On Dec. 24, with memories of the calamity of Sept. 11 still fresh, The Chronicle published my reflections on a painting by Piet Mondrian that the San Francisco Museum of Modern Art owns and displays.

The painting having been made in wartime during the period of Mondrian's reluctant escape from Europe to New York, I wondered whether it might show us something about how a mind stabilized itself against the pressure of untoward events.

My commentary prompted the following exchange of e-mails between me and Professor Didier de Fontaine of the University of California at Berkeley. It touches on issues that still exercise people skeptical of abstraction or of modern art as a whole.

De Fontaine mentions Alan Sokal, a physicist who duped the editors of Social Text into publishing a nonsensical scientific paper. Sokal's bogus 1996 paper argued that cultural biases condition certain discoveries of modern physics that scientists regard as objective fact. Eager to show that cultural perspective slants all knowledge -- i.e., that objectivity is really ideology - - this is just what the editors at Social Text had wanted to hear.

The relevance of the Sokal hoax in this context is debatable, and we debated it.

Far more pertinent is the "Mondrian Test," which readers can take, as de Fontaine's second letter explains.

It was devised by painter Alan Lee, who is honorary visiting scholar in the philosophy department of Flinders University, New South Wales, Australia. Lee presented a dozen images to respondents, including recognized art professionals, and asked them to find the true Mondrians among the simulations.

The "test" images are reproduced here; the answers appear at the end of this article.

Finding that his subjects' choices were somewhat less accurate than "blind guessing" would have been, Lee concluded that "there seems to be no demonstrable difference between the designs Mondrian did create and almost any random combination of the same elements."

Mondrian thought he could devise abstract compositions that would have a recognizable, if not objective, aesthetic primacy. Lee argues that he was instead "fruitlessly involved with . . . the problem of choice without preference."

Most people engaged with visual art believe, like Mondrian, that it can produce experiences, even awakenings, that are real but not necessarily available to objectivity. Skeptics such as Lee and de Fontaine appear to believe that anything unavailable to objective study must be merely subjective,

therefore only a step away from chicanery and private fantasy.

The meaning of artworks appears only to someone who enters into their structure in an alert, imaginative and informed way. Obvious in the case of literature, this is no less true of abstract paintings.

Most important: Entry into artworks comes not merely by the private pursuit of curiosity but also through dialogue such as the exchange that follows.

Dear Mr. Baker -- I have just read your interesting article on Piet Mondrian in the San Francisco Chronicle of Dec. 24. Though I admire Mondrian's work in general, I am a physicist and as such take exception to the rather ridiculous literature that has sprung up concerning art and literary criticism.

Alan Sokal, then Bricmont and Sokal, has performed a long-overdue debunking of some of those trendy texts, and it seems to me that your article comes perilously close to following in the footsteps of those French intellectuals who have, in my opinion, made absolute fools of themselves and richly deserve the ridicule heaped upon them by Sokal and Bricmont.

In the caption of the Mondrian reproduction in your article, we read: "Mondrian's 'Composition in Red, Yellow and Blue' . . . shows the tension of the era of Nazi oppression with its incompatible scales and sight lines." How can anyone in his right mind read the evils of Nazism in the straight lines of the painting?

Moreover, whatever do you mean by "incompatible scales and sight lines?" Surely you do not mean "incommensurate scales," because the two scales of the divisions shown on the vertical lines in the painting are perfectly commensurate, in fact are quite compatible, as they lie precisely opposite each other. Then why are sight lines incompatible? All lines are either parallel or orthogonal to one another, so what are you talking about?

But there is more: "It makes the painting emanate a sourceless inner light, as if by incandescence of its physical matter." If the inner light is caused by the burning of its physical matter (do you know of any matter that is unphysical?), then it is not "sourceless."

And more: "Mondrian's 'Composition' . . . objectifies the effort of a mind not to cave in to anxieties such as these. It still offers us a scaffold from which to see beyond determinist visions of a doomed future." Whoa, easy there! You may see all that yourself in Mondrian's abstraction, but why foist your purely gratuitous interpretations on an unsuspecting public who may thus be misled into seeing profundity in what is merely an exercise in wordy self- indulgence?

Of course, you may think that because I am a scientist, as are Sokal and Bricmont, I take things too literally and cannot appreciate the value of "art- crit." Not so. We can surely see beauty in original works of art (painting, music, poetry), but we object when critics string together perfectly decent words of the English (or French) language and distort their meaning in order to create a meaningless concoction that is intelligible, at best, only to themselves (i.e. to the writer himself, but not even to other critics, whose personal vocabulary may well be distorted in a completely different manner).

In conclusion, please leave Piet Mondrian alone and allow his soul to rest in peace. Amen.

DIDIER DE FONTAINE

department of materials science

University of California at Berkeley. .

Dear Professor de Fontaine -- I certainly agree that the "social constructionists" caught out by the Sokal hoax had it coming, but it's a stretch to accuse me of verging on that kind of excess. No fishy theories and no jargon sully what I wrote. (I suggest you steer clear of Mondrian's own woolly-minded writings.) You misquote me in making your accusation anyway. I didn't say, nor would I say, that Mondrian registered the tension of dreading the Nazi onslaught in his painting's incompatible scales and sight lines. The point was to ask whether Mondrian's "Composition," the product of a time and a mind even more full of apprehension than our own, might show us anxiety successfully transcended, or sublimated, as Freud would say. The answer can come only as a matter of perceptual experience.

This experience is one you seem not to have had. Fair enough; there are no guarantees where artworks are concerned. But to say that it is not possible is to make a much bigger claim: to deny the participatory nature of viewers' engagement with paintings.

My description of Mondrian's "Composition" in terms of incommensurate scales and sight lines was an attempt to get the process of participation going on the part of an imaginary reader who might take the trouble to stand before the work itself.

"Scale," in this context, refers to a perceived quality -- a virtual one, if you like -- not the measurable dimensions of the forms mapped on the canvas,

but their optical insinuations. In this sense, the two sides of the painting definitely break into impressions of frontality (and transparency) on the right, and an opaque aerial viewpoint on the left. Mondrian studiedly does not make these things explicit, which is one reason they embarrass any attempt to put them into words.

Not the tension between these aspects of the painting alone matters, but the perceived resolution of that tension through all the adjustments of form and quantity and intensity of color.

That resolution, I tried to say, manifests itself perceptually as an improbable (we might almost say hallucinated) radiance of light by the painting itself. This is not a mystical experience (though Mondrian would have had no problem with that). It is, simply, one way of perceiving the painting as meaningful.

A theory of perception does lie behind what I write about art. But I borrow it from Michael Polanyi, not from any French trendsetter. As you probably know,

Polanyi (1981-1976) was a research chemist for most of his career. He retired to write several important books about perception, meaning and social issues. The most significant is "Personal Knowledge," a critique of objectivity from the perspective of a practicing scientist -- critique in the Kantian sense not of dismantling but of a probing for limits.

Polanyi explains better than anyone else why the meanings of things such as art objects seem rarely, if ever, to be identical with their material substrates. I will not recount his argument here, but I hope you will read it (if only in the form of the very brief book, "The Tacit Dimension"), if you have not already.

My Mondrian commentary was a humble instance of Polanyian thinking applied to a specific artwork, occasioned by specific recent events.

For the record, I don't think that art or criticism or any other creative undertaking will benefit by trying to deny what science has shown us humans we can confidently claim to know. But in the newspaper setting, I rarely have a chance to explain my viewpoint in sufficient detail -- I simply have to speak from it and hope that readers catch whatever implications come through.

KENNETH BAKER

Dear Mr. Baker: Sorry to trouble you once more with a sequel to l'affaire Mondrian, but I have just become aware of new developments. In the Feb. 28 issue of the science journal Nature, there is a reproduction of Mondrian's "Composition With Red, Yellow and Blue," accompanied by a short review of a conference held recently at the Australian National University in Canberra, with the title "The Art of Seeing and the Seeing of Art."

Naturally, I read the piece, from which I now quote: "(Mondrian) maintained that the correct arrangement (of primary colors and straight lines) would deliver a profound impact; sometimes he spent weeks deciding on the precise positioning of a single line. Remarkably, Australian artist Alan Lee told the conference audience that the theory collapses when put to the test. Lee created eight of his own paintings based on Mondrian's basic design elements of intersecting black vertical and horizontal lines enclosing colored regions. However, he composed his patterns randomly. In visual perception tests, 10 art experts and more than 100 art students were presented with an array of 12 paintings and asked to identify the four of Mondrian's carefully composed patterns and the eight random patterns produced by Lee. The results were the same as if the subjects had been blindfolded -- the two types of patterns were indistinguishable."

I was, of course, delighted by the outcome of this clever experiment, so I wrote to Lee, who promptly sent me a copy of his article by e-mail along with a JPEG copy of his "Mondrian Test." Since the artist invited me to take the test and to share it with friends, I am attaching a copy of the test with this e-mail.

Lee is careful not to criticize Mondrian himself, only those who see mystical meaning in his vertical and horizontal lines, positioned with such exquisite care. Sound familiar? In his letter to me, Lee wrote: "If you have the time to read my paper you may be surprised to see how close your own arguments against the art critic at the San Francisco Chronicle are to my arguments against what I think of as the 'official' art-world view of Mondrian.

Your arguments were very likely dashed off in the heat of the moment, whereas mine were drafted many years ago, and have been polished through repeated drafts." Forgive me for gloating.

DIDIER DE FONTAINE

Dear Professor de Fontaine -- I too am impressed by the cleverness of Alan Lee's "Mondrian Test" experiment, but it has at least one crucial flaw. In effect, Lee assumes that Mondrian was a designer, not a painter.

Many people who saw Mondrian's abstract work up close for the first time in the 1995 retrospective in Washington or New York were startled by its physicality. Some of it even looks a little shabby partly, because of condition problems, but also because Mondrian was not as fastidious a craftsman as his legend suggests.

Mondrian continually met the resistance of physical stuff in his search for supreme compositional rightness. He was not dragging lines and color blocks around frictionlessly on a computer screen; his search for an ideal order involved much more than optical responses.

Whatever Mondrian's delusions about his work, they rested on the experience of fabricating things, not just of designing them.

He hoped that aesthetic epiphany -- given an armature of optimal composition -- might free involved viewers from the philosophical inertia of the arid materialism that the art object, regarded as a mere thing, betokens.

He naturally assumed -- as we in a media-saturated culture may not -- that the necessary aesthetic recognition could occur only in a firsthand encounter with his work.

So, to be really decisive, Lee's Mondrian Test would have to involve eyes- on exposure to genuine Mondrians side by side with truly convincing forgeries. Hardly feasible.

Looking at the JPEGs, I took Lee's "Mondrian Test" before I read his paper. I happened to spot three out of the four that he says are genuine. None of the fakes convinced me.

Interestingly, though, I am hard put to say why those three struck me as credible and the rest did not: further corroboration, if it were needed, of Polanyi's contention that "we know more than we can tell."

I found myself saying things like "Mondrian wouldn't have put that much red in that position, wouldn't have had so many lines intersecting so nearby each other," and so on. But the basis of those intuitions eludes me, as it probably did Mondrian himself.

To me the Mondrian Test proves only that what matters about Mondrian's abstractions -- including the way contemporary events impinge on their meaning -- cannot be skimmed off in reproduction.

-- Kenneth Baker

TAKE THE TEST



Click to View Full Size

Which of these images are real Mondrians? The answers are shown below.

Test answers: The real Mondrians are: D, F, H and K.