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      Computation in Science (Second Edition)

      From concepts to practice

       Konrad Hinsen

       Centre de Biophysique Moléculaire, CNRS Orléans, Orléans, France

      IOP Publishing, Bristol, UK

      Copyright © IOP Publishing Ltd 2020

      All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher, or as expressly permitted by law or under terms agreed with the appropriate rights organization. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency, the Copyright Clearance Centre and other reproduction rights organizations.

      Permission to make use of IOP Publishing content other than as set out above may be sought at [email protected].

      Konrad Hinsen has asserted his right to be identified as the author of this work in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

      ISBN 978-0-7503-3287-3 (ebook)

      ISBN 978-0-7503-3285-9 (print)

      ISBN 978-0-7503-3288-0 (myPrint)

      ISBN 978-0-7503-3286-6 (mobi)

      DOI 10.1088/978-0-7503-3287-3

      Version: 20200901

      IOP ebooks

      British Library Cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library.

      Published by IOP Publishing, wholly owned by The Institute of Physics, London

      IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK

      US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia, PA 19106, USA

      Contents

       Preface

       Acknowledgements

       Author biography

       1 What is computation?

       1.1 Defining computation

       1.1.1 Numerical computation

       1.1.2 From numbers to symbols

       1.1.3 Non-numerical computation

       1.2 The roles of computation in scientific research

       Computation as a tool

       Computation for understanding

       Computation as a form of scientific knowledge

       Computation as a model for information processing in nature

       1.3 Analog computing

       1.4 Further reading

       References

       2 Computation in science

       2.1 Traditional science: celestial mechanics

       2.1.1 Empirical models for planetary orbits

       2.1.2 Newton’s physical model

       2.2 Scientific models and computation

       2.2.1 Characterizing models by computational effort

       2.2.2 Empirical models: from linear regression to data science

       2.2.3 Explanatory models: from simple to complex systems

       2.2.4 Measuring the complexity of a model

       2.2.5 Getting rid of the equations

       2.3 Computation at the interface between observations and models

       2.3.1 Matching models and measurements

       2.3.2 Mixing models and measurements

       2.4 Computation for developing insight

       2.5 The impact of computing on science

       2.6 Further reading

       References

       3 Formalizing computation

       3.1 From manual computation to rewriting rules

       3.2 From computing machines to automata theory

       3.3 Computability

       3.4 Restricted models of computation

       3.5 Computational complexity

       3.6 Computing with numbers

       3.6.1 Floating-point numbers

       3.6.2 Rational

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