Abstract: This is a description of my habilitation work (post-doctoral degree), which is entitled MathArt and consist of six multimedia installations: The Remainder, Zeno2, Definite Integral Figures, Limits of the Circle, Inflection Points and Extrema and Exhausting image. These works creatively refer to selected problems of mathematics, while in the formal layer they are characterized by geometric minimalism. The cognitive aspect of these works is as important as their aesthetic value, so I called this kind of artistic creation “the art of cognition”. The text also summarizes my artistic and scientific achievements as well as didactic, educational and popularizing activities.
Abstract: The circle and the sphere, in philosophical speculations,exist as symbols of perfection, as metaphors of divinity, as models of eternity as well as approximations of essential properties ofcognitive acts. Their geometry is also an excuse for visual speculations of an artistic nature. In this article, we discuss some chosen metaphors based on the circle and sphere which refer to both ontological and epistemological issues pertaining to various models of knowledge and the cognitive process..
Abstract: In film, like in any other media which uses a dynamic picture, the illusion of movement appears as a result of a quick projection of an arranged sequence of static frames. Movement, or actually its illusion, appears out of stillness. The author starts the analysis of this paradoxical phenomenon by differentiating between the terms of continuity and discreteness and introduces the definition of discrete illusion of movement. He investigates the history of scientific-artistic attempts at recreating physical movement and discusses the basic properties of visual perception thanks to which the illusion of movement is able to occur. The author’s deliberations on the properties of a moving picture lead him to the questions about the nature of movement and other foundations of physical reality – time and space. The theoretical discussion is accompanied with a presentation of chosen artistic projects, the makers of which (staff and students of the Media Art Department) not only use a moving picture, but also consciously refer to the mechanism in which that moving picture is created.
Abstract: In this article we would like to draw attention to the cognitive potential hidden in an image and in the art which employs it. We will focus on the visualization of basic mathematical objects e.g. irrational numbers. Our starting point will be the easy and intuitive case of the square root of two, as it is observed in the diagonal of a square. Next we will move over to the golden ratio hidden in a regular pentagon. To visualize this irrational number φ we will use a looped, endless animation. Finally, we will have a closer look at the famous number π and we will suggest an attempt to represent it in a clearly visual way. In the last section of the article we will consider the possibility of representing rational and irrational real numbers by dimensionless points on a straight line. We will also try to present a straight line on a flat surface which – as we know has length – but has no width. The above issues will enable us to see the extent to which mathematics may be inspirational for art, as well as how art may familiarize us with mathematical issues and explain them.
Abstract: This article focuses on the cognitive function of the image and the role the visual imagination plays in education and the popularization of science. We will look at the possibilities offered in this field created by the modern, moving and programmable digital media. They provide a highly effective, but still not fully utilized tool in popularizing the complex issues of science. The article discusses examples of both the visualizations of didactic character as well as artistic works which relate to the classic problems of mathematics, physics and philosophy in a creative way.
Abstract: In this paper I wish to suggest that images that we are familiar with are lossy in regard to what they represent. This applies to both imagined images and those preserved in matter or memory, as well as static or moving images. We never experience the world in its entirety, the reason being, among others, that our sensual perception is of a discrete nature. Digital images also have the character of non-continuous and in consequence of lossy character too. Although they are the most perfect form of recording currently known. It is worth asking the question: how much do we lose of the world, deciding or rather being doomed to its discrete representations?
Article only in Polish. Abstract EN: We used to identify the scientific reflection over the idea of the chance with mathematics or philosophy. In this paper we shall look at the problem from the perspective of visual arts. The history of philosophy and science shows that the idea of the chance was understood in many different ways. Also today we can differentiate at least three distinct paths of apprehending the topic: 1) the objective chance – when we presume that random events exist actually in nature, 2) the subjective chance – when what we presume to be random, results from the lack of sufficient knowledge about what could happen, and 3) the dynamic chance – when the randomness appears as an effect of complex interactions in determined systems. It seems that all the faces of the chance find their examples in arts, too. We notice them in the heritage of great masters, such as Leonardo da Vinci, Max Ernst, André Masson, Marcel Duchamp, Jackson Pollock, or Ryszard Winiarski. We also see that the chance plays a crucial role in contemporary arts.
Article only in Polish. Abstract EN: Why the humankind had to wait so long for the creation of the motion picture or any other more primordial mechanical form of motion’s representation? The attempt of answering this vital for this paper question directs us towards Henri Bergson’s and William James’s philosophy, particularly to the conception of the cinematographic mechanism of thinking proposed by Bergson. This in turn takes us back to antiquity to the aporeia of Zeno of Elea. We shall pay special attention to the argument called the Arrow in which the idea of creating the illusion of motion from static images was already present. The synthetic look at intellectual achievements of the ancients in mathematics, technique, philosophy or aesthetics will allow us to debate what factors had influenced them that they did not direct their thoughts towards the mechanical representation of the motion although, as it seems, all the required elements were available for them.
[in:] TRACES IN SPACES – AIAS workshops and symposium 2011, ed. B. Ludwiczak, A. Trzuskolas, Wrocław, 2011, ISBN 978-83-60520-70-3.
Abstract: A major part of art projects begins with drawing the straight line. It is seldom that we realize how many problems we touch drawing the straight. I would like to attract your attention to such uncommon issues whose solutions are to be looked for in geometry and set theory. An attempt to count the number of points placed on even the shortest segment of the straight leads us to the idea of uncountable sets. Drawing the straight line long enough takes us into the area of non-Euclidean geometry. Willingness of measuring the length of the irregular line edge zoomed in with microscope opens before us the world of fractal geometry. At last the analysis of the movement of the hand drawing the straight lets us to understand the difference between continuous and discrete phenomena. An artist sketching the line is not often conscious of finding oneself on the threshold of contemporary science.
Abstract: Using the wavelet mapping of sleep spindles we investigated influence of focal epilepsy on spindle generation. We found that the maximum of sleep spindle intensity is usually localized away from the epileptic focus. We discuss the possibility of the application of wavelet mapping for localization of epileptic foci prior to epileptic neurosurgery.