Martin Kemp: Linear Perspective from Durer to Galileo

(this is Chapter Two of Martin Kemp's "The Science of Art".
Quoted text is in YELLOW.
Text quoted from other authors is in GREEN)

Durer (1471-1528): Presentation in the Temple, 1504


I hope to indicate that there are certain patterns to be discerned in those countries in the forefront of the quest for what we may call 'scientific illusion' in art.

Kemp must have been reading the Cataline speeches of Cicero. Whatever the orator says often enough, eventually the audience will suspect that it may be true.



The Presentation in the Temple shows how perspectival devices can be utilized powerfully in a narrative context -- to convey a sense of the solemn and imposing dignity of the ancient temple


But then, Kemp notes that the coffering in the ceiling is incorrectly drawn, and shows a "corrected version" done by Jean Pelerin only 5 years later.

Pelerin assumes that the ceiling bays are all squares of the same size, which would result in the rear bay appearing much smaller, and would move its supporting column much further to the right, substantially changing its relationship to the figures in the foreground.

Kemp allows that Pelerin's "correction" might be considered pedantic, and even detrimental to the design, but then quotes this passage that Durer wrote in a letter in 1506:

I shall be finished here in ten more days, then I shall ride to Bologna where someone is willing to teach me the secrets of perspective. I intend to stay there about eight days. Here I am a gentleman, at home I am a parasite."

And then the speculation begins.

Who was his teacher - and what was he taught?

But as Durer's concern about being perceived as a gentleman might suggest, these lessons in perpective may have been more connected to his interest in social status than in enhancing his paintings - much as students in MFA programs today learn more about how to talk like an artist rather than about making things. Durer needed to fit into the humanist princely courts of his day - just as our conteporary artists need to fit into university art programs.

Or, maybe he was just curious about mathematics.

In 1525 he published his own treatise: "Instuction in Measurement with compass and ruler in lines, planes, and solid bodies", directed at young German artists who "have grown up in ignorance, like unpruned trees. Although some of them have achieved a skilful hand through continual practice, their works are made intuitively and solely according to their own taste"

The work which can most obviously sustain a full-scale analysis is his brilliant St. Gerome engraving of 1514. This is his supreme demonstration of the engraver’s arts in union with the perspectivist’s scientia. Using a radically off-centre viewpoint he has openly delighted in extremes of transformation and plunging space, providing a strenuous course of perspectival gymnastics for the observer’s eye.

To me, this appears to be a rather straighforward application of an Albertian picture box, except, of course, that there is no pattern of square tiles on the floor or ceiling.

Kemp believes that he has found the remnant of one, in that the opposing corners of the table create a diagonal line that intersects the diagonal connecting the bottoms of two chair legs, and that intersection is on the same horizon line established by the vanishing point from all the receding orthogonals of the wall and ceiling. But even if that is not a coincidence, just how, exactly does that enhance the sense of space in the room? It certainly does not incrementally measure it out, the way that a grid on the floor or ceiling would.

He also notes that the spatial construction is not accompanied by a geometric pattern on the surface of the picture plane, as he finds in the paintings of Italian masters like Piero. And he feels that the orthogonals are "plunging in a willfully independent way to their common vanishing point" , the features in perspective seem "more obtrusive"and sometimes "overtly peculiar" with a feeling of "dynamic freedom".

So he wants to talk about the emotional effects of composition.

But how can this topic be raised without reference to narrative -- i.e. what is St. Jerome doing in that pleasant, sunlit room, with a lion and mangy little dog on the floor?

With neither the narrative features (that Smith would have discussed) or the compositional problems (that interested White), Kemp's discussion of Durer and his St. Jerome was a bit thin, and I'm not sure why he discussed him at all, other than his status as
"the last major painter who was also a significant geometer"

But I am very grateful for his introducing me to another Nuremburg artist, the metal worker, Wenzel Jamnitzer, who published a book of delightfully whimsical engravings, the Perspectiva Corporum Regularium in 1568.

Apparently, these geometric solids represented the various Platonic states of matter.

But more than that, they are just fun to look at, and remind us that, for whatever reason, Germans make such good machinists.

Here is what Wenzel did for a living.

Jean Pelerin (1445-1524)

Here are some illustrations from yet another book about perspective from the early 16th C. - this is the fellow who "corrected" the Durer woodcut shown earlier.

Some very simple, enjoyable views, that would be commendable if done today, though in his era of great book illumination, it's quite modest.

Jean Cousin (1500 - 1593)


And here's another guy who wrote a book about perspective

In this case, he was also a great painter, but unfortunately, there aren't any perspective views of buildings in his paintings so Kemp has no reason to discuss them.

The next painting he discusses is Raphael's "Marriage of the Virgin" which demonstrates "an impressive mastery of the orthodox description of architectural forms in space" and "a sense of mathematical harmony worthy of his great predecessor"

Kemp offers no further discussion for this piece, but I can't help but digress into comparing it with its prototype done by Raphael's teacher, Perugino. four years earlier.

Raphael has given that gazebo in the background 8 sides instead of six, which does, I suppose, make its rendering in perspective a little more complicated. He has also set it further back, giving more space to the intervening plaza. But that extra space does present a problem for the Albertian system that uses only one vanishing point. Those extended horizontal lines in the pavement badly need to curve back,especially since they are set against the curving edges of the octagon behind them. But Raphael has kept them straight, making the scene feel unreal.

But on the other hand, Perugino has certainly made his version feel unreal as well - with the priest appearing to be some kind of magician, the center of this little drama, while Raphael has given greater emphasis to the Virgin.

Why has this wedding ceremony been set into a palatial garden that includes a public square and monumental gazebo? That's a question that Norris Kelly Smith would have liked to answer.

Kemp next brings our attention to the faux architecture that Raphael painted in the Loggie of Leo X at the Vatican. He claims that it applied a "new mode of operation", but does not explain it.

I couldn't find any images on the internet, except for one of the scenes, shown above, that was set into the architectural framework of the ceiling.

Carlo Urbino

Further discussion then follows regarding that golden age of illusionistic ceilings of the 16th C. Were they designed using projective geometry -- or by building a miniature architectural model and viewing it on an angled mirror ?

Carlo Urbino is credited as being the author of a practical handbook for how to make them -- but I'm only interested in these illusions if I find the painting as a whole to be compelling, and I think there's good reason why Carlo is known only to specialists.

I'd like to read some further speculation on why Italians of that era were so fond of illusionistic holes in the ceilings of their churches - but Kemp doesn't go there.

As Kemp notes, the fondness for illusion in that era led the humanist-aristocrat Daniele Barbaro to commission Veronese's decoration of his villa in Maser, so wonderfully celebrated 400 years later by Josef Losey's film of Don Giovanni (where you might note in the linked video, Losey uses actors to create the illusion of an illusionistic painting)

But as Kemp also notes, Barbaro seemed to be more interested in geometry (he wrote and critiqued essays on this subject) than in aesthetic effect, aand he scolded artists for being "content with a simple procedure which misses the true divinity of geometry". Kemp then looks at the writings of Egnatio Danti. His brother Vincenzo, was a great sculptor, but Egnatio was a priest who served as a university professor of mathematics as well as a consultant to the Pope. So he is far less interesting to me than to Kemp who calls him “the most intelligent, useful, and thoroughly informative book on perspective construction to have appeared at that date”

At least his next author, Giovanni Paolo Lomazzo (1538-1592), was a painter until he went blind, but even then Kemp does not discuss his paintings. Lomazzo wrote "Trattato dell'arte della pittura, scoltura et architettura" which Wikipedia calls "a milestone" in the development of art criticism, but apparently it has not been considered important enough to have been published in an English translation. According to Kemp, Lomazzo had some difficulty with Michelangelo's dictum that the artist should have calipers in his eyes rather than base his proportions on numerical or geometric calculations. How could that super-human artist be wrong? Apparently Lomazzo suggested that Michelangelo's dictum only applied to those who were as deeply schooled in the rules of perspective as he was. BTW, Lomazzo also believed that the eye emits rays and vision is the result of those rays bouncing back to it - a theory which was restated a few years ago by an Indian fellow on the Aesthetic-L discussion list.

Federico Zuccari (1540-1609), the next author Kemp discusses, was also an artist, and even if he wasn't as good as Michelangelo, at least he agreed with him:

I say strongly, and I know I say the truth, that the art of painting does not derive its principles from the mathematical sciences and has no need of recourse to them to learn the rules and means for its practice, for art is not the daughter of mathematics, but of nature and design

I happen to agree with Zuccari, and obviously if Kemp did as well, the book I am now discussing would not have been written.

And BTW, a similar assertion has been made regarding the practice of scientific research: No practicing scientist learned the craft of research from books or articles, Polanyi argued. Rather, they had to practice craftlike skills, which they internalized via social relationships like apprenticeship training. Scientists developed an aesthetic sense for what counted as good science, according to Polanyi, and used any means available to convince colleagues from rival research schools to believe a given result. Scientists often formed their beliefs from an immersion in particulars that resisted explicit articulation; he likened the experience to religious conversion. To Polanyi, the routines of scientific research could never be captured by recipes, and therefore any effort to steer the direction of research, or subject science to central planning, was bound to fail. As Kemp notes, subsequent treatises on projective geometry tended to ignore pictorial applications and moved on to issues of ballistics and astronomy.

But the very first art academies, like the Accademia Del Designo in Florence and the Accademia di San Luca in Rome did indeed offer instruction in mathematics.

And as Kemp has us note in the above detail from a painting by Lodovico Cigoli, the Virgin is standing upon a moon that is as pockmarked as Galileo described it in his calculations from the shadows observed on its round surface.

Observation and calculation as practiced in the beginning decades of the Scientific Revolution did indeed have at least some impact upon artistic practice. Though it seems rather minimal to me - since, after all, no telescope has ever seen the Virgin standing in heaven.

As it turns out, Cigoli and Galileo had quite an ongoing correspondence, as they both shared an interest in mathematics and representation. Galileo was even elected to become a member of the Accademia del Designo in Florence, though that did not prevent him from writing the following two decades later: "Philosophy [i.e., physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth."

Which seems, at least to me, to be as direct an attack upon the mimetic visual arts as could possibly be made.

Here's a drawing by Cigoli, showing both his strength in figurative detail and his weakness in spatial design.

He was almost an exact contemporary of Caravaggio who was born 10 years later but died before him.

So ends Kemp's discussion of "Linear perspective from Durer to Galileo" - a title which, one may sadly note, ends with the name of a non-artist, reminding us that Kemp is not focusing on visual art, as Smith and White had done.

He also does not seem to be doing a thorough, insightful history of geometry, but I admit that this subject does not interest me enough to re-create the various methods illustrated by the diagrams that he has included.