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THE THEORY of MATHEMATICAL SUBTRACTION in ARISTOTLE By
THE THEORY OF MATHEMATICAL SUBTRACTION IN ARISTOTLE by Ksenia Romashova Submitted in partial fulfilment of the requirements for the degree of Master of Arts at Dalhousie University Halifax, Nova Scotia August 2019 © Copyright by Ksenia Romashova, 2019 DEDICATION PAGE To my Mother, Vera Romashova Мама, Спасибо тебе за твою бесконечную поддержку, дорогая! ii TABLE OF CONTENTS LIST OF FIGURES .................................................................................................................. iv ABSTRACT ............................................................................................................................... v LIST OF ABBREVIATIONS USED ....................................................................................... vi ACKNOWLEDGEMENTS ..................................................................................................... vii CHAPTER 1 INTRODUCTION ............................................................................................... 1 CHAPTER 2 THE MEANING OF ABSTRACTION .............................................................. 6 2.1 Etymology and Evolution of the Term ................................................................... 7 2.2 The Standard Phrase τὰ ἐξ ἀφαιρέσεως or ‘Abstract Objects’ ............................ 19 CHAPTER 3 GENERAL APPLICATION OF ABSTRACTION .......................................... 24 3.1 The Instances of Aphairein in Plato’s Dialogues ................................................. 24 3.2 The Use of Aphairein in Aristotle’s Topics -
(12) United States Patent (10) Patent No.: US 8,513,329 B2 Lake Et Al
USOO8513329B2 (12) United States Patent (10) Patent No.: US 8,513,329 B2 Lake et al. (45) Date of Patent: Aug. 20, 2013 (54) CHEMICAL ADDITIVES TO MAKE 6,296,889 B1 10/2001 Ott et al. POLYMERIC MATERALS 6,635,692 B1 10/2003 Christie et al. 7,037,983 B2 5/2006 Huang et al. BODEGRADABLE 7,053,130 B2 5/2006 Nagarajan 7,067,596 B2 6/2006 Bastioli et al. (75) Inventors: John Allen Lake, Cedar Crest, NM 7,265,160 B2 * 9/2007 Oka et al. ..................... 521 50.5 (US); Samuel David Adams, 7,368,503 B2 5/2008 Hale Albuquerque, NM (US) 7,369,503 B2 * 5/2008 Takahashi et al. ............ 370,236 s 7,560,266 B2 7/2009 Bramucci et al. 7,812,066 B2 10/2010 Takenaka et al. (73) Assignee: Bio-Tec Environmental, LLC, 7.816,424 B2 10/2010 Takahashi et al. Albuquerque, NM (US) 8.222,316 B2 7/2012 Lake et al. 2003. O157214 A1 8/2003 Bonsignore et al. (*) Notice: Subject to any disclaimer, the term of this 2004.0068059 Al 42004 Katayama et al. patent is extended or adjusted under 35 3.SSA A. 2. MEC. et ca.ea U.S.C. 154(b) by 158 days. 2005. O1541 14 A1 7, 2005 Hale 2005/O181157 A1 8, 2005 Otome (21) Appl. No.: 12/113,844 2005/0181158 A1 8/2005 Otome et al. 2005/0208095 A1 9, 2005 Hunter et al. (22) Filed: May 1, 2008 2007, OO 10632 A1 1/2007 Kaplanet al. -
Trimpin Above, Below, and in Between Trimpin
TRIMPIN ABOVE, BELOW, AND IN BETWEEN BELOW, ABOVE, SEATTLE SYMPHONY LUDOVIC MORLOT TRIMPIN Above, Below, and In Between, A site-specific composition Part 1 .............................................................................1:36 Part 2 ............................................................................ 2:55 Part 3 – For Jessika ..................................................... 4:20 Part 4 ............................................................................ 2:34 Part 5 ............................................................................ 6:00 Part 6 ............................................................................ 5:00 Jessika Kenney, soprano; Sayaka Kokubo, viola; Penelope Crane, viola: Eric Han, cello; David Sabee, cello; Jordan Anderson, double bass; Joseph Kaufman, double bass; Ko-ichiro Yamamoto, trombone; David Lawrence Ritt, trombone; Stephen Fissel, trombone TOTAL TIME ............................................................... 22:30 SEATTLESYMPHONY.ORG � & © 2016 Seattle Symphony Media. All rights reserved. Unauthorized copying, hiring, lending, public performance and broadcasting of this record prohibited without prior written permission from the Seattle Symphony. Benaroya Hall, 200 University Street, Seattle, WA 98101 MADE IN USA Photo: Larey McDaniel Larey Photo: SEATTLE SYMPHONY Founded in 1903, the Seattle Symphony is one of America’s leading symphony orchestras and is internationally acclaimed for its innovative programming and extensive recording history. Under the leadership -
Continuity and Mathematical Ontology in Aristotle
Journal of Ancient Philosophy, vol. 14 issue 1, 2020. DOI: http://dx.doi.org/10.11606/issn.1981-9471.v14i1p30-61 Continuity and Mathematical Ontology in Aristotle Keren Wilson Shatalov In this paper I argue that Aristotle’s understanding of mathematical continuity constrains the mathematical ontology he can consistently hold. On my reading, Aristotle can only be a mathematical abstractionist of a certain sort. To show this, I first present an analysis of Aristotle’s notion of continuity by bringing together texts from his Metaphysica and Physica, to show that continuity is, for Aristotle, a certain kind of per se unity, and that upon this rests his distinction between continuity and contiguity. Next I argue briefly that Aristotle intends for his discussion of continuity to apply to pure mathematical objects such as lines and figures, as well as to extended bodies. I show that this leads him to a difficulty, for it does not at first appear that the distinction between continuity and contiguity can be preserved for abstract mathematicals. Finally, I present a solution according to which Aristotle’s understanding of continuity can only be saved if he holds a certain kind of mathematical ontology. My topic in this paper is Aristotle’s understanding of mathematical continuity. While the idea that continua are composed of infinitely many points is the present day orthodoxy, the Aristotelian understanding of continua as non-punctiform and infinitely divisible was the reigning theory for much of the history of western mathematics, and there is renewed interest in it from current mathematicians and philosophers of mathematics. -
The Hell Harp of Hieronymus Bosch. the Building of an Experimental Musical Instrument, and a Critical Account of an Experience of a Community of Musicians
1 (114) Independent Project (Degree Project), 30 higher education credits Master of Fine Arts in Music, with specialization in Improvisation Performance Academy of Music and Drama, University of Gothenburg Spring 2019 Author: Johannes Bergmark Title: The Hell Harp of Hieronymus Bosch. The building of an experimental musical instrument, and a critical account of an experience of a community of musicians. Supervisors: Professor Anders Jormin, Professor Per Anders Nilsson Examiner: Senior Lecturer Joel Eriksson ABSTRACT Taking a detail from Hieronymus Bosch’s Garden Of Earthly Delights as a point of departure, an instrument is built for a musical performance act deeply involving the body of the musician. The process from idea to performance is recorded and described as a compositional and improvisational process. Experimental musical instrument (EMI) building is discussed from its mythological and sociological significance, and from autoethnographical case studies of processes of invention. The writer’s experience of 30 years in the free improvisation and new music community, and some basic concepts: EMIs, EMI maker, musician, composition, improvisation, music and instrument, are analyzed and criticized, in the community as well as in the writer’s own work. The writings of Christopher Small and surrealist ideas are main inspirations for the methods applied. Keywords: Experimental musical instruments, improvised music, Hieronymus Bosch, musical performance art, music sociology, surrealism Front cover: Hieronymus Bosch, The Garden of Earthly -
The Evolution of the Performer Composer
CONTEMPORARY APPROACHES TO LIVE COMPUTER MUSIC: THE EVOLUTION OF THE PERFORMER COMPOSER BY OWEN SKIPPER VALLIS A thesis submitted to the Victoria University of Wellington in fulfillment of the requirements for the degree of Doctor of Philosophy Victoria University of Wellington 2013 Supervisory Committee Dr. Ajay Kapur (New Zealand School of Music) Supervisor Dr. Dugal McKinnon (New Zealand School of Music) Co-Supervisor © OWEN VALLIS, 2013 NEW ZEALAND SCHOOL OF MUSIC ii ABSTRACT This thesis examines contemporary approaches to live computer music, and the impact they have on the evolution of the composer performer. How do online resources and communities impact the design and creation of new musical interfaces used for live computer music? Can we use machine learning to augment and extend the expressive potential of a single live musician? How can these tools be integrated into ensembles of computer musicians? Given these tools, can we understand the computer musician within the traditional context of acoustic instrumentalists, or do we require new concepts and taxonomies? Lastly, how do audiences perceive and understand these new technologies, and what does this mean for the connection between musician and audience? The focus of the research presented in this dissertation examines the application of current computing technology towards furthering the field of live computer music. This field is diverse and rich, with individual live computer musicians developing custom instruments and unique modes of performance. This diversity leads to the development of new models of performance, and the evolution of established approaches to live instrumental music. This research was conducted in several parts. The first section examines how online communities are iteratively developing interfaces for computer music. -
Forms of Intelligence. Concept Cards for Co-Species Care
forms of intelligence. concept cards for co-species care. by kaajal modi 2 forms of intelligence. concept cards for co-species care. 3 contents. the cards. 4 card footnotes. 7 cross-species collaborators. 34 the team. 39 symbols & symbioses. 41 Forms of Intelligence is an ongoing project led by Knowle references. 47 West Media Centre exploring how expanded understandings of ‘intelligence’ can inspire the design and creation of new technologies and systems for the benefit of all. Commissioned by Knowle West Media Centre and Digital Cultures Research Centre © September 2020 4 forms of intelligence. concept cards for co-species care. 5 who are they for? the The cards are designed to act as conversation starters and inspirational prompts. for anyone involved in a making process. How often do you challenge yourself to stop and think cards. differently, to see from a different perspective, or think deeply about who or what is being impacted by your decisions? The cards are draw on different forms of animal, plant and microbial intelligence that often get overlooked in human- what are they? led projects and processes. They also invite you to reflect on The cards and this booklet were commissioned by Knowle the humans who are connected to these organisms, whether West Media Centre as part of the Forms of Intelligence directly, by working with them, or indirectly, by sharing land project, and were made by artist and researcher Kaajal Modi. and resources with them. The cards have been made in response to and are inspired by If you are looking for inspiration and ready to open your a series of collaborative workshops between eight people from mind to think more expansively about all living beings, then Knowle West, Bristol, Kent, and Colombia with expertise in these cards are for you. -
From Point to Pixel: a Genealogy of Digital Aesthetics by Meredith Anne Hoy
From Point to Pixel: A Genealogy of Digital Aesthetics by Meredith Anne Hoy A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Rhetoric and the Designated Emphasis in Film Studies in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Whitney Davis, co-chair Professor Jeffrey Skoller, co-chair Professor Warren Sack Professor Abigail DeKosnik Professor Kristen Whissel Spring 2010 Copyright 2010 by Hoy, Meredith All rights reserved. Abstract From Point to Pixel: A Genealogy of Digital Aesthetics by Meredith Anne Hoy Doctor of Philosophy in Rhetoric University of California, Berkeley Professor Whitney Davis, Co-chair Professor Jeffrey Skoller, Co-chair When we say, in response to a still or moving picture, that it has a digital “look” about it, what exactly do we mean? How can the slick, color-saturated photographs of Jeff Wall and Andreas Gursky signal digitality, while the flattened, pixelated landscapes of video games such as Super Mario Brothers convey ostensibly the same characteristic of “being digital,” but in a completely different manner? In my dissertation, From Point to Pixel: A Genealogy of Digital Aesthetics, I argue for a definition of a "digital method" that can be articulated without reference to the technicalities of contemporary hardware and software. I allow, however, the possibility that this digital method can acquire new characteristics when it is performed by computational technology. I therefore treat the artworks covered in my dissertation as sensuous artifacts that are subject to change based on the constraints and affordances of the tools used in their making. -
Media Ecologies: Materialist Energies in Art and Technoculture, Matthew Fuller, 2005 Media Ecologies
M796883front.qxd 8/1/05 11:15 AM Page 1 Media Ecologies Media Ecologies Materialist Energies in Art and Technoculture Matthew Fuller In Media Ecologies, Matthew Fuller asks what happens when media systems interact. Complex objects such as media systems—understood here as processes, or ele- ments in a composition as much as “things”—have become informational as much as physical, but without losing any of their fundamental materiality. Fuller looks at this multi- plicitous materiality—how it can be sensed, made use of, and how it makes other possibilities tangible. He investi- gates the ways the different qualities in media systems can be said to mix and interrelate, and, as he writes, “to produce patterns, dangers, and potentials.” Fuller draws on texts by Félix Guattari and Gilles Deleuze, as well as writings by Friedrich Nietzsche, Marshall McLuhan, Donna Haraway, Friedrich Kittler, and others, to define and extend the idea of “media ecology.” Arguing that the only way to find out about what happens new media/technology when media systems interact is to carry out such interac- tions, Fuller traces a series of media ecologies—“taking every path in a labyrinth simultaneously,” as he describes one chapter. He looks at contemporary London-based pirate radio and its interweaving of high- and low-tech “Media Ecologies offers an exciting first map of the mutational body of media systems; the “medial will to power” illustrated by analog and digital media technologies. Fuller rethinks the generation and “the camera that ate itself”; how, as seen in a range of interaction of media by connecting the ethical and aesthetic dimensions compelling interpretations of new media works, the capac- of perception.” ities and behaviors of media objects are affected when —Luciana Parisi, Leader, MA Program in Cybernetic Culture, University of they are in “abnormal” relationships with other objects; East London and each step in a sequence of Web pages, Cctv—world wide watch, that encourages viewers to report crimes seen Media Ecologies via webcams. -
1976-77-Annual-Report.Pdf
TheCanada Council Members Michelle Tisseyre Elizabeth Yeigh Gertrude Laing John James MacDonaId Audrey Thomas Mavor Moore (Chairman) (resigned March 21, (until September 1976) (Member of the Michel Bélanger 1977) Gilles Tremblay Council) (Vice-Chairman) Eric McLean Anna Wyman Robert Rivard Nini Baird Mavor Moore (until September 1976) (Member of the David Owen Carrigan Roland Parenteau Rudy Wiebe Council) (from May 26,1977) Paul B. Park John Wood Dorothy Corrigan John C. Parkin Advisory Academic Pane1 Guita Falardeau Christopher Pratt Milan V. Dimic Claude Lévesque John W. Grace Robert Rivard (Chairman) Robert Law McDougall Marjorie Johnston Thomas Symons Richard Salisbury Romain Paquette Douglas T. Kenny Norman Ward (Vice-Chairman) James Russell Eva Kushner Ronald J. Burke Laurent Santerre Investment Committee Jean Burnet Edward F. Sheffield Frank E. Case Allan Hockin William H. R. Charles Mary J. Wright (Chairman) Gertrude Laing J. C. Courtney Douglas T. Kenny Michel Bélanger Raymond Primeau Louise Dechêne (Member of the Gérard Dion Council) Advisory Arts Pane1 Harry C. Eastman Eva Kushner Robert Creech John Hirsch John E. Flint (Member of the (Chairman) (until September 1976) Jack Graham Council) Albert Millaire Gary Karr Renée Legris (Vice-Chairman) Jean-Pierre Lefebvre Executive Committee for the Bruno Bobak Jacqueline Lemieux- Canadian Commission for Unesco (until September 1976) Lope2 John Boyle Phyllis Mailing L. H. Cragg Napoléon LeBlanc Jacques Brault Ray Michal (Chairman) Paul B. Park Roch Carrier John Neville Vianney Décarie Lucien Perras Joe Fafard Michael Ondaatje (Vice-Chairman) John Roberts Bruce Ferguson P. K. Page Jacques Asselin Céline Saint-Pierre Suzanne Garceau Richard Rutherford Paul Bélanger Charles Lussier (until August 1976) Michael Snow Bert E. -
Galileo, Ignoramus: Mathematics Versus Philosophy in the Scientific Revolution
Galileo, Ignoramus: Mathematics versus Philosophy in the Scientific Revolution Viktor Blåsjö Abstract I offer a revisionist interpretation of Galileo’s role in the history of science. My overarching thesis is that Galileo lacked technical ability in mathematics, and that this can be seen as directly explaining numerous aspects of his life’s work. I suggest that it is precisely because he was bad at mathematics that Galileo was keen on experiment and empiricism, and eagerly adopted the telescope. His reliance on these hands-on modes of research was not a pioneering contribution to scientific method, but a last resort of a mind ill equipped to make a contribution on mathematical grounds. Likewise, it is precisely because he was bad at mathematics that Galileo expounded at length about basic principles of scientific method. “Those who can’t do, teach.” The vision of science articulated by Galileo was less original than is commonly assumed. It had long been taken for granted by mathematicians, who, however, did not stop to pontificate about such things in philosophical prose because they were too busy doing advanced scientific work. Contents 4 Astronomy 38 4.1 Adoption of Copernicanism . 38 1 Introduction 2 4.2 Pre-telescopic heliocentrism . 40 4.3 Tycho Brahe’s system . 42 2 Mathematics 2 4.4 Against Tycho . 45 2.1 Cycloid . .2 4.5 The telescope . 46 2.2 Mathematicians versus philosophers . .4 4.6 Optics . 48 2.3 Professor . .7 4.7 Mountains on the moon . 49 2.4 Sector . .8 4.8 Double-star parallax . 50 2.5 Book of nature . -
NEWSLETTER Published by the Institute for Canadian Music, Faculty of Music, University of Toronto
Vol. 1, no. 1 · January 2003 ISSN 1705-1452 NEWSLETTER Published by the Institute for Canadian Music, Faculty of Music, University of Toronto Editor: Robin Elliott _______________________________________________________________________________________ The Institute for Canadian Music The aim of the Institute for Canadian Music larger community of those with an interest in music (ICM) is to promote, support, and produce scholarship both here in Canada and abroad. in all areas of Canadian music studies. The ICM was founded at the University of Toronto in 1984 at the This newsletter will feature current research in same time as the Jean A. Chalmers Chair in Canadian Canadian music and will include reports on important Music. John Beckwith served as the founding Director events such as publications, concerts, and celebratory of the ICM and was the first holder of the Chalmers milestones. Please contact the ICM at the address listed Chair; he was succeeded in both capacities by Carl below if you would like to receive a complimentary Morey in 1991. The ICM has sponsored or participated subscription to the Newsletter, inform the ICM about in conferences; has issued two series of publications, your own research on Canadian music, or submit an CanMus Documents (five vols., 1987-91) and CanMus article or report for publication in the Newsletter. The Handbooks (four vols., 1986-90); and has subsidized next issue will appear in May 2003; the deadline for recording and publishing projects. Robin Elliott submissions is April 15th, 2003. became the new Jean A. Chalmers Chair in Canadian Music and Director of the ICM on 1 July 2002.