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Geometry and Meaning

Dominic Widdows

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 everyday 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.

Dominic Widdows received his doctorate in differential geometry from Oxford in 2000, after which he spent three years as a Senior Researcher at Stanford University's Center for the Study of Language and Information. He is now a Senior Research Engineer working for MAYA Design in Pittsburgh, Pennsylvania.

Visit the author's web site for Geometry and Meaning.



  • Foreword ix
  • Introduction xvi
  • 1 Geometry, Numbers and Sets 1
  • 2 The Graph Model: Networks of Concepts 41
  • 3 The Vertical Direction: Concept Hierarchies 68
  • 4 Measuring Similarity and Distance 98
  • 5 Word-Vectors and Search Engines 132
  • 6 Exploring Vector Spaces in One and More Languages 167
  • 7 Logic with Vectors: AmbiguousWords and Quantum States 200
  • 8 Concept Lattices: Binding Everything Loosely Together 246
  • Conclusions and Curtain Call 289
  • References 304
  • Index 314

ISBN (Paperback): 9781575864488 (1575864487)
ISBN (electronic): 9781575866468 (released May 2013)

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