Astrolinguistics

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Astrolinguistics

Alexander Ollongren

Astrolinguistics

Design of a Linguistic System for Interstellar Communication Based on Logic Alexander Ollongren Advanced Computer Science Leiden University Leiden The Netherlands

ISBN 978-1-4614-5467-0 ISBN 978-1-4614-5468-7 (eBook) DOI 10.1007/978-1-4614-5468-7 Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2012945935

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Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com) To the memory of Prof. Dr. Hans Freudenthal and to Gunvor Ollongren

Preface

In my perception the author of the present book appeared all of a sudden “from elsewhere” on the scene of academics and others concerned with various projects in the fi eld of the search for extraterrestrial intelligence (SETI). This was in 1998. Dr. Ollongren’s entrance in the fi eld was due to a change in his research interests. They had apparently shifted from dynamical astronomy and theoretical computer science to the topic of the art and science of communication with extraterrestrial intelligence (CETI)—closely related to my work at the SETI Institute. His approach was and is, however, completely different from mine where human psychology is always prominently present in the background. This emeritus professor, astronomer, and theoretician whom I got to know, had a keen interest and experience in mathematics and logic. He seemed, though hesitatingly, prepared to consider formally modeling psychological aspects of human behavior in connection with interstellar message construction for possible contacts with alien highly developed intelligent societies. I, on the other hand, recognized immediately that Dr. Ollongren’s approach for the design of a Lingua Cosmica was fundamentally new, rested on a solid and sound base in logic, and carried great potential for applications. His LINCOS has only very little in common with the interesting language for cosmic intercourse of the same name introduced in 1960 by his fellow countryman and colleague Professor Hans Freudenthal. The present book describes the new LINCOS, also at work. This lingua with a simple formal language at the base is actually a system because of the multilevel structure as explained in the book. Certain aspects of the system are in my view most remarkable. The fact that LINCOS assertions can (and need to) be verifi ed within LINCOS itself means that the system is strongly self-contained—a property of natural languages, but unusual for formal systems. The implication of this property (in fact considered to be a requirement in the design) is that formal assertions are always correct. This aspect in its turn has important consequences for the prob- lem of decoding and interpretation. An alien receiver of a message coded in Ollongren’s LINCOS can in principle apply a universal semantic engine for unrav- eling structural properties of the system. Furthermore there is the prominent absence of logical reasoning according to tertium non datur (the rejection of the law of the

vii viii Preface excluded middle)—not one of the fi rst concerns in my research in psychological aspects of human reasoning fi guring in the topic of construction of interstellar messages. The overall most important aspect and viewpoint of the material in this book is, however, that the linguistic system designed and employed is constructive and deterministic. An extension of the typing system employed to weak typing (involv- ing consequently non-determinism) and symbolic computing is innovative. Ways and means (with roots in intuitionism) for attaining all of this are explained in some detail. The erected framework with a beauty of its own is most useful for applications in and development of CETI. In my opinion efforts in the fi eld of construction of messages for ETI should also take into consideration possibilities of symbolically coding human behavior. Fortunately LINCOS has in the realm of declarative (i.e. introductive) sentences a practically unlimited capacity of describing static aspects of this kind. This is for example illustrated in Dr. Ollongren’s paper with a treatment of human morality in my as yet unpublished book. In addition there is also a potential for describing dynamic interactions between humans. Examples of these are provided in the present book. Humans exchanging information is one case studied and explained. Since human behavior often (indeed not always) exhibits logic structure, the new Lingua Cosmica provides a powerful apparatus for formal analysis of some classes of behavioral actions. Products of such analyses can in turn be sublimated in messages for ETI. I was very interested to learn that Springer has agreed to publish the present book as the relatively new discipline called astrolinguistics by the author is gaining importance all the time due to advances in observational astrophysics, astrochemis- try, and astrobiology, but of course also cosmology. Building stones for life as we know it exist in interstellar space. It is no exaggeration to state today that our galaxy apparently teems with planets; there is ample observational evidence of that. On at least one habitable planet the symbolic species living there is concerned with devel- oping methods and means enabling them to contact other completely unknown symbolic intelligent species. The views taken and the material presented in the present book can play a prominent role in the nontrivial efforts on Earth in this fi eld. I certainly hope that the book will attract a wide circle of readers and will help to advance future work on the construction of interstellar messages. I wish the book a bright future. Professor Douglas A. Vakoch PhD, SETI Institute and California Institute of Integral Studies, Mountain View, California, United States Contents

Part I Calculus of Constructions

1 Types and Declarations ...... 3 Intention ...... 3 Typed Entities ...... 3 Functions ...... 5 References ...... 7 2 Functions and Induction...... 9 Intention ...... 9 Constructing Entities ...... 9 Inductive Entities ...... 11 Facts ...... 14 Connectives, Continued ...... 16 Typing Existence and Equality ...... 17 Booleans ...... 19 3 Hypotheses ...... 23 Intention ...... 23 Contradictions ...... 23 Double negation ...... 25 Hypotheses ...... 28 Reference ...... 28 4 Higher Orders and Inductive Structures ...... 29 Intention ...... 29 The Combinators ...... 30 Bounded Matrjoshka ...... 32 Syntactic Structures ...... 35 Reference ...... 38

ix x Contents

Part II Facts

5 Simple Facts ...... 41 Intention ...... 41 Elementary Facts ...... 41 Non-elementary Facts, Elimination Applied ...... 43 Annotation 1 ...... 44 Annotation 2 ...... 45 Existence Revisited ...... 45 6 Compounds ...... 47 Intention ...... 47 Commutativity, Transitivity and Distributivity ...... 47 Modus Tollens ...... 48 Logic in Sentences ...... 48 Complexity of the Stage ...... 52 7 Aristotelian Theatre ...... 53 Intention, Logic of Sentences ...... 53 Simple Cases ...... 54 Aristotelian Conversions ...... 56 Logical Implications ...... 57 Figures ...... 60 Reference ...... 63 8 Wittgenstein’s Theatre ...... 65 Intention ...... 65 Introduction ...... 65 Verification Machinery ...... 67 Setting the Stage ...... 68 Simple Facts Verified ...... 69 Less Simple Facts Verified ...... 70 Generalisation, More Advanced Verifications ...... 73 Notes on Computer Implementation ...... 74

Part III Annotations in LINCOS

9 Logic Contents of Texts ...... 77 Intention ...... 77 Considerations ...... 77 An Ancient Text ...... 78 Message Content ...... 78 Simonides’ Definition of Justice ...... 80 Thrasymachos’ Definition of Justice ...... 80 Socrates’ Definition of Justice ...... 82 Discussion ...... 84 References ...... 84 10 An Astrolinguistic Experiment ...... 85 Intention ...... 85 About the Second Level ...... 85 The Experiment ...... 86 Interpretation ...... 89 The Experience Learns … ...... 90 Appendix ...... 91 References ...... 91 11 Aspects of Truth ...... 93 Intention ...... 93 Teaching Truth ...... 93 Verification of Truth ...... 95 Enriching the Environment ...... 97 Static Relations ...... 98 Super- and Subvenience ...... 99 12 Human Altruism ...... 101 Intention ...... 101 Introduction ...... 101 Altruism ...... 103 Moralism ...... 103 Types of Moral Behaviour ...... 104 Duty and Obligation ...... 105 Summary and Conclusion ...... 105 References ...... 108

Part IV Interpretation of LINCOS

13 Self-interpretation ...... 111 Caption ...... 111 Intention ...... 111 Disposing of ELIM ...... 112 Conjunction ...... 113 Disjunction ...... 114 Inductive Self-interpretation ...... 115 References ...... 116 14 Pictorial Representations ...... 117 Intention ...... 117 Pioneer Plaque ...... 117 A Course in Latin ...... 118 Individuals ...... 119 Intentions of Subjects ...... 121 Reference ...... 121

xi xii Contents

15 Representation of Music ...... 123 Intention ...... 123 Considerations ...... 123 Musical Units in Gamelan ...... 124 Gamelan Performance ...... 126 Explaining LINCOS ...... 128 Notes ...... 129 References ...... 130 16 Signature of LINCOS ...... 131 Intention ...... 131 Introduction ...... 131 Subjects and Predications Revisited ...... 132 Implication and Maps ...... 132 Subjects and Predications, an Example ...... 134 l and the Signature ...... 134 Note ...... 135 Reference ...... 135

Part V Processes in LINCOS

17 Representing Processes ...... 139 Intention ...... 139 Introduction ...... 139 Sequences ...... 140 Channels ...... 141 Example: Production of Strings of Symbols ...... 142 State Vectors ...... 142 Example: A Producer/Consumer System ...... 143 Example: A Producer/Client System ...... 144 Note ...... 145 18 Cooperating Sequential Processes ...... 147 Intention ...... 147 Introduction ...... 147 Concurrency ...... 148 Arbitration ...... 148 Five Dining Philosophers ...... 149 Conclusion ...... 150 References ...... 151 19 Hamlet in LINCOS ...... 153 Intention ...... 153 Introduction and Basics ...... 153 Parallel Processes ...... 154 The Arbiter for Parallel Processes ...... 155 Contents xiii

Application, Opening Act in Hamlet ...... 156 Conclusion ...... 158 References ...... 159

Part VI Symbolic Computation

20 Basics ...... 163 Intention ...... 164 Introduction ...... 164 LINCOS Enriched ...... 165 Metric Two-Dimensional Space ...... 167 Reference ...... 168 21 Relativistic Particle Motion ...... 169 Intention ...... 169 Non-relativistic Space ...... 169 Special Relativity Theory in LINCOS+ ...... 171 General Relativity (GRT) in LINCOS+ ...... 172 Conclusion ...... 174 Reference ...... 175 22 Two-Body Motion ...... 177 Intention ...... 177 Co-ordinates ...... 177 Orbital Elements ...... 178 Euclidean Metric ...... 179 Conclusion ...... 179 References ...... 179

Part VII (Un)Certainty

23 Certain Existence ...... 183 Intention ...... 183 Introduction ...... 183 Propositions Exist ...... 184 All and Lambda Binding ...... 184 All and Some in Existence Maps ...... 185 Procreation ...... 186 Conclusion ...... 188 Reference ...... 188 24 The Uncertain Alien ...... 189 Intention ...... 189 Background ...... 189 Peirce’s Law Uncertain ...... 190 Uncertainty Risks ...... 191 xiv Contents

Uncertainty Instead of Falsity ...... 192 An Open Question for ETI ...... 193 Notes ...... 194 Reference ...... 194

Appendix A: Declaration of Principles Concerning the Conduct of the Search for Extraterrestrial Intelligence ...... 195

Appendix B: Preliminaries ...... 197

Appendix C: History ...... 207

Appendix D: A Gentle Introduction to Lambda and Types...... 217

Appendix E: Postscriptum ...... 227

Appendix F: Summary in Russian ...... 239

Appendix G: Curriculum Vitae of Alexander Ollongren (* 1928, Sumatra) ...... 241

Index ...... 243 About the Author

Alexander Ollongren began his career as a mathematical astronomer at the Department of Astronomy in Leiden University in the Netherlands, where he obtained his PhD. He then left the university and worked almost 2 years at the Research Center of Celestial Mechanics at Yale University in the USA. Ollongren returned to Holland and became director of the newly established computer center of Leiden University. He spent a sabbatical leave as a visiting scientist at the IBM Laboratory in Vienna and was later appointed full professor of theoretical computer science at the Department of Computer Science of Leiden University. He was a guest professor in the same science for about a year at Linköping University in Sweden. After retirement he became a member of the Permanent Study Group Search for ExtraTerrestrial Intelligence (PSGSETI) of the International Astronautical Academy. He has written books and scientiﬁ c articles on the semantics of program- ming languages.