Monday, January 18, 2016

A note on peppers

Black_Pepper_(Piper_nigrum)_fruitsThe Indian subcontinent is well known for its spices, and one of its stellar contributions is the ubiquitous black pepper. Native to South India and Southeast Asia (see unripe green fruits in picture), it’s been around for thousands of years, making its way very early to Europe and other parts of Asia by trade. Black pepper and the related long pepper may have been the most prevalent hot spices east of the Atlantic. That was until Columbus blundered onto the Americas in 1492, inadvertently connecting the Americas – which at the time had a unique ecological and cultivation history because of its isolation – to Europe, Africa and Asia.

In the newly globalized world since 1492, American ‘peppers’, better known as chilies, began to make their way to the rest of the world and took hold quickly. Indeed, all the chili peppers that the world uses today, without exception – from the mild bell peppers used primarily for their deep flavors to the hot ones that Indian, Thai, Chinese, Korean and other cuisines take for granted – all are descended from the varieties cultivated for millennia by pre-Hispanic farmers in southern North America (Mexico primarily) and northern South America (Peru and Bolivia have many varieties). The fiery habanerowhich scores high on the Scoville Heat Scale, is originally from the Amazon from where it reached Mexico.

While traveling in Oaxaca (southern Mexico) last week, I saw and tasted the dizzying variety of chili peppers, small and large, fresh, dried and smoked, each imparting a different color, flavor and odor to the salsas, the region’s famous moles, and other Mexican classics such as poblano rajas. At one restaurant dozens of dried chilies, types I had never seen before, were patched to the wall.

Thai_peppersEtymology provides some interesting clues. The word ‘pepper’ apparently has its roots in a South Indian word pippali, referring to the long pepper plant, whereas ‘chili’ is from Nahuatl, a pre-Hispanic Mexican language (Nahuatl, though diminished since the Spanish conquest of 1521, is still spoken in Mexico). The word for chilies in Tamil, my mother tongue, is milagai – a modification of the word milagu, the word for black pepper. It makes sense that this new entrant and competitor for creating heat should be linked by name to its older rival. Both milagu and milagai now co-exist in South Indian cuisine. The introduced chilies haven’t diminished the use of the peppercorns at all. Indeed, the potent garam masala, a signature mix of spices widely prevalent in India – Abbas has a recipe for it in his new book – uses only peppercorns for heat and not chilies.

All said, it's hard to imagine Indian cooking without chilies today. If somebody had asked me about the origin of chilies in high school or college, I would have claimed them as Indian without a second thought. It was a huge surprise when I learned, in my mid twenties, that chilies were introduced, that before the 16th or 17th centuries, they were not part of the cuisine at all! K.T. Achaya, the author of The Story of Our Food notes that "in one of the sections of the Ain-i-Akbari, written in 1590, there is a list of 50 dishes cooked in the [emperor] Akbar's court: all of them use only [black] pepper to impart spiciness." Similarly, the red chili paste and sauces that you find in so many Korean dishes and Thai curries are relatively recent. Of course, chilies are not unique in this regard. The same idea applies to tomatoes, potatoes, a lot of grains -- the list could go on and on.

It is fascinating how things that were once foreign can integrate so seamlessly and become so familiar that they now feel ‘native’, as if they were timelessly associated with a place and people.
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Cross-posted here.

Wednesday, December 23, 2015

Reflections on War and Peace, and the Inner Work of Pierre Bezukhov

First published over at 3 Quarks Daily.
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War-and-peace-pevearI finished reading War and Peace recently. It took me three years but I did try to read it carefully. Tolstoy defined art "as that human activity which consists in one person's consciously conveying to others, by certain external signs, the feelings he or she has experienced, and in others being infected by those feelings and also experiencing them." This is a wonderfully robust definition – especially because it does not impose which types of "human activity" or "external signs" qualify. And I was certainly infected by the themes of War and Peace: I felt on many occasions that the book was speaking especially to me. I took notes and copied down everything that struck me.

War and Peace operates in two distinct parts. There's the story of two upper class Russian families and individuals – the Bolkonskys, the Rostovs and the inimitable Pierre Bezukhov – whose lives are directly affected by the Napoleonic wars from 1805-1812, including the French invasion of and subsequent retreat from Moscow. Here the narrative flows so seamlessly from one character to another, from one high society intrigue to the next, and so clear is the psychological detailing that it never feels like anything is being overdone. This despite the fact that Tolstoy likes to intervene constantly. His style goes against the "show but don't tell" advice that is nowadays given to writers. He takes great pains to tell us what's going on in each character's mind, how things have changed since we last met this or that person. Everything, internal or external – estates, battlegrounds, soirees, dinners, military offices, forests – is described with great precision. Sudden twists are not Tolstoy's style; the suspense instead comes from how a character will respond to changes in her circumstances.

The other part of War and Peace consists of what can only be called the author's own essays. Tolstoy inserts them throughout the book at regular intervals, having put the story on pause. The essays, though long-winded and difficult to get through, are nevertheless an integral part of the book. Tolstoy uses them to continually emphasize how difficult it is to attribute causes to events in history, how the so called "big men" such as Napoleon (whom Tolstoy particularly dislikes) do not have the kind of agency that historians like to credit them. 

L.N.Tolstoy_Prokudin-GorskyThe gist of these essays is best illustrated by an analogy Tolstoy uses. In classical mechanics, Tolstoy notes, the continuous motion of an object or a combination of objects is accurately described and predicted by the integration of infinitesimally small quantities. The development of calculus in the 17th century made this possible. Likewise history too is continuous and can only be approached as an integral, as "the sum of all individual wills". The historian's typical approach, however, is to isolate discrete events or periods, assume that they are independent, and assign proximate discrete causes to the events. By this method, powerful individuals such as Napoleon, are said to cause events and drive history. But are such conclusions really correct? What of the wills the hundreds of thousands of soldiers and other citizens across Europe and Russia who were involved? In Tolstoy's view "only by admitting an infinitesimal unit for observation – a differential of history, that is, the uniform strivings of people – and attaining to the art of integrating them (taking the sums of these infinitesimal quantities) can we hope to comprehend the laws of history."

Tolstoy wrote this in the 1860s. In 2015, the laws of history are still not clear. There seems to be no way to define a "differential of history" let alone integrate "individual wills". We still have lengthy, inconclusive debates on what exactly caused an event. We can sense, intuitively, that there are innumerable causes which we cannot fully list, all of which interact in complex ways. Nicholas Nassim Taleb described it well in The Black Swan: "History is opaque. You see what comes out, not the script that produces events, the generator of history." 

The Inner Work of Pierre Bezukhov

There's a lot more one can say about the analytical or theoretical parts of War and Peace. But the main focus of this piece is Pierre Bezukhov.

Pierre Bezukhov and two pairs of siblings – Natasha and Nikolai Rostov; Marya and Andrei Bolkonsky –  make up the five major characters of the book. Each has a different personality but they share important features. They are all extremely sincere. They introspect a lot, learn lessons from the major events in their lives and are aware of their flaws. They continuously seek happiness, the kind of happiness that does not depend on external circumstances. At least three of them – Pierre, Andrei and Marya – are engaged in some kind of religious or spiritual search or a search for meaning and wisdom.

The phrase that comes up in the book a few times is "inner work". And I felt the inner work of Pierre Bezukhov especially crystallizes what Tolstoy is trying to convey. In what follows, I provide a compressed chronological version of Pierre's development in three parts along with key quotes. I can't claim that what I present is original. War and Peace has been endlessly analyzed and I may well be repeating what more qualified readers and critics have already noted. Also there are spoilers here, though I tried to minimize them by mainly focusing on Pierre's questions. All the quotes are from the acclaimed Pevear-Volokhonsky translation. The artistic rendition of Pierre Bezukhov by D. Shmarinov is from this website. The collage of Napoleon's invasion and retreat from Russia is from here.  

"What for? Why? What's going on in the world?"
Bezukhov
When War and Peace begins in 1805, Pierre Bezukhov, the illegitimate son of a wealthy count, has just returned from Europe. He is a good-natured but bumbling, absent-minded and somewhat naïve. He admires Napoleon. He is not particularly interested in wealth but loves the good life. Physically, he is big and fat; he eats and drinks a lot. His father's exceptional wealth, which he accidentally inherits, brings him naturally into the orbit of Russian high society. He is introduced to Elena, the daughter of the well connected Prince Kuragin. Infatuated with Elena's beauty, he marries her. But quickly it becomes clear there is no real connection. When Elena flirts with a Russian officer, Dolokhov, Pierre nonetheless becomes jealous and challenges Dolokhov to a duel. He injures Dolokhov in the leg but the matter is hushed up. Pierre gets away with the implications. Afterwards Pierre has a quarrel with Elena who taunts him, and they separate.  

This is exactly the point at which Pierre's inner work begins. While traveling, he has a chance meeting with a man who belongs to the "brotherhood of Freemasons". Pierre has no belief in God or religious abstractions. In the past he even made fun of Masonic beliefs. But Pierre is fascinated by this stranger who argues convincingly that "the supreme wisdom is not based on reason alone" and can only be obtained by purifying oneself inwardly. With his life in disarray, Pierre is eager to embrace something that will give him purpose.  He becomes a Mason, putting himself through the cultish initiation rituals of the brotherhood. Despite the strangeness of these rituals, Pierre is rejuvenated by the message of the Masons that "the source of blessedness is not outside, but inside us."

Moments like this, however, are always fleeting in Tolstoy's world. Like life itself everything moves and changes. Just when you think there is some kind of stability, it begins to disappear. So it is with Pierre's Masonic moment. Even as he becomes an advocate of his new beliefs, Pierre notices that his excesses in food, wine and the amusements of "bachelor parties" (Tolstoy's phrase for the company of women) continue as before.

As he participates in events of the society around him and leads a dissipated life, a doubt keeps nagging him:
"What for? Why? What's going on in the world?"
He also notices that everyone around him seems to be doing something to distract themselves so as to fill the gaps in their life:
"Sometimes Pierre remembered stories he had heard about how soldiers at war, taking cover under enemy fire, when there is nothing to do, try to find some occupation for themselves so as to endure the danger more easily. And to Pierre all people seemed to be such soldiers, saving themselves from life; some with ambition, some with cards, some with drafting laws, some with women, some with playthings, some with horses, some with politics, some with hunting, some with wine, some with affairs of the state. "Nothing is trivial or important, it's all the same; only save yourself from it as best you can!" thought Pierre. "Only not to see it, that dreadful it.[Tolstoy's italics.]
How relevant these observations are even today! As if the activities of our "physical self" aren't enough – all the occupations and hobbies Pierre mentions above – we now have the innumerable pleasures and distractions of a life online! I was also struck by the claim: "Nothing is trivial or important; it's all the same." 

"A limit to suffering and a limit to freedom…"

In 1811 and 1812 – the years the Great Comet could be seen in the night sky – Pierre is caught up in the Russian resistance to the looming French advance. It endows Pierre, whose life had been drifting aimlessly, with a new purpose. He is not capable of serving as a soldier. But he attends meetings where funds are being raised for the militia; he cooks up occult theories that suggest that he himself will somehow obstruct Napoleon's apocalyptic advance. He feels a need to "undertake something and sacrifice something" though he cannot articulate "what he wanted to sacrifice it for".  

This begins a fascinating phase where the clumsy and militarily clueless Pierre walks straight into the war when all other citizens are trying to escape. We see the great Battle of Borodino through Pierre who, in good humor, blunders on to the most dangerous parts of the battlefield. Initially considered a nuisance, the soldiers slowly take a liking to this strangely dressed Russian count unexpectedly in their midst. We see him on the retreat along with soldiers. We see the burning of Moscow after the city has emptied out and Napoleon's army occupies it. Pierre stays on in Moscow, has comical plans of assassinating Napoleon with a pistol he possesses, ends up rescuing those trapped in fires, gets arrested for arson (something he was never guilty of), observes the harrowing public execution of fellow prisoners and himself narrowly escapes from being executed. Finally, he travels as a prisoner along with others under the harshest physical conditions as Napoleon's army begins to retreat from Moscow. 
French_invasion_of_Russia_collage
It is in these challenging external circumstances – the three week walk in captivity, away from Moscow – that Pierre gains his deepest insights. 

He learns "not with his mind, but with his whole being". He notices, to his own surprise, his ability to adapt to the difficulties very well. Depleted French reserves mean that Pierre is fed horsemeat, which he finds "tasty and nutritious" and "the saltpeter bouquet of gunpowder they used instead of salt was even agreeable". It is fall, the weather is cold, but walking keeps him warm and even "the lice that ate him warmed his body pleasantly". His feet are full of sores and are frightful to look at, but Pierre simply and very naturally thinks of other things. This teaches him "the saving power of the shifting of attention that has been put in man, similar to the safety valve in steam engines, which releases the extra steam as soon as the pressure exceeds a certain norm".

A fellow prisoner, a peasant foot-soldier named Platon Karataev, inspires Pierre with his genuine simplicity and cheer.  

Pierre realizes that "as there is no situation in the world in which a man can be happy and perfectly free, so there is no situation in which he can be perfectly unhappy and unfree." Further:    
"He had learned that there is a limit to suffering and a limit to freedom, and those limits are very close; that a man who suffers because one leaf is askew in his bed of roses, suffers as much as he now suffered falling asleep on the bare, damp ground, one side getting cold as the other warmed up; that when he used to put on his tight ballroom shoes, he suffered just as much as now, when he walked quite barefoot (his shoes had long since worn out) and his feet were covered with sores. He learned that when, by his own will, as it had seemed to him, he had married his wife, he had been no more free than now, when he was locked in a stable for the night."
What really elevates these sentences is the quality of the examples and the contrasts they set up. The claims are simple yet striking. They are those truths that we perhaps know intuitively but have not articulated yet.  

"People must join hands…"

Pierre is eventually rescued, and with the war finally reaching its end, he returns to normal life. Even though he falls ill, he is filled joy and recovers. When, "by old habit", he asks himself: "Well, and what then? What am I going to do?" immediately the answer comes to him: "Nothing. I'll live. Ah, how nice!"

The search for a purpose, Pierre has realized, is precisely that which keeps one unhappy. The purpose seems simply to live, to get on with things cheerfully if possible, rather than looking for abstractions. Pierre has emerged a renewed man.  

But just because we've gained some wisdom does not necessarily mean that we will adhere to it all the time. We see this again and again in War and Peace. (It also works the other way: a lack of enthusiasm for life never lasts either and a person finds himself revived one way or another.) Prince Andrei, Pierre's friend, keeps experiencing blissful moments when he feels that the world has been transcended. Such as when, lying injured at the Battle of Austerlitz, he glimpses something indescribably special in the "lofty sky", something that renders everything else insignificant. But however profound such moments may be, they always fade. Prince Andrei's sister, Marya Bolkonsky, who unlike her atheist brother and father, is devout, has an unshakeable faith, and tries very hard to elevate her character through religion – Marya discovers again and again that despite her best efforts and sincere intentions all kinds of irritations and jealousies torment her.  

Pierre changes at the end too, but it's a lot more subtle. The Epilogue is set a few years after the war. Pierre is happily married and has children. He retains much of his newfound joy in life; people still love to be around him. You would think this would be a good way to finish, literally a "happily ever after" ending. But somehow, inexplicably, Pierre now decides to participate in political intrigue. He has just returned from an important meeting in Petersburg. He feels the current administration in Petersburg is not doing the right things, there's "thievery in the courts", "what is young and honest, they destroy". So "people must join hands, in order to avoid the general catastrophe". 

War and Peace ends with Pierre hinting at the creation of a rebel group – something's cooking, and it will eventually lead to the Decembrists revolt of 1825. So Pierre, who had learned from his experiences in war a few years back that there is no need for abstract purposes, now ends up again arguing for and participating in one.

To the very end, Tolstoy remains faithful to the fact that not even the most profound realizations withstand the dynamism and change that is life.

Monday, May 11, 2015

Unconditioned by the past

Exploring the Memoryless property of the Exponential Distribution. Cross posted over at 3 Quarks Daily.
1. Waiting For the Next Customer

Suppose you run a small business, a barber shop or a small restaurant that takes walk-ins only. A customer has just left, your place is empty, and you are waiting for the next customer to come in. You've figured out that on average the time between two successive arrivals is 15 minutes. However, there is variation and the variation follows the Exponential probability curve shown in the figure below. This is not an arbitrary choice: time between successive random and independent arrivals does actually follow the Exponential. The average time between arrivals depends on whether it is a busy or slow time of the day, but the general shape of the Exponential curve keeps showing up again and again when empirical data is plotted (one example here).    
Exponential
The height of the curve is an indicator of where the greatest probability densities are. Most arrivals happen in quick succession (the curve is tall when t is small), but there will be occasions when a long time elapses before the next arrival happens. At t=0, when the last customer just left, if you calculated the probability of the next customer arriving within 5 minutes (0 < t < 5) you would get the value 0.283. Equivalently you could say that the probability you will wait 5 minutes or more is (1 - 0.283) = 0.717. 

Now here's the interesting part. Suppose twenty minutes have now passed and the next customer still hasn't arrived. You are starting to get a little impatient; after all you don't want your productive time to be idle. So at t=20, you again calculate the probability of a customer arriving in the next 5 minutes (20 < t < 25), given that no one has come so far. You would think this new probability, based on how much time has elapsed, should be higher than 0.283. But, surprisingly, the probability that a customer will arrive in the next 5 minutes, given that twenty idle minutes have passed, is still 0.283! And the probability that you will wait 5 minutes or more is still 0.717.

This is precisely the Memoryless property of the Exponential: the past has been forgotten; the probability of when the next event will happen remains unconditioned by when the last event happened. Fast forward even more: let's say you've waited for half an hour. No one has shown up so far. Frustrated, you recalculate the probability of someone arriving in the next 5 minutes (30 < t < 35). Still 0.283!

The behavior that we see in the Exponential is because your customers are arriving independently of one another -- remember that you allow only walk-ins. There is no "memory" or predetermined schedule connecting any two successive arrivals (in the same way that the outcome of a coin that is tossed now has no memory or connection with the outcome of a coin tossed at some point of time in the past). A barber shop, a small restaurant, a shoe-shop, a cab-driver, a car mechanic, a self-employed person who earns a living doing Japanese-English translation requests – one can find many contexts that experience the Memoryless property. Bigger retail firms also experience the same problem, but they hire (and fire) many people, cross-train their employees to do multiple tasks and thereby have ways to reduce the risk of staying idle.

In small businesses, the wait for the next customer is felt far more personally and acutely. Recently, I spoke to Abel (not his real name), an Ethiopian man who had started a restaurant in a small Midwestern town. The Ethiopian dishes I tasted were excellent. Yet Abel said there were many difficult evenings he would be alone, waiting for someone to come in. To cut costs, he was both the cook and the server on such slow days. But Abel noted that he would, unexpectedly, get busy. This is the flip side of the Exponential: a string of closely spaced arrivals is very likely since the probability densities are front heavy, as seen in the shape of the curve. So you can go from being idle for an hour to suddenly having a long line of people waiting. Now you have a different problem – you are too busy and your customers are unhappy! 

2. A Visual Illustration

Let's look closer why exactly the Memoryless property holds true for the Exponential. Instead of showing the algebra, I'll try illustrating visually. I struggled with the Memoryless property myself for many years; so at the very least, I'll put my own thoughts in order. Please let me know if something does not sound right.   

The Exponential is a continuous distribution used to characterize the probability of time durations, such as the time between two successive randomly occurring events. Naturally the smallest possible value is 0. The Exponential curve is asymptotic – a fancy word for the idea that the probability curve keeps dipping as we move to the right and gets closer and closer to the x axis, but never quite dips enough to touch the x-axis. The dipping curve stretches to infinity. So very long time between events (long periods of idleness) are theoretically possible, although in practice they are very, very unlikely. The area under the Exponential probability curve, if we calculate the limit, tends to 1 (as it must for any continuous probability distribution).   
Rescale2Let's return to the original example. Time between successive arrivals follows an Exponential Distribution with a mean of 15 minutes. Currently, twenty minutes have passed since the last arrival, so we are at t=20. We are trying to find out the probability that an arrival will happen in the next 5 minutes -- in the interval 20 < t < 25. To do so, we now only need to consider the area under the Exponential curve to the right of the t=20 mark. The total area under the curve to the right of t=20 is 0.263. We "rescale" this area such that 0.263 now becomes equivalent to an area of 1 -- we do this because this is the relevant conditional probability space we are now interested in. Further, the x axis is re-scaled: t=20 becomes t=0; t=25 becomes t=5; and so on, so that in the newly re-scaled or conditioned area we can calculate the probability of an event happening in the next 5 minutes.  

Surprisingly, the re-scaled area is exactly the original Exponential probability curve! Even the height of the curve corresponding to every time value on the x-axis is exactly as it was when the last customer left.

It's not a precise analogy, but just as the same pattern keeps repeating itself in a fractal no matter how much you magnify the original, so the same exact Exponential curve we started with keeps appearing again and again upon re-scaling no matter how much time has elapsed. It does not matter if 10, 30, 100 or 2000 minutes have passed without an arrival; the probability that an arrival will happen in the next five minutes will always be 0.283. This makes mathematical calculations very straightforward -- the past does not need to be kept track of, and the same formulas can be used at any stage.

There is something about how the curve decays or dips, more specifically the rate at which it decays, which gives Exponential this unique property among continuous probability distributions. In fact, if you knew that time durations follow the Memoryless property you can work backwards and prove that the original probability curve has to be Exponential. 

As a contrast, other well known continuous distributions, say the Normal or Lognormal, do not have the Memoryless property. The Lognormal distribution is a more relevant comparison since, like the Exponential, it allows only values greater than 0, unlike the normal which allows negative values and is therefore not always appropriate for modeling time durations. In the Lognormal and Normal, the probability of a future event is not unconditioned by how much time has passed. This means that you have to keep track of the past when you calculate the possibility of a future event -- and this quickly gets very cumbersome and computationally expensive. 

For a further contrast, I've created a couple of roughly equivalent images, Figure 1 and Figure 2, for the continuous uniform distribution -- a relatively simple, bounded distribution with a flat curve. Here we see that the probability of an event happening in the next five minutes was originally 0.1667; after twenty minutes, it went up to 0.5.  

Among discrete distributions, the Geometric distribution has the Memoryless property.

3. Lifetime of a Device

I'd like to end the piece by raising a couple of questions. Probability textbooks routinely mention that the Exponential distribution can be used to model the lifetime of a device: time from when the device is put into operation to its failure. Here the Memoryless property seems puzzling to me.

If a device has worked for 3000 hours, the probability that it will work for another 1000 hours is exactly the same as when the device started operating. I find that quite amazing. Such a property is possible only if the failure of the device has nothing to do with wear and tear caused due to time. Otherwise, the longer the device works, the more likely it is to fail in the next time interval -- just as at the age of 70, the probability that we will die in the next 10 years is much higher than the same probability calculated at the age of 40. From what I've read, the lifetime of semiconductor components follows exponential time to failure distributions. But then how is it that these devices escape wear and tear caused due to time? And are there other examples?

Tuesday, April 14, 2015

The Traveling Moose # 6


I was reminded of the  traveling salesman problem (TSP) in an unlikely context, thanks to a display at the New York State Museum in Albany (click on image for better view). The display showed the zigzagging journeys made not by a salesman, but a radio collared moose, simply called #6. The moose seems to have traveled a lot, but the explanatory note on the display said otherwise: "Most New York moose have settled into limited travel routines...From February 1998 to November 2000 radio-collared moose #6 ranged over 350 square kilometers (217 square miles) east of Great Sacandaga Lake."   

Tuesday, February 17, 2015

A mobile surgical unit in Ecuador

Latest 3 Quarks Daily column is about my healthcare-themed trip to Cuenca, Ecuador last October. Full essay is here. This is how it begins: 
Since 1994, a small team of clinicians has been bringing elective surgeries to Ecuador's remotest towns or villages, places that have do not have hospitals in close proximity. From the city of Cuenca – Ecuador's third largest town, where they are based – the team drives a surgical truck to a distant village or town. Though a small country by area, the barrier of the Andes slices Ecuador into three distinct geographic regions: the Pacific coast in the west; the mountainous spine that runs through the middle; and the tremendously bio-diverse but also oil rich jungle expanse to the east, El Oriente, home to many indigenous tribes. Apart from a few major cities – Quito, Guayaquil, Cuenca – towns and villages tend to be small and remote.   
Isuzu Truck 2

Each year the team goes on 12 surgical missions, roughly one per month. A trip lasts around 4 days: a day's drive to get to the place; 2 days to conduct 20-30 surgeries (sometimes more sometimes less); and then a day to return. Patients pay a nominal/reduced fee if they can: the surgeries are done irrespective of the patient's ability to pay. The clinicians belong to a foundation called Cinterandes (Centro Interandino de Desarollo – Center for Inter-Andean Development).   
Amazingly, the very same Isuzu truck (see above) has been in use for more than 850 missions and has seen 7458 surgeries from 1994-2014! The truck itself is not very large; in fact, it cannot be, because it has to reach places that do not have good roads. The mobile surgery program has the lowest rates of infection in the country. Not a single patient has been lost. The cases to be operated on have to be carefully chosen. Because of the lack of major facilities nearby, only surgeries with a low risk of complication can be done. Hernias and removal of superficial tumors are the most common. Hernias can be debilitating, yet patients may simply choose to live with them for many years rather than visit a far-off urban hospital. For many, leaving work for a few days and traveling to get a health problem fixed is not an option.

A sky full of monarchs


A sky full of the famous monarch butterflies in Michoacan, Mexico. It's hard to capture this special phenomenon -- millions of butterflies congregating, after a 2000 mile journey from Canada and northern US, in a few fir/oyamel forests in Central Mexico -- on camera. This picture I took last week is not very good, but every black speck in the sky, however faint, is a butterfly. This year's monarch numbers seem to be better than last year, although still well below the average across two decades.

Monday, January 19, 2015

Birds seen this winter

It's hard to spot new birds during Massachusetts winters (I don't own a house with a yard or a bird feeder, which makes it doubly hard). The hundreds of species that make their home or pass through here are more easily observed in spring, summer and early fall. But last Tuesday – a bone chillingly cold but sunny day in Amherst – I ran into four species all at once. I had come out for a walk in a quiet part of town, a dead end street where an unpaved hiking trail leads to a pond. The unusually high levels of noise in the trees suggested that a lot of birds were active. The repeated deep thuds I was hearing indicated that woodpeckers were around, hammering on tree trunks.

Birds_All4

So here are the species that I spotted, from left to right (picture assembled from Wikipedia images): the eastern blue bird; the black capped chickadee; the female downy woodpecker (the male has slight red marks on the head); the misleadingly named red-bellied woodpecker because the prominent red or orange patch is actually on the bird's curved head. The chickadee is the smallest of the four, and the red-bellied woodpecker the largest. Overall, nothing really surprising here – these are all common winter birds. But as an amateur bird watcher, I felt a special joy stumbling upon them; it felt, at least in those few moments, as if some special secret of nature had been unexpectedly revealed.

Some other things I've noticed this winter: (1) starlings, dozens of them somersaulting gracefully in the air in unison, literally a dance to avoid death, an attempt to disorient hawks that are hunting them (something similar to what's happening in this video. On a different note, the 150 million starlings in North America today are descended from the 60 odd European starlings that were deliberately introduced to New York's Central Park in 1890 by "a small group of people with a passion to introduce all of the animals mentioned in the works of William Shakespeare" -- talk about literature influencing ecology!); (2) young wild turkey, moving black specks from a distance, foraging in a snow covered meadow (here's a previous piece on wild turkey); and (3) a few weeks ago, at twilight, the mysterious, round faced barred owl, the only owl I've ever seen, well camouflaged against the bark of a tree, very similar to this picture.   

(This piece was cross-posted here.)

Tuesday, December 30, 2014

The resettlement of refugee farmers in East Punjab after Partition

A different version of this piece was published back in 2009, in the OR/MS Today magazine.
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It is well known that the partition of the Indian subcontinent in 1947 had terrible consequences. Tens of thousands of people died. Millions were displaced and lost their cherished ancestral homes: Muslims left India for Pakistan, and Hindus and Sikhs left Pakistan for India. It was the greatest mass migration in history. But what is less understood is the manner in which the vast numbers of refugees were accommodated and settled into the newly divided regions. The greatest mass migration in history inevitably became the largest resettlement operation in the world.

How was this monumental task achieved? That question might take up many books, and perhaps many have already been written. But we get a glimpse of how it was done in the Indian side of the Punjab (East Punjab) in Refugees and the Republic a chapter in Ramachandra Guha’s post-independence historical narrative India after Gandhi. 


Guha’s chapter appealed to me for a different reason. My specialization is the field of operations research: the quantitative or optimization methods that are now used widely in the attempt to make service systems more efficient. The resettlement or land allocation problem set up by Guha in the chapter seemed to fall squarely in the realm of optimization. I was curious to know how the reallocation of land had been carried out in practice.  

Punjab was one of the partitioned provinces; the eastern part found itself in India while the western in Pakistan. A large number of Muslims had left East Punjab for Pakistan. But there was an even greater influx of Hindus and Sikhs into the east from Pakistan. Most of these refugees were farmers. Together they had abandoned 2.7 million hectares of land in Western Punjab but across the border in India where they now had to make a living only 1.9 million hectares had been left behind by Muslim farmers who had fled the opposite way. The problem was made more complex by three additional factors:
  • Each refugee family had a claim on how much they had owned prior to emigrating.
    http://www.orms-today.org/cleardot.gif
  • The fertility of the land differed; there were dry, unirrigated districts as well as lush, irrigated regions.
    http://www.orms-today.org/cleardot.gif
  • There were demands that families and neighbors be relocated in the same way as they had been in West Punjab. If possible entire village communities had to be recreated.
From the comfort of hindsight – and given how far computing power has grown in the last 6-7 decades – I can imagine formulating the land allocation problem as a large scale mathematical optimization model. The decisions (the x variables in the problem, which the model would be solved for) would be how much land to allocate to each family and where to allocate. The objective, expressed as  a function of the decisions, would be to minimize the difference between claims and actual allocations. The constraints would be equations that expressed limits such as the total land allocated could not exceed the total  land available. There could be other constraints to ensure that families and neighbors are relocated together. The mathematical model would also have to capture the spatial aspect, the variation in fertility and relate them somehow to the allocation decisions.

Even by today’s standards this is a very difficult optimization problem; it also has human or qualitative dimensions that are difficult to capture mathematically. The unenviable task of reallocating land fell upon the Indian government and its civil service workers. As a first step, they assigned each family of refugee farmers 4 hectares irrespective of its past holding; they also gave loans to buy seed and equipment. Viewed from an optimization lens, this 4-acre allotment is an “initial solution” – a feasible assignment to the decisions (the x’s) to get things going, but very far from optimal.

As families began to sustain themselves, applications were invited for them to claim more land, depending on what they had owned in West Punjab. Within a month, there were 500,000 claims. These claims were then “verified in open assemblies consisting of other migrants from the same village. As each claim was read out by a government official, the assembly approved, amended or rejected it.” Refugees tended to exaggerate of course, but were deterred by the open assembly method; if a claim turned out to be false they were punished by a reduction in land.

Sardar Tarlok Singh of the Indian Civil Service and a graduate of the London School of Economics led the rehabilitation operation. He used two simple but interesting rules (we call them heuristics) for allocating land, and this is where the pragmatism in the whole operation comes most clearly to light. Though claims had been filed, because of the reduced acreage, none of the refugees could be assigned as much land as they'd originally owned. Everybody’s claim had to be reduced by a certain percentage. Plus, there had to be some way of accounting for the differing fertility of land.

Sardar Tarlok Singh came up with two measures, the standard acre and the graded cut, which dealt with these issues: 

“A standard acre was defined as that amount of land which could yield ten to eleven maunds of rice. (A maund is about 40 kilograms.) In the dry, unirrigated districts of the east, four physical acres were equivalent to one standard acre; but in the lush “canal colonies” [where irrigation was strong], one physical acre was about equal to one standard acre. The innovative concept of the standard acre took care of the variations in soil and climate across the province.

The idea of the graded cut, meanwhile, helped overcome the large discrepancy between the land left behind by the refugees and the land now available to them – a gap that was close to million acres. For the first ten acres of any claim, a cut of 25% was implemented – thus one got only 7.5 acres instead of ten. For higher claims the cuts were steeper: 30% between ten and 30 acres, and on upward, so that those having more than 500 acres were taxed at the rate of 95%.”

With this rule, there clearly were losers, and the losers, of course, were those who had once owned huge tracts of land: “The biggest single loser was a woman named Vidyawati who had inherited land (and lost) her husband’s estate of 11,500 acres spread across thirty-five villages of the Gujranwala and Sialkot districts. In compensation she was allotted mere 835 acres in a single village of Karnal.”

It’s unclear what analysis motivated Tarlok Singh to come up with the specific ranges and the cuts. It’s possible that the taxing mechanism might have left too much land unassigned, and many claimants dissatisfied. Or, given that the overall reduction in total land was about 38 percent (the farmers had left 2.7 million hectares behind and now were being resettled on 1.7 million hectares), the taxing may not have been strict enough. The exact details are unknown.

What is known, though, is that by November 1949, a year and a half after the resettlement began, “Tarlok Singh had made 250000 allotments distributed equitably across the districts of East Punjab”. Even the soft constraints, such as settling families and neighbors together, were met to a large extent, though “the recreation of entire village communities proved impossible.” The resettlements were so successful that “by 1950, a depopulated countryside was alive once again.” Tarlok’s heuristics might have been simple, but they helped solve a complex, large-scale allotment problem in the aftermath of a traumatic event.

Halfway across the world, in the summer of 1947 — the same year that the partition of the Indian subcontinent took place — George Dantzig conceived the famous Simplex Algorithm. In the next decades the Simplex Algorithm, helped by advances in the computing capability, would provide fast solutions to large linear optimization problems. Each fall I teach the algorithm to graduate students from many disciplines. But in 1947, the Simplex algorithm could only tackle a small version of the classical diet problem: optimally choosing food items for a family to minimize costs while ensuring minimum nutritional needs are met. That particular diet problem had only 9 constraints and 27 variables, but took 120 man-days to solve; worksheets were glued together and spread out like a tablecloth to assist in determining the optimum solution [1].

This puts the enormity of resettlement problem in perspective. With half a million people making claims – which means there would be hundreds of thousands of variables and constraints – even an awareness of Dantzig’s algorithm could not have helped the Indian Civil Service.

Nearly 7,000 officials were needed for the resettlement effort; they constituted a refugee city of their own. The problem occupied them for a period of three years. Imagine the paperwork and the records that had to be kept and retrieved; imagine the disputes among the refugees, the flared tempers and the jealousies. But imagine also the perseverance of everyone involved. It made me think about what it is exactly that makes certain large scale operations successful and others not. It’s hard to make generalizations, but one feature seems to be effective coordination across large groups of people: largely error-free lunch deliveries by the Dabbawalas of Mumbai is an example that comes to mind.

Related notes:

1. Guha ends the chapter in his book poignantly. The resettlement, Guha says, may have been successful, but the general sense of loss could not be undone. The migrating Sikhs had left behind a beloved place of worship, Nankana Sahib, the birthplace of the founder of their faith, Guru Nanak. Muslims migrating from East Punjab too had left behind the town of Qadian, the center of the Ahmadiya sect of Islam; the Ahmadiya mosque was visible for miles around. Very few Muslims now lived in Qadian, which was full of Hindu and Sikh refugees. Guha quotes the editor of the Calcutta newspaper Statesman, who wrote that in both Qadian and Nankana Sahib there was “the conspicuous dearth of daily worshippers, the aching emptiness, the sense of waiting, of hope and…of faith fortified by humbling affliction.”

2. The picture shows a boy at a Delhi refugee camp in 1947. Here is the source. The largest refugee camp, though, was at Kurukshetra, consisting of nearly 300,000 people. For their entertainment, film projectors were brought in and Disney specials featuring Mickey Mouse and Donald Duck were screened at night. It was, as one social worker described it, a “two-hour break from reality”. 

References
1. Bazaraa, M., Jarvis, J., and Sherali, H., 2005, Linear Programming and Network Flows, Wiley 3rd Edition

2. All quoted parts in the piece are from Ramachandra Guha’s India After Gandhi

Tuesday, December 23, 2014

The Undocumented Journey North, Through Mexico

Latest column is up. A bit long, some typos here and there, but hopefully still interesting. Here is an excerpt: 
From 2000-2006, I was a graduate student at Arizona State University in the Phoenix metro area. My neighborhood, a ten minute walk from the university, had cheap apartments where Asian students lived alongside immigrants from south of the US-Mexico border. We students had visas, had made safe journeys on flights, and now worked and studied on campus. Many Hispanic immigrants, in contrast, had made life threatening journeys and had crossed the border illegally. They now did construction, farm, and restaurant jobs for a living. At the neighborhood Pakistani-Indian restaurant, I remember seeing – through a decorative window shaped as a Mughal motif – three Hispanic workers in the kitchen patiently chopping the onions and tomatoes that would go into the curries that I enjoyed.
Some Indian students looked down on these immigrants, blaming them for petty bicycle thefts and how unsafe the streets were at night. And just as all East Asians were "Chinkus", the immigrants from south of the border were "Makkus" – a twist on "Mexican", used mostly (but not always) in a negative sense. No one, though, had a clear sense what the stories of these immigrants were. While it is true that a large percentage of those who cross the border are from Mexico, tens of thousands each year come from the troubled countries further south – Guatemala, El Salvador, Honduras. This year, an estimated 60,000 unaccompanied minors from Central American countries, fleeing violence in their home towns, will cross the border. Surprisingly, even hundreds of undocumented South Asians cross via Mexico – but more on that later.
More here. Towards the end, I talk of the South Asian angle, including a Bangladeshi man I met in Quito, Ecuador, hoping to make the undocumented journey to the US: 
The South Asian Angle: A 2009 report by Homeland Security estimated that India was number six – after Mexico, the Central American countries, and Philippines – with 200,000 undocumented immigrants currently in the US. Between 2009 and 2011, 2600 Indians were detained by the Border Patrol along the US-Mexico border. This coincided with a visa-on-arrival policy that Guatemala and other Central American countries allowed for Indian passport holders. So Indians could fly in to Guatemala City and start the journey north. The cross continental flight suggests Indian migrants had more money than most Central Americans - perhaps the money bought them a safer passage. Guatemala has now stopped visa on arrival for Indians. 
A Bangladeshi in Quito: In October this year – in one of those strange, unlikely encounters that happen during travel – I met met a Bangladeshi man selling samosas, 3 for $1, in the old town of Quito, Ecuador. He was the only South Asian among many Ecuadorian street vendors. The samosas were in a container - perhaps a hundred of them. Business was brisk. To appeal to the locals, he had cleverly called the samosas "Empanadas de India".  
I spoke with him in Hindi. He had been in Ecuador for five years and was fluent in Spanish. Life had been reasonable, he said; accommodation, food and cost of living were inexpensive in Quito. He was in a position now to apply for an Ecuadorian passport. But his interest had always been in migrating to the United States – the same route via Mexico that others take. Some acquaintances of his had made it there already. He asked me about jobs in the US. Unfortunately, I had no concrete sense on what an undocumented immigrant could expect. I did tell him that the journey through Mexico, from what I'd heard, was risky. But he seemed intent and had a more optimistic view. All this was before I read Martinez's book -- if I had known of The Beast, I would have urgently recommended it to him. 
How unusual and compelling his story is: here was a man from Bangladesh in, of all places, Ecuador, biding his time patiently, saving up money by selling that most South Asian of snacks, samosas, and even securing a backup citizenship, so that he could risk the journey north! 

Monday, December 01, 2014

A 1000-year old witness



History in the rings of a 1021 year old redwood tree -- from Muir Woods National Monument, north of San Francisco. The tree was born 930 AD and fell in 1930, and was alive during key events in North American history: a millennium of great tumult, especially since 1492. Each year produces a natural growth ring, varying in size depending on the type of year (dry, rainy etc.) so there are approximately 1021 rings in this cross section. Redwood trees are massive (350 feet tall), which is not conveyed by these pictures. Sorry for the poor images and the flash -- the forest created by these tall trees is dark even during the day, and my cell phone has poor resolution.

Thursday, November 20, 2014

Essays at 3 Quarks Daily

If you've been wondering why I haven't posted here for so long -- well, it's not because I've been busy with work. In fact it's been a good year for writing essays. I've been writing this year for a website called 3 Quarks Daily since this January. So far I have nine essays, all collected here. Comments welcome! I should be cross posting the essays here too, but I've been lazy. Maybe, with the 3QD pieces coming regularly, I'll find some way to post more informally here. Though I've probably lost what little readership I had. 

Tuesday, October 22, 2013

Erzurum

1.
On July 12th this year, after three days in Istanbul, I traveled with my friend Serhat, to Erzurum, a regional city about 770 miles away in Northeastern Anatolia.

The flight was 2 hours long. After takeoff, the plane first took a northwards course: the dark blue waters of the Black Sea were beneath us. A few minutes before, I’d glimpsed the 32-km-long Bosphorous Strait, Istanbul’s iconic landmark. Istabulites know the maritime significance of their city very well, but to me it was a revelation: a ship traveling from Odessa, a Ukrainian city on the north cost of the Black Sea can travel via the narrow Bosphorus to the Sea of Marmara; and from there through the Dardanelles Strait to the Aegean and Mediterranean Seas; and finally through the Strait of Gibraltar to the Atlantic Ocean.  

  
The marked spot to the right of the map indicates Erzurum

The plane eventually steered eastward, following Turkey’s Black Sea coast, and during the last half hour, it turned inland to northeast Turkey. The landscape was consistently mountainous: sometimes lush green (especially when close to the Black Sea), sometimes covered with cloud, sometimes dry, the ridges on the slopes of brown mountains casting shadows in the late afternoon light, creating a distinctive visual texture. 

Erzurum, a town of about 367,000, lay in a sprawling plain at the base of one such dry mountain range (Mt Palandöken is a ski resort near Erzurum). A haphazard checkerboard of farms stretched for miles and miles around the city. Many of them, I discovered later, were hay farms, important in a region whose economy depends heavily on stock breeding  We rented a car at the airport. The small airport, the plains around and the mountains in the distance reminded me a little of Bozeman, Montana. On our way to Erzurum center, we passed by the gates of Ataturk University. With 30-40,000 students and medical school to boot, this is a major university and contributor to the economy. 

By the time we had checked into the Esadaş Hotel, along Cumhuriyet Caddesi, Erzurum’s main thoroughfare, it close to iftar time; light was fading fast and the Ramazan fast would soon be broken -- at 7:53 pm.  We started walking to the popular Gelgör Restaurant.  On the way, we passed by two historic mosques: the Yakutiye and Lala Pasha. Erzurum, like the rest of Anatolia, has seen many layers of history: it has been influenced by Greek, Roman, Arab, Persian, regional Georgian and Armenian Christian, Seljuk and Mongol rulers.

In the courtyard of the Lala Pasha, we ran into two boys, aged between six and ten. The younger one was selling toilet paper or rolls of tissue neatly folded in a plastic cover; the older was carrying some small contraptions, one of which looked like a low plastic bench.

We did not buy anything, but Serhat got to talking with them. He told them that I was from Hindistan. Almost immediately, the boys started repeating a few words frantically to me. The younger one said, “Amita..bhaccha” at least five times, before I realized they were referring to Amitabh Bachchan. The older one was saying Shahrukh Khan in his own way. Bollywood’s popularity in unexpected places is not unusual --  from West African taxi drivers in Minneapolis, to painters on the streets in Lima (Peru), to an Uzbek man I met on a Grand Canyon hiking trip: everyone is familiar with Bollywood. The bigger surprise was that these kids, making do with basic Turkish, were not locals but from Kabul, Afghanistan. Serhat learned that they had entered Turkey illegally in what must have been a very long journey from home.

Just then there was a loud explosion and puff of smoke: this was the city cannon signaling the end of the fast. Prayers immediately reverberated from the minarets all around. When I looked at the twilight sky above, I saw large numbers of swallows emitting low shrill sounds and flying very fast like quivers of arrows – their excitement probably had nothing to with the excitement of a Ramazan evening, but in my mind at least it seemed so. The fact that I was traveling in a predominantly Muslim city in a far corner of Anatolia had until then only been a fact. But the impressions of that evening – the unlikely meeting with the kids from Kabul; the firing of the cannon; the azans; the swallows – all came together with special force to make that moment personal.  

2.

We continued to walk towards the restaurant. Ramazan is a time to be with family and friends, so the streets were completely deserted, and this reminded me of the bleakness of American suburban neighborhoods. But Gelgör was bustling with people relishing their kebabs delivered non-stop on skewers by busy waiters. Here it was easy to feel the festive, communal atmosphere of Ramazan.

After dinner and a rich dessert – the kadayıf dolması – we walked through the streets and alleyways of Erzurum, and came across more old tombs and mosques. The emptying out of streets at iftar time had given the impression that the night life of the town was over. But after 9 pm the streets got busier and busier.

Tea houses are a distinctive feature of Turkish life: male Turkish life, if you are in a conservative town. In alleyways and the main streets of Erzurum, I saw plenty of informal, open-air tea houses: large, stylish and what looked like stainless steel samovars (heated, in one case, atop a hearth with wooden sticks); men chatting with other men, tea cup in one hand, cigarette in the other; dark red tea in glass cups pleasing to the eye. Even the little cubes of sugar provided on the side have aesthetic value. This tea habit – one cup is never enough and each cup costs less than a lira -- reminded me Dostoevsky and Tolstoy’s novels, where in the large gatherings, parties or soirees of the aristocracy, the presence of tea served in samovars is mentioned without fail, often at the expense of other items (Dostoevsky hardly ever describes food items other than tea, which left me to wonder if Russian food at the time was very dull).

Back at Cumhuriyet Caddesi, which runs through the city center, families – plenty of women and children – were out in full force; the noise and the traffic was incredible, given how late it was. Near the Yakutiye and Lala Pasha mosques, a stage had been set up and there would perhaps be skits and other entertainment. Glass-fronted dessert and ice-cream shops were doing quick business. There were billboards advertising stylish and expensive Islamic wear for women: the elegant black dresses and ornamented head wear had a touch of modern fashion in them even if their basic function was conservative. Overall, Erzurum conveyed a sense of prosperity and wealth.    

3.

There were many questions I had about Turkey and Erzurum, and Serhat did his best to fill me in. He pointed out the billboard of a radical Islamic party with the motto, “Morality and Spirituality First”; the party wanted to appeal to all Turkic peoples of Central Asia. This affinity to the broader ethnic group stemmed from history: the Turks as a people were originally from someplace in south Siberia; they had slowly, over a millennia or more, made their way westwards, interacting with many other cultures along the way -- borrowing loan words from the Persians and the Arabs (this is perhaps why many Hindi and Turkish words mean the same thing, because India too was ruled by Central Asians). The westward movement of the Turks finally culminated in the creation of the Ottoman Empire. In Eastern Anatolia the Seljuk Turks, whose architectural remnants are a major attraction in Erzurum, were prominent a few centuries before the Ottomans arrived on the scene. 

This idea of Turkic groups conquering new lands raised some issues. How did the rulers bring the original inhabitants of Anatolia, who would have had their own diverse traditions and languages, into their fold? I was also curious how, in the early 20th century, the Turkish state had been fashioned by Ataturk, especially this far away in Anatolia, and the tensions inherent in the transition from an empire to a nation-state. I had questions, too, about the predominance of a single language and religion in Turkey. To my eyes – perhaps because I had grown up in India – Turkey seemed remarkably homogeneous, but I knew that couldn't be entirely true. Whatever its history and politics, Turkey seemed to have done much better than India in some essential aspects: its regional cities were cleaner, more organized and better equipped in terms of infrastructure. 

To the questions on history, I found some partial answers in the Rebel Land, a non-fiction book -- a very personal one -- by the English correspondent Christopher de Bellaigue. About a 5-10 years ago, Bellaigue visited the seemingly nondescript town of Varto, 3 hours south of Erzurum, for extended periods, in the attempt to unearth “the riddle of history in a Turkish town”.

Fluent in Turkish, Bellaigue was able to talk to the town mayor, civil servants, army men, businessmen and shepherds. In the process he unveils a complex and tangled history bringing to fore fault lines in modern Turkish history: the Kurdish question; the Alevis who were at odds with the majority Sunni Muslims; the Armenian mass deportation and killings that had happened in the chaos of shifting alliances in the First World War, a time when the Ottoman Empire was on its last legs, its Christian subjects in Europe had become nation states, and Russia was advancing into Ottoman territory in Eastern Anatolia.  

In an early chapter of Rebel Land de Bellaigue is still deciding which town he should choose for the book.  In Ankara, he meets a Kurdish friend for dinner. The friend tells him about Varto, “a small place in the southeast… but not far south as to be caught up in regular fighting…a little north of the great Armenian monastery of Surp Karapet.”  De Bellaigue’s friend had “got to know Varto through his wife, also an Alevi, who had relations there.  The Alevis of Varto generally spoke Zaza, he said, and the Sunnis Kurmanji; both were Kurdish languages”. He then said that the “Alevis of Varto suffer from a peculiar existential angst. They are divided over whether they are Turks or Kurds.” 

These were precisely the sort of nuances I had no idea about. Recently, a native of Erzurum, now living in the US, confirmed how her home town stood out sharply as a Turkish Sunni bastion even among the generally conservative towns of Eastern Anatolia. In a few days, I would visit the much smaller and poorer town of Kars, close to the eastern border with Armenia. Almost immediately after getting off the bus, I could tell that Kars was messier but more diverse and relaxed in its outlook. Maybe I was biased; maybe I felt that way because there were many good places, with vegetarian options, open for lunch in Kars; lunch during Ramazan at a restaurant in Erzurum does not seem to be possible.

After that evening in Erzurum, Serhat and I left early the next day. We drove north through the mountains, to the town of Rize – the hometown of the current prime minister, Erdogan – on the Black Sea Coast. From there, we headed east towards a group of villages (part of a United Nations Biosphere) located in a lush green, mountainous region on the border between Turkey and Georgia. After twelve hours of driving we finally got to our accommodation at 8 pm. I will describe this journey by road in my next post.