In the Italian Renaissance, Filippo Brunelleschi’s dome for the Church of Santa Maria del Fiore in Florence (1420-36) conceals a double shell filled with a trellis to disperse the load, as in the Pantheon. The façades designed by Leon Battista Alberti at the Palazzo Rucellai (1455, Figure 3.1) and Santa Maria Novella (1456-70) in Florence, and at Sant’Andrea in Mantua (1476, Figure 3.2), visually present a structural system which has no relation to the building behind it. Alberti, an active member of the Platonic Academy and a friend of Marsilio Ficino, distinguished between lineament, or the line in the mind of the architect, and matter in architecture, as described in his treatise on architecture, De re aedificatoria, or On the Art of Building (1443-52). For Alberti, architecture depends on a Platonic idea separate from and contradictory to sensual perception or physical presence. In the treatise, “It is quite possible to project whole forms in the mind without any recourse to the material” (Alberti 1988 [1452]: I.1). Architecture is the projection of the idea onto the material, as Ficino asks in his De amore, or Commentary on Plato’s Symposium on Love (1484), “Who will deny that the house is a body and that it is very much like the architect’s incorporeal Idea, in the likeness of which it was built?” (Ficino 1985 [1484]: V.5). This disjunction between geometrical form and structural function would become a hallmark of Renaissance architecture, especially in Italy, where there was a deliberate desire to contrast the visual structure or scaffolding of visual reality with an underlying structure inaccessible to sensation, one of the core ideas of the Neoplatonism at the base of Renaissance expression, as seen in paintings as well as buildings. In paintings this can be seen in deliberate contradictions of natural elements, as in the Mona Lisa (1503-7) of Leonardo da Vinci or the Tempest (1506-8) of Giorgione da Castelfranco, where different elements of the landscape do not correspond to each other; or it can be seen in the distinction between the Platonic idea of beauty and physical beauty, as represented in the Birth of Venus

(1485) of Alessandro Botticelli, where the idea of beauty, represented by Venus emerging from the sea, is transformed into physical beauty when she arrives on shore and is clothed by Flora, the personification of Florence, in contemporary Florentine costume. The painting by Botticelli is seen as an allegory of the project of the Florentine Renaissance, to transform the idea of beauty from Classical philosophy into physical manifestations of beauty in the objects of the arts. Such a theme in the painting was probably dictated by Marsilio Ficino, director of the Platonic Academy, for the Medici family, for whom the Birth of Venus was painted. In Renaissance buildings, the disjunction can be seen in the façades which have no relation to the pre-existing structures, such as the façades by Alberti. It can also be seen in the recurring disjunction between the design of interior elevations in Italian Renaissance architecture and the structure of the building. In the churches of Sant’Andrea in Mantua by Alberti (Figure 3.2), San Pietro in Rome by Carlo Maderno, around 1600, in the mannerist period, and San Carlo alle Quattro Fontane in Rome by Borromini (Figure 3.6), around 1640, in the Baroque period, for example, the vaults appear to be supported by the trabeated systems of the interior elevations, as they would be in Classical architecture. The interior elevations are only decorative though, pure geometry, while the structural work is being done by Gothic-style buttresses hidden in bays behind the walls. At Sant’Andrea in Mantua the visual structural system of the façade is continued in the elevations of the nave, which appear to support the coffered barrel vault, but the vault is in fact supported by the hidden buttresses. The scaffolding of the material world is inaccessible to the senses, as in the Platonic archetype, and the creation of the Christian God, in a perfect fusion of Renaissance Neoplatonism. The same system can be found in the nave of St. Peter’s in Rome, designed by Carlo Maderno. This device appears to be intended to correspond to the Platonic idea that the visual reality as given by perception is false, and that the world can only be understood by recognizing the intelligibles, those things that can be thought and understood but not perceived. The real structure of reality lies beneath the surface, in the archetypes or intelligibles, in the Golden Ratio or Pythagorean Harmonies, for example. For Plato, in the Timaeus, the real structure could only be found in an Idea which was separate from human intelligence, the archetypes; for Aristotle, in the De anima, the real structure could be found in the intelligibles in human thought itself. Both of these treatises were available to scholars in England at the beginning of the thirteenth century, as they were to scholars in Florence and Rome in the fifteenth, sixteenth, and seventeenth centuries. The Timaeus was partly translated into Latin by Calcidius in the fourth century. And many other circulating manuscripts incorporated these ideas, in the form of Neoplatonism: the Liber de Causis (1180), paraphrasing the Elements of Theology of Proclus, and the Theology of Aristotle (ninth century) paraphrasing the Enneads of Plotinus, for example. The façade of the Palazzo Rucellai (Figure 3.1), designed for Giovanni Rucellai by Alberti around 1455, consists of seven vertical bays divided into three tiers, with two doors. The proportion of the door bays is 3:2; the proportion of the bays above the doors is 7:4; the proportion of the other bays is 5:3. The bays of

the façade are seen by Alberti as areas, each being a square which is proportionally enlarged according to a consistent ratio. Seen as extended squares, the bays on the façade of the Palazzo Rucellai are one plus a half, one plus two-thirds, and one plus three-quarters. These three ratios are the octave or diapason (1:2), fifth or diapente (2:3), and fourth or diatessaron (3:4) of the Pythagorean Harmonies. Alberti explained in his treatise on architecture, written around 1450, that in architectural design “an area may be either short, long or intermediate. The shortest of all is the quadrangle. … After this come the sesquialtera [diapente], and another short area is the sesquitertia [diatesseron]” (Alberti 1988 [1452]: IX.6). Alberti explained that “the musical numbers are 1, 2, 3, and 4. … Architects employ all these numbers in the most convenient manner possible” (IX.5), because “the numbers by means of which the agreement of sounds affects our ears with delight, are the very same which please our eyes and our minds.” Marsilio Ficino, in his Opera Omnia, called Alberti a “Platonic mathematician.” The belief was that if the architecture contained the same numerical ratios as harmonic music composed with the octave, fifth, and fourth, then the architecture would be insured a visual harmony, a concinnitas or delight. The harmony and concinnitas are in the lineament, the line in the mind of the architect or viewer, and not in the matter. The harmony is in the form of the architecture, rather than in the function or structure of the building. To the typical tripartite division of the Florentine palazzo, Alberti added three orders of Classical columns: Doric on the ground level and Ionic/Composite on the piano nobile and mezzanine. This type of ornamentation on a building would have been identified as an imperial motif associated with the Roman Empire, as almost every important state building in Rome contained the same tripartite division and hierarchy of orders. Alberti’s design is thus a historicist collage, combining two unrelated building

Figure 3.1 Leon Battista Alberti, Palazzo Rucellai, 1455

types, and divorcing the form of the buildings from their functions. Alberti turned the Greek column into a pilaster and placed it under an arch, contradicting the relation between the form and function of the column, though only as a façade motif. Early Christian churches featured arches placed on columns, probably intended as a deliberate contradiction of the principles of pagan architecture. The façade of Sant’Andrea in Mantua (Figure 3.2) is similarly a historicist collage combining two unrelated building types-the Greek temple front and Roman triumphal arch-visually combined using underlying geometry and mathematics, resulting in a contradiction between the form of the façade (pagan Classical) and the function of the building (Catholic pilgrimage church).

Figure 3.2 Leon Battista Alberti, Sant’Andrea in Mantua, 1470-6