Saturday, March 4, 2017

De Chirico's Perspective

by  William Rubin, “De Chirico and Modernism,” De Chirico,  1982

pp. 58-59

That the early de Chirico is routinely (if wrongly) said to have resurrected fifteenth century perspective(17) – indeed, even “academic perspective”(18) – as an aspect of his supposed classicism, any review of the de Chirico literature will confirm. Even Soby speaks of his “revival” of “illusory, linear perspective.”(19) Ironically, it is precisely through a careful comparison of de Chirico’s perspective with that of his presumed Renaissance model that we can best begin to isolate the peculiarly twentieth-century character of the painter’s early aesthetic.

Fifteenth-century perspective was, in its most profound sense, a branch of humanism. For the first time – at least in a systematic manner – the world was imaged not according to a hierarchy of collective values attributed to the subject matter, but rather as the subject matter would be perceived from the vantage point of an individual, the now mobile viewer. Systematic focus perspective was, of course, an abstract geometrical system whose project did not conform exactly to the nature of visual reality. But they came much closer to that reality than had earlier ways of imaging. The scientific underpinning of perspective enhance its humanistic aim of picturing the world as made up of logically related entities situated in a rational, measurable space. And while this system would later be employed by the Mannerists to make convincing illusions of asymmetrical, anticlassical scenography, the Renaissance painters who created it used it to reinforce precisely the qualities of symmetry and order fundamental to their classical world view.

Renaissance perspective projects a space that is secure and eminently traversable. De Chirico’s tilted ground planes, on the contrary, produce a space that, when not positively obstructed, is shallow and vertiginous. The viewer understands fifteenth –century space as an illusory continuation of his own space; his place in relation to the
donnée of the picture – and thus, by extension, to the general scheme of things – is clear and logical. And the unity of that relationship is expressed mathematically and visually in fifteenth-century perspective by its systematic focus, which draws all orthogonals to a single vanishing point. Consider, by way of contrast, de Chirico’s Enigma of a Day (below, left).

Here the orthogonals of the arcaded building at the left meet not at, but above, the horizon line, to the left of the lower smokestack; those of the right-hand building meet at the foot of the other chimney; and the vanishing point of those of the statue’s socle is somewhere far outside the pictorial field. The same multiplicity of vanishing points is evident in
Gar Montparnasse (above, right). In this powerful composition, the virtually continuous alignment of the station’s front lintel (parallel to the picture plane) with its side on (receding from it) forces us to fix our perspectival eye at the lintel’s height in space – so that we feel suspended insecurely in a void (as is also the case of Enigma of a Day), rather than having our feet firmly planted on the ground at the point where the space begins, as in fifteenth century perspective. The multiple vanishing points of these de Chirico’s thus subvert the coherence of Renaissance perspective by confronting the viewer with a network of conflicting spatial tensions that undermine, psychologically speaking, any initial impression of quietude or stability.

De Chirico alludes to the irrational, indeed, fantastical nature of his perspective in occasionally including, as a picture within a picture, a canvas shown at the preliminary stage of its line drawing. In The Seer (above), for example, a mannequin sits before an easel on which the framed picture is a perspectival plan for a painting showing a long arcade behind which looms a toga-wrapped figure earlier borrowed by de Chirico from Böcklin’s Odysseus and Calypso for his 1910 Enigma of the Oracle (below). At first glance, the image, the image on the easel almost appears an exercise in the science of perspective; its diagrammatic form and negative light-on-dark drawing also suggest an engineer’s or architect’s blueprint, recalling the materials of the painter’s engineer father.  We see architecture and space projected within a context of perspective orthogonals, compass and ruler forms, numbers and upper- and lower-case letter resembling the keys to cross sections or elevations, and the cryptic city name, “Torino” (Turin)

On closer inspection, however, the diagrammatic image in The Seer reveals itself as a fantasy of science – a cabalistic project no closer to systematic focus perspective than to actual plans of an architect or engineer, and in that sense parallel to Duchamp’s “funny physics.” The looming Odysseus figure interrupts the scale established in the architecture, overturning that logic and order which Renaissance perspective imposed on pictures (though making the figure all the more menacing and thus satisfactory to de Chirico’s expressive needs). And the geometrical projections, like the orthogonals, turn out to be either illogical or (in any rational sense) meaningless, the numbers and letters as cryptic as the “Torino”(20) What all this adds up to here and elsewhere in the early work is a virtual parody of perspective, an “irrationalization” of a system that in the fifteenth century was a branch of projective geometry. The “classical” thus finally emerges in de Chirico’s early work – whether as a formal structure or as a subject – essentially as a metaphor. By subverting classicism, by turning it inside out, he communicates the singular malaise of modern life.

But de Chirico’s modernist instinct undercuts traditional perspective in still other, even more radical ways. The illusionism of fifteenth-century painting was not a matter of linear perspective in and of itself. The linear schema was but a web of coordinates within which the figures and objects were – as a necessary concomitant – modeled in the round. Hence the realistically illusioned solid forms (Berenson’s “tactile values”). In Renaissance painting, the mass of the figure is seen quantitatively, with modeling in the round creating the illusion of a continuous turning that completes the cylinder of the mass while the empty space acts as a foil to the relief of the figures and objects, enhancing their tangibility by contrast. Moreover, in the mid-fifteenth century, painters learned to “shade” the empty air, so to speak, by reinforcing their illusion of deeply receding space through the technique of aerial, or atmospheric, perspective.

Pp 61-62
The standard comparison, the, which pits the modernity of the Futurists (loudly proclaimed, but ultimately ambivalent, as we shall see) with a supposed revival of classical Renaissance techniques in de Chirico seem to me thoroughly wrongheaded. No matter that statements by the Pictor Classicus himself (published, as noted, after he had given up his early style in favor of old-fashioned illusionism) provided whatever “authority” was needed for most critics to assume that even his early work pointed in a direction opposite to the modernism of his contemporaries.

Fifteenth-century Italian painting, like old-mater art, is illusionistic. De Chirico’s early painting, like all great modern art, is nonillusionistic. Sofflici had intuited this fact, insisting that “if geometry and the effects of perspective constitute the principal elements of [de Chirico’s] art…it is also true that his work resembles no other work…based on the same elements.” Yet how, the reader may legitimately ask, can an art using perspective lines, however scrambled, be considered nonillusionistic? The answer follows from the definition of illusionism itself.

The modern effect of the early de Chirico depends upon the fact that his linear perspective – and this is the nub of the matter – by not being reinforced through the traditional concomitants of modeling in the round and /or aerial perspective, remains a purely schematic scaffolding that does not force a picture into a condition of spatial illusionism.
The common denominator of all the great modern styles – whether figurative or not- is the suppression of illusionism (an optical effect alien, in any case, to simple or schematic forms of representation). When linear perspective is supported by modeling in the round and atmospheric perspective, as in Renaissance (or academic)  art, the eye is confronted by an indivisible illusion of receding space, to which perception it is obliged to respond. But perspective orthogonals alone – because they propose deep space conceptually rather than optically – leave the eye a choice. As long as the orthogonal lines are disengaged from modeling, their position on the surface remains equivocal and permits a double reading: they can be understood as a schematic indication of three-dimensional space, or they can bee seen, alternatively , as simply a pattern of lines on the flat surface, a pattern that in no way interrupts the lateral continuity of the configuration. De Chirico’s early work abounds in the fruit of this perception. Consider the magnificently shaped sunlit plaza whose ambivalent plane “recedes” to the distant train in Gare Montparnasse (p. 32). While we understand this plane as retreating in space, de Chirico’s handling of linear perspective and shadow tilts it so vertically that the eye is strongly invited to see this powerful geometrical shape as parallel to the picture place.

Nor was de Chirico unique in the recognition of this particular ambiguity. Matisse’s Red Studio (fig. 9), executed in 1911, just as de Chirico was forming his style, is an object lesson in the principle involved. The orthogonal lines of Matisse’s floor and table indicate three dimensional space, but they do not illusion it, because the normal concomitants of shading and modeling are suppressed. The chance that the eye will read these lines as retreating in space – and thus interrupt the image’s lateraldeocrative continuity – is further minimalized by the painter’s having endowed the walls, floor, table, and chair with a common Indian red that becomes identified with the picture plane. Like the de Chirico (pl.61), but in a different spirit and with other expressive aims, Matisse also inverts the perspective of foreground objects, as witness the orthogonals of the chair, which narrow toward the viewer rather than away from him. Indeed, with magisterial wit, Matisse continues the game of ambiguity – of eye versus mind, perception versus conception, illusion versus schematic representation – by applying local color only, or almost only, to objects which are themselves flat (the oil paintings, wainscoting, and decorated dish).

The paintings of Klee are also replete with indications of deep space that somehow never destroy his surface unity or compromise the modernity of his style – and for the same reasons. In his Zimmerperspektive mit Einwohnern (fig. 10), for example , we are presented with what appears at first a classic “perspective box.” As in de Chirico and Matisse, however, the “receding” planes of Klee’s room seem to cling to the two-dimensional  surface. While this results in part from the “unfocus” of Klee’s perspective – the absence of a unified vanishing point – it has even more to do with the suppression of supportive modeling or shading along the orthogonals of his forms. There is, to be sure, considerable shading in the image, and it does create a kind of atmosphere. But the lights and darks of that shading form an autonomous pattern that not only disengages from but contradicts the perspectival indications of both objects and empty space. Finally, with a wit less sovereign but more affectionate than Matisse’s, Lee introduces a pun based on the ambiguity of the potential readings. Are we to see the man, woman, and child in the lower right as standing up or lying on the floor?

The Surrealists most influenced by de Chirico’s early art – Tanguy, Dali, Magritte, and Delvaux – understood its poetry but failed to grasp the essence of its plasticity. They made the same mistake as so many of de Chirico’s commentators: they mistook the perspective referents of his spatial theater as constituting a revival of old-master illusionism. Compare the Tanguy and de Chirico paintings [on this page] (figs. 11, 12). To many viewers, the Tanguy would seem the more modern picture because it represents abstract forms rather than recognizable ones. Yet I find that the Tanguy looks old-fashioned, indeed, academic, while the de Chirico has a modern appearance. Tanguy’s academicism lies precisely in the smoothly graduated modeling in the round and the aerial perspective with which he endows respectively his solids and empty spaces.  Together, these techniques make the Tanguy an illusionistic picture in a way that the de Chirico is not. Hence, the unfamiliar, “abstract” shapes of Tanguy appear more real – more solid in the tactile sense – than the identifiable shapes in the early de Chirico. And Tanguy’s sculptural biomorphs displace a space that – because of aerial perspective – obliges the eye to accept an illusion of great depth.

17 Raffaele Carrieri finds characteristically that de Chirico's elaborate constructions" are nevertheless realized "with a perfect knowledge of the rules of perspective" (Giorgio de Chircio" in Forme [Milan: Milano-Sera-Editrice, 1949], p. 72). H. H. Amason summarizes the common assumption in stating that "de Chircio's space is uncompromisingly that of Renaissance perspective" (History of Modern Art  [New York: Abrams, 1968], p. 286).

18. Giorgio Castelfranco and Marco Valsecchi, Pittura e scultura italiance dal 1910 al 1930 (Rome: De Luca Editore, 1956), p. 19.

19. Soby, "The Scuola Metafisica," p. 19.

Saturday, September 17, 2016

Real Hexadecimal Numbers Have Curves

by Andrew Martin

37-24-35  38-26-37  41-25-38  35-25-35  36-25-36  37-26-45  34-24-35  34-26-38  36-26-40

These are the "measurements" of famous, beautiful, curvy celebrities: Madonna, Kate Upton, Dolly Parton, Lynda Carter, Katy Perry, Nicki Minaj, Rihanna, Beyoncé, and Kim Kardashian.

I was always perplexed as a kid when men fantasized over numbers like these. They were too abstract, I was too young to understand, and they seemed to be bantered about by the type of guys who also traded baseball and other sports statistics with each other that got decoded in their meaty heads into an actual performance, and in the case of the women's measurements, erotic visions of impossible pin-up girls. Maybe a lonely submarine sailor sending Rita Hayworth's 36-24-36 and other "bomber girls" measurements by Morse code to another poor enlisted seaman was the first instance of electronic sexting. Which reminds me of an article I once read about two former American servicemen who returned to Plzeň a half a century after liberating the Czech city during WWII. One shouted to the other "Incoming at 11 o'clock!" and his buddy spun around in time to catch a glimpse a Slavic beauty pass by.

I recently wondered if arrangements of these six numbers correlated to anything other than womanly curves. How might they look as a patch of RGB color space values? I envisioned a psychedelic matrix of hot pinks and purples.

When I tried that all I got was a dull grid of bluish black squares except for one slightly brighter area because Nick Minaj's big butt bumped up the blue value. A little disappointed by this, I converted the inches to centimeters and entered those values as RGB: a little lighter and brighter with a bump again from Minaj's rump. So I decided to switch over to CMYK color space and alter the K (black) value by another measurement unique to each woman. The greater the value of K, the darker the box.

The first time I did this, I used height as the variable, which is why the just-shy-of-six-foot Kate Upton (top middle of the left matrix) is the darkest. The next box, centered here, uses weight as a variable. And finally the far right box uses age as the variable, which is probably the most interesting of all the matrices because even though Dolly Parton, Lynda Carter, and Madonna are all attractive older ladies, there is a real sense of mortality in the darkening of the squares.

Despite all the variations I was still disappointed and was hoping for something more insightful. I tried placing the numbers as global coordinates such as 36°25'36" but the South West coordinates dropped everyone in the South Atlantic Ocean, South East in the Indian Ocean, and North West smack in the middle of the Atlantic Ocean. 

And then finally, miraculously, the North East coordinates parachuted these beauties into Turkish territories, with Dolly Parton busting into neighboring Georgia. Maybe she figured Nashville was just a short haul from there. 

Most surprisingly, Katy Perry and Kim Kardashian were strategically positioned near the Syrian border not far from Aleppo. Maybe this new information will help Gary Johnson, the Libertarian Party candidate for US president, to remember this location of this war-torn Syrian city.

Tuesday, February 16, 2016

Putting Art into Perspective

by Andrew Martin

Mathematics is an abstract language created by humans, which interprets universal patterns. It started in the physical/visual world as a way to quantify things: land, livestock, building materials, etc. Through its abstraction and withdrawal from specific computations it evolved to stand on its own as mathematics for mathematics' sake.

I recently watched the four-part BBC documentary, The Story of Maths, presented by Oxford professor Marcus du Sautoy, who does a great job of crunching the history of math into four hours, while taking the viewer around the world.

I tuned into the series more as visual thinker than as a mathematician. It is easy enough to see how a quantity (of whatever) can be represented with symbols. Sautoy offers that even 0 as a symbol for nothing, a concept that eluded the early mathematicians including the Greeks and Chinese, may have come from the circular divet that was left in the earth when a counting stone was removed from its place.

What I found most interesting is that while some mathematics can be visualized, most situations are formalized through a formula. That is, except for perspective, whose solution was in the command of vanishing points. Of course there are numbers behind that system but it was a case of mathematics whose problem arose through two-dimensional representation of a three-dimensional world, but was solved through a purely mechanical act by artists.

Basic geometry is a very visual kind of math but the question is, which came first the shape or the possibility of the shape? With a set of numbers/coordinates I can generate a shape but I can also create a shape that calls into play a set of numbers. Are the geometric forms we observe and (re)create merely byproducts of these "numbers" or do the shapes create a case for the numbers? Or is it that they are one in the same - the same information that can be represented visually or numerically?

[image source:]

That being said, the geometry of a cube is very different than the geometry behind the workings of perspective because in a cube the lines of opposing sides are parallel but through perspective they are angled to one, two, or three vanishing points. What this means though is that I can never observe a true cube because I will always be influenced by a perceived perspective.

A working perspective was not developed until the early Renaissance and was hailed as a truth. Ironically, within a few hundred years it became reputed as a lie. It seems, however, that the trickery is in our skewed observation: our stereoscopic eyes and visually comprehensive minds create an illusion that is as false in reality as it is on a wall or a canvas.

In terms of art history it is interesting to note that the use of perspective was often not used merely to recreate an environment so much as it was a way to create a more believable world to tell a story, especially one that no one was still around to refute. Pictured above is Raphael's School of Athens, completed in 1511 to depict a hypothetical mashup of ancient philosophers.

I find that the most interesting use of perspective was by the surrealists, who did not abandon it during Cubism, Abstract and other movements, because it gave them the power to create a space for their strange worlds, as we see 420 years later with Salvador Dalí's The Persistence of Memory.