Abstract of: A Geometric Surprise in Dürer’s Engraving of St. Jerome in His Study

In Albrecht Dürer’s engraving St. Jerome in His Study (Fig. 1), sunshine projects the small round glass window panes onto nearby cove walls to make luminous spots. The window panes are patterned in close packing with horizontal rows (Pattern A in Fig. 2); they do not make vertical columns. The sun’s projection onto the cove wall shows images of the round panes in vertical columns. The projected light pattern implies window panes in Pattern B (Fig. 2). This pattern switch, a geometric error but perhaps not an artistic error, is the subject of the paper.

Fig. 1.

Albrecht Dürer, St. Jerome in His Study, 1514, engraving, 244 × 185 mm.

(Photo: © The Trustees of the British Museum, 1868, 0822.185)

Fig. 2.

Circle Packing Patterns. (Illustration: Dennis Couzin)

How or why did Dürer do this? Was it a blunder or a finesse? Most people quickly prefer one or the other explanation. An aim of the paper is to weaken both prejudices. Two simplified hypotheses are formulated, “Purely Careless” and “Purely Purposeful,” and after much examination of the engraving and of Dürer’s abilities, the paper cannot decide between the hypotheses. We simply do not know enough. Certain historical facts, such as what window patterns Dürer’s now restored house originally had, could help in the decision, but the matter might be historically undecidable. Whatever its cause, after the pattern switch is recognized the picture looks different. Now the engraving represents light as mischievous. Other writers have interpreted the light with other qualities.

The paper establishes that Patterns A, B and C of round panes were used in windows in Dürer’s time and place. He was surely sensitive to their different effects in the architecture. His Underweysung [1] includes an illustration distinguishing Patterns A and C. Writing as a mathematician, B was equivalent to A and unnecessary to illustrate. Dürer’s formative conception of pattern, revealed in his language, is considered in judging the hypotheses.

The projection error is different from a geometric perspective error. The sun’s projection of the window panes onto the cove wall belongs to the scene, whereas geometric perspective is the artist’s projection of the scene into the picture plane. The paper shows how perfect perspective is not required to identify projection errors in the scene.

It is widely believed that the architectural geometric perspective in this Dürer engraving is impeccable, albeit extreme. But H. Schuritz [2] in 1919 found one large anomaly in the architectural perspective. Indeed it is in the size and shape of the windows, which is inconsistent with their holding such patterns of round panes. This perspective anomaly can be confirmed by calculation or seen with one eye from the “correct” position (found by calculation). The projection error, however, is recognized the moment it is pointed out, by simple pictorial logic.

The paper develops an idea expounded by M.H. Pirenne [3] (which he attributes to J. de La Gournerie) of pictures having an architectural “shell” drawn in strict geometric perspective, plus “filler”. In this engraving, the ostensibly architectural window is filler.

In Panofsky’s Dürer [4], to which the paper is greatly indebted, the opposition of engraving techniques used for the windows and their projections is noted, but not the geometrical, horizontal vs. vertical, opposition. The richness of detail in the windows and the perceptiveness in the light projections (including refraction by the rippled glass) show the importance Dürer gave to the couple: object and projection. There is a connection between the ontological opposition implied by Panofsky and the geometric one.

The paper can only speculate on why art historians missed the projection error. Now prompted to see it, art historians can introspect and perhaps explain what prevented this before.

Artists noticed the projection error early. Examination of two versions of Psyche Attended in Her Bath from the 1530s shows how Agostino Veneziano (or another in his school) noticed it and then corrected it. Any artist...