Perspective, Projections and Design

Technologies of Architectural Representation

Mario Carpo, Frédérique Lemerle, Mario Carpo, Frédérique Lemerle

• Publisher: Routledge
• Year: 2013
• eBook ISBN: 9781135657079
• Edition: 1
• Topic: Architecture
• Subtopic: Architecture General

The essays selected for this book, presented in chronological order, discuss various aspects of image-making technologies, geometrical knowledge and tools for architectural design, focusing in particular on two historical periods marked by comparable patterns of technological and cultural change. The first is the Renaissance; characterized by the rediscovery of linear perspectives and the simultaneous rise of new formats for architectural drawing and design on paper; the second, the contemporary rise of digital technologies and the simultaneous rise of virtual reality and computer-based design and manufacturing.

Many of the contributing authors explore the parallel between the invention of the perspectival paradigm in early-modern Europe and the recent development of digitized virtual reality. This issue in turn bears on the specific purposes of architectural design, where various representational tools and devices are used to visualize bi-dimensional aspects of objects that must be measured and eventually built in three-dimensional space.

1 The theory and practice of perspective in Vitruvius's De architectura

PIERRE GROS

The subject I am supposed to address is clearly inspired by the interplay between various aspects of a practice and a theory that Hubert Damisch described as “one of the most difficult enigmas in cultural history, yet which simultaneously represents one of the most powerful forces behind the development of the arts.”¹ The problem is that Vitruvius did not leave even so much as a sketch of a theory of perspective, a concept for which he and his contemporaries had no name. The sense in which we have understood this concept since Brunelleschi and Alberti² was basically alien to him; furthermore, it is impossible to assess his actual practice, for that would require that at least some of the drawings in his treatise had been preserved by manuscript tradition, which has not been the case.³ Whatever the situation, we would at least know more about the representation of volumes in Greek pictorial space if any of the works on the use of mathematics in painting, such as the one attributed to the fifth-century B.C.E. artist Pamphilos, had survived the total loss of technical literature from that period.⁴

Such a topic may nevertheless find its place in the context of this symposium, assuming that we agree with Panofsky that the crucial question is to know, for each period of history, not whether people knew about perspective, but which perspective they knew.⁵ That perhaps explains why the two very short passages by Vitru-vius on the depiction of buildings on a flat surface (I: 2.2 and VII: Praef. 11) have always constituted what G. J. Kern referred to disobligingly as “a favorite site for frolics by philologists infatuated with artistic exegesis.”⁶

The list of interpretations of those passages as drawn up by Kern in 1938 has since grown considerably, and I confess I hesitate to reopen a file that authors such as Agnès Rouveret and R. A. Tybout have globally addressed and expanded in recent years.⁷ It might just be useful, however, in the light of the most recent studies, to reexamine the means and goals of Vitruvius’s reflections on a mode of representation whose full potential he certainly did not realize and which in no case constituted a rational method for comprehending space, yet which nevertheless embodied a major stage in the conception of relationships between object and beholder. Of course Vitruvius, here as elsewhere, was no more than a more or less skilled transmitter of various traditions that were more or less ancient and sometimes very heterogeneous.⁸ So although the historical conjuncture of De architectura is not easy to reconstruct, its author remains representative of a culture and sensibility whose main elements, in the sphere that concerns us here, are recoverable.

A treatise such as his is structured, between the lines, by a fragmented yet retrievable logic, which calls for an interpretive strategy based on a knowledge of contemporary modes of expression and the value system that implicitly organized them.⁹

The conflict between reality and appearances

Now, the great debate of the first century B.C.E. concerned the conflict between reality and appearances. The idea was hardly new — Plato, in several passages of the Sophist and the Republic had long ago defined the optical foundations of the phenomenon, which would then be theorized by Euclid.¹⁰ But in Rome this idea was given a singular twist, and was updated, so to speak, by the clash between Epicureans and other Hellenistic doctrines. This philosophical “moment” was marked, among other things, by the Tropes of Aenesidemos of Knossos, an intransigent skeptic who is now assumed to be a contemporary of Cicero, which would date his intellectual activity to the period of Vitruvius’s cultural and technical apprenticeship.¹¹ To judge by the versions of his text transmitted by Sextus Empiricus and Diogenes Laertius, Aenesidemos developed the most devastating critique of all sensory perception by placing the notion of diaphônia, that is to say discordance or dissimilarity, at the heart of his theory.¹² This notion operates at all levels: not only between humans and animals, because flies and cats do not see the world the same way as we do, but also between humans, because ill, insane, and healthy people do not experience things in the same way. Worse, none of these specific perceptual modes can claim to offer an objective expression of the nature of things; none can assert itself as normal or normative, against which all others would be abnormal — a sober man, for example, enjoys no superiority over a drunken one in this sphere. From the series of optical illusions that Aenesidemos, following others, delights in listing, I will retain, from his third Trope, the example of a painting that seems to present images in relief but which, when touched, turns out to be flat.¹³ This example was employed in similar terms by Vitruvius in VI: 2.2, where it heads the list of false visual impressions.¹⁴ Also worth mentioning, from the fifth Trope of Aen-esidemos, is the instance of alterations resulting from the position of the beholder when viewing a painting, which can lead to an impression of flatness from one angle but an impression of projecting and retreating features from another angle; this example allows us to understand, as we shall see below, one of the crucial expressions employed by Vitruvius in VII: Praef. 11.¹⁵ Compared to these radical expositions, the oft-cited observations made by Cicero and Lucretius, which partly flow from them, seem rather tame.¹⁶

Taking optical illusions into account

Vitruvius was nourished on all of this, probably through a more or less basic doxography, and he retained above all the idea that our eyes are the origin of erroneous judgments. Although he did not, of course, enter into the philosophical debate, Vitruvius drew from it—artist that he basically was, despite the often prosaic nature of his precepts — an optical sensibility, or, to borrow a concept from Antonio Corso, an optico-scenographic sensibility, which was expressed in specific ways.¹⁷

Vitruvius appears to be primarily concerned with anomalies of vision not because he was interested in the physiology of perception,¹⁸ but because deformations of reality generated by human vision required corrections to be made to the modular system of symmetria.¹⁹ There are numerous passages where Vitruvius proposes, faithful to the tradition of his late classical and Hellenistic models, adjustments (temperaturae) to proportional relationships as soon as the parts of a building are to be viewed by the beholder from a certain distance.²⁰ The most demonstrative passages are those in Book III that deal with corrections which must be made to the columns, base, and pediment of a temple to prevent them from appearing malformed or misplaced with respect to the whole.²¹ Vitruvius was clearly indebted here to a series of widely disseminated manuals or guides, whose traces may be detected in the terminology of De architectura. Thus Vitruvius’s apparent indifference to the exact mechanism behind sight, expressed in VI: 2.3, stems not only from the rhetorical practice of multiple explanations (which involved stating existing hypotheses without favoring one or the other²²), but quite simply imitates an approach typical of expositions on the science of optics, for which Hero of Alexandria, a compiler and transmitter from the first century C.E., provides an exact equivalent in Greek.²³ Still more clearly, the famous exposition on the notion of scenography in the Pseudo-Damianus version, sometimes attributed to Geminos of Rhodes and also found in Hero’s Definitiones,²⁴ was lifted so literally by Vitruvius that he, too, refers to the construction of colossal statues (III: 5.9) even though they were clearly alien to his topic; he furthermore referred to them by the Greek term colossicotera, which he merely transliterated.²⁵ The scientific explanation he gave for all these visual adjustments was based on the theory that under certain conditions, human vision, whose rays allegedly traveled in straight lines but through layers of air of different densities (and therefore differing resistance), provided no guarantee of presenting the real appearance of a building.²⁶ When confronted with certae res, that is, material elements with a definite struc-ture,²⁷ human eyes often form imagines incertae, that is to say poorly defined images based on confused information on the proportions of those elements (incertam modulorum quantitatem).²⁸ This situation calls for a corrective intervention on appearances, which must be modified in order to recover what Vitruvius calls, in VI: 3.11, the non dissimi-les veris symmetriis venustates, that is to say a harmony that does not contradict the real modular relationships, which are true insofar as they correspond to the reality of construction yet must be modified in order to appear true. This is symmetria based on appearances, pros phantasian, according to the terms of the Greek text on scenography cited above.²⁹

The concept of asperitas

But we need to go further. Taking optical illusions into account not only had an effect on given proportional relationships, it might also influence the overall conception of a building. Thus, in the hierarchy of species, that is to say different styles or ways of positioning columns around a temple,³⁰ Vitruvius ranked highest those most likely to create an impression of relief by allowing sufficiently deep zones of shadow on both sides of the vertical supports, projecting the columns in question toward the beholder. The pseudipteral style, erroneously attributed to Hermo-genes, was the plan best suited to this kind of effect, given the asperitas of its intercolumniation.³¹ The many commentators on references to perspective in De architec-tura have barely noted this concept of asperitas, which better than any other term in the treatise expresses the idea of “high relief” engendered by the play of...

Table of contents

• Cover
• PERSPECTIVE, PROJECTIONS AND DESIGN
• Title
• Copyright
• Contents
• Notes on contributors
• Acknowledgments
• Introduction
• 1 The theory and practice of perspective in Vitruvius's De architectura
• 2 Geometries of Phàntasma
• 3 Computer vision and painters' visions in Italian and Netherlandish art of the fifteenth century
• 4 Alberti's Media Lab
• 5 Constructing perspective in sixteenth-century Nuremberg
• 6 Sebastiano Serlio prospettico: stages in his artistic itinerary during the 1520s
• 7 Sebastiano Serlio: placing perspective at the service of architects
• 8 Sophisticated geometry, baroque composition
• 9 "The eye of the Sun": Galileo and Pietro Accolti on orthographic projection
• 10 Fortification and military perspective in seventeenth-century France
• 11 Pictorial versus intellectual representation: teaching perspective to architectural students at the École des Beaux-Arts in Paris (1824-1900)
• 12 From rationality to utopia: Auguste Choisy and axonometric projection
• 13 Project and projections: some advantages of the principle of opacity
• 14 Architectural embodiment: prosthetics and parasites
• Index