Human nature and wild nature

Edward Wilson, yet again with a startling insight, in the 25th anniversary foreword to Sociobiology: The New Synthesis:

Human nature – the epigenetic rules – did not originate in cities and croplands, which are too recent in human history to have driven significant amounts of genetic evolution. They arose in natural environments, especially the savannas and transitional woodlands of Africa, where Homo Sapiens and its antecedents evolved over hundreds of thousands of years. What we call the natural environment or wilderness today was home then – the environment that cradled humanity. Before agriculture the lives of people depended on their intimate familiarity with wild biodiversity, both the surrounding ecosystems and the plants and animals composing them.

The link was, on a scale of evolutionary time, abruptly weakened by the invention and spread of agriculture and then erased by the implosion of a large part of the agricultural population into the cities during the industrial and postindustrial revolutions. As global culture advanced into the new, technoscientific age, human nature stayed back in the Paleolithic era.

Hence the ambivalent stance taken by modern Homo Sapiens to the natural environment. Natural environments are cherished at the same time they are subdued and converted. The ideal planet for the human psyche seems to be one that offers an endless expanse of fertile, unoccupied wilderness to be churned up for the production of more people. But Earth is finite, and it still exponentially growing human population is rapidly running out of productive land for conversion. Clearly humanity must find a way simultaneously to stabilize its population and attain a universal decent standard of living while preserving much of Earth’s natural environment and biodiversity as possible.

Conservation, I have long believed, is ultimately an ethical issue. Moral precepts in turn must be based on a sound, objective knowledge of human nature…I am persuaded that as the need to stabilize and protect the environment grows more urgent in the coming decades, the linking of the two natures – human nature and wild Nature – will become a central intellectual concern.

The art instinct

Edward Wilson writes in Sociobiology: The New Synthesis:

Artistic impulses are by no means limited to man. In 1962, when Desmond Morris reviewed the subject in The Biology of Art, 32 individual non-human primates had produced drawings and paintings in captivity. Twenty three were chimpanzees, 2 were gorillas, 3 were orangutans, and 4 were capuchin monkeys. None received special training or anything more than access to the necessary equipment. In fact, attempts to guide the efforts of the animals by inducing imitation were always unsuccessful. The drive to use the painting and drawing equipment was powerful, requiring no reinforcement from human observers. Both young and old animals became so engrossed with the activity that they preferred it to being fed and sometimes threw temper tantrums when stopped. Two of the chimpanzees studied extensively were highly productive. “Alpha” produced over 200 pictures, “Congo”, who deserves to the called the Picasso of the great apes, was responsible for nearly 400. Although most of the efforts consisted of scribbling, the patterns were far from random. Lines and smudges were spread over a blank page outward from a centrally located figure. When a drawing was started on one side of a blank page the chimpanzee usually shifted to the opposite side to offset it. With time the calligraphy became bolder, starting with simple lines and progressing to more complicated multiple scribbles. Congo’s patterns progressed along approximately the same developmental path as those of very young human children, yielding fan-shaped diagrams and even complete circles. Other chimpanzees drew crosses.

The artistic behavior of chimpanzees may well be a function of their tool using behavior. Members of the species display a total of about ten techniques, all of which require manual skill. Probably all are improved through practice, while at least a few are passed as traditions from one generation to the next. The chimpanzees have considerable faculty for inventing new techniques, such as the use of sticks to pull objects through cage bars and to pry open boxes. Thus the tendency to manipulate objects and to explore their uses appears to have an adaptive advantage for chimpanzees.

The same reasoning applies a fortiori to the origin of art in man…Human beings have been hunter-gatherers for over 99 per cent of their history, during which time each man made his own tools. The appraisal of form and skill in execution were necessary for survival, and they probably brought social approval as well. Both forms of success paid off in greater genetic fitness. If the chimpanzee Congo could reach the stage of elementary diagrams, it is not too hard to imagine primitive man progressing to representational figures. Once that stage was reached, the transition to the use of art in sympathetic magic and ritual must have followed quickly. Art might then have played a reciprocally reinforcing role in the development of culture and mental capacity. In the end, writing emerged as the idiographic representation of language.

How a spider balloons itself, and Anthill

The [ballooning] method is widespread and ancient among spiders. When an immature spider possessing this ability wishes to travel a long distance, it crawls to an unrestricted site on a blade of grass or twig of a bush, lifts the rear part of its body to point the spinnerets at the tip upward, and lets out a line of silk. The delicate little thread is the spiderling’s kite. The air current lifts and pulls at it until the young spider feeling the tension, gradually lengthens the thread. When the strength of the pull exceeds its own body weight, it lets go with all eight feet and sets sail. A flying spiderling can reach thousands of feet of altitude and travel miles downwind. When it wishes to descend, it pulls in the silk thread and eats it millimeter by millimeter, heading for a soft if precarious landing. The risk it takes offers good odds. Sailing aloft under its silk balloon, the spiderling can reach land still uncrowded by competing spiders.
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That’s from The Anthill Chronicles, a short, self-contained novella within the famous biologist E.O. Wilson’s first novel. The novella, one of the most beautiful and mysterious stories I’ve read in a while, is about the rise and fall of four ecologically intertwined ant colonies on a small tract of land, a longleaf pine savanna in rural Alabama. One of the ant societies is a "supercolony" that runs rampant. Wilson, wisely, does not make the ants speak as humans do; instead, he uses his immense scientific knowledge to tell us what goes on in their subterranean nests. The execution is superb; there is probably no better narrative description of how the world appears to ants. The ants' quest for territory and foraging grounds, brutal wars, cycles of dominance and decline -- epics condensed in time and space --are strikingly similar to ours; and yet there are some contrasts. Ant colonies, for example, are fanatically communist and are heavily dominated by females; males play a peripheral, utilitarian role.

Deftly interlinked with the story of the ants is the story of the protagonist, Raff Semmens Cody, a child of the American south (like Wilson himself). Raff is fascinated by the same tract of land that contains the anthills and is interested in protecting it. This dual structure of novel – one at the level of the ants, the other the level of humans, but both examining in understated fashion the perils of overburdening the ecosystem – allows for an unusual perspective.

The fun in teaching probability

My last class this semester will be on Monday. Whether you are a student or professor, the end of the semester is always something to look forward to, especially if a four month long summer free of classes awaits. This time, though, I won’t feel the same way – the sentiment is primarily because I've been teaching probability and statistics. Both these topics are so rich and full of startling revelations that I will, for the first time, miss preparing for lectures. The class itself, consisting of ninety undergraduates, was a lot of fun (even if grading was not); I used the personal response system which worked well (I ask students a question and have their answers displayed immediately, enabling instant feedback, like an audience poll in a game show).

The mathematician Steven Strogatz, whose short pieces in the New York Times have thrilled many readers, recently wrote about conditional probability, a notoriously twisted concept. I spent two weeks covering it. Using a common example, I tried to tell my students that “testing positive if you have the disease” is not the same as “having the disease if you test positive”. To some this is mere semantics or subterfuge -- and indeed, much of probability can seem like smoke and mirrors, like the Monty Hall Problem -- but trust me it is not. Strogatz provides another example:

Perhaps the most pulse-quickening topic of all is “conditional probability” — the probability that some event A happens, given (or “conditional” upon) the occurrence of some other event B. It’s a slippery concept, easily conflated with the probability of B given A. They’re not the same, but you have to concentrate to see why. For example, consider the following word problem.

Before going on vacation for a week, you ask your spacey friend to water your ailing plant. Without water, the plant has a 90 percent chance of dying. Even with proper watering, it has a 20 percent chance of dying. And the probability that your friend will forget to water it is 30 percent. (a) What’s the chance that your plant will survive the week? (b) If it’s dead when you return, what’s the chance that your friend forgot to water it? (c) If your friend forgot to water it, what’s the chance it’ll be dead when you return?

I am too tired to give a detailed answer; moreover, conditional probability is just one concept in probability. There are plenty others, and this semester I often felt like I've stumbled upon a treasure trove of delightful ideas. Even this week I was discovering some that I had glossed over as a student. Someday, I will write extended pieces on what I have learned and how they apply to common situations.

Meanwhile, for those of you who would like to be tested, here are a couple of questions I asked in my exams -- up to the challenge? The first one (credit Leonard Mlodinow's The Drunkard's Walk) is easier than the second; it does not need any prior knowledge of probability.

a. Two students were partying in another state the day before their final chemistry exam. They got back only after the exam was over. However, they made up an excuse. They lied to the professor that they had a flat tire while returning and asked if they could take a make-up test. The professor agreed, wrote out a test, and sent the two students to separate rooms to take it. The only question on the test, worth 100 points, was: “Which tire was it?”

What is the probability that both students will give the same answer?

b. Suppose you toss a coin once and roll a die 4 times (these are two independent sets of experiments). Success in a coin-toss is getting a heads, while success in a die roll is getting a 5 or a 6. What is the probability that the number of successes in the coin toss equals the number of successes in the 4 die rolls?

Socialism in ant colonies and its lack in human societies: E.O. Wilson's perspectives

I recently chanced upon an old, 1997 interview of the famous biologist Edward Wilson. Wilson is known for his work on ant societies and in the interview he provides some good insights. Ant societies are well and truly socialist -- why so and why not human societies? The answer might lie in the differences in reproductive abilities. Long excerpts below:

There are about 9.500 known species of ants, many of whom you studied, but there is only one species of Homo. Why?

I think I have the answer for that. That is because we are so big. We are giant animals. The bigger the animal, the larger the territory and home range that the animal needs. Ant-species, consisting of very tiny organisms, can divide the environment up very finely. You can have one species that lives only in hollow twigs at the tops of trees, another species that lives under the bark, and yet another species that lives on the ground. Human beings, being giant animals and particularly being partly carnivorous, cannot divide the environment up finely among different Homo-species. There have been episodes in which there were multiple hominid-species, probably two or three species of Australopithecus, co-existing perhaps with the earliest Homo. But it is evidently the tendency of hominid species and particularly of Homo to eradicate any rivals. It is a widespread idea among anthropologists that when Homo sapiens came out of Africa into southern Europe about a hundred-thousand years ago, it proceeded to eliminate Homo neandertalensis, which was a native European species that had survived very well along the fringe of the advancing glacier.

You write that ants often share food among themselves. Why, and how did you find out?

Back in the fifties Tom Eisner, a colleague of mine, and I did I believe the first experiments tracing radio-active label led sugar-water through colonies of ants. We were able to estimate the rate at which the food was exchanged, and the volume that was exchanged. Not only do many colonies exchange food with fanatic dedication, but in the colonies of many ant species the workers regurgitate food back and forth at an extraordinarily high rate. Now we understand that the result of this is that at any given time, all the workers have roughly the same food-content in their stomach. It is sort of a social stomach. So that an ant is informed of the status of a colony by the content of its own stomach. It therefore knows what it should be doing for the colony. If you only had a small number of extremely well-fed ants and the rest were hungry, the workers would go out hunting for more food, whereas in fact it might be a bad time to hunt for food.

Why doesn't this sort of communism exist among humans?

What I like to say is that Karl Marx was right, socialism works, it is just that he had the wrong species. Why doesn't it work in humans? Because we have reproductive independence, and we get maximum Darwinian fitness by looking after our own survival and having our own offspring. The great success of the social insects is that the success of the individual genes are invested in the success of the colony as a whole, and especially in the reproduction of the queen, and thus through her the reproduction of new colonies.

This was I think one of the main contributions of the idea of kin-selection. We now understand quite well why most species of social insects have sterile workers, and therefore can have communist-like systems. In which the colony is all, the individual is only a part of the colony, and the success of the whole community is what counts far above the success of the individual. The behavior of the individual social insect evolved with reference to what it contributes to the community, whereas the genetic fitness of a human being depends on how well it can individually use the society. We have become insect-like only by extreme contractual arrangements.

You write that a major difference between humans and ants is that we send our young men to war, while they send their old females. Why is that?

Well first of all, all the worker-ants are female. In the bee, ant and wasp-societies sisters are extremely closely related to one another, and therefore it pays to be altruistic toward sisters, whereas brothers do not benefit by giving anything to sisters. So the females are the ones who are fanatically devoted to one another.

Why are they old? Once again it comes down to this matter of what is best for the colony. As the workers grow older, they put more and more of their time outside, and as they become quite old or injured or sick, they spend their time either outside of the colony or right at the edge. The advantage of this is that the individuals that are going to die soon anyway, having already performed a lot of services, are the individuals that sacrifice themselves. It is the cheapest for the colony.

Whereas in humans, not only are the young males the strongest, but by being mammals in a competitive society young males tend to be greater risk-takers, braver and more adventurous. They are moving up in the ladder of status, rank, recognition, and power. And to be a member of the warrior-class when it is needed, has always been a rapid way of moving up. So that appears to be the main reason why we send young men out, and they are willing to go.

Perelman and the Poincaré Conjecture

A riveting account of the life and mathematical achievements of the recluse Grigory (Grisha) Perelman, who recently cracked the Poincaré Conjecture:

Masha Gessen’s Perfct Rigor is a fascinating biography of Grigory (Grisha) Perelman, the fearsomely brilliant and notoriously antisocial Russian mathematician. Perelman proved the Poincaré Conjecture, one of mathematics’ most important and intractable problems, in 2002—almost a century after it was first posed, and just two years after the Clay Mathematics Institute offered a one-million-dollar prize for its solution.

[...]

Up until March of this year, there remained one more chapter to the Perelman saga. Would he accept the one-million-dollar prize promised by the Clay Mathematics Institute for solving one of the seven so-called Millennium Problems? While the rules say that a proof must appear in a peer-reviewed mathematics journal (not just in an Internet posting), the mathematicians mentioned above have published papers in such journals expounding and amplifying the proof. Surely Perelman deserves the prize, which he was finally and officially offered on March 18.

Five days later, on March 23, Perelman rejected the Clay prize. He reportedly said through the closed door to his spartan apartment, “I have all I want.” The comments he made after rejecting the Fields Medal probably reflect his present state of mind as well:

"I don’t want to be on display like an animal in a zoo. I’m not a hero of mathematics. I’m not even that successful. That is why I don’t want to have everybody looking at me."

Some might argue that monetary awards for mathematical work are inappropriate, or that the Poincaré Conjecture is of little practical value and not worth the one-million-dollar prize. The aesthetic and epistemic value of the proof is priceless, however, and it may eventually yield more earthly consequences as well. As for the size of the award—how many no-name hacks are there on Wall Street who make a million dollars or more not just once but every year, and contribute exactly what? Whether Perelman has practical need for the money or not, he could use it to help support his mother or mathematicians of his liking, or to advance the kind of education conceived by Andrei Kolmogorov, or for some purpose only he could imagine. Reconsider your decision, Grisha.

On Kim Plofker's Mathematics in India

That the concept of zero and the now widely used, indispensable decimal numeric system (imprecisely called Arabic numerals) came from India is old news -- a piece of trivia circulated often enough to have little or no surprise value. There is more, much more, to ancient Indian mathematics than these iconic contributions. Though I am trained in the quantitative sciences, I learned all of it – linear algebra, the theory of probability, and combinatorics – from the classrooms and labs of US universities, and very little from India. So it is only appropriate – though also ironic in another way – that the knowledge of ancient India should be made available to me through the painstaking research of a Western historian of mathematics, Kim Plofker.

Plofker has plowed through a range of Indian texts, beginning from the Vedic period – that’s three thousand years ago – to the eighteenth century to produce Mathematics in India. Hers is an achievement as much of linguistics, translation and history as of mathematics. The book sits on my desk, and there it shall be for some years, gathering dust, as I dip in only occasionally. It’s not the type that can be easily read from cover to cover – no book of mathematics is – but Plofker tries her best to make terms and concepts accessible.

Luckily, David Mumford, winner of the Fields Medal – the most prestigious prize in mathematics – has written a six-page essay on the book, which captures, concisely, the major achievements of Indian mathematics. There is the use of Pythagoras’ famous theorem in the construction of pillars, some centuries before the Greek philosopher is said to have postulated it in fifth century BC; Pāṇini’s rules of Sanskrit grammar and recursion, which “without exaggeration…anticipated the basic ideas of modern computer science”; Pingala, whose study of Sanskrit verses led to the binary notation and the development of Pascal’s famous triangle, useful in the calculation of binomial coefficients (which, coincidentally, is what I am teaching now); and Madhava of Sangamagramma (circa 14th century), the genius of the Kerala School, who contributed along with others, to "the discoveries of the power series expansions of arctangent, sine, and cosine" (a text on this in Malayalam has survived).

But what interested me most was the applied orientation of Indian mathematics. Like the ancient Mexicans, who designed sophisticated calendars (and who also used the concept of zero, probably earlier than the Indians did, though such rat races about who did what first are useless beyond a point), the mathematicians of India were spurred by the questions of astronomy. But the applied orientation goes even further than that. Mumford writes:

"It is important to recognize two essential differences here between the Indian approach and that of the Greeks. First of all, whereas Eudoxus, Euclid, and many other Greek mathematicians created pure mathematics, devoid of any actual numbers and based especially on their invention of indirect reductio ad absurdum arguments, the Indians were primarily applied mathematicians focused on finding algorithms for astronomical predictions and philosophically predisposed to reject indirect arguments. In fact, Buddhists and Jains created what is now called Belnap’s four-valued logic claiming that assertions can be true, false, neither, or both. The Indian mathematics tradition consistently looked for constructive arguments and justifications and numerical algorithms [Mumford's italics]. So whereas Euclid’s Elements was embraced by Islamic mathematicians and by the Chinese when Matteo Ricci translated it in 1607, it simply didn’t fit with the Indian way of viewing math. In fact, there is no evidence that it reached India before the eighteenth century."

This is particularly pleasing to me, because my own research, coincidentally, is about using mathematics in computationally feasible ways for various applications, rather than basking in the beauty and abstraction of theorems. (I will admit, however, that I was once obsessed with writing a paper that had only theorems and proofs in it; I did manage something, but only by borrowing significantly from the work of others; and still, months of edits await the paper before it can find its way to print.)

What might be an example of this “applied” orientation? Mumford writes of the “the discovery of the formula for the area and volume of the sphere by Bhaskara II” (circa 12th century):

“Essentially, he [Bhaskara II] rediscovered the derivation found in Archimedes’ On the Sphere and the Cylinder I. That is, he sliced the surface of the sphere by equally spaced lines of latitude and, using this, reduced the calculation of the area to the integral of sine. Now, he knew that cosine differences were sines but, startlingly, he integrates sine by summing his tables! He seems well aware that this is approximate and that a limiting argument is needed but this is implicit in his work. My belief is that, given his applied orientation, this was the more convincing argument. In any case, the argument using the discrete fundamental theorem of calculus is given a few centuries later by the Kerala school, where one also finds explicit statements on the need for a limiting process, like: “The greater the number [of subdivisions of an arc], the more accurate the circumference [given by the length of the inscribed polygon]” and “Here the arc segment has to be imagined to be as small as one wants. . . [but] since one has to explain [it] in a certain [definite] way, [I] have said [so far] that a quadrant has twenty-four chords.”

One of the delightful bits in the excerpt is the choice of “twenty-four chords” – it implies a casual, intuitive approach, yet the same is preceded by knowledge of what needs to be done to achieve exactness. That’s the essence of a “heuristic” or an approximation, which engineers use all the time.

Finally, the closing paragraph of Mumford’s essay:

It is high time that the full story of Indian mathematics from Vedic times through 1600 became generally known. I am not minimizing the genius of the Greeks and their wonderful invention of pure mathematics, but other peoples have been doing math in different ways, and they have often attained the same goals independently. Rigorous mathematics in the Greek style should not be seen as the only way to gain mathematical knowledge. In India, where concrete applications were never far from theory, justifications were more informal and mostly verbal rather than written. One should also recall that the European Enlightenment was an orgy of correct and important but semirigorous math in which Greek ideals were forgotten. The recent episodes with deep mathematics flowing from quantum field and string theory teach us the same lesson: that the muse of mathematics can be wooed in many different ways and her secrets teased out of her. And so they were in India: read this book to learn more of this wonderful story!

The beauty of mathematics

Steven Strogatz's column on mathematics -- the first of many to come -- in the New York Times:

[Numbers] apparently exist in some sort of Platonic realm, a level above reality. In that respect they are more like other lofty concepts (e.g., truth and justice), and less like the ordinary objects of daily life. Upon further reflection, their philosophical status becomes even murkier. Where exactly do numbers come from? Did humanity invent them? Or discover them?

A further subtlety is that numbers (and all mathematical ideas, for that matter) have lives of their own. We can’t control them. Even though they exist in our minds, once we decide what we mean by them we have no say in how they behave. They obey certain laws and have certain properties, personalities, and ways of combining with one another, and there’s nothing we can do about it except watch and try to understand. In that sense they are eerily reminiscent of atoms and stars, the things of this world, which are likewise subject to laws beyond our control … except that those things exist outside our heads.

This dual aspect of numbers — as part- heaven, and part- earth — is perhaps the most paradoxical thing about them, and the feature that makes them so useful. It is what the physicist Eugene Wigner had in mind when he wrote of “the unreasonable effectiveness of mathematics in the natural sciences.”

Teaching probability

This semester I am teaching an undergraduate introductory class on probability. I don’t typically announce my courses here, but teaching probability is a special enough task to deserve mention -- for me at least.

As a high school student, I used to dread questions about blue, black and red balls drawn at random from an opaque box. The typical question went like this: if the first three balls are blue, what is the chance a black one will be next? The initial questions were innocuous enough, but they quickly got complicated. They also tested your ability to count – to figure the number of permutations or combinations, without which you couldn't answer. At the incredibly difficult mathematics examination for admission to the prestigious Indian Institutes of Technology (IITs), there were quite a few of these counting questions. Let’s just say that I did not even attempt them.

College contributed nothing to my knowledge about probability (college, to be frank, was a four year vacation and I have no regrets). It was only during graduate school, where I took a number of statistics courses, that I was introduced to the mathematics of randomness. And over the last few years, much of my research has involved probability models – some very sophisticated ones at that, thanks to my colleagues who have majors in math and physics. Even now, my early lack of aptitude for the field and poor undergraduate training comes back to haunt me.

But there’s no better way to drive insecurities away than by teaching. The cliché that the best way to learn is to teach is very, very true. Which is why I am excited about my class this semester. The material itself is not difficult, since it’s an undergraduate class. But even the simplest topics in probability can cause confusion; and what better way to tackle them than at the foundational level.

Last week, I went to check my classroom. It was late in the afternoon and the campus was empty. The classroom was in the Chemistry building, and had tiered, auditorium style seating; the seats were bright red. It was a grand setting, and I could imagine it bustling with sophomore year students -- there are ninety students enrolled at this time. And for the first time I’ll be using what is called the PRS clicker system: I will ask students multiple choice questions during each lecture. Students will choose what they think is the right answer on their personal clickers (they’ll press a button, in other words). A slide will immediately display how many clicked each option, as in a game show. Wouldn’t it be fascinating to have this type of instant interaction – and, importantly, feedback on how well the class is understanding the material – especially in a class about probability, as slippery a topic as any in the whole of mathematics?

Fancy embellishments aside, the real grandness of probability lies in its elusive, mysterious quality. Everything we do in life is governed by chance. Our instinct toward religion partly stems from the uncertainty that always seems to stalk our futures. The theory of probability lends mathematical formalism to uncertainty. But it also makes us think of some very vexing questions: What does it mean when we say things are truly random? Why do things turn out the way they do?

That’s the charm of it: it’s more philosophy than mathematics.

Where did the time go?

How the brain processes the passing of time is a mystery. There is of course the objective passing of time, but our perception of it is very different. Some days can seem like months, but at other times weeks can slip by rather quickly. The last twenty days, when I traveled to new places (more on that in the coming weeks), seemed like a long time – two months, say – probably because of the number of things I did within a short period. Here’s a recent article that discusses new research on this topic. Excerpt:

In fact, scientists are not sure how the brain tracks time. One theory holds that it has a cluster of cells specialized to count off intervals of time; another that a wide array of neural processes act as an internal clock.

Either way, studies find, this biological pacemaker has a poor grasp of longer intervals. Time does seem to slow to a trickle during an empty afternoon and race when the brain is engrossed in challenging work. Stimulants, including caffeine, tend to make people feel as if time is passing faster; complex jobs, like doing taxes, can seem to drag on longer than they actually do.

And emotional events — a breakup, a promotion, a transformative trip abroad — tend to be perceived as more recent than they actually are, by months or even years.

In short, some psychologists say, the findings support the philosopher Martin Heidegger’s observation that time “persists merely as a consequence of the events taking place in it.”

Now researchers are finding that the reverse may also be true: if very few events come to mind, then the perception of time does not persist; the brain telescopes the interval that has passed. [link]

This year will be tenth that I have been abroad in the United States -- I came to study in the United States in August 2000, a few days before my twenty first birthday. A decade seems to have slipped by quickly, but then if I think of what I have experienced in that time, ten years seems about right.

What is the nature of the self?

The physician and neuroscientist Vilayannur Ramachandran explores this fundamental, still unsolved philosophical conundrum in the last chapter of his book Phantoms in the Brain (co-written in the late 1990s with Sandra Blakeslee). This is how the chapter begins:

In the first half of the next century science will confront its greatest challenge in trying to answer a question that has been steeped in mysticism and metaphysics for millennia. What is the true nature of self? As someone who was born in Indian and raised in the Hindu tradition, I was taught that the concept of the self – the “I” within me that is aloof from the universe and engages in lofty inspection of the world around me – is an illusion, a veil called maya. The search for enlightenment, I was told, consists of lifting this veil and realizing that you are really “One with the cosmos.” Ironically, after extensive training in Western medicine and more than fifteen years of research on neurological patients and visual illusions, I have come to realize that there is much truth in this view – that the notion of a single unified self “inhabiting” the brain may indeed be an illusion. Everything I have learned from the intensive study of both normal people and patients who have sustained damage to various parts of their brains points to an unsettling notion: that you create your own “reality” from mere fragments of information, that what you “see” is a reliable – but not always accurate – representation of what exists in the world, that you are completely unaware of the vast majority of events going on in your brain. Indeed, most of your actions are carried out by a host of unconscious zombies who exist in peaceful harmony along with you (the “person”) inside your body!

Nevertheless, many people find it disturbing that all the richness of our mental life – all our thoughts, feelings, emotions, even what we regard as our intimate selves – arises entirely from the activity of little wisps of protoplasm in the brain. How is this possible? How could something as deeply mysterious as consciousness emerge from a chunk of meant inside the skull? The problem of mind and matter, substance and spirit, illusion and reality, has been a major preoccupation of both Western and Eastern philosophy for millennia, but very little of lasting value has emerged. As the British psychologist Stuart Sutherland has said, “Consciousness is a fascinating but elusive phenomenon: it is impossible to specify what it is, what it does, or why it evolved. Nothing worth reading has been written on it.”

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Why this post suddenly? Because I've been thinking about the idea of "soul", and whether we are more than just an aggregation of the the physical body, the brain and its interior functions. This soul or, less metaphysically, "consciousness" is what marks us out, but how is it linked to the body? Some scientists are beginning to tackle that question, which is what prompted this post.

Introducing: Operations Research

At heart, I am a humanities person; that is why this blog has existed for as long it has. But I do lead another, very different life that consumes most of my waking time. I am an academic in a field called “operations research” – a baffling term for those unaware of its existence. Briefly, operations research can be described as “the science of efficiency”, or “the science of planning well”; the most popular version, though, is the glib-sounding “the science of better”.

Still puzzled? Well, let me try again, this time with an analogy.

We are surrounded by technological marvels. It seems magical – to me at least – that a plane carrying hundreds of passengers and tons of luggage, actually manages to take flight; that there are such things as wireless phones; that there is a large, scattered yet miraculously unified network called the “Internet”. Amazing right? Each of these applications is possible because of engineering, which makes clever use of the underlying science, be it fluid dynamics, signal processing, or fiber optics. Such engineering is not always obvious, but the lay person is aware that there are specialists -- aerospace engineers, computer scientists, electrical engineers to name just a few -- who make these things work.

In the same way, do you wonder how your FedEx package from the Philippines arrived without delay to the small Midwestern town you live in; how the Netflix movie you ordered gets to your address exactly on the day their email claimed; how large airports, such as Heathrow and JFK, manage their flights, schedules, and air traffic? We take these systems for granted, but they work because they are engineered. This type of systems level engineering – the science of allocation and scheduling in the face of uncertainties and the fluctuating dynamics of supply and demand – is called operations research. In business schools it is called management science. Since it is a less tangible kind of engineering, the lay person is generally unaware of it.

You might argue that many systems are rarely well managed. What’s in a science that produces long lines and sapping delays? True, systems may be dysfunctional because of bad planning but this is not unique to operations research. A mechanical problem – arguably caused by the traditional “nuts and bolts” engineer – can stop a flight from taking off as well. In fact, an operationally conscious airline will have a contingency schedule that minimizes the traveler’s disruption in case of a cancellation. Think of all the flight groundings and cancellations that happened on and post 9/11. Have we given close thought to what it took to bring everything back to normal?

Operations research is a mongrel field. Like other engineers, the operations researcher uses mathematical methods, but she also may dabble in statistics, economics, and computer science. She will also need knowledge of the domain she is working in; and importantly, if her domain involves people, she will need to know that people do not behave as rigidly or rationally as her math models assume. This mongrel quality of the field makes it breathtakingly versatile – applications have advanced well beyond the “operations” realm and have entered even areas such as designing beam angles for radiation therapy. The flip side of the coin, however, is that some think of it as an “anything-goes” field with no real identity.

My work is in healthcare operations research. I look at how medical practices can provide timely care while trying to rein in costs. This coincides with the ongoing upheaval in the US healthcare system. Cost and coverage are major issues and they have the power throw askew the balance of supply and demand and influence the quality and timeliness of care. For example, emergency departments in the United States – one setting which I study in my research – experienced a 32% increase in demand over the last decade. The number annual ED visits in the US went up from 90 million in 1996 to 119 million in 2006. This has led to crowded conditions, especially during late afternoons and evenings. Can better staffing, improved coordination of processes alleviate the long wait times of patients? Perhaps -- at least that is what my hypothesis is.

I have also recently discovered – to my great delight – the many ways in which operations research can intersect with the humanities. Let me list a few examples. The resettlement of refugee farmers in India after the partition of the Indian subcontinent in 1947 was a difficult problem in every sense. Nearly a million people had to be allotted new land, and the partition had been extremely violent. Yet it was successfully done, without computers: a classic example of hands-on operations research in which people management and administrative organization are the main skills. The person who led it was Sardar Tarlok Singh of the Indian Civil Service, a graduate of the London School of Economics.

More recently a Markov model (in more plain terms, a probability model) was used to identify syntactic patterns in the as yet undeciphered Indus script of nearly 3000-3500 years ago -- another unconventional application that has nothing to do with “operations”. I am also fascinated by how humanitarian organizations – the UN World Food Program (WFP), Medicines Sans Frontiers – deliver their services in resource constrained settings; understanding why FEMA messed up post-Katrina; and how the dreaded LTTE efficiently coordinated rescue operations post-Tsunami in Sri Lanka.

In short, there’s plenty to learn and explore.

This post comes as I travel to San Diego for the annual meeting of the Institute of Operations Research and Management Science (INFORMS09). Nearly 4000 people will attend the conference; it’s a great way to catch up with friends from graduate school and make new friends. I was also invited to be one of their twelve official bloggers (that gives me an excuse to point to this post there).

This isn’t the first time I’ve mentioned operations research. Here are a few earlier posts: My Adventures During a Queuing Study; Queues and Illegal Immigration; A Visit to an Emergency Room; The Mathematics of Matching Kidneys.

Climate change cuts both ways

Jared Diamond surveys the impact of climate change research on three roughly contemporaneous civilizations in the most recent issue of Nature (subscription needed): Maya, Khmer, and Inca. The first two might have declined because of environmental changes, but the Incas, who built their empire in high altitudes, benefited from it. We are talking of the period between the 9th and 12th centuries CE. Excerpts:

From time to time, separate archaeological projects on different societies end up by suggesting common themes to events in the ancient world. Thus, two new studies point to parallels between the collapse of cities on opposite sides of the globe — the southern lowland Maya cities in Central America, and Angkor, the centre of the Khmer empire in what is now Cambodia. These parallels include the effects of climate change, which hurt both the Maya and the Khmer. By contrast, as a third report indicates, climate change seems to have benefited another ancient civilization, the Incas of South America.

[...]

This reminds us that climate can change in either direction, and that in the past such change has variously helped or hurt human societies. But human overexploitation of environmental resources never helps. As Lentz and Hockaday note, "Tikal's inhabitants became trapped in a positive feedback loop wherein increasing demands on a shrinking resource base ultimately exceeded the carrying capacity of their immediate environs. The ecological lessons learned from the Late Classic Maya, with their meteoric population increase accompanied by environmental overstretch, serve as a distant mirror for our own cultural trajectory." Amen.

The same Nature issue also has articles on the genetic history of Indians -- a loaded issue, no doubt. For an abstract of the study, see here.

I'll try to avoid subscription only links in the future -- my apologies to readers.

The women scientists of India

Asha Gopinathan reviews Lilavati's Daughters: The Women Scientists of India in Nature (subscription may be required):

A collection of 98 short biographies, the book stems from a project initiated by the Women in Science panel of the Indian Academy of Sciences, Bangalore, to provide young girls with inspiring role models (see http://www.ias.ac.in/womeninscience). The diverse personal stories span many disciplines and regions of India — and are inspiring.

The earliest chronological entry is for Anandibai Joshi, the first Indian woman to go abroad and study to become a doctor. From 1883 to 1886 she attended the Women's Medical College in Philadelphia and was awarded an MD degree for her thesis Obstetrics Among Aryan Hindoos. Unfortunately, she contracted tuberculosis and had to return to India. She received no treatment: Western doctors refused to treat a brown woman and Indian doctors would not help her because she had broken societal rules. Joshi died in 1887 at 22 years of age.

[...]

Many of those highlighted were the first to break into male-dominated professions: Asima Chatterjee was the first Indian woman to be awarded a DSc; E. K. Janaki Ammal was elected a fellow of the Indian Academy of Sciences the year it was founded; Kamala Sohonie was the first female director of the Institute of Science, Mumbai; and Bimla Buti is a former director of plasma physics at the International Centre for Theoretical Physics in Trieste, Italy.

It is interesting that many of these women scientists came from ordinary middle-class families. Most grew up not in the nation's big cities but in rural areas, where getting an education in any discipline, let alone in science, is difficult. In rural Punjab, mathematician R. J. Hans-Gill had to pretend to be a boy and wear a turban to attend school — a secret that was kept between her family and the headmaster. Biologist Chitra Mandal was accompanied to school in rural Bengal by her grandmother because the teacher would not let the four-year-old in without someone to look after her.

Ma for the brain, Pa for food and sex

Maternal and paternal genes don't contribute equally to the child's genetic makeup, this Scientific American article suggests; they actually compete to silence the other's influence. This is pretty normal, but if the process goes awry, neurological disorders result. And here's the interesting bit: apparently mothers are more responsible for cerebral stuff -- stuff to do with language, thought and complex activities -- while fathers are more responsible for pleasures of the senses: eating and mating.

Needless to say, all this is emerging knowledge, and is to be taken cautiously. But the next time you meet your parents, you may look at them strangely now that you have read the article. Ah, so this is why, you will secretly think, I have this strange, unmentionable fetish; this is why I love jalebis and candy; this is why I am poor in music and math!

Key concepts from the article [link]:

1. When passing on DNA to their offspring, mothers silence certain genes, and fathers silence others. These imprinted genes usually result in a balanced, healthy brain, but when the process goes awry, neurological disorders can result.

2. Imprinting errors are responsible for rare disorders such as Angelman and Prader-Willi syndromes, and some scientists are beginning to think imprinting might be implicated in more common illnesses such as autism and schizophrenia.

3. Even typical brains are the result of asymmetric contributions from Mom and Dad. Higher cognitive function seems to be disproportionately controlled by Mom’s genes, whereas the drive to eat and mate is influenced by Dad’s.

Does language shape our worldview?

Lera Boroditsky thinks so. And she presents a fascinating example:

Follow me to Pormpuraaw, a small Aboriginal community on the western edge of Cape York, in northern Australia. I came here because of the way the locals, the Kuuk Thaayorre, talk about space. Instead of words like "right," "left," "forward," and "back," which, as commonly used in English, define space relative to an observer, the Kuuk Thaayorre, like many other Aboriginal groups, use cardinal-direction terms — north, south, east, and west — to define space.1 This is done at all scales, which means you have to say things like "There's an ant on your southeast leg" or "Move the cup to the north northwest a little bit." One obvious consequence of speaking such a language is that you have to stay oriented at all times, or else you cannot speak properly. The normal greeting in Kuuk Thaayorre is "Where are you going?" and the answer should be something like " Southsoutheast, in the middle distance." If you don't know which way you're facing, you can't even get past "Hello."

The result is a profound difference in navigational ability and spatial knowledge between speakers of languages that rely primarily on absolute reference frames (like Kuuk Thaayorre) and languages that rely on relative reference frames (like English).2 Simply put, speakers of languages like Kuuk Thaayorre are much better than English speakers at staying oriented and keeping track of where they are, even in unfamiliar landscapes or inside unfamiliar buildings. What enables them — in fact, forces them — to do this is their language. Having their attention trained in this way equips them to perform navigational feats once thought beyond human capabilities. Because space is such a fundamental domain of thought, differences in how people think about space don't end there. People rely on their spatial knowledge to build other, more complex, more abstract representations. Representations of such things as time, number, musical pitch, kinship relations, morality, and emotions have been shown to depend on how we think about space. So if the Kuuk Thaayorre think differently about space, do they also think differently about other things, like time? This is what my collaborator Alice Gaby and I came to Pormpuraaw to find out.

To test this idea, we gave people sets of pictures that showed some kind of temporal progression (e.g., pictures of a man aging, or a crocodile growing, or a banana being eaten). Their job was to arrange the shuffled photos on the ground to show the correct temporal order. We tested each person in two separate sittings, each time facing in a different cardinal direction. If you ask English speakers to do this, they'll arrange the cards so that time proceeds from left to right. Hebrew speakers will tend to lay out the cards from right to left, showing that writing direction in a language plays a role.3 So what about folks like the Kuuk Thaayorre, who don't use words like "left" and "right"? What will they do?

The Kuuk Thaayorre did not arrange the cards more often from left to right than from right to left, nor more toward or away from the body. But their arrangements were not random: there was a pattern, just a different one from that of English speakers. Instead of arranging time from left to right, they arranged it from east to west. That is, when they were seated facing south, the cards went left to right. When they faced north, the cards went from right to left. When they faced east, the cards came toward the body and so on. This was true even though we never told any of our subjects which direction they faced. The Kuuk Thaayorre not only knew that already (usually much better than I did), but they also spontaneously used this spatial orientation to construct their representations of time.

The mathematics of matching kidneys

“Kidneys are unusual organs,” says the blogger and academic Michael Trick, “We are given two, though we can get by with one. So, unlike the heart, say, we each have a 'spare' that we can donate to others.” Indeed, for patients suffering from kidney failure – known more technically as end stage renal disease – one option is transplantation: taking somebody else’s healthy kidney and grafting it in the patient. In the United States, there are estimated to be more than 60,000 patients waiting for such transplants to happen. Kidneys of deceased as well as living donors can be used, and both approaches have their pros and cons. But transplants involving living donors are increasing – in the United States they are 47% of all transplants.

If a transplant involves a living donor, then who might such a donor be? Perhaps someone close to the patient – a sister, a relative, a friend. But it turns out you can’t just use any kidney. You can accept a kidney only if your blood group and the donor’s are compatible. An O recipient can accept only O kidneys; A can accept O and A; B can accept O and B; and AB can accept any kidney. And there may be other medical reasons and patient preferences too that may disallow certain transplants.

So, from the above discussion, you may end up with an incompatible donor-recipient pair, and this frequently happens in practice. But this is not a dead-end; what you can do is find another incompatible donor-recipient pair, such that the blood group of the donor in the first pair is compatible with that of the recipient in the second pair, and vice-versa. If this is the case, an exchange can happen, as shown below.

Figure 1 (Picture from here)

Both pairs are now set. Simple enough. But if you look at this from the larger, societal point of view, the problem is more nuanced. There may be thousands of such incompatible donor-recipient pairs in the waiting list. If you just go from the point of view of one pair, you are likely to find a match, but you may end up ruining options for others.

How can this happen? Well, let’s look at this simple example involving just five pairs. Each pair is represented using a node, while the edges indicate that an exchange is possible. So an exchange of the type shown in figure 1 is possible between pairs 1 and 2; 2 and 3; 2 and 4; 4 and 5. Since there is no edge between 1 and 5, the pairs cannot exchange – this might be, say, because the donor of 1 belongs to blood group B but the recipient of 5 belongs to O, ruling out an exchange.

Figure 2 (mine)

Now let’s look at possible solutions. If 2 decides to exchange with 4, then only one match is possible. Three other pairs (1, 3 and 5) will have to wait for future pairs to enter the list – until then, the recipient in each pair will be on dialysis, which is extremely expensive. But there exists a better solution: let 1 exchange with 2 and let 4 exchange with 5. Four pairs now get matches, and only one pair has to wait. Thus the latter solution maximizes the number of matches in the graph, while the former solution leaves many dissatisfied.

Imagine now that there are thousands of pairs with myriad linkages – as there indeed are in reality. Can you visually think of a graph of the type above and come up with a solution? Clearly, it’s not feasible – unless we develop the superhuman ability to delineate complex and dense graphs in our minds and traverse them. Fortunately, though, the matching of kidneys turns out to be equivalent to a well studied problem in graph theory called maximum matching. Even better, there exists an algorithm that will give a solution in quick time no matter how large your graph is. Got a thousand pairs in your list? No problem – you’ll get a solution in a few seconds! The algorithm was first proposed way back in 1965, in a groundbreaking paper by Jack Edmonds. Edmonds clearly was not into sleep-inducing technical titles that are the norm in most publications: his paper is stylishly called Paths, Trees and Flowers [1] and can be accessed easily online.

Thus did the solution to a puzzle in graph theory become relevant for a pressing medical problem of today – and it is not always possible to see such happy marriages. Not that this one is perfect: the kidney matching problem in reality is not as simple as the maximum matching problem of graph theory. Medical problems – especially transplantations – are riddled with ethical, political, logistical and cost issues. Despite this, the kidney matching problem (or the paired donation problem) is something to be celebrated. It’s a neat, easy-to-understand application, and its importance can’t be overstated.

Picture from here

The problem became known in the medical community due to a paper in the prestigious Journal of the American Medical Association (JAMA) [2]. Sommer Gentry and Dorry Segev were the principal researchers. If graph theory in an organ transplantation context seems like a unique marriage, then is it any surprise that it emerged from an actual marriage - between a mathematician and a transplant surgeon? Sommer is the mathematician; Dorry the surgeon. I met Sommer at a conference in Philadelphia last year, and chatted with her over lunch (which is how I became aware of the problem). She is currently at the US Naval Academy, while Dorry is a surgeon at John Hopkins; they live in Anapolis, near Baltimore.

But to return to the paper. There is an extensive discussion in it about the challenges that come up in kidney transplantations: national vs. regional matching, logistical issues, and how to deal with patients with greater need. The national vs. regional question is especially worth mentioning. Local and regional kidney donation programs already exist in the United States, but what if a national system was to be tried out? Clearly the availability of a larger pool of kidneys would mean more matches. But then travel and the cost of transporting organs becomes an issue. But here's the twist: the paper demonstrates that in the national system, the number of matches would increase and yet only 2.9% of the national pool would actually need to travel. Who would have guessed! But this is precisely the sort of counterintuitive insight that a mathematical model is capable of providing.

Finally, why have we discussed only 2-way exchanges so far? Indeed, we can do better. Let's consider three pairs. The donor of Pair 1 could donate to the recipient of Pair 2; the donor of Pair 2 then donates to the recipient of Pair 3; and lastly, to complete the cycle, the donor of Pair 3 donates to recipient of Pair 1. That's a 3-way exchange. Perhaps longer ones can be identified in a pool but what effect does the length of a cycle have on the number of matches in the overall pool? This is a fertile area of research, and some it has already been implemented. Recently, at the Johns Hopkins Hospital in Maryland, there was a six-way exchange – the largest of its kind – involving twelve people. And the cycle of six was completed because of an altruistic donor who was unrelated to the twelve people involved, yet gave away his/her kidney.

Indeed, if you are going to have an impact on twelve rather than two, wouldn’t you be more inclined to be altruistic?

References

[1] Paths, trees and Flowers, by Jack Edmonds, Canadian Journal of Mathematics (1965).

[2] Kidney paired donation and optimizing the use of live donor organs, Segev D., Gentry S., Warren D., Reeb B., and Montgomery R. Journal of the American Medical Association (2005).

The story of numbers

One of India’s greatest contributions to the world is the number system that everyone uses today. What the world knows today as Arabic numerals are really Indian numerals – including the controversial Zero. In the first millennium AD, they traveled from the Indian subcontinent westward to Baghdad, where the mathematician Musa Al Khwarizmi – who also initiated the field of algebra (al jabr) – wrote a treatise on them. At the time, Europe was using the cumbersome Roman numeral system. Watch this playful video that describes this history; watch how Indians used zeroes and ones to create stupendously large numbers.

(I should mention also that ancient Mexico also had its own sophisticated number system, and this system also included zero. Their inventions however are not always acknowledged in the history of mathematics - partly because history is not just Eurocentric, it is "Old-World centric".)

Video via Atanu. Also: An earlier post on the same topic; and the mysterious Ishango Bone of Africa.

A visit to an emergency room

No, nothing to be alarmed about: I did not visit as a patient. My research focuses on developing methods that can make healthcare run more efficiently, and I’ve just begun to explore how emergency room (ER) operations can be improved. For a country that is the leader in just about everything – especially medical research, technology and innovation – the United States has a lamentable health care delivery system. And nowhere is it more evident than in emergency rooms across the country. Patients, even patients who have had a stroke, may have to wait hours before getting care. Some wait seven to eight hours. In major cities, ambulances carrying patients to an emergency room are diverted to other emergency rooms, simply because there is no capacity and queues are long. (Queues again! Haven’t we talked about queues before?)

The ER I visited is in Baystate Medical Center, in Springfield, Massachusetts. In terms of volume, this is one of the largest in the country. About 110,000 patients use it each year; about 300 patients come to the ER every day, 80 of them brought by ambulances. Others just show up by car, accompanied by friends or relatives.

Some have ordinary ailments, like a cold or sore throat. Instead of going to visit a primary care doctor, they use the ER. They do this probably because they don’t have a doctor. And that in turn is probably because they don’t have insurance. The statistic that crops up in just about every major discussion about the US healthcare system is that there are about 45 million uninsured patients in the country – a colossally high number; indeed an unforgivable number if you compare with other developed countries. Massachusetts is a bit ahead of the curve and has tried to fix the problem, but other states lag.

So if you don’t have insurance, and if you have a medical condition, you end up using the ER and pay a huge bill. But even if you have insurance, you might use the ER because you could not obtain an appointment with your doctor. ERs cannot refuse care; they have to treat everyone who shows up, irrespective of whether the patient has a trivial condition or is uninsured.

ERs, thus, are a safety net; they soak up the consequences of inefficiencies whose root causes lie elsewhere.

____

At the Baystate ER, patients with minor ailments are sent to a Fast Track section. That way they do not interfere with the more critical patients who are sent to the main area. But the name Fast Track has become something of a joke. Waiting times for getting into Fast Track can be very long. So to pacify patients and ensure they don’t feel mocked, the Fast Track area was recently renamed the General Treatment section.

Needless to say, only the name has changed; the waiting times have not.

When I visited the Baystate ER, it was about 2 pm in the afternoon. It was crowded. Early mornings are the least busy hours; but by noon things start picking up. By late afternoon, early evening, the ER is packed. This too is a US-wide trend – and perhaps true worldwide as well.

In the waiting area, there were patients and their relatives and friends. A couple of the patients were in wheelchairs; they were elderly, clearly sick, and their faces had a resigned and faded look to them. Their faces told also of the passage of time: seconds had become minutes and minutes hours, yet they were still waiting. If sicker patients arrive, they tend to preferred, thus increasing the waits for less sick patients. But assessments of sickness are to some extent subjective, inevitably so.

The main emergency area – entered from the waiting area through double doors – was a world apart. It was a buzz of activity and felt surreal. Constant activity and motion: like a video on fast-forward. There was a central square, the inner portion of which consisted of staff working hastily with computers, records, paperwork. On the outside, doctors, nurses, assistants swirled around immobile beds with prostate patients. These beds are supposed to be in rooms, but to create capacity, beds had been added to the hallway. Monitors displayed constantly changing information: how much time each patient had been in the ER, whether the tests that had been ordered had returned, which resident or doctor was assigned to the patient. The charge nurse, who was in charge of operations, had tough decisions to make. Whom to admit next? Which nurse to assign to which patient? Should another bed be added to the already overcrowded hallway?

The staff, even though busy constantly attending to something, seemed cheerful enough; their cheer was much needed, considering the bleak faces of the patients.

Patients, once they are treated, are either discharged or admitted to the nearby Baystate Hospital. And here too there is a crunch. Hospital beds are a scarce resource, and generally there is no availability. So the patients continue to wait in ER beds, effectively denying beds to other patients waiting for hours for treatment in the waiting area. Such as the elderly patients I'd seen upon entering, waiting in wheelchairs and with tormented looks.

So it goes. Emergency rooms are not supposed to be pleasant places. The nurses and doctors who work there know there is no room for sentimentalism. Work just needs to be done. But ERs are also a barometer of the larger issues that ail a healthcare system. The US healthcare system is badly fragmented and inefficient; and a large part of the cost is borne by ERs.

The professor's webpage

is up. You'll find a picture of yours truly - with a silly smile - and a resume full of impossible-to-understand terms: combinatorial optimization, genetic algorithms and suchlike. Isn't that what academia is all about - parading the incomprehensible and the esoteric?

More seriously, I'll try to write in this space - which has focused on history, current affairs, literature and travel - about my research as well. If and when I write about my research, I promise to make it as accessible and readable as possible (this recent post, for instance, is related to one area that I study: queuing).

But if you still fall asleep...well that's not such a bad thing.