Envisaging a Comprehensible Global Brain As a Playful Organ
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How to Juggle the Proof for Every Theorem an Exploration of the Mathematics Behind Juggling
How to juggle the proof for every theorem An exploration of the mathematics behind juggling Mees Jager 5965802 (0101) 3 0 4 1 2 (1100) (1010) 1 4 4 3 (1001) (0011) 2 0 0 (0110) Supervised by Gil Cavalcanti Contents 1 Abstract 2 2 Preface 4 3 Preliminaries 5 3.1 Conventions and notation . .5 3.2 A mathematical description of juggling . .5 4 Practical problems with mathematical answers 9 4.1 When is a sequence jugglable? . .9 4.2 How many balls? . 13 5 Answers only generate more questions 21 5.1 Changing juggling sequences . 21 5.2 Constructing all sequences with the Permutation Test . 23 5.3 The converse to the average theorem . 25 6 Mathematical problems with mathematical answers 35 6.1 Scramblable and magic sequences . 35 6.2 Orbits . 39 6.3 How many patterns? . 43 6.3.1 Preliminaries and a strategy . 43 6.3.2 Computing N(b; p).................... 47 6.3.3 Filtering out redundancies . 52 7 State diagrams 54 7.1 What are they? . 54 7.2 Grounded or Excited? . 58 7.3 Transitions . 59 7.3.1 The superior approach . 59 7.3.2 There is a preference . 62 7.3.3 Finding transitions using the flattening algorithm . 64 7.3.4 Transitions of minimal length . 69 7.4 Counting states, arrows and patterns . 75 7.5 Prime patterns . 81 1 8 Sometimes we do not find the answers 86 8.1 The converse average theorem . 86 8.2 Magic sequence construction . 87 8.3 finding transitions with flattening algorithm . -
Inspiring Mathematical Creativity Through Juggling
Journal of Humanistic Mathematics Volume 10 | Issue 2 July 2020 Inspiring Mathematical Creativity through Juggling Ceire Monahan Montclair State University Mika Munakata Montclair State University Ashwin Vaidya Montclair State University Sean Gandini Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Monahan, C. Munakata, M. Vaidya, A. and Gandini, S. "Inspiring Mathematical Creativity through Juggling," Journal of Humanistic Mathematics, Volume 10 Issue 2 (July 2020), pages 291-314. DOI: 10.5642/ jhummath.202002.14 . Available at: https://scholarship.claremont.edu/jhm/vol10/iss2/14 ©2020 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Inspiring Mathematical Creativity Through Juggling Ceire Monahan Department of Mathematical Sciences, Montclair State University, New Jersey, USA -
Happy Birthday!
THE THURSDAY, APRIL 1, 2021 Quote of the Day “That’s what I love about dance. It makes you happy, fully happy.” Although quite popular since the ~ Debbie Reynolds 19th century, the day is not a public holiday in any country (no kidding). Happy Birthday! 1998 – Burger King published a full-page advertisement in USA Debbie Reynolds (1932–2016) was Today introducing the “Left-Handed a mega-talented American actress, Whopper.” All the condiments singer, and dancer. The acclaimed were rotated 180 degrees for the entertainer was first noticed at a benefit of left-handed customers. beauty pageant in 1948. Reynolds Thousands of customers requested was soon making movies and the burger. earned a nomination for a Golden Globe Award for Most Promising 2005 – A zoo in Tokyo announced Newcomer. She became a major force that it had discovered a remarkable in Hollywood musicals, including new species: a giant penguin called Singin’ In the Rain, Bundle of Joy, the Tonosama (Lord) penguin. With and The Unsinkable Molly Brown. much fanfare, the bird was revealed In 1969, The Debbie Reynolds Show to the public. As the cameras rolled, debuted on TV. The the other penguins lifted their beaks iconic star continued and gazed up at the purported Lord, to perform in film, but then walked away disinterested theater, and TV well when he took off his penguin mask into her 80s. Her and revealed himself to be the daughter was actress zoo director. Carrie Fisher. ©ActivityConnection.com – The Daily Chronicles (CAN) HURSDAY PRIL T , A 1, 2021 Today is April Fools’ Day, also known as April fish day in some parts of Europe. -
Toward a New Science of Information
Data Science Journal, Volume 6, Supplement, 7 April 2007 TOWARD A NEW SCIENCE OF INFORMATION D Doucette1*, R Bichler 2, W Hofkirchner2, and C Raffl2 *1 The Science of Information Institute, 1737 Q Street, N.W. Washington, D.C. 20009, USA Email: [email protected] 2 ICT&S Center, University of Salzburg - Center for Advanced Studies and Research in Information and Communication Technologies & Society, Sigmund-Haffner-Gasse 18, 5020 Salzburg, Austria Email: [email protected], [email protected], [email protected] ABSTRACT The concept of information has become a crucial topic in several emerging scientific disciplines, as well as in organizations, in companies and in everyday life. Hence it is legitimate to speak of the so-called information society; but a scientific understanding of the Information Age has not had time to develop. Following this evolution we face the need of a new transdisciplinary understanding of information, encompassing many academic disciplines and new fields of interest. Therefore a Science of Information is required. The goal of this paper is to discuss the aims, the scope, and the tools of a Science of Information. Furthermore we describe the new Science of Information Institute (SOII), which will be established as an international and transdisciplinary organization that takes into consideration a larger perspective of information. Keywords: Information, Science of Information, Information Society, Transdisciplinarity, Science of Information Institute (SOII), Foundations of Information Science (FIS) 1 INTRODUCTION Information is emerging as a new and large prospective area of study. The notion of information has become a crucial topic in several emerging scientific disciplines such as Philosophy of Information, Quantum Information, Bioinformatics and Biosemiotics, Theory of Mind, Systems Theory, Internet Research, and many more. -
Class of 1965 50Th Reunion
CLASS OF 1965 50TH REUNION BENNINGTON COLLEGE Class of 1965 Abby Goldstein Arato* June Caudle Davenport Anna Coffey Harrington Catherine Posselt Bachrach Margo Baumgarten Davis Sandol Sturges Harsch Cynthia Rodriguez Badendyck Michele DeAngelis Joann Hirschorn Harte Isabella Holden Bates Liuda Dovydenas Sophia Healy Helen Eggleston Bellas Marilyn Kirshner Draper Marcia Heiman Deborah Kasin Benz Polly Burr Drinkwater Hope Norris Hendrickson Roberta Elzey Berke Bonnie Dyer-Bennet Suzanne Robertson Henroid Jill (Elizabeth) Underwood Diane Globus Edington Carol Hickler Bertrand* Wendy Erdman-Surlea Judith Henning Hoopes* Stephen Bick Timothy Caroline Tupling Evans Carla Otten Hosford Roberta Robbins Bickford Rima Gitlin Faber Inez Ingle Deborah Rubin Bluestein Joy Bacon Friedman Carole Irby Ruth Jacobs Boody Lisa (Elizabeth) Gallatin Nina Levin Jalladeau Elizabeth Boulware* Ehrenkranz Stephanie Stouffer Kahn Renee Engel Bowen* Alice Ruby Germond Lorna (Miriam) Katz-Lawson Linda Bratton Judith Hyde Gessel Jan Tupper Kearney Mary Okie Brown Lynne Coleman Gevirtz Mary Kelley Patsy Burns* Barbara Glasser Cynthia Keyworth Charles Caffall* Martha Hollins Gold* Wendy Slote Kleinbaum Donna Maxfield Chimera Joan Golden-Alexis Anne Boyd Kraig Moss Cohen Sheila Diamond Goodwin Edith Anderson Kraysler Jane McCormick Cowgill Susan Hadary Marjorie La Rowe Susan Crile Bay (Elizabeth) Hallowell Barbara Kent Lawrence Tina Croll Lynne Tishman Handler Stephanie LeVanda Lipsky 50TH REUNION CLASS OF 1965 1 Eliza Wood Livingston Deborah Rankin* Derwin Stevens* Isabella Holden Bates Caryn Levy Magid Tonia Noell Roberts Annette Adams Stuart 2 Masconomo Street Nancy Marshall Rosalind Robinson Joyce Sunila Manchester, MA 01944 978-526-1443 Carol Lee Metzger Lois Banulis Rogers Maria Taranto [email protected] Melissa Saltman Meyer* Ruth Grunzweig Roth Susan Tarlov I had heard about Bennington all my life, as my mother was in the third Dorothy Minshall Miller Gail Mayer Rubino Meredith Leavitt Teare* graduating class. -
A New Transdisciplinary Paradigm for the Study of Complex Systems?", In: Self-Steering and Cognition in Complex Systems, Heylighen F., Rosseel E
Heylighen F. (1990): "A New Transdisciplinary Paradigm for the Study of Complex Systems?", in: Self-Steering and Cognition in Complex Systems, Heylighen F., Rosseel E. & Demeyere F. (ed.), (Gordon and Breach, New York), p. 1-16. A NEW TRANSDISCIPLINARY PARADIGM FOR THE STUDY OF COMPLEX SYSTEMS? Francis Heylighen Transdisciplinary Research Group Free University of Brussels ABSTRACT: two paradigms for studying the relation between autonomy and cognition are reviewed and contrasted: the "artificial" paradigm, which sees autonomous systems as linear, information-processing organizations, and the "autopoietic" paradigm, which sees them as circular, self-producing organizations. It is argued that these two paradigms are not inconsistent but complementary, and that they can be synthesized in an encompassing paradigm based on the self-organization of complex systems through variation-and-selective retention, leading to the emergence of relatively autonomous subsystems. Some implications of such an encompassing paradigm on the level of science, technology, individual persons and society are outlined, with reference to the papers in this collection. It is argued that the further development of such a transdisciplinary approach will lead to a new "science of complexity". 1. Introduction In the preface to this book it was argued that some recent trends in different disciplines seem to converge around the concepts of self-organization, autonomy and cognition. Whether these developments really announce the emergence of a new paradigm remains to be proven. Only time can tell. In this position paper, I will assume that they do, and investigate where this new paradigm would be coming from, and where it might be heading to. -
Artificial Intelligence
Intelligence, Artificial Intelligence and Wisdom in the Global Sustainable Information Society Fourth International Conference on Philosophy of Information, IS4SI Summit Berkeley 2019, UC Berkeley, 2-6 June 2019 Wolfgang Hofkirchner Director, GSIS – The Institute for a Global Sustainable Information Society, Vienna Contents 1 A complex systems view 1.1 The Great Bifurcation 1.2 The Transformation into a Global Sustainable Information Society 2 Conditions for thriving and surviving 2.1 Globality 2.2 Sustainability 2.3 Informationality 3 Intelligence, AI, and wisdom 1 A complex systems view Seen from a complex systems view, the evolution of mankind faces a Great Bifurcation. Global challenges might cause the extermination of mankind. At the same time, global challenges can be mastered through a transformation into a global sustainable information society. 1.1 The Great Bifurcation Civilisation at the breakthrough to a higher level crossroads (rise of complexity): integration of differentiated, interdependent social systems into a single meta-/suprasystem – Global Sustainable Information global space of possible Society challenges trajectories (multicrisis in all techno-, eco-, social breakdown (decline of complexity): subsystems) impossible trajectories disintegration and tipping point* falling apart of civilisation * Ervin László 1.2 Transformation Metasystem transition* agency system n interacting agency (proto-element) (network) * Francis Heylighen et al. system n+1 (proto-element) 1.2 Transformation Metasystem …organisational transition -
Towards a Cybernetic Foundation for Natural Resource Governance
Towards a Cybernetic Foundation for Natural Resource Governance A Thesis Presented to the Academic Faculty by Talha Manzoor In Partial Fullfilment of the Requirements for the Degree of Doctor of Philosophy in Electrical Engineering Supervisor: Abubakr Muhammad (LUMS) Co-supervisor: Elena Rovenskaya (IIASA) arXiv:1803.09369v1 [cs.SY] 20 Mar 2018 Syed Babar Ali School of Science and Engineering Lahore University of Management Sciences December 2017 © 2017 by Talha Manzoor To Marwa and her never-ending quest for adventure. Abstract This study explores the potential of the cybernetic method of inquiry for the problem of natural resource governance. The systems way of thinking has already enabled scientists to gain considerable headway in framing global environmental challenges. On the other hand, technical solutions to environmental problems have begun to show significant promise, driven by the advent of technology and its increased proliferation in coupled human and natural systems. Such settings lie on the interface of engineering, social and environmental sciences, and as such, require a common language in order for natural resources to be studied, managed and ultimately sustained. In this dissertation, we argue that the systems theoretic tradition of cybernetics may provide the necessary common ground for examining such systems. After discussing the relevance of the cybernetic approach to natural resource governance, we present a mathematical model of resource consumption, grounded in social psychological research on consumer behavior. We also provide interpretations of the model at various levels of abstraction in the social network of the consuming population. We demonstrate the potential of the model by examining it in various theoretic frameworks which include dynamical systems, optimal control theory, game theory and the theory of learning in games. -
Creating a Board Game to Influence Student Retention and Success
ENROLLED: CREATING A BOARD GAME TO INFLUENCE STUDENT RETENTION AND SUCCESS by Andrew H. Peterson This dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Education Ferris State University November 2018 © 2019 Andrew H. Peterson All Rights Reserved ENROLLED: CREATING A BOARD GAME TO INFLUENCE STUDENT RETENTION AND SUCCESS by Andrew H. Peterson Has been approved November 2018 APPROVED: Jonathan Truitt, PhD Committee Chair David Simkins, PhD Committee Member Paul Wright, PhD Committee Member Dissertation Committee ACCEPTED: Roberta C. Teahen, PhD, Director Community College Leadership Program ABSTRACT This dissertation documents the justification, creation, and refinement of a traditional board game to be used in first-year experience (freshman seminar) courses. The board game enRolled allows students to play college in a guided classroom environment. The game creates a low-stakes environment for students to be able to fail at college without risking time and money. Further, it is designed to give students a relatable topic to debate. By having a common experience, students can distance themselves from what their expectations of college are and deliberate on the tangible game they have played. The discussions that stem from this play and the modification of the game elements are designed to help the students take ownership over the experience. Having a game experience to discuss allows a student to objectively analyze their player’s path through the academic setting and debate realistic and perceived unrealistic challenges. Through these discussions, it is possible for students to engage with content while having little to no firsthand knowledge. It is the hope of this author that the creation of enRolled leads to a more engaging curriculum in first-year experience courses. -
The Emergence of Distributed Cognition: a Conceptual Framework
submitted for Proceedings of Collective Intentionality IV, Siena (Italy), to be published as a special issue of Cognitive Systems Research The Emergence of Distributed Cognition: a conceptual framework Francis HEYLIGHEN, Margeret HEATH and Frank VAN OVERWALLE Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium {fheyligh, mheath, fjvoverw}@vub.ac.be ABSTRACT: We propose a first step in the development of an integrated theory of the emergence of distributed cognition/extended mind. Distributed cognition is seen as the confluence of collective intelligence and “situatedness”, or the extension of cognitive processes into the physical environment. The framework is based on five fundamental assumptions: 1) groups of agents self-organize to form a differentiated, coordinated system, adapted to its environment, 2) the system co-opts external media for internal propagation of information, 3) the resulting distributed cognitive system can be modelled as a learning, connectionist network, 4) information in the network is transmitted selectively, 5) novel knowledge emerges through non-linear, recurrent interactions. The implication for collective intentionality is that such a self-organizing agent collective can develop “mental content” that is not reducible to individual cognitions. Extended Mind: collective intelligence and distributed cognition From a cybernetic perspective [Heylighen & Joslyn, 2001], a cognitive system cannot be understood as a discrete collection of beliefs, procedures, and/or modules. Cognition is a continuously evolving process which relates present perceptions via internal states to potential further perceptions and actions. It thus allows an agent to anticipate what may happen, adapt to changes in its environment, and moreover effect changes upon its environment [Kirsch & Maglio, 1994]. -
Rafael Capurro's Full Text [.V2]
In Search of Ariadne's Thread in Digital Labyrinths Rafael Capurro International Center for Information Ethics (ICIE) Karlsruhe, Germany "Times, they are 'a changin" Bob Dylan Abstract The aim of the following presentation is to provide a brief personal account of the results of some of the panels and sessions that took place at the Vienna Summit 2014 "The Information Society at the Crossroads" (June 3-7, 2015) in which I was involved as a participant and speaker. I will first summarize what I learned regarding some of the challenges in the fields of information ethics, dealing particularly with issues of social responsibility, critical theory, robotics, global brain, and philosophy of information. Secondly, I will relay the results of an email exchange that took place following the Vienna Summit conference between a number of colleagues and myself in which we explored our perceptions of the issues at hand and the stakes involved and whether or not we were able to trace to any length the myth of Ariadne's thread in digital labyrinths. I will clarify how even though such labyrinths and digital threads are a part of today's societies they are often confused with society and with our being-in-the- world itself. To signify my argument, and to show how such confusion can result in mortal consequences, I will conclude by outlining the case of the Chinese poet and migrant worker Xu Lizhi (aged 24) who committed suicide after three years' working for Foxconn. Introduction In 1994 a group of scholars and scientists started an initiative called "Foundations of Information Science" (FIS). -
Comments on Donald T. Campbell's
Contents W. Callebaut/R. Riedl 2 Preface Donald T. Campbell 5 From Evolutionary Epistemology Via Selection Theory to a Sociology of Scientific Validity Linnda R. Caporael 39 Vehicles of Knowledge: Artifacts and Social Groups W. D. Christensen/C. A. Hooker 44 Selection Theory, Organization and the Development of Knowledge Andy J. Clark 49 Evolutionary Epistemology and the Scientific Method Ed Constant 55 Comments on Donald T. Campbell’s “From Evolutionary Epistemology Via Selection Theory to a Sociology of Scientific Validity” Steve Fuller 58 Campbell’s Failed Cultural Materialism Francis Heylighen 63 Objective, Subjective, and Intersubjective Selectors of Knowledge Aharon Kantorovich 68 The Rationality of Innovation and the Scientific Community as a Carrier of Knowledge Elias L. Khalil 71 Can Artificial Selection Remedy the Failing of Natural Section with Regard to Scientific Validation? Kyung-Man Kim 75 D. T. Campbell’s Social Epistemology of Science Marc De Mey 81 Vision as Paradigm: From VTE to Cognitive Science Erhard Oeser 85 The Two-stage Model of Evolutionary Epistemology Henry Plotkin 89 Knowledge and Adapted Biological Structures Massimo Stanzione 92 Campbell, Hayek and Kautsky on Societal Evolution Franz M. Wuketits 98 Four (or Five?) Types of Evolutionary Epistemology Evolution and Cognition: ISSN: 0938-2623 Published by: Konrad Lorenz Institut für Evolutions- und Kognitionsforschung, Adolf-Lorenz-Gasse 2, A-3422 Alten- Impressum berg/Donau. Tel.: 0043-2242-32390; Fax: 0043-2242-323904; e-mail: [email protected]; World Wide Web: http://www.kla.univie.ac.at/ Chairman: Ru- pert Riedl Managing Editor: Manfred Wimmer Layout: Alexander Riegler Aim and Scope: “Evolution and Cognition” is an interdisciplinary forum devoted to all aspects of research on cognition in animals and humans.