Cover image for Science in the looking glass : what do scientists really know?
Science in the looking glass : what do scientists really know?
Davies, E. B. (Edward Brian)
Publication Information:
Oxford ; New York : Oxford University Press, 2003.
Physical Description:
x, 295 pages : illustrations ; 25 cm
Perception and language -- Theories of the mind -- Arithmetic -- How hard can problems get? -- Pure mathematics -- Mechanics and astronomy -- Probability and quantum theory -- Is evolution a theory? -- Against reductionism -- Some final thoughts.
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Q175.3 .D39 2003 Adult Non-Fiction Central Closed Stacks

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In this wide-ranging book, Brian Davies discusses the basis for scientists' claims to knowledge about the world. He looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. He rejects the claim that all scientificknowledge is provisional, by citing examples from chemistry, biology and geology. A major feature of the book is its defence of the view that mathematics was invented rather than discovered. A large number of examples are used to illustrate these points, and many of the deep issues in today's worlddiscussed - from psychology and evolution to quantum theory, consciousness and even religious belief. Disentangling knowledge from opinion and aspiration is a hard task, but this book provides a clear guide to the difficulties.

Author Notes

Educated at the University of Oxford, Brian Davies is Professor of Mathematics at King's College, London and a Fellow of the Royal Society. He developed the theory of open quantum systems, writing a monograph on the subject, which became the standard text. He has published almost 300 articles and four books on subjects ranging from quantum theory to pure mathematics, and is currently working in both computational analysis and the philosophy of science. He has held visiting positions at a number of leading universities in Europe and the USA.

Reviews 1

Choice Review

Contemplating the nature of scientific knowledge as that knowledge is reflected in an unforgiving empiricist mirror, Davies (mathematics, King's College, London) has produced a wholly engrossing, highly readable, immensely wise, though at times curmudgeonly, study. But reader beware--Davies is anything if not opinionated, and he is forthright about those opinions as well. Perhaps surprising for an author mathematician, the theme that threads its way through the book--whether the chapter subject is mind, astronomy, quantum physics, physiology, evolution, or mathematics itself--is that there is no basis for seeing mathematics as anything other than a fallible, convenient, invented tool--end of mystery. Stating that opinion has Davies frankly chastising colleague Roger Penrose ("Penrose's idea ... is simply wrong"), Kurt Godel ("... can only serve to confuse"), and Steven Weinberg ("I have struggled to understand what he means ..."). Nor does Davies refrain from other bracing first-person interjections. Still, there is so much in this book that is brilliantly synthesized, eloquently written about, and, yes, persuasively argued as to make it a near indispensable contribution to the literature. A small drawback is an inadequate index, to be remedied, one hopes, in a second edition. ^BSumming Up: Highly recommended. General readers; upper-division undergraduates through faculty. M. Schiff College of Staten Island, CUNY

Table of Contents

1 Perception and Languagep. 1
1.1 Preamblep. 1
1.2 Light and Visionp. 3
Introductionp. 3
The Perception of Colourp. 4
Interpretation and Illusionp. 6
Disorders of the Brainp. 13
The World of a Batp. 15
What Do We See?p. 16
1.3 Languagep. 18
Physiological Aspects of Languagep. 18
Social Aspects of Languagep. 22
Objects, Concepts, and Existencep. 24
Numbers as Social Constructsp. 27
Notes and Referencesp. 31
2 Theories of the Mindp. 33
2.1 Preamblep. 33
2.2 Mind-Body Dualismp. 34
Platop. 34
Mathematical Platonismp. 37
The Rotation of Trianglesp. 41
Descartes and Dualismp. 43
Dualism in Societyp. 46
2.3 Varieties of Consciousnessp. 49
Can Computers Be Conscious?p. 50
Godel and Penrosep. 52
Discussionp. 54
Notes and Referencesp. 59
3 Arithmeticp. 61
Introductionp. 61
Whole Numbersp. 62
Small Numbersp. 62
Medium Numbersp. 64
Large Numbersp. 65
What Do Large Numbers Represent?p. 66
Additionp. 67
Multiplicationp. 68
Inaccessible and Huge Numbersp. 71
Peano's Postulatesp. 75
Infinityp. 78
Discussionp. 80
Notes and Referencesp. 83
4 How Hard can Problems Get?p. 85
Introductionp. 85
The Four Colour Problemp. 87
Goldbach's Conjecturep. 88
Fermat's Last Theoremp. 89
Finite Simple Groupsp. 90
A Practically Insoluble Problemp. 91
Algorithmsp. 93
How to Handle Hard Problemsp. 96
Notes and Referencesp. 97
5 Pure Mathematicsp. 99
5.1 Introductionp. 99
5.2 Originsp. 100
Greek Mathematicsp. 100
The Invention of Algebrap. 103
The Axiomatic Revolutionp. 103
Projective Geometryp. 107
5.3 The Search for Foundationsp. 109
5.4 Against Foundationsp. 113
Empiricism in Mathematicsp. 116
From Babbage to Turingp. 117
Finite Computing Machinesp. 123
Passage to the Infinitep. 125
Are Humans Logical?p. 127
5.5 The Real Number Systemp. 130
A Brief Historyp. 131
What is Equality?p. 134
Constructive Analysisp. 135
Non-standard Analysisp. 137
5.6 The Computer Revolutionp. 138
Discussionp. 139
Notes and Referencesp. 140
6 Mechanics and Astronomyp. 143
6.1 Seventeenth Century Astronomyp. 143
Galileop. 146
Keplerp. 151
Newtonp. 153
The Law of Universal Gravitationp. 154
6.2 Laplace and Determinismp. 157
Chaos in the Solar Systemp. 158
Hyperionp. 160
Molecular Chaosp. 161
A Trip to Infinityp. 163
The Theory of Relativityp. 164
6.3 Discussionp. 166
Notes and Referencesp. 170
7 Probability and Quantum Theoryp. 171
7.1 The Theory of Probabilityp. 171
Kolmogorov's Axiomsp. 172
Disaster Planningp. 174
The Paradox of the Childrenp. 175
The Letter Paradoxp. 175
The Three Door Paradoxp. 176
The National Lotteryp. 177
Probabilistic Proofsp. 178
What is a Random Number?p. 179
Bubbles and Foamsp. 181
Kolmogorov Complexityp. 182
7.2 Quantum Theoryp. 183
History of Atomic Theoryp. 184
The Key Enigmap. 186
Quantum Probabilityp. 188
Quantum Particlesp. 190
The Three Aspects of Quantum Theoryp. 192
Quantum Modellingp. 193
Measuring Atomic Energy Levelsp. 195
The EPR Paradoxp. 196
Reflectionsp. 198
Schrodinger's Catp. 199
Notes and Referencesp. 202
8 Is Evolution a Theory?p. 203
Introductionp. 203
The Public Perceptionp. 204
The Geological Recordp. 205
Dating Techniquesp. 209
The Mechanisms of Inheritancep. 213
Theories of Evolutionp. 217
Some Common Objectionsp. 225
Discussionp. 230
Notes and Referencesp. 232
9 Against Reductionismp. 235
Introductionp. 235
Biochemistry and Cell Physiologyp. 238
Prediction or Explanationp. 240
Moneyp. 242
Information and Complexityp. 243
Subjective Consciousnessp. 245
The Chinese Roomp. 246
Zombies and Related Issuesp. 248
A Physicalist Viewp. 250
Notes and Referencesp. 251
10 Some Final Thoughtsp. 253
Order and Chaosp. 253
Anthropic Principlesp. 256
From Hume to Popperp. 259
Empiricism versus Realismp. 266
The Sociology of Sciencep. 270
Science and Technologyp. 274
Conclusionsp. 276
Notes and Referencesp. 279
Bibliographyp. 281
Indexp. 289