Tuesday, June 30, 2009

Elegant Geometry

Byrhtferth’s Diagram; Computus Diagrams

Above: Byrhtferth’s Diagram; Computus Diagrams (detail), from the Thorney Computus, Cambridgeshire, England, ca. 1102–10, Saint John’s College, Oxford, MS 17.

I have long been fascinated by medieval diagrams. Even before this exhibition provided the opportunity to unpack their often arcane content, I appreciated their elegant geometry. Although the systems of thought and basic formats of these diagrams often come from antiquity, I like to think their aesthetic potential was only fully realized by medieval thinkers and draftsmen.

We attribute the form of the magnificent diagram from a twelfth-century manuscript known as the Thorney Computus (shown above) to Byrhtferth, a monk and scholar who lived at Ramsey Abbey in England around the year 1000. Like all effective graphs and charts, whether modern or medieval, the diagram seeks to convey a maximum amount of information in a clear, concise, and aesthetically pleasing manner. Byrhtferth’s diagram coordinates the many quaternities—or four-part schemes—used by ancient and medieval thinkers to organize and explain natural phenomena. Thus at a single glance we can see how the four elements, the four directions, the four ages of man, the four winds, the four seasons, the twelve signs of the zodiac (divisible into four), among other pieces of information, could be mapped one on top of the other. With its multiple sets of neat correlations, the diagram also gave visual affirmation to the medieval idea that the cosmos is a splendid system, organized according to the divine geometry of God. (These systems of fours appear again in a wind diagram that is also on view in the exhibition.)

As mentioned above, Byrhtferth’s Diagram is found in a computus book, replete with some one hundred other fascinating diagrams. (Computus refers to the measurement of time, particularly as it concerns the complex calculations required to determine the dating of Easter and its associated feasts.) I can’t begin to tell you how most of these diagrams work, but I can admire their beauty. Many of the diagrams in this manuscript are framed by architectural elements, and as I first turned the pages, I felt I was on an extraordinary architectural tour. The care with which these diagrams were rendered, the lively use of color, the quality of the parchment, and the relatively large size of the book gives a sense of how much the monks at Thorney Abbey, where this book was housed, valued its content. McGill University has created a digitized version of the manuscript (see http://digital.library.mcgill.ca/ms-17/index.htm) that allows visitors to see each of its pages, along with helpful commentary written by Prof. Faith Wallis, the leading expert on the Thorney Computus.

The most geometrically perfect diagram in the entire exhibition may be the Consanguinity Chart (Bayerische Staatsbibliothek, Munich, Clm. 13031), which was found within a copy of a medieval encyclopedia. It is a meticulously symmetrical composition made up of rigid straight lines, perfect circles, tidy triangles, and neatly detailed inscriptions that adhere to the chart’s overall geometric aesthetic. The purpose of the chart is to determine degrees of kinship—important in matters of marriage or inheritance.

Studying medieval diagrams has made me all the more appreciative of well-designed graphs and charts of any era, and in that regard, I’ve learned the most from Prof. Edward Tufte, who has been called “the Leonardo da Vinci of data.” Prof. Tufte has graciously agreed to speak about medieval diagrams at the Metropolitan Museum on Sunday, July 19, at 3:00 p.m. I hope many of you can join us for what will surely be an enlightening program.

—Melanie Holcomb

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Comments (6)

  1. Rodrigo Says:

    Dear Ms. Holcomb,

    Thank you very much for such an outstanding exhibit. It was very nice to have so much information accompanying each piece and furthermore, the information you are adding in this blog (and the links) have extended the delight for several more hours.
    I have also been fascinated by the geometry embedded in all these diagrams, maybe by my mathematical background, so hopefully I will be able to attend Prof. Tufte’s talk.

    Best regards,

  2. Doug Says:

    It was a stroke of genius to think of inviting Tufte to talk in connection with this exhibition. I attended the lecture yesterday and found myself fascinated, and driven to re-examining my own cognitive reactions to each of the images in the exhibition, in light of Tufte’s “rules” of effective visual communication. The great conceptual distances between what the medieval draftsmen were trying to convey and what we today think of as “understanding” and “evidence” seem perfectly suited to putting Tufte’s claims of “universality” (a word he used often, though often qualified) to a real test.

    The consanguinity chart, for example, seems to meet most of his standards and to make its case beautifully. The Sawley Map, on the other hand, is a tougher case, one that I feel certain Tufte would consider a failure, given his admiration for the very modern-looking Chinese map, complete with rectilinear grid, that he displayed in his talk. Does the medieval appreciation for the Sawley map challenge the universality of Tufte’s rules?

  3. Tom Benthin Says:

    Do you, by any chance, have any record of the Tufte lecture that can be posted?

  4. Melanie Holcomb Says:

    Dear Doug,

    What a great question. I was thinking about similar issues myself when listening to Prof. Tufte speak–how far can we apply some of principles of analytical design to medieval diagrams? And where we can’t, what might be an alternative set of principles we could use to judge “graphical excellence” (to use a Tufte phrase) in the Middle Ages? As you point out, the Sawley Map with its mix of literary, mythical, and actual places and its disregard for geographical accuracy in the modern sense does put Tufte’s standards to the test. In many ways the map does adhere to his principles. For instance, it does offer “multivariate analysis” (principle 3) and an “integration of evidence” (principle 4). I suspect the real difficulty for Tufte might not lie in the map’s design, but in the kind of information it conveys and the premise on which it was created. After all, it does not seek to present information based on empirical evidence. It is not grounded in the physical laws of nature.

    But would it be fair to expect or want that in a medieval diagram?

    Medieval scientific knowledge and the diagrams used to explain it had an entirely different set of aims from our own and those aims were predicated upon a different set of questions–questions posed by smart people. (Part of why I love studying the Middle Ages is that it allows me to better see the historical particularity of our moment.) Medieval thinkers thought it paramount to explain the cosmos in a comprehensive fashion and present it as a coherent system. As a number of scholars of medieval maps have suggested, the goal of maps such as Sawley was to convey in a glance the totality of both time and space. Sawley very much speaks to the encyclopedic ambitions of medieval scholars and diagram-makers. They were eager to offer a truly all-embracing and integrated view of the world. By that criterion, it seems to me Sawley is eminently successful as a form of visual communication.

    If you want to read more about medieval maps, Evelyn Edson has written a marvelous introduction to the topic in her book called Mapping Time and Space: How Medieval Mapmakers Viewed their World.

  5. Melanie Holcomb Says:

    Dear Tom Benthin,

    The Tufte lecture will be posted on YouTube and iTunesU before the end of the month. In the meantime, you can have a look at the chapter called “The Fundamental Principles of Analytical Design” in his 2006 book, Beautiful Evidence. He published there many of the ideas he presented.

  6. Melanie Holcomb Says:

    The Tufte lecture is now posted on YouTube. Here’s the link:

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