The Spatial Reformation

The Spatial Reformation offers a sweeping history of the way Europeans conceived of three-dimensional space, between 1350 and 1850, and calls for a deliberate reconsideration not only of what constitutes the intellectual foundation of the early modern era but also of its temporal range.

The Spatial Reformation
Euclid Between Man, Cosmos, and God

Michael J. Sauter

2019 | 344 pages | Cloth $89.95
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Table of Contents


Introduction. The Spatial Reformation
Chapter 1. From Sacred Texts to Secular Space
Chapter 2. The Renaissance and the Round Ball
Chapter 3. Divine Melancholy
Chapter 4. Eden's End
Chapter 5. Modest Ravings
Chapter 6. Strangers to the World
Conclusion. Prosaic Reflections


Excerpt [uncorrected, not for citation]


This book took too long to complete and was supposed to be a study of public clocks and time discipline in the late eighteenth century. These two things are related. Initially, I was interested in how, at the eighteenth century's end, people across Europe yielded the right to define local time to astronomers, an exclusive group whose knowledge and skills were expressly not local, but were tethered to a far-flung community of specialists. My work on this matter appeared in 2007 as a journal article, in which I detailed eighteenth-century Berlin's experience with modern time regimes. At that moment, I intended to write a book on Europe's elaboration of a system of uniform public time. This work would have concentrated on Geneva, London, Berlin, and Paris, since these cities installed the first citywide master clocks. Everything went awry, from there.

In order to pursue the formation of what I understood to be modern time sense, I undertook to study the history of astronomy. (I believe, now, that I was wrong about time discipline's "modernity." This discipline was, in fact, early modern—for reasons that will become clear.) Thus, when I first expanded my inquiry, I was interested in how astronomy's maturation into a continental discipline sustained multiple takeovers of local time regimes. In short, I wanted to explore how time ceased to be a form of "local" knowledge, in the sense that Clifford Geertz has used the term, and became a "scientific" form of knowledge that was incorporated rapidly into the European state's burgeoning disciplinary apparatus.

As I tumbled backward into the history of astronomy, however, I detected similarities in early modern astronomical textbooks with philosophical works that I had previously studied. I recalled, for instance, that the German philosophers Immanuel Kant and Johann Gottfried Herder had deployed in their writings the same astronomical knowledge that I was encountering within eighteenth-century astronomical works. Herder, for instance, dedicated the entire first book of his anthropological work Ideas on the History of Humanity (1788-1791) to a description of the cosmos, imagining for his readers terrestrial and extraterrestrial realms that he had never seen, before analyzing a humanity that he could not have fully known. Thus, the great unseen cosmos—to which Herder had access through books, scientific instruments, and the university lectures that he heard in Prussian Königsberg—was an essential (and essentially imagined) frame of reference for his anthropology. When I noticed that the initial volume of Herder's work appeared one year after Berlin, Prussia's capital city, had installed its first master clock, it appeared that astronomy was behind a much broader change.

Further research in the history of anthropological thought revealed that Herder was not alone in projecting an unseen cosmos as the essential backdrop for a proper study of humanity. The same phenomenon appeared in other fundamental eighteenth-century works of anthropology, including Natural History (1749-1804) by the Comte de Buffon, "Essay on Man" (1734) by Alexander Pope, and Reasonable Thoughts on the Workings of Nature (1725) by Christian Wolff. Moreover, as I examined seventeenth-century anthropology and, in turn, looked to its sixteenth-century predecessor, I observed that an imagined cosmos usually framed the attending anthropological study. Against this backdrop, it immediately became important that eighteenth-century cosmology was expressly heliocentrist, while its sixteenth-century predecessor remained geocentrist. In this respect, the shift from geocentrism to heliocentrism indicated that changes in cosmology might have wrought changes in anthropology. My pursuit of the potential interconnections between the two disciplines became, in the end, Chapter 6, "Strangers to the World," in which I explore the background to (and significance of) anthropology's embrace of heliocentrism.

This project's conceptual starting point thus forms the resulting monograph's final chapter. I note this fact in order to elucidate how an investigation into the rise of public clocks metastasized into a history of spatial thought. This book was researched and written backward. The various astronomical texts that I read pulled me back nolens volens to earlier times and into other disciplinary fields. It turned out, for example, that eighteenth-century and seventeenth-century textbooks in astronomy linked the discipline to geography, often claiming cheekily that geographers would be lost were astronomers not around to tell them where they were. Nor did geographers dispute the point. Subsequent research into the terrestrial discipline, beginning with the eighteenth century and moving back into the seventeenth, then led me into yet more branches of learning, including sixteenth-century cosmography and fifteenth-century globe making. Thus, I began to see how astronomers, geographers, cosmographers, and globe makers produced collectively what Europeans could not see. Not coincidentally, I became lost in space.

While pursuing what struck me as interrelated traditions of imagining unseen realms, I noticed that texts from the varied disciplines paid homage to geometry. More significantly, perhaps, the works in question often recommended that readers study early modern geometry's cornerstone, Euclid's Elements. That the exhortations were made so easily and so regularly suggested, in turn, that ancient geometry had already become fundamental to early modern thought, before the astronomical issues that I was pursuing rose to prominence. Thus, I began to formulate—fitfully and amid frequent bouts of swearing—a "geometric" reading of European intellectual history that produced (in reverse order) Chapter 5, "Modest Ravings," Chapter 4, "Eden's End," Chapter 3, "Divine Melancholy," and Chapter 2, "The Renaissance and the Round Ball." In each chapter I explore how Euclidean geometric space's reception not only changed the discipline in question, but also wrought a broad consensus: that geometry undergirded all forms of natural knowledge.

The unraveling of my project on public clocks did not, however, end there. Further research on Euclid's early modern career revealed just how widely his Elements had diffused, as I discovered that no important early modern figure, from Leonardo da Vinci to G. W. F. Hegel, failed to read ancient geometry's jewel. Nevertheless, although I had a sense for geometry's significance, I had no explanation for why its rise would have wrought such profound changes. In order to address this problem, I initiated the research that culminated in Chapter 1, "From Sacred Text to Secular Space." In this chapter I trace how Euclid's Elements diffused and why its cultivation of nothing clashed with the anthropological, cosmological, and theological traditions that long suffused medieval thought. I concluded, thus, that geometry's history suggested a profoundly different take on European intellectual history's scope and development.

The final break with my original project came with the realization that Euclid's career identified both the beginning and the end of a deeper transformation. Additional investigations revealed that prior to 1350, Euclid's Elements was read quite differently than it was after 1350. Medieval students of geometry absorbed a relatively narrow view of space from the Elements, because they usually concentrated on the initial six books, which cover plane geometry alone. Early modern readers, in contrast, delved increasingly into books seven through thirteen, which cover the continuity of number and explicate the foundations of spherical geometry. Concomitantly, as I incorporated this discovery into my narrative, I came to appreciate more fully the significance of post-1850 changes in geometry. Euclid's reign ended when mathematicians invented systems of spatial reckoning that functioned beyond Euclid's vision of three-dimensional space. Thus, it seemed possible to organize a history of European thought with respect to Euclid's rise and decline.

The problem remained, nevertheless, to create an analytical approach that captured both the depth and breadth of Euclid's effects. Additional research in ancient and medieval intellectual history cast light on an intellectual framework that I call the Western triad of anthropology, cosmology, and theology. I cannot trace this triad's long history in this book, but I offer instead an introductory sketch on which I will expound in a subsequent work.

From the beginning of the Christian era until about 1350, anthropology, cosmology, and theology were locked in an alliance that required that a change in any one (say, a new emphasis in the vision of God) be matched by changes in the other two. Although the Western triad was not initially hostile to homogeneous space, it became so as a consequence of Neoplatonism's rise in the late third century AD, which (crucially, for my story) cultivated a hierarchy of being. I cannot properly explicate the philosophical issues here. Instead, I must simply assert that hierarchical being and homogeneous space did not mix well. Thus, when early Christian thought absorbed Neoplatonism's vision of a great chain of being, in the fourth century, this guaranteed Euclidean space's long marginalization within Western thought.

Once I had formulated the triad as an analytical frame, I began to see why Euclid's full return—comprising both the Elements' planar and its spherical space—had wrought such profound changes. On the one hand, this space slowly dissolved the triad's conceptual bonds and, in so doing, inspired transformations across multiple areas of thought. On the other hand, space's profusion through the triad altered each of its elements so thoroughly that, by 1850, the three could not be allied again. Indeed, in the end, anthropology was left to stand alone, as the European vision of Man became so expansive that it simply absorbed both the cosmos and God.

The pursuit of Euclidean space across time could not explain, however, why contemporary scholarship has underemphasized this phenomenon's effects. Continuing my study of geometry beyond the year 1850 suggested a potential answer: by about 1900, Continental philosophy had incorporated non-Euclidean geometry so fully that three-dimensional space lost its philosophical significance. This transformation had one profoundly important effect. As I detail in the conclusion, postmodern thinkers followed modern philosophers in denying philosophical validity to Euclidean visions of space—and for exactly that reason, postmodernism has greatly underestimated geometry's historical significance. In effect, on account of developments in modern mathematics, postmodern thinkers are blind to precisely the thing that distinguished early modernity from modernity.

Having traced the genesis of this book's interpretive outlines, I turn to what I see as its methodological contributions. As an intellectual historian by training, I have long emphasized the study of printed and written texts. While researching this book, however, I borrowed from historians of science who insist (rightly, in my view) on the significance of material culture to all aspects of early modern culture. This scholarship's potential to send intellectual history in new directions crystalized for me in 2012, during a visit to the Museum of Natural Sciences in Raleigh, North Carolina. I was carrying my four-year-old daughter when she extended her arm and spoke one word, "Erde," which is German for Earth. When I turned, I saw a large terrestrial globe. Obviously, in my enthusiasm I had subjected the poor child to the study of globes. Nevertheless, my moment in Raleigh threw into relief two things. First, knowledge of unseen spaces and places is learned, which makes its acquisition a historical phenomenon. Second, illustrations of unseen things are not simply representations of something real, but are also products of the human imagination. Thus, beneath what many scholars have seen as a history of discovery lies, in turn, a history of humanly elaborated spatial regimes. It is along these lines, that I call particular attention to this book's cover image, because it highlights how there is no separating the history of spatial thought from the pedagogical system that taught (and still teaches) everyone how to imagine the unseen.

All this leads me to this work's title. Given that early modern culture infused space through (and into) everything, it seemed appropriate to summarize the concomitant intellectual changes in a term that connected space to its multivalent anthropological, cosmological, and theological resonances. Thus, I have chosen the title The Spatial Reformation in order to capture the multifarious churning that Euclid brought to early modern thought, before modern mathematics superseded his vision of space. Thus, for me, both this work's title and the analyses within each chapter represent not the discovery of something new, but the recovery of something old. I suggest, in short, that our ostensibly postmodern gaze now trace a line within a fully realized three-dimensional space that (for me) was first demarcated by a little girl's extended arm.