How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong?
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 defence of the view that mathematics was invented rather than discovered. While experience has shown that disentangling knowledge from opinion and aspiration is a hard task, this book provides a clear guide to the difficulties.
1. Perception and Language; 2. Theories of the Mind; 3. Arithmetic; 4. How Hard can Problems get?; 5. Pure Mathematics; 6. Mechanics and Astronomy; 7. Probability and Quantum Theory; 8. Is Evolution a Theory?; 9. Against Reductionism; 10. Some Final Thoughts
...it is a brilliant work, beautifully written, and brimming with surprising information and stimulating philosophical speculations. Notices of the AMS, December 2005, Volume 52, Number 11. ... the leading mathematician E. Brian Davies is a refreshingly dissident voice ... One of the most impressive aspects of Davies' treatment is its breadth - he covers both the physical and life sciences and touches on philosophy ... those who read the book will find much to set them thinking, especially about the blind worship of mathematics that is often taken for granted in popular science books. The Times Higher Education Supplement ... all professionals are sure to learn something new ... I feel justified in commending this well-written book to the readership of Materials Today ... This will not help the reader to design a spintronic device, improved magnetic memory, or photonic 'crystal', but will reassure that, as a scientist in the 21st century, he or she is heir to an enormously varied and honorable tradition. Looking backwards contentedly leads to looking forward hopefully. materialstoday Science in the Looking Glass is worth reading in your leisure time. It is stimulating even when you disagree with the author. Physics Today Davies writes in an accessible, non-technical style. He favours concrete examples and down-to-earth refutations. He is not interested in engaging in the layers of scholarship and theoretical debates that surround virtually every idea that he examines, preferring instead to carve his own uncluttered path through the issue. This allows him to move swiftly and to cover much terrain ... The result can be fresh and exhilarating. Brian Rotman, Times Literary Supplement Science in the Looking Glass is an original and superbly intelligent attempt by someone who knows and loves the subject, to challenge the misconceptions and transcendental mysteries that cling so beguilingly to mathematics. Brian Rotman, Times Literary Supplement The value of this book for a mathematician lies in a number of mathematical examples that one can use to popularize mathematics ... an interesting and fairly exciting reading. Zentralblatt MATH