Science in the Looking Glass What Do Scientists Really Know?

by Davies, E. Brian

• ISBN13: 9780198525431
• ISBN10: 0198525435
• Format: Hardcover
• Copyright: 2003-10-09
• Publisher: Oxford University Press

Summary

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 scientific knowledge is provisional, by citing examples from chemistry, biology and geology. A major feature of the book is its defense 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 world discussed-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 provided a clear guide to the difficulties.

Author Biography

E Brian Davies, Tutorial Fellow at St John's College, Oxford in 1970 and one of two editors for the Quarterly Journal of Mathematics, Oxford. Developed the theory of open quantum systems, writing a monograph on the subject, which became the standard text. Appointed to the Chair of Pure Mathematics at King's College, London in 1981 and researched heat kernels and spectral theory. Subsequently became a Fellow of the Royal Society in 1995. His monograph on heat kernels, involving several hundred publications and having applications in many parts of mathematics, is the authoritative text on the subject. Founded the London Mathematical Society Student Text Series in the 1980s, and has recently become Senior Editor for the LMS Monographs. Has previously been a member of the National Advisory Board of the Isaac Newton Institute and sat on the Research Assessment Exercise Panel for Pure Mathematics in 2001. Published over 180 papers.

Table of Contents

Perception and Language	1	(32)
Preamble	1	(2)
Light and Vision	3	(15)
Introduction	3	(1)
The Perception of Colour	4	(2)
Interpretation and Illusion	6	(7)
Disorders of the Brain	13	(2)
The World of a Bat	15	(1)
What Do We See?	16	(2)
Language	18	(15)
Physiological Aspects of Language	18	(4)
Social Aspects of Language	22	(2)
Objects, Concepts, and Existence	24	(3)
Numbers as Social Constructs	27	(4)
Notes and References	31	(2)
Theories of the Mind	33	(28)
Preamble	33	(1)
Mind-Body Dualism	34	(15)
Plato	34	(3)
Mathematical Platonism	37	(4)
The Rotation of Triangles	41	(2)
Descartes and Dualism	43	(3)
Dualism in Society	46	(3)
Varieties of Consciousness	49	(12)
Can Computers Be Conscious?	50	(2)
Godel and Penrose	52	(2)
Discussion	54	(5)
Notes and References	59	(2)
Arithmetic	61	(24)
Introduction	61	(1)
Whole Numbers	62	(1)
Small Numbers	62	(2)
Medium Numbers	64	(1)
Large Numbers	65	(1)
What Do Large Numbers Represent?	66	(1)
Addition	67	(1)
Multiplication	68	(3)
Inaccessible and Huge Numbers	71	(4)
Peano's Postulates	75	(3)
Infinity	78	(2)
Discussion	80	(3)
Notes and References	83	(2)
How Hard can Problems Get?	85	(14)
Introduction	85	(2)
The Four Colour Problem	87	(1)
Goldbach's Conjecture	88	(1)
Fermat's Last Theorem	89	(1)
Finite Simple Groups	90	(1)
A Practically Insoluble Problem	91	(2)
Algorithms	93	(3)
How to Handle Hard Problems	96	(1)
Notes and References	97	(2)
Pure Mathematics	99	(44)
Introduction	99	(1)
Origins	100	(9)
Greek Mathematics	100	(3)
The Invention of Algebra	103	(1)
The Axiomatic Revolution	103	(4)
Projective Geometry	107	(2)
The Search for Foundations	109	(4)
Against Foundations	113	(17)
Empiricism in Mathematics	116	(1)
From Babbage to Turing	117	(6)
Finite Computing Machines	123	(2)
Passage to the Infinite	125	(2)
Are Humans Logical?	127	(3)
The Real Number System	130	(8)
A Brief History	131	(3)
What is Equality?	134	(1)
Constructive Analysis	135	(2)
Non-standard Analysis	137	(1)
The Computer Revolution	138	(5)
Discussion	139	(1)
Notes and References	140	(3)
Mechanics and Astronomy	143	(28)
Seventeenth Century Astronomy	143	(14)
Galileo	146	(5)
Kepler	151	(2)
Newton	153	(1)
The Law of Universal Gravitation	154	(3)
Laplace and Determinism	157	(9)
Chaos in the Solar System	158	(2)
Hyperion	160	(1)
Molecular Chaos	161	(2)
A Trip to Infinity	163	(1)
The Theory of Relativity	164	(2)
Discussion	166	(5)
Notes and References	170	(1)
Probability and Quantum Theory	171	(32)
The Theory of Probability	171	(12)
Kolmogorov's Axioms	172	(2)
Disaster Planning	174	(1)
The Paradox of the Children	175	(1)
The Letter Paradox	175	(1)
The Three Door Paradox	176	(1)
The National Lottery	177	(1)
Probabilistic Proofs	178	(1)
What is a Random Number?	179	(2)
Bubbles and Foams	181	(1)
Kolmogorov Complexity	182	(1)
Quantum Theory	183	(20)
History of Atomic Theory	184	(2)
The Key Enigma	186	(2)
Quantum Probability	188	(2)
Quantum Particles	190	(2)
The Three Aspects of Quantum Theory	192	(1)
Quantum Modelling	193	(2)
Measuring Atomic Energy Levels	195	(1)
The EPR Paradox	196	(2)
Reflections	198	(1)
Schrodinger's Cat	199	(3)
Notes and References	202	(1)
Is Evolution a Theory?	203	(32)
Introduction	203	(1)
The Public Perception	204	(1)
The Geological Record	205	(4)
Dating Techniques	209	(4)
The Mechanisms of Inheritance	213	(4)
Theories of Evolution	217	(8)
Some Common Objections	225	(5)
Discussion	230	(2)
Notes and References	232	(3)
Against Reductionism	235	(18)
Introduction	235	(3)
Biochemistry and Cell Physiology	238	(2)
Prediction or Explanation	240	(2)
Money	242	(1)
Information and Complexity	243	(2)
Subjective Consciousness	245	(1)
The Chinese Room	246	(2)
Zombies and Related Issues	248	(2)
A Physicalist View	250	(1)
Notes and References	251	(2)
Some Final Thoughts	253	(28)
Order and Chaos	253	(3)
Anthropic Principles	256	(3)
From Hume to Popper	259	(7)
Empiricism versus Realism	266	(4)
The Sociology of Science	270	(4)
Science and Technology	274	(2)
Conclusions	276	(3)
Notes and References	279	(2)
Bibliography	281	(8)
Index	289