From futurism and cubism to expressionism and architectural deconstructivism, perspectival images were proclaimed dead many times over in the course of the twentieth century. Modernist avant-gardes may have had few things in common, but they were united in their aversion to Renaissance perspective and to the perspectival view of the world. Yet, due to the domination of optical, mechanical, and then digital technologies for the creation of perspectival images, still or moving, perspective remained the dominant paradigm of our visual culture, and a staple of our culture at large, until very recently. Today, at long last, the demise of projected images may be happening for good—this time around, however, not by proclamation, but by sheer technological obsolescence. A major upheaval of our visual, cultural, and technical environment is taking shape, comparable to that which was brought about by the invention of perspectival and then photographic images. Indeed, these are the primary, albeit not the only, kinds of projected images that are being phased out by the rise of digital technologies for 3-D scanning and 3-D printing; parallel projections, long favored by the technical and design professions, have already been mostly replaced by computer-based 3-D modeling.
In the brief span of less than one generation, digital technologies have moved from word processing to image processing to 3-D processing—from verbal to visual to spatial operations. This is due in the first place to steady technical advancement: words use less data than pictures and pictures use less data than three-dimensional models; as computers have grown ever more powerful and cheaper, they have been able to take on bigger and bigger data. Today, for most practical applications, the marginal cost of advanced computation is close to zero. As discussed at length in the preceding chapter, one of the consequences of the ubiquity and affordability of processing power is that there is now less urgency to laboriously cull, select, and compress data to make information leaner and easier to deal with. As a result, many technologies for data compression that were developed during the early days of computing, and more generally throughout the history of cultural technologies, are being dropped or shelved. Projected images are a case in point.
Alphabetical writing records the infinite modulations of the human voice using a very limited number of standard graphic signs. Alphabetical files are data-light: a typed page contains approximately two kilobytes of data, which is more or less the amount of data that Cicero could have inscribed on a wax tablet when taking notes in the Roman senate. The same page, if recorded as a photographic picture in coarse black or white (binary) pixels, would weigh approximately 1,000 kilobytes, or five hundred times its alphabetic equivalent. This incidentally disproves the old (but in fact very modern) saying that a picture is worth a thousand words: in purely quantitative terms the opposite is true, and in the example I gave, each word is worth approximately 3,000 binary digits (bits) of images. This is one reason why, in the early days of electronics, when processing and storage power were still rare and costly, computers recorded each letter of the alphabet as such (translated into a number).1 But the difference in cost between the storage of a slim alphabetical file and that of the same page recorded as a pictorial image is now practically irrelevant; in fact many textual or archival databases now routinely keep both. Alphabetical files still offer plenty of advantages (for example, they are searchable for words), but we no longer need them to compress oral or visual data due to technical limitations or cost. Today, we can digitally record and process sound as sound and images as images, as need be.
Just as the alphabet was extraordinarily successful in converting an infinite number of sounds into a limited register of signs drawn on a flat surface, so perspectival images were extraordinarily successful in converting infinite distances in space into a limited register of points and lines drawn on a flat, measurable picture plane. There is no easy mathematical way to quantify the advantage of data compression in this instance, because the number of points that exist in space behind the picture plane in a perspectival construction is infinite to the power of three, while the number of points on the picture plane itself is infinite to the power of two. In practice, however, and from its early modern beginnings, the great idea behind perspective was that the points and distances behind the perspectival screen could be, in Leon Battista Alberti’s cautious wording, “almost infinite,”2 whereas the picture plane upon which this infinity is geometrically projected is not: the painting is drawn on a finite and measurable surface. A tool that can convert infinite distances in space into a measurable notation on paper is indeed a great technology for data compression, which is one reason why perspectival images have been used by all and for all kinds of purposes, from their invention to this day—regardless of the acerbic and at times jealous hostility of so many avant-garde artists.
Today, however, technologies already exist that can almost instantly record the spatial configuration of three-dimensional objects in space by notating as many points as needed in precise x, y, z (spatial) coordinates. This may not yet apply to landscapes or vast distances in open air,3 but it does to most interior spaces and full-round objects at the size of human bodies, statuary, or even buildings. In all such instances, a 3-D scan can now be taken almost as easily as a perspectival (photographic) snapshot, and the resulting file can be saved, edited, and processed almost as easily. A 3-D scan can evidently capture much more information than any perspectival picture ever could—and today, at almost the same cost. It is easy to predict that soon and almost inevitably, as has occurred many times before in the history of cultural technologies, ceci tuera cela. It is equally easy to predict that the idea of the superiority of two-dimensional over three-dimensional copies, which is so ingrained in Western culture, may linger for some time—if for no other reason than old habits die hard. This idea was invented—indeed, created, almost out of the blue—by a handful of Renaissance artists, writers, and scientists. It was at the time a great, modern, revolutionary idea, and it was perfectly justified—back then.
3.1 Verbal to Visual
The rapid progress of contemporary digital technologies from verbal to visual to spatial media in the course of the last thirty years curiously reenacts, in a telescoped timeline, the entire development of Western cultural technologies. Before the Renaissance, the main vehicle for the recording and transmission of visual data was verbal, not visual: images were described using words; written words were forwarded in space and time, images were not. The last encyclopedist of classical culture, Isidore of Seville, famously epitomized the ancient mistrust for all forms of visual communication in a few memorable lines: images are always deceitful, never reliable, and never true to reality.4 From a modern point of view, we could easily find two main reasons for that: first, although some classical painters appear to have been very good at copying nature, classical antiquity bequeathed, and likely knew, no geometrical rules for making pictures—rules whereby every painter could make the same copy of the same object, and each viewer could extract the same data from the same drawing. Second, in the absence of identical reproductions in print, all manual copies of drawings were at the mercy of the talent and good will of each individual illuminator, miniaturist, or draftsman. These two conditions combined hindered the use of images for most practical and even artistic purposes; in the absence of reproducible images, most classical books had no images at all, and the illustration of works on science or technology was limited to a handful of geometrical diagrams.5 As Richard Krautheimer pointed out long ago, in the Middle Ages even imitation in the visual arts was “almost emphatically non-visual,” and works of art were often known and reproduced from verbal, not visual descriptions.6
All this changed dramatically in the fifteenth century, due to the concomitant rise of two image-making technologies: perspective and xylography. Alberti famously defined perspectival images as the trace left on a picture plane by a pyramid of visual rays intersecting it: Alberti’s images are prints made by light—that is, by nature itself. In Alberti’s theory, the painter must choose the point of view and the direction of the central ray of the perspectival construction, but when that is done, each point of the drawing is mathematically determined: given the same geometrical conditions, every painter following the rules of Alberti’s perspective will make the same drawing. When that drawing is made, each point of the three-dimensional object being drawn will translate into one point on the picture plane, and the other way around—with some exceptions, as in all projections.7 With those exceptions made, Alberti’s technology can univocally convert three-dimensional objects in space into planar notations, and in reverse, from the perspectival notation it is theoretically possible to reconstruct most visible proportions of the original object (and with some luck, or one or two additional measurements, its actual dimensions, too). That was the magic of Alberti’s construction and its capital technological and ideological breakthrough: yes, perspectival images look more or less like the things we see. But, by the way they are made, they also measure whatever they portray.
At almost the same time, these new kinds of mathematical images began to be mechanically printed from woodblocks. As each woodblock generates more or less identical printed copies, the indexical logic of print multiplies the indexical objectivity of perspectival drawings. From their capture to their dissemination, modern images thus acquired a double indexical guarantee of trustworthiness: true to nature when drawn by the artist; true to the artist’s drawing when reproduced by the printer.8 At long last, these were images one could trust and use. And most people did. After so many centuries of undisputed dominion of the word, in the Renaissance the West simply went visual—and it has remained so, mostly, to this day.
3.2 Visual to Spatial
Perspectival images were so effective in emulating the three dimensions of nature that soon, according to a well-known historiographical interpretation, modern visual knowledge phased out the classical primacy of direct, tactile experience: as we learned to trust images instead of the objects they represent, the eye replaced the hand in the hierarchy of senses (and of knowledge).9 This shift from tactile to visual values is hinted at, curiously, and almost surreptitiously, in a brief passage at the beginning of the second book of Alberti’s On Painting.10 Both Pliny and Quintilian had cited projections as the natural phenomenon at the origin of the art of painting: according to the classical topos they relayed, the first painters only traced, then copied the contour of a human shadow projected by sunlight onto a wall (and, Pliny added, a similar projection is at the origin of sculpture, too).11 Alberti acknowledges but dismisses these precedents, saying he would rather side with “the poets” who think the first painter was Narcissus, beholding his own image reflected in water. But Alberti does not name his sources, and as none have been found to date, that idea may well have been his own: Alberti, who first formalized painting as a mathematical theory of projections, sees the first painting as what today we would call a selfie, and in geometrical terms a very particular projection, now known as specular reflection.12 As we know from Ovid’s myth, however, Narcissus’s ur-selfie was fleeting and treacherous, and it would vanish as soon as the self-admiring youth would try to touch or kiss the surface of the water. Just like the perspectival images projected on Alberti’s picture plane, or veil, Narcissus’s reflection is meant to be seen, not touched. Touch it, and the spell is over—as Narcissus learned the hard way.13
With tactility out of the game, three-dimensionality, and its replication in sculpture and other plastic arts, would soon find itself in a weakened, almost ancillary position in the new hierarchy of early modern art. Alberti, who also wrote a treatise on sculpture, nonetheless admits his preference for painting.14 And following Alberti, for at least two centuries and with few exceptions, artists and writers on the arts celebrated the primacy of “painting” (whereby they meant perspectival images)15 over all other forms of communication. Painting came to be seen as equal to the written word, even competing with poetry. And on another front, the internecine strife for primacy among the new “arts of drawing,” almost every person of taste and culture in early modern Europe agreed that images could replicate nature much better than any three-dimensional (sculptural) copy.
The battle of painting against poetry was an easy one, and largely consensual. Horace’s famous saw, “ut pictura poesis,” in its original anecdotal context meant what it still literally means: namely, that poetry is as good as painting. Yet, as Rensselaer W. Lee argutely noted long ago, Renaissance writers seemed to read the simile in reverse, and take it to mean that painting can be as good as poetry.16 They had a point: the painters they knew were no longer lowly artisans, and painting had at long last become a fine art, or a liberal art—almost as fine and liberal as poetry had always been. No one in the Renaissance would have disputed that. To prove that painting was a better art than sculpture (and painters better artists than sculptors) was, however, a trickier matter, and the dispute, then known as the paragone between the arts, culminated around the mid-sixteenth century, when the Florentine humanist and historiographer Benedetto Varchi (1503–1565) posted a call for papers on the subject—Panofsky called it “the earliest public opinion poll”—and then published the replies he received in a volume, preceded by his own lengthy essay.17 Michelangelo, the only contributor Varchi cites on the title page, not surprisingly championed sculpture. As always, Michelangelo was going against the stream.
From today’s media-savvy point of view, it is easy to infer that the rise of the new print technologies in early modern Europe gave visual communication a winning edge against less easily reproducible media, including sculpture. Yet Renaissance writers on the arts do not appear to have had any awareness of, nor interest in, the reproducibility of images: the paragone was a scholarly dispute on the nature, functioning, and mimetic efficacy of unique, nonreproducible works of art, and only incidentally an assessment of the tools and processes that artists employed for that unique creation. The main arguments in favor of painting were set forth by Leonardo at the close of the fifteenth century, in several passages now found in the Codex Urbinas Latinus 1270.18 Painting is more powerful than sculpture because it can represent all distances and all materials, including transparent ones, such as water, glass, or clouds; painters imitate the colors of nature, whereas, Leonardo claims—and it was universally assumed in the Renaissance—sculptors would not. Painting does not require physical exertions and painters can dress neatly and elegantly when they work, whereas sculptors toil and sweat like the worst “mechanical” artisans, their faces and bodies always caked in marble dust, like bakers covered with flour.19 Yet even Leonardo must admit that sculpture is closer to nature when reproducing freestanding bodies.
Evidently, sculpture can reproduce a full-round object in all of its three dimensions, as we would say today, and a three-dimensional model contains much more information than any single planar projection of the same. But on this too Leonardo offers a counterargument: full-round sculpture, he claims, only provides twice as much information as perspectival drawing, as two perspectival views from two opposite vantage points (typically, front and back) show the same as a full-round sculpture. This statement was as ungenerous as it was disingenuous, as Leonardo must have known that it takes more than two drawings to make a head or bust, for example (and indeed he says so elsewhere).20 Starting with Lorenzo Lotto, Renaissance painters sometimes provided full identification of their subjects by combining three, not two, views in the same a painting. Lotto appears to have rotated his model by approximately one hundred and twenty degrees at a time, thus offering a partial view from the back;21 when Van Dyck was commissioned to draw a full-round view of Charles I’s head to ship to Rome so Bernini could make a bust of the king without traveling, he represented Charles I in a neat architectural combination of front view, side view, and one view at forty-five degrees.22 Why Philippe de Champaigne, given a similar utilitarian commission, represented Richelieu’s bust at a slight angle and then in two identical specular profiles is not clear, and in purely notational terms it seems somewhat a waste: Richelieu’s prominently gibbous nose looks exactly the same from both sides.23
3.3 The Technical and Cognitive Primacy of Flatness in Early Modern Art and Science
Around 1492, Leonardo had another, stronger argument to advocate the primacy of projected images over three-dimensional copies. Full-round sculptures are seen in perspective by whoever beholds them, he claimed, without any merit of their sculptors; but paintings are put into perspective by their painters (actually, into two perspectives, Leonardo famously claimed—one made with lines, the other with colors). This the painter does by “science,” “marvelous artifice,” and “a very subtle investigation of mathematical studies,” so that the final drawing is a “demonstration” where all proportions and foreshortening derive from the “laws” of perspective.24 Leonardo should thus be credited with first claiming scientific precision, rather than realism, as the main strength and advantage of painting over sculpture. Indeed, who could claim that a drawing on paper is closer to its three-dimensional original than an identical copy of the original itself—with all of its appearances (except perhaps for color) and actual dimensions in space? As the elegant writer (and Raphael’s occasional ghostwriter) Baldesar Castiglione (1478–1529) would point out only a few years later, that would be the same as claiming that the copy is better than the original—or, in this instance, that a picture contains more information than the three-dimensional original it represents.25 And rightly so, Castiglione concluded: because reality is what it is, but a perspectival drawing represents (in a sense, reenacts) reality through the laws of perspective, hence in a perspectival drawing all we see is “measured.”26 Today we would say that perspectival drawings are a form of “augmented reality”: they embed the proportional measurements of what they show.
Throughout the sixteenth century and beyond, the Albertian definition of painting as an “entirely mathematical”27 construction—of perspectival images as a tool of quantification—will be the main argument invoked by the advocates of painting in the dispute between the arts. If tested for realism alone, sculpture would have easily won. Indeed, it would take one of the greatest scientists of all times, Galileo, to prove that planar drawings, regardless of their scientific superiority, are also—against all appearances—closer to nature than three-dimensional copies. Shortly after the publication of Sidereus Nuncius (1610), which included his famous drawings of the surface of the moon, Galileo was invited by his close friend, the painter Ludovico Cigoli, to take sides in the still ongoing paragone between the arts. Galileo knew perspective well, and famously used geometrical projections to calculate the height of the lunar mountains and the position of the sunspots. Yet in this instance Galileo did not insist on perspective as a scientific, measuring tool; instead, he based his essay-length reply to Cigoli on a skillful and original amplification of the topos of the superior “artificiality” of painting as an imitative art (“artificiosissima imitazione”): sculpture imitates nature while retaining its natural, three-dimensional measurements, whereas painting does so in an artificial, man-made format (by projecting volumes on a plane). Thus Galileo can, paradoxically, praise perspectival images for their higher degree of realism: projected images are in fact closer to nature than sculpture—not closer to nature as it is, in three dimensions, but closer to nature as we see it, through planar images that take shape in our eyes.
It is noteworthy that the theory of perspective, in the Albertian tradition, had never before taken into account the physiology of human sight. Indeed, Alberti had explicitly claimed that, in order to describe the geometry of the perspectival construction as it happens outside of the eye, he had to make abstraction from all other physical and physiological aspects of vision.28 Galileo does not follow Alberti. Sculpture, Galileo claims, is a faulty mode of imitation, for it provides spatial information our eyes don’t need. As human eyesight cannot see through solid bodies, three-dimensional data are always lost on the eye. Sculpture may simulate depth through shade and shadows, just as painting does, but not by being three-dimensional, because no eye can see in depth. Galileo stops short of claiming that sculpture cheats the eye (an argument more often associated with painting), but his repudiation of three-dimensional imitation is as trenchant as it is definitive: since the human eye can only see the world exactly as notated in a monocular perspectival construction, all visual representation of depth above and beyond perspectival foreshortening (and its shadowing) is unnecessary, or worse.29
We now know that Galileo in this instance was wrong, even though this was not the main error for which he would be blamed during his lifetime (and beyond). From science and engineering to consumer electronics, stereoscopy is now ubiquitous (and has been for a while, always tantalizingly on the verge of breaking through), and today everyone knows that our vision is based on two slightly different retinal images. Just as surveyors and topographers have always used triangulations (alignments from two vantage points) to calculate distances, our mind calculates distances based on the discrepancies between two monocular perspectival views. The results are not shown as actual measurements or numbers on a screen, the way a mathematician or a computer would do, but through the cognitive rendering of images in relief—as this is the way our mind works. Yet, strange as it may seem, stereoscopy was discovered only in 1838 by the Victorian inventor Charles Wheatstone, today better known for his contributions to electrical technology, cryptography, and telegraphy.30 In his first groundbreaking and truly astounding paper on the subject, the great scientist (a self-taught artisan of humble birth) soberly noted that the phenomenon of “binocular vision,” whereby the human mind creates “the most vivid belief of the solidity of an object,”31 albeit possibly adumbrated by Leonardo in a passage of the Codex Urbinas,32 was entirely neglected by all subsequent studies on vision. In fact, the possibility of any cognitive perception of distances beyond that offered by planar perspectival projections had been bluntly negated by none other than the founder of modern science.
Two centuries after Alberti’s invention of perspectival images and their meteoric rise to prominence due to their mimetic qualities, their mensural reliability, and their easy reproducibility in print, the new culture and technology of planar projections came full circle, so to speak, when Galileo proclaimed planar projections to be the true and only notation of our cognitive experience of the physical world. Monocular perspectival images are identical to nature because that’s the way we see things, Galileo claimed. Anyone who ever tried to pass a thread through the eye of a needle with one eye intermittently open and closed could easily attest to the opposite, yet until very recently it appears that nobody did: with Galileo’s cognitive endorsement of perspectival images, the world went flat. That was a strange destiny for a technology of vision originally meant to emulate the visual perception of distances in space: in the end, the planarity of the perspectival medium became its main message—an idea that has famously held sway over modern Western art history and criticism to this day.33 After Galileo authoritatively put it to rest, the notion of an experiential, extra-perspectival cognition of space would only be revived in the nineteenth century by a scientist of genius who could probably discover stereoscopy precisely because he was unacquainted with the history and theory of Western art. But Wheatstone’s invention of “solid images” was almost exactly coeval to that of argentic photography, which gave perspectival images an extraordinary new lease on life, and made the Albertian paradigm of vision even more dominant than it had ever been. In spite of its artistic, scientific, and even medical significance, stereoscopy thus remained a marginal image-making technology, until recently confined mostly to toys, fairs, shows, and other extravaganzas.
3.4 The Underdogs: Early Alternatives to Perspectival Projections
Alberti was the chief inventor of perspectival images, but he should not be blamed for the subsequent hegemony of the perspectival paradigm. True, perspective ended up being one of the most successful of his ideas, but at the beginning it was only one in a panoply of many complementary media technologies that Alberti had designed to record and transmit the place and shape of three-dimensional objects in space. Perspective was meant to be the primary notational instrument for painters; for architects and sculptors Alberti devised other, more suitable tools.
Alberti must have been fully aware of the mensural limits of central projections. The first known attempt to reverse a perspectival image to extract some of the metrics it contains—an operation known today as photogrammetry—was made by Pietro Accolti, another Florentine Academician and a contemporary of Galileo.34 The procedure was of limited practical interest then, as it presupposed a perspectival drawing obtained through nongeometrical means (for example, using Alberti’s veil or Dürer’s window); photogrammetry would become more valuable after the invention of photography, which provides a reliable, machine-made perspectival image. Photogrammetry is still taught as a branch of descriptive geometry, but it is a notoriously aleatoric and difficult operation—albeit today much facilitated by computers.35
3.4 Pietro Accolti, Lo inganno de gl’occhi. Prospettiva Pratica (Florence: Cecconcelli, 1625), 86.
Technical drawings evidently require an easier and more direct way to notate spatial measurements. In a famous passage of his treatise On Building, Alberti recommends that architects should avoid perspective and use instead other kinds of nonforeshortened, scaled drawings, similar to what modern designers would call parallel projections in plans, elevations, and side views.36 Mathematically formalized by Gaspard Monge only at the end of the eighteenth century, parallel projections remained the primary notational tool of all design professions almost to this day.37 Monge’s method used two sets of parallel projections to univocally notate the position of any point in space onto two planes that, if needed, can be drawn on the same sheet of paper: descriptive geometry is a brilliant mathematical invention. When put to practical tasks, its efficacy is formidable: no one could store the Seagram Building in reality—it is quite a big building—but many offices could store (and some did, in fact, store in a few drawers) the batch of drawings necessary to make it, and, if needed, to remake it. With parallel projections (and axonometric views, which likewise were long used empirically before their mathematical rules were set forth in the early nineteenth century),38 the art of compressing big 3-D objects onto small flat sheets of paper (or parchment or canvas or Mylar) reached the apex of modern quantitative precision: parallel projections do not even try to look like the objects they represent, but they aim at recording and transmitting the measurements of their volumes in space as precisely and economically as possible. Crucial until recently, such data cheapness is increasingly unwarranted today: using digital technologies we can already keep not only a huge number of planar drawings but also full 3-D avatars of buildings on a single memory chip—including all the data we need to simulate that building in virtual reality, or to build it in full. Oddly, even this latest technological leap had been anticipated by Alberti himself.
3.5 Alberti’s measuring device for statuary replication, from the first publication in print of Alberti’s De Statua, translated into Italian and illustrated by Cosimo Bartoli in Opuscoli morali di Leon Batista Alberti gentil’huomo firentino …, (Venice: Francesco Franceschi, 1568), 299.
In his treatise On Sculpture, Alberti had introduced a revolutionary 3-D design and fabrication method, entirely based on digital data, to the exclusion of all drawings. Using a measuring device centered above the top of the body to be measured, sculptors should take down the spatial coordinates of as many points of a model as needed, then use this numeric log alone to make copies. Alberti claims that by using his technology, different workshops in distant places can be tasked to reproduce parts of the same statue, which, when assembled, would perfectly fit together.39 The idea to use a digital scan to notate and replicate full-round objects in space must have seemed outlandish, or worse, when Alberti first conceived of it, and until recently scholars and historians were quick to dismiss Alberti’s treatise on sculpture as an abstruse exercise on the proportions of the human body. Indeed, the scanning process Alberti describes would have been laborious to carry out in his time, and Alberti does not even try to explain how the resulting numeric file could have been used to actually execute a sculpture. That would have been a most arduous task using traditional artisanal tools, either by subtraction (per forza di levare) or addition of material (per via di porre).40 Several equally unfruitful attempts to develop a similar replicating technology are recorded at the onset of the mechanical age. Samuel F. B. Morse, a Yale College graduate and noted painter before he rose to fame for his contributions to telegraphy, strived to develop a marble carving machine that would automatically and exactly replicate “perfect copies of any model,” and he even tried to patent one in 1823, together with a New Haven craftsman (only to find out that the patent would have infringed on another one).41 Morse was appointed professor of painting and sculpture at New York University on October 2, 1832; his title was changed to professor of literature of the arts of design in 1835.42 In one of his lectures on the arts (delivered in 1826) he mentions Leonardo’s Treatise on Painting, first published in 1651 together with Alberti’s De Statua.43 Several circular saw mills and programmable lathes were developed throughout the nineteenth century, but on March 28, 1842, Henry Dexter, of Boston, appears to have patented a fairly precise replica of Alberti’s scanning machine, suitably doubled in that instance by a similar replicating apparatus—with no better success than his Florentine predecessor.44 For Alberti’s technology would have required a seamless connection between a number-based scan and a similarly number-based fabrication process, which no manual tool or mechanical technology could effectively provide. Today’s cheap and increasingly ubiquitous 3-D scanners and 3-D printers work exactly that way.
3.6 US Patent 2,519, “Apparatus for Sculptors to be Employed in Copying Busts, etc.,” to Henry Dexter of Boston, March 28, 1842. Source: United States Patent and Trademark Office, http://www.uspto.gov.
3.5 The Digital Renaissance of the Third Dimension
In the early 1990s architects of the first digital age started tweaking existing engineering (and, often, medical) 3-D scanning technologies to adapt them to the scale and processes of then nascent computer-aided design and prototyping. The first experiments in Frank Gehry’s office to scan and digitize Gehry’s own hand-made sculptural maquettes are still legendary,45 but digital manufacturing tools in the 1990s were bulky and expensive; the subtractive CNC milling machine, which many avant-garde architects then championed, can only cut and carve matter out of a solid block, and its performance is limited by the number of axes on which its drill can operate. The real breakthrough in the history of digital stereopoiesis came only in the twenty-first century, with a new generation of 3-D scanners and additive fabrication tools. The best-known manufacturer of desktop 3-D printers, MakerBot, was founded in 2009. Its first preassembled 3-D printer, the MakerBot Replicator, cost $1,749 when it was launched, in January 2012,46 but when Michael Hansmeyer and Benjamin Dillenburger wanted to 3-D print the twenty-square-meter room of their first Grotto Prototype (2012–13: see chapter 2), they had to resort to a much bigger, industrial grade Voxeljet machine, normally used to 3-D print disposable molds for the mass production of metal components.47 Many now see 3-D printing as a turning point in the history of technology—as US president Barack Obama said in his 2013 State of the Union address, a new technology that “has the potential to revolutionize the way we make almost everything.”48 At the same time, however, the seamless connection between 3-D scanning, 3-D printing, and virtual reality tools is also likely to change the way we see almost everything, and represent and know the world around us.
The first irruption of affordable 3-D scanning in mainstream architectural education came, once again, from the creative appropriation of a machine originally developed for other purposes. Launched in 2010, the Microsoft Kinect was a mass-marketed, motion-sensing device sold as a plug-in for videogame consoles; it allowed players to interact with a videogame through motion and voice.49 It contained an ingenious depth sensor that worked by triangulations, using a laser projector and a camera. The measurements it provided proved very accurate at short distances, and several applications were soon developed to use the machine as a stand-alone scanner. In 2012 students in schools of architecture around the world were using the Kinect to scan small objects of all sorts; the scans were imported into standard CAD software, and edited at will.50 Depth-sensing technologies are evolving quickly; some use traditional laser or infrared beams, and calculate distances based on the time of rebound (also known as “time of flight”), or, increasingly, by reading the difference in phase between outgoing and returning beams; some use triangulations, like the earlier Kinect machines did, with a laser beam sending a marker to the target and a camera, in another vertex of the triangle, to read it (variants of this method are known as structured-light depth sensors); and so on. All these methods require some specific hardware to send or read signals; some can measure actual distances, while others can render solid shapes proportionally but cannot calculate measurements. New technologies are also being introduced to reconstruct three-dimensional volumes from a stream of simple photographs—that is, from a sequence of planar, perspectival projections.
As Wheatstone had already explained, our mind builds up solid volumes by interpreting two synchronic perspectival images taken from two slightly different vantage points, but in the absence of the second image, similar results can be obtained by comparing monocular images taken in a quick sequence from a moving vantage point.51 Contemporary computational depth sensors can reenact both processes, in the case of the latter by using any existing digital camera as the only input tool. Snapshots taken from a camera suitably moving around the same object can be collated and merged, and its solid shape (but not its actual dimensions) reconstructed by computational triangulations. This seems to be the mathematical logic behind Autodesk’s 123D Catch, a software that can generate a point cloud of any stationary, full-round object from snapshots taken from a camera moving around it.52 The data, fed by a cell phone, can in turn be imported into proprietary CAD software, edited and solid modeled using wireframes, meshes, or subdivisions, 3-D printed, or, with additional measurements and some manual work, converted into scaled architectural blueprints in plans, elevations, and sections—thus fulfilling Pietro Accolti’s dream of 1625. Project Tango, by Google, uses a more complicated, purpose-built hardware (including both motion sensing and depth sensing) to obtain a 3-D model of interior spaces from the natural movements of someone walking through it.53 Using similar technologies, the Madrid-based company Factum Arte has specialized in museum work and conservation facsimiles;54 the ScanLab at the Bartlett School of Architecture in London, known for its 3-D replicas of landscapes and large-scale artifacts, is also developing a range of visual tools to exploit all sorts of images derived from solid models.55
Three-dimensional models can be visualized using perspectival images or axonometric or parallel projections, navigable and scalable at will; other interfaces may include virtual reality or augmented reality tools. But each of these planar renderings is only, in a sense, a way to visit an actual model—each visit being different, based on contingent requirements and intentions. The only stable part, and the keystone and kernel of the whole system, is the 3-D model itself. And, of course, any 3-D model can be 3-D printed, in full or in part, and (in theory) at any scale.
3.7 ScanLAB Projects, London, and BBC, Rome’s Invisible City—3-D Scan of the Mithras Temple Hidden Below Modern Rome (2014).
3.8 ScanLab Projects, London, 3-D Scan of Greenpeace’s icebreaker The Arctic Sunrise (2011).
The modern technologies we were familiar with until recently would typically allow us to take a snapshot of any full-round model—say, a cat—and print that out as a photographic, perspectival picture. Soon, most cell phones will take 3-D scans, not pictures; and keeping, editing, and sending a statuary selfie will cost the same as saving, editing, viewing, sharing, or even printing a pictorial one. Today’s technology already allows us to take a snapshot scan of a cat and print that out, right away, as a sculpture;56 soon we shall visualize a full-round model of said cat in three-dimensional, VR simulations. Planar images still have many practical advantages over 3-D models: for example, a picture of a cat printed on photographic paper is lighter than a statue of the same printed in resin, plastic, or sandstone, at cat-size—or even smaller. Likewise, just like most traditional (planar) photographs stopped being printed long ago, to be shown and seen only on electronic displays, a sequence of electronic images is often the easiest and least cumbersome way to simulate or navigate a 3-D model.
The first commercial light field camera, the Lytro, was released in 2012; it was advertised as a camera that allows users to refocus every picture, and marginally shift the vantage point of each picture, after the snapshot has been taken.57 It was not a commercial success, partly due to the limits of light-field technologies for depth sensing, but the spirit of the game was clear: when you take a picture that way, you do not project it onto a screen (the Albertian way) once and for all; you create a 3-D model in space that you can eventually visit at will—looking in different directions and moving around it (in Albertian terms, rotating the central ray and changing the point of view). At the time of writing (summer 2016) some sports events have already been broadcast live in virtual reality (including from the Rio Olympics), to be experienced through head-mounted displays. The degree of immersivity supported by these VR technologies is variable: the vantage point of the end user may be fixed or movable and the angle of rotation of the head more or less wide; the headsets do not have to be stereoscopic, although it helps if they are.
Alongside virtual reality, a new generation of head-mounted displays supports augmented reality and mixed reality reenactements:58 the ways to exploit and experience a 3-D model, once it is made, are countless, and as long as we have eyes to see, we shall keep using monocular images (better if paired and synced for stereoscopy) for all kinds of reasons and tasks. But the competitive edge that projected images enjoyed for centuries over 3-D models was as much due to physical lightness as to data lightness: from Alberti until recently, projected images were the easiest way to capture, record, transmit, and replicate all sorts of full-round originals, because projections (perspectival or other) compress a lot of spatial information into small and portable planar files—most of the time, as small as a piece of paper. That still holds true, but it matters less and less, because data is now so easy to gather and so cheap to keep and copy.
3.9 PHOTOMATON® S.A.S. corporate website page detailing the French company’s 3-D photo booth service (2015). PHOTOMATON® is a registered trademark owned by the Photomaton Company. Courtesy of the Photomaton Company.
Almost one generation ago, the rise of digital photography first dented the cultural and technical primacy of modern projected images. Digital photographs may look like film-based (argentic) photographs, but they are no longer the indexical trace left by a beam of light on a photosensitive surface; they are, regardless of the way they are captured, the occasional and always ephemeral end product of a number-based algorithm. As the late William J. Mitchell pointed out at the very beginning of the digital turn, verisimilitude, or the indexical value of proof, which was the main source of the power of modern photography, was simply obliterated by the technical logic of digital photography.59 Cultural critics and modernist art historians for the most part stubbornly declined to take notice, and thus fell out of kilter with the new world of digitally generated images that we have been living with for the last twenty years. Much more of that is happening now, and it may henceforth be more difficult—even for modernists—to look the other way. For after losing their indexical value during the first digital turn, digital images are now losing all their residual notational functions.
At the end of the Middle Ages the conflation of a new technology for capturing and compressing images, and of a new technology for reproducing them, changed the history of the West. Today, the conflation of new technologies for capturing and reproducing reality directly in three dimensions, without the mediation of images, is likely to have similar epoch-making consequences. Around the mid-sixteenth century Jacopo Pontormo, the lunatic Florentine painter, could claim that while God needed three dimensions to create nature, painters needed only two to recreate it: which, he concluded, “is truly a miraculous, divine artifice.”60 As we can represent and reproduce the world just as it was made—in three dimensions—we need far less of that artifice today. Three-dimensional models have replaced text and images as our tools of choice for the notation and replication, representation and quantification of the physical world around us: born verbal, then gone visual, knowledge can now be recorded and transmitted in a new spatial format.
