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Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur Si Muove: Biomimetic Embedding of N-Tuple Helices in Spherical Polyhedra - /
Alternative view of segmented documents via Kairos 23 October 2017 | Draft Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra - / - Introduction Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension? Dynamic bonding patterns in n-tuple helices engendering n-fold rotating symbols Embedding the triple helix in a spherical octahedron Embedding the quadruple helix in a spherical cube Embedding the quintuple helix in a spherical dodecahedron and a Pentagramma Mirificum Embedding six-fold, eight-fold and ten-fold helices in appropriately encircled polyhedra Embedding twelve-fold, eleven-fold, nine-fold and seven-fold helices in appropriately encircled polyhedra Neglected recognition of logical patterns -- especially of opposition Dynamic relationship between polyhedra engendered by circles -- variously implying forms of unity Symbol rotation as dynamic essential to engaging with value-inversion References Introduction The contrast to the geocentric model of the solar system was framed by the Italian mathematician, physicist and philosopher Galileo Galilei (1564-1642). His much-cited phrase, " And yet it moves" (E pur si muove or Eppur si muove) was allegedly pronounced in 1633 when he was forced to recant his claims that the Earth moves around the immovable Sun rather than the converse -- known as the Galileo affair. Such a shift in perspective might usefully inspire the recognition that the stasis attributed so widely to logos and other much-valued cultural and heraldic symbols obscures the manner in which they imply a fundamental cognitive dynamic. Cultural symbols fundamental to the identity of a group might then be understood as variously moving and transforming in ways which currently elude comprehension. -
Cabineta Quarterly of Art and Culture
A QUARTERLY OF ART AND CULTURE ISSUE 18 FICTIONAL STATES CABINET US $10 CANADA $15 UK £6 inside this issue THERMIDOR 2005 Sasha Archibald • John Bear • Robert Blackson • William Bryk • Sasha Chavchavadze • Mark Dery • Allen Ezell • Charles Green • Invertebrate • Craig Kalpakjian • Peter Lamborn Wilson • David Levi Strauss • Brian McMullen • Glexis Novoa • George Pendle • Elizabeth Pilliod • Patrick Pound • Bonnie and Roger Riga • Lynne Roberts-Goodwin • Tal Schori • Cecilia Sjöholm • Frances Stark • Michael Taussig • Christopher Turner • Jonathan Ward • Christine Wertheim • Tony Wood • Shea Zellweger cabinet Cabinet is a non-profit 501 (c) (3) magazine published by Immaterial Incorporated. 181 Wyckoff Street Contributions to Cabinet are fully tax-deductible. Our survival is dependent on Brooklyn NY 11217 USA such contributions; please consider supporting us at whatever level you can. tel + 1 718 222 8434 Donations of $25 or more will be acknowledged in the next possible issue. Dona- fax + 1 718 222 3700 tions above $250 will be acknowledged for four issues. Checks should be made email [email protected] out to “Cabinet.” Please mark the envelope, “Rub your eyes before opening.” www.cabinetmagazine.org Cabinet wishes to thank the following visionary foundations and individuals Summer 2005, issue 18 for their support of our activities during 2005. Additionally, we will forever be indebted to the extraordinary contribution of the Flora Family Foundation from Editor-in-chief Sina Najafi 1999 to 2004; without their generous support, this publication would not exist. Senior editor Jeffrey Kastner Thanks also to the Andy Warhol Foundation for the Visual Arts for their two-year Editors Jennifer Liese, Christopher Turner grant in 2003-2004. -
Let the Mirrors Do the Thinking
BRIDGES Mathematical Connections in Art, Music, and Science Let the Mirrors Do the Thinking Glenn Clark Shea Zellweger Department of Mathematics Department of Psychology Mount Union College Mount Union College Alliance, Ohio 44601 Alliance, Ohio 4460 I 1. Introduction Our story begins with a simple example. Suppose that someone asked you to keep a record of your thoughts, exactly, and in terms of the symbols given, when you are making an effort to multiply XVI times LXIV. Also suppose that, refusing to give up, you finally arrive at the right answer, which happens to be MXXIV. We are sure that you would have had a much easier time of it, to solve this problem, if you would have found that 16 times 64 equals 1024. This example not only looks at what we think and what we write. It also looks at the mental tools, the signs and symbols, that we are using when that thinking and that writing is taking place. How we got these mental tools is a long story, one that includes new developments today. What follows will run a replay of what happened when Europe took several centuries to go from MXXIV to 1024. This replay in not for numbers: it is for logic. Modem logic starts in the middle 1800s and with George Boole. This means that we have had only about 150 years to establish the symbols we now use for symbolic logic. These symbols leave a lot to be desired. We hope thatwe can draw you into taking a look at a lesson in lazy logic. -
Bridges: Mathematical Connections in Art, Music, and Science. Conference Proceedings 1998
Nexus Esecutivo 19-01-2004 9:19 Seite 149 Reza Sarhangi ed. Bridges: Mathematical Connections in Art, Music, and Science. Conference Proceedings 1998. Winfield, Kansas: Southwestern College, 1998 Reviewed by Solomon Marcus. The Emergence of Bridges The key word, giving the motivation of the most contributions in this volume, is BRIDGES. The title of the volume is just the slogan under which the Conference was announced at the beginning of the year 1998. This slogan requires some explanations. The noun “bridge” and the verb “to bridge” became, in the last decades, one of the most frequent metaphors to which a reference is made when the adopted approach crosses different fields. Is it equivalent to what is traditionally called interdisciplinarity? It seems that “bridge” is in some sense less and in some other sense more. We will not speak of bridging mathematics and mechanics, because their collaboration is very old. “Bridge” is reserved for fields or trends not yet connected or insufficiently connected. But this is not the only difference. Interdisciplinarity is usually understood in a unidirectional binary way: some ideas, tools, results or methods from a discipline A are used in approaching a problem in another discipline B. “Bridging A and B” may refer also to the case when A and B are entities of another type than disciplines, for instance one can bridge nature and culture (the slogan of an international congress of semiotics was “Semiotics Bridging Nature and Culture”), the quantum level and the cosmic level of reality (like in quantum cosmology), exactness and abstraction (like in mathematics), Plato and Leonardo da Vinci (like in some artistic works), objective and subjective (like in some philosophical approaches), etc. -
El Alfabeto L´Ogico De Zellweger
El Alfabeto Logico´ de Zellweger Zellweger's Logic Alphabet Oscar Abel Cardona-HurtadoI Resumen. Una de las notaciones mas´ importantes para los conectivos proposicionales binarios fue creada en 1953 por Shea Zellweger. Este sistema, denominado Alfabeto Logico,´ posee diversas propiedades logicas,´ algebraicas y geometricas´ de las cuales no goza la notacion´ tradicional. Ademas´ de varias propiedades individuales y de m´ultiples relaciones entre los conectivos, las simetr´ıas del sistema completo de los conectivos proposicionales binarios se evidencian de manera visual en los signos propuestos por Zellweger. Palabras clave: Shea Zellweger, conectivo proposicional, tabla de verdad, operacion,´ simetr´ıa. Abstract. One of the most important notations for the binary propositional connectives was created in 1953 by Shea Zellweger. This system, called Logic Alphabet has several the logical, algebraic and geometric properties which does not enjoy the usual notation. Besides several individual properties and numerous relations between connectives, the IProfesor de catedra,´ Departamento de Matematicas´ y Estad´ıstica, Universidad del Tolima symmetries of the complete system of connectives are visually reflected in the signs proposed by Zellweger. Keywords: Shea Zellweger, propositional connective, truth table, operation, symmetry. 1. Introduccion´ El calculo´ proposicional clasico´ se caracteriza por el uso de ciertos conectivos logicos´ que sirven para indicar un nexo entre proposiciones, generando as´ıexpresiones com- puestas. En las presentaciones usuales se tienen en cuenta la negacion,´ la conjuncion,´ la disyuncion,´ la implicacion´ y la equivalencia. Dado que en la logica´ clasica´ solo se con- sideran dos valores de verdad, estos conectivos se pueden definir mediante las llamadas tablas de verdad que se muestran a continuacion.´ A ∼A V F F V Tabla 1. -
Ideas in Action: Proceedings of the Applying Peirce Conference
IDEAS IN ACTION Proceedings of the Applying Peirce Conference Edited by: Mats Bergman, Sami Paavola, Ahti-Veikko Pietarinen, Henrik Rydenfelt Nordic NSP Studies in Pragmatism 1 IDEAS IN ACTION Nordic Studies in Pragmatism Series editors: Mats Bergman Henrik Rydenfelt The purpose of the series is to publish high-quality monographs and col- lections of articles on the tradition of philosophical pragmatism and closely related topics. It is published online in an open access format by the Nordic Pragmatism Network, making the volumes easily accessible for scholars and students anywhere in the world. IDEAS IN ACTION PROCEEDINGS OF THE APPLYING PEIRCE CONFERENCE Nordic Studies in Pragmatism 1 Edited by Mats Bergman, Sami Paavola, Ahti-Veikko Pietarinen & Henrik Rydenfelt Nordic Pragmatism Network, NPN Helsinki 2010 Copyright c 2010 The Authors and the Nordic Pragmatism Network. This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. CC BY NC For more information, see http://creativecommons.org/licenses/by-nc/./ www.nordprag.org ISSN-L - ISSN - ISBN ---- This work is typeset with Donald Knuth’s TEX program, using LATEX2ε macros and the ‘Nnpbook’ class definition. Contents Preface iv Note on References v 1 Reconsidering Peirce’s Relevance 1 Nathan Houser Part I 2 Serving Two Masters: Peirce on Pure Science, Useless Things, and Practical Applications 17 Mats Bergman 3 The Function of Error in Knowledge and Meaning: Peirce, Apel, Davidson 38 Elizabeth F. Cooke 4 Peircean Modal Realism? 48 Sami Pihlstr¨om 5 Toward a Transcendental Pragmatic Reconciliation of Analytic and Continental Philosophy 62 Jerold J. Abrams 6 Reflections on Practical Otherness: Peirce and Applied Sciences 74 Ivo Assad Ibri 7 Problems in Applying Peirce in Social Sciences 86 Erkki Kilpinen 8 Peirce and Pragmatist Democratic Theory 105 Robert B. -
Comprehension of Requisite Variety Via Rotation of the Complex Plane Mutually Orthogonal Renderings of the Mandelbrot Set Framing an Eightfold Way -- /
Alternative view of segmented documents via Kairos 15 July 2019 | Draft Comprehension of Requisite Variety via Rotation of the Complex Plane Mutually orthogonal renderings of the Mandelbrot set framing an eightfold way -- / -- Introduction Mandelbrot sets rendered in a mutually orthogonal configuration of 3 complex planes Psychosocial and strategic implications of distinct octants Reframing an eightfold way by entangling imagination and reality? Comprehension of coherence currently constrained by convention Memorability: "comprehension tables" as complement to "truth tables" Metaphors associated with trigram and tetragram encodings Confrontation of highly "incompatible" frameworks as a vital necessity in times of chaos? Coherence of a cognitive nexus comprehended dynamically Fractal comprehension of coherence requiring an 8-fold uncertainty principle? References Introduction Faced with global crises, it is useful to recall the variants of the well-known insight: There Is Always a Well-Known Solution to Every Human Problem -- Neat, Plausible, and Wrong. How many of the advocated global strategies can be recognized in that light? There is no lack of recognition of the complexity of "strategic space" within which the articulation and display of strategies could be compared metaphorically to the competitive challenge faced by flowers (Keith Critchlow, The Hidden Geometry of Flowers: living rhythms, form and number, 2011). Missing is any sense of the requisite complexity within which otherwise incommensurable strategies may need to be embedded in order for their collective coherence to become comprehensible. The tendency to organize any such articulation into multiple sections -- multi-petalled "strategic flowers" -- can then be compared with the branching 3-fold, 5-fold, N-fold patterns in the animations presented separately (Dynamics of tank comprehension and enclosure, 2019). -
The Mathematics of Charles Sanders Peirce
Cybernetics & Human Knowing, Vol.8, no.1–2, 2001, pp. 79–110 The Mathematics of Charles Sanders Peirce Louis H. Kauffman1 I. Introduction This essay explores the Mathematics of Charles Sanders Peirce. We concentrate on his notational approaches to basic logic and his general ideas about Sign, Symbol and diagrammatic thought. In the course of this paper we discuss two notations of Peirce, one of Nicod and one of Spencer-Brown. Needless to say, a notation connotes an entire language and these contexts are elaborated herein. The first Peirce notation is the portmanteau (see below) Sign of illation. The second Peirce notation is the form of implication in the existential graphs (see below). The Nicod notation is a portmanteau of the Sheffer stroke and an (overbar) negation sign. The Spencer-Brown notation is in line with the Peirce Sign of illation. It remained for Spencer-Brown (some fifty years after Peirce and Nicod) to see the relevance of an arithmetic of forms underlying his notation and thus putting the final touch on a development that, from a broad perspective, looks like the world mind doing its best to remember the significant patterns that join logic, speech and mathematics. The movement downward to the Form (“we take the form of distinction for the form.”[9, Chapter 1, page 1]) through the joining together of words into archetypal portmanteau Signs can be no accident in this process of return to the beginning. We study a system of logic devised by Peirce based on a single Sign for inference that he calls his ‘Sign of illation". -
Studies in Logic Foundations of Semiotics
STUDIES IN LOGIC FOUNDATIONS OF SEMIOTICS General Editor ACHIM ESCHBACH (University of Essen) Advisory Editorial Board Erhard Albrecht (Greifswald);Herbert E. Brekle (Regensburg) Geoffrey L. Bursill-Hall (Burnaby, B.C.);Eugenio Coseriu (Tübingen) Marcelo Dascal (Tel-Aviv);Lambertus M. de Rijk (Leiden) Max H. Fisch (Indianapolis); Rudolf Haller (Graz) Morman Kretzmann (Ithaca, N.Y.);W. Keith Percival (Lawrence, Kansas Jan Sulowski (Warszawa);Jürgen Trabant (Berlin) Volume 1 Charles S. Peirce (ed.) Studies in Logic STUDIES IN LOGIC by Members of the Johns Hopkins University (1883) edited by Charles S. Peirce With an Introduction by Max H. Fisch and a Preface by Achim Eschbach JOHN BENJAMINS PUBLISHING COMPANY AMSTERDAM/PHILADELPHIA 1983 © Copyright 1983 - John Benjamins B.V. ISBN 90 272 3271 7 No part of this book may be reproduced in any form, by print, photoprint, microfilm or any other means, without written permission from the publisher. CONTENTS Peirce as Scientist, Mathematician, Historian, Logician, and Philosopher Max H. Fisch vii The History of Semiotics and Charles S. Peirce Achim Eschbach xxxiii Peirce's marked and cut copy of the STUDIES IN LOGIC lv * * * STUDIES IN LOGIC. By members of the Johns Hopkins University Facsimile of the edition Boston, 1883 lix vi, 203 pp. Charles S. Peirce (Probably this photograph was taken not later than 1884, not much earlier than 1879, perhaps between those years.) PEIRCE AS SCIENTIST, MATHEMATICIAN, HISTORIAN, LOGICIAN, AND PHILOSOPHER* MAX H. FISCH At a bicentennial international congress devoted to Peirce and held in Europe, we may well begin by remarking that Peirce himself was in Europe in the centennial year 1876. -
Symmetry and the Crystallography of Logic Shea Zellweger Mount Union College 1988 Alliance, Ohio 44601 U.S.A
Symmetry and the Crystallography of Logic Shea Zellweger Mount Union College 1988 Alliance, Ohio 44601 U.S.A. The history of logic has been divided into three periods. The "traditional" period starts with Aristotle. The "algebraic" period starts with Boole. The "logistic" period starts when Russell successfully rescues the ideas of Frege. In what fol- lows I will be going back to the middle period, back to the time of Boole, Schroeder, and Peirce. More specifically, what follows will focus on a direct contin- uation of two of the main ideas that were emphasized by Peirce. In reference to logic, especially to what is called the proposi- tional calculus, he understood the importance of s~m~etry. In reference to notation, he understood the importance of iconicity. But he did not go far enough. What follows will show that, when we start with a custom-designed notation, it is an easy step to go from symmetry-iconicity to the crystallography of ~. In 1902 Peirce devised three iconic notations for the 16 binary connectives (and,-or, if, etc.). Before we push his work a small notch ahead, let us look at a simple example in binary logic. It expresses the duality of "and" and "or," as in |1) and (2). A mental grasp of (i) and (2} can be maintained in three ways. Mem- (i) (A and B) ~ Not(Not-A or Not-B) (2) (A . B) ~ N(NA v NB) (3) N(A . B) ~ (NAv NB) (4) N(A v B) ~ (NA . NB) orize it, derive it from something else that has been memorized, such as we see in De Morgan’s laws [(3) and (4)], or work it out again and again, each time coming back to the truth table method. -
The Art-Science Marriage, from Quarrel to Understanding
BRIDGES Mathematical Connections in Art, Musk, aoo Science The Art-Science Marriage, From Quarrel to Understanding. Review of articles in BRIDGES: Mathematical Connections in Art, Music, and Science. Conference Proceedings, Southwestern College, Winfield, Kansas, July 1998. Solomon Marcus Romanian Academy, Mathematics Calea Victoriei 125, Bucuresti, Romania [email protected] The Emergence of Bridges The key word, giving the motivation of the most contributions in this volume, is BRIDGES. The title of the volume is just the slogan under which the Conference was announced at the beginning of the year 1998. This slogan requires some explanations. The noun "bridge" and the verb "to bridge" became, in the last decades, one of the most frequent· metaphors to which a reference is made when the adopted approach crosses different fields. Is it equivalent to what is traditionally called interdisciplinarity? It seems that "bridge" is in some sense less and in some other sense more. We will not speak of bridging mathematics and mechanics, because their .collaboration is very old. "Bridge" is reserved for fields or trends not yet connected or insufficiently connected. But this is not the only difference. Interdisciplinarity is usually understood in a unidirectional binary way: some ideas, tools, results or methods from a discipline A are used in approaching a problem in another discipline B. "Bridging A and B" may refer also to the case when A and B are entities of another type than disciplines, for instance one can bridge nature and culture (the slogan of an international congress of semiotics was "Semiotics Bridging Nature and Culture"), the quantum level and the cosmic level of reality (like in quantum cosmology), exactness and abstraction (like in mathematics), Plato and Leonardo da Vinci (like in some artistic works), objective and subjective (like in some philosophical approaches), etc. -
Modern Logic 1850-1950, East and West Editors Francine F
Studies in Universal Logic Francine F. Abeles Mark E. Fuller Editors Modern Logic 1850 –1950, East and West Studies in Universal Logic Series Editor Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council, Rio de Janeiro, Brazil) Editorial Board Members Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary) Mark Burgin (University of California, Los Angeles, USA) Razvan˘ Diaconescu (Romanian Academy, Bucharest, Romania) Josep Maria Font (University of Barcelona, Barcelona, Spain) Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France) Arnold Koslow (City University of New York, New York, USA) Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan) Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia) Grzegorz Malinowski (University of Łód´z, Łód´z, Poland) Darko Sarenac (Colorado State University, Fort Collins, USA) Peter Schröder-Heister (University Tübingen, Tübingen, Germany) Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia) This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discussions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers. More information about this series at http://www.springer.com/series/7391 Francine F. Abeles • Mark E. Fuller Editors Modern Logic 1850-1950, East and West Editors Francine F.