Alicia Boole Stott, a Geometer in Higher Dimension
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Victorian Network
Victorian Network Volume 7, Number 1 Summer 2016 Victorian Brain © Victorian Network Volume 7, Number 1 Summer 2016 www.victoriannetwork.org Guest Editor Sally Shuttleworth General Editor Sophie Duncan Founding Editor Katharina Boehm Editorial Board Megan Anderluh Sarah Crofton Rosalyn Gregory Tammy Ho Lai-Ming Sarah Hook Alison Moulds Heidi Weig Victorian Network is funded by the Arts & Humanities Research Council and supported by King’s College London. Victorian Network Volume 7, Number 1 (Summer 2016) TABLE OF CONTENTS GUEST EDITOR’S INTRODUCTION: VICTORIAN BRAIN 1 Sally Shuttleworth ARTICLES Lucid Daydreaming: Experience and Pathology in Charlotte Brontë 12 Timothy Gao Two Brains and a Tree: Defining the Material Bases 36 for Delusion and Reality in the Woodlanders Anna West ‘The Apotheosis of Voice’: Mesmerism as Mechanisation 61 in George Du Maurier’s Trilby Kristie A. Schlauraff Female Transcendence: Charles Howard Hinton 83 and Hyperspace Fiction Patricia Beesley The Hand and the Mind, the Man and the Monster 107 Kimberly Cox BOOK REVIEWS A Cultural History of the Senses in the Age of Empire, 137 Vol. 5, ed. Constance Classen (Bloomsbury, 2014) Ian Middlebrook Popular Fiction and Brain Science in the Late Nineteenth Century, 142 by Anne Stiles (Cambridge, 2011) Arden Hegele Thomas Hardy’s Brains: Psychology, Neurology, and Hardy’s Imagination, 148 by Suzanne Keen (Ohio State, 2014) Nicole Lobdell Victorian Network Volume 7, Number 1 (Summer 2016) The Poet’s Mind: The Psychology of Victorian Poetry 1830-1870, 153 by Gregory Tate (Oxford, 2012) Benjamin Westwood Theatre and Evolution from Ibsen to Beckett, 158 by Kirsten Shepherd-Barr (Columbia, 2015) Katharina Herold Victorian Network Volume 7, Number 1 (Summer 2016) Sally Shuttleworth 1 VICTORIAN BRAIN SALLY SHUTTLEWORTH, PROFESSOR OF ENGLISH (UNIVERSITY OF OXFORD) In April 1878 the first issue of Brain: A Journal of Neurology was published. -
Geometry Course Outline
GEOMETRY COURSE OUTLINE Content Area Formative Assessment # of Lessons Days G0 INTRO AND CONSTRUCTION 12 G-CO Congruence 12, 13 G1 BASIC DEFINITIONS AND RIGID MOTION Representing and 20 G-CO Congruence 1, 2, 3, 4, 5, 6, 7, 8 Combining Transformations Analyzing Congruency Proofs G2 GEOMETRIC RELATIONSHIPS AND PROPERTIES Evaluating Statements 15 G-CO Congruence 9, 10, 11 About Length and Area G-C Circles 3 Inscribing and Circumscribing Right Triangles G3 SIMILARITY Geometry Problems: 20 G-SRT Similarity, Right Triangles, and Trigonometry 1, 2, 3, Circles and Triangles 4, 5 Proofs of the Pythagorean Theorem M1 GEOMETRIC MODELING 1 Solving Geometry 7 G-MG Modeling with Geometry 1, 2, 3 Problems: Floodlights G4 COORDINATE GEOMETRY Finding Equations of 15 G-GPE Expressing Geometric Properties with Equations 4, 5, Parallel and 6, 7 Perpendicular Lines G5 CIRCLES AND CONICS Equations of Circles 1 15 G-C Circles 1, 2, 5 Equations of Circles 2 G-GPE Expressing Geometric Properties with Equations 1, 2 Sectors of Circles G6 GEOMETRIC MEASUREMENTS AND DIMENSIONS Evaluating Statements 15 G-GMD 1, 3, 4 About Enlargements (2D & 3D) 2D Representations of 3D Objects G7 TRIONOMETRIC RATIOS Calculating Volumes of 15 G-SRT Similarity, Right Triangles, and Trigonometry 6, 7, 8 Compound Objects M2 GEOMETRIC MODELING 2 Modeling: Rolling Cups 10 G-MG Modeling with Geometry 1, 2, 3 TOTAL: 144 HIGH SCHOOL OVERVIEW Algebra 1 Geometry Algebra 2 A0 Introduction G0 Introduction and A0 Introduction Construction A1 Modeling With Functions G1 Basic Definitions and Rigid -
Dimension Guide
UNDERCOUNTER REFRIGERATOR Solid door KURR114KSB, KURL114KSB, KURR114KPA, KURL114KPA Glass door KURR314KSS, KURL314KSS, KURR314KBS, KURL314KBS, KURR214KSB Detailed Planning Dimensions Guide Product Dimensions 237/8” Depth (60.72 cm) (no handle) * Add 5/8” (1.6 cm) to the height dimension when leveling legs are fully extended. ** For custom panel models, this will vary. † Add 1/4” (6.4 mm) to the height dimension 343/8” (87.32 cm)*† for height with hinge covers. 305/8” (77.75 cm)** 39/16” (9 cm)* Variant Depth (no handle) Panel ready models 2313/16” (60.7 cm) (with 3/4” panel) Stainless and 235/8” (60.2 cm) black stainless Because Whirlpool Corporation policy includes a continuous commitment to improve our products, we reserve the right to change materials and specifications without notice. Dimensions are for planning purposes only. For complete details, see Installation Instructions packed with product. Specifications subject to change without notice. W11530525 1 Panel ready models Stainless and black Dimension Description (with 3/4” panel) stainless models A Width of door 233/4” (60.3 cm) 233/4” (60.3 cm) B Width of the grille 2313/16” (60.5 cm) 2313/16” (60.5 cm) C Height to top of handle ** 311/8” (78.85 cm) Width from side of refrigerator to 1 D handle – door open 90° ** 2 /3” (5.95 cm) E Depth without door 2111/16” (55.1 cm) 2111/16” (55.1 cm) F Depth with door 2313/16” (60.7 cm) 235/8” (60.2 cm) 7 G Depth with handle ** 26 /16” (67.15 cm) H Depth with door open 90° 4715/16” (121.8 cm) 4715/16” (121.8 cm) **For custom panel models, this will vary. -
Spectral Dimensions and Dimension Spectra of Quantum Spacetimes
PHYSICAL REVIEW D 102, 086003 (2020) Spectral dimensions and dimension spectra of quantum spacetimes † Michał Eckstein 1,2,* and Tomasz Trześniewski 3,2, 1Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, ulica Wita Stwosza 57, 80-308 Gdańsk, Poland 2Copernicus Center for Interdisciplinary Studies, ulica Szczepańska 1/5, 31-011 Kraków, Poland 3Institute of Theoretical Physics, Jagiellonian University, ulica S. Łojasiewicza 11, 30-348 Kraków, Poland (Received 11 June 2020; accepted 3 September 2020; published 5 October 2020) Different approaches to quantum gravity generally predict that the dimension of spacetime at the fundamental level is not 4. The principal tool to measure how the dimension changes between the IR and UV scales of the theory is the spectral dimension. On the other hand, the noncommutative-geometric perspective suggests that quantum spacetimes ought to be characterized by a discrete complex set—the dimension spectrum. We show that these two notions complement each other and the dimension spectrum is very useful in unraveling the UV behavior of the spectral dimension. We perform an extended analysis highlighting the trouble spots and illustrate the general results with two concrete examples: the quantum sphere and the κ-Minkowski spacetime, for a few different Laplacians. In particular, we find that the spectral dimensions of the former exhibit log-periodic oscillations, the amplitude of which decays rapidly as the deformation parameter tends to the classical value. In contrast, no such oscillations occur for either of the three considered Laplacians on the κ-Minkowski spacetime. DOI: 10.1103/PhysRevD.102.086003 I. -
Zero-Dimensional Symmetry
Snapshots of modern mathematics № 3/2015 from Oberwolfach Zero-dimensional symmetry George Willis This snapshot is about zero-dimensional symmetry. Thanks to recent discoveries we now understand such symmetry better than previously imagined possible. While still far from complete, a picture of zero-dimen- sional symmetry is beginning to emerge. 1 An introduction to symmetry: spinning globes and infinite wallpapers Let’s begin with an example. Think of a sphere, for example a globe’s surface. Every point on it is specified by two parameters, longitude and latitude. This makes the sphere a two-dimensional surface. You can rotate the globe along an axis through the center; the object you obtain after the rotation still looks like the original globe (although now maybe New York is where the Mount Everest used to be), meaning that the sphere has rotational symmetry. Each rotation is prescribed by the latitude and longitude where the axis cuts the southern hemisphere, and by an angle through which it rotates the sphere. 1 These three parameters specify all rotations of the sphere, which thus has three-dimensional rotational symmetry. In general, a symmetry may be viewed as being a transformation (such as a rotation) that leaves an object looking unchanged. When one transformation is followed by a second, the result is a third transformation that is called the product of the other two. The collection of symmetries and their product 1 Note that we include the rotation through the angle 0, that is, the case where the globe actually does not rotate at all. 1 operation forms an algebraic structure called a group 2 . -
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! Revising Space Time Geometry: A Proposal for a New Romance in Many Dimensions Renate Quehenberger* Quantum Cinema - a digital Vision (PEEK) Department of Mediatheory at the University of Applied Arts, Vienna August 25, 2012 Abstract The ontological positioning of our existence, deeply connected with the hierarchy problem concerning the dimensions of space and time, is one of the major problems for our understanding of the “ultimate” nature of reality. The resulting problem is that mathematical concepts that need so-called “extra-dimensions” have been widely disregarded owing to a lack of physical interpretation. This article reviews conventions, imaginations and assumptions about the non-imaginative by starting at the origins of the of 4D and 5D space-time concepts and proposing a new geometrical approach via a hyper- Euclidian path for a mentally accessible vision of continuous AND discrete complex space configuration in dimensions up to higher order. e-mail address: [email protected] 1 RCZ Quehenberger “Time and Space... It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.” [Henri Poincaré, 1905] Introduction The general physicists’ assertion is that we are living in a three-dimensional world with one time- dimension and cosmic space is curved in the fourth dimension is based on a relativistic world view that has gained general acceptance. In fact this is a post-Copernicanian world view which does not pay attention to the consequences of Max Planck’s revolution and the development in quantum physics of the past 100 years. -
Creating a Revolve
Always begin your creo session by selecting your working directory If you select working directory at the beginning, that folder will be the default location when you try to open files, as well as when you save files. It makes everything a lot easier if you select your working directory first. For help opening/saving/downloading files see basics, for help creating an extrude see basic solids. Creating a Revolve Open a new part file, name it something unique. Choose a plane to sketch on Go to sketch view (if you don’t know where that is see Basic Solids) Move your cursor so the centerline snaps to the horizontal line as shown above You may now begin your sketch I have just sketched a random shape Sketch Tips: ● Your shape MUST be closed ● If you didn’t put a centerline in, you will get radial instead of diameter dimensions (in general this is bad) ● Remember this is being revolved so you are only sketching the profile on one side of the center line. If you need to put in diameter dimensions: Click normal, click the line or point you want the dimension for, click the centerline, and click the same line/point that you clicked the first time AGAIN, and then middle mouse button where you want the dimension to be placed. After your sketch is done, click the checkmark to get out of sketch, then click the checkmark again to complete the revolve The part in the sketch will look like this: . -
The Practical (And Artistic) Utility of Hyperspace
The Practical (and Artistic) Utility of Hyperspace I have felt and given evidence of the practical utility of handling space of four dimensions as if it were conceivable space. -James Joseph Sylvester, 30 December 1869 The best way to show how four-dimensional geometry has enriched my artwork is to show how my artwork has enriched four-dimensional geometry. Of course, I had teachers. Hypercubes Tessellated In the summer of 1979, when I was 35, I traveled to Brown University to meet Tom Banchoff, chair of the mathematics department, and to see his computer representation of a hypercube rotating in four- dimensional space. Banchoff was generous with his time, and with time on his million-dollar VAX computer. Subsequent visits, hand-written letters, which I have cherished and kept, proofs of my conjectures, invitations to conferences, and authentication of my computer programs and of the mathematical content of my work - all this followed. Do you know the plane if you only know a square? Wouldn’t it be better to contemplate a whole page of squares fitted together, a tessellation of squares? Likewise, do you know space if you only know a cube? Soon after I visited Banchoff for the first time and learned to replicate his program for the rotating hypercube (at Pratt Institute with Herb Tesser and his million-dollar VAX), I programed 9 Tessellated Hypercubes, linked here - tonyrobbin.net/quasi/TessHyperCubes.mp4, and see drawing at the end of this file. One hypercube above, one below, to the left, to the right, in front of and in back of, and also one fore and one aft in the fourth dimension were place around a central hypercube. -
Quaternions: a History of Complex Noncommutative Rotation Groups in Theoretical Physics
QUATERNIONS: A HISTORY OF COMPLEX NONCOMMUTATIVE ROTATION GROUPS IN THEORETICAL PHYSICS by Johannes C. Familton A thesis submitted in partial fulfillment of the requirements for the degree of Ph.D Columbia University 2015 Approved by ______________________________________________________________________ Chairperson of Supervisory Committee _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Program Authorized to Offer Degree ___________________________________________________________________ Date _______________________________________________________________________________ COLUMBIA UNIVERSITY QUATERNIONS: A HISTORY OF COMPLEX NONCOMMUTATIVE ROTATION GROUPS IN THEORETICAL PHYSICS By Johannes C. Familton Chairperson of the Supervisory Committee: Dr. Bruce Vogeli and Dr Henry O. Pollak Department of Mathematics Education TABLE OF CONTENTS List of Figures......................................................................................................iv List of Tables .......................................................................................................vi Acknowledgements .......................................................................................... vii Chapter I: Introduction ......................................................................................... 1 A. Need for Study ........................................................................................ -
The Cubes of Hinton
THE CUBES OF HINTON Taneli Luotoniemi matharts.aalto.fi WIKIPEDIA SOURCES: https://en.wikipedia.org/wiki/Four-dimensional_space https://en.wikipedia.org/wiki/Tesseract https://en.wikipedia.org/wiki/Charles_Howard_Hinton https://en.wikipedia.org/wiki/Alicia_Boole_Stott HYPERSPACE PHILOSOPHER British mathematician Charles Howard Hinton, played a key part in the popularization of ‘hyperphilosophy’ by publishing many writings during the years 1884–1907, speculating on the physical as well as spiritual aspects of 4–space. He also anticipated the hidden dimensions of string theory by stating that the fourth dimension could perhaps be observed on the smallest details of physical matter. Hinton coined the names ana and kata, which refer to the positive and negative directions along the axis of the fourth spatial dimension. Charles Howard Hinton, (1853–1907) HYPERSPACE PHILOSOPHER Hinton developed a mnemonic system of some tens of thousand cubes with individual names in Latin, serving as a 3-dimensional mental retina of a kind on which to visualize the successive cross-sections of objects in 4-space. Interested in Eastern thought, he also sought to eliminate the ‘self elements’ of his system by memorizing the different orientations and mirror reflections of the cubes. Later he developed the system into a self- help method to visualize the fourth dimension, which consisted of manipulation of coloured cubes. The cubes were available Charles Howard Hinton, (1853–1907) for purchase from his publisher. Frontispiece of The Fourth Dimension (1901) ALICIA BOOLE STOTT Hinton was a frequent guest at the household of Mary Everest Boole, whose husband George was famous of his Boolean algebra. -
1 Introduction
Notes 1 Introduction 1. H. G. Wells, Interview with the Weekly Sun Literary Supplement, 1 December 1895; reprinted in ‘A Chat with the Author of The Time Machine, Mr H. G. Wells’, edited with comment by David C. Smith, The Wellsian, n.s. 20 (1997), 3–9 (p. 8). 2. Wells himself labelled his early scientific fantasies as ‘scientific romances’ when he published a collection with Victor Gollancz entitled The Scientific Romances of H. G. Wells in 1933, thus ensuring the adoption of the term in subsequent critical discussions of his work. The term appears to have origi- nated with the publication of Charles Howard Hinton’s Scientific Romances (1886), a collection of speculative scientific essays and short stories. 3. It should be noted, however, that Wells’s controversial second scientific romance, The Island of Doctor Moreau (1896), did not appear in a serialised form. However, The Invisible Man was published in Pearson’s Weekly in June and July 1897, When the Sleeper Wakes was published in The Graphic between January and May 1899, The First Men in the Moon was published in the Strand Magazine between December 1900 and August 1901 and A Modern Utopia was serialised in the Fortnightly Review between October 1904 and April 1905. 4. A number of Wells’s most significant scientific essays have been available for some time in an anthology, H. G. Wells: Early Writings in Science and Science Fiction, ed. by Robert M. Philmus and David Y. Hughes (London: University of California Press, 1975). 5. ‘A Chat with the Author of The Time Machine’, p. -
Introduction to Speculations on the Fourth Dimension: Selected Writings A/Charles H
Rudy Rucker's introduction to Speculations on the Fourth Dimension: Selected Writings a/Charles H. Hinton, (Dover Publications, New York 1980). Many ofthe book's Hinton selections can be found online at http://www.ibiblio.org/eldritch/chh/hinton.html. INTRODUCTION Introduction Copyright (C) Rudy Rucker 2009. The father James Hinton was an ear surgeon who was best known for The Mystery of Pain, a little book which sets forth the Panglossian thesis that "all that which we feel as painful is really giving-some thing that our fellows are better for, even though we cannot trace it." It gives some idea of the tum of the son CQaries Hinton's mind to lea:rn that he wrote a piece, "The Persian King," in which he at tempted to use higher dimensions and infinite series to obtain a mathematically accurate model of this idea. Charles Howard Hinton was a professional mathematician-he took the master's degree at Oxford, taught at Princeton, and published pure mathematics related to work of Morley, Hamilton, and Cayley-but for him formal mathematics was never an end in itself. Hinton's touchstone was, rather, dir«t and intuitive knowledge of four-dimensional space. The bulk of his writings are aimed at develop ing in the reader the power to think about 4-D space; and the rest of his work focuses on using a knowledge of higher space to solve various problems in physics and in metaphysics. Hinton was born in London in 1853, the first son in his family. He was schooled at Rugby, and matriculated at Oxford in 1871.