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Springer Handbook of Model-Based Science Springer Handbook of Model-Based Science Springer Handbooks provide a concise compilation of approved key information on methods of research, general principles, and functional relationships in physical and applied sciences. The world’s leading experts in the fields of physics and engineering will be as- signed by one or several renowned editors to write the chapters com- prising each volume. The content is selected by these experts from Springer sources (books, journals, online content) and other systematic and approved recent publications of scientific and technical information. The volumes are designed to be useful as readable desk reference book to give a fast and comprehen- sive overview and easy retrieval of essential reliable key information, including tables, graphs, and bibli- ographies. References to extensive sources are provided. HandbookSpringer of Model-Based Science Lorenzo Magnani, Tommaso Bertolotti (Eds.) With 263 Figures and 42 Tables HK Editors Lorenzo Magnani University of Pavia Department of Humanities Piazza Botta 6 Pavia 27100, Italy Tommaso Bertolotti University of Pavia Department of Humanities Piazza Botta 6 Pavia 27100, Italy ISBN: 978-3-319-30525-7 e-ISBN: 978-3-319-30526-4 DOI 10.1007/978-3-319-30526-4 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2017935722 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Production and typesetting: le-tex publishing services GmbH, Leipzig Typography and layout: schreiberVIS, Seeheim Illustrations: Hippmann GbR, Schwarzenbruck Cover design: eStudio Calamar Steinen, Barcelona Cover production: WMXDesign GmbH, Heidelberg Printing and binding: Printer Trento s.r.l., Trento Printed on acid free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland V Foreword: Thinking Inside and Outside Hardly a minute of our lives goes by without reasoning, on elegant distinctions) or look for without “going beyond the information given” (Bruner, them in the brain. On this view, rep- 1966). Reasoning happens without our awareness and resentations are internalized percep- without our intention. Our visual system rapidly parses tions. However, representations cannot light arriving to the retina into figures and ground, be copies, they are highly processed. into the faces, bodies, objects, scenes, and actions that They are interpretations of the content we recognize in fractions of a second and that en- that is the focus of thought. They may ter awareness. The gist stays with us, but the details select some information from the world are not recorded, a process revealed in change blind- and ignore other information, they may ness. Perception is deeply and inherently tied to action, rework the information selected, and epitomized in mirror neurons, single cells in a mon- they may add information, drawing on key cortex that respond both to perceiving an action information already stored in the brain. and to performing it, linking perception and action in In this sense, representations are mod- Barbara Tversky a single neuron. The world we see is constantly chang- els. On this view, operations are inter- Stanford University and ing; in order to act, perception is used to predict what nalized actions, which are analogous Columbia Teachers College happens next, allowing us to catch balls and avoid to actions in the world. Operations act on represen- collisions. Experienced chess and basketball players tations, transforming them and thereby creating new parse and predict at a more sophisticated level, but representations. Examples are in order. We may form a the underlying processes seem to be similar, extensive representation of the arrangement of furniture in a room practice in seeing patterns, interpreting them, and se- or a corporate structure. We can then draw inferences lecting appropriate actions. This kind of reasoning is from the representations by imagining or carrying out fast thinking (Kahneman, 2011) and the kind of rea- actions on the representations, such as comparing parts soning thoughtfully and thoroughly analyzed in this or tracing paths, for example that the coffee table is too impressive volume is slow thinking, thinking that is de- far from the couch or the route from one division to liberate and reflective and that can unfold over weeks another is too circuitous. You have probably noted that and years and even centuries. those inferences also depend on functional information How does deliberative reasoning happen? It hap- stored between the ears. We can then transform the pens in a multitude of ways, as is shown insightfully in arrangements to create new configurations and act on the many domains analyzed in the chapters that follow. those to draw further inferences. Seen this way, repre- Might there be a way to encompass all of them? Here sentations can be created by operations; these processes is one view of thinking, let us call it the inside-outside are iterative and reductive. However, momentarily, rep- view, a view inspired by theories of Bruner (1966), resentations are regarded as static and transformations Piaget (1954), Norman and Rumelhart (1975), Shep- as active, changing representations to generate infer- ard (1984), and Vygotsky (1962), among others, who, ences that go beyond the information given to yield new however, cannot be held responsible for the present thoughts and discoveries. formulation. The inside part is the thinking that hap- The ways that we talk about thinking suggest gen- pens between the ears; the outside part is the thinking erality to this view. When we understand, we say that that gets put into the body and the world. This view we see something; we have an image or an idea, or a is iterative, as what gets put in the world can get thought or a concept. These are static and they stay still internalized and then get worked on inside. Inside think- to be acted on. Then we pull ideas together, compare ing can be further separated into representations and them, turn them inside out, divide them up, reorganize operations. Representations and operations are useful them, or toss them out. fictions, ways to think and talk about thinking. Do Forming representations, keeping them in mind, not expect philosophical precision from them (there and transforming them can quickly overwhelm the is a temperamental difference between and psychol- mind. When thought overwhelms the mind, the mind ogists and philosophers: psychologists live on gener- puts thought in the body and the world. Counting is alities that ignore sloppy variability, philosophers live a paradigmatic example: actions of the finger or the VI Foreword: Thinking Inside and Outside hand (or the head or the eye) on an array of ob- different representations capture different information, jects in the world, pointing to them or moving them, highlight different relationships, and encourage differ- while keeping track of the count with number words. ent inferences. A pilot’s map will not serve a hiker or Counting is a sequence of actions on objects linked a bicyclist, or a surveyor. Chemists have a multitude one-to-one to a sequence of concepts. If representa- of representations of molecules, human biologists of tions are internalized perceptions and transformations the body, statisticians of a set of data, each designed of thoughts are internalized actions, re-externalizing to simplify, highlight, explain, understand, explore, or representations and transformations should promote discover different aspects of multifaceted, often elusive, thought. Moreover, they do, as counting and countless phenomena. other examples demonstrate. The actions of the body This very simple view hides enormous complexity. on the objects in the world exemplify the outside kind It can be accused of being an oversimplification. If it of thinking and, importantly, they are linked to internal were all that simple, design, science, and mathemat- actions, in this case, keeping track of the count. ics would be done with, and they are not. Fortunately, Putting thought into the world expands the mind. the volume at hand corrects that oversimplification. In- Putting thought into the world allows physical actions troducing this volume is a humbling task. So many to substitute for mental ones. Putting thought in the kinds of reasoning are revealed so perceptively in so world
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