Arielle Saiber's Giordano Bruno and the Geometry of Language is a study that is as rewardingly rich and strange as its subject. While Saiber provides a wealth of context for her relatively short study, situating her work within the explosion of Bruno scholarship that emerged in conjunction with the 400th anniversary of Bruno's death (1600-2000), this book is not an entry point to Bruno, his ideas, or the scholarship on him. As a companion text to one of many biographies of Bruno, such as Dorothea Walley Singer's Giordano Bruno: His Life and Thought (1950) or Frances Yates's Giordano Bruno and the Hermetic Tradition (1964), this book has great potential as a text in a graduate-level History or English seminar, particularly one focused on the history of language and ideas. Scholars of Italian history and language - like Saiber - will likewise see rewarding uses for this book.

Saiber's primary argument throughout is that as a "poet and architect of ideas" (1), Bruno intertwines rhetorical concepts and language with mathematical concepts and language. While this was frequently a conscious project by Bruno, Saiber suggests that the connections fusing the "figurative" languages of geometry and rhetoric at times even inform Bruno's work in ways unforeseen by the sixteenth-century polymath. Saiber pairs geometric figures with rhetorical figures in order to analyze what the convergence of these "figuratives" conveys concerning Bruno's philosophy and "gnoseology."

Appropriately then, following a brief introduction that serves in part as a recommended reading list of works one perhaps ought to have some familiarity with in order to fully appreciate what Saiber offers, she pursues this analysis across six chapters each with an appropriate mathematical title: "Axioms," "Foci," "Lines," "Angles," "Curves," and finally, "The Point." Saiber's "Axioms" is sub-divided into two parts: "Theories of Geometric Space and Form in Literature Pre-Bruno" and "Post-Bruno." The resulting survey is a kind of condensed history of critical theory as it relates to notions of space. "Foci" begins to narrow the analysis more sharply to Bruno, Geometry, and Language as Saiber explores her central claim that "Geometry was for [Bruno] a warehouse of metaphors and structures that could be called upon to help reinforce the scaffolding of his philosophical and scientific thought. Bruno saw geometry's figures as equivalent to language's figuratives, and he used both kinds of figurations to signify, refer to one another, and indicate an integrated vision of the universe and all that is in it" (17).

Beginning with Chapter 3, "Lines: The Candle Bearer," Saiber offers a detailed example of her general claim that geometric figures and rhetorical figures converge and coalesce in Bruno's writing. Specifically here she explores Bruno's playful engagement with lists of brachylogia and rectilinear form in his play Il Candelio (The Candle Bearer). Bruno refuses, Saiber argues, to be confined by rule-like lists of expectations and linear forms in his construction of the play. He counters such expectations with copious lists and devices that suggest exaggerated accumulation and retention - brachylogia, systrophe, hyperbaton - of his own in order to fashion a syntax and semantics that imply a sort of "hyper-linearity" that "bursts into radiating vectors of potential and possible knowledge" (86).

Chapter 4, "Angles: The Heroic Frenzies," pairs the angle with the axial form of chiasmus illuminating the importance of the visual in both the geometric study of angles and its corresponding rhetorical implications. For Saiber, the Furori (Heroic Frenzies) is "replete with rhetorical devices that syntactically simulate the semantic meaning of co-incidence" (91). Characterizing the work as a "textual labyrinth" and a "palatial maze", Saiber argues that Bruno's Furori "is a colloquy between vision and desire, and the angles of approach, angles of incidence, symmetry, and the prismatic" (114). Appropriately for a work that is a response to and part of a "heightened interest in the impossibility of measuring and comprehending the infinite" (89), Bruno's treatise represents in visual and linguistic terms the "fragmented journey one must travel to gain knowledge of an ultimately illusive goal" (114).

In Chapter 5, "Curves: The Ash Wednesday Supper," Saiber equates the circle with circumlocution arguing that Bruno fills the Cena with a kind of "curved" figurative language including hyperbolic exaltations, elliptical speech and confounding geometrical figures, and circumlocution, "not only in the circuitous journey to the supper, but throughout the debates between The Nolan [an indirect representation of Bruno himself] and the Oxford professors" (119). Hyperbolic praise has its geometric equivalence in the hyperbola and in a similarly etymologically neat concurrence, ellipsis relates to the ellipse, as both suggest a kind of paradoxical empty fullness: "Ellipsis is…simultaneously empty in its lack of word, and full in its potential for words" (129). At the heart of this chapter, however, is the circle and the relationship between circularity and perfection, and circumlocution as a trope of concealment and avoidance. Saiber notes that Bruno "never specifically discussed the rhetorical device of circumlocution as a manifestation of the power of circles, [but] he used it nonetheless in much the same way he used circles in his geometric diagrams to refer indirectly to his philosophy of nature" (135).

In a brief final chapter, appropriately entitled "The Point", Saiber concludes that the convergence of the geometric and the rhetorical in Bruno's writing stems from his desire to "teach people to see thought" (144). Saiber's point throughout is to demonstrate the rich interworkings of Bruno's geometric rhetoric; she amply succeeds in convincing her reader that Bruno understood in deep and profound ways that geometry is a part of language and as such a useful tool for visualizing, conceiving and expressing language in form and concept. Those interested in exploring the common language of literature, rhetoric and mathematics - as opposed to the obvious divergences - will find much rewarding material to reflect upon in Saiber's compelling, highly readable study.