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T H E F R O N T I E R S C O L L E C T I O N Bernd-Olaf Küppers THE COMPUTABILITY OF THE WORLD How Far Can Science Take Us? 123 THE FRONTIERS COLLECTION Series editors Avshalom C. Elitzur Iyar The Israel Institute for Advanced Research, Rehovot, Israel e-mail: [email protected] Zeeya Merali Foundational Questions Institute, Decatur, GA 30031, USA e-mail: [email protected] T. Padmanabhan Inter University Centre for Astronomy and Astrophysics (IUCAA), Pune, India e-mail: [email protected] Maximilian Schlosshauer Department of Physics, University of Portland, Portland, OR 97203, USA e-mail: [email protected] Mark P. Silverman Department of Physics, Trinity College, Hartford, CT 06106, USA e-mail: [email protected] Jack A. Tuszynski Department of Physics, University of Alberta, Edmonton, AB T6G 1Z2, Canada e-mail: [email protected] Rüdiger Vaas Bild der wissenschaft, Redaktion Astronomie, Physik, 70771 Leinfelden‐Echterdingen, Germany e-mail: [email protected] THE FRONTIERS COLLECTION Series Editors A.C. Elitzur Z. Merali T. Padmanabhan M. Schlosshauer M.P. Silverman J.A. Tuszynski R. Vaas The books in this collection are devoted to challenging and open problems at the forefront of modern science, 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 thedeeper implicationsandfascinating questions involved.Taken asa whole,theseriesreflectstheneedforafundamentalandinterdisciplinaryapproach to modern science. Furthermore, it is intended to encourage active scientists in all areas to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, conscious- ness 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 Forafulllistofpublishedtitles,pleaseseebackofbookorspringer.com/series/5342 ü Bernd-Olaf K ppers The Computability of the World How Far Can Science Take Us? 123 Bernd-Olaf Küppers Munich Germany Translated by PaulWoolley Berlin Germany ISSN 1612-3018 ISSN 2197-6619 (electronic) THEFRONTIERS COLLECTION ISBN978-3-319-67367-7 ISBN978-3-319-67369-1 (eBook) https://doi.org/10.1007/978-3-319-67369-1 LibraryofCongressControlNumber:2017953800 TheoriginalversionofthisbookwaspublishedinGermanunderthetitle„DieBerechenbarkeitderWelt: GrenzfragenderexaktenWissenschaften“in2012byS.HirzelVerlag(Stuttgart). ©SpringerInternationalPublishingAG2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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 authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface “If one tries to discover something new in science, one should avoid following well-wornpaths.Alongthemthereisnothingtobegained.Instead,onehastoleave the road and to cross untrodden spaces”. This advice was given in the Age of Enlightenment by the German physicist GeorgChristophLichtenberg.Itcontainsavaluablenuggetoftruthaboutthenature of scientific progress. In fact, the ascendance of science in modern times has only beenpossiblebecausescience,againandagain,hascrossedborderlinestoabandon its well-trodden paths. Such border crossings are also the subject of this book. It asks the provocative question of the computability of the world. This is done by reference to the all-embracing phenomena that—in the traditional view—seem to lie beyond rig- orous scientific computability: life, time and history. Behind this hides the deeper question of whether the complex phenomena of our world, which are often loaded withsenseandmeaning,canbecomethesubjectofanabstractsciencethatisbased on experiments and mathematics. Howfar cantheexistence andthecolourfulvarietyofliving beings,theunique character of information and language, the compelling beauty of Nature, the mysterious essence of temporality and the singular historicity of the world be explained and understood within the framework of the exact sciences—which by their very nature are designed to investigate comparatively simple phenomena of our world? It is obvious that the philosophical question of the possibilities and limitsofhumanperceptionandknowledgewillalwaysresonatethroughoutthisset of problems. The chapters of this book are based upon lectures that I have given on various occasionsforinterdisciplinaryaudiences.Eachchapterhasbeenthoroughlyrevised andattunedtotheothers,withfurthermaterialadded,tomakeup(Ihope)aunified whole. Nevertheless, one has to regard this book, to use another phrase of Lichtenberg, as an “experiment with ideas”. As is characteristic of any true v vi Preface experimentinscience,theoutcomewillultimatelyonlyteachuswhichofourideas waswrong.Thisalsomustbeseenastheconsequenceofanopen-mindedscience, which is permanently changing and progressing. Munich, Germany Bernd-Olaf Küppers January 2012 Note on the English Edition The questions dealt with in this book were the subject of a series of lectures that I have given over the last 30 years, mainly in Germany. In order to make these lecturesaccessibletoawideraudience,thepublisherhasencouragedmetoprepare anEnglishtranslationandtoreviseandtoupdatethematthesametime.Aboveall, IhavefelttheneedtoimproveChaps.3and5,inwhichIhavenowincludedrecent advances in the objectification and quantification of semantic information. The researchinthisparticularfieldseemstometobeofgeneralrelevance:notonlyfor thescienceofinformationitself,butalsoforthetheoreticalfoundationsofmodern biology, which rests largely upon the concept of information. As far as possible, the references have been rearranged to include only articles and books published in English. Foreign-language quotations are taken verbatim from English translations of the originals wherever an authorized translation is available. All other quotations, mostly from German philosophy and literature of the eighteenth and nineteenth century, have been translated directly from the originalinclosecooperationwiththetranslatorofthisbook,PaulWoolley,whomI wish to thank for his dedicated work. Munich, Germany Bernd-Olaf Küppers July 2017 vii Contents 1 Is Absolute Knowledge of the World Possible?. . . . . . . . . . . . . . . . 1 1.1 The Dream of Parmenides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 In Search of the Archimedean Point of Knowledge. . . . . . . . . . . 3 1.3 Utopian Fallacies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 From the Absolute to the Relative . . . . . . . . . . . . . . . . . . . . . . . 11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 Are There Unsolvable World Enigmas? . . . . . . . . . . . . . . . . . . . . . 17 2.1 The “Ignorabimus” Controversy . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Crossing Boundaries in Science. . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 The Whole and Its Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Concerning Hypothetical Truth . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 We Must Search, We Will Search . . . . . . . . . . . . . . . . . . . . . . . 30 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 How Could Life Have Originated? . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1 What Is Life?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 How Complex Is Living Matter? . . . . . . . . . . . . . . . . . . . . . . . . 43 3.3 How Does Information Originate? . . . . . . . . . . . . . . . . . . . . . . . 50 3.4 Evolution in the Test-Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.5 Are We Alone in the Universe?. . . . . . . . . . . . . . . . . . . . . . . . . 61 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4 What Is Information? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1 Dimensions of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.2 Naturalism Versus Constructivism . . . . . . . . . . . . . . . . . . . . . . . 71 4.3 Information in Living Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.4 On the True Nature of Information . . . . . . . . . . . . . . . . . . . . . . 80 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 ix x Contents 5 Is Language a General Principle of Nature?. . . . . . . . . . . . . . . . . . 85 5.1 The Structure of Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.2 Towards a Radical Linguistic Turn . . . . . . . . . . . . . . . . . . . . . . 90 5.3 Approaching the Semantic Dimension of Language . . . . . . . . . . 93 5.4 The Language of Genes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6 Can the Beauty of Nature Be Objectified? . . . . . . . . . . . . . . . . . . . 103 6.1 Science and the Ideal of Beauty . . . . . . . . . . . . . . . . . . . . . . . . 104 6.2 Features of Natural Complexity. . . . . . . . . . . . . . . . . . . . . . . . . 106 6.3 Algorithms of Natural Beauty . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.4 What is Ultimately Beauty?. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7 What Is Time? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.1 The Thermodynamic Arrow of Time . . . . . . . . . . . . . . . . . . . . . 126 7.2 Weak and Strong Temporality. . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.3 Cosmological Foundations of Temporality . . . . . . . . . . . . . . . . . 136 7.4 The Entanglement of Time Modes. . . . . . . . . . . . . . . . . . . . . . . 140 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 8 Can History Be Condensed into Formulae? . . . . . . . . . . . . . . . . . . 145 8.1 History and Causal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 8.2 The Essence of Historicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 8.3 The World of Boundaries and Constraints . . . . . . . . . . . . . . . . . 153 8.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 9 Where Is Science Going? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 9.1 The Search for the Unity of Knowledge. . . . . . . . . . . . . . . . . . . 166 9.2 The General and the Particular . . . . . . . . . . . . . . . . . . . . . . . . . 168 9.3 Scientific Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.4 The Ascent of Structural Sciences . . . . . . . . . . . . . . . . . . . . . . . 176 9.5 Towards a Technology of Knowledge . . . . . . . . . . . . . . . . . . . . 179 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Figure Sources. .... .... .... ..... .... .... .... .... .... ..... .... 187 Author Index.. .... .... .... ..... .... .... .... .... .... ..... .... 189 Subject Index.. .... .... .... ..... .... .... .... .... .... ..... .... 191 Titles in This Series .... .... ..... .... .... .... .... .... ..... .... 195

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