Impossibility : The Limits of Science and the Science of Limits

John Barrow is increasingly recognized as one of our most elegant and accomplished science writers, a brilliant commentator on cosmology, mathematics, and modern physics. Barrow now tackles the heady topic of impossibility, in perhaps his strongest book yet. Writing with grace and insight, Barrow argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. He first examines the limits on scientific inquiry imposed by the deficiencies of the human mind: our brain evolved to meet the demands of our immediate environment, Barrow notes, and much that lies outside this small circle may also lie outside our understanding. Barrow investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines the deeper theoretical restrictions on our ability to know, including Godel's theorem--which proved that there were things that could not be proved--and Arrow's Impossibility theorem about democratic voting systems. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. For instance, if the secrets of the atom are to be found only by recreating extreme environments at great financial cost, just how much should we devote to that quest? Weaving together this intriguing tapestry, he illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe. Title 2 Preface 3 Contents 6 Chapter 1: The art of the impossible 9 The power of negative thinking 9 Of faces and games 11 Those for whom all things are possible 15 Paradox 20 Visual paradox 21 Linguistic paradox 27 Limits to certainty 29 A cosmic speed limit 32 Summary 34 Chapter 2 : The hope of progress 35 Over the rainbow 35 The voyage to Polynesia via Telegraph Avenue 39 Progress and prejudice 45 The big idea of unlimited knowledge 49 Negativism 53 Some nineteenth-century ideas of the impossible 56 Summary 63 Chapter 3 : Back to the future 65 What do we mean by the limits of science? 65 Possible futures 66 Higgledy-piggledyology 73 Selective and absolute limits 76 Will we be builders or surgeons? 78 The futures market 80 How many discoveries are there still to be made? 91 Summary 92 Chapter 4 : Being human 93 What are minds for? 93 Counting on words 99 Modern art and the death of a culture 101 Complexity matching: climbing Mount Improbable 104 Intractability 108 The frontier spirit 115 The end of diversity 117 Does science always bring about its own demise? 119 Death and the death of science 121 The psychology of limits 122 Summary 124 Chapter 5 : Technological limits 126 Is the Universe economically viable? 126 Why we are where we are 128 Some consequences of size 130 The forces of Nature 133 Manipulating the Universe 136 Criticality: the riddle of the sands 146 Demons: counting the cost 150 Two types of future 155 Is technological progress inevitable ( or always desirable) ? - a fable 158 Summary 161 Chapter 6 : Cosmological limits 163 The last horizon 163 Inflation - still crazy after all these years 172 Chaotic inflation 177 Is the Universe open or closed? 178 Eternal inflation 179 The natural selection of universes 182 Topology 184 Did the Universe have a beginning? 186 Naked singularities: the final frontier 190 Dimensions 192 Symmetry-breaking 193 Summary 196 Chapter 7 : Deep limits 198 Patterns in reality 198 Paradoxes 203 Consistency 205 Time travel: is the Universe safe for historians? 207 Completeness 215 Impossible constructions 219 Metaphorical impossibilities 223 Summary 224 Chapter 8 : Impossibility and us 226 Gödel's theorem and physics 226 Does Gödel stymie physics? 229 Gödel, logic, and the human mind 238 The problem of free will 240 The reaction game 244 Mathematics that comes alive 246 A stranger sort of impossibility 247 The Arrow Impossibility Theorem 250 Summary 254 Chapter 9 : Impossibility: taking stock 256 Telling what is from what isn't 256 Notes 261 Chapter 1 261 Chapter 2 263 Chapter 3 267 Chapter 4 269 Chapter 5 270 Chapter 6 274 Chapter 7 276 Chapter 8 278 ISBN:,0198518900 In this book, John D. Barrow argues that there are limits to human discovery, that some phenomena are ultimately unknowable, undoable, or unreachable. He first examines the limits of the human mind: our brain evolved to meet the demands of our immediate environment, and much that lies outside this small circle may also lie ouside our understanding. He also investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? And if our knowledge of the cosmos is limited, is this also true for our technological knowledge? While pondering such questions, Impossibility studies the deeper theoretical restrictions on what we can and cannot know, including Godel's theorem, which proved certain things could not be proved. Finally, having explored the scientific limits imposed on us from without, the book considers whether there are limits we should impose on ourselves. Along the way, it illuminates some of the most profound questions of physics, from the possibility of time travel to the structure of the universe. In Impossibility, John D. Barrow - one of our most elegant and accomplished science writers - argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. Barrow first examines the limits of the human mind: our brain evolved to meet the demands of our immediate environment, and much that lies outside this small circle may also lie outside our understanding. He investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines deeper theoretical restrictions on our ability to know, including Godel's theorem, which proved that there were things that could not be proved. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. Weaving together this intriguing tapestry, Barrow illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe. Explores The Frontiers Of Knowledge, Discussing The Restrictions That May Be Imposed Upon A Full Understanding Of The Physical Universe By The Limits Of Technology, Computers, Cost, And Complexity; And Considering How The Mind's Awareness Of The Impossible Influences Perceptions Of Reality. Explores The Frontiers Of Knowledge, Discussing The Restrictions That May Be Imposed Upon A Full Understanding Of The Physical Universe By The Limits Of Technology, Computers, Cost, And Complexity; And Considering How The Mind's Awareness Of The Impossible Influences Perceptions Of Reality. John D. Barrow. Includes Bibliographical References (p. [253]-274) And Index. Illuminating some of the most profound questions faced by science, the author demonstrates the limitations imposed on human knowledge and discovery by evolution, possibility, ethics, and other factors