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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000003820812 | QA141 C52 1994 | Open Access Book | Book | Searching... |
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Summary
Summary
The story of numbers is a rich, sweeping history that shows how our mathematical achievements contributed to the greatest innovations of civilization. Calvin Clawson, acclaimed author of Conquering Math Phobia, weaves a story of numbers that spans thousands of years. As Clawson so clearly shows, numbers are not only an intrinsic and essential thread in our modern lives, but have always been an integral part of the human psyche - knit into the very fabric of our identity as humans. Clawson travels back through time to the roots of the history of numbers. In exploring early human fascination with numbers, he unearths the clay beads, knotted ropes, and tablets used by our ancestors as counting tools. He then investigates how numeric symbols and concepts developed uniquely and independently in Meso-America, China, and Egypt. As he persuasively argues, the mathematical concepts that arose and flourished in the ancient world enabled the creation of architectural masterpieces as well as the establishment of vast trade networks. Continuing the journey, Clawson brings us to the elegant logic of numbers that soon came to distinguish itself as a discipline and the language of science. From the concepts of infinity contemplated by the Greeks to the complex numbers that are indispensable to scientists on the cutting edge of research today, Clawson breathes life and meaning into the history of great mathematical mysteries and problems. In this spirit of inquiry, he explores, in their times and places, the discovery of numbers that lie outside the province of counting, including irrational numbers, transcendentals, complex numbers, and the enormous transfinite numbers. The personalities and the creative feats surrounding each mathematical invention come alive vividly in Clawson's lucid prose. In this work of breathtaking scope, Clawson guides us through the wonders of numbers and illustrates their monumental impact on civilization.
Reviews 2
Booklist Review
The ability to use numbers is so basic to our existence that we rarely realize how sophisticated our number system is. It was not always so: early number systems were crude and cumbersome. Clawson takes us on a mathematical adventure that reveals the history of numbers as a reflection of the evolution of culture. He shows how this science was born out of necessity in agriculture and commerce, not out of virtue. As our technology progressed, so did our math, and from the Chinese, Mayans, and Greeks came new numerical concepts and increased abstractions. The views and discoveries of Pythagoras, Des~cartes, Gauss, and perhaps a dozen more heavy-hitters are discussed, with Clawson maintaining a sense of humor to keep it enjoyable. Even those with little knowledge of formal mathematics will find the first half of this book easy going; it gets a little sticky later, delving into irrational, infinite, and "really big" transfinite numbers. The text becomes pure philosophy at this point, but if the reader can stick with it, the experience will be worthwhile. ~--David Siegfried
Choice Review
Clawson makes his thesis very clear: numbers are so fundamental to human nature that we could not function without them. With history as context, he begins with the conscious notion of a number, then develops both the concept of and the need for the different types of numbers--counting, integers, rationals, irrationals, transcendentals, complex, and the transfinites. Interesting side trips are taken to explore the world of the prodigy-calculators, the numerical abilities of animals, the ontology of numbers, and fractal theory as being the "eye of God." Throughout, readers will find themselves arguing with Clawson's thesis and choice of content. For example, he not only defines mathematics too narrowly as "the study of numbers" but also assumes a very simplistic view when branching into the realms of philosophy, anthropology, psychology, and anatomy. Complemented by chapter endnotes, a useful glossary, and an adequate bibliography, the book will be a useful resource. General; undergraduate. J. Johnson; Western Washington University
Table of Contents
| Acknowledgments | p. vii |
| Introduction | p. 1 |
| Chapter 1 How Do We Count? | p. 5 |
| Chapter 2 Early Counting | p. 19 |
| Chapter 3 Counting in Other Species How Smart Are They? | p. 37 |
| Chapter 4 Ancient Numbers | p. 49 |
| Chapter 5 Chinese and New World Numbers | p. 77 |
| Chapter 6 Problems in Paradise p. 95 | |
| Chapter 7 the Negative Numbers | p. 121 |
| Chapter 8 Dealing with the Infinite | p. 135 |
| Chapter 9 Dedekind's Cut Irrational Numbers p. 161 | |
| Chapter 10 the Story of ¿ Transcendental Numbers | p. 181 |
| Chapter 11 Expanding the Kingdom Complex Numbers | p. 207 |
| Chapter 12 Really Big Transfinite Numbers | p. 223 |
| Chapter 13 the Genius Calculators | p. 233 |
| Chapter 14 What Does It All Mean? | p. 247 |
| Chapter 15 Numbers Past, Present, and Future | p. 263 |
| End Notes | p. 281 |
| Glossary | p. 289 |
| Bibliography | p. 299 |
| Index | p. 303 |
