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The Old Testament Trinity of Andrey Rublyov: Geometry and Philosophy ABSTRACT

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The Old Testament Trinity of Andrey Rublyov: Geometry and Philosophy ABSTRACT HISTORICAL PERSPECTIVE The Old Testament Trinity of Andrey Rublyov: Geometry and Philosophy ABSTRACT The philosophical and theo- Alexander V. Voloshinov logical content of a masterpiece of Old Russian icon-painting— Andrey Rublyov’s Trinity—is re- garded in the light of its geom- etry. The aspects under study are the geometrical properties of the rectangle of the Trinity (which gen- erate a sequence of circumfer- ANDREY RUBLYOV AND of the soul this infinite, imper- ences related by the golden pro- turbable, indestructible peace, HIS OLD TESTAMENT TRINITY portion) and also some of the “the lofty peace” of the celestial peculiarities in the composition of Andrey Rublyov (1360~1370–1430) is the pride and glory of world . And this inexplicable the icon. The roles of the circle, Russian culture. The creator of the famous Old Testament Trin- world . this incomparable sky- the octagon and inverse perspec- blue—not the earthly sky-blue, ity (Fig. 1) was one of the three most significant persons of tive in the Trinity are discussed. but the true heavenly azure, this medieval Russia; the other two being Sergius of Radonezh The author establishes correspon- unspeakable dream of Lermontov, dence between the theological (1321–1391) and Dmitry Donskoy (1350–1389). This Russian who longed for it, this ineffable triad Revelation- Illumination-Trans- trinity left such a deep trace on the national culture that all grace of the mutual bows, this formation, which makes up the three were canonized by the Russian Orthodox Church. If peaceful unwordliness, this infi- fundamental content of the Trinity, nite submissiveness to each the names of Sergius of Radonezh and Dmitry Donskoy sym- and the mirror and dynamic sym- other—we consider the artistic metries of the icon. bolize the spiritual and military renaissance of Old Rus and contents of the “Trinity” [4]. the first steps towards liberation from the Mongol and Tartar yoke, the name of Rublyov is connected not only with the flowering of Russian art but also with the revival on Russian THE CONSTRUCTION ground of the Byzantine art that had been ruined in the Osmanli fire [1]. OF THE RECTANGLE OF THE ICON Already in Rublyov’s lifetime his icons were worth their Let us note that Old Russian icons were necessarily painted in weight in gold: they were hunted by collectors, who did not an arc. The linear parameters of the margins of the arc of the stop far from violence and fraud. Rublyov’s authority was so Trinity (the height of the margins h0 and its width l0) are pro- high that, when the canons of painting the Trinity were con- portional to the linear parameters of the arc h, l and to the sidered at the Stoglavy Sobor in 1551 in Moscow, the verdict linear parameters of the icon itself H, L: was unequivocal: “To paint from ancient samples like Greek − − h0 ==h H =Hh = Ll artists painted and like Andrey Rublyov painted . .” [2]. (,).hool It is quite understandable that, since the name of Rublyov l0 l L 22 was so popular, there appeared a huge number of icons as- This fact is evident from the similarity of the triangles: the di- cribed to the hand of the great master. The wave of uncritical agonals of the icon are at the same time the diagonals of the attitude towards the heritage of Rublyov was followed by a arc. As a result, it makes no difference whether the propor- hypercritical one. Nowadays only one icon of Rublyov’s circle tions of the composition of the icon are calculated on the in- (excluding the famous frescos from the Cathedral of the ner outline—the outline of the arc—or on the outer contour Dormition of the Virgin) is an undoubtedly genuine work. of the whole icon. According to the logic of a pictorial com- But what an icon it is! It is the masterpiece of the great mas- position, the proportions of the composition should be corre- ter—the icon Trinity from the Trinity Cathedral in the Trinity- lated with its inner contour. But from the point of view of per- St. Sergius Monastery. In Sergiev Posad (thanks to the glory ceiving the icon as a whole, the parameters of the of Sergius of Radonezh and Andrey Rublyov this small town composition should correlate with the outer contour of the not far from Moscow became the capital of the Russian Or- icon. By keeping the proportion the same, Rublyov solves this thodox Church). Still the exact date of creation of the icon is problem [5]. unknown—it could be either 1411 or 1425–1427 [3]. But how was the rectangle itself constructed? Since If the name of Rublyov personifies the art of Old Russia, Trinity symbolizes the highest peak of that culture. Rublyov H h 5 =≈125., = and his Trinity became synonyms for the Russian people, and L l 4 for a foreigner the whole history of Russian Art is not infre- the answer seems evident: the proportions of the rectangle of quently overshadowed by this glaring peak. the Trinity are determined by the ratio of integers 5:4. The What marvels, startles and almost scorches us in Rublyov’s construction of the rectangle with the help of a circumfer- work is not at all the subject, or the numeral “three,” or the ence inscribed in the four squares is evident from Fig. 2. cup on the Communion table . but the fact that it showed us truly the Revelation beheld by him. Among the restless cir- cumstances of the time, among the discords, the local wars, Alexander V. Voloshinov (mathematician, philosopher), Saratov State Technical Univer- the general savagery and the Tartar interventions, among this sity (SSTU), 6 Delovaya St., Apt. 14, Saratov 410040, Russia. E-mail: lack of peace that had depraved Rus, there opened to the eye <[email protected]>. © 1999 ISAST LEONARDO, Vol. 32, No. 2, pp. 103–112, 1999 103 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/002409499553082 by guest on 29 September 2021 applying musical proportions in spatial arts. The same ancient masters were too sophisticated in the arts and in math- ematics to confine themselves merely to the integer proportions. On the wooden panel from Hesire’s sepulcher in Saqqarah (twenty-eighth century B.C.), the architect Hesire is shown with two measuring canes in his hands, the lengths of which are related as the side 1 AC== OE φ2 , (1) and the diagonal ( 2 ) of the 1 AC== OE φ2 , double square 2 :1. There is only one step from the diagonal of the double square to the coefficient of the golden Φ section = ( 5 + 1)/2 = 1.618033989 φ Φ . or its inversion = 1/ = ( 5 – 1)/ 2 = 0.618033989 . That very step was made by Euclid in his Elements [11]. Masterpieces of Ancient Greece and Rome and Old Russian art testify to the fact that old masters knew the propor- tions based on irrational relations such 1 1 AC== OE φ2 , AC== OE φ2 , as ( 2 :1, 2 :1 and, finally, ( 2 + 1)/ 2:1. The same Vitruvius recommends the relation 2 :1 [12] as well as the musical integer proportions of atria. Old Russian masters, who were ac- quainted with the wisdom of Antiquity through Byzantium, were sure to know the secrets of the golden proportion. Such being the case, while making up the boards for his Trinity, Rublyov could have marked not the “musical” rect- angle 5:4 but the “golden” rectangle Φ :1, the diagonal of which is the co- efficient of the golden section Φ. The Fig. 1. Andrey Rublyov, The Old Testament Trinity, tempera on wood, 142 × 114 cm, c.1420. geometry of constructing that rect- The icon from the Trinity Cathedral in the Trinity-St. Sergius Monastery in Sergiev Posad. angle, based on the modification of Eu- clidean method of two squares, is evi- dent from Fig. 3. The rectangles 5:4 and Φ :1 are al- The integer ratios of the sides are The ancient theory that proportions most indistinguishable from each other characteristic of Russian icon-painting in that are pleasant to the ear should be to the eye (Fig. 4): the relative differ- general. As the well-known proportion also pleasant to the eye was accepted and ence of their diagonals ∆ = 1.05%. But theorist A. Titz [6] established, the inte- developed in the time of the Renais- behind the outer equality of the two ger ratios of H:L dominate in Russian sance. Leon Battista Alberti wrote: rectangles there are two contrary phi- icons of the fourteenth and fifteenth “There are numbers, with the help of losophies of art: the philosophy of the centuries, namely: 4:3 (~30%); 5:4 which the harmony of sounds fascinates modulus—the arithmetical addition of (~30%); 3:2, 6:5, 7:5 (~12% each). Only the ear, the same numbers fill the eyes the multiple to the modulus magni- approximately 4% of these icons are and soul with wonderful delight. We tudes, leading to “musical” propor- made up by non-integer ratios of their must use the proportions, taken from tions, and the philosophy of the coeffi- linear parameters. musicians, who are great masters in that cient—the geometrical multiplication From ancient times, integer propor- kind of numbers” [10]. by the coefficient of the increase, lead- tions have traditionally played a leading When Rublyov was choosing the inter- ing to the irrational proportions and, in role in spatial arts, especially in architec- val of major third (5:4) as the proportion particular, to the golden ones. ture, which has been conditioned in its of the rectangle of the Trinity, he could What philosophy did Rublyov pro- turn by the exceptional role of the inte- not have known this statement of his fess? We do not know the answer.
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