In writing Florence & Baghdad: Renaissance Art and Arab Science, Professor Hans Belting has given us a grimly relevant book.
His aim is to effect what he terms a Blickwechsel - a German word that means both changing the way you look at something and exchanging glances with that something - and his whole book, which is densely written, profusely illustrated and enjoyably challenging, constitutes a large scholarly step in that direction.
His task is daunting. Tensions - between the West (here represented by Florence) and the Middle East (here represented by Baghdad) are today greater than they have been for many centuries and what is inimical must also be incurious. A group of the most reactionary factions of both worlds is something dangerously close to Belting's central contention here - that East and West actually see the world differently.
Belting, a professor of art history at the Academy for Design in Karlsruhe, Germany, is aware of the peril that his topic will be misunderstood, but he strikes a quintessentially humanist note early on and sticks to it throughout. "One can speak of differences," he calmly tells us, "only where there is common ground."
The differences at the heart of his book centre on "perspective", both as a term of science dealing with mathematics and as a term of art dealing with aesthetics.
Much depends on this twinning of the word's meaning. In its original medieval conception, perspective was an almost purely mathematical concern dealing with the propagation and calculation of light rays. It was to art what the science of acoustics is to the Baroque concerto - you could study the former for a lifetime without ever imagining, much less requiring, the presence of the latter.
Crucial to Belting's undertaking here is that readers recall the fact that this medieval conception of perspective was Arabic in origin - it arose from early western translations of the works of the Arab mathematician Abu Ali al-Hasan Ibn Al-Haytham (965-1040), known to early translators by the name Alhazen.
One of the many pleasant services Florence & Baghdad performs for its readers is to introduce them to this "Arab Archimedes" and acquaint them with the vast body of his work, including his pivotal text, Kitah Al-Manazir (Book of Optics), in which he not only proved that rays of light could be precisely calculated but also attempted to "close the gap between mathematics and empirical observation".
It was only with the advent of such massively influential Renaissance figures as the architect Filippo Brunelleschi and the artist Leon Battista Alberti that perspective took on a definition first allied to and then radically divergent from the original, and Belting is quick to stress that this in no way implies a hierarchy.
"If we wish to examine cultures of both the Middle East and the West without a colonialist bias, there can be no privileged standpoint from which an older culture is admitted to have exercised an 'influence' on a modern one," he tells us. "Cultural studies today should give up on using the West ('modernity') as a universal standard."
In Middle Eastern illustrated works, "images and texts entered into an alliance that serves to tame the gaze", whereas in the western adaptation of perspective, images became destinations all by themselves.
Hierarchies here might be illusory but the divergence was all too real and, as Belting points out, largely secular. "The contrast between Arab visual theory and western pictorial theory existed for cultural rather than scientific reasons. In Middle Eastern culture, making pictures in the western sense was long regarded as taboo, while in the West it was celebrated as the royal road to knowledge."
In Baghdad, one definition of perspective was used to perfect the arts of calligraphy and geometrical design, with any pictorial representation standing strictly subordinate.
In Florence, as Belting says: "There is probably no greater contrast to the pictures we have just been discussing than the modern western kind that look at us or - let's just say it right away - look back at us when we direct our gaze toward them."
Brunelleschi and especially Alberti used the principles of perspective to invent a new kind of picture and a new way of looking at pictures.
Suddenly, the images represented were not subordinate to anything, including the viewer - they were an alternate world, one which used the mathematical principles of perception to create the visual representation of perspective.
Viewers could feel themselves drawn in and regarding the picture they could feel themselves regarded in turn.
In a series of fascinating chapters, Belting examines in loving and elaborately illustrated detail not only the workings of Alhazen's optical workings, but also the dynamics of western pictorial representation.
We are introduced to the early Renaissance humanist Biagio Pelacani, who knew Alhazen's work and used it to underpin his own visual theories, which were well known to later artists of the period.
"By introducing empty space into post-Islamic visual theory," Belting explains, "Biagio laid the foundations for the pictorial theory of linear perspective, which was invented in Florence during the last years of his life."
That pictorial theory - its manifestations in an endless profusion of Renaissance-era paintings - is served to readers refreshingly cleansed of the ideological tinges that clung to it in more religious eras.
"Space as measured in human terms becomes synonymous with visual space and dependent on a gaze from a human body," he writes, adding another typically humanist qualification: "Since the eye can be deceived, the area of the gaze must be measured."
One of Belting's many interesting elaborations deals with the gradual expansion of that visual deception. He centres this discussion both on the concept of the infinite horizon and that of the window that looks out on it. It's a thing most westerners take for granted when looking at pictures, so essential has it become to the West's idea of representational art.
In that idea, the frame of the picture is the window through which the viewer gazes into the world of the picture itself, which stretches out infinitely to the horizons of that picture's world.
This is foreign to the Baghdad way of looking at pictures and one of Belting's most telling points is that it would have been equally foreign to the Florence (or London, or Lisbon) way of looking at pictures in, say, the 8th or 9th centuries.
In medieval times, artists conveyed the concept of the horizon non-linearly, as a thing ordained by God rather than perceived by mere mortals. It was, as Belting says, "a turning point in cultural history when artists linked the horizon to the human gaze".
Jumping off from translated Arabic visual treatises, western artists reached that turning point and have never looked back - although the proximity between such a study of the human gaze and plain narcissism gets some extended, and rather droll, treatment from Belting, and several of his most telling critiques of the West are gently but insistently implied.
On the purely pragmatic level, this is the divide between the two cultural worlds - in Baghdad, perspective is enlisted to measure light, while in Florence, it is used to measure the human gaze.
In the closing section of his book, Belting masterfully illustrates this divide, in the shape of mashrabiya, the old and gorgeously elaborate carved wooden screens for windows and balconies that are still seen throughout the Middle East today. The intricate designs of the mashrabiya serve to shape light itself, creating an ever-shifting pattern throughout the day, rather than a fixed pattern that merely uses light as a means to an end.
Analogies with western stained glass are curiously unexplored here - and there is virtually no mention of, for example, the Pantheon's very intentional use of ambient light or the chaotic glories of Hagia Sophia - but the point will be carried home regardless by the strength of the superb illustrations in this part of the book, especially to anyone who has ever sat immersed in the hot, miraculous light show a mashrabiya creates, immersed in the sublime rather than, in the western sense, observing and commanding it.
It is a fitting end for a book of such even-handed and ultimately compassionate erudition - windows that are not windows, two linked but fundamentally different ways of looking.
The real Blickwechsel Belting is attempting here is commendably large-scale and he stresses a combining, mutually appreciative method at every opportunity.
"Studying perspective as a cultural or symbolic form," he writes, "is meaningful only if the goal is to give equal acceptance to other forms and rules for guiding the eyes." He avoids the pitfall of characterising these two forms as active and passive and readers should avoid that pitfall as well.
As Belting points out, the concepts of "inside" and "outside" stand in very different relationship to each other depending on whether you are in Baghdad or Florence and the functions of looking - and of light itself - are radically different: "In one case the subject becomes active in his or her gaze, while in the other the subject experiences light - that is to say, a suprapersonal force - as a cosmic drama."
The gentle message underneath this book's fluid, inviting prose and sumptuous illustrations is that both perceptions are equally valid and have much to teach each other.
In a world that now exists largely on edge, that is a welcome message indeed.
Steve Donoghue is managing editor of Open Letters Monthly.