Polytropy

This is about our second visit to the Nesin Mathematical Village in Şirince this year. The first visit was to attend the Summer School Around Valuation Theory, May 22–26. Now we have come back to teach, as usual, in the Turkish Mathematical Society Undergraduate and Graduate Summer School. This time we are teaching not just one week, but two: July 14–27. My own course, as several times in the past, is on nonstandard analysis. Each course meets every day but Thursday, two hours a day.

The Math Village only increases in beauty every year, as I mean to suggest by posting a few photographs below.

I shall also state an opinion. The summer school here in the Village used to receive some funding from TÜBİTAK (the Scientific and Technological Research Council of Turkey); but apparently this funding is no longer forthcoming. Nonetheless, the Nesin Mathematical Village is the kind of venture that governments at their best will support. Certain Libertarians, desiring minimal government, still want government to maintain property rights, so that citizens can make money. Other people look to government to create jobs more directly. But money by itself is worthless, and some jobs are more worth doing than others. I do not say that the Nesin Mathematical Village should be supported for the technological gains that mathematics can make possible. I say that participating in the activities of the Village is itself a gain. What are you going to do when your basic animal needs are satisfied? You could do a lot worse than spend time on mathematics.

One might be critical of particular educational practices at the Village. Sitting in lectures is of little value by itself; students must also work on their own. But there is little time for this, and little motivation: courses here have no examinations and no grades. I want to think that students come here for the love of mathematics; but they may also come with the idea of getting ahead in their regular studies. This is probably a mistake, unless students go home with their notes and study them. Having sat through twelve hours of lectures on group theory does not mean you have learned group theory; but some students may want to think that it does. This is a reason why courses here should not be on topics that are normally covered at university—as indeed they usually are not.

Students may come here, just to be with their friends, away from their parents, in this beautiful place. That is fine. That is why we teachers come, except perhaps for the part about parents. The pleasure of being here is our only payment. I like to think it is good for students to see this: to see that there are rewarding activities that may require great effort, but serve no further purpose. When the Turkish authorities practically shut down Istanbul to prevent May Day observances, what do they think people should be doing with their time?

We arrived here in Şirince this year on Sunday, July 13, having spend three days in Foça. Our seaside holiday was a kind of buffer between the crowds of Istanbul and the crowds of students here in the hills above old Ephesus. The crowds here are the denser, because of the greater need for tuition payments of students, owing to the lack of TÜBİTAK support that I mentioned. Maybe it is good that more students should be here; but more people means more noise and less ability to sit and think.

On Monday, I sat in on the first hour of Ayşe’s course on finite geometries; as I knew, she would talk about the Fano plane. Her classroom was the Aziz Nesin amfisi (“amphitheater”), one of the original teaching spaces of the Village, and perhaps the most romantic. Its ranks of railroad-tie seats were laid down around the existing olive trees.

The amfi used to be shaded by canvas; now vines are doing the job. Before Ayşe’s course, I also used the amfi. My assigned space was the Langlands dersliği; this however is covered by a traditional roof, albeit a roof with a pine tree growing through it. I proposed moving outdoors, and the students agreed. However, on Tuesday, they requested to meet in the Langlands classroom, where they could put their notebooks on desks, rather than on their knees.

The official English name of the Nesin Matematik Köyü seems to be the Nesin Mathematics Village. I am calling it the Mathematical Village, in homage to Thomas Jefferson, who founded the University of Virginia as the Academical Village. On its website, the University says,

For Thomas Jefferson, learning was an integral part of life. The “academical village” is based on the assumption that the life of the mind is a pursuit for all participants in the University, that learning is a lifelong and shared process, and that interaction between scholars and students enlivens the pursuit of knowledge.

These words could apply to the Nesin Mathematical Village. In fact, when I was in high school and was considering which college to attend, I visited the University of Virginia with a classmate. We talked to one of the elite students who lived in the little houses of Jefferson’s original Village. I was not particularly impressed by this student. His school was known for heavy drinking. It was a Friday, and in the afternoon, as my friend and I wandered around campus, the smell of liquor wafted from windows.

I do not know how much drinking the students at the Nesin Math Village do: when they are doing it, I am usually asleep. But when they are intently studying their computers, they are more likely to be looking at a game or a movie than a mathematics text. Serious study cannot be forced; the best we can do is offer a place where it can happen.

Such a place might be the Heaven Garden (Cennet Bahçesi), around the corner from the Nesin Amfisi, made more enchanting by the afternoon sun on the stone wall.

The croaking of the frogs in the lily pool nearby can be heard during lectures. Is the sound conducive to thought, or is it a distraction? Perhaps some people work best in a windowless office, where the only sound is the hum of a ventilator.

Next morning I went for a hike with a fellow teacher (from the Netherlands, working now in England). I paused at the beginning to take this photo of the Nişanyan Library and Bol Kepçe Lokantası (Full Ladle Diner).

The following two photos are taken from just outside the bedroom of Ayşe and me. The setup puts me in mind of Ravello, Italy, where we have attended mathematics conferences twice. (The last time, last year, some nonmathematical reading turned into a blog article: “Books hung out with.”) Ravello sits on a hilltop, from which you can descend by stairs to the sea; but the stairs will take you through settlements at various elevations on the hillside. So too there are stairs at the Math Village taking you from the Village Square (Köy Meydanı), past student and teacher residences, down to the so-called Fakirhane (Poorhouse) of Ali Nesin himself, and then to the nearby Theatre Madrasa (Tiyatro Medresesi).

The Theatre Madrasa caused me a lot of trouble last year, because our bedroom, then as now, overlooked it. Practicing actors make noise, be it in the afternoon when I want to take a nap, or after dark when I want to sleep for the night. Oddly, when other people happen to be up before dawn like me, they whisper; but not at other times. When I went down the stairs to the Theatre Madrasa to complain about the noise, I received apologies; but I also received a sense that artists had the right to work whenever they wanted.

In any case, the noise from the Theatre Madrasa does not bother me this year, either because I have become less uptight, or because we are not staying in the house with the concave semicircular wall facing the Madrasa; possibly that wall gathered and amplified the sound.

An actor at the Madrasa agreed with me that art and mathematics were very close: Kesinlikle (“definitely”) he said. Students and teachers from the Math Village go down to attend performances at the Theatre Madrasa; but I am not aware that actors come up for math lectures.

Why was the Madrasa built next to the Village? Since the construction of the Village and Madrasa seem to have been done illegally, it was thought that more construction would be better, so that any government attacks would be more newsworthy. Unfortunately the mastermind behind this idea is now in prison—caught for now in the web of the state.