DOCSLIB.ORG

Digital Mechanics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Digital Mechanics Working Draft Do not Circulate Working Draft Digital Mechanics Edward Fredkin Carnegie Mellon University Digital Mechanics DM-Book5c.doc 1 © December, 2000 Ed Fredkin Moskito Island, BVI Working Draft Do not Circulate Working Draft Preface The Amazing Glorious Gift Somehow, when I was still a child, I was given a wondrous gift. I don’t know how or why; I didn’t even understand or appreciate it for decades. Neither did I realize that, apparently, this gift was given only to me. As the vast implications began to filter into my consciousness, my first reaction was to try to share my gift; but it was not to be. The pieces first started to fall into place some 20 years later, about 1960. Since then I have been able to glimpse and learn more and more about something unknown to others. Over many years this vision slowly transitioned from totally murky to almost clear in certain directions. Puzzling aspects have loomed like great glaciers, which only revealed their secrets as they quietly melted away. But still, even stranger than the Gift itself, is the fact that it has remained mine alone for all these years. I never ever thought to keep it a secret. In fact I sort ran to the rooftops and shouted to all who might listen "…maybe this is it, this could be how things work…" but no one has ever understood what I was trying to say. My reaction was always strange. I knew how beautiful it was yet I never had any concern for all those who couldn’t understand. But now, the biggest picture is starting to come into focus and the totality of this amazing glorious gift is slowly being revealed. To me it is so staggering that I must try once again to pass it on to others. It’s made difficult by my refusal to treat these concepts more modestly or more conventionally. It’s not that I am immodest or unconventional, it’s that the subject matter is totally revolutionary and to understand it or even evaluate it requires an open mind. More specifically it requires one to change their frame of reference so as to have a new viewpoint. One cannot understand or appreciate what is revealed here except from the vantage point of the Digital Perspective. I will try my best to explain all this so that you might be able to share what I have seen. You can read about it here. You should be able to understand it. But it’s far out, hard to swallow, difficult to digest. And when all is said and done, it might still be mine alone.1 As a child, I loved arithmetic and mathematics. I could understand the process of doing addition. Because, in some ways I was slow to get educated, I was allowed the pleasure of discovering many mathematical ideas for myself. This ranged from Fermat’s Little Theorem to the binary number system. As time went by I came to realize that 99% of my mathematical discoveries were old hat, with most 1 Of course, this is an exaggeration. Other people have shared some aspects of my vision. Most notable was Konrad Zuse. Today there are scattered throughout the world a very small number of individuals who have some similar thoughts such as Joel Dobrzelewski or Plamen Petrov, but I know of no one in the Physics Establishment. Many of my colleagues and students understand my vision, but none that I know of admit to believing in it. Digital Mechanics DM-Book5c.doc 2 © December, 2000 Ed Fredkin Moskito Island, BVI Working Draft Do not Circulate Working Draft of them thought of by Euler. I don’t know exactly when I first realized that the way I thought was different. When I was young I thought that those differences reflected something wrong with me. I couldn't seem to accept things that everyone else seemed comfortable with. I couldn't figure out things that others could easily figure out. My mind seemed to me to be in some ways defective even though I knew I was smart. I puzzled over simple things, such as trying to understand exactly what kind of machinery could be at work so that the progeny of two living things could inherit traits from both of them. Sex was complicated enough but inherited characteristics posed the same problem I saw in Newtonian motion. I now understand that what I wanted to know in detail was how the informational process worked. What was it in a seed that determined the color of the petals in a flower? What was it in a particle that determined the speed with which it moved? What was the mechanism that led to Mendel's2 laws? What was the mechanism that led to Newton’s laws? I knew that if a pea plant with red flowers and one with white flowers produced a seed, that the “red” and “white” had to be written somewhere and somehow in the seed. I knew that when two particles were about to collide, somehow, in some kind of language, the momentum of each had to be written down in some way associated with each particle. During the interaction this information had to be combined then re-divided between the two particles. I mistakenly thought Biology too complex to be understandable at the level I was seeking; I mistakenly imagined that physics ought to be easier. I merely wanted to figure out, in perfect detail, how that information had to be represented and how the informational process that we call “physics” functioned. But at the time, I didn’t even know how to state what it was that I wanted to figure out. I was not only missing a key, but I didn’t even know the language in which to describe the problem. My friends, who also liked math and science could neither understand what I was looking for nor understand why I persisted in such folly. I was seeking a different kind of understand. Mathematics deals with many kinds of numbers. The integers, 0, 1, 2, 3… are not too hard to understand. The rational numbers are easy too since each can be represented by two integers, e.g. ¾. Yet within mathematics are all kinds of other numbers such as irrational, real and transcendental. These numbers, most of which cannot be written down exactly as an ordinary decimal, include the square root of 2 and Pi (Approximately 1.4142135623730950… and 3.14159265358793… respectively). We can represent the square root of 2 exactly by the symbol 2 and Pi by the symbol π . What we cannot do is to write down an exact representation as a 2 Gregor Johann Mendel, 1822-1884, discovered the laws of heredity. Working with garden peas, he found that there were dominant and recessive genes. Before Mendel, it was widely held that offspring more or less blended characteristics of their parents. Mendel discovered that inherited traits came in two kinds, recessive and dominant, where purebreds expressed their trait and hybrids only expressed the dominant trait. Further, of the offspring of a purebred dominant trait and a purebred recessive trait, ¼ were purebred dominant, ¼ purebred recessive and ½ hybrid, showing only the dominant trait. This changed the picture of inherited characteristics from some kind of continuous blending of all one’s ancestors traits, to a simple discrete process. It was a kind of atomic theory of genetics; now understandable as a consequence of processes involving DNA. Digital Mechanics DM-Book5c.doc 3 © December, 2000 Ed Fredkin Moskito Island, BVI Working Draft Do not Circulate Working Draft number, just with digits. This means that arithmetic with such strange numbers cannot be performed as with the integers. I had to learn that one could understand these strange things exactly, but not as numbers with digits. In a sense one had to understand the ideas about these strange things without understanding the digital, numerical representations themselves. This was annoying to me, yet among my acquaintances who were also interested in math and physics, none of them shared my problem. When I learned about Newton’s laws, I was told that they were the laws of motion. So be it. With Newton’s Laws I could solve homework problems. But even with them, I still couldn't understand motion. I couldn't conceive of what sort of thing could be going on that allowed a body to move relative to other bodies. The problem of motion became of overwhelming interest to me. My first observation was that a particle in motion had to know what it was doing. If I thought about an isolated particle coasting along with no forces acting upon it, I wondered “How can a particle remember, from one instant in time to another, which way it is supposed to be going?” Why don’t particles go in random directions and at random speeds? I couldn't ask anyone these questions without their thinking of me as an idiot. Of course I learned about Newtonian Relativity and Conservation of Momentum, but those were only confirmations of the mystery; just different ways of stating the same observation that somehow objects do mysterious things: they move, and they remember what they are and which way they are moving. To me, remembering which way something was moving can be facilitated by writing it down. "I am moving due North at 3 miles per hour." If it is written down, then there is no problem remembering what it is. However, then we have the problem that something must read what is written down and actually translate that into motion.
Load more

Recommended publications
  • HUI What Is a Digital Object Metaphilosophy.Pdf
    bs_bs_banner © 2012 The Author Metaphilosophy © 2012 Metaphilosophy LLC and Blackwell Publishing Ltd Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK, and 350 Main Street, Malden, MA 02148, USA METAPHILOSOPHY Vol. 43, No. 4, July 2012 0026-1068 WHAT IS A DIGITAL OBJECT? YUK HUI Abstract: We find ourselves in a media-intensive milieu comprising networks, images, sounds, and text, which we generalize as data and metadata. How can we understand this digital milieu and make sense of these data, not only focusing on their functionalities but also reflecting on our everyday life and existence? How do these material constructions demand a new philosophical understand- ing? Instead of following the reductionist approaches, which understand the digital milieu as abstract entities such as information and data, this article pro- poses to approach it from an embodied perspective: objects. The article contrasts digital objects with natural objects (e.g., apples on the table) and technical objects (e.g., hammers) in phenomenological investigations, and proposes to approach digital objects from the concept of “relations,” on the one hand the material relations that are concretized in the development of mark-up languages, such as SGML, HTML, and XML, and on the other hand, Web ontologies, the temporal relations that are produced and conditioned by the artificial memories of data. Keywords: digital objects, phenomenology, metadata, Stiegler, Simondon. In this article I attempt to outline what I call digital objects, showing that a philosophical investigation is necessary by revisiting the history of philosophy and proposing that it is possible to develop a philosophy of digital objects.
    [Show full text]
  • Calculating Space) 1St
    Konrad Zuse’s Rechnender Raum (Calculating Space) 1st. re-edition1 written in LATEX by A. German and H. Zenil As published in A Computable Universe: Understanding & Exploring Nature as Computation, World Scientific, 2012 Painting by Konrad Zuse (under the pseudonym “Kuno See”). Followed by an Afterword by Adrian German and Hector Zenil 2 1with kind permission by all parties involved, including MIT and Zuse’s family. 2The views expressed in the afterword do not represent the views of those organisations with which the authors are affiliated. 1 Calculating Space (“Rechnender Raum”)z Konrad Zuse Contents 1 INTRODUCTION 1 2 INTRODUCTORY OBSERVATIONS 3 2.1 Concerning the Theory of Automatons . .3 2.2 About Computers . .5 2.3 Differential Equations from the Point of View of the Automa- ton Theory . .8 2.4 Maxwell Equations . 10 2.5 An Idea about Gravitation . 13 2.6 Differential Equations and Difference Equations, Digitalization 13 2.7 Automaton Theory Observations of Physical Theories . 14 3 EXAMPLES OF DIGITAL TREATMENT OF FIELDS AND PARTICLES 19 3.1 The Expression “Digital Particle” . 19 3.2 Two-Dimensional Systems . 27 3.3 Digital Particles in Two-Dimensional Space . 30 3.4 Concerning Three-Dimensional Systems . 34 4 GENERAL CONSIDERATIONS 37 4.1 Cellular Automatons . 37 4.2 Digital Particles and Cellular Automatons . 39 4.3 On the Theory of Relativity . 39 zSchriften zur Datenverarbeitung, Vol. 1, 1969 Friedrich Vieweg & Sohn, Braun- schweig, 74 pp. MIT Technical TranslationTranslated for Massachusetts Institute of Tech- nology, Project MAC, by: Aztec School of Languages, Inc., Research Translation Division (164), Maynard, Massachusetts and McLean, Virginia AZT-70-164-GEMIT Massachusetts Institute of Technology, Project MAC, Cambridge, Massachusetts 02139—February 1970 2 4.4 Considerations of Information Theory .
    [Show full text]
  • Collision-Based Computing Springer-Verlag London Ltd
    Collision-Based Computing Springer-Verlag London Ltd. Andrew Adamatzky (Ed.) Collision-Based Computing , Springer Andrew Adamatzky Facu1ty of Computing, Engineering and Mathematical Sciences, University of the West of England, Bristol, BS16 lQY British Library Cataloguing in Publication Data Collision-based computing l.Cellular automata 1. Adamatzky, Andrew 511.3 ISBN 978-1-85233-540-3 Library of Congress Cataloging -in -Publication Data A catalog record for this book is available from the Library of Congress. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. ISBN 978-1-85233-540-3 ISBN 978-1-4471-0129-1 (eBook) DOI 10.1007/978-1-4471-0129-1 http://www.springer.co. uk © Springer-Verlag London 2002 Originally published by Springer-Verlag London Berlin Heidelberg in 2002 The use of registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.
    [Show full text]
  • Quantum Mechanics Digital Physics
    Quantum Mechanics_digital physics In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is, at heart, describable byinformation, and is therefore computable. Therefore, according to this theory, the universe can be conceived of as either the output of a deterministic or probabilistic computer program, a vast, digital computation device, or mathematically isomorphic to such a device. Digital physics is grounded in one or more of the following hypotheses; listed in order of decreasing strength. The universe, or reality: is essentially informational (although not every informational ontology needs to be digital) is essentially computable (the pancomputationalist position) can be described digitally is in essence digital is itself a computer (pancomputationalism) is the output of a simulated reality exercise History Every computer must be compatible with the principles of information theory,statistical thermodynamics, and quantum mechanics. A fundamental link among these fields was proposed by Edwin Jaynes in two seminal 1957 papers.[1]Moreover, Jaynes elaborated an interpretation of probability theory as generalized Aristotelian logic, a view very convenient for linking fundamental physics withdigital computers, because these are designed to implement the operations ofclassical logic and, equivalently, of Boolean algebra.[2] The hypothesis that the universe is a digital computer was pioneered by Konrad Zuse in his book Rechnender Raum (translated into English as Calculating Space). The term digital physics was first employed by Edward Fredkin, who later came to prefer the term digital philosophy.[3] Others who have modeled the universe as a giant computer include Stephen Wolfram,[4] Juergen Schmidhuber,[5] and Nobel laureate Gerard 't Hooft.[6] These authors hold that the apparentlyprobabilistic nature of quantum physics is not necessarily incompatible with the notion of computability.
    [Show full text]
  • Introducing the Computable Universe
    Introducing the Computable Universe∗ Hector Zenil Department of Computer Science, The University of Sheffield, UK; IHPST (Paris 1 Panth´eon-Sorbonne/ENS Ulm/CNRS), France; & Wolfram Science Group, Wolfram Research, USA. Abstract Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic arguments giving foundation to these visions. We will focus on the algorithmic and quantum aspects, and how these may fit and support the computable universe hypoth- esis. 1 Understanding Computation & Exploring Nature As Computation Since the days of Newton and Leibniz, scientists have been constructing elab- arXiv:1206.0376v1 [cs.IT] 2 Jun 2012 orate views of the world. In the past century, quantum mechanics revolu- tionised our understanding of physical reality at atomic scales, while general relativity did the same for our understanding of reality at large scales. Some contemporary world views approach objects and physical laws in terms of information and computation [25], to which they assign ultimate responsibility for the complexity in our world, including responsibility for complex mechanisms and phenomena such as life. In this view, the universe ∗Based in the introduction to A Computable Universe, published by World Scientific Publishing Company and the Imperial College Press, 2012. See http://www.mathrix.org/experimentalAIT/ComputationNature.htm 1 and the things in it are seen as computing themselves. Our computers do no more than re-program a part of the universe to make it compute what we want it to compute. Some authors have extended the definition of computation to physical objects and physical processes at different levels of physical reality, ranging from the digital to the quantum.
    [Show full text]
  • INFORMATION– CONSCIOUSNESS– REALITY How a New Understanding of the Universe Can Help Answer Age-Old Questions of Existence the FRONTIERS COLLECTION
    THE FRONTIERS COLLECTION James B. Glattfelder INFORMATION– CONSCIOUSNESS– REALITY How a New Understanding of the Universe Can Help Answer Age-Old Questions of Existence THE FRONTIERS COLLECTION Series editors Avshalom C. Elitzur, Iyar, Israel Institute of Advanced Research, Rehovot, Israel Zeeya Merali, Foundational Questions Institute, Decatur, GA, USA Thanu Padmanabhan, Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India Maximilian Schlosshauer, Department of Physics, University of Portland, Portland, OR, USA Mark P. Silverman, Department of Physics, Trinity College, Hartford, CT, USA Jack A. Tuszynski, Department of Physics, University of Alberta, Edmonton, AB, Canada Rüdiger Vaas, Redaktion Astronomie, Physik, bild der wissenschaft, Leinfelden-Echterdingen, Germany THE FRONTIERS COLLECTION The books in this collection are devoted to challenging and open problems at the forefront of modern science and scholarship, including related philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science and research. Furthermore, it is intended to encourage active academics in all fields to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, conscious- ness, language and complex systems—the Frontiers Collection will inspire readers to push back the frontiers of their own knowledge. More information about this series at http://www.springer.com/series/5342 For a full list of published titles, please see back of book or springer.com/series/5342 James B.
    [Show full text]
  • There's Plenty of Boole at the Bottom: a Reversible CA Against
    Minds & Machines DOI 10.1007/s11023-016-9401-6 There’s Plenty of Boole at the Bottom: A Reversible CA Against Information Entropy 1 2 Francesco Berto • Jacopo Tagliabue • Gabriele Rossi3 Received: 11 May 2016 / Accepted: 19 September 2016 Ó The Author(s) 2016. This article is published with open access at Springerlink.com Abstract ‘‘There’s Plenty of Room at the Bottom’’, said the title of Richard Feynman’s 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the links between physical reality and information processing. Not all the physical requirements of optimal computation are captured by traditional models—one still largely missing is reversibility. The dynamic laws of physics are reversible at microphysical level, distinct initial states of a system leading to distinct final states. On the other hand, as von Neumann already conjectured, irreversible information processing is expensive: to erase a single bit of information costs *3 9 10-21 joules at room temperature. Information entropy is a thermodynamic cost, to be paid in non-computational energy dissipation. This paper addresses the problem drawing on Edward Fredkin’s Finite Nature hypothesis: the ultimate nature of the universe is discrete and finite, satisfying the axioms of classical, atomistic mereology. The chosen model is a cellular automaton (CA) with reversible dynamics, capable of retaining memory of the information present at the beginning of the universe. Such a CA can implement the Boolean logical operations and the other building bricks of computation: it can develop and host all-purpose computers.
    [Show full text]
  • Toward a Computational Theory of Everything
    International Journal of Recent Advances in Physics (IJRAP) Vol.9, No.1/2/3, August 2020 TOWARD A COMPUTATIONAL THEORY OF EVERYTHING Ediho Lokanga A faculty member of EUCLID (Euclid University). Tipton, United Kingdom HIGHLIGHTS . This paper proposes the computational theory of everything (CToE) as an alternative to string theory (ST), and loop quantum gravity (LQG) in the quest for a theory of quantum gravity and the theory of everything. A review is presented on the development of some of the fundamental ideas of quantum gravity and the ToE, with an emphasis on ST and LQG. Their strengths, successes, achievements, and open challenges are presented and summarized. The results of the investigation revealed that ST has not so far stood up to scientific experimental scrutiny. Therefore, it cannot be considered as a contender for a ToE. LQG or ST is either incomplete or simply poorly understood. Each of the theories or approaches has achieved notable successes. To achieve the dream of a theory of gravity and a ToE, we may need to develop a new approach that combines the virtues of these two theories and information. The physics of information and computation may be the missing link or paradigm as it brings new recommendations and alternate points of view to each of these theories. ABSTRACT The search for a comprehensive theory of quantum gravity (QG) and the theory of everything (ToE) is an ongoing process. Among the plethora of theories, some of the leading ones are string theory and loop quantum gravity. The present article focuses on the computational theory of everything (CToE).
    [Show full text]
  • FOOTPRINTS of GENERAL SYSTEMS THEORY Aleksandar Malecic Faculty of Electronic Engineering University of Nis, Serbia Aleks.Maleci
    FOOTPRINTS OF GENERAL SYSTEMS THEORY Aleksandar Malecic Faculty of Electronic Engineering University of Nis, Serbia [email protected] ABSTRACT In order to identify General Systems Theory (GST) or at least have a fuzzy idea of what it might look like, we shall look for its traces on different systems. We shall try to identify such an “animal” by its “footprints”. First we mention some natural and artificial systems relevant for our search, than note the work of other people within cybernetics and identification of systems, and after that we are focused on what unification of different systems approaches and scientific disciplines should take into account (and whether or not it is possible). Axioms and principles are mentioned as an illustration of how to look for GST*. A related but still separate section is about Len Troncale and linkage propositions. After them there is another overview of different kinds of systems (life, consciousness, and physics). The documentary film Dangerous Knowledge and ideas of its characters Georg Cantor, Ludwig Boltzmann, Kurt Gödel, and Alan Turing are analyzed through systems worldview. “Patterns all the way down” and similar ideas by different authors are elaborated and followed by a section on Daniel Dennett’s approach to real patterns. Two following sections are dedicated to Brian Josephson (a structural theory of everything) and Sunny Auyang. After that the author writes about cosmogony, archetypes, myths, and dogmas. The paper ends with a candidate for GST*. Keywords: General Systems Theory, unification, patterns, principles, linkage propositions SYSTEMS IN NATURE AND ENGINEERING The footprints manifest as phenomena and scientific disciplines.
    [Show full text]
  • The Use of Interdisciplinary Approach for the Formation of Learners’ Situational Interest in Physics
    Asia-Pacific Forum on Science Learning and Teaching, Volume 18, Issue 2, Article 5, p.1 (Dec., 2017) Igor KORSUN The use of interdisciplinary approach for the formation of learners’ situational interest in Physics The use of interdisciplinary approach for the formation of learners’ situational interest in Physics Igor KORSUN Ternopil Volodymyr Hnatiuk National Pedagogical University, UKRAINE E-mail: [email protected] Received 18 Jan., 2017 Revised 11 Dec., 2017 Contents Abstract Introduction Method Results Discussion Conclusion References Appendices Abstract The aim of this article is to prove the advisability of using the interdisciplinary approach for the formation of learners’ situational interest in physics. The general method of using the interdisciplinary approach in physics teaching has been created. The study of new material, the formation of abilities and skills, and the work on projects are the forms of the interdisciplinary links in physics teaching. The scheme for interest formation towards physics in the context of development of situational and individual interest has been analyzed. According to the interdisciplinary approach, the tools for the formation of learners’ situational interest in physics have Copyright (C) 2017 EdUHK APFSLT. Volume 18, Issue 2, Article 5 (Dec., 2017). All Rights Reserved. Asia-Pacific Forum on Science Learning and Teaching, Volume 18, Issue 2, Article 5, p.2 (Dec., 2017) Igor KORSUN The use of interdisciplinary approach for the formation of learners’ situational interest in Physics been allocated. These are phenomena of nature, phenomena of everyday life, link between theory and practice. The results showed that interdisciplinary approach in physics teaching increases the level of learners’ situational interest.
    [Show full text]
  • There's Plenty of Boole at the Bottom: a Reversible CA Against Information Entropy
    UvA-DARE (Digital Academic Repository) There's Plenty of Boole at the Bottom: A Reversible CA Against Information Entropy Berto, F.; Tagliabue, J.; Rossi, G. DOI 10.1007/s11023-016-9401-6 Publication date 2016 Document Version Final published version Published in Minds and Machines License CC BY Link to publication Citation for published version (APA): Berto, F., Tagliabue, J., & Rossi, G. (2016). There's Plenty of Boole at the Bottom: A Reversible CA Against Information Entropy. Minds and Machines, 26(4), 341-357. https://doi.org/10.1007/s11023-016-9401-6 General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:27 Sep 2021 Minds & Machines (2016) 26:341–357 DOI 10.1007/s11023-016-9401-6 There’s Plenty of Boole at the Bottom: A Reversible CA Against Information Entropy 1 2 Francesco Berto • Jacopo Tagliabue • Gabriele Rossi3 Received: 11 May 2016 / Accepted: 19 September 2016 / Published online: 6 October 2016 Ó The Author(s) 2016.
    [Show full text]
  • Creating an Active-Learning Environment in an Introductory Acoustics Course
    Creating an active-learning environment in an introductory acoustics course Tracianne B. Neilsen,a) William J. Strong, Brian E. Anderson, Kent L. Gee, Scott D. Sommerfeldt, and Timothy W. Leishman Acoustics Research Group, Department of Physics and Astronomy, Brigham Young University, N283 ESC, Provo, Utah 84602 (Received 18 April 2011; accepted 1 May 2011) Research in physics education has indicated that the traditional lecture-style class is not the most ef- ficient way to teach introductory physical science courses at the university level. Current best teach- ing practices focus on creating an active-learning environment and emphasize the students’ role in the learning process. Several of the recommended techniques have recently been applied to Brig- ham Young University’s introductory acoustics course, which has been taught for more than 40 years. Adjustments have been built on a foundation of establishing student-based learning outcomes and attempting to align these objectives with assessments and course activities. Improvements have been made to nearly every aspect of the course including use of class time, assessment materials, and time the students spend out of the classroom. A description of the progress made in improving the course offers suggestions for those seeking to modernize or create a similar course at their insti- tution. In addition, many of the principles can be similarly applied to acoustics education at other academic levels. VC 2012 Acoustical Society of America. [DOI: 10.1121/1.3676733] PACS number(s): 43.10.Sv [ADP] Pages: 2500–2509 I. INTRODUCTION tual understanding that serves as a foundation for more advanced courses in acoustics.
    [Show full text]