Geometry and Meaning - Companion website

Author : Dominic Widdows

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Publisher : CSLI Publications

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Purchase here : University of Chicago Press

From the earliest applications in astronomy, music, and biology, to the design of today's user interfaces and search engines, geometric insights have provided powerful tools and accurate scientific predictions. In Geometry and Meaning, these threads are gathered together and told as a single evolving story. Mathematical models from ancient times to the present are described for the general reader, together with the stories behind their discovery, and their applications in the new and vibrant field of natural language processing.

As well as a historical survey, Geometry and Meaning presents startling new research to the scientific public for the first time. Computers can now learn about the meaning of a word just by reading every day documents, even recognizing ambiguity and idiom. The logic used to explore the meanings of an ambiguous word depends on whether the underlying spatial model is continuous or discrete, and this relates the design of search engines to one of today's great scientific mysteries - the relationship between classical physics and quantum mechanics. In a surprising conclusion, Aristotle, long thought of as a great scientist and philosopher but a poor mathematician, shines through as the unlikely hero of modern geometry.

Reviews

• Konstantinos Nedas, Amazon.com.
  "A wonderful work ... The strongest point of the book is its clarity."


• Annalisa Crannell, Mathematical Association of America.
  "I can say quite honestly that this book opened up a whole new world to me ... When I next teach Linear Algebra, I have a whole new set of examples close at hand."


• P. R. Van Emburg, Amazon.com.
  "A polymathic gem ... Science education is greatly enriched by books like "Geometry and Meaning"."


• Anthony J. Duben, Association for Computing Machinery, Computing Reviews.
  "This is an unusual book. It tackles the problem of representing meaning in human language mathematically, and it does so with style and substance ... It would be a good purchase for a library, and for many personal bookshelves."


• Andra Waagmeester, Universiteit Maastrict.
  "The world of sophie" was a brief but good introduction to Filosophy. "Geometry and Meaning" gives the same clear and brief introduction to Text Mining ... It reads like a novel and is very suitable as a book you read during traveling.


• Albert A. Mullin (Madison), Zentrallbatt Math.
  "This book will be most useful to the intelligent general reader interested in novel uses of mathematics, language and computers."


• Keith van Rijsbergen, Computational Linguistics. Prof. van Rijsbergen is the author of The Geometry of Information Retrieval.
  "It is an enjoyable read, as intended by the author, and succeeds as a sort of tourist guide to the subject at hand ... It may be the first steps along the way to recasting some old problems in terms of some new mathematics."


• Vikram Bhandoh, Amazon.co.uk
  "This is an excellent book. Widdows explains each of the concepts in great detail. You don't need a degree in maths to understand this book and if you want to find out a bit more about how search engines work then this the chapter on vectors and search engines is worth the price of the entire book."

Sample Chapter

Contents

Foreword, by Pentti Kanerva

Introduction and Timeline

Chapter 1. Geometry, Numbers and Sets

Chapter 2. The Graph Model: Networks of Concepts

Chapter 3. The Vertical Direction: Concept Hierarchies

Chapter 4. Measuring Similarity and Distance

Chapter 5. Word-Vectors and Search Engines

Chapter 6. Exploring Vector Spaces in One and More Languages

Chapter 7. Logic with Vectors: Ambiguous Words and Quantum States

Chapter 8. Concept Lattices: Binding Everything Loosely Together

Epilogue. Conclusions and Curtain Call

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Acknowledgments and Thanks

Typesetting and Programming

Errata

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