Polytropy

This is about the morning of Thursday, December 18, 2014, a morning I spent by the Bosphorus, thinking mostly about poetry, and photographing the sky.

When I first came to Turkey in August of 1998, I travelled with my future spouse Ayşe, and it was her recommendation that we bring a guidebook from the United States. The one we selected was Turkey: The Rough Guide (third edition, London, March 1997), by Rosie Ayliffe, Marc Dubin, and John Gawthrop, with additional contributions by Stephanie Capparell, Bradley Mayhew, Dave Muddyman, and Sevan Nişanyan. I write out the names here, on the general principle of giving credit where it is due, and because of the significance of one of those names. Sevan Nişanyan has been in prison for more than a year now, serving a sentence of something like fifteen years, although originally it was less; and as far as I know, his nominal crime was building a house on protected land. His lawyers ask if anybody else has ever served prison time for such a crime, and no answer has been forthcoming. Nişanyan’s illegal house is outside Şirince, Selçuk, İzmir; and it is used as a dormitory for the Nesin Mathematics Village. That village has been a summer retreat for Ayşe and me for several years now.

The Bosphorus Strait can serve as a more local retreat for somebody living in Istanbul. I have always remembered what the Rough Guide says about the strait (p. 71):

The Bosphorus—the straits dividing Europe and Asia—should be visited as often as possible during the course of a trip, since how much you enjoy Istanbul may well depend on how often you can escape to its shores.

I remembered this, for the thirteen years that I came to Istanbul as a visitor from Ankara; but I did not see that it was true. There is not a lot on the Bosphorus for the visitor to do, but most sightseeing is likely to be inland.

When Ayşe and I would visit the European side of Istanbul, for the film festival perhaps, or a mathematics conference, or a wedding, and our time in the city was up, we would usually then take a ferry over to Harem on the Asian side. This was a pleasant way to travel. From Harem, we would take the next bus back to Ankara.

The views around the Nesin Mathematics Village are an important part of my sense of the place. What one sees are olive orchards, and vineyards, and pine trees higher up on the slopes. It is important to me that I can hike into the landscape. I do this regularly when I am there. I have found circuits that can be walked in two or three hours.

When I lived in Ankara, the Bosphorus never seemed to have an importance like that of the Şirince landscape. When the opportunity arose, it was good to see the Bosphorus and to be out on it; but I did not long to see it while I was away. Now that I actually live in Istanbul, I do.

The original purpose of this article is to record the experience of one session by the Bosphorus. I use the word “session” here in its root sense of sitting. For a couple of hours, I just sat by the Bosphorus, unless I was moved to get up and take a photograph of the sky above the water.

I was at the building used first for the lower house of the Ottoman Parliament. That house was, in modern Turkish, Mebuslar Meclisi, the “Deputies Chamber”; but the Persian Turkish used in Ottoman times was Meclis-i Mebusân, “Chamber of Deputies.” This is still the name of the section of the shore road that passes the building; nonetheless, the building itself came to be used for the Mekteb-i Sanayi-i Nefise-i Şâhâne, the “School of Arts Fine Imperial”—in English order, the Imperial School of Fine Arts. This ultimately became Mimar Sinan Güzel Sanatlar Üniversitesi, “Mimar Sinan Fine Arts University.”

That is where Ayşe and I work today; but we work in the mathematics department, which is housed away inland. The central administration stays in the old building, which is why we had to visit. My business was quickly taken care of, though Ayşe’s was not. As the day was looking fine, and my time was my own, I stayed and sat by the water.

I am sorry that I had not studied the university’s original name when I was talking to students a few weeks ago about mathematics as a fine art. We say güzel sanat for this today; but the Ottoman expression was sanayi-i nefise, and today the Arabic word sanayi is used for industry, as in oto sanayii, “automobile industry;” but sanayi is related to sanat, “art.”

As I mentioned Sevan Nişanyan before, I should point out that one of my resources on Turkish words is his book, Sözlerin Soyağacı: Çağdaş Türkçenin Etimolojik Sözlüğü (“The Family Tree of Words: An Etymological Dictionary of Contemporary Turkish,” Istanbul; first edition, October, 2002; third edition, expanded and corrected, March 2007). In the preface, Nişanyan thanks the provincial bureaucrats who gave him the opportunity to finish the dictionary—in Selçuk Prison. Selçuk is the district where the village of Şirince lies, and Nişanyan went to prison for—illegal construction.

Before heading out to the Bosphorus, I was studying a mathematical proof in a book. I noticed that, instead of referring to a finite set {x₁, …, x_n}, from which one derives something denoted by

one can just refer to a finite set X, from which one derives

From graduate school, I remember an algebraic topology textbook that used austere notation like this. We seem normally to be taught that a finite set with n elements should be “indexed” by the first n counting numbers; but we can more simply use the elements of the set to index themselves.

Working yesterday on these things, I thought of the sequence of four human backs in relief, sculpted over the years by Matisse and on display in the sculpture garden of the Hirshhorn Museum in Washington. Our art teacher called the sequence to our attention when he took us to the museum in fourth grade. It was a good trip we had then, albeit an elitist one: out of a class of forty-four boys, only eight or ten were chosen to visit the Hirshhorn. This made general discussions in front of specific works possible; but then there should have been several visits, giving all students the chance to visit the museum, even if they seemed uninterested in art. Every student had to practice drawing and painting in class; why not give them all the opportunity to think about what it was all for? I hope that today we give our students at Mimar Sinan the opportunity to think about what mathematics is for. I hope that they will understand that mathematics can be as useful as a painting in a museum.

Matisse’s sculptures of backs become more abstract as the artist grows older. Did Matisse know where he was going when he made the first? I seem to recall wondering why he did not just make the last sculpture first. The simplest answer to the question is that Matisse could not yet see so simply.

Sitting by the Bosphorus yesterday, I read from the November (2014) issue of Poetry magazine. I had found it in Pandora bookshop here in Istanbul. I had been aware of the magazine since a ninth-grade English class, when we were given a poem by one E. McKim:

horses move across unlighted landscapes        
 of the dream. overhead the golden crows       
  form galaxies; in the foreground we are      
   shown a room, a thousand corridors, some    
    place to move, falter, or become before    
     the red storms come to scatter precious   
      emblems: horse crows men rooms all into  
       a warmer place protected from the winds 
        and sensed obscurities the mind can see

        and sensed obscurities the mind can see
       a warmer place protected from the winds
      emblems: horse crows men rooms all into
     the red storms come to scatter precious
    place to move, falter, or become before
   shown a room, a thousand corridors, some
  form galaxies; in the foreground we are
 of the dream. overhead the golden crows
horses move across unlighted landscapes

I transcribe the poem from the mimeographed sheet that I kept from school. According to the sheet,

This poem is from the October 1970 issue of Poetry, an American magazine of verse founded in 1912.

E. McKim was educated at Vassar, the Alliance Française in Paris, Trinity College, Boston University, and Cummington Community of the Arts. She lives in Brookline, Massachusetts. This poem marked her first appearance in Poetry.

In the spirit of Karl Ove Knausgaard perhaps, a spirit of self-exposure, I transcribe my essay about the E. McKim poem. If I feel pleased that I appreciated art, even in fourth grade, I should acknowledge how much my sense of good writing has changed. The essay also shows the psychic effects of the Cold War on one young person. At the age of fourteen and seven months, I wrote:

The untitled poem by E. McKim is very interesting. The second of its two stanzas is the same as the first except the lines are in reverse order. In the poem very strange events are described, yet is the poem just nonsense, or is it actually meaningful?

The poem is apparently about a dream. The poem opens on a lightless world that is having galaxies created above it. We, the people viewing this world, are given a complex building where we can do as we will and can have protection from the red storms and their emblems. The storms eventually destroy the building, however, so we are shown another building. In the end the world is without light once more.

The poem could be about a war with the Communists, hence “red storms.” We are protected against the Communists for a while, but they eventually destroy our protection. We must move into underground passages, perhaps Communist prisons, since the earth overhead has been destroyed by the war.

Of course, my interpretation of the poem’s meaning may be wrong, as my interpretation does not explain such things as the horses and the golden crows. However, the poem is so obscure that perhaps it does not have one definate [sic] meaning but, in fact, means whatever the reader thinks it means.

That was an entire ninth-grade essay, taking up a page and a third when written out by hand on ruled paper. I write that much now, just to get started; I hope I no longer write anything like the opening sentence.

In eighth grade, in a political geography class, I had written a term-paper called “The Principles of Communism,” based mainly on the Communist Manifesto. In a speech in French given in a ninth-grade French class, I said that Cold-War tensions made no sense to me: why could not each side explain why its way was better, then let the people decide? I had no specific proposal for how this deciding could take place. My adolescent thoughts may illustrate how I ended up in mathematics: here, at least, there is a clear standard for truth, and nobody has to go to war to settle a dispute.

My ninth-grade English teacher took issue with my closing sentence about the McKim poem, and I do think he was right: “Probably so,” he wrote, “within limitations imposed by the words themselves.” The meaning that you assign to a poem still has to fit the words. You cannot just decide that E. McKim means the same thing in her poem that Andrew Marvell does in “To His Coy Mistress,” unless you are prepared to make an argument based on the texts.

In recent years I have taken part in discussion and analysis of some modern poems; but I do not know how much the analysis aids the appreciation. I am not sure what to make of the poems I read now in Poetry. The November issue that I read from yesterday is “The Translation Issue.” The translation from the French by Rosanna Warren of a poem by Max Jacob called “Périgal-Nohor” ends with the following couplet:

Scholar foolscap collar we wear a crown that glows
The one who receives is worth him who bestows.

I was grabbed just by the music of the verses. The rhythm calls to my mind the closing couplet of a crudely erotic poem called “Wedding Dance,” in the collection Five Chambered Heart (New York: Persea Books, 1986) by the late St John’s College tutor Charles Greenleaf Bell:

Red bang—green bang—horn hot hole:
One God-swot in the all-God whole.

I transcribe the verses from the physical book that I bought at a reading given by Mr Bell at the College, in Santa Fe. I do remember the sound of Mr Bell as he read some of the poems. I do not think he read “Wedding Dance.” In any case, there is no particular reason to connect a particular Charles Bell poem to the Max Jacob poem translated in Poetry. The sound in English of the latter just reminds me of the former. Ideally the Jacobs poem would stand on its own. This assertion is a reflection of words of Collingwood on “The Comparative Method” in what its editors have called “Notes on Historiography”:

This is the apotheosis of anti-historicism in a positivistic interest. You cease to care about what a thing is, and amuse yourself by saying what it is like. (A critical discussion of the idea of similarity would be useful here.) Imagine a ‘comparative pathology’. This condition is like nasal catarrh (but it is scarlet fever).

This is from page 238 of R. G. Collingwood, The Principles of History, edited by W. H. Dray and W. J. van der Dussen; Oxford, 1999, reprinted 2003. If you actually have scarlet fever, you do not want your doctors to spend time talking about a resemblance to nasal catarrh.

I was amusing myself by the Bosphorus, reading poems in Poetry, snapping photographs, and then reading an essay in the magazine called “The Medium of the English Language,” by James Longenbach. “Nothing is automatically an artistic medium,” says Longenbach—and that sounds right—, “though anything could be.” This brings out some comparisons:

A medium, says the psychoanalyst Marion Milner in On Not being Able to Paint, is a little bit of the world outside the self that, unlike the resolutely stubborn world at large, may be malleable, subject to the will while continuing to maintain its own character. The medium might be chalk, which cannot be made to produce the effects of watercolor. It might be a copper plate coated with a thin layer of silver and exposed to light. It might be a rosebush, pruned and fertilized into copious bloom, or an egg, exquisitely poached. In the realm of psychoanalysis, the medium is the analyst, a person who can be counted on to respond to the wishes of the analysand without needing to assert his own, as any person in an ordinary human relationship inevitably would.

In The Principles of Art, Collingwood is at pains to distinguish art from craft, and gardening and cookery would seem to be crafts; but then so can drawing and photography be used merely as crafts. I think one is bound to grant the possibility that cooking an egg or pruning a rosebush might rise, from being mere craft, to the level of art. Collingwood himself fancifully suggests that Archimedes’s mere cry “Eureka” might itself rise to the level of communicating, to a sufficiently tuned-in scientist, what problem Archimedes had solved.

The pliancy of the analyst is an interesting suggestion. Meanwhile Longenbach’s main theme is the multiculturalism of the English language, a language where German and Latin words live side by side, working in harmony, at least in the hands of a master like Shakespeare.

Shakespeare was a powerful writer who in his lifetime was poised at exactly the right moment to take advantage of the medium that the English language had only recently become. He could reach for effects that had been unavailable to the poets of both “The Seafarer” and The Canterbury Tales, and because of the particular power with which he did so, poems we think of as great, poems that harness the full capacity of the medium, tend to sound to us Shakespearean. But what we are really hearing in such poems is the medium at work; what we are hearing is the effort of a particular writer to reach for the effects that Modern English most vigorously enables.

I close with the analogy that Descartes introduced the language in which modern mathematics is done. But when it is said that ancient mathematicians were hampered for their lack of this language, I have to observe that language is a human creation in the first place. If we want and need the language, we find it.