Geometry and Meaning [Paperback]

Geometry and meaning is an amazing book. It discusses NLP (natural language processing) and how common geometric ideas and theories can be applied in NLP with often excellent or quite satisfactory results.

The strongest point of the book is its clarity. Widdows has a gift in writing. For a book that attempts to convey so many ideas it is surprisingly refreshing to see that it accomplishes its task with the minimal amount of jargon (if any at all indeed). Besides the main text, the insets with historic or scientific references are very enjoyable as well.

I would have personally preferred some more detail on the methods developed for similarity and distance in hierarchies in chapter 4 (there is only the formulae from Leacock's and Resnik's algorithms) as well as a more in-depth coverage of the word-document vector model in chapter 5. Still these details can be found by consulting the very detailed and carefully compiled bibliography at the end of the book.

With the exceptions of NLP experts who may find such a book rather simplistic and a reference to things they already know, I suspect that the rest of us who want a clear and consise introduction to the field will greatly benefit from it. And at such a reasonable price I dont see why any one interested in the subject wouldnt want this gem in their library.

A related book which makes a case for the application of geometry in the way humans reason and judge similarities between objects and concepts is Gardenfors' Conceptual Spaces--another wonderful book--albeit slightly more difficult to understand.

This book is a pleasant introduction to natural language processing (NLP) as used, for example, in the design and operation of internet search engines. In addition, it identifies a number of interdomanial connections, the most interesting one I consider to be that between NLP and quantum theory. Quantum theory is a subject many intellectuals once in their life pledge themselves to attempt to get a grasp of. To increase their chance of success they intend to restrict their effort to the theory's core. Typically, they cannot find suitable educational material. Texts on quantum mechanics appear to inextricably link the imagined core with a large body of structure perceived by the aspirant grasper as excess baggage. In postponing their attack their notion grows that the core is mathematical. Consequently, they resolve to attempt to get a grasp of the kind of math involved. Their intended first move is to learn just enough of it to be able to decide whether or not to immerse themselves in it to achieve a more complete understanding. Accordingly, they want a simple but informative exposition of what the mathematical core of quantum theory 'looks like'. Dominic Widdows most admirably succeeds in providing an essential part of such an exposition.

His masterstroke is using the geometry and the logic used in both NLP and quantum theory in combination with showing how logic can be defined with reference to geometry. Everybody is familiar with language, most of us are with the use of internet search engines, and many remember what a vector is from physics diagrams including forces, velocities etc. All of us know from zero to three-dimensional Euclidian space and some types of curved spaces, e.g. spherical and saddle-shaped. Widdows does a superb job to exploit this knowledge to the full. I found his book valuable both in giving a concise view of methods used in relevant domains and as a means for orienting myself for further study of NLP as well as quantum logic. Another quality of the book is that the material is given a historical background, not profusely but just stimulatingly, and with the effect on the reader that historical digressions in texts on exact subjects tend to have, a synergetic mix of broadening and relaxing the mind.

To put this review in a proper perspective, although it may temper its reader's enthusiasm, I must admit that I possibly represent the perfect audience targeted by the book in the sense of being well-prepared to appreciate its content. This is partly accidental and thus can be seen as a flaw in the book's didactics. To explain, having mentioned in the previous paragraph high-school material necessary for grasping Widdows' topics concerning vectors, geometrical spaces and logic, it has to be noted that this does not prepare for his treatment of logic associated with lattices and concepts. The following implies that I already had knowledge of the latter subject before I read "Geometry and Meaning". After finishing my study of the chapter on formal concept analysis in B. A. Davey and H. A. Priestley's "Introduction to Lattices and Order" (2002) it struck me that Aristotle's attribution of distinct pairs of qualities to four elements might well be the first example of an implicitly defined concept lattice. Having worked out its math and graphics, I supplied the keywords |earth fire air water concept lattice| to Google and was referred to Widdows' book in the topmost result that the search engine returned.

What immediately enticed me to order it was that it was said to have a foreword by Pentti Kanerva. A year after its publication I had bought Kanerva's "Sparse Distributed Memory" (1988) on Douglas R. Hofstadter's recommendation in its flap text, the first part of which runs: "This book, because of its pristine mathematical beauty and its great clarity, excited me deeply when I read it, and I believe it will have the same effect on many others, whether they are ... [specialists in the same scientific domain as its author] or not." Indeed, Kanerva's and Widdows' books share important qualities. There is a positive way to define the most important of these, which, however, is predominantly ignored, being perceived by many as painful and, moreover, disparaged as unproductive. It is the books' demonstration of the superiority, the power and fertility of what I would call their authors' generalistic ability (avoiding use of the more obscure term interdisciplinarity). In my view, science needs precisely this ability of scientists, their use of which makes them polymaths, to be made as productive as possible (realizing that the personal building of the ability depends on possession of a rare talent restricting the number of scientists capable of attaining it). The clarity of Kanerva's and Widdows' books shows their talent for exposition. Its marriage to polymathy spawns the best educational material. In the past two decades, exposition of scientific subjects has acquired improved and novel tools. Widdows light-footedly equipped his text with shaded special-interest boxes and web links. Effective as these may be, they raise the issue of publishing texts in the category of "Geometry and Meaning" completely as web documents, which allow use of a much greater variety of expository tools. Kanerva in his foreword rightly stresses the importance of math in science. But today still none of the major websites collecting mathematical subjects, MathWorld, PlanetMath, and Wikipedia, even remotely presents the best possible quality in knowledge transmission, for example, only very sparsely containing instructive animations despite ideas for them readily suggesting themselves. Perfected with regard to the indicated quality, they could valuably support books like "Geometry and Meaning" as references for its math.

Science education is greatly enriched by books like "Geometry and Meaning". Incongruously, any acknowledgement of this by representatives of the larger societal institutions is at odds with the observation that the building of their authors' generalistic ability is not supported by them, which is particularly apparent in local communities. On the contrary, it is usually discouraged to protect social-psychological interests, every pertinent entity, beginning with family and continuing to include even university faculty, perversely controlling the individual whose aspiration is perceived as deviant. The simple explanation for this treatment is that the ability in question, as its product polymathy, is sour grapes for the exclusive specialists who are a majority almost everywhere. Fortunately, today's internet technology points to the only feasible way to neutralize its effect. Like "Geometry and Meaning", simply publish web links to resources allowing the generalistic-ability builder to educate himself, resources that probe an entire world like that of science, sufficient to provide a solid cognitive foundation, as well as efficient means for orientation.

Keeping science in focus, the proposed self-education resource contains the hint for NLP research to actively involve itself, with its methods and techniques, in a synthetic effort to sanitize the language that is used in science. This effort could also be a response to Widdows' critical remark that (p. 137, footnote) "... the excessive jargonization of all contemporary fields is getting out of hand ... the proliferation of science itself scattering us in a technological Tower of Babel". I imagine a balanced three-part activity consisting of (1) using NLP to rationalize scientific language, (2) searching on internet for self-education resources, and (3) building generalistic ability (not only by an individual but also by workgroups in science). Science is creative, giving it an attractive element of magic. Clear exposition reveals the reality of this element by outlining objects a significant part of whose generation is not objective because it is the unobservable work of the mind. A polymathic scientist can produce superior outlines if he can integrate the various domanial approaches he masters. But only if he combined his integrations with the talent for presenting them in the way Widdows shows in his "Geometry and Meaning" could he present a work of comparable caliber.

This is a great overview of NLP and various geometric methods of linguistic analysis. I do research in the field of computational linguistics and it was refreshing to see how Widdows was able to distill the essence of many important, influential papers and present these topics in an interesting and engaging manner. He includes numerous examples, graphs, and other supplemental material that do an effective job at getting his points across. Those with little formal mathematical background might find some parts intimidating, but if they stick it out, they'll find it to be worth the effort.