Information and Its Role in Nature PDF
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the frontiers collection the frontiers collection SeriesEditors: D.Dragoman M.Dragoman A.C.Elitzur M.P.Silverman J.Tuszynski H.D.Zeh Thebooksinthiscollectionaredevotedtochallengingandopenproblemsattheforefront of modern physics and related disciplines, including philosophical debates. In contrast totypicalresearchmonographs,however,theystrivetopresenttheirtopicsinamanner accessiblealsotoscientificallyliteratenon-specialistswishingtogaininsightintothedeeper implicationsandfascinatingquestionsinvolved.Takenasawhole,theseriesreflectsthe needforafundamentalandinterdisciplinaryapproachtomodernscience.Itisintendedto encouragescientistsinallareastoponderoverimportantandperhapscontroversialissues beyond their own speciality. Extending from quantum physics and relativity to entropy, time and consciousness – the Frontiers Collection will inspire readers to push back the frontiersoftheirownknowledge. InformationandItsRoleinNature ByJ.G.Roederer RelativityandtheNatureofSpacetime ByV.Petkov QuoVadisQuantumMechanics? EditedbyA.C.Elitzur,S.Dolev,N.Kolenda Life–AsaMatterofFat TheEmergingScienceofLipidomics ByO.G.Mouritsen Quantum–ClassicalAnalogies ByD.DragomanandM.Dragoman KnowledgeandtheWorld ChallengesBeyondtheScienceWars EditedbyM.Carrier,J.Roggenhofer,G.Ku¨ppers,P.Blanchard Quantum–ClassicalCorrespondence ByA.O.Bolivar Mind,MatterandQuantumMechanics ByH.Stapp QuantumMechanicsandGravity ByM.Sachs J. G. Roederer INFORMATION AND ITS ROLE IN NATURE With35Figures 123 ProfessorDr.JuanG.Roederer UniversityofAlaska GeographicalInstitute KoyukukDrive903 Fairbanks,AK99775-7320,USA SeriesEditors: Prof.DanielaDragoman UniversityofBucharest,PhysicsFaculty,SolidStateChair,POBoxMG-11, 76900Bucharest,Romania email:[email protected] Prof.MirceaDragoman NationalResearchandDevelopmentInstituteinMicrotechnology,POBox38-160, 023573Bucharest,Romania email:[email protected] Prof.AvshalomC.Elitzur Bar-IlanUniversity,UnitofInterdisciplinaryStudies, 52900Ramat-Gan,Israel email:[email protected] Prof.MarkP.Silverman DepartmentofPhysics,TrinityCollege, Hartford,CT06106,USA email:[email protected] Prof.JackTuszynski UniversityofAlberta,DepartmentofPhysics,Edmonton,AB, T6G2J1,Canada email:[email protected] Prof.H.DieterZeh UniversityofHeidelberg,InstituteofTheoreticalPhysics,Philosophenweg19, 69120Heidelberg,Germany email:[email protected] Coverfigure:Detailfrom‘Zeroof+1/−1Polynomials’byJ.BorweinandL.Jorgensen.CourtesyofJ.Borwein ISSN1612-3018 ISBN-103-540-23075-0SpringerBerlinHeidelbergNewYork ISBN-13978-3-540-23075-5SpringerBerlinHeidelbergNewYork LibraryofCongressControlNumber:2005924951 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationor partsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,in itscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliableto prosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia. springeronline.com ©Springer-VerlagBerlinHeidelberg2005 PrintedinGermany Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. TypesettingbyStephenLyleusingaSpringerTEXmacropackage FinalprocessingbyLE-TEXJelonek,Schmidt&Vo¨cklerGbR,Leipzig CoverdesignbyKünkelLopka,WerbeagenturGmbH,Heidelberg Printedonacid-freepaper SPIN:10977170 57/3141/YL-543210 To my children Ernesto, Irene, Silvia and Mario ... my greatest pride and joy Foreword Accordingtosome,theAgeofInformationwasinauguratedhalfacenturyago in the nineteen forties. However, we do not really know what information is. By “we” I mean everybody who is not satisfied with the trivial meaning of information as “what is in the paper today,” nor with its definition as ”the number of bits in a telegraph” and even less with the snappy “negentropy.” But we do feel that the revival of the ancient term in a modern scientific discourseistimelyandhasalreadystartedaquietrevolutioninourthinking aboutlivingmatter,aboutbrainsandminds,arevolutionperhapsleadingto a reunification of Culture, for centuries tragically split between the Human- ities and Science. Who are the natural philosophers whose thinking is broad enough to encompass all the phenomena that are at the basis of the new synthesis? Erwin Schro¨dinger comes to mind with his astonishing book “What is life?”, astonishingbecauseitcomesfromonewhohadalreadybeenarevolutionary in the foundation of the new physics. Another one is Norbert Wiener whose mathematical-poetic Cyberneticswaspowerfulenoughtopenetrateeventhe farthest reaches of futuristic science fiction (cybernauts in cyberspace, etc.). But also Juan Roederer comes to mind. Here is one whom I have heard producing torrents of baroque music on a majestic pipe organ. One who learned his physics from the greatest mas- ters of quantum theory including Werner Heisenberg but did not deem it beneath him to apply his art to the down-to-earth subject of geophysics (of the magnetosphere, to be sure). One who regaled us with a classic text on the physics and psychophysics of music. A theorist who does not shy away from the theory of his own self. One who did his homework very thoroughly in modern biology and brain science. Inoursearchforaproperplaceof“information”inaTheoryoftheWorld we have been barking up the wrong tree for centuries. Now we are beating around the bush from all sides. Reading Roederer I get the impression that he knows exactly where the prey is hiding. Valentino Braitenberg Director Emeritus Max Planck Institute for Biological Cybernetics Tu¨bingen, Germany January 2005 Preface The roots of this book can be traced back to the early nineteen seventies. At that time I was teaching, as a departmental out-reach action, a course on musical acoustics at the University of Denver. Preparing material for my classes, I began to realize that the acoustical information-processing inside the head was as interesting a topic for a physicist as the physics of what happens outside, in the instrument and the air. As a consequence, the scope of my lectures was expanded to include the mechanisms of musical sound perception. This led me to some “extracurricular” research work on pitch processing, the organization of the “Workshops on Physical and Neuropsy- chological FoundationsofMusic”inOssiach,Austria,andthefirstedition of my book “Physics and Psychophysics of Music”. It did not take me long to become interested in far more general aspects of brain function, and in 1976 I organized a course called “Physics of the Brain” (a title chosen mainly to circumvent departmental turf conflicts). Stimulated by the teaching and the discussions with my students, I published an article in Foundations of Physics, [91] launching my first thoughts on information as the fundamental concept that distinguishes physical interactions from the biological ones – sort of central theme of the present book. My directorship at the Geophysical Institute of the University of Alaska and, later, the chairmanship of the United States Arctic Research Commis- sion prevented me from pursuing this “hobby” for many years. In 1997 I became Senior Adviser of the International Centre for Theoretical Phys- ics(ICTP)inTrieste,Italy;myoccasionaldutiesthereofferedmetheoppor- tunity to participate and lecture at Julia´n Chela Flores’ fascinating astrobi- ology and neurobiology summer schools and symposia. This put me back on trackintheinterdisciplinary“troika”ofbrainscience,informationtheoryand physics. Of substantial influence on my thinking were several publications, most notably B.-O. Ku¨ppers’ book “Information and the Origin of Life” [64] and J. Bricmont’s article “Science of Chaos or Chaos of Science?” [21], as wellasenlighteningdiscussionswithValentinoBraitenbergathiscastle(yes, it is a castle!) in Merano, Italy. I am deeply indebted to Geophysical Institute Director Roger Smith and ICTP Director Katepalli Sreenivasan for their personal encouragement and institutional support of my work for this book. Without the help of X Preface the Geophysical Institute Digital Design Center and the competent work of KirillMauritswhoproducedtheillustrations,andwithoutthediligentcoop- erationoftheICTPLibrarystaff,particularlychieflibrarianMariaFasanella, the preparation of the manuscript would not have been possible. MyspecialgratitudegoestoValentinoBraitenbergoftheMaxPlanckIn- stituteforBiologicalCyberneticsinTu¨bingen,mysonMarioRoedererofthe National Institutes of Health in Bethesda, Maryland, GianCarlo Ghirardi of theICTPandtheUniversityofTrieste,DanielBesoftheUniversityFavaloro inBuenosAires,andGlennShawoftheUniversityofAlaskaFairbanks,who have read drafts of the manuscript and provided invaluable comments, criti- cism and advice. And without the infinite patience, tolerance and assistance of my wife Beatriz, this book would never have materialized. Juan G. Roederer Geophysical Institute, University of Alaska Fairbanks and The Abdus Salam International Centre for Theoretical Physics, Trieste http://www.gi.alaska.edu/∼Roederer February 2005 Contents Introduction.................................................. 1 1 Elements of Classical Information Theory................. 7 1.1 Data, Information and Knowledge: The “Conventional Wisdom”.............................................. 7 1.2 Playing with an Idealized Pinball Machine................. 11 1.3 Quantifying Statistical Information ....................... 14 1.4 Algorithmic Information, Complexity and Randomness...... 23 1.5 TheClassicalBitor“Cbit”:APreludetoQuantumComputing 28 1.6 Objective and Subjective Aspects of Classical Information Theory................................................ 32 2 Elements of Quantum Information Theory................ 35 2.1 Basic Facts about Quantum Mechanics.................... 36 2.2 Playing with a Quantum Pinball Machine ................. 43 2.3 The Counterintuitive Behavior of Quantum Systems ........ 48 2.4 Basic Algorithms for Single-Particle Quantum Systems ...... 51 2.5 Physics of the Mach–Zehnder Interferometer ............... 54 2.6 Polarized Photons ...................................... 61 2.7 Quantum Bits, Quantum Information and Quantum Computing ............................................ 64 2.8 Entanglement and Quantum Information .................. 69 2.9 Dense Coding, Teleportation and Quantum Information ..... 75 3 Classical, Quantum and Information-Driven Interactions.. 79 3.1 The Genesis of Complexity and Organization .............. 81 3.2 Classical Interaction Mechanisms ......................... 90 3.3 Classical Force Fields ................................... 98 3.4 Quantum Interactions and Fields ......................... 105 3.5 Information-Driven Interactions and Pragmatic Information.. 111 3.6 Connecting Pragmatic Information with Shannon Information 121 4 The “Active” Role of Information in Biological Systems .. 125 4.1 Patterns, Images, Maps and Feature Detection ............. 126 4.2 Representation of Information in the Neural System ........ 132 XII Contents 4.3 Memory, Learning and Associative Recall.................. 140 4.4 Representation of Information in Biomolecular Systems ..... 148 4.5 Information and Life.................................... 155 5 The ‘Passive’ Role of Information in Physics.............. 161 5.1 Turning Observations into Information and Knowledge ...... 162 5.2 Models, Initial Conditions and Information ................ 166 5.3 Reversibility, Determinism and Information ................ 170 5.4 Microstates and Macrostates............................. 173 5.5 Entropy and Information ................................ 181 5.6 Physical Laws, Classical and Quantum Measurements, and Information........................................ 187 6 Information and the Brain................................ 199 6.1 What the Brain Does and What It Does Not............... 199 6.2 Sensory Input to the Brain: Breaking Up Information into Pieces............................................. 207 6.3 Information Integration: Putting the Pieces Together Again.. 213 6.4 Feelings, Consciousness, Self-Consciousness and Information . 217 6.5 “Free Will” and the “Mind–Body Problem”................ 223 References.................................................... 225 Index......................................................... 231
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