Geometry and Meaning - Companion website
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
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.
Here are links to the reviews that Geometry and Meaning has
received. Please contact the author if you are aware of others.
Konstantinos Nedas, Amazon.com.
"A wonderful work ... The strongest point of the book is its clarity."
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."
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."
Chapter 5, Word Vectors and Search Engines, was used for the
2003 Computational Word Learning course at Stanford. You can download
this as a sample chapter.
The links below contain the introductory section to each chapter, and
a summary of the contents of each section. Some of these summaries are
still under development.
Foreword, by Pentti Kanerva
Introduction and Timeline
Geometry, Numbers and Sets
The Graph Model: Networks of
The Vertical Direction: Concept Hierarchies
Measuring Similarity and Distance
Word-Vectors and Search Engines
Exploring Vector Spaces in One and
Logic with Vectors: Ambiguous Words
and Quantum States
Concept Lattices: Binding
Everything Loosely Together
Conclusions and Curtain Call
Acknowledgments and Thanks
Typesetting and Programming
Last modified: Sun Sep 18 21:47:06 EDT 2005
Dominic Widdows, Geometry and Meaning : Dominic Widdows, Geometry and
Meaning : Apologies for this repetition, "widdows geometry and
meaning" is the query suggested at the end of the book, I had better
make sure it works, and this query is bringing up a lot of library
catalogue listings now! : Dominic Widdows, Geometry and Meaning :
Dominic Widdows, Geometry and Meaning