Circling Round Vitruvius, Linear Perspective, and the Design of Roman Wall Painting

Abstract

Many scholars believe that linear perspective existed in classical antiquity, but a fresh examination of two key texts in Vitruvius shows that 1.2.2 is about modularity and symmetria, while 7.Pr.11 describes shading (skiagraphia). Moreover, these new interpretations are firmly based on the classical understanding of optics and the history of painting (e.g., Pliny the Elder). A third text (Philostratus, Imagines 1.4.2) suggests that the design of Roman wall painting depends on concentric circles. Philostratus’ system is then used to successfully make facsimiles of five walls, representing Styles II, III, and IV of Roman wall painting. Hence, linear perspective and its relatives, such as Panofsky’s vanishing vertical axis, should not be imposed retrospectively where they never existed.

Two systems for designing Pompeian wall paintings have dominated modern scholarship: a one- or center-point perspective and a vanishing vertical axis.1 Neither method works for all the variations seen on the walls of Styles II–IV. The vanishing vertical axis is considered a precursor of linear perspective, whereas center-point construction is a form of linear perspective. Many scholars believe that linear perspective was invented by the Greeks, only to be forgotten during the Middle Ages and “reinvented” in the Renaissance.2 In contrast, I propose that linear perspective was not known in any form in antiquity but, rather, was an invention of the Renaissance, which also created its putative ancient pedigree.

1. Background

1.1. Definitions

First, it is important to define four key terms.

“Perspective” applies loosely to a wide range of systems that convert a three-dimensional scene to two dimensions. Most scholars, however, mean “linear perspective” when they use the unqualified term “perspective”. No standard definition exists for linear perspective, but only linear perspective obeys the rules of projective geometry. Formal definitions refer to “station points” (the point or place for the “eye” of the “viewer” and/or “artist”), vanishing points, horizon lines, and picture planes, among other aspects. Horizontal lines converge to the “center point” or, in the case of “two-point” linear perspective, to two points, one on either end of a “horizon” line. Only “center-point” perspective is claimed for classical antiquity. Center-point perspective shares some characteristics with non-perspectival representations: (1) Foreshortening and diminution are not examples of linear perspective, but developed separately and independently. As Philip Thibodeau puts it, “linear perspective presupposes diminution, while diminution does not imply the use of linear perspective. Pompeian wall-paintings, for example, typically display consistent diminution, without showing anything like consistent central point perspective.”3 (2) Similarly, an oblique view of a building showing only the front and one side may look as if it were portrayed in linear perspective, but if the orthogonals do not converge, as in Chinese and Japanese art, then it is not linear perspective.4 (3) Likewise, the presence of vanishing points is not exclusive to linear perspective. (4) Finally, most important of all and most diagnostic for identifying linear perspective is that linear perspective applies to the whole representation and determines how all elements are depicted. It should be noted that “perspectiva” is not a classical but a medieval word from the twelfth century, which referred to the “science of optics”. In the sixteenth century, it became “perspective”, as we use it today.5

“Skenographia”, a Greek word, is generally translated as “perspective”.6 The Latin form, “scaenographia”, appears in Vitruvius (1.2.2). Its two parts literally mean “painting (of) the stage”, that is, the theater’s façade (scaenae frons), or freely “scene painting”. Aristotle (Poetics 1449a18), in its earliest extant citation, associates it with Sophocles and hence the theater. Its usage bifurcated during the Hellenistic period. On the one hand, its definition expanded to include “cityscapes” (e.g., Polybios 12.28a.6), which, in turn, later broadened to “painting” in general (e.g., Clement, Stromata 6.7.56). On the other hand, its use was restricted to a technical, architectural drawing or plan, as in Vitruvius (1.2.2) and Heron (Definitions 135.13.1–2).

“Skiagraphia”, from its two components, means “shadow painting” or “shading”. It also first occurred in the fifth century BCE. Over time “skenographia” and “skiagraphia” became synonymous (Hesychius, fifth-century CE lexicographer).7

Lastly, vanishing vertical axis (fishbone or herringbone) is the term that encapsulates Erwin Panofsky’s theory about the design of Roman wall painting.8 It refers to a central vertical “line” or axis in a painting with an unspecified number of points for the placing of diagonal lines that ideally define significant parts of a scene.

1.2. Brief History of Skenographia as Linear Perspective

The idea that linear perspective existed in classical antiquity goes back to the Renaissance and translations of Vitruvius’ treatise on architecture into Italian.9 Vitruvius in 1.2.2 lists three plans required for a building. The first two, a ground plan (ichnographia) and an elevation (orthographia), are straightforward, even if dressed up in Vitruvius’ idiosyncratic use of Greek words.10 The sentence about the third plan, however, is one of the most contested passages in Vitruvius. Literally, it (Appendix A No. 1) says: “Likewise scaenographia is a drawing of the front and the receding sides and the correspondence (harmonious relationship) of all lines to the center point of the compass.”11

Early Renaissance translators were not familiar with the word “scaenographia”.12 Undaunted, they substituted a word they knew, “sciografia” (Greek skiagraphia), a word not used by Vitruvius.13 The change in vocabulary did not clarify what Vitruvius meant, but the illustrations for sciografia showed the façade and one side of a rectangular building in perspective (Figure 1). Claude Perrault in his French translation of 1684 (p. 10 n. 7) conclusively restored skenographia, while still translating it as “perspective”.

2. Literary Sources

2.1. Vitruvius 7. Preface. 11

Scholars cite one other passage from Vitruvius (7.Pr.11 = Appendix A No. 2) to support their claims of linear perspective. Vitruvius says that Agatharcus “built a scaena (stage building) and wrote a treatise about it”. Two philosophers, Democritus and Anaxagoras

learned from it [the treatise] and in turn wrote about the same subject [res]: that is in what way lines should respond in a natural relation [ratio naturalis] to the point [acies] of the eyes and the extension of the rays [radii] once a fixed [certus] place [locus] has been established as the center, in order that from a dimly perceived object precise images of buildings in the paintings of the stage-buildings [imagines aedificiorum in scaenarum picturis] [may] reproduce an appearance [species] with some [lines] seen extending [prominentia] and others receding when depicted on the vertical [directus] surfaces and fronts [of a stage-building/scaena].14

While the passage presents a number of problems, its reference to rays, a center point, projection, and recession are believed to describe linear perspective. The dates of Agatharcus and the two philosophers indicate the origin of skenographia in the fifth century BCE. That Vitruvius does not explicitly mention skenographia or connect this passage with 1.2.2 and vice versa is considered unimportant.

A comparison of 7.Pr.11 to other classical texts, describing projection and recession, however, confirms that it is not about linear perspective. Painters instead used color, shading, and shadows to achieve three-dimensionality. “Aristotle” (Appendix A No. 3), in one of the earliest citations on the topic, says: “Just as in a picture, if an artist represents two objects in colour, one as though it were at a distance and the other as though it were close at hand, the former object appears to us to be sunk into the background of the picture and the latter stands out in the foreground, even though both appear on the same surface.”15 “Alexander” of Aphrodisias (Appendix A No. 4), a second-century AD philosopher, in his commentary on Aristotle’s On the Soul, explains the following:

For the light does not fall in a similar way on all parts of what is uneven, because some of them are concave, some convex, some sideways on to the [source] of the illumination, some opposite to it. On account of these differences, even if what is seen is of a single colour, some [parts] of it seem dimmer, others more conspicuous, and thus some will be seen as recessed and others as projecting. Painters imitate this when they want to show on the same plane what is uneven, and make some parts light while shading others. Thus some [parts] of [what they paint] appear projecting, others recessed, and as projecting those that are made more light, as recessed those that are shaded.16

This description echoes that of 7.Pr.11 while unambiguously stating that color and shades produce projection and recession.

Next, “Alexander” (Appendix A No. 4) explains how the use of light and shading he just described fits within the system of optics:

For it [sight] sees the things that it sees by a cone which has the pupil as its vertex and as its base the line which defines what [part] of the perceived body is seen and what not. … and the colouring, as it were, that comes about … in straight lines in a similar way to light …. It is by the angles of these cones that [sight] judges larger and smaller and equal things. For it sees [as] equal those things the sight of which involves equal angles, [as] larger than those which involve larger ones.17

First, whatever we see comes to or goes from the eyes in straight lines. Hence, straight lines and rays are not exclusive to linear perspective. Second, Democritus and Anaxagoras then, to their surprise, realized that shading and shadows made things look “real”, in our terms three-dimensional, and notably did so not with curved rays, but the usual straight ones.

Alexander’s passage raises another crucial point: “[Sight] sees and judges size by the angle of the cone which is formed towards the sight.” According to Gérard Simon:

[T]he perspective of the ancients (at least in its theoretical exposition) is ‘angular’ (or curvilinear), instead of being ‘planar’ as that of the Renaissance: in the perspective of the ancients, the apparent size of a receding object diminishes not as a function of its distance, but as a function of the angle under which it is seen—which does not amount to the same.18

My interpretation of projection and recession is confirmed in a number of other passages.19 Porphyry (Appendix A No. 5), in his commentary on Ptolemy’s Harmonics, uses painting as an analogy for how music works: “Thus just as in painting, when someone uses colours to make one thing resemble what is far away and another resemble what is nearby, one of them seems to us to recede from the painting and the other to stand forward, though both of them are on the same surface, so it is too with sounds and the voice.”20

Before his full discussion of the history of painting, Pliny the Elder (Appendix A No. 6) summarizes the major advances in painting:

At length the art [of painting] differentiated itself and invented light and shades, using a diversity of colors which enhanced one another through their interaction. Finally splendor was added, which is something quite different from light. That which exists between light and shade they called tonos, and the transition from one color to another they called harmoge.21

Pliny emphasizes the role of “light” (lumen) whether in contrast to “shade” (umbra) or “highlight”, as “splendor” is commonly translated.22 Completely absent is any mention of skenographia. Pliny’s emphasis on color, along with light and shade, reflects the ancient assessment of painting. Philostratus (Appendix A No. 7), in the following century, also defines painting as “imitation by the use of colours… [it] reproduces light and shade.”23

Artists and philosophers, such as Anaxagoras and Democritus in Vitruvius 7.Pr.11, were interested in the same phenomena—shading and shadows. Anaxagoras and Democritus were known for their investigations of vision, how colors change, and how eclipses work.24 Thus, these two philosophers had good reason for reading Agatharcus’ treatise with its discussion of how shading and shadows produce an impression of projection and recession.

2.2. Lucretius, On the Nature of Things, 4.426–431

A passage in Lucretius’ De rerum natura (Appendix A No. 8) has also been misinterpreted:

When we gaze from one end down the whole length of a colonnade, though its structure is perfectly symmetrical and it is propped throughout on pillars of equal height, yet it contracts by slow degrees in a narrowing cone that draws roof to floor and left to right till it unites them in the imperceptible apex of the cone [donec in obscurum coni conduxit acumen].25

At first, Lucretius seems to refer to a vanishing point and therefore central projection. Euclid (Optics, Definition 2; Appendix A No. 9), however, uses similar wording that precludes the idea of a vanishing point: “and that the form of the space included within our vision is a cone, with its apex [κορυφὴν] in the eye and its base at the limits of our vision.”26 If the top of the cone vanished, so would the image. Lucretius, instead, means that objects are not viewable from a distance. Lastly, classical depictions of colonnades do taper from the sides to the center but never come close to meeting, much less disappearing.

In conclusion, wishful thinking lies behind the interpretation of the three “core” classical texts as proof of linear perspective. Agnès Rouveret, for example, remarks that “their judgments [Roman writers on art and especially Pliny the Elder] magnified the ‘invention’ of light and shades, based on the fascinating power of color and not only on the perfect mastering of the line.”27 The idea that what Pliny says accurately reflects ancient painting has been passed over despite the numerous references to light, shading, and shadows in classical texts.

3. The Evidence from Classical Art

Scenes interpreted as using linear perspective, such as the abovementioned literary references, are few and problematic. Despite the purported origin of skenographia in the fifth century BCE, the earliest cited objects are fourth-century South Italian vases. The scene on an Apulian volute-krater with the death of Thersites epitomizes the problems.28 In the aedicula, Phoenix and Achilles are shown head-on despite the fact that building’s rafters are seen from below. The figures and objects around the aedicula are also depicted orthogonally in their own spaces with separate ground lines. Greek and Roman artists do not think in terms of whole scenes, but only the parts. Hence, classical artists often combined various “techniques” within one picture, such as hierarchical and semi-bird’s eye perspective.29 Linear perspective, however, imposes it rules on all elements of a representation, something rarely achieved in classical art.

No one disputes that Roman wall painting displays three-dimensionality, only how it was achieved. Shading and shadows do not need linear perspective to look so three-dimensional that crows see real grapes.30 Linear perspective alone, however, fools no birds.31 Such effects are easy to achieve, as the dado in the cubiculum from Boscoreale shows (Figure 2 and Figure 3).32 The green rectangular panels appear to be set within a red frame, because the left vertical and lower horizontal parts of the frame are highlighted, whereas a darker or shadowy line defines the upper horizontal and right side. If the two sets of lines are reversed, placing the highlight on top, the panel projects, as on the dado on the back wall of the cubiculum.

According to the literary sources, the use of shading and shadows began in the fifth century BCE—the same era in which skenographia appeared. Plutarch (Appendix A No. 10) calls Apollodorus “the first man to discover the art of mixing colors and shading”.33 He was known as the “skiagraphos”, a word related to the word substituted for skenographia in early translations of Vitruvius. Nothing of his work or any other Greek monumental painter cited in ancient sources has survived. Although vase painting was technically limited in showing gradations of colors, three methods suggested shading: (1) darker paint strokes over a lighter “wash”;34 (2) color added after a vase had been fired, though it often flaked off;35 and (3) hatching—a series of lines, often following contours, closely spaced together. The last technique is well suited for vase painting and may have been invented by a vase painter. The earliest extant example appears on a shield on an Attic red-figure vase from the first quarter of the fifth century BCE (Figure 4).36 Hatching occurred regularly in tomb paintings from Macedonia from the fourth century BCE on, as well as in Etruscan and Roman painting. It was also used to depict cast shadows.37 Lastly, Pliny details each painter’s contribution to the development of shading and shadows from the late fifth century and Apollodorus through the fourth century to Apelles and Pausias. It took over a century to understand how shading and shadows worked in art, and even then, the later Roman painters added their own contributions.38

Roman wall painting in Styles II–IV with architectural frames is considered the best evidence for linear perspective in classical antiquity. Yet, no wall, much less room, consistently portrays linear perspective.39 More telling perhaps is the absence of linear perspective in narrative scenes, both mythological and historical, as well as in scenes of genre. Some modern “reconstructions” of painted walls show the structures that the painters purportedly had in mind. For example, a Second Style wall from the House of the Cryptoporticus at Pompeii has been modified to demonstrate what it would look like if linear perspective had been used (Figure 5).40 Parts of the building, such as the two outside colonnades, invade the viewer’s space to such a disturbing degree that linear perspective, as an organizing principle for Roman wall painting, is unlikely.

Finally, linear perspective is complex. It took approximately one hundred years in the Renaissance for artists to understand more or less how it worked. Classical painters spent a similar amount of time in refining their depictions of shading and shadows. Yet, classical scholars posit linear perspective springing whole, like Athena from Zeus’ head, in the fifth century BCE with no antecedents.41

4. The Purpose of Vitruvius’ Skenographia

The usefulness of ground plans and elevations for buildings is obvious, but the purpose of a skenographia has never been adequately explained. Before listing the three types of drawings, Vitruvius (Appendix A No. 11) discusses how they fit within the overall planning of a building:

Ordinatio [order] is the ordinary [modica] aptness [commoditas] of the parts of the work separately and together, a comparison [comparatio] of proportion [proportio] to symmetria. This is based on size [quantitas], which is called posotes in Greek. Size [quantitas], moreover, is the taking [sumptio] of modules from the parts of the work itself and the harmonious result [conveniens effectus] [comes] from the individual sections of the parts.

First, a clarification must be made: English has only one word for “proportion”, whereas Greek and Latin have two words—analogia and symmetria for Greek and proportio and symmetria for Latin. Analogia is more or less equivalent to our use of “proportion”. Symmetria, however, did not mean “symmetry” in the modern sense of a mirror-image arrangement. It referred instead to the balance or commensurability among the individual parts of a whole. An extremely large head, for example, looks incongruous on a diminutive body. Thus, analogia refers to the relationships between whole things, while symmetria refers to the relationships within a single thing or whole. I use symmetria for the classical word and symmetry for our concept.42

Because Vitruvius repeatedly wrote about modularity, proportion, and symmetria, the absence of a drawing to guide their implementation would be surprising. Recall his definition of skenographia (Appendix A No. 1): “Likewise scaenographia is a drawing of the front and the receding sides and the correspondence [harmonious relationship] of all lines to the center point of the compass.” Vitruvius explains what he means in 1.2.4 (Appendix A No. 12):

Likewise symmetria is the consistent agreement among the elements of the work itself and the proportionate [ratae partis] correspondence [responsus] of the separate parts to the appearance of the whole form. As in the human body from cubit, foot, palm, finger, and the other small parts, the nature of eurythmia is symmetros (proportionate), so it is with the finishing of the work.

In Book 3 on temples, Vitruvius expands on 1.2.4. He uses a drawing of a man to show how proportion, based on a module, produces the “best” structures. He begins (3.1.1 = Appendix A No. 13) by rephrasing 1.2.2:

The composition of a temple is based on symmetry, whose principles architects should take the greatest care to master. Symmetry derives from proportion, which is called analogia in Greek. Proportion is the mutual calibration of each element of the work and of the whole, from which the proportional system is achieved. No temple can have any compositional scheme without symmetry and proportion, unless, as it were, it has an exact system of correspondence to the likeness of a well-formed human being.43

Hence, Vitruvius recommends using modules rather than precise measurements, because modules are far easier to work with. Only the size of the module, not the individual measurements, has to be altered for resizing. All structures, no matter their size, using the same plan or model have the same number of modules, because modules do not have a fixed measurement until implemented. A modular system also circumvents problems arising from the absence of standardized measurements in classical antiquity.44

The similarities between a skenographia of a building and the Vitruvian Man (3.1.2-4), as the drawing is now called, are striking (Figure 6). Both are placed within a compass-drawn circle with a center point. Significantly both texts use a form of “respondeo” to describe how the parts “correspond” to the whole.45 Vitruvius (3.1.9 = Appendix A No. 14) concludes the following:

Therefore: if it is agreed that the numerical system was derived from human members, and that there should be a commensurable relationship [commensus fieri responsum] based on accepted units between those members taken separately and the form of the body as a whole, it remains for us to demonstrate the greatest respect for those who, when building temples for the immortal gods, arranged the elements of the buildings in such a way that, thanks to the proportions and symmetriae [proportionibus et symmetriis], the arrangement of the individual elements and whole corresponded to each other.46

Now, the most troublesome section of Vitruvius’ definition of skenographia becomes clear. Vitruvius really does mean “all lines” are to “correspond” to the “center point”, because he is not talking about linear perspective but symmetria. His qualification of “sides” with “receding” describes how they look.

Only Cesare Cesariano, an independent and cantankerous translator (he included in his 1521 edition of Vitruvius a full-page illustration depicting an allegory of his wretched life), followed Vitruvius’ directions (Figure 7).47 Cesariano used the Duomo in Milan as his example. While the two sides show recession with diagonal lines, as Vitruvius prescribes, overall, the Duomo looks flat (Figure 8. Similar flat depictions of buildings with a single side and the façade occur in Roman representations. For example, the reverse of a bronze sestertius shows one side and the front of the shrine of Janus Geminus, see Figure 9).48 Alberti (On the Art of Building, 2.1) also recommends a plain, flat drawing with no shading. James Ackerman explains that “The major Renaissance theorists opposed the use of perspective as a means of architectural representation because the receding lines would be unmeasurable and therefore misleading.”49 Furthermore, the three plans are not “presentation” drawings for a client, because what few ancient references we have indicate rough sketches not formal views. For example, Aulus Gellius (19.10.2–4) mentions plans on “membranulis”, little pieces of parchment. Vitruvius, instead, prescribes the three kinds of drawings a builder needs.

In conclusion, neither of the two Vitruvian passages cited as evidence for linear perspective is about linear perspective. Vitruvius requires a skenographia for two reasons: to set the module for the construction of the entire building and to show how the parts of the building relate to each other and the building as a whole. The second passage, 7.Pr.11, likewise, is not about linear perspective, but shading and shadows, which first occurred in art in the fifth century BCE. The question, then, is what system did the Romans use to design their wall paintings?

5. Designing Roman Wall Paintings

5.1. The Evidence from Philostratus

Vitruvius depends on two simple tools, the compass and straight edge, for his plans of virtually all structures, whether for a house, temple, theater, or even the layout of a city.50 Like the skenographia and Vitruvian Man, these plans all begin with a circle. Therefore, it is reasonable that the painted “architectural” Roman walls also used circles for their design. Textual support comes from Philostratus (Appendix A No. 15) in his description of a painting of the Seven against Thebes:

The clever artifice of the painter is delightful. Encompassing the walls with armed men, he depicts them so that some are seen in full figure, others with the legs hidden, others from the waist up, then only the busts of some, heads only, helmets only, and finally just spear-points. This, my boy, is perspective; since the problem is to deceive the eyes as they travel back along with the proper receding planes of the picture.51

The last sentence refers to “perspective” and “planes”, as is common in modern translations—a very free interpretation of the Greek.52 Literally, however, the sentence says: “These are proportions [analogia], oh child. For it is necessary that the eyes be deceived, going back along the usual circles [kykloi].” Analogia, as I discussed above, concerns “size” in the sense of enlargement and diminution, based on a module, a circle in this case. Hence, Philostratus says that recession or depth was achieved not with linear perspective, but by using proportionate concentric circles. This method differs from the recession produced by shading and shadows. First, the concentric circles apply to the whole scene. Second, individual elements within a scene may also show shading.

5.2. The Circle Method of Design

Using concentric circles as the organizing principle, I have replicated whole Roman painted walls from scratch, no matter how complex, in each of the Pompeian Styles II–IV.53 The system needs only five tools: a straightedge, cord and a peg or nail to anchor the cord for drawing circles, charcoal or chalk to make the guidelines, and sinopia for laying out the design.54 I used PowerPoint to test the theory, because I already owned it, knew the program well, and could annotate each step on the slides. Moreover, its ubiquity means that scholars can easily test my results and even try their own experiments. These advantages were countered by PowerPoint’s inability to render small details accurately. So, I simplified repetitive sections such as colonnades by reducing the number of columns. Small bits and pieces are sometimes slightly out of whack. Nonetheless, the facsimiles are sufficiently accurate and recognizable to demonstrate that the system works for all three styles. I chose the walls frequently discussed by scholars as exemplars of linear perspective and their respective styles. Each style has at least one facsimile. Second Style walls, most often the focus of discussions, have three examples. Here, I give a brief description of how the system works using the cubiculum from Boscoreale in the Metropolitan Museum of Art, New York, as the example (Figure 2a [full wall] and Figure 10). Please see Supplementary Materials S1 for the other facsimiles, including a detailed analysis of the columns in the room from Oplontis (slides 5–10).

The wall is divided into four, not three or five, sections (Figure 2a). Since a pilaster separates the end section from the other three, I “recreated” only those three sections.

I began with a rectangle, the equivalent of a blank wall, on which I marked the center by dropping two diagonals from the top corners to the bottom corners (Figure 11).

I then divided the space vertically and horizontally into four equal, symmetrical parts, analogous to laying out the cardo (vertical line for north/south) and decumanus (horizontal line for east/west) of a city (Figure 12). Alberti remarks, “We then relate all the measurements to those two lines. This works wonderfully in every way: the parallel lines are easily drawn, the angles can be defined accurately, and the parts conform and correspond exactly to one another.”55

Next, I removed the two diagonal lines for finding the center, because they were no longer necessary. Then, I added a set of concentric circles, using the center of the wall as their center point (Figure 13). The number of circles depends on the complexity of the wall: the more complex the more circles. My circles extend beyond the confines of the wall, because incomplete circles and arcs are difficult to make in PowerPoint (see Supplementary Materials S1). The Roman designer would have drawn only the arcs; that is, the circles would be left open on top and bottom.

Because painted architecture, unlike a real building, does not have to obey the laws of physics, I usually placed lines by eye to match the models. So, I next placed the major divisions of the wall: the three vertical sections with the center wider and the two horizontal divisions of the dado and frieze area. Because there is not a significant crowning moulding, I did not mark it. To make the process easier to understand, I have highlighted the circles here and in the following steps that define where each part is placed. The fifth circle from the center (colored red) determined the width of the center panel and hence the placement of the two vertical dividers (dark blue heavy lines; also at left and right edges). I next placed an orange horizontal line a little above the green horizontal line for the top of the “front” row of structures. Once the major divisions were set, I could work on any section in any order. The circles work like a grid for placing parts, which I discuss below. Because the designs are all bilaterally symmetrical, the painter has to design only half of the wall, as in the preliminary sketch from Oplontis, and then flip it element by element to the other half of the wall.56 I followed the same procedure. In the case of the cubiculum from Boscoreale, the designer needed to plan only one vertical section, because both long walls are virtual twins.

Next, I worked on the central panel and its niche in orange (Figure 14). Four circles guided me. The inmost red circle (No. 1) defined the width of the niche. The outermost red circle (No. 6) determined the top of the “arch” over Hekate. Note how the inside lines of its two “pillars” likewise define the inside of the red niche “below” it. Hence, one vertical line suffices for both structures. To make the indentation of the niche, I used circles No. 4 and No. 5: No. 5 marked the bottom of the niche and No. 4 the recession. The two diagonal lines were placed by eye.

I then added the basic structures in orange in the lower portion (Figure 15). The two outer red circles defined the placement of the tall left and right structures, while the purple circles aided in the placement of the of the sections with doors. You do not have to locate the pertinent circles by counting from the center (or outside in). Just follow the appropriate circle from the left to the right side for accurate placement. Note how the purple circles define both the building and the recession for the side walls. At this point, it became clear that the flanking panels should have been a bit wider to more accurately reflect the doors in the actual frieze. Because I was studying the feasibility of using circles for the design, I did not think it was necessary to make any changes.

Next, I blocked out the tops of the buildings in the upper section (Figure 16). The pediment of the yellow structure on the outside of each panel is an example of the problem of exactly aligning small elements in PowerPoint.

Details were added throughout the frieze: the loggias and divisions for various buildings in the upper portion, the windows and doors in the lower part, and the central niche and recessed panels in the dado. The dado area was reduced to allow for the green area in front of the lower buildings (Figure 17).

All guidelines were removed and final adjustments were made (Figure 18). For example, the dark blue vertical dividers were “brought to the front” to cover the ends of the pale blue horizontal lines.

From my experiment I learned a number of things:

• At no time did I need or use exact measurements. In PowerPoint, I copied each line segment on one side and then pasted it on the other side. In practice, a painter would mark a line segment from one side on a straight edge (or use a compass/calipers to measure the length) and place it in its equivalent circle on the other side of the central vertical divider.
• Because the system is modular, as Vitruvius recommends, copying a motif or design from one building to another, such as the wall from the cubiculum of Boscoreale and its twin in the House of the Labyrinth, is relatively simple.57 Scholars assume that grids were used to make the copies, but concentric circles also work well.
• I automated the process by reusing the same rectangles and circles for different walls. I did not test whether the Romans also did so.
• The system worked for all walls, no matter the style, no matter the shape (the narrow wall from the House of the Vettii vs. the other walls).

5.3. Variations as Before, I Use the Cubiculum from Boscoreale as My Example

5.3.1. Using Squares Instead of Circles

I converted the circles to nested squares (Figure 19). The squares, similar to the circles, enable one to maintain bilateral symmetry. On the one hand, squares are easier to work with in that their verticals and horizontals can sometimes be directly incorporated as elements of the scene. Note the central panel with the squares defining the vertical elements. On the other hand, it is easier to use a central peg and inscribe arcs with a piece of charcoal at the end of a cord than to measure the squares and align them exactly. Less significant, perhaps, is the absence of textual support. Although Vitruvius does place Vitruvian man in a square as well as a circle, he prefers circles as the base, as mentioned above (Figure 6).58

5.3.2. Grids

The circles can be used either independently or in conjunction with grids. If the two are used together, then more points for placing elements are available (Figure 20).

As is well known, grids alone also work (Figure 21).

It is also possible that grids were used for placing “built” and landscape elements of a scene, while the circles defined the proportions of people. For example, the center of a scene, as the focus, might be largest with smaller flanking figures on the same ground line. Lastly, grids may have been used in earlier paintings and the circles deployed sometime in the second century, as noted in the Philostratus passage.

5.3.3. Other Applications of the Circle System

At least one example of the modular use of circles in art has survived. The back of the Season Sarcophagus at the Metropolitan Museum of Art, New York, was used like “scratch paper”, because it was never meant to be seen. According to Elizabeth Bartman, the artist selected one set of test concentric circles to control the relationships and sizes of the figures on the front of the sarcophagus.59 This sarcophagus dates to roughly the time of Philostratus.

As the Bartman example shows, concentric circles, unlike “linear perspective”, were not restricted to the design of painted “architectural” walls, but could appear in any scene, no matter the subject nor the medium—a topic to be explored elsewhere.

Note that the idea of concentric circles for figured scenes goes back to the description of the “second” shield of Achilles in the Iliad (18.478–608). Perhaps even more significant is the use of ring composition (i.e., concentric circles) for the text of the Iliad and the Odyssey.

5.4. The Vertical Vanishing Axis

5.4.1. Facsimiles Using a Central Vertical Vanishing Axis

I tried designing the same walls with a central vertical vanishing axis.60 It was such a nightmare that I have no completed examples. I was in a quandary about where to place points on the vertical axis and at what angles to draw the diagonals. Each circle is numbered, so to speak, which enables one to count either from the edge or from the center to produce mirror images. “Arbitrary” decisions by eye for what goes where were easy to make, because the circles provided obvious starting and finishing points. With the vertical vanishing axis, each element had to be individually placed and measured. Keeping bilateral symmetry was complex, because it was no longer a matter of flipping elements from one side to the other, but of making each measurement twice, once for each half. In fact, the precise measuring and layout required for linear perspective are also necessary for a vanishing vertical axis.

Most important of all, however, was my realization that if I began with a vanishing vertical axis and laid down the diagonals in the beginning to guide my placement of the elements, then all the “pairs” of diagonals must cross the vertical axis together. Yet, no one has managed to get such uniform agreement within a single wall, when imposing diagonals on the actual wall paintings. The cubiculum from Boscoreale is a typical example (Figure 22). Hence, I believe that it is highly unlikely that a vanishing vertical axis was used—a conclusion reinforced by the next experiment.61

5.4.2. Drawing Diagonals for the Vertical Vanishing Axis over My Circle Reconstructions

I analyzed my finished facsimiles the same way that scholars analyze actual wall paintings (see Supplementary Materials S2). Here, I again used Boscoreale as my example (Figure 22). I restored the vertical axis and then drew sets of matching diagonals from “significant” points (Figure 23). The results matched those drawn by others, including some of the near misses. All my facsimiles produced false vanishing vertical axes, because bilateral symmetry by definition must be organized around either a horizontal or, in the case of Roman wall paintings, a vertical axis. Moreover, the diagonal lines seem to vanish only if one considers each diagonal as two separate diagonals joined end to end rather than as a single diagonal. This experiment proved two things. First, the idea of the vanishing vertical axis should vanish. Second, analyzing the “surface geometry” of finished works of art is too subjective to be of value.62

5.5. Summary

The passage from Philostratus documents the use of circles in Roman wall painting certainly for his own time (ca. 200 CE) and most likely earlier. His use of “analogia”, “proportion”, links this method of design with that of Vitruvius, who likewise emphasizes proportion (“scaenographia” [1.2.2], “Vitruvian man” [3.1], among many). Finding traces of concentric circles or grids is difficult, because they were likely drawn in charcoal and plastered and painted over to achieve the final product. It is clear, however, that either circles or grids or a combination are sufficient for the design of Roman painted walls. At this stage of our knowledge, what was used when and where remains open. We do know, however, that complex systems of design, such as the vanishing vertical axis or linear perspective, are unlikely.

6. Implications

The new interpretations of the two passages from Vitruvius have major implications for our understanding of ancient art, which I can only briefly sketch here. First and foremost, if linear perspective was unknown in classical antiquity, then not only are painting and relief affected but also architecture. Construction of buildings would resemble that of the Middle Ages without precise plans drawn to scale. Second, Pliny the Elder’s account of the history of art makes sense. His emphasis on proportion and shading as the major forces in painting need to be taken at face value. In particular, proportion was not just a literary or philosophical issue63 but directly affected art from the end of the sixth century BCE, if not earlier.64 Third, the new interpretations fit well with their understanding of optics. Fourth, the dominant scholarly theory that theater was a major influence on Roman wall painting needs to be reconsidered, as well as what skenographia was and where it appeared on theaters. Fifth, while “ring” theory, i.e., concentric circles, from Homer on is well known to classicists, it has not been considered for art and how it might organize the way stories are told pictorially.65

7. Closing Remarks

Edward R. Murrow (1908–1965), the war correspondent and early television newscaster, said: “The obscure we see eventually. The completely obvious, it seems, takes longer.”66 Many scholars still believe that the Greeks alone—not the Etruscans or the Romans—produced art. This assumption means that any “worthwhile” technique must have its origins in Greek art. Thus, the Renaissance misinterpretation of skenographia as “perspective” led inevitably to the conclusion that linear perspective is a Greek invention of the fifth century BCE.

My analysis of the two key passages in Vitruvius has resulted in two radically different interpretations that resolve much of the contradictory evidence and agrees with their understanding of optics. 7.Pr.11 actually describes the major advance in Greek painting of shading and shadows in the later fifth century BCE, which was probably associated with the Greek word skiagraphia. The other passage, 1.2.2, about skenographia finally makes sense, because it describes the “missing”, crucial plan—the definition of the module that governs the relationship between the parts of a building to produce a harmonious whole. In turn, a major and currently disfavored theme of classical art, proportion, needs to be revived.67 Particularly striking is that Pliny the Elder’s coverage in the Natural History of proportion in ancient painting matches his emphasis on shading and shadows. Together the two produced art that truly in classical terms was “the imitation of nature” (e.g., Aristotle Physics 194a21).

Next, a long-neglected passage from Philostratus explains the system of concentric circles that were used to design Roman wall paintings. Put simply: the system works. It requires only five tools. It is not based on precise measurements, but, as Vitruvius advises, is modular. It is the first proposed system that can be used for entire walls for all three styles. Furthermore, it demonstrates that the idea of the vanishing vertical axis is not the beginning of design but an artifact of the finished design.

Finally, I present this overview of my reinterpretation of two passages in Vitruvius and one in Philostratus not as a conclusion but as a beginning to open discussion.