Parallel Universes
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Does the Category of Multisets Require a Larger Universe Than
Pure Mathematical Sciences, Vol. 2, 2013, no. 3, 133 - 146 HIKARI Ltd, www.m-hikari.com Does the Category of Multisets Require a Larger Universe than that of the Category of Sets? Dasharath Singh (Former affiliation: Indian Institute of Technology Bombay) Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria [email protected] Ahmed Ibrahim Isah Department of Mathematics Ahmadu Bello University, Zaria, Nigeria [email protected] Alhaji Jibril Alkali Department of Mathematics Ahmadu Bello University, Zaria, Nigeria [email protected] Copyright © 2013 Dasharath Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In section 1, the concept of a category is briefly described. In section 2, it is elaborated how the concept of category is naturally intertwined with the existence of a universe of discourse much larger than what is otherwise sufficient for a large part of mathematics. It is also remarked that the extended universe for the category of sets is adequate for the category of multisets as well. In section 3, fundamentals required for adequately describing a category are extended to defining a multiset category, and some of its distinctive features are outlined. Mathematics Subject Classification: 18A05, 18A20, 18B99 134 Dasharath Singh et al. Keywords: Category, Universe, Multiset Category, objects. 1. Introduction to categories The history of science and that of mathematics, in particular, records that at times, a by- product may turn out to be of greater significance than the main objective of a research. -
Dark Energy and Dark Matter As Inertial Effects Introduction
Dark Energy and Dark Matter as Inertial Effects Serkan Zorba Department of Physics and Astronomy, Whittier College 13406 Philadelphia Street, Whittier, CA 90608 [email protected] ABSTRACT A disk-shaped universe (encompassing the observable universe) rotating globally with an angular speed equal to the Hubble constant is postulated. It is shown that dark energy and dark matter are cosmic inertial effects resulting from such a cosmic rotation, corresponding to centrifugal (dark energy), and a combination of centrifugal and the Coriolis forces (dark matter), respectively. The physics and the cosmological and galactic parameters obtained from the model closely match those attributed to dark energy and dark matter in the standard Λ-CDM model. 20 Oct 2012 Oct 20 ph] - PACS: 95.36.+x, 95.35.+d, 98.80.-k, 04.20.Cv [physics.gen Introduction The two most outstanding unsolved problems of modern cosmology today are the problems of dark energy and dark matter. Together these two problems imply that about a whopping 96% of the energy content of the universe is simply unaccounted for within the reigning paradigm of modern cosmology. arXiv:1210.3021 The dark energy problem has been around only for about two decades, while the dark matter problem has gone unsolved for about 90 years. Various ideas have been put forward, including some fantastic ones such as the presence of ghostly fields and particles. Some ideas even suggest the breakdown of the standard Newton-Einstein gravity for the relevant scales. Although some progress has been made, particularly in the area of dark matter with the nonstandard gravity theories, the problems still stand unresolved. -
The Universe, Life and Everything…
Our current understanding of our world is nearly 350 years old. Durston It stems from the ideas of Descartes and Newton and has brought us many great things, including modern science and & increases in wealth, health and everyday living standards. Baggerman Furthermore, it is so engrained in our daily lives that we have forgotten it is a paradigm, not fact. However, there are some problems with it: first, there is no satisfactory explanation for why we have consciousness and experience meaning in our The lives. Second, modern-day physics tells us that observations Universe, depend on characteristics of the observer at the large, cosmic Dialogues on and small, subatomic scales. Third, the ongoing humanitarian and environmental crises show us that our world is vastly The interconnected. Our understanding of reality is expanding to Universe, incorporate these issues. In The Universe, Life and Everything... our Changing Dialogues on our Changing Understanding of Reality, some of the scholars at the forefront of this change discuss the direction it is taking and its urgency. Life Understanding Life and and Sarah Durston is Professor of Developmental Disorders of the Brain at the University Medical Centre Utrecht, and was at the Everything of Reality Netherlands Institute for Advanced Study in 2016/2017. Ton Baggerman is an economic psychologist and psychotherapist in Tilburg. Everything ISBN978-94-629-8740-1 AUP.nl 9789462 987401 Sarah Durston and Ton Baggerman The Universe, Life and Everything… The Universe, Life and Everything… Dialogues on our Changing Understanding of Reality Sarah Durston and Ton Baggerman AUP Contact information for authors Sarah Durston: [email protected] Ton Baggerman: [email protected] Cover design: Suzan Beijer grafisch ontwerp, Amersfoort Lay-out: Crius Group, Hulshout Amsterdam University Press English-language titles are distributed in the US and Canada by the University of Chicago Press. -
Cantor, God, and Inconsistent Multiplicities*
STUDIES IN LOGIC, GRAMMAR AND RHETORIC 44 (57) 2016 DOI: 10.1515/slgr-2016-0008 Aaron R. Thomas-Bolduc University of Calgary CANTOR, GOD, AND INCONSISTENT MULTIPLICITIES* Abstract. The importance of Georg Cantor’s religious convictions is often ne- glected in discussions of his mathematics and metaphysics. Herein I argue, pace Jan´e(1995), that due to the importance of Christianity to Cantor, he would have never thought of absolutely infinite collections/inconsistent multiplicities, as being merely potential, or as being purely mathematical entities. I begin by considering and rejecting two arguments due to Ignacio Jan´e based on letters to Hilbert and the generating principles for ordinals, respectively, showing that my reading of Cantor is consistent with that evidence. I then argue that evidence from Cantor’s later writings shows that he was still very religious later in his career, and thus would not have given up on the reality of the absolute, as that would imply an imperfection on the part of God. The theological acceptance of his set theory was very important to Can- tor. Despite this, the influence of theology on his conception of absolutely infinite collections, or inconsistent multiplicities, is often ignored in contem- porary literature.1 I will be arguing that due in part to his religious convic- tions, and despite an apparent tension between his earlier and later writings, Cantor would never have considered inconsistent multiplicities (similar to what we now call proper classes) as completed in a mathematical sense, though they are completed in Intellectus Divino. Before delving into the issue of the actuality or otherwise of certain infinite collections, it will be informative to give an explanation of Cantor’s terminology, as well a sketch of Cantor’s relationship with religion and reli- gious figures. -
Fine-Tuning, Complexity, and Life in the Multiverse*
Fine-Tuning, Complexity, and Life in the Multiverse* Mario Livio Dept. of Physics and Astronomy, University of Nevada, Las Vegas, NV 89154, USA E-mail: [email protected] and Martin J. Rees Institute of Astronomy, University of Cambridge, Cambridge CB3 0HA, UK E-mail: [email protected] Abstract The physical processes that determine the properties of our everyday world, and of the wider cosmos, are determined by some key numbers: the ‘constants’ of micro-physics and the parameters that describe the expanding universe in which we have emerged. We identify various steps in the emergence of stars, planets and life that are dependent on these fundamental numbers, and explore how these steps might have been changed — or completely prevented — if the numbers were different. We then outline some cosmological models where physical reality is vastly more extensive than the ‘universe’ that astronomers observe (perhaps even involving many ‘big bangs’) — which could perhaps encompass domains governed by different physics. Although the concept of a multiverse is still speculative, we argue that attempts to determine whether it exists constitute a genuinely scientific endeavor. If we indeed inhabit a multiverse, then we may have to accept that there can be no explanation other than anthropic reasoning for some features our world. _______________________ *Chapter for the book Consolidation of Fine Tuning 1 Introduction At their fundamental level, phenomena in our universe can be described by certain laws—the so-called “laws of nature” — and by the values of some three dozen parameters (e.g., [1]). Those parameters specify such physical quantities as the coupling constants of the weak and strong interactions in the Standard Model of particle physics, and the dark energy density, the baryon mass per photon, and the spatial curvature in cosmology. -
Galaxy Redshifts: from Dozens to Millions
GALAXY REDSHIFTS: FROM DOZENS TO MILLIONS Chris Impey University of Arizona The Expanding Universe • Evolution of the scale factor from GR; metric assumes homogeneity and isotropy (~FLRW). • Cosmological redshift fundamentally differs from a Doppler shift. • Galaxies (and other objects) are used as space-time markers. Expansion History and Contents Science is Seeing The expansion history since the big bang and the formation of large scale structure are driven by dark matter and dark energy. Observing Galaxies Galaxy Observables: • Redshift (z) • Magnitude (color, SED) • Angular size (morphology) All other quantities (size, luminosity, mass) derive from knowing a distance, which relates to redshift via a cosmological model. The observables are poor distance indicators. Other astrophysical luminosity predictors are required. (Cowie) ~90% of the volume or look-back time is probed by deep field • Number of galaxies in observable universe: ~90% of the about 100 billion galaxies in the volume • Number of stars in the are counted observable universe: about 1022 Heading for 100 Million (Baldry/Eisenstein) Multiplex Advantage Cannon (1910) Gemini/GMOS (2010) Sluggish, Spacious, Reliable. Photography CCD Imaging Speedy, Cramped, Finicky. 100 Years of Measuring Galaxy Redshifts Who When # Galaxies Size Time Mag Scheiner 1899 1 (M31) 0.3m 7.5h V = 3.4 Slipher 1914 15 0.6m ~5h V ~ 8 Slipher 1917 25 0.6m ~5h V ~ 8 Hubble/Slipher 1929 46 1.5m ~6h V ~ 10 Hum/May/San 1956 800 5m ~2h V = 11.6 Photographic 1960s 1 ~4m ~2.5h V ~ 15 Image Intensifier 1970s -
Molecular Symmetry
Molecular Symmetry Symmetry helps us understand molecular structure, some chemical properties, and characteristics of physical properties (spectroscopy) – used with group theory to predict vibrational spectra for the identification of molecular shape, and as a tool for understanding electronic structure and bonding. Symmetrical : implies the species possesses a number of indistinguishable configurations. 1 Group Theory : mathematical treatment of symmetry. symmetry operation – an operation performed on an object which leaves it in a configuration that is indistinguishable from, and superimposable on, the original configuration. symmetry elements – the points, lines, or planes to which a symmetry operation is carried out. Element Operation Symbol Identity Identity E Symmetry plane Reflection in the plane σ Inversion center Inversion of a point x,y,z to -x,-y,-z i Proper axis Rotation by (360/n)° Cn 1. Rotation by (360/n)° Improper axis S 2. Reflection in plane perpendicular to rotation axis n Proper axes of rotation (C n) Rotation with respect to a line (axis of rotation). •Cn is a rotation of (360/n)°. •C2 = 180° rotation, C 3 = 120° rotation, C 4 = 90° rotation, C 5 = 72° rotation, C 6 = 60° rotation… •Each rotation brings you to an indistinguishable state from the original. However, rotation by 90° about the same axis does not give back the identical molecule. XeF 4 is square planar. Therefore H 2O does NOT possess It has four different C 2 axes. a C 4 symmetry axis. A C 4 axis out of the page is called the principle axis because it has the largest n . By convention, the principle axis is in the z-direction 2 3 Reflection through a planes of symmetry (mirror plane) If reflection of all parts of a molecule through a plane produced an indistinguishable configuration, the symmetry element is called a mirror plane or plane of symmetry . -
Representation and Metaphysics Proper
Richard B. Wells ©2006 CHAPTER 4 First Epilegomenon: Representation and Metaphysics Proper The pursuit of wisdom has had a two-fold origin. Diogenes Laertius § 1. Questions Raised by Representation The outline of representation presented in Chapter 3 leaves us with a number of questions we need to address. In this chapter we will take a look back at our ideas of representation and work toward the resolution of those issues that present themselves in consequence of the theory as it stands so far. I call this look back an epilegomenon, from epi – which means “over” or “upon” – and legein – “to speak.” I employ this new term because the English language seems to have no word that adequately expresses the task at hand. “Epilogue” would imply logical conclusion, while “summary” or “epitome” would suggest a simple re-hashing of what has already been said. Our present task is more than this; we must bring out the implications of representation, Critically examine the gaps in the representation model, and attempt to unite its aggregate pieces as a system. In doing so, our aim is to push farther toward “that which is clearer by nature” although we should not expect to arrive at this destination all in one lunge. Let this be my apology for this minor act of linguistic tampering.1 In particular, Chapter 3 saw the introduction of three classes of ideas that are addressed by the division of nous in its role as the agent of construction for representations. We described these ideas as ideas of the act of representing. -
ARCHITECTS of INTELLIGENCE for Xiaoxiao, Elaine, Colin, and Tristan ARCHITECTS of INTELLIGENCE
MARTIN FORD ARCHITECTS OF INTELLIGENCE For Xiaoxiao, Elaine, Colin, and Tristan ARCHITECTS OF INTELLIGENCE THE TRUTH ABOUT AI FROM THE PEOPLE BUILDING IT MARTIN FORD ARCHITECTS OF INTELLIGENCE Copyright © 2018 Packt Publishing All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews. Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the author, nor Packt Publishing or its dealers and distributors, will be held liable for any damages caused or alleged to have been caused directly or indirectly by this book. Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information. Acquisition Editors: Ben Renow-Clarke Project Editor: Radhika Atitkar Content Development Editor: Alex Sorrentino Proofreader: Safis Editing Presentation Designer: Sandip Tadge Cover Designer: Clare Bowyer Production Editor: Amit Ramadas Marketing Manager: Rajveer Samra Editorial Director: Dominic Shakeshaft First published: November 2018 Production reference: 2201118 Published by Packt Publishing Ltd. Livery Place 35 Livery Street Birmingham B3 2PB, UK ISBN 978-1-78913-151-2 www.packt.com Contents Introduction ........................................................................ 1 A Brief Introduction to the Vocabulary of Artificial Intelligence .......10 How AI Systems Learn ........................................................11 Yoshua Bengio .....................................................................17 Stuart J. -
Modelling Insight to Ball Eyes for Higher Dimensional Hyperspace Vision
Physical Science & Biophysics Journal MEDWIN PUBLISHERS ISSN: 2641-9165 Committed to Create Value for Researchers Modelling Insight to Ball Eyes for Higher Dimensional Hyperspace Vision Shaikh S* Letter to Editor Aditya Institute of Management Studies and Research (AIMSR), India Volume 5 Issue 2 Received Date: July 16, 2021 Sadique Shaikh, Aditya Institute of Management Studies and *Corresponding author: Published Date: July 26, 2021 Research (IMSR), Jalgaon, India, Email: [email protected] DOI: 10.23880/psbj-16000183 Letter to Editor To understand this complicated conceptual idea let Quality vision even some animals, reptiles, birds and insect has good vision as compare to human eyes. To understand me begin first with the definition of VISION and then after toDIMENSIONS create animated (Figure CONSCIOUSNESS 1). The Vision inis theability help to ofacquire Brain “Dimensional-Vision” some depicts as given below. callsurrounding Observable with Life,input Planet,light, shapes, Universe places, and color Multiverse. to brain and Control to enhance, develop and shape planet earth and Equally Vision also important to grow Brain Intelligence term Dimensions as the ability of Eyes to scan surrounding at present observable Universe. Now I would like to define possibleavailable anglesVision and with geometry Left, Right, and Top,provide Bottom, data toReflection, Brain to Rotation, Transformation, Spinning and Diagonal with all universe and multiverse. For our understanding purpose create high definition Consciousness of environment, planet, understand are 3D Three-Dimensional World as X-Axis, we labeled the Dimensions which we (Human) can see and TIME and Brain create 3D consciousness using X, Y and Z Y-Axis and Z-Axis with additional fourth Dimension virtually Figure 1: has ability to see in three dimensions hence very easily can Axis’s Vision Data after input processed. -
Teleportation
TELEPORTATION ESSAY FOR THE COURSE QUANTUM MECHANICS FOR MATHEMATICIANS ANNE VAN WEERDEN SUPERVISOR DR B.R.U. DHERIN UTRECHT UNIVERSITY JUNE 2010 PREFACE The aim of this essay is to describe the teleportation process in such a way that it will be clear what is done so far, and what is still needed, to develop a teleportation device for humans, which would be my ultimate goal. However much is done already, there are thresholds that still have to be overcome, some of which will need real ingenuity, and others brute computing power, far more than we are now capable of. But I will show why I have confidence that we will reach this goal by describing the astonishing developments in the field of teleportation and the speed with which computing, or technology, evolves. The discovery that teleportation really is possible came about while I was in my thirties, but I was largely unaware of its further developments until I started the research for this essay. Assuming that I am not the only one who did not know, I wrote this essay aimed at people from my age, in their fifties, who, like me, started out without television and computer, I even remember my Mother telling me how she bought a transistor radio for the first time, placed it in a closet and closed the door, just to be amazed that it could still receive signals and play. We saw it all come by, from the first steps on the Moon watched on the television my parents had only bought a few years earlier, I clearly remember asking my Father who, with much foresight, got us out of our beds despite my -
The Philosophy and Physics of Time Travel: the Possibility of Time Travel
University of Minnesota Morris Digital Well University of Minnesota Morris Digital Well Honors Capstone Projects Student Scholarship 2017 The Philosophy and Physics of Time Travel: The Possibility of Time Travel Ramitha Rupasinghe University of Minnesota, Morris, [email protected] Follow this and additional works at: https://digitalcommons.morris.umn.edu/honors Part of the Philosophy Commons, and the Physics Commons Recommended Citation Rupasinghe, Ramitha, "The Philosophy and Physics of Time Travel: The Possibility of Time Travel" (2017). Honors Capstone Projects. 1. https://digitalcommons.morris.umn.edu/honors/1 This Paper is brought to you for free and open access by the Student Scholarship at University of Minnesota Morris Digital Well. It has been accepted for inclusion in Honors Capstone Projects by an authorized administrator of University of Minnesota Morris Digital Well. For more information, please contact [email protected]. The Philosophy and Physics of Time Travel: The possibility of time travel Ramitha Rupasinghe IS 4994H - Honors Capstone Project Defense Panel – Pieranna Garavaso, Michael Korth, James Togeas University of Minnesota, Morris Spring 2017 1. Introduction Time is mysterious. Philosophers and scientists have pondered the question of what time might be for centuries and yet till this day, we don’t know what it is. Everyone talks about time, in fact, it’s the most common noun per the Oxford Dictionary. It’s in everything from history to music to culture. Despite time’s mysterious nature there are a lot of things that we can discuss in a logical manner. Time travel on the other hand is even more mysterious.