David Pierce // Matematik (Mathematics) // M.S.G.S.Ü.



Photograph of fairy chimneys    Photograph of Uçhisar, a big
rock with many rooms carved out of it

Here is an account of a trip to Cappadocia in January of 2006. After the trip, I wrote a first version of this account, in words only. Later, I obtained the electronic photographs taken by one of our companions, Alexandre Borovik. Thanks to Sasha for making this visual record. Some of the photographs are now summoned by links in the text below. (If you use Javascript, the pictures should open in a separate window. There is also a version of this page without Javascript.) Other links below, in small caps like the foregoing, are to other resources (often Wikipedia).

Hospitality and Eschatology

We had the hotel to ourselves for our first two nights in Cappadocia. Several other groups showed up for our third and final night. One of these groups was a couple of middle-aged Americans on their first visit to Turkey. I overheard them at dinner. The man told the hostess about a stroll in the village that he and his wife had taken that afternoon. They had met a young boy named Mustafa, who tried out his few words of English on them. The three then went to a tea-house, where the Americans were treated as guests in the proper sense. They were not permitted to pay for their tea.

I heard the man tell the story two more times at breakfast the next morning. He had been amazed by the hospitality of Turkish people. I think it is a common occurrence. Then I met Mustafa for myself, or another boy of that name, along with two of his friends. One of the friends was named Ali, but I forgot the other one's name; let us call him Hasan. Hasan and his friends were not yet old enough to shave. Hasan explained something to me—in Turkish, along with the English word “hot”—: For being a Christian, I was going to burn in hell.

The boys and I were standing in a narrow stream valley, whose walls, centuries ago, had been carved out to make dwellings, some for Christian monks. Some of the villagers still used those dwellings, at least for their chickens and geese—and for baking bread.

A nearby village had housed well-to-do Christians, until they were all shipped to Greece during the population exchanges of the 1920s.


Orthodox Christmas fell during our visit to Cappadocia. It was a poignant event for one of us. Sasha had been my spouse's doctoral advisor in England, but was originally from Siberia. He and Ayşe continue to collaborate on mathematical research; they also now share two students of mathematics here at Middle East Technical University, namely Şükrü and Gökhan. These two came to Cappadocia, along with Emrah (now on the faculty here, in applied mathematics) and his companion Özlem.

So we were seven (that's six of us, not counting the photographer). On a rainy Thursday afternoon, January 5, 2006, we took two taxis from METU to Ankara's enormous bus terminal, for our 15.00 ride to Ürgüp via Nevşehir. At 16.30, we had a half-hour break at a facility called Kapadokya, where we ate gözleme. At 20.00, we reached Nevşehir and packed into a smaller bus, which made drop-offs at Göreme and Avanos before leaving us at Ürgüp. There a van from the Gamirasu Hotel in the town of Ayvali met us; we reached the hotel around 21.00.

It was unfortunate for our guest from abroad that most of our trip had to be in darkness. Perhaps Sasha did not mind; he spent most of the trip talking mathematics with Şükrü and Gökhan. The headlights of the van to the hotel did give some hint of the remarkable geography that we would be living in for the next few days.

I always enjoy bus trips in Turkey. I am tall enough to see out the front window; the tall side windows let me the sky; the seats are comfortable; and we are on our way to somewhere interesting. A bus trip takes you away from the crowds of the cities into wide open spaces. Also, a Turkish bus is like an airplane: there is an attendent who brings tea and snacks periodically. When I first came to Turkey, the bus attendants would also shake out dashes of cologne into the cupped hands of passengers. I enjoyed this ritual, and was sorry when most companies switched to moistened towels in foil packs. But Nevşehirliler Turizm ve Seyahat, the bus company that we used for this last trip, are still using real cologne in a bottle.

Ethereal companion

On this trip, after dark, I either slept, or read from Gibbon's History of the Decline and Fall of the Roman Empire. I had bought the first of the three Penguin volumes of Gibbon a few years before in the former Constantinople. I was reading this volume in Rome in 2002. There was not much time for reading then; but at least I could say that Gibbon had been with me in both capitals of the Empire. For a child of the New World who never dreamed of travelling, this was something.

In 2004, in Milan, I was just starting the second of the Penguin volumes, Gibbon's Chapter XXVII—hence I was reading about Ambrose, Bishop of Milan, who “considers the toleration of the Jewish, as the persecution of the Christian, religion”; Ambrose will not permit Emperor Theodosius to punish the fanatics of Callinicum, who destroyed a Jewish synagogue.

Now, travelling to a land of abandoned and desecrated Christian churches in the eastern part of the old Empire, I read of the rise of Christianity in the west—in particular, of an event that I knew from a painting in the National Gallery of Art of Washington: the baptism of Clovis:

Till the thirtieth year of his age Clovis continued to worship the gods of his ancestors. His disbelief, or rather disregard of Christianity, might encourage him to pillage with less remorse the churches of an hostile territory: but his subjects of Gaul enjoyed the free exercise of religious worship, and the bishops entertained a more favourable hope of the idolater than of the heretics. The Merovingian prince had contracted a fortunate alliance with the fair Clotilda, the niece of the king of Burgundy, who in the midst of an Arian court was educated in the profession of the catholic faith. It was her interest as well as her duty to achieve the conversion of a Pagan husband; and Clovis insensibly listened to the voice of love and religion. He consented (perhaps such terms had been previously stipulated) to the baptism of his eldest son; and though the sudden death of the infant excited some superstitious fears, he was persuaded a second time to repeat the dangerous experiment. In the distress of the battle of Tolbiac, Clovis loudly invoked the God of Clotilda and the Christians; and victory disposed him to hear with respectful gratitude the eloquent Remigius, bishop of Rheims, who forcibly displayed the temporal and spiritual advantages of his conversion. The king declared himself satisfied of the truth of the catholic faith and the political reasons which might have suspended his public profession were removed by the devout or loyal acclamations of the Franks, who showed themselves alike prepared to follow their heroic leader to the field of battle or to the baptismal font.

[The quotation continues…]

Islam was a religion of warriors, almost from the beginning; Christianity was so within a few centuries of its founding.

A strange land

The Gamirasu Hotel is built from an old Byzantine monastery. Probably some of the hotel is new, like the room given to Ayşe and me: this was in a free-standing stone building with a vaulted ceiling. Some other rooms were in caves.

The thing about Cappadocia is that it was once covered by layers of volcanic ash. It seems you can easily dig into the ash, once a hole is started; then, in time, the exposed surfaces harden. A child can build sand-castles at the beach; in Cappodocia, grown-ups can build castles to live in, with some of the same techniques.

The problem is that the grown-up-size castles are not much more durable than sand-castles. Almost every sloping surface in Cappadocia has holes, dug some time over the last few thousand years. Often those holes had been intended for access to an inner room. Then the outer wall of the outer room collapsed, some time in the ensuing centuries. One such collapse in the Zelve Valley in the 1950s killed two people; alternative above-ground accommodation was found for the remaining troglodytes there, and the valley became a park, with the areas judged more dangerous fenced off.

We would visit Zelve on Saturday. On Thursday night, we ate in our hotel's cave dining room, next to a toasty wood-fired stove and a Christmas tree. We arranged with the hostess to hire a driver and a guide for the next two days; the guide would plan an itinerary with us.

We did the planning at breakfast next morning in an adjacent cave room. Our first stop was an underground city like those apparently mentioned by Xenophon in the Anabasis. (I haven't read this, but it is on my list now.)

First we drove past potato-fields; the hills behind the fields had doors in them leading to warehouses hollowed out from the rock.

Our guide Remzi explained it all (though sometimes I explained to him). Remzi Bey certainly seemed to enjoy his work. Giving us the motor-mouth symbol with his hand, he told us he would be explaining things to us all day: there was so much to talk about in Cappadocia.


We walked past some Greek-built houses of dressed stone, then numerous stalls of trinkets in order to reach the entrance to Kaymaklı (“Creamy”) underground city. But we were the only tourists around. We bought our tickets to the caves and went down several floors, having to crouch very low to traverse some passages. As we went, a cat accompanied us. Remzi Bey pointed out kitchens, storage areas, an air shaft, a well. Everything is well lit with electricity, and you can imagine living there, until you think about how the place would have been illuminated hundreds of years ago. You would be there only because invading armies were overhead. You would not want smoke from fires to be seen…

This trip was my second to Cappadocia. My first had been in the fall of 1998, when I went with my mother while Ayşe was teaching. (I wasn't working then.) The first time, I just enjoyed the fascination of what people could do with the right kind of stone. This time, Cappodocia had the air of people close to the edge. You wouldn't live in a house that could collapse on you, with little or no natural light, unless you had no choice.

Life may have been good when the region was defended by the Roman Army and supplied fine horses for the nobility of Constantinople.

Ihlara Valley

With my mother, I had seen the other major excavated underground city of Cappadocia, called Derinkuyu ("Deep Well"). I had also seen the Ihlara Valley, which was our next stop on Friday (after a brief visit to a crater lake). I cannot imagine a more beautiful place. The valley is a rift in the earth with a river running through, watering trees and grass. The valley walls are cliffs, in which Christians dug churches, like the so-called Sümbüllü (“hyacinthine”) Church).

According to Remzi Bey, some of the churches were built after the Muslim Seljuk Turks had taken power: Either the Seljuks tolerated People of the Book, or these people were well-protected in their valley.

We passed some sheep, said hello to a dog, and milled about or visited the loo before buying our tickets and descending into the valley, noting the pistachio trees along the way.

Some of the churches have crude geometric designs on their walls, painted by Iconoclasts; others have frescoes of saints, or of the Pantocrator himself. Sometimes eyes or faces of these have been scratched out. I used to think that the scratching had always been done by devout Muslims opposed to depictions of holy beings. But Remzi Bey suggested that a devout Christian with an eye disease might scratch out the eyes of a fresco saint in order to make a healing potion. It was a plausible explanation. One fresco we saw the next day in Göreme had carefully scratched-out feet.

The frescoes in Ihlara Valley are reachable by anybody who pays the small entrance fee to the valley. Some people today scratch their initials in the painted plaster. Gökhan was quite shocked at this. I was too, but I could remember the idle destructiveness of my own youth. We were in a country filled with all kinds of ancient stuff, much of it belonging to an obsolete version of monotheism (if one thinks that newer means better).

It would be expensive to keep guards at the churches in Ihlara Valley, and unpleasant to lock them up. I should like to see posted messages from Muslim leaders about the respect due to People of the Book (if not to all people). On the other hand, Turkey is a country where people light up cigarettes beneath No Smoking signs; words from authorities may not mean much.

We walked along the river among the trees—and among the boulders that had fallen from the valley walls. Many of the trees are coppiced periodically for firewood; also, after a while, we reached a ploughed field. Animals must do the work, as well as any transport of produce to the outside world.

Road access was made only some four kilometers into our walk. There was a village, Belisırma, with a few restaurants by the river, most seemingly closed for the season. One was open, and the host there agreed to put tables outside for us, in the sunshine. Though there was some snow on the ground, we were warm from our walk. We had salad, meat or menemen, and Efes Pilsen in half-liter bottles. What could be more pleasant, than to walk by a flowing stream, and then to sit with a beer, with the sun on one's face, in January?


At the end of our meal, the sun dipped below the rim of the valley, and we piled into the van that was waiting for us. We drove around to the end of the valley, to the village of Selime. There we could poke around a cliff face carved full of rooms going up several floors.

Sometimes, for various reasons, the volcanic tuff in Cappadocia has formed cones and pillars. There was such an eminence at Selime, all hollowed out inside. The floor of its upper room had holes into the lower room. The holes were not supposed to be there. How sound was that floor? How much stress did a room full of tourists place on it? I wondered whether engineers ever looked at these places. Our one EU citizen laughed at this possibility.

Remzi Bey had expressed wishes that Turkey would join the EU, so that more archeological projects could be funded. Sasha thought the current situation preferable in this regard, because less subject to regulation.

The cliff complex at Selime was quite elaborate in its day. Some of its rooms had been carved out of the stone as if they had been built up from stone blocks; traces of paint remained, along with a cross in a ceiling. But the walls of many rooms went missing a long time ago.


Our last stop for the day was Ağzıkarahan, a great Seljuk caravansaray, built to accommodate merchants on the Silk Road. The walls are plain, but the entrance is elaborate. In the middle of its courtyard, raised on pillars, is the mescit; one can climb to its roof. (A mescit is a small mosque, a “chapel”. Perhaps it is technically distinguished from a mosque by not having a Friday sermon. But the word “mescit” is cognate with the English “mosque”.)

There are rooms around the courtyard, and, on the left, the passage to a larger roofed-over area (now with collapsed dome) for your beasts of burden; other beasts were outside the walls as we left.

We were returned to our hotel in the dark. After dinner there, Sasha brought out the bottle of Laphroaig whisky that he had carried from Britain.


Saturday was overcast and rainy. The sites to be visited were closer together. First was the Göreme Open Air Museum, a UNESCO World Heritage site. It it is a collection of cave churches and communal residences (where one can sit, for example, at a long stone dining table).

One of the Göreme churches is reached by stairs and an additional entrance ticket. Called the Dark Church, it is now brightly lit with electricity, showing its restored frescos. The restoration would seem to have been faithful, in the sense of not filling in the scratched-out parts.

Elsewhere in the museum, one can see faded frescos, exposed by rockfalls. But the frescos in the Tokalı (“Buckle”) Church are in good shape. In one alcove is a Crucifixion.

It was a day to see many cone houses. We left the Göreme Open Air Museum, stopping to look down into the Göreme Valley. Here the walls are not so tall or steep as in the Ihlara valley. The rock is softer, seeming quite close to wet sand. The valley floor features rock pillars (hollowed out by humans) surrounded by orchards. Idyllic. It might have been in such a place that the French farmer settled whom we had seen on Turkish TV: he had paid a visit and fallen in love with the land. Would you like to live there?


One more stop before lunch: Uçhisar, "Point castle". (Some books say Üçhisar, but that would mean "Three castles".) The castle was not built up, but rather hollowed out of an existing rock. Probably the internal stairs are no longer safe; an external stairway takes you above the minaret of the local mosque for a spectacular view from the top.

A mathematical puzzle

Lunch was in an old Greek house in Ürgüp town and was disappointing, if only because one person's meal was not served before the rest of us had finished ours. We were the only customers. The dining room had the same vaulted ceiling that Ayse and I had in our bedroom in Ayvalı: it wasn't quite round, like a Roman arch; it wasn't pointed, like a Gothic arch; what was it? Remzi Bey called it an “Ottoman arch”.

Sasha observed that an arch can be constructed with convex blocks and no mortar, as long as the ends are properly secured. He claimed that an “inverse arch”, bending down rather than up, could be constructed under the same conditions. Lying in bed early on Sunday morning, I figured out how to do it. (Hints available on request.)

Sasha claimed that convexity was an “intuitive” mathematical concept. (A body is convex if, whenever you pick two points inside the body, the line segment joining them lies entirely inside the body.) I asked for an example of a non-intuitive concept, and he proposed Hopf algebras. I had to ask what they were. I will allow that they are harder to define than convex bodies.

Peri bacaları

Some of the rock cones in Cappadocia have been formed because hard boulders once sat on top of the volcanic ash. Rain washed away the ash that was not beneath the boulders, leaving behind the pillars called fairy chimneys (peri bacaları). After lunch we visited an area called Devrent Valley where we could wander among these chimneys. I wandered ahead, while Remzi Bey told the others what he thought each pillar looked like (a seal, a camel, the Virgin Mary…). When he found me later, he insisted on repeating his assessments to me. The motor-mouth sign he had given the previous morning had not necessarily been a good sign. But I still found him interesting. He has at least one child at university in the US, and he had given lectures in the US himself. I think he knew what he was talking about somewhat better than the young tour guides we get for the excursions at our annual Antalya Algebra Days meeting.

Remzi Bey was probably confused on one point though. The fairy chimneys in Devrent Valley were too small and soft to be hollowed out practically for shelter. Our next stop was Paşabağı, “Pasha's Vineyard,” where the chimneys could make dwellings. Remzi Bey said Saint Simeon Stylites had lived there, when I was pretty sure he spent his life around Antioch. It so happened that I had been reading Gibbon's supercilious comments on the saint, who spent years atop a pillar:

Among these heroes of the monastic life, the name and genius of Simeon Stylites [395–451] have been immortalised by the singular invention of an aerial penance. At the age of thirteen the young Syrian deserted the profession of a shepherd, and threw himself into an austere monastery. After a long and painful novitiate, in which Simeon was repeatedly saved from pious suicide, he established his residence on a mountain, about thirty or forty miles to the east of Antioch. Within the space of a mandra, or circle of stones to which he had attached himself by a ponderous chain, he ascended a column, which was successively raised from the height of nine, to that of sixty, feet from the ground. In this last and lofty station, the Syrian Anachoret resisted the heat of thirty summers, and the cold of as many winters. Habit and exercise instructed him to maintain his dangerous situation without fear or giddiness, and successively to assume the different postures of devotion. He sometimes prayed in an erect attitude, with his outstretched arms in the figure of a cross; but his most familiar practice was that of bending his meagre skeleton from the forehead to the feet; and a curious spectator, after numbering twelve hundred and forty-four repetitions, at length desisted from the endless account. The progress of an ulcer in his thigh might shorten, but it could not disturb, this celestial life; and the patient Hermit expired without descending from his column. A prince, who should capriciously inflict such tortures, would be deemed a tyrant; but it would surpass the power of a tyrant to impose a long and miserable existence on the reluctant victims of his cruelty. This voluntary martyrdom must have gradually destroyed the sensibility both of the mind and body; nor can it be presumed that the fanatics who torment themselves are susceptible of any lively affection for the rest of mankind. A cruel, unfeeling temper has distinguished the monks of every age and country: their stern indifference, which is seldom mollified by personal friendship, is inflamed by religious hatred; and their merciless zeal has strenuously administered the holy office of the Inquisition.

Perhaps the monks of the Pasha's Vineyard had been inspired by the saint. (They may have been inspired independently by the geography, since such landforms can be seen in icons, as Sasha pointed out.) Today you can climb to the two-level cell of a Cappadocian monk by means of footholds in a vertical shaft. I did this seven years ago, though the guide then discouraged it; this year, Remzi Bey encouraged it, and three of us, then two more, ascended.

In the fading light, we visited Zelve Valley, which I mentioned at the beginning. It was after dark when we got to Mustafapaşa, the former Greek village of Sinassos, which I also mentioned. We went there because our department chair had recently praised its beauty. Its above-ground houses of dressed stone did bespeak wealth. Remzi Bey spoke sadly of the population exchanges that had driven abroad the owners of the houses (the houses were then assigned by lottery to Muslims from Greece). Remzi Bey told of how the grandson of one of those owners had come from Greece recently to see his grandfather's house, on a tour that Remzi Bey had been involved in.

One complaint I had with Remzi Bey's talk was his reference to the Turkish invaders of Anatolia as “our ancestors”. I think the genes of all peoples who have ever lived here remain here. The people called “Turk” are Hittite, Greek, Armenian,—Phrygian, Urartian, Galatian,…—as well as Turk. This may be an exaggeration in any one case; still, I am told that, if you take a group of Mediterraneans, you cannot tell what country they are from by looking at their genes.

Evening out

Our hotel's website said they would take us to or from Ürgüp as late as ten at night. We took advantage of this service on Saturday evening, visiting a bar recommended by the fellow who drove us. Though we were almost the only customers, the bar was smoky. When the live music began, most of us didn't like it; so the decision was made to move to a bar in a cave downstairs. The live music was more congenial there; still, some of us were worried about catching our ride back to the hotel at ten.


Sunday morning was bread-baking time across the valley from the hotel. Sasha went over there with Gökhan. Women (and a boy) seemed to do most of the work, with some help from a man, who otherwise seemed to stand around just making sure nothing went wrong. Sasha had wanted to buy some bread; but as Gökhan had warned him, the villagers would just give him bread, without taking money.

Truth and progress

A few of us walked up the stream valley a bit before it was time to go to Ürgüp for our return home. Not having good boots, I was returning to the hotel early; that is when I met Mustafa, Ali, and Hasan, and had the conversation that I mentioned at the beginning.

I said that my name was David, or “Davut” in Turkish. Hasan knew the name, and said the original David had been Muslim. How could David have been Jewish (my claim) if he had prayed to Allah?

I asked Hasan how he knew about what he was telling me; he said the Koran. I said that the Koran was a book, and there were many books. The Koran was unique among books, said Hasan. By this time, my companions had arrived, and they could say things that I struggled to express in Turkish. How did Hasan know that the Koran was special? His grandfather had told him. As Ayşe pointed out, if everybody in this country were just like his grandfather, how would this country move forward?

(As a friend who read the first version of these notes observed, Hasan's father did not want to move forward: he wanted his descendents' world-view to be consistent with the “truth” as expressed in the Koran, rather than to correspond better and better to the truth of how the world really was.)

I hope we haven't made the villagers angry that a hotel for infidels has been founded in their midst.

We walked back downstream to the hotel, packed our things, and reversed the steps by which we had arrived.

Son değişiklik: Tuesday, 12 June 2012, 15:52:50 EEST