Descartes' Dream The World According to Mathematics

by Davis, Philip J.; Hersh, Reuben

• ISBN13: 9780486442525
• ISBN10: 0486442527
• Format: Paperback
• Copyright: 2005-03-24
• Publisher: Dover Publications

Summary

These provocative essays take a modern look at the seventeenth-century thinker's dream, examining the influences of mathematics on society, particularly in light of technological advances. They survey the conditions that elicit the application of mathematic principles; the applications' effectiveness; and how applied mathematics transform perceptions of reality. 1987 edition.

Author Biography

Philip J. Davis is Professor Emeritus, Division of Applied Mathematics, Brown University Reuben Hersh is Professor Emeritus, University of New Mexico, Albuquerque

Table of Contents

Preface	p. xi
Acknowledgements	p. xvii
This Mathematized World	p. 1
Descartes' Dream	p. 3
Where the Dream Stands Today	p. 9
The Limits of Mathematics	p. 13
Are We Drowning in Digits?	p. 15
The Stochastized World: A Matter of Style?	p. 18
Feedback and Control: The Equilibrium Machine	p. 33
Computer Graphics and the Possibility of High Art	p. 43
The Social Tyranny of Numbers	p. 55
Mathematics and Rhetoric	p. 57
The Criterion Makers: Mathematics and Social Policy	p. 74
The Computerization of Love	p. 87
Testing	p. 93
Mathematics as a Social Filter	p. 99
A "Marxian" Analysis of the Role of Computing in Organizations	p. 105
Cognition and Computation	p. 113
The Descriptive, Predictive, and Prescriptive Functions of Applied Mathematics	p. 115
The Intellectual Components of Technology, Mathematics and Computation: Four Lists	p. 122
Metathinking as a Way of Life	p. 132
Three Meanings of Computation	p. 139
What Scientific Computation is for	p. 154
Why Should I Believe a Computer: Computation as Process and Product	p. 159
The Whorfian Hypothesis: Ends and Means in Computer Languages	p. 165
The Programming Milieu	p. 179
Perspectives Through Time	p. 187
Of Time and Mathematics	p. 189
Non-Euclidean Geometry and Ethical Relativism	p. 203
The Unreasonable Effectiveness of Computers. Are We Hooked?	p. 218
Mathematics and Ethics	p. 229
Platonic Mathematics Meets Platonic Philosophy of Religion: An Ethical Metaphor	p. 231
The Computer Thinks: An Interpretation in the Medieval Mode	p. 240
Mathematics and the End of the World	p. 262
Personal Meanings	p. 269
Mathematics and Imposed Reality	p. 271
Loss of Meaning through Intellectual Processes: Mathematical Abstraction	p. 278
Envoi	p. 301
Bibliography	p. 307
Index	p. 317
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