*E. Brian Davies*

- Published in print:
- 2007
- Published Online:
- September 2008
- ISBN:
- 9780199219186
- eISBN:
- 9780191711695
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219186.001.0001
- Subject:
- Physics, History of Physics

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? This book ...
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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? This book discusses the basis for scientists' claims to knowledge about the world. It looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. The book 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. Including many examples and quotations, and with a scope ranging from psychology and evolution to quantum theory and mathematics, this book aims to bring alive issues at the heart of all science.Less

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? This book discusses the basis for scientists' claims to knowledge about the world. It looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. The book 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. Including many examples and quotations, and with a scope ranging from psychology and evolution to quantum theory and mathematics, this book aims to bring alive issues at the heart of all science.

*David D. Nolte*

- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198805847
- eISBN:
- 9780191843808
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805847.003.0005
- Subject:
- Physics, History of Physics

This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who ...
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This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.Less

This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.