geometry and our own discontents

Geometry and Our Own Discontents: Notes towards yet another book I cannot write


One of Glen Baxter’s funniest comments on art criticism is a pair of nearly identical cartoons (I describe here from memory) showing three august-looking gentlemen holding a nearly blank canvas. In the first cartoon, the canvas contains a dot near one corner; in the second, the dot is in the opposite corner. The captions are, “The three men were in agreement: it was a work of no merit” and “The three men were in agreement: it was a work of some merit.”

And in fact the emotional and/or aesthetic impact of geometry has a history in art and architecture that has been amply explored; but as with most topics of human history, and a good many of natural history as well, the subject matter gets carved up misleadingly, and the interconnections often go
unrecognized.

Gurdjieff, whether taking his cue from Pythagoras or from the Sufis, believed there was such a thing as “objective art” and “objective architecture”; and certainly there has been enough occultist passion expended over the topic, including Hazrat Inayat Khan’s conviction that Rudolf Steiner’s first Goetheanum was fatally opposed to all the principles of spiritually correct construction, an opinion in which he felt fully justified when the building burned down before it was completed.

Empirically speaking, geometric architecture makes us happy or downright ill, but it doesn’t make all of us nauseated or filled with joy at the same time, in the same way.

It’s easy enough to agree on the rational uses of geometry, and I’m looking forward to reading Hannah B. Higgins’ The Grid Book, which recounts the many uses of the grid as operational metaphor and as useful organizing method (a selective rather than comprehensive survey, given the sheer number of different uses to which the grid has been put and has yet to be put). Even something so humble and, one would think, emotionally unarousing as the grid has been the subject of a great deal of theory-mongering over the centuries.

So it’s no surprise that the century that gave us Science for the Soul (the title of a survey of the contradictory motivations behind what looks like merely irrational occultism in late nineteenth and early twentieth century Germany) bore within it such hard-to-fathom motivations for the uses of geometry in architecture and art alike.

In the early 1920s, Wassily Kandinsky was trying to get with the program proposed by the anti-metaphysical Russian Constructivists, Rodchenko and Popova in particular, and was handing out questionnaires designed to determine the range of responses to colors and shapes. (It has been suggested, incidentally, that this whole fascination with the topic may have stemmed from an experimental program of elementary education that emphasized refining children’s understanding of the world by games with color and elementary geometric forms, but that would take us too far afield at the moment.)

Despite his inclination to be didactic on such matters, I doubt if Kandinsky found much empirical justification for his theories from his surveys. I forget what Clark Poling opined in his catalogue of “Kandinsky: Russian and Bauhaus Years.”

It’s intriguing that there have been arguments over whether the most mathematically pleasing relationships really translate into visual pleasure in a one-to-one relationship; it[s certainly been argued that despite the reverence for it from the Greeks onward, the Golden Section really isn’t all that pleasant a set of visual relations to impose on the world.

What brought all this to mind (a subjective fact which is relevant because this is a blog post, not a proposal for a book) is the depressing quality of most of the modernist buildings thrown up in Britain and in Germany in the late 1940s and the 1950s, ubiquitous because they were the easiest things to construct in the wake of wartime construction; but also loved in Germany because they conveyed a model of modern rationality that was as opposite to Völkisch organicism as one could get.

The Amerika Häuse housing cultural functions of the United States in cities throughout West Germany were meant to be modernist architecture as metaphor: the predominance of glass symbolized democratic openness. (But the history of earlier dreams of “glass architecture” or Glasarchitektur, apparently unknown to the American architects, leads off in directions both rationalist and occultist, sometimes both concurrently.)

The vulgarization of Corbu and Mies for convenience was one thing; the use of glass and of grid construction as metaphor for transparency and democracy contained a serious irony.

For the fabled Casa del Fascio that was the pinnacle of Italian Rationalism (since Terragni’s equally poetic Danteum never got built) was designed to maximize the use of glass precisely to symbolize the notion that Fascism conducted the people’s business out in the open, without the shabby backroom deals made by outworn bourgeois democracies.

Neither the architectural idealizations of Mussolini’s governing style nor those of Cold War democratic politics bore much resemblance to reality, albeit for different historical reasons. And Mussolini, after 1936, came to prefer a more grandiose stripped-down classicism like that being propounded by his newfound ally to the north.

We won’t go into the delusions of the modernists in 1933 that National Socialism might opt for the same relationship to modernity that was being carried out in architectural programs to the south. (There are books that deal more or less adequately with that curious moment in history.) There were patrons of modernism within the movement that made it a seemingly rational hope for those who chose to overlook a few problematic elements of the new order of things.

It is, in fact, interesting that authoritarian movements have so often managed to incorporate contradictory impulses and would-be programs, sometimes for the sake of cynical manipulation but just as often because the movements actually embodied contradictory wishes on the part of genuine believers. The history of literal purges (and of the bouts of mutual recrimination Americans refer to as a circular firing squad) attests to the problem this creates for political forces that stand for a putative national unity not even reflected in their own party.

That isn’t where I wanted to go, however. For what struck me again this morning is how much more visually pleasing Italian Rationalist architecture of the 1930s is in comparison to the functionally similar architecture that dominated the 1950s.

This aspect of architectural solutions giving visual pleasure led to a reassessment of Giuseppe Terragni and his compatriots in the 1980s (one might note that an opposing architectural theorist also took a fresh look at Albert Speer—the father, not the son).

That question of visual pleasure takes us back to the problem of objective art. Some people hate geometric art and architecture in general, and some find pleasure in all of it. (Some buildings are universally hated because the final design was determined by economics—cheaper-to-build shortcuts—rather than aesthetics.) Some like some parts of geometrical aesthetics and detest other parts of it, whether the parts be modernist architecture or Minimalist sculpture and painting.

De gustibus non disputandum? By no means. Denis Dutton’s The Art Instinct argues in favor of representational art by citing (and misunderstanding) Komar and Melamid’s “Most Wanted Painting” project, wherein the artists found through multiple choice surveys that people like landscapes, pictures of historical figures, and pictures of ballerinas, and hate pictures of rectangles and triangles. (K & M produced a fake Popova as their “Least Wanted Painting.”)

Their project also burlesques Kandinsky’s earnest survey questions at INKhUK, or whatever the combination of lower-case and capital letters might be the case in the name of the art institute at which he taught before decamping for the Bauhaus.

So efforts to figure out why some buildings or paintings work better than others are more likely to attract snarky remarks and parodies than serious queries regarding what is going on. But the fact that anybody at all likes geometric figuration as art, or adores stripped-down geometric architecture, poses problems for Dutton’s brand of Darwinism just as the whole human endeavor ultimately does: not refutations, just problems. For given enough generations, there are survival advantages in having an inclination to study the abstract structure of a world that is not shaped to fulfill human wishes.

As I’ve remarked before, the remarkable thing is that so many traits that don’t foster survival survive anyway; some of them should have been eliminated centuries ago through the failure of the possessors of the traits to reproduce, or to preserve the lives of whatever children they might have had.

I think Terragni’s stuff is terrific and the boxy stuff from the ‘50s sucks, but that‘s just me. I would like to know why it is just me, plus an unknown number of others. We are back to those “types and conditions of human beings” that psychologists have mapped out and correlated to aesthetic preferences—albeit not very reliably; and the social-constructionists are right when it comes to our capacity to be swayed by group enthusiasms manipulated by marketers. How much people have things in their closet to which the only possible response is the proverbial “What was I thinking?” But of course the same can be said of most people’s passing infatuations, so what we think of geometry (or anything else) may somehow be tied up with our deepest biological underpinnings.

It just isn’t as simple or single-caused as people think it is. And I don’t find that most of the attempted attempts* at explicating with greater complexity show a sufficient awareness of history, or of psychology, or of sociology, or of…well, there is always some deficient factor. In my case, it would have something to do with the grades I got in first-year geometry; one can’t really get at the relationship between emotions and mathematics without having a more or less equal comprehension of the causal factors involved in the two. Whether or not one believes in Jung’s formulation of it, there is a reason why Jung deemed portions of the personality, as he mapped them out on a grid, to be the “inferior function”: it is not just the portions at which one is more inept, but the portions most likely to be polluted by the distortions of early childhood experience or primally irrational passions simply because one can’t combine all the necessary contrasting functions quite as well in that department.

So the job is to widen the area of consciousness: to compensate for one’s inferior functions by having recourse to tools of analysis plus opinions for which others have given “good reasons” to trust their reliability.

If Baxter’s three men were in agreement, two of them were probably agreeing for the wrong reasons.

*Note: My repeated repetitions are rhetorically deliberate actions, even when they are purely accidental.

and a footnote with an illustration from Vyborg

I had no sooner finished the draft of the previous post when a review copy arrived of Alvar Aalto: Architecture, Modernity, and Geopolitics, addressing perfectly some of the problems I raised in the post in question.

For Aalto's "quasi-organic forms" as the press release has it are said to be somehow both regionally inflected and cosmopolitan and internationalist, and indeed everybody likes Aalto, except for the people who do not.

So I look forward to reading and writing about this book, along with the other related books still awaiting formal reviews from me.

I have just been handed a review of an exhibition in Helsinki that I need to proofread and edit—no joke—so this note will be truncated. Aalto's Viipuri / Vyborg library has been a cause beloved of restorationists for some years now: the photo above is several years old.