied in the analysis of art works from various eras.It has to be noted that the structure of groups exists within the intellectual structure of man, as well in the crystallization of matter, and in the development laws of natural forms where geometric shapes are often found: shells, tree leaves, forms following the minimum energy principle and being formed as ‘minimum area surfaces’ (bubbles, actinozoa, etc.).The use of the group concept and of the structure systems that are met in the natural creations is of particular importance for the artist since it suggests a way to follow a creative path parallel to nature.Within this context, our work is characterised by an effort to deve- lope a “system”, a mental and artistic discipline, having as its theoretical basis the introduction of mathematical concepts and structures into the organization of our works.Studying the works of Mondrian and the constructivists helped me to understand this doublesided process between art and intellect, a precious and valuable relationship, specially in certain periods, from antiquity to contemporary art. Essentially I continue to follow, in the wider sense, constructivist ideas as mainly described in the Realistic Manifesto of Gabo and Pevsner, where the pictorial representation of natural forms is replaced by pure creation. Besides Plato’s definition of poetic and artistic creation precisely describes the relationship which exists between the artist —creator and the researcher— scientist, because both are seeking to uncover and manifest the unknown (Plato, Symposium). We could recall many different aesthetic concepts around the interpretation of nature. But I would like to note the fact that phenomenally non-geometrical forms (clouds, coastlines, trees, etc.) cannot be described through the basic constructs of Euclidian geometry, while other more recent scientific ideas and related interpretations of space (B. Riemann, N. Lobatchevski), with the aid of new technology (electronic computers, laser beams) grant us new possibilities and totally fresh images of nature.These explorations into the interpretation of the forms of nature which are expressed through transcendental equations and often based on the harmonious proportions of the Golden Section, have occupied my attention in the last few years. I must here mention that making the relevant programs requires great perseverance and effort and the results continuously produce surprises since they refer to and arise from an area of unforseeable fractional numbers of infinitesimal nature. To state it simply, I would say that the role of technology in my work is dual. It expands the boundaries of my research into plastic form and theory, while at the same time uncovering new and extensive areas of quest into visual form which unveil and make visible the internal or subtle structure of reality with a continuous process of transformation from the foreseeable and symmetrical to the unforeseeable and chaotic in an ‘imperceptible’ and yet ‘inexorable’ manner. Often the creative artist, as indeed the research scientist, works in absolute and pure clarity, in a space of clear, cold light but at a certain moment he advances alone, unaided, into absolute darkness. He then feels he is being led into areas and situations that are indescribable, fleeting, undefinable and intransmissible. I believe that these moments are decisive for the final formation of a work.As a conclusion, it should be added that mathematical “laws” and "rules” as applied in the arts do not possess any expressional potential by themselves, but they provide mechanisms offering a great variety of combinations to the artist, thus helping him into the purity and harmony of his work.And also that the new technology is created by man, who exerts controls over it by selecting what the classic Greeks called “kalon”, since man —according to Protagoras— is the “measure of everything and of infinite depth”.

• Arts
• Philosophy, Ethics and Religion

• Τέχνη
• Αισθητική
• Classicism in art
• Φιλοσοφία, Αρχαία

Ανακοίνωση σε Σεμινάριο Τέχνης που πραγματοποιήθηκε στο Κέντρο Σύγχρονης Τέχνης της Βαρσοβίας στις 5 και 6 Μαΐου 1993 και τελούσε, υπό την Αιγίδα της Πρεσβείας της Ελλάδος στη Βαρσοβία, Περιέχει εικόνες