When a crazy theory comes around, some reject it out of hand, or desperately hope that it is not true. I understand this–I myself very much hope, for example that intelligent alien life does not exist–and theories that they do in fact exist are not wildly crazy. Their presence would destabilize our view of the cosmos and our place in it far too much. When it comes to history, some reject any different theory as inherently destabilizing. Some adopt the Bill Hader approach, and seem to only want to make others squirm. For me–new theories generally appeal because I find them fun. In a world where every traditional narrative now has a target on its back, even flat-earth theories have made a comeback. Alas, it seems quite certain that we inhabit a spherical world, but wouldn’t it be fun if it was indeed flat? What a hilarious and tremendous flip of the script that would be.*

In 1946, at the tail end of the crisis that in hindsight dramatically weakened western civilization, William Ivins wrote Art and Geometry: A Study in Space Intuitions. This admittedly boring title concealed a powerful punch in the form of a sustained attack on the veneration of Greek sculpture so prevalent in the west at that time, or at least prevalent until 1914. Ivins admits the foolish impossibility of judging some art as superior to other art, but then proceeds to do just that (this was the right call–obviously we have the faculty to judge such things–we do it all the time–but should do so carefully). Greek sculpture, in fact, had little real vitality, little real understanding of geometry and its relationship to the body. Here we have what seems like a crazy idea, and what’s more, Ivins enjoys himself, writing with confidence and panache.

As his book involves geometry along with sculpture, one of his main criticisms involves the Greek’s apparent lack of spatial relatedness, of their inability to put their figures in relation to other people or things. He writes:

I have happened on no evidence to show that any Greek ever sat down and drew a view, or a group of figures, or a congeries of objects, such as his tables and chairs, as they appeared relatively to each other in their shapes and sizes, and positions from a single point of view.

And,

The celebrated battle friezes from the temple at Bassae or Phigaleia . . . were removed and sold before any record was made of their respective positions. They were taken to London, where for 100 years intelligent men of all nations labored to discover the order in which they had been originally set up. . . . Then at last, a brilliant young American solved the problem . . . Reasoning that the slabs must have been held to the wall by dowels, he went to the still standing temple and compared the dowel holes in the slabs to that of the temple walls. He solved the problem, in the most literal sense of the word, without ever having to look at the faces of the sculptures themselves [which gave no clue to the solution].

Ivins also lays into the Greeks for their persistent abstraction and the resulting aloofness of nearly all their subjects.

The extremely small number of Greek portrait heads is significant. . . . They are what we call “idealized” or “ennobled” portraits, i.e., abstractions with only the faintest personal character and psychological value–really no more than “composite group photographs.”

Compare any Greek figure to the quietly seated Pythagoras of the Cathedral at Chartes. He is only making an erasure in his manuscript, but his personality and the intentness and tensions of his mind and body probably cannot be equaled in all of Greek sculpture. It is as perfect a demonstration of the nonsense of the Aristotelian definition of fine art as an be imagined.

To illustrate his point, first the Pythagoras from Chartes**

And Greek sculpture

He continues his argument by linking the limitations of Greek art to their geometric theory. Whatever the greatness of Euclid and his successors, they had significant limitations. Ivins writes,

Basically the Greeks thought about their geometry in terms of an unexpressed chalk line or yard stick which they held in their two hands. . . . The way Euclid proved his basic theorem (I.4) that two triangles, having two sides and the angle between them equal, are equal to each other–was by picking one triangle up and superimposing it upon the other. . . . Euclid’s geometry was based on the tactile-muscular intuitions . . . neither Euclid or his successors had any notion of infinity.

And,

The story of Peithon and Serenus, two geometers of the 4th century AD, affords a striking example of how the Greeks missed out. [It goes] as follows:

“In the propositions (29-33) from this point to the end of the book Serenus deals with what is really an optical problem. Peithon, not being satisfied with Euclid’s treatment of parallels, thought to define them by means of an illustration, observing that parallels are such lines as are shown on a wall or roof by the shadow of a pillar with light behind it. This definition was generally ridiculed; and his friend Serenus seeks to rehabilitate Peithon by showing his statement as mathematically sound. He proves with regard to the cylinder that if any number of rays outside the cylinder are drawn touching it on all sides, all the rays pass through the parallelogram–Prop. 29–and if they are produced farther to meet any other plane parallel to that of the parallelogram the point in which they meet will lie on two parallel lines. He adds that the lines will not seem parallel.

Ivins then charts the problems with not challenging assumptions, and so on, until the era of the Renaissance. The Renaissance obviously borrowed from the classical world and the classical ideal of beauty and proportion. But in Ivins’ judgment improvements in geometric theory beginning in the early 15th century greatly improved the art of the time. This book stretched my very weak mathematical knowledge throughout, especially so as geometric theory got more complex. For Ivins, the key leap came from the renowned Alberti:

It has been said that Alberti’s greatest discovery was that the picture plane was a section of the cone of vision, but really it was something in addition to that. Up to his time the problem had been thought of as a simple two-term beholder-object relation that was really insoluble. His great contribution, though doubtless he was not aware of it, was that in fact he discarded the simple two term relation and discovered other relations sufficient to permit a solution–in other words he discovered that form and position were functions of each other, and thus were relative and not absolute . . .

Advances in geometric theory set the stage for a dramatic shift in art, with several Renaissance painters making full use of perspective.

Ivins comments,

Looked at in retrospect it seems almost incredible that the Greeks should not have discovered these things, which today seem intuitive in their simplicity and obviousness. The probable reason for this failure is that they were so obsessed by measuring and working out the relations between measurments in each of the separate conics that they were never able to see the descriptive qualities that ran through a whole series of conics.

I confess that I could not understand much of what Ivins said related to geometry, but I found his applications of geometry to art clear, and made obvious by any number of examples.

Ivins continues in his conclusion,

There is much talk of how much we owe the ancient Greek ideas, but most of this talk seems to be based on some vestigial legend of a “Golden Age,” which in this case extended for several hundred years, in a definite historical time with its origin in a definite historical place [i.e. Athens]. In general people who talk this way show little acquaintance to what we owe other peoples, and to what we owe ourselves.

Indeed the end of W.W. II ended in many respects the dream of a unified and confident western culture. Ivins’ reevaluation of the greek inheritance in geometry presaged an entire rethinking of western civilization itself. Seventy-odd years after Ivins, the west has yet to fully deal with its identity crisis.

I admire Ivins for his pluck, and I agree that there is something “off” about Greek art. Their sculptures invariably do reveal a problematic detachment, and possibly, even a kind of brutality in their subjects. But a common theme running through many of a scientific bent is that pauses in scientific knowledge, or moments when the world seems “stuck” in a particular mode of thinking, can invariably get reduced to some cruel twist of fate, or some power structure holding things back, or some basic lack of imagination due to a historical accident, or some other such “linear” explanation solved by restarting the stuck timeline.

In this area I depart with Ivins. If an idea persists, I say we should look for the reason for its persistence. We should assume that people are smart, and not hoodwinked or trapped for centuries on end.^ Judging the superiority of one kind of art over another quickly gets problematic. Still, I believe that the persistence of certain styles/ideas is evidence not of some trick of fate or conspiracy, but instead points to the idea having legs–it must have a point of connection with reality that people intuitively recognize.

Whatever we might think of the classical style, it dominated the ancient Mediterranean world for 800 years, give or take. I agree with Ivins that its revival ca. 1700-1900 AD was problematic and unfortunate in certain ways. But still–we should not attribute the dominance of this style merely to the power of the Greeks and Romans, and its revival merely to the power of England and France. They, and those around them, must have found something intuitively “right” about the classical approach.

In certain ways the Renaissance artists had more skill and worked with more developed geometric ideas. We can commend them for this. But . . . the Renaissance artistic style lasted perhaps 100 years at most, and failed to spread much beyond southern Europe. If we use the criteria of “long-term reception by ‘the people'” then we have to conclude that using advanced ideas of perspective did not make for “better” art. Ivins may overrate the place of perspective in important cultural creations.

There exists another example of an artistic style that consciously abandons certain principles of perspective that has lasted longer than the classical model–around 1500+ years–and still continues today, that being . . . Christian iconography.

We cannot attribute the persistence of this style to power (sometimes the Church had “power” and sometimes not), nor the limitations of geometric knowledge (the style began before Alberti and others revolutionized geometry, but continued long after). Though different cultures developed their own iconographic style, and though certain changes have taken place within iconography over time, no one has ever fully integrated perspective into icons. At times icons seem to deliberately reject perspective.

I am no student of iconography and will say little about the theology behind these choices, except that the power of art may reside in its ability not to accurately reflect the world as we see it, but to show us the spiritual tension we feel between we what we see, and what we “know.” We feel, not in our gut, but in our bones, that we live between two worlds, between the physical and the spiritual, between heaven and earth. Nearly all of human history testifies to our desire to somehow unite these two elements of our knowledge and experience. History shows us that most of the time we fail badly in our attempts.

Icons reveal part of the reason why we misfire so often. Our nearly exclusive focus on how people and objects relate to one another in space has made us look only at linear explanations for reality that cannot satisfy. Certainly advances in geometric knowledge did not cause this problem, but our exclusive focus on this aspect of reality (the linear/spatial) has brought about a new view of reality. Our perception is warped. We also need a way to see how we relate to each other in time, as well as space, and this, icons seek to display.

I love Ivins’ panache and willingness to go a little crazy. But maybe the truth doesn’t always extend forward, maybe sometimes it bends back around in a circle.

Dave

*Yes, some crazy ideas are really crazy . . . but perhaps there is a part of you that would want to have a conversation with this guy . . . ?

**His choice of Pythagoras to make his point is interesting–obviously this sculpture would have been regarded as a minor part of the whole edifice–and yet still something definite of his personality shines through.

^Though Ivins rightly points out the west’s immoderate attachment to the Greeks (something not really present, btw, during the Middle Ages), especially in the Victorian era, he failed to reckon what might happen when we gave up the idea of any kind of cultural center at all.