This book describes a gradual transformation in the way Western societies represent and understand the world. It argues that, from the eighteenth century onwards, direct sense perception and mimetic forms of representation have been replaced by others, which are based on the combination of outputs from recording devices and symbolic graphical mathematical expressions. Two more connected arguments are at the core of this book: that current virtual scenarios such as that of computer-aided open-eye surgery, the example its authors use to open the book, are the culmination of that historical process of gradual transformation, and that the origins of such virtual scenarios, currently conceptualized as those where different forms of knowledge inform action, are to be found in the pages of Diderot and d'Alembert's Encyclopedia, a comprehensive treatise traditionally hailed by scholars as the Enlightenment's biggest print project.

According to Bender and Marrinan, the Encyclopedia was a space where one of the central ‘ambitions of Scholasticism’ (p. 74), that of a single unifying vision, as informed by Renaissance Albertian perspective, began to be challenged. Central to this challenge was its prolific use of diagrams; that is, visual arrangements where image and text juxtapose and combine arrays of data and information originating in different bodies of knowledge (scientific, aesthetic, etc.). Diagrams thus brought up conditions for the emergence of the modern viewer, a creative self that, by being able to visually scan and synthesize those verbal and visual realms of knowledge, produced new readings and new understandings (p. 82).

The authors use William Hogarth's engraving Satire on False Perspective (1754) as a case that ‘parallels and prefigures the diagrams of the Encyclopedia’ (p. 61). It was the coexistence in Hogarth's work of ‘sharp juxtapositions’, ‘multiple points of view’ and ‘radical shifts of scale’ (p. 63) that, as with the diagrams of the Encyclopedia, demanded from the viewer an active exercise of correlation among all those different epistemic and aesthetic domains. Key for the production of new knowledge through correlation was the existence of white spaces between the different pictorial and written domains. Whiteness eased viewers' conceptual synthesis and created places were seeing was possible without actually being there (p. 69).

One key aspect the authors are keen on highlighting is that the diagrammatic knowledge emerging in the plates of the Encyclopedia, rather than being an isolated phenomenon, belonged to a rich and varied eighteenth-century ‘cultural matrix’ (p. 150), which was composed by other realms also defying the norms for knowledge production set by the Renaissance. From painting, for instance, Jacques-Louis David's The Oath of the Horatii (1784) is identified by the authors as a visual space where ‘disparate passages of localized illusion coexist in strained relationships to one another’ (p. 147). Bender and Marrinan also identify the eighteenth-century reforms of design that took place at the Palais Royal of the Académie française, where the stage was separated from the auditorium (p. 115), alongside Marmotel's stage theory entailing ‘a subtle play of illusion with a self-conscious awareness of its operation’ (p. 121), as another example of that ‘cultural matrix’ that invited spectators to adopt a multifaceted and more creative role that thus challenged the Renaissance single view.

The production of new understanding beyond direct sense perception and away from ‘the protocols of mimesis’ (p. 205) initiated in the diagrams of the Encyclopedia was given a renewed impetus, in the authors' view, in the nineteenth and subsequently the twentieth century, as more and more ‘recording devices’ entered scientific practice, and scientists increasingly relied on the appliance of mathematical and statistical methods such as calculus and probability (p. 55).

The worth of Bender and Marrinan's book is better appreciated when compared with two other books recently published: Lorraine Daston and Peter Galison's Objectivity (2007), and Bas van Fraassen's Scientific Representation (2008) – a renewed version of ‘constructive empiricism’. Although not a universalistic account of the history of representation in Western culture, The Culture of the Diagram differs from Objectivity in that it conceptualizes its history as a much more simple, stable and continuous phenomenon (representation pre- and post-Renaissance). And by uncritically assuming that instruments and their outputs extend our visual ‘sensorium’, The Culture of Diagram seems to endorse a simple version of scientific realism, a position whose shortcomings have been meticulously exposed by Van Fraassen.

Despite these minor points, the Culture of Diagram is a well-crafted book. Its originality resides in the authors' capacity to recognize a running theme from the eighteenth century to the present in the history of representation in different domains such as painting, illustration, literature, aesthetics, theatre and science, and in establishing key connections between ideas such as the rupture of description of space by David's eighteenth-century paintings and von Helmholtz's nineteenth-century conceptualization of it (rather than an absolute one, as a co-constructed category between the world and sensory experience). The power of Bender and Marrinan's work also derives from the historical perspective they give to Michael Lynch's argument of a growing mathematization of imagery in twentieth-century natural sciences (‘The Externalised retina: selection and mathematization in the visual documentation of objects in the life sciences’, in M. Lynch and S. Woolgar (eds.), Representation in Scientific Practice (1990), pp. 153–186).

Last, but not least, this book creates a renewed ground for reflection on the relation between mathematics as a form of knowledge and the physical world, a long-standing but always thought-provoking philosophical theme. For the promoters of the transformation towards diagrammatic (mathematically and device-dependent) knowledge the expectation was and still is that these expressions could not only reveal nature's otherwise concealed secrets, but also provide ways for its manipulation. Regardless of particular cases of success or failure in achieving these aims, what the culture of diagram has brought about is the idea of a reality that is co-constructed (even modified in Bohr's view) by the interaction between the world and a viewer equipped with a ‘sensorium’, which is enhanced, so the story goes, by the combined use of mathematics and registering devices.