J.L. Heilbron, The Sun in the Chuch. Cathedrals as Solar Observatories. Cambridge, MA: Harvard University Press, 1999. To order this book from Amazon.com, click here.

Reviewed by Paul A. Calter and Kim Williams

One of the criticisms often aimed at analyses of the proportions or geometry of a sacred building is that they are too complex, and that their very complexity argues against their possible use as design generators. It has been argued that simple systems were necessary in order that workers might understand what they were building, and that even designers were apt to conceive their most sophisticated creations with eloquent simplicity. But if ever an argument exists for the mathematical complexity that underlies theology it is found in J.L. Heilbron's exposition of the computations required by the early Christian church to fix the date of Easter each year, in spite of the lack of algebra to aid their computations ("God knows how they did it" [p. 28]). Fixing Easter was of the utmost importance to the Christians, partly because celebrating Easter on the wrong day might endanger the souls of the faithful, partly because choosing to celebrate on different days was a sign of adhering to the "wrong" Catholics. One way to determine Easter was set forth by the Alexandrians; another way was set forth by the Romans; still another by the Greeks. When a "definitive" system was set forth by Dionysius Exiguus at the behest of Pope John I in 525, the churches of all regions accepted it except those of England and Ireland, which preferred to remain with the Roman traditions. For this reason in 669 Archbishop Theodor of Tarsus excommunicated the clergy until they agreed to adopt the new reckoning of the date. The close relationship between astronomy, in particular the study of lunar and solar cycles, and theology is thus demonstrated. But what also is made evident in this discussion is the importance of mathematics to the clergy. Bede's De temporum ratione said that the church was built of four subjects: divine canon, grammar, history and "number, by which the events of the future and the Lord's feasts are reckoned" (p. 35). Heilbron reminds us that Saint Augustine had said that a man who could not compute was not worthy to be a priest (p. 36).

One main thesis of this book is Heilbron's dispute of the claim that the church was hostile to science. He points out that the church supported astronomy for the six centuries, from the late middle ages into the enlightenment, and that the meridian makers had careers largely underwritten by the church. The condemnation of Copernican theories by the church was largely ignored by clerics, and those willing to call a theory a hypothesis could publish any astronomy they wanted. The Jesuits were teaching heliocentrism before the end of the seventeenth century using the convenient fiction that it was a convenient fiction. Heilbron says that many clerics felt that math and astronomy had no fundamental connection to the rest of the body of knowledge, and therefore could have no effect on the truths of faith. Again, the main reason for these astronomical investigations, according to Heilbron, was to fix the date of Easter.

Another main contribution of this book concerns meridian lines or meridiane, astronomical instruments hardly ever mentioned in books on astronomy. The calculation of the date of Easter depended on exact values of the periods between successive vernal equinoxes and between successive full moons. The key parameter for the calculation was the time for the sun to return to the same equinox. The best tool for determining this was the meridian line, a north-south line in a dark building with a hole in its roof. One observed how long it takes the sun to return to the same spot on the line. Much of this book is devoted to the history of the development of such meridiane.

But what this book is not is a discussion of what influence astronomy had on sacred architecture, a subject so clearly but not exhaustively discussed by Robin Evans in The Projective Cast. Architecture and Its Three Geometries. Evans describes how the notion of the supposedly circular orbits of the planets was translated into the architecture of domes and circular-plan spaces during the Renaissance, giving way to the elliptical plans of the Baroque after the general acceptance of Kepler's discovery of elliptical orbits. In contrast, to Heilbron the architecture of the church is almost incidental; churches were long, and so the meridians fit. He explains that churches were the most convenient sites for the placement of meridians for observing the sun's movements, due to their shape and the protected environment they provides, as well as the fact that those most interested in observing the sun were the clergy, for whom "science [was] a by-product of advancing the core interests of the church" (p. 36).

This book offers a different kind of travel guide for the "mathematical tourist", providing an itinerary of Italian cities and churches in which to find meridians, analemmas, armillary spheres and gnomons. These are good reminders of the role of the church in the history of science and testify to the fact that everything applied to the church, even the most apparently ornamental, served a didactic purpose.

However, it is not easy reading. It contains a good history of astronomy in general, and the development of the calendar over the centuries, but many readers will get bogged down in the mass of minute detail of historical developments, such as that for each meridian line. The calculations in this book were very difficult to follow, even for a mathematics textbook author.
One sometimes feels that many of Heilbron's opaque derivations were more designed to impress than enlighten. Fortunately many of these arcane calculations can be skimmed over without harm to understanding the main argument.

ABOUT THE REVIEWERS
Paul A. Calter is a Visiting Scholar at Dartmouth and Professor Emeritus of Mathematics at Vermont Technical College. He has interests in both the fields of mathematics and art. He received his B.S. from Cooper Union and
his M.S. from Columbia University, both in engineering, and his Masters of Fine Arts Degree at Vermont College of Norwich University. Calter has taught mathematics for over twenty-five years and is the author of ten mathematics textbooks and a mystery novel. He has been an active painter and sculptor since 1968, has participated in dozens of art shows, and has permanent outdoor sculptures at a number of locations in Vermont. Calter developed the MATC course "Geometry in Art & Architecture" and has taught it at Dartmouth and Vermont Technical College, as well as giving workshops and lectures on the subject.

Kim Williams is the Editor in Chief of the Nexus Network Journal and director of the Nexus conferences on architecture and mathematics.

Paul Calter and Kim Williams presented a joint paper on the survey of a doorway by Michelangelo in the Laurentian Library in Florence at the Nexus 2000 conference on architecture and mathematics.