Basic Forms and Nature From Visual Simplicity to Conceptual Complexity Markus Rissanen Basic Forms and Nature From Visual Simplicity to Conceptual Complexity Publisher: The Academy of Fine Arts at the University of the Arts Helsinki The copyrighted material in Appendices A and B are reproduced with permission from The Bridges Organization / Tessellations Publishing, Phoenix, Arizona, USA, and Springer Science+Business Media, New York, USA. Graphic Design: Eija Kuusela Printing: Oy Fram Ab, 2017 ISBN 978-952-7131-34-3 (printed) ISBN 978-952-7131-35-0 (pdf) Ulpulle ja Urmakselle Preface According to the rules of the Doctoral Studies Program of the Academy of Fine Arts, University of the Arts Helsinki, the candidate for the degree must give a public demonstration displaying a high level of skill, knowledge and research in their own field. After three pre-examined exhibitions, this dissertation completes my doctoral work. When presenting my own paintings in this thesis, I have also given a continuously- running chronological number, which I have given to all of my paintings since my graduation from the Finnish Academy of Fine Arts in 2000. This number is in square brackets after the title of the work, for example: Blueprints for Landscapes, [M125]. The letter M can be taken to stand for maalaus, “painting” in Finnish. Most of the material I refer to in this work is in printed form. At some point, however, I realized just how much printed material is already available online. Whenever I have noticed that a book or an article also has a free online version, I have provided the proper address. Where possible, I have favored a link where the context of the publication is also visible, even if access to the actual content requires a quick look and one extra click, over the alternative where the content just pops up out of the blue. Compare, for example, A. K. Dewney’s article “Computer recreations; a computer microscope zoom in for a look at the most complex object in mathematics” in the August 1985 issue of the Scientific American at https://www.scientificamerican.com/article/mandelbrot-set/ within a clear and comprehensible context, versus exactly the same article at https://www. scientificamerican.com/media/inline/blog/File/Dewdney_Mandelbrot.pdf, with no explanatory context. With online sites, the access date is given as: (accessed 2017-05-20). If the available space in a footnote was especially tight, the access date was simply given as (2017-05-20). A descending notation for the dates (Year- Month-Day) is systematically used. With all of my visits to such online resources, I often had the feeling of living in a world that was anticipated more than 70 years ago in an essay by William J. Wilson, “The Union Catalog of the Library of Congress”, published in the journal Isis, Vol. 33, No. 5, March 1942: “In the more distant future still stranger things may happen through television and its allied inventions. If these can be perfected for general use, as have the radio and the telephone, the results will be revolutionary indeed. While the facilities are lacking, already the principles are known by which any library could be equipped to show a rare book or a section of its card catalog to a distant scholar, sitting in his own study before his television screen and turning the pages or flipping the cards by remote control!” Nowadays all of this has become so 6 familiar to us that we barely give it a second thought. For me, on several occasions, the kind of library just described has been the Internet Archive (https://archive.org). The psychological roller-coaster ride caused by these doctoral studies, and especially this written part, is well expressed by Marjorie Hope Nicolson (1894–1981), an American scholar of 17th-century literature, in the title of her 1955 published book Mountain Gloom and Mountain Glory. For artistic research, this is indeed a suitable phrasing as being taken from the heads of chapters XIX and XX of the Part V of Volume 4 of the five-volume bookModern Painters (1843–60) by the Victorian art critic John Ruskin (1819–1900). Acknowledgements To begin with, I thank Koneen Säätiö for their financial support, which made this research possible, as well as my parents Seija and Pentti Rissanen for similar types of reasons :-) I express my sincere gratitude, in no particular order, to Lauri Anttila, Alan H. Schoen, Edmund Harriss, Dirk Frettlöh, Christoph Fink, João Francisco Figueira, Hannah B. Higgins, Tarja Knuuttila, Jarkko Kari, Reino Niskanen, Osmo Pekonen, Kristof Fenyvesi, Juha Merimaa, Taneli Luotoniemi, Arto Huopana, Iina Kohonen, Jouko Koskinen, Simo Kivelä, Perttu Pölönen, Kalle Ruokolainen, Kari Saikkonen, Marjo Helander, Elma Helander, Anita Seppä, Tuula Närhinen, Shoji Kato, Hanna Johansson, Riikka Stewen, Tuomas Nevanlinna, Jan Kaila, Henri Wegelius and Michaela Bränn. I also thank Mika Elo, professor of artistic research, my supervisors Jan Svenungsson and Tapio Markkanen, my pre- examiners Irma Luhta, Nina Roos, and Jyrki Siukonen, for valuable comments and helpful suggestions, Vadim Kulikov for proofreading chapters with mathematical contents, Lynne Sunderman, not only for her gargantuan efforts in correcting my English, but also for her precious remarks and questions, which prompted me to rework many parts of this book at the eleventh hour, Eija Kuusela for the graphic design of this book, Dr Nina Samuel for accepting the invitation to act as the examiner of this thesis, and, most of all, my wife Henna Helander for drawing my tiling sketches with ArchiCAD and enduring all the rest as well; pus pus! The author can be reached via email at: [email protected] 7 INTRODUCTION In this chapter I present the topic and the research questions of this thesis. I also discuss the key concepts, such as the “basic forms” as well as the notions of figure, form, shape, structure, and pattern. Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics and its characters are triangles, circles, and other geometrical figures without which it is humanly impossible to understand a single word of it; without these, one wanders about in a dark labyrinth. Galileo Galilei, Il Saggiatore (1623)1 I am not a scientist, nor a philosopher, and the theme of this thesis is not words or dark labyrinths. As an artist doing research, I have studied basic forms, their characters and their presence in nature. The main forms, which I consider basic, are the square, circle, and triangle. In addition to these three simple forms, I also introduce two other forms under the category of basic forms: firstly, the branching tree-like2 form, or dendrite, which also constitutes a bridge from classical geometry to fractals, a class of non-Euclidean forms often met in nature; and secondly, rhombuses, a class of simple shapes of Euclidean geometry. I acknowledge that the rhombus does not possess a profound visual or logical simplicity in the same way as the square, circle, triangle, and tree-like forms do. The rhombus, however, plays a prominent role in this thesis, especially in the last chapters and appendices. For these reasons, all five aforementioned forms are included in the category of the basic forms in this study. 1 Il Saggiatore “the Assayer”, 1623, reprinted in Discoveries and Opinions of Galileo, translated with an introduction and notes by Stillman Drake, 1957, pp. 237–238. 2 With the designation tree-like, I emphasize that such a form does not necessarily depict a physical tree, but any entity with a branching and hierarchic structure, either physical or abstract. 9 Perceptual and Conceptual Forms Representing Nature Two new concepts introduced in this thesis – perceptual forms representing nature and conceptual forms representing nature – need to be clarified right in the beginning.3 The first one refers to mimetic depictions of visible forms and structures that we can see in nature either with our bare eyes or by using instruments. The second one designates the seemingly artificial and typically geometric forms that we humans have invented by accident or constructed with purpose to visualize phenomena or functions of nature in systematic, theoretical, data- oriented, or, broadly speaking, “scientific” ways. I could summarize the essence of these two modes by saying that by using the former, we aim to show how nature appears, and by the latter, we aim to show how nature works.4 The perceptual forms representing nature, in other words, are made for the eye, and the conceptual forms the mind. The Structure of This Study My own paintings are often connected to these two modes of depiction. On the one hand, I use imitation to represent recognizable objects or scenes in nature. On the other hand, I deploy representations connected to scientific constructions and visualizations. I will speak more of my paintings in Chapter 1. I start with the square, the circle, and the triangle because they constitute the very set most often introduced in the history of visual arts education, especially in teaching the elements of drawing. The triad square-circle-triangle is a visual manifestation of the Platonic concept of eternal and indestructible ideas, and these shapes also 3 For a relatively long time I referred to these categories as perceived forms of nature and constructed forms of nature. My principal supervisor, artist Jan Svenungsson, pointed out to me the philosophical weaknesses of such terms: we humans perceive all visible forms, no matter if they are ‘constructed’ or not.