Polytropy

After five years in Istanbul, we continue to learn how much there is still to discover here. Now we have been to the Asian borough of Beykoz. Much of what we saw there was rural, and the topography and flora reminded me of Appalachia. I have nothing to say about the poverty and ignorance that might be suggested by this term; for me, Appalachia was always a locus for holidays, mostly at my late uncle’s place in West Virginia, but also in the form of bicycle tours. Travelling now to Beykoz, Country roads, I could think, take me home, to the place I belong! We got there by public bus from our European borough of Şişli.

Polonezköy, Beykoz, 2016.08.14

We have not really spent five years trying to discover Istanbul. Our work has come first. In principle, as academics, we are always at work. Rather, we always can be at work, especially as mathematicians, since mathematics is done by thought alone. We may use pen and paper in the process of creating and recording and communicating our thoughts. For the final communication, a computer is essential; but taking one of these along during one’s physical explorations is becoming more and more easy.

A habit for mental explorations may distract from the appeal of the physical ones. This could be a danger, as was warned about in the original pilot for Star Trek. The Cage was about a planet called Talos IV, which had become practically unlivable, after the Talosians had learned to create pleasurable illusions with which to pass their time. It was hoped that humans could rehabilitate the planet. And yet humans today are creating their own dead world. When we visit Maçka Park here in Şişli these days, and we find the park full of people with their faces glued to their mobiles, looking out for Pokémon, then I think we are living in the future that Gene Roddenberry warned about.

Trash by the Black Sea, Riva, Beykoz, 2016.08.13

The distracted academic is different though. She or he is not the recipient of somebody else’s illusions, but the creator of new ideas. I do not mean to suggest that my spouse or I am always thinking about mathematics. Usually we are not, at least not consciously. But then an idea might arise unbidden at any moment, as it did to Henri Poincaré, by the account of Robert Pirsig in Zen and the Art of Motorcycle Maintenance (chapter 22):

…He left Caen, where he was living, to go on a geologic excursion. The changes of travel made him forget mathematics. He was about to enter a bus, and at the moment when he put his foot on the step, the idea came to him, without anything in his former thoughts having paved the way for it, that the transformations he had used to define the Fuchsian functions were identical with those of non-Euclidian geometry. He didn’t verify the idea, he said, he just went on with a conversation on the bus; but he felt a perfect certainty. Later he verified the result at his leisure.

A later discovery occurred while he was walking by a seaside bluff. It came to him with just the same characteristics of brevity, suddenness and immediate certainty. Another major discovery occurred while he was walking down a street. Others eulogized this process as the mysterious workings of genius, but Poincaré was not content with such a shallow explanation. He tried to fathom more deeply what had happened.

Mathematics, he said, isn’t merely a question of applying rules, any more than science. It doesn’t merely make the most combinations possible according to certain fixed laws. The combinations so obtained would he exceedingly numerous, useless and cumbersome. The true work of the inventor consists in choosing among these combinations so as to eliminate the useless ones, or rather, to avoid the trouble of making them, and the rules that must guide the choice are extremely fine and delicate. It’s almost impossible to state them precisely; they must be felt rather than formulated.

Poincaré died in 1912, at the age of 58. That mathematics doesn’t merely make the most combinations possible according to certain fixed laws: this was proved by Gödel, in a sense, in his 1931 Incompleteness Theorem: the complete first-order theory of the natural numbers with addition and multiplication cannot be obtained by cranking out all logical consequences of a certain list of axioms, even an infinite list. An infinite list here must be understood as generated by a rule: it is recursively enumerable. Emil Post drew out the implications of Gödel’s result in 1944, in a paper called Recursively enumerable sets of positive integers and their decision problems (Bull. Amer. Math. Soc. 50, 284–316):

mathematical thinking is, and must remain, essentially creative. To the writer’s mind, this conclusion must inevitably result in at least a partial reversal of the entire axiomatic trend of the late nineteenth and early twentieth centuries, with a return to meaning and truth as being of the essence of mathematics.

Now, Mojżesz Presburger had shown in 1929 that the first-order theory of the natural numbers with addition alone could be obtained by cranking out all logical consequences of a certain list of axioms. Thus, in short, some complete theories can be recursively axiomatized, so that they are decidable; and some cannot. Which theories does one wish to test for decidability? This now becomes a matter of feeling.

Black Sea at Riva, Beykoz, 2016.08.13. Photo by Ayşe Berkman

Reading Pirsig in high school, I may have been too taken with the notion that we must feel our way through the world. At least I feel ashamed now of certain verbal expressions that I made of this idea. I have learned since then that Poincaré’s feeling of immediate certainty about a discovery can be undeserved. I have made mathematical mistakes that have seduced me and others, even to the point of being published in a journal. Still, a mistake is not absolutely useless. If Theorem A turns out to be false, this means one still has a theorem, namely the negation of A. In any case, it is true that ideas may arise anywhere. The key idea of my doctoral thesis came to me in bed one Sunday morning.

Somerset Maugham had a way of starting a story with a personal observation that was outside the plot of the story proper, but that might be the most interesting aspect of the story as a whole. The opening paragraph of Maugham’s Honolulu (1921) may offer good advice to one living in Istanbul, where it seems one must harden one’s heart, lest it be pierced when each old tree is cut down, and each new high-rise goes up:

James McNeill Whistler (American, 1834–1903), Wapping, 1860–64, oil on canvas, John Hay Whitney Collection, National Gallery of Art, Washington

The wise traveller travels only in imagination. An old Frenchman (he was really a Savoyard) once wrote a book called Voyage autour de ma Chambre. I have not read it and do not even know what it is about, but the title stimulates my fancy. In such a journey I could circumnavigate the globe. An eikon by the chimneypiece can take me to Russia with its great forests of birch and its white, domed churches. The Volga is wide, and at the end of a straggling village, in the wine-shop, bearded men in rough sheepskin coats sit drinking. I stand on the little hill from which Napoleon first saw Moscow and I look upon the vastness of the city. I will go down and see the people whom I know more intimately than so many of my friends, Alyosha, and Vronsky, and a dozen more. But my eyes fall on a piece of porcelain and I smell the acrid odours of China. I am borne in a chair along a narrow causeway between the padi fields, or else I skirt a tree-clad mountain. My bearers chat gaily as they trudge along in the bright morning and every now and then, distant and mysterious, I hear the deep sound of a monastery bell. In the streets of Peking there is a motley crowd and it scatters to allow passage to a string of camels, stepping delicately, that brings skins and strange drugs from the stony deserts of Mongolia. In England, in London, there are certain afternoons in winter when the clouds hang heavy and low and the light is so bleak that your heart sinks, but then you can look out of your window, and you see the coconut trees crowded upon the beach of a coral island. The sand is silvery and when you walk along in the sunshine it is so dazzling that you can hardly bear to look at it. Overhead the mynah birds are making a great to-do, and the surf beats ceaselessly against the reef. These are the best journeys, the journeys that you take at your own fireside, for then you lose none of your illusions.

Such is Maugham’s advice. Perhaps one cannot take it before actually doing some travelling, on the ground or in books. Having been born in 1874, Maugham was in his forties when he wrote Honolulu. I first read the story in my thirties, in a vegetarian hamburger joint in Berkeley, California. From the local library I had the first volume, East and West, of the two volumes of Maugham’s Complete Short Stories. A year later, I bought the volumes from a used bookshop in Hamilton, Ontario. I remember where I first read Honolulu, because I was impressed by the analogy with which Maugham modified, in his second paragraph, the advice of his first paragraph. I would say now that the elaboration of the analogy in the second sentence of that second paragraph was not needed, but could have been inferred by the reader. On the other hand, in the first paragraph, I actually like the parenthetical remark about the Savoyard origin of Xavier de Maistre. In any case, the second paragraph of Honolulu is as follows.

But there are people who take salt in their coffee. They say it gives a tang, a savour, which is peculiar and fascinating. In the same way there are certain places, surrounded by a halo of romance, to which the inevitable disillusionment which you must experience on seeing them gives a singular spice. You had expected something wholly beautiful and you get an impression which is infinitely more complicated than any that beauty can give you. It is like the weakness in the character of a great man which may make him less admirable but certainly makes him more interesting.

Nothing had prepared me for Istanbul…

Actually it is not Istanbul that Maugham names in the third paragraph, but Honolulu. However, the substitution works. Maugham goes on to describe a place that does not meet his expectations for an Asian city; it is rather a blend of East and West. But this is a cliché for Istanbul, the city that sits on two continents.

The city began as Byzantium (Βυζάντιον), founded by the legendary Byzas. Modern scholars gave the name of the city of Byzas to the Eastern Roman Empire, after the Empire itself had been extinguished by the Ottoman Turks. Thus the Empire became Byzantine. But Byzantium itself had become Constantinople in being resurrected as the capital of the Empire by Constantine I in the year 330. Either the name Κωνσταντινούπολις evolved into Istanbul, or else, as is suggested, the current name derives from εἰς τὴν Πόλιν, into the city.

The road west into Riva, Beykoz, 2016.08.13

The metropolis of Istanbul is now coextensive with the province of Istanbul, and as such it covers about 5300 square kilometers (I take my figures from Wikipedia). Of American states, only Delaware and Rhode Island have smaller land areas. The land area of New York City is less than 800 square kilometers, which is less than a sixth of Istanbul. But then Istanbul has more than six times as many boroughs as New York. The boroughs of New York range in density from 28,000 for Manhattan to 3200 for Staten Island: the figures are in persons for each square kilometer. The density figures for the Istanbul boroughs range from 44,000 all the way down to 31 (that’s thirty-one, with no zeros; the borough is Şile). The density of Şişli is 11,000; of Beykoz, where we spent our last weekend, 1000.

John Ash begins his Byzantine Journey (London, 2006) with a wonderful epigraph from Stephen Runciman that concludes:

Ever since our rough crusading forefathers first saw Constantinople and met, to their contemptuous disgust, a society where everyone read and wrote, ate food with forks and preferred diplomacy to war, it has been fashionable to pass the Byzantines by with scorn and to use their name as synonymous with decadence.

Second- or nth-growth forest at Polonezköy, 2016.08.14

Ash goes on to develop an analogy with New York, the Byzantium of the New World. After living there for five years, his passion for writing a book about the original Byzantium had only increased:

A passage in Mark Girouard’s Cities and People seemed to cast some light on my growing obsession. The passage describes the impression Constantinople made on visitors arriving from the West in the ninth and tenth centuries: When the first view of Constantinople exploded on their vision, it must have filled the with the same kind of awe and amazement as filled immigrants from Europe when they approached Manhattan from the sea.

When I was young, I imagined New York as an incredibly crowded place where you could hardly walk down the street without getting mugged. When I first travelled to the city, in the summer after college graduation, I went immediately to the Cloisters, thus finding a lot of undeveloped space around an excellent museum. I found out later that in the boroughs, you could have a house with a large garden, at least if you had money to buy it; but in any case you could visit a park with virgin forest.

Maquis, Riva, Beykoz, 2016.08.15

Now I know that in the metropolis of Istanbul there are open spaces where you can go bird-hunting. At least that was probably what the fellows with dogs were doing, next to the development where we spent our weekend, out in what I suppose was maquis.

I take the term maquis from Ernle Bradford, Mediterranean: Portrait of a Sea (London: Penguin, 2000). Bradford describes four stages in the evolution of the Mediterranean landscape. First there were the evergreen forests:

If man had not arrived on the scene, this primeval forest would have remained. But man changes everything. Once he moves in as a hunter—long before he becomes an agriculturalist—he attacks the trees, burning them down to make open clearings…

With the clearance of the forest trees, the whole aspect of the landscape alters. Man with his tools and his animals (particularly the goat, which browses on saplings) soon sets in motion a process that, unless it is arrested, leads to desert land. After the evergreen forest has disappeared, there is left the maquis. This is a term for that typical Mediterranean plant-growth familiar to all who have visited Corsica. Maquis consists of thickets of shrubs, sometimes as high as five or six feet—largely broom and cystus. Myrtle, tree heather, holm oak, and Aleppo pine are also found in what is defined as high maquis. In low maquis there are no trees at all, only a tangled growth of herbs such as rosemary and sage, as well as other small bushes, none of which grow more than three feet high.

A third stage in the destruction of a forest area is reached when even the maquis has been cleared (used by man for charcoal, resin, and fibres) and there emerges another characteristic type of landscape, the garigue. The term means waste land, but the land has not yet become total desert…

…Beyond the garigue, at the far end of the scale, comes the steppe—land where the soil has been almost totally destroyed, and only plants with deep roots systems can survive…

It is not clear that Bradford’s use of terminology is universal. If I use it, I suppose the treeless expanse next to the gated community where we stayed was maquis. I don’t know whether, if left alone, it would return to forest. I read somewhere recently that cleared forests along the Black Sea did recover naturally, though they would not do so elsewhere in the country.

Water buffalo, Riva, Beykoz, 2016.04.13

At the edge of the maquis where we were, water buffalo roamed free. The guards told us there was a farm to which the buffalo returned at night. If only children were like that, suggested our host, father of a ten-year-old. Our host normally lives near us with his wife and son, albeit in the borough of Beşiktaş; but the family had rented a flat in Riva on the Black Sea coast for the summer. Thus they had effected what had once been described in an issue of New York magazine. We bought the issue in an American airport before a return to Turkey, and I now regret having thrown it out. However, the issue is on line, dated September 28, 2009. The specific article in question is, The Staycation House: Escapes from the city—within the city, by S. Jhoanna Robledo:

Sure, a vacation house can be dreamy, but getting to one rarely is. These three homeowners have figured out an alternative: Their weekend hideaways are actually in the five boroughs, all within taxi or subway range. Yes, you really can get everything in New York—including relief from it.

One of the weekend hideaways is still in Manhattan, but on Central Park West. I suppose the nearest equivalent in Istanbul would be having a house on the Bosphorus itself.

Shore at Riva, Beykoz, 2016.08.13

Ayşe and I headed out to Riva on Saturday, August 13, 2016, by bus as I said. In fact two busses were needed. It was a cool, rainy day, the first such day in a long time. The windows of the second bus became so fogged up, we could not see the surrounding countryside very well. When we made our way down to the local beach in the afternoon, we found nobody else. On a cool day in August, the water felt like a bath; but it was rough. There was plenty of evidence of humanity all around, in the form of litter. Why people would trash such a gorgeous place, I do not know.

When I was adolescent, my friends across the street were moved by their parents to another part of town. Perhaps the parents wanted to take their boys away from the harmful influences in our neighborhood. But similar influences were to be found in the new neighborhood. This was near what we knew as the Masonic Temple: the George Washington Masonic National Memorial in Alexandria, Virginia. On the beautiful lawns of the terraces around the Temple, where you were out of sight of King Street, the local youth would have parties on weekend nights. They would leave behind a ring of beer cans. If they had cleaned up after themselves, they might have been able to continue the parties indefinitely. As things were, the police started breaking up the parties. Presumably the Masons had got sick of picking up the trash.

I think no police will be breaking up the beer parties on the beach outside Riva. Such parties are not illegal, as far as I know. On Sunday though, we saw families camped out at the beach. I don’t suppose they would consider doing the good deed of picking up some of the trash around them when they left. I fear it is more likely that they ended up leaving their own trash behind. Somebody once recalled to me that in the old days, all trash was organic and would quickly degrade. One need not then have worried about cleaning up after oneself. Today some people continue not to worry, though they drink their water out of plastic bottles, and carry their food in plastic bags.

Polonezköy, 2016.08.14

We saw more of the Beykoz countryside on Sunday, when we drove over to Polonezköy, Polish Village, settled in the nineteenth century by Polish emigrés. To appearances, it could have been a Virginia town like Middleburg, attracting sightseers from the city. However, in Polonezköy, one could not really stroll about town. I did not see any sidewalks. There was a trail through the woods though, said to be 4.8 kilometers.

Polonezköy trail, 2016.08.14

Some of us took to the trail after we all had tea and cake at an establishment called Polina. Most of the other customers were finishing up a long breakfast. After us, two men with motorcycle helmets came in together. One of them sported a gray ponytail; the other, the jacket of the Red Devils Turkey MC. I don’t know if the gentlemen felt like the trio in Easy Rider, who were served with nothing but insults in a restaurant in Louisiana; but like the motorcyclists in the movie, the Turkish Red Devils got up and left after a few minutes, having received no attention from a waiter. Our own table was not attended to for a while either. But one does not visit such an establishment if one is in a hurry; one is there for a long slow meal.

Polonezköy trail, 2016.08.14

Out on the trail, I wondered how one would distinguish the land and the forest from those of Appalachia. Probably the trees were all different; but there are not a lot of trees that I myself recognize at a glance. In the US, one would probably not encounter a hiker in full chador, as I did in Polonezköy. (Most women in chador in Turkey may be tourists from the Persian Gulf.)

Leonardo Restaurant, Polonezköy, 2016.08.14

It turns out that Polonezköy is mentioned neither in Lonely Planet Istanbul (8th edition, February 2015, by Virginia Maxwell), nor in Istanbul & the Turkish Coast (Moon Handbooks, first edition, October 2010, by Jessica Tamtürk). The village is however mentioned in our old Turkey: The Rough Guide (third edition, March 1997, by Rosie Ayliffe, Marc Dubin, and John Gawthrop). In the 1990s then, Polonezköy was apparently a place you could go to eat pork, at least at Leonardo Restaurant. We had lunch there ourselves after our hike. I didn’t notice pork on the menu, though I did not think to look. The two other males in our company ate big pieces of an animal, but Turgay told me the animal had been a sheep. In any case, the servers seemed to be tired out after a long morning of serving brunches; it took a while for them to bring ice for the rakı that went with the meze consumed by Ayşe and me.

Dawn sky, Riva, Beykoz, 2016.08.15

Next morning, Mustafa had business at his university, so he gave us a ride back into town. Meanwhile, having engaged in my habit of getting up way before everybody else, I enjoyed the colors of the morning sky.

Sunrise, Riva, Beykoz, 2016.08.15

(Article first published August 16, 2016, as a draft; copy-edited and expanded, the next day; further revised, October 20, 2016.)