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Reviewer: Robert Goldberg

Statistical graphics based on an algebraic model are presented in this book. This is considered a novel approach by statisticians, one that differs from the historical perspectives. Tufte [1] considers Minard's 1869 statistical graphic depicting Napoleon's 1812-1813 march on Moscow [2] as the classic graphic that led the way to pictorial displays of data. His technique was the ancestor of the current visualization approach used by most statisticians. With this book, Wilkinson intended to provide a comprehensive foundation that could enable the encapsulation of all statistical (and general) graphics. Wilkinson's interest was not merely theoretical; at SPSS laboratories, he created nViZn as a Java class for analytical graphics. To understand the philosophical differences in the approaches, consider an example provided by the author at a workshop of statisticians: Media and journal experts use pie charts to display the results of a survey. The proportional nature of the slice areas makes this a reasonable choice. The pie chart's radial display enhances this by displacing most of the area to the perimeter of the display, which is more perceptible to the eye. Contrast this with Wilkinson's statement about pie charts at that workshop: "There is no such thing as a pie chart" [3]. Instead, a pie chart is actually a stacked bar graph, which has been transformed into polar coordinates. This book is recognized by statisticians as a groundbreaking attempt at providing a formal (and fundamental) theory for displaying and presenting visualizations of data in the manner that leaves the most significant impact on the reader. As a computer scientist, I can appreciate the importance of generating (drawing) appropriate graphs depicting data obtained by survey or experimentation. Computer scientists generally interpret the word "grammar" within the context of formal language theory and the word "graphics" within the context of imaging. As such, the grammar of graphics could make people think of works about Lindenmayer systems [4,5], or the early works of Mercer and Rosenfeld [6,7]. However, this magnum opus should be perceived more as a formal analysis of presenting information or visualizing data. In this regard, its purpose is more similar to that of Tufte's visualization work [1]. The analysis provided in the chapters is more algebraic (described in chapters 2 and 5) than it is linguistic. Yet, the text does not rely on the prior knowledge of mathematics per se. The presentation of each chapter and the examples therein center around a set of attributes that describe functions, the composition of which can generate curves, surfaces, and graphs. Chapter 19 does discuss graphics grammars in the context of a graphics "reader," but the word "grammar" does not appear in the subject index of this book. The author is very concerned that the reader of this text should properly understand from the onset what the book is about, by describing "what it is not" in chapter 1. In addition to the erudite presentation of each chapter, the author has gone out of his way to present the material in a clear manner, including illustrations (319 in color plus 91 in grayscale) and introductions and summaries in each chapter. The author should be congratulated for completing this monumental task. Researchers interested in a total picture of how to generate statistical graphics will find this text most informative. Online Computing Reviews Service