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De Divino Errore ‘De Divina Proportione’ Was Written by Luca Pacioli and Illustrated by Leonardo Da Vinci
De Divino Errore ‘De Divina Proportione’ was written by Luca Pacioli and illustrated by Leonardo da Vinci. It was one of the most widely read mathematical books. Unfortunately, a strongly emphasized statement in the book claims six summits of pyramids of the stellated icosidodecahedron lay in one plane. This is not so, and yet even extensively annotated editions of this book never noticed this error. Dutchmen Jos Janssens and Rinus Roelofs did so, 500 years later. Fig. 1: About this illustration of Leonardo da Vinci for the Milanese version of the ‘De Divina Proportione’, Pacioli erroneously wrote that the red and green dots lay in a plane. The book ‘De Divina Proportione’, or ‘On the Divine Ratio’, was written by the Franciscan Fra Luca Bartolomeo de Pacioli (1445-1517). His name is sometimes written Paciolo or Paccioli because Italian was not a uniform language in his days, when, moreover, Italy was not a country yet. Labeling Pacioli as a Tuscan, because of his birthplace of Borgo San Sepolcro, may be more correct, but he also studied in Venice and Rome, and spent much of his life in Perugia and Milan. In service of Duke and patron Ludovico Sforza, he would write his masterpiece, in 1497 (although it is more correct to say the work was written between 1496 and 1498, because it contains several parts). It was not his first opus, because in 1494 his ‘Summa de arithmetic, geometrica, proportioni et proportionalita’ had appeared; the ‘Summa’ and ‘Divina’ were not his only books, but surely the most famous ones. For hundreds of years the books were among the most widely read mathematical bestsellers, their fame being only surpassed by the ‘Elements’ of Euclid. -
Voegelin's History of Political Ideas and the Problem of Christian Order
Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2003 Voegelin's History of Political Ideas and the problem of Christian order: a critical appraisal Jeffrey Charles Herndon Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Political Science Commons Recommended Citation Herndon, Jeffrey Charles, "Voegelin's History of Political Ideas and the problem of Christian order: a critical appraisal" (2003). LSU Doctoral Dissertations. 2487. https://digitalcommons.lsu.edu/gradschool_dissertations/2487 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. VOEGELIN’S HISTORY OF POLITICAL IDEAS AND THE PROBLEM OF CHRISTIAN ORDER: A CRITICAL APPRAISAL A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy In The Department of Political Science By Jeffrey C. Herndon B.A., Southwest Texas State University, 1989 M.A., Southwest Texas State University, 1993 May 2003 Acknowledgements Contrary to the mythology of authorship, the writing of a book is really a collective enterprise. While invariably the names of one or two people appear on the title page, my own experience leads me to believe that no book would ever be finished without the help, love, support, and some degree of gentle authoritarianism on the part of those prodding the author forward in his or her work. -
On the Human Role in Generative Art: a Case
ON THE HUMAN ROLE IN GENERATIVE ART: A CASE STUDY OF AI-DRIVEN LIVE CODING ANTONIO POŠĆIĆ Independent Scholar [email protected] GORDAN KREKOVIĆ Visage Technologies [email protected] https://doi.org/10.34632/jsta.2020.9488 ABSTRACT The constant evolution of philosophical views on art is interwoven with trajectories of accelerating technological development. In the current vehement emergence of generative algorithms there is an immediate need for making sense of modern technologies that increasingly seem to step in the realm that has been reserved for humans – creativity. This paper aims to understand the role of the human in generative art by demystifying Vol. 12, n. 3 (2020): pp. 45-62 implications of black-box generative algorithms and their applications for artistic purposes. First, we present examples of current practice and research in generative art with a special interest in music that served as foundation for our work. Then, we introduce Anastatica (2020), a part performance, part installation built on the basis of data-driven generative live coding. Finally, we discuss the various implications of AI in art through a case study rooted in Anastatica’s development and performance. Here we trace the path from algorithms to intelligence, applying both musical and computer science theory to a practical case of generating a live coding musical performance, with special focus given to aesthetic, compositional, conceptual, and phenomenological implications. Journal of Science and Technology of the Arts, of the Journal of Science and Technology Keywords: Artificial intelligence; Generative art; Live coding; Generative music; Computer art. 46 1. INTRODUCTION In broad terms, artificial intelligence (AI) is any sort of intelligence exhibited by machines (Nilsson 1998). -
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Media-N | The Journal of the New Media Caucus 2019: Volume 15, Issue 1, Pages 69–81 ISSN: 1942-017X Media-N | The Machines Wave Back CHAD M. EBY Assistant Professor, Herron School of Art + Design, IUPUI ABSTRACT This paper examines notions of autonomy and agency in the context of understanding artist and rules system relationships within an Autonomous Art System (AAS). The concept of Create / Read / Update / Delete is borrowed from computer engineering as a metaphor for a role-based (rather than medium-based) framework for classifying AASs and, combined with the discussion of autonomy and agency, forms the basis for a new taxonomic system of Autonomous Art Systems for analysis, categorization and comparison. “A chipped pebble is almost part of the hand it never leaves. A thrown spear declares a sort of independence the moment it is released.” – Isaac Asimov, “The machine and the robot” in Robot Visions “The machines aren’t very smart yet, but we’re teaching them this stuff all the time. We’re giving them eyes and ears and we’re giving them access to our world. We’re sharing our social spaces with them increasingly. They increasingly live like the render ghosts, on the borders of our world, and they’re starting to share it with (us). – James Bridle, “Waving at the Machines” INTRODUCTION The purpose of this paper is to propose a way to describe degrees of autonomy and agency in Autonomous Art Systems (hereafter, AAS) to aid in analysis, categorization and comparison of such systems, and to consider their boundary conditions in an art-making context. -
The Creativity of Artificial Intelligence in Art
The Creativity of Artificial Intelligence in Art Mingyong Cheng Duke University October 19th, 2020 Abstract New technologies, especially in the field of artificial intelligence, are dynamic in transforming the creative space. AI-enabled programs are rapidly contributing to areas like architecture, music, arts, science, and so on. The recent Christie's auction on the Portrait of Edmond has transformed the contemporary perception of A.I. art, giving rise to questions such as the creativity of this art. This research paper acknowledges the persistent problem, "Can A.I. art be considered as creative?" In this light, the study draws on the various applications of A.I., varied attitudes on A.I. art, and the processes of generating A.I. art to establish an argument that A.I. is capable of achieving artistic creativity. 1 Table of Contents Chapter One ..................................................................................................................................... 4 1.1 Introduction ............................................................................................................................ 4 2.1 Overview ................................................................................................................................ 7 2.2 Defining Artificial Intelligence .............................................................................................. 8 2.3 Application of AI in Various Fields .................................................................................... 10 2.3.1 Music ............................................................................................................................ -
Simple Rules for Incorporating Design Art Into Penrose and Fractal Tiles
Bridges 2012: Mathematics, Music, Art, Architecture, Culture Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles San Le SLFFEA.com [email protected] Abstract Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1 1 Introduction M.C. Escher was the most prominent artist working with tessellations and space filling. Forty years after his death, his creations are still foremost in people’s minds in the field of tiling art. One of the reasons Escher continues to hold such a monopoly in this specialty are the unique challenges that come with creating Escher type designs inside a tessellation[15]. When an image is drawn into a tile and extends to the tile’s edge, it introduces incongruencies which are resolved by continuously aligning and refining the image. This is particularly true when the image consists of the lizards, fish, angels, etc. which populated Escher’s tilings because they do not have the 4-fold rotational symmetry that would make it possible to arbitrarily rotate the image ± 90, 180 degrees and have all the pieces fit[9]. -
The Imaginative Tension in Henry David Thoreau's Political Thought
THE CATHOLIC UNIVERSITY OF AMERICA Arcadian Exile: The Imaginative Tension in Henry David Thoreau’s Political Thought A DISSERTATION Submitted to the Faculty of the Department of Politics School of Arts and Sciences of the Catholic University of America In Partial Fulfillment of the Requirements For the Degree Doctor of Philosophy © Copyright All Rights Reserved By Joshua James Bowman Washington, D.C. 2016 Arcadian Exile: The Imaginative Tension in Henry David Thoreau’s Political Thought Joshua James Bowman, Ph.D. Director: Claes G. Ryn, Ph.D. Henry David Thoreau‘s writings have achieved a unique status in the history of American literature. His ideas influenced the likes of Gandhi and Martin Luther King Jr., and play a significant role in American environmentalism. Despite this influence his larger political vision is often used for purposes he knew nothing about or could not have anticipated. The purpose of this dissertation is to analyze Thoreau’s work and legacy by elucidating a key tension within Thoreau's imagination. Instead of placing Thoreau in a pre-conceived category or worldview, the focus on imagination allows a more incisive reflection on moral and spiritual questions and makes possible a deeper investigation of Thoreau’s sense of reality. Drawing primarily on the work of Claes Ryn, imagination is here conceived as a form of consciousness that is creative and constitutive of our most basic sense of reality. The imagination both shapes and is shaped by will/desire and is capable of a broad and qualitatively diverse range of intuition which varies depending on one’s orientation of will. -
Leonardo Universal
Leonardo Universal DE DIVINA PROPORTIONE Pacioli, legendary mathematician, introduced the linear perspective and the mixture of colors, representing the human body and its proportions and extrapolating this knowledge to architecture. Luca Pacioli demonstrating one of Euclid’s theorems (Jacobo de’Barbari, 1495) D e Divina Proportione is a holy expression commonly outstanding work and icon of the Italian Renaissance. used in the past to refer to what we nowadays call Leonardo, who was deeply interested in nature and art the golden section, which is the mathematic module mathematics, worked with Pacioli, the author of the through which any amount can be divided in two text, and was a determined spreader of perspectives uneven parts, so that the ratio between the smallest and proportions, including Phi in many of his works, part and the largest one is the same as that between such as The Last Supper, created at the same time as the largest and the full amount. It is divine for its the illustrations of the present manuscript, the Mona being unique, and triune, as it links three elements. Lisa, whose face hides a perfect golden rectangle and The fusion of art and science, and the completion of the Uomo Vitruviano, a deep study on the human 60 full-page illustrations by the preeminent genius figure where da Vinci proves that all the main body of the time, Leonardo da Vinci, make it the most parts were related to the golden ratio. Luca Pacioli credits that Leonardo da Vinci made the illustrations of the geometric bodies with quill, ink and watercolor. -
Leonardo Da Vinci's Study of Light and Optics: a Synthesis of Fields in The
Bitler Leonardo da Vinci’s Study of Light and Optics Leonardo da Vinci’s Study of Light and Optics: A Synthesis of Fields in The Last Supper Nicole Bitler Stanford University Leonardo da Vinci’s Milanese observations of optics and astronomy complicated his understanding of light. Though these complications forced him to reject “tidy” interpretations of light and optics, they ultimately allowed him to excel in the portrayal of reflection, shadow, and luminescence (Kemp, 2006). Leonardo da Vinci’s The Last Supper demonstrates this careful study of light and the relation of light to perspective. In the work, da Vinci delved into the complications of optics and reflections, and its renown guided the artistic study of light by subsequent masters. From da Vinci’s personal manuscripts, accounts from his contemporaries, and present-day art historians, the iterative relationship between Leonardo da Vinci’s study of light and study of optics becomes apparent, as well as how his study of the two fields manifested in his paintings. Upon commencement of courtly service in Milan, da Vinci immersed himself in a range of scholarly pursuits. Da Vinci’s artistic and mathematical interest in perspective led him to the study of optics. Initially, da Vinci “accepted the ancient (and specifically Platonic) idea that the eye functioned by emitting a special type of visual ray” (Kemp, 2006, p. 114). In his early musings on the topic, da Vinci reiterated this notion, stating in his notebooks that, “the eye transmits through the atmosphere its own image to all the objects that are in front of it and receives them into itself” (Suh, 2005, p. -
Byeong Sam Jeon
BYEONG SAM JEON Personal Website: www.bsjeon.net Organizational Website: www.koian.com Email: [email protected] Office: 82-2-2038-8290 Address: 7F Sinmyeong BD. 834-44, Yeoksam-dong, Gangnam-gu, Seoul, Korea BIOGRAPHY Byeong Sam Jeon is an internationally recognized artist, researcher, and educator working at the confluence of art and science. His interests include Telematic Culture, Robotic Art, Embodied Interaction, Physical Computing, Trans-Humanism, and STEAM Education. For a decade, Jeon has been invited to present his artwork and research worldwide including: SIGGRAPH (USA), ISIMD (Turkey), LIFE: Version of Science (Russia), ArtBots (Ireland), AsiaGraph (China), SALON (Cuba), Netfilmmakers (Denmark), Siggraph-ASIA (Singapore), DALSMA (Korea), and elsewhere. One of his well-known projects, 'Telematic Drum Circle' has gathered more than 300,000 Internet users and offline participants from 59 countries to perform tele-robotic sound improvisation together since it was premiered at the California Institute for Telecommunications and Information Technology in September 2007. Jeon, as a theater director, has produced the world-first robot musical 'Robotata' (2011), the main performance of Korea Science Fest ‘Science for Dream’ (2010), and the opening performance of the 60th International Astronautical Congress ‘Feast of Space’ (2009). As a curator, he directed the international new media art exhibition 'ThisAbility'(China), 'Machine Dreams'(Korea), 'Interactive Playground'(USA), and several others. Byeong Sam Jeon currently works as the -
The State of the Arts in the Middle East
Viewpoints Special Edition The State of the Arts in the Middle East The Middle East Institute Washington, DC Middle East Institute The mission of the Middle East Institute is to promote knowledge of the Middle East in Amer- ica and strengthen understanding of the United States by the people and governments of the region. For more than 60 years, MEI has dealt with the momentous events in the Middle East — from the birth of the state of Israel to the invasion of Iraq. Today, MEI is a foremost authority on contemporary Middle East issues. It pro- vides a vital forum for honest and open debate that attracts politicians, scholars, government officials, and policy experts from the US, Asia, Europe, and the Middle East. MEI enjoys wide access to political and business leaders in countries throughout the region. Along with information exchanges, facilities for research, objective analysis, and thoughtful commentary, MEI’s programs and publications help counter simplistic notions about the Middle East and America. We are at the forefront of private sector public diplomacy. Viewpoints are another MEI service to audiences interested in learning more about the complexities of issues affecting the Middle East and US rela- tions with the region. To learn more about the Middle East Institute, visit our website at http://www.mei.edu Cover photos are credited, where necessary, in the body of the collection. 2 The Middle East Institute Viewpoints: The State of the Arts in the Middle East • www.mei.edu Viewpoints Special Edition The State of the Arts in the Middle East The Middle East Institute Viewpoints: The State of the Arts in the Middle East • www.mei.edu 3 Also in this series.. -
Linking Math with Art Through the Elements of Design
2007 Asilomar Mathematics Conference Linking Math With Art Through The Elements of Design Presented by Renée Goularte Thermalito Union School District • Oroville, California www.share2learn.com [email protected] The Elements of Design ~ An Overview The elements of design are the components which make up any visual design or work or art. They can be isolated and defined, but all works of visual art will contain most, if not all, the elements. Point: A point is essentially a dot. By definition, it has no height or width, but in art a point is a small, dot-like pencil mark or short brush stroke. Line: A line can be made by a series of points, a pencil or brush stroke, or can be implied by the edge of an object. Shape and Form: Shapes are defined by lines or edges. They can be geometric or organic, predictably regular or free-form. Form is an illusion of three- dimensionality given to a flat shape. Texture: Texture can be tactile or visual. Tactile texture is something you can feel; visual texture relies on the eyes to help the viewer imagine how something might feel. Texture is closely related to Pattern. Pattern: Patterns rely on repetition or organization of shapes, colors, or other qualities. The illusion of movement in a composition depends on placement of subject matter. Pattern is closely related to Texture and is not always included in a list of the elements of design. Color and Value: Color, also known as hue, is one of the most powerful elements. It can evoke emotion and mood, enhance texture, and help create the illusion of distance.