Hari Jagannathan Balasubramanian

Learning From the Frequency Illusion

First published at 3 Quarks Daily.

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A fire hydrant on my daily walk that I never noticed until recently.

In the long and evolving list of cognitive biases, the ‘frequency illusion’ feels most familiar: I’ve experienced it so many times that it seems almost ordinary. This is roughly how it works. First, you encounter something – an unusual word like ‘topology’, or the title of a new book or a movie – that makes you stop and notice. Then, in the days after, the same word or title crops up again and again in unrelated places, making it seem more frequent than it is (hence the name). A friend brings it up unprompted, or you unexpectedly see it at a museum exhibit. It’s not only about words or titles, of course: anything in your conscious experience – a sound, an image, a fragrance – that makes an impression can be a point of entry. Buy a new car and in the weeks that follow, you will likely start noticing others driving the same model.

The most wonderful thing about this illusion is that with each seemingly unplanned encounter there’s a thrill of recognition, a feeling that the universe is signaling to you. The rationalists among us, however, will point to a more mundane explanation: that our cognitive processes have simply been primed to notice or identify the word, image, or sound among all sensory experiences. The illusion works in concert with two other biases: selective attention, the act of focusing on certain things while excluding others; and confirmation bias, the tendency to seek evidence that supports one’s beliefs while overlooking evidence to the contrary.

The recognition that these are only tricks of the mind can be somewhat deflating. But the processes that decide what we pay attention to and what we ignore remain mysterious. Something can be frequent in my everyday experience – say, a fire hydrant that I walk past each day – yet I may not notice it at all for years. Or I might be only vaguely aware of the hydrant’s presence, as if it lives in the background of my conscious experience. Then one day, I ‘stumble’ upon it, as if I am seeing it for the first time. Details such as its shape, color, and peeling paint register in a way they never had before. From that point on, I will naturally notice fire hydrants elsewhere. But I am seeing what was already commonplace; the frequency is not an illusion.

So the more intriguing question is: Why do things that we overlook all the time, things that are hiding in plain sight, suddenly catch our attention one fine day? And what is it about our cognitive processes that filters out certain stimuli and emphasizes others? Certainly, there’s an element of chance that puts you in the right place and at the right time to experience a stimulus. And each time you find yourself in the same place, the experience is subtly different, and you notice something new (in the same way that reading a book again seems to highlight things we’d missed). There also seems to be an inner realignment: an increased interest or receptivity to the stimulus that was previously absent.

The stimulus doesn’t have to be something sensory. Almost every semester, while teaching concepts that I’ve gone over plenty of times before, some nuance that had been hiding in plain sight will bubble to the surface, and I’ll wonder: Why didn’t I think of this before? And many years ago, while starting a meditation practice, I remember being startled by chaotic thought patterns that ran rampant in my mind. But the thought patterns also felt familiar – the difference was that I’d never given them proper attention before.

The terms ‘illusion’ and ‘bias’ suggest that we should look past the synchronicities that feel meaningful to us. That’s certainly true – there’s always a risk of reading too much into illusory patterns and of slipping into echo chambers; and online recommendation algorithms only worsen these tendencies.

But when used in the context of enhancing one’s observation skills, the frequency illusion can lead to a constructive form of learning. It makes you ‘zoom in’ on one thing, so to speak, and as you encounter it repeatedly, something else captures your attention, and you zoom in on that. This process of moving from one thing to the next continues, and soon you are discovering and learning in an endless sequence. Endless because there isn’t a limit to the new things you can notice, even in very familiar settings. And because this process of learning happens at a leisurely pace and is driven by what naturally captures our interest, it is deeper and more lasting.

In my case, the frequency illusion has led to a decade and a half of ‘recreational ecology’ (a slight twist on ‘recreational biology’, a term used by the Stanford bioengineering professor Manu Prakash).

It started in the spring of 2010 — my third year in Amherst, Massachusetts — when I saw a male cardinal for the first time. Cardinals are among the most common birds in North America, so it was a classic case of noticing something that was already frequent. I didn’t know anything about birds back then, and I was wonder-struck by the beauty of the male cardinal: its redness, the patches of black around its beak and crest. That spring, I ran into cardinals all the time, and each time I felt as if I had access to a special secret. Soon, I started to see (and hear) other all-season, backyard species that, like cardinals, were hidden in plain sight. First gold finches, then blue jays, then woodpeckers, nuthatches, house finches, and so on and so forth. It felt as if a portal into nature had opened up.

Clockwise from top left: snapping turtle; a red trillium; monarch caterpillar on a milkweed; and a slug, the only gastropod I’ve ever seen.

This kind of sequential and serendipitous discovery resembles a concept I teach in my probability courses: a biased random walk on a graph where in each step you probabilistically jump from one state (also called a node or vertex) to another. With a large number of steps, you can end up in less-explored states of the graph.

My ecological random walks have led me to lesser-known birds (my favorite this year is the Blackburnian Warbler), but also to so much else: bobcats, phantom craneflies, snapping turtles, rare seasonal flowers like Pink Lady’s Slipper, ferns, lichens. Each discovery illuminates a tiny piece of a vast and unfathomable ecological jigsaw. The process continues even when I am traveling. Soon after I had become familiar with the belted kingfisher in Amherst, I ran into the riotously colorful white-throated kingfisher near my parents’ flat in Bangalore, India.

The simple act of paying attention to visual, auditory, and olfactory cues can take you far, but learning can also happen in other ways. A few weeks after reading Elizabeth Tova-Bailey’s The Sound of a Wild Snail Eating, I saw my first gastropod: not quite a snail, but a slug, its antennae quivering the wet asphalt of a parking lot (it still remains my only gastropod sighting). Often, reading something about a species can deepen the impact of observing it in the wild. The monarch butterfly is striking enough visually, but to know that it undertakes a seemingly impossible 2,000-mile overwintering journey from New England to central Mexico adds a different kind of wonder. I was so inspired that one winter I traveled to the forests of Michoacan to see millions of congregating butterflies.

(This coming together of the senses and the intellect reminds me of something the physicist Richard Feynman said. When an artist friend chided Feynman that scientific reductionism minimized the aesthetic beauty of a flower, Feynman disagreed and claimed that the opposite was true. The visual beauty was available to him too, and the scientific backstory – why the flower evolved colors, the fact that insects can also see colors and may even have an aesthetic sense – could only enhance “the excitement, the mystery and the awe of a flower.”)

One of the pleasures of learning in this way is the element of surprise: you can’t predict what will intrigue you next. This year, for instance, I am drawn to the towering transmission lines that run through state parks, carrying electricity from natural gas, nuclear, and hydroelectric plants scattered around New England. The lines run through a 50-meter-wide corridor that was hacked through dozens of miles of forest. This has created a unique ecology: an elongated clearing in a landscape otherwise dense with trees. The clearings are preferred by smaller bushes such as the mountain laurel, whose pink-and-white flowers bloom in June, and by prairie warblers, whose high-pitched song (heard only for a few weeks) always makes me pause.

Imposing, symmetrical, and extending far into the horizon like an infinite relay, the transmission lines bring a different kind of beauty to the landscape. I often found myself marveling at them during my hikes this year. From the tops of mountain peaks, I’ve used my binoculars to track them as they run like arteries through forests, towns, and substations. And now I am also paying attention to the smaller, T-shaped wooden poles – the capillaries of the network – that run through every street, carrying a tangle of cables and contraptions, connecting each home to the grid.

In the past, I seem to have tuned out these essentials of our infrastructure, possibly because I’d prioritized nature and rejected human-made things – what is called the ‘appeal to nature’ or ‘naturalistic’ fallacy. Maybe the hold of that fallacy has loosened somewhat. Or, the engineer in me is (finally!) starting to emerge. Whatever the reason, it feels like a welcome shift. The transmission lines have also led me to notice cell towers with their antenna arrays, the solar farms that seem to be popping up everywhere, and the fenced water stations that draw from aquifers.

Who knows, some years from now, to my recreational ecology, I might also add a recreational study of infrastructure!

Intuition and Formalism in David Bessis’s “Mathematica”

First published at 3 Quarks Daily.

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I’ve spent twenty-five years in a branch of applied mathematics called operations research; I’ve published papers and taught graduate engineering courses on probability, statistics, and optimization. But even with so much exposure to numbers and quantitative reasoning, I’ve never felt comfortable with math. That might sound like false modesty but it’s not: it’s the truth!

It’s been like that for as long as I can remember. In high school, I dreaded questions where different-colored marbles were drawn randomly from opaque jars. Derivatives and integrals in college courses were equally incomprehensible: I did them mechanically, through rote learning, not knowing why they were being calculated or what they meant. These days I am more familiar with notation, but it’s still not easy. Papers in my field are so crowded with sets and subsets, exponents and logarithms, theorems and lemmas, that I tend to give up very quickly.

My academic colleagues, friends, and some of my students, in contrast, seem far more comfortable. They walk through notation like they are reading prose and seem to grasp ideas much faster than I do. This leads to some awkward — and comical — situations. I end up nodding sagely when somebody is explaining an algorithm or an equation, even if I am not getting it. This nodding reflex, I realize, hides certain fears: the fear of accepting how little one knows, or the fear of interrupting a conversation with too many naive clarifications.

Mathematica, a recent book by David Bessis (not to be confused with the software of the same name!), spoke directly to my experience. I finally understood why I feel the way I do. Bessis is a mathematician and I was a bit apprehensive about starting the book. But from the very first pages, I was drawn to his engaging and sincere tone. Anyone, especially those who fear math, can draw solace and inspiration from the book. Indeed, the content is so unusual at times – there’s advice on how to remember one’s dreams, visualize the details of a room from a different vantage point (the ceiling, for instance), and discover our latent ability to echolocate – that it can feel quite tangential to its main theme. But that is precisely the point. Mathematics is not what it appears to be.

In Bessis’s view, there are two sides to math. The “official” side is the formalism and complicated notation that dominates textbooks, research papers, and classrooms. The formal language of math is indispensable since it is the best method we have to communicate ideas logically and precisely. But, as Bessis notes, “this artificial language is so inhuman and so incompatible with our usual way of thinking” that many of us throw up our hands in despair and give up.

The “unofficial” side of math – its joyful essence – is what happens in our minds: how we visualize and manipulate geometric representations to understand a problem better; how we might get intrigued by the puzzle-like quality of certain problems and develop intuitions that evolve over weeks, months, and years. This hidden activity of our imagination is where new ideas and breakthroughs come from. The notation we see on paper is only a second-hand (but, again, necessary) version of this creative insight. In Bessis’ view, if we could “see” or “sense” each other’s intuitions and images directly – perhaps there is a virtual reality world that might make this happen in the future – math would be quite exciting:

“If the mental actions of mathematicians were visible, research institutes would have glass walls. Passersby would stop to look, as they would at people who are kitesurfing or rock climbing. In high school, mathematics would be more popular than skateboarding.”

Bessis illustrates the difference between intuitive math and formal math through simple examples. Early in the book, he asks: Can a straight line intersect a circle at three points? The moment this question registers, you start imagining a circle and a line in your mind’s eye. Then you move the line around this way and that: the line can be a tangent or intersect the circle at two points on its circumference but never three points. The entire process of understanding the problem and figuring out the answer is by visualizing the geometry of the problem. Now try proving this with mathematical notation without images – how much harder that would be!

A different example is fitting variously shaped blocks into matching depressions on a slab: the kind of puzzle that we all might have encountered as infants. Again, the problem is quite easy once you see it but imagine you had to write a precise algorithm that defines the shapes of the blocks and the depressions. Bessis shows how that is done in the simplest way possible, using language that anyone can understand, but even this description, which spans many pages, is so much harder than understanding it intuitively.

Turns out even seasoned mathematicians (Bessis included) struggle to read notation-heavy textbooks, and they too rely on mental imagery (at a very different level, of course, like trying to imagine objects in twenty-four dimensions). Alexander Grothendieck, winner of the Fields Medal in 1982 and considered one of the best mathematicians of the 20^th century, wrote this:

“All my life, I’ve been unable to read a mathematical text, however simple or trivial it may be, unless I am able to give this text a ‘meaning’ in terms of my experience of mathematical things, that is unless the text arouses in me mental images, intuitions that give it life.”

In his famous book Thinking Fast and Slow, Daniel Kahneman proposed that there are two ways of thinking: fast, intuitive thinking that comes quickly and naturally to us (System 1); and slow, deliberate, and intentional thinking that requires much more effort (System 2). Effortless visualizations of circles and lines, or intuitions that flash into our minds, belong to System 1. Writing a complicated proof with lots of notation or creating new mathematical abstractions is part of System 2. System 1 is quick but not always correct. System 2 is harder but is the basis of logical, rational thinking and therefore better decisions.

Bessis agrees with Kahneman’s two-systems framework but argues there is more to the story. He proposes System 3: the attempt to reconcile and integrate the often-inaccurate intuitions of System 1 with the rigors of mathematical writing and communication. As you begin to express your vaguely felt intuitions systematically in notation or explain it to someone else, you begin to spot the gaps in your understanding: what Bessis calls “the dissonance between intuition and logic”. Recognizing and clarifying this dissonance corrects and improves your intuition. Your imaginative powers grow, and you gain a deeper perspective of the problem. Your writing becomes more precise. System 3 refers to this iterative dialogue between Systems 1 and 2. There’s a lovely table in which Bessis tries to explain the attributes of the three systems.

This matches with my own experience. Back in the early 2000s, my PhD advisor, John Fowler, introduced me to scheduling problems that came up in the highly controlled clean-room environments of semiconductor manufacturing. These problems involved scheduling “jobs” (batches of integrated circuits) on “machines” (burn-in ovens, photolithography equipment). Each job had its own unique “processing time”, the time needed by a machine to complete the job. Each job also had a “due date”, the time by which had to be delivered. There were cost penalties if a job was completed later than its due date.

The scheduling problem was typically framed like this: How should the jobs be assigned to the machines and in what sequence should the jobs be processed on each machine so that lateness penalties are minimized? Even with, say, 100 jobs and 5 machines, there are a staggering number of possible sequences. The fastest computers today cannot parse through that many sequences to find the best one.

I was quite absorbed by these abstract combinatorial puzzles. I had not liked questions that involved permutations and combinations in high school, but this was different: I had learned to think of scheduling problems visually. I imagined each job as a rectangle with width equal to its processing time (left image in figure below). I would play around with collections of rectangles in my head, swapping them this way and that to see which sequences were better. I would draw them on paper and mull over them to devise new algorithms. All this I preferred to do with minimal notation. Since these algorithms relied on intuition, they were called heuristics. This was very much System 1 thinking: quick and possibly good answers but with no guarantee that they were the best.

At the same time, through the doctoral courses I was required to take, I learned something called mathematical optimization. Instead of visualizing a scheduling problem, you write line after line of equations (or inequalities) to precisely and completely describe it (right image in figure above). You feed this logic to a computer to find, using some clever algorithmic techniques, the best possible sequence among billions or trillions of possible candidate sequences. I found this approach quite difficult, even unnatural, but I eventually got the hang of it. Writing the problem mathematically required precision and generality that my visualizations, which always dealt with toy examples, could not handle.

All along, without knowing it, I had been using Bessis’ System 3: reconciling my System 1 intuition with the mathematical rigor of System 2.

When I started teaching a graduate optimization course at UMass, I had a similar bias toward System 1. I avoided writing equations as much as I could. I would show two- or three-dimensional geometric representations on the board (such as this 3-D image of a polyhedron) and try to generalize from these examples. There was a lot of waving of hands as I tried to express the intuition I felt within. In turn, I followed the body language of the students closely to gauge whether anything was getting through. However, a pedagogy that relied entirely on System 1 was not sustainable. Textbooks and reference materials use a lot of symbols, and there was no way to convey concepts through gestures and geometry alone. I eventually trained myself to write equations on the board. This was much harder than I realized: it’s easy to make mistakes, and you feel vulnerable if the logic does not quite work out. Surprisingly, it was during these moments of uncertainty, when the silence in the classroom felt awkward, that my System 3 thinking kicked into high gear.

The most powerful pedagogical technique for engineering classes is linking math with practical applications. The mood in the classroom shifts, and students begin to emotionally engage with the content. I would classify this under System 3, since an abstract model or concept must be reconciled with nitty-gritty practical details. Students sense where the math works, but equally important, they see where it fails.

Bessis emphasizes the tension between intuition and formalism throughout — perhaps too many times. Like many non-fiction books, there’s a lot of repetition and the content towards the end is diffuse.

Luckily, there are plenty of vignettes and quirky ideas that keep the pages turning. For instance, Bessis recommends certain sensory exercises to sharpen our mathematical abilities. One example is walking in a room with eyes closed, creating an internal map of one’s movements in relation to where the walls and furniture are. Another is trying to remember the precise details of a place – colors, textures, sounds – from memory. And it’s not always about visual intuition. There’s the remarkable example of Ben Underwood, whose eyes were removed at age two due to retinal cancer but who learned echolocation (the art of navigating by sound) on his own, without any training, by age five. This allowed him to ride a bicycle, skateboard, and play basketball.

There’s also a lot on how dreams can be a conduit for mathematical breakthroughs. The Indian mathematician Srinivasan Ramanujan who learned math without any formal training claimed that “his formulas were correct…because his family’s goddess Namagiri Thayar had revealed them to him in a dream.” Among the more bizarre examples is of Rob Thomasen. Thomason was working on a paper when another mathematician Thomas Trobaugh, who had passed away three months ago, appeared in his dream and told him how to solve a difficult final step of a proof. So insistent was “Tom’s simulacrum” that Thomason listed Trobaugh as a coauthor. (Here’s the full quote.)

Sensory perceptions, the importance of dreams, and other sub-conscious mechanisms: Bessis is trying to reshape our current view of analytical thinking. I found it all quite fascinating. Mathematica has also unexpectedly softened my resistance to formalism. If the goal is to develop intuitions and mental imagery that can creatively absorb you – things that unfold in your mind when talking a walk or clarify themselves unexpectedly in the shower – then perhaps formalism is worth embracing after all.

References

1. Mathematica was originally written in French. Kevin Frey was involved in the English translation. The figure with differently shaped blocks and depressions and the table on attributes of the three systems are photographs I took from the book.

2. The scheduling figure and the accompanying mathematical formulation are from this paper.

3. The 3-D polyhedron image is from the textbook Combinatorial Optimization by Christos Papadimitriou and Kenneth Steiglitz.

Biodiversity, Latitude And Conservation: An Essay On Ecological Patterns

First published at 3 Quarks Daily.

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Ecology is quite distant from my academic work in engineering, but I’ve developed a great love for it in recent years. To learn the basics, I’ve tried many books and articles, but I often turn to the college-level biology textbook Principles of Life. Like many academic texts, this one is not suited for cover-to-cover reading – at over 1000 pages, it is too heavy even to hold comfortably! Still, every time I’ve flipped through its pages, there’s been something interesting to reflect on.

My favorite figure is from the book’s ecology section, and it leads us to the biodiversity theme of this essay. The biological diversity of a region can be quantified in many ways. One intuitive measure is the number of distinct species of a taxonomic group in the region — for instance, the number of species of birds, mammals, or primates found there.

The bar graph on the right shows how the number of butterfly species in the swallowtail family (x-axis) varies by latitude in the Americas (y-axis). In the formal taxonomic system, the family is called Papilionidae and it contains over 550 species. It’s fascinating that the species count distribution follows something like a bell curve centered around the equator: swallowtail diversity increases as we move from the higher latitudes in the north and south toward the equator, where it peaks. (The curve has a longer tail in North America, possibly because there’s more land area there.)

If we analyzed the global distribution of all known ant species (about 14,000 so far) and all known beetle species (an incredible 400,000 described so far and counting!), we would observe a similar bell curve: most species would be concentrated in the tropics, and counts would taper off towards the poles. In the 1970s, the entomologist Terry Erwin found over a thousand species of beetles in a sample of just 19 trees in a tropical forest in Panama. (Erwin fogged the canopy with biodegradable insecticide and collected dead bugs that fell from the high reaches of the trees into a net below – cruel, but that’s how scientists do their work sometimes.)

Since latitude influences species counts, this ecological pattern is called the latitudinal species gradient. The gradient is not limited to insects. With a few exceptions — conifers, salamanders, and lichen which have the opposite gradient (increasing diversity moving toward the poles) — it shows up in most other groupings of species (taxa) as well: marine invertebrates, vertebrates, plants, and animals. Consider the case of birds. About 400 species of birds have been identified in New England. In Florida, that number goes up to 538. Farther south, in Costa Rica, it jumps to 948. And in Colombia, not far from the equator, the tally stands at 1907.

Among trees, the gradient is even more dramatic. A single hectare in Yasuni National Park in Ecuador – often considered the most bio-diverse place on earth – contains 655 tree species. In the entire 50-hectare Yasuni site managed by ForestGEO (a Smithsonian Institution-led consortium that studies forest plots around the world), a total of 1,150 species of trees have been identified. Compare that with the 800-900 tree species in all of the United States. How amazing is that: the sum total of tree species across a range of habitats – from the rainforests of the Pacific Northwest to the temperate forests of New England, to the mangrove swamps of Florida – is matched by a few dozen hectares in tropical forests!

The trend holds in marine environments, too: Coral reefs, most of which are found in tropical and subtropical waters, have some of the densest concentrations of species. They are aptly called the “rainforests of the sea.”

Causes and Nuances

What is so special about the tropics – why do they have such exceptional diversity? This has been a hard question for ecologists to answer definitively. But there are a few working explanations. Abundant and steady sunlight and rainfall in the tropics are obvious candidates. Less obvious is the point that the tropics have had more stable climates since the asteroid strike 66 million years ago which caused the extinction of 75% of all plant and animal species — and famously ended the reign of the non-avian dinosaurs. Stability over millions of years allows greater evolutionary diversification. In contrast, the higher latitudes have been subjected to eight glacial cycles – ice ages – in the last 740,000 years. The most recent of these ice ages ended 10,000 years ago when the glaciers that covered large parts of North America receded. (Somewhat startling to contemplate that the forests of New England, where I spend a lot of my free time now, didn’t even exist then!) Ice ages naturally lead to extinctions and constant adjustment of geographic ranges for species, resulting in less stable conditions for biodiversity.

Many other explanations – seasonality, aridity, the physical structure of habitats, competition among species, to list just a handful – have been hypothesized, which are too long to get into here.

Some of the best work on explaining biodiversity patterns comes from David Currie, of the University of Ottawa. In his 1991 paper, Currie divided Canada and the USA into 336 quadrats. Each quadrat is a small parcel of land, typically rectangular. He then compiled species counts for trees, amphibians, mammals, and reptiles in each quadrat. Next, he created contour lines which connect quadrats that have (approximately) the same number of species.

Broadly speaking, the latitudinal gradient does indeed hold in all four contour maps: we see a gradual increase in species counts moving south. But the contours can be quite wobbly, suggesting there are other factors at work. The number of tree species in the Pacific Northwest (60), for instance, is double that of the number in the American Southwest (30), even though the former is at a higher latitude. That’s not surprising – the Pacific Northwest gets a lot more rainfall and the Southwest is famous for its starkly arid landscapes. A further subtlety is that more trees don’t necessarily mean more reptiles: there are more reptile species in the Southwestern deserts than in the Pacific Northwest. Currie found using statistical models, which include 21 environmental variables in each of the quadrats, that warm, humid environments support more species of trees, while hotter places, even if not humid, favor mammals, birds, reptiles, and amphibians.

So, the biodiversity picture that emerges from Currie’s analysis is quite nuanced, even if the gradient generally aligns with expectations.

Another piece of the puzzle is how changes in elevation affect biodiversity. This pattern is called the elevational diversity gradient. Anyone who has traveled – either by car or a strenuous hike – from the base of a mountain range to a peak that is over 10,000 feet, would have noticed this gradient. There is often evidence of a “diversity bulge” in the middle elevations, but as you go higher, biodiversity decreases: trees disappear after a certain point and there’s a noticeable drop in all types of plants. Higher altitudes in the tropics, however, will still have higher diversity than the same altitudes farther north or south — for instance, at a given elevation, a mountain in Borneo is likely to be more biodiverse than a mountain in Alaska or one in South Africa.

Biodiversity Hotspots

The geographic variation of biodiversity might seem like an interesting curiosity. But it also has implications for a central question in conservation science: how should the Earth’s millions of species, spanning different phyla and kingdoms and inhabiting a range of ecosystems be protected in a time of mass extinction?

Conservation is not only a matter of being “kind” to other species or enjoying the aesthetic pleasures of nature, though that would be motivation enough. The webs of life that link species together in ecosystems – from micro-organisms to plants to apex predators – give us a range of benefits called ecosystem services. Pollination, the natural purification of water, clean air, and the recycling of soil nutrients are just a few examples. With ecosystems disappearing or being altered so quickly worldwide, the services that we’ve long taken for granted are now threatened.

In the 1980s and 1990s, the British environmentalist Norman Myers and his colleagues in Conservation International published several studies, culminating in a highly influential paper in the journal Nature. The paper’s central premise is that conservationists cannot protect all species because extinctions are proceeding too fast and there are constraints on resources and funding. Conservation efforts, therefore, must be triaged: they must be prioritized in parts of the world with the greatest needs.

Myers and his team looked at regions around the world and for each region, they compiled the number of endemic plant and vertebrate species: species found nowhere else in the world. They also compiled the losses in habitat experienced by each region and the percentage that was protected. Regions that had the highest number of endemic species and had suffered the most significant habitat losses were called biodiversity hotspots. The paper argues that conservation efforts must be prioritized in these hotspots.

The originally proposed 25 hotspots are shown in green on the map; 11 blue hotspots were added later as the concept was refined (further details are here). Thanks to the latitudinal species gradient, the tropics are strongly represented. One hotspot (not as prominent on the map) is the thin mountainous strip that runs along India’s southwestern coast, called the Western Ghats. The southern end of the Ghats is not far from my uncle’s farm in Tamil Nadu. All of Central America is also a hotspot. During my travels in Costa Rica, I often heard naturalist guides proudly claim that their country covers a mere 0.03% of the Earth’s area but hosts an outsize 5% of the total species on Earth. And all of island-rich Southeast Asia is a hotspot, with Indonesia featuring prominently (though I am surprised why Papua New Guinea is not included – perhaps data was lacking).

The hotspots concept has been quite popular and has mobilized a great deal of funding from conversation organizations. I am also struck by the amount of work that must have gone into tallying endemic species in all parts of the world: the foundational work that enabled Myers and his team to compile their data.

But there are shortcomings too. Because Myers’s study relies largely on counts of endemic species, ecosystems that are vital in other ways do not make the list. The iconic Serengeti – the semi-arid grasslands in East Africa, home to a breathtaking diversity of large mammals: zebras, giraffes, wildebeests, gazelles, elephants, lions, cheetahs, hyenas – is not a hotspot, simply because it does not contain enough endemic plant and vertebrate species to make the threshold.

Similarly, the Arctic wilderness, which spans Canada, Greenland, Alaska, and Siberia, has a low count of endemic plant species but contains large quantities of permafrost: soil that has remained frozen for hundreds of thousands of years. Permafrost contains millennia-old remains of dead organisms (including megafauna like mammoths) that microbes have not fully decomposed due to sub-zero temperatures. This makes it a vast natural storehouse of carbon. As the permafrost melts due to increased global temperatures and the biomass decays, the stored carbon dioxide and methane will be released into the atmosphere, accelerating warming. Thus, while the Arctic wilderness is not a biodiversity hotspot, it plays a critical ecological role. Other parts of the world — grasslands, mangrove forests, salt marshes — may be similarly excluded even if they provide valuable services.

These examples suggest that the concept of biological value — quantifying why an ecosystem is important — needs to include many more dimensions than the raw counts of endemic species and habitat losses. In the final analysis, the Earth system is the sum total of all its ecosystems and living organisms. It’s only in the last century that scientists have begun piecing together the complicated pathways through which energy and matter (water, nutrients, and elements such as nitrogen, carbon, and phosphorous) flow between the biotic (living) and abiotic (physical and chemical) components of our planet. Biodiversity is a vital feature and consequence of these pathways, but not the only one.

Much of this meandering essay grew from my reading – I’ve mentioned several articles throughout. However, E.O. Wilson’s dense but strangely beautiful The Diversity of Life was the biggest influence. The essay also grew from the many hours I spent on trails in and around Amherst, Massachusetts: I would become curious about, say, a lichen, a moth, or a bird, and that would prompt me to look them up. Mary Holland’s Naturally Curious has filled many pieces of the New England biodiversity puzzle for me.

An urge to experience tropical diversity firsthand took me to the La Selva and Las Cruces research stations in the rainforests of Costa Rica, where biologists from around the world converge to do fieldwork and collect data for their projects. I talked to researchers who studied stingless bees, nitrogen-fixing bacteria, and the relationships between hummingbirds and the plants they pollinated. The emphasis on fieldwork was a welcome contrast to the abstract mathematical models and algorithms that my academic specialty (operations research) demands.

Finally, and somewhat surprisingly, natural history museums, which never interested me earlier, have now turned into sources of great inspiration. Especially the Smithsonian Museum of National History in Washington DC and the Beneski Museum of Natural History in Amherst, Massachusetts: I can’t remember the number of times I’ve felt goosebumps or a sense of wonder when reflecting on their exhibits.

Reflections on a milestone in my academic career

I was promoted from Associate Professor to Full Professor recently. For those of you who might not be aware, here’s how things work at American universities. You start as an “Assistant Professor”; if your research and teaching record after six years is good, you are promoted to “Associate Professor” and receive something called “tenure”. Tenure is a sought-after milestone since it guarantees a permanent job at the university (and is recognized elsewhere too). Continue to do well after tenure and you become a “Full Professor”, though there isn’t a timeline for this second — and last — promotion.

The titles are decidedly odd: it’s not clear whom one is “Assisting” or “Associating” with, or what is one is “Full” of. One colleague suggested that you become – officially – full of yourself, which may well be true!

In my case, I joined UMass, Amherst in 2008 as an Assistant Professor in Industrial Engineering. Because of my post-doctoral training at the Mayo Clinic, I was recruited to start a research program to improve healthcare delivery — a nascent field at the time but now mainstream in most Industrial Engineering departments. I was promoted to Associate with tenure in 2014.

Tenure came with a great sense of relief and allowed me to work at a more relaxed pace. I began exploring publicly available healthcare datasets that contained a wealth of interesting epidemiological patterns and started a long-running collaboration with a New Jersey-based organization called the Camden Coalition. The post-tenure years also allowed me to experiment with new ways to engage students in the classroom. Even with courses that I’d taught many times, I noticed there was always something new to learn: nuances that I had previously glossed over would come to light, or an entirely new way of explaining a mathematical concept would begin to take shape.

The benefits of tenure went well beyond my expected research and teaching duties. While academia is all about deepening one’s expertise in a highly specialized domain, I felt an urge to explore fields far removed from my own — from ecology to earth sciences to physics to geology. My desire to learn the fundamentals of these fields rose to levels that astonished me sometimes. (Where was all this curiosity and hunger in high school and college when there was more time?) Most nights, I would pick up Feynman Lectures on Physics or the college-level biology textbook, Principles of Life, or read through the latest print version of the journal Science or the magazine Natural History. I visited research stations of the Organization of Tropical Studies in Costa Rica and met biologists doing fieldwork in rainforests. So far I don’t have much to show for these forays but I do dream of one day applying my quantitative skills in ecology.

Left to my own devices I would have probably continued along off-the-beaten paths and not worried about promotions. But the academic ecosystem runs on metrics — publications, grants, citations, and awards — that keep tugging at you. And as the years ticked by and my hair turned gray, the question of the next advancement on the academic ladder kept coming up. Colleagues asked about it at conferences. My parents brought it up all the time. And even distant acquaintances in my parents’ flat complex in Bangalore would ask: “Have you been promoted yet?”

So in the fall of last year, not long after I received my third NSF grant and a teaching award, I decided to put that question to test. Like all other promotions, mine went through a months-long process and involved lots of committees and evaluations. In June this year, I learned it was successful.

Credit goes to colleagues in my department and in other universities who wholeheartedly supported my case and wrote long letters of support. Take all the letters written by full professors from other universities, different university committees, and students, and it would add up to at least thirty people involved in the promotion effort. Tally all the hours – as we often do in Industrial Engineering time studies – and it might add up to more than a hundred hours of work on somebody else’s behalf. I am very grateful to anyone who gave their time.

Since students are such an integral part of academic life, I want to share a few graduation pictures with my former PhD students. The left image in the first panel is from May 2014, with my first PhD student Asli, and the one on the right from May 2015 is with Xiaoling and Joanne (both were co-advised by Ana Muriel). The left image in the next panel is from May 2021 with Ekin Koker (again co-advised with Ana; Ekin’s wife Mari is to his left); and finally with Prashant Meckoni in May 2022.

I also want to acknowledge two of my current doctoral students – Sindhoora Prakash and Ali Jafari – who have worked hard in the last year to keep my research active. Both have been awarded fellowships – Ali a departmental fellowship and Sindhoora the Dean’s First Year Fellowship. They are also co-authors – along with my former master’s student Arjun Mohan and colleague Chaitra Gopalappa – on a 30-page tutorial that was recently accepted in the INFORMS Tutorials in Operations Research series. The tutorial is a distillation of my research in healthcare over the last six years and it took us the best part of this year to put it together.

Two more pictures. The first is with undergraduate students at an end-of-semester “bar crawl” in December 2019. As the name suggests, you start at a bar at 9 pm and then to move another and then another until closing time. Certainly challenging for someone who does not drink at all! I retired early but not before this picture was taken.

And this is a recent picture from a hike to Bare Mountain, a short distance from campus, with the current cohort of PhD students, and my faculty colleagues Ana Muriel and Chaitra Gopalappa. (Many thanks to Chaitra who organized it and for the group selfie!) I’ve gone up this mountain – a 600-foot ascent that usually takes 20-30 minutes – so many times over the last five years that I’ve subconsciously memorized the shapes of the rocks and the trees; my legs seem to know exactly where the footholds are. Like many other spots in Amherst, Bare Mountain feels very much like home.

The Fossils that Became Fuels

Did you know that fossil fuels – coal, oil, natural gas: the much-reviled hydrocarbons of today – are remains of long-dead organisms, essentially graveyards from hundreds of million years ago that were absorbed into the Earth’s bedrock? That coal is extracted from what’s left of ancient tropical forests and oil and natural gas from the remains of ancient marine microorganisms?

In these climate-challenged times, these should be well-known facts. But I wasn’t aware of them for many years. I’d thought of fossil fuels the same way I thought of minerals: as resources to be extracted from the earth, more abundant in some parts of the world than others. The qualifier fossil, which so unequivocally points to ancient life and distinguishes the fuels from the minerals, had completely escaped my attention. What kinds of fossils had left hydrocarbon molecules in such large quantities that are now fueling our lives and warming the world? How and when were they formed? I’d never bothered to consider these questions. Just goes on to show how shallow our understanding of everyday concepts can be! (Ask me about the phases of the moon or how a refrigerator works and I might struggle in the same way.)

The upside is that ignorance can turn into a source of wonder. I see now that every time we power our cars with gasoline, or consume electricity that comes from a coal or natural gas plant, or use the myriad products of petroleum (from asphalt to plastic bags to synthetic fibers), we are linked (however indirectly) to lifeforms from hundreds of millions of years ago. Fossil fuels should never have been burned in such large quantities, but they are a fascinating illustration of how the Earth’s deep history – stuff that we think belongs only to natural history museums and geology textbooks – is tangibly a part of our daily lives.

The Plants That Became Coal

Modern coal deposits date back to the tropical forests of the Carboniferous (literally coal-bearing) geologic period, which began about 323 million years ago. According to Wikipedia, coal is “formed when dead plant matter decays into peat which is converted into coal by the heat and pressure of deep burial over millions of years.”

Rocks from that period reveal the haunting imprints of plants that grew in these tropical forests. Take this fossil exhibit from one of my favorite spots in Amherst — the Beneski Museum of Natural History. It shows the 310-million-year-old trace of an ancient fern in a slice of Ohio rock. While the ferns I see every day in Massachusetts are short and carpet forest floors, back in the Carboniferous, they were tree ferns that grew nearly 65 feet tall (there are still tree ferns today in the tropics: the first image below shows the silhouette of one I recently saw in Costa Rica).

The environmental journalist Janet Marinelli describes other classes of plants that dominated the Carboniferous in this article . In addition to ferns, she highlights lycopods, ancestors of today’s club mosses. I have learned to recognize club mosses (second image below) on my daily walks. They are only a few inches tall — I incorrectly thought of them as ‘baby conifers’ or ‘hemlock nurseries’ — but a few hundred million years ago, they grew to an astonishing 130 feet. Marinelli also mentions calamites, ancestors of modern horsetails that I often spot along trails (third image below). They are short, but in the swamp forests of the Carboniferous, they rose to 50 feet.

Ancient ferns, club mosses, horsetails, and the earliest ancestors of the conifers: these, then, were the kinds of plants that got buried under dirt and rock for hundreds of millions of years. Heat and pressure slowly converted them to coal.

Here are some artistic renditions of what a tropical coal forest might have looked like. The visual feel of such a forest and the species of animals that inhabited it would have been quite different. Flowering plants and trees that dominate landscapes around the world today had not evolved at the time – they evolved much more “recently”, in the last 100 million years. This is why you won’t find oak, banyan, acacia, or any wildflower fossils in remnants of coal forests. The earth was also much warmer and more humid during the Carboniferous and the continents were differently aligned – North America, South America, and Africa were lashed together into a single supercontinent called Pangea. Places such as Pennsylvania and Virginia, where modern coal deposits are found, were at that time closer to the equator.

(If all this talk of geologic periods and tectonic activity is too much, I totally understand! There was a time when my eyes would glaze over too — the esoteric names and jargon-filled descriptions seemed so inaccessible. It wasn’t until I began to connect them with what we now take for granted that the Earth’s deep history started to resonate powerfully. Take something as vital as oxygen — the planet didn’t have much oxygen at all until the photosynthetic activity of cyanobacteria, starting two billion years ago, made it abundant on Earth, in the process creating the ozone layer that now protects us from harmful radiation. Or consider how plants and fungi established a symbiotic partnership on land 400 million years ago, turning barren continental rocks into the fauna-filled forests, savannas, and agricultural landscapes of today. Or consider how a large asteroid crashed into the Earth 66 million years ago, ending the reign of the dinosaurs, but not all of them – for we still have some of their descendants, the 9000-odd species of birds on Earth today.)

The Microorganisms that Became Oil and Natural Gas

The story of oil and natural gas is more complicated – at least for someone like me with only a faint idea of geology and microbiology. The current theory is that oil comes from the remains of tiny organisms that once thrived in warm, shallow seas in the Cretaceous and Jurassic geologic periods. This is roughly 200 to 66 million years ago, during the age of the dinosaurs. The sources of oil and natural gas are therefore younger than the coal forests of the Carboniferous.

I recently learned that plankton is the name given to a diverse class of marine micro-organisms that turned into oil and natural gas. A common feature of plankton is that they drift in the water and are unable to propel themselves against currents of water or wind. They include both microscopic plants (phytoplankton), which serve the same indispensable purpose as land plants, fixing the sun’s energy and thereby enabling other lifeforms; and microscopic animals (zooplankton) which feed on phytoplankton. The zooplankton in turn are a major source of food for larger organisms – whales, for example, feed on a type of zooplankton called krill.

Unlike land plants, which I can see and appreciate easily, these microscopic lifeforms are harder to relate to. (I can’t remember the last time I peered into a microscope – was it back in college or high school?) A 2010 New York Times article by William Broad discusses a type of single-celled phytoplankton called diatoms and claims they are “the source of the vast majority of the world’s oil”. There’s a lovely image in that article (below) that shows the varied geometry of diatoms – elongated, triangular, circular, star-shaped – and their iridescent colors.

If the marine micro-organisms theory is correct, then it implies that any oil-rich terrestrial region – North Dakota, Texas, the Middle East – must have been underwater once. (Such is the nature of continental movements that even North Dakota which seems so far inland and landlocked now was once covered by a shallow sea!) Just as important, the seas that covered the region must have had plenty of sunlight and nutrients that enabled an abundance of marine micro-organisms. When the shallow seas withdrew to expose land, the sediments – accumulated remains of dead micro-organisms collected over millions of years – became a source of oil and natural gas. The graphic above (from here) conveys it quite well.

The Middle East, which used to be under the Tethys Ocean, is an excellent example. The Tethys no longer exists but it was a predecessor to today’s Mediterranean Sea, the Indian Ocean, and the Black and Caspian Seas. When the continents slowly changed their alignments, the Tethys receded, exposing the sediment-rich Middle East. Thus, a fortuitous combination of tectonic activity and ancient marine life made the Middle East rich in oil and geopolitically important in the 20^th century. Another example, I suppose, of the Earth’s deep history manifesting in the modern world!

In closing, I should mention two books I leafed my way through while researching this article. They provide further context on the topics I’ve discussed here. The first is Echoes of Life: What Fossil Molecules Reveal about Earth History and the second is Vanished Ocean: How Tethys Reshaped the World. I also highly recommend the Deep Time exhibit at the Smithsonian National Museum of Natural History — it provides an engaging and awe-inspiring overview of Earth’s four-billion-year-old history.

The Farm in Sathyamangalam

In January this year, I visited my perippa and perimma’s (uncle and aunt’s) farm in a small town called Sathyamangalam. Sathy, as it is fondly known, is one of a series of agricultural towns in the southern state of Tamil Nadu along the Bhavani River, a tributary of the better-known Cauvery. On either side of the roads in this region, you’ll find plots of banana trees organized in neat rows, rice paddies sparkling with water, and – ever pleasing to look at – tall coconut trees with thin, elegantly curving trunks.

The farm in Sathy has been and continues to be a special place for everyone in my extended family. I’ve always felt welcomed and at home there, and my perippa and perimma have guided me through some vexing and important personal decisions. I’ve been visiting the farm since middle school. When I went to college in Tiruchirappalli (also in Tamil Nadu), I used to take inter-city buses to Sathy during the holidays. Even after moving to the United States, I’ve managed to return once in a few years.

As a town, Sathy has grown considerably, but the farm still looks about the same. There’s the white house with the slanting red roof that comes into view soon after you enter the dirt road off the highway; there’s the spacious patio where my perippa often sits to work these days. Walk around a bit and you run into the sheds for the cows, the wells for water, and the rectangular plots for crops — turmeric, coconut, areca nut this year, and in the past rice, sugarcane, and Casuarina trees. I love standing on a ledge of the wells to see the steeply rising mountains in the distance. The cloudy weather on the days that I visited only enhanced the beauty of the farm. I spotted kingfishers, peacocks, owls, and woodpeckers with little effort. The place felt more a wildlife preserve than a place for cultivation.

My perippa’s family has owned the farm for at least two centuries. In the 1960s, with the coming of the Green Revolution and high-yielding crop varieties to India, the family started to use synthetic fertilizers and pesticides. Perippa wholeheartedly adopted these newer Western methods: what he now calls “chemical farming”. His brother worked in Rallis, a company that sold agricultural products. The farm served as an informal center for R&D. Agricultural scientists and researchers from Rallis visited Sathy to test the effectiveness of the company’s products.

In the 1990s, however, after noticing the detrimental effects of chemical farming on soil health – and in fact his own health – perippa shifted to organic farming. Perimma has jointly managed the farm since her marriage in 1973 and has been an equal partner in this transformation. The two of them have turned the 10-acre plots into a model organic farm that is famous in southern India.

Every day my perippa – now 82 years old and unmistakable in his lean, upright frame – attends to a constant stream of messages and calls from other farmers who need his assistance. His six decades of experience, equally split between chemical and organic farming, is highly valued. Visitors from far-off villages drop by unannounced. He is invited often to give seminars and workshops in Tamil Nadu and other states. There are plenty of YouTube videos (in English as well as Tamil) in which he tells his story. (The first video has some good views of the farm.)

In all his interviews, perippa credits other farmers who have successfully tried alternative cultivation approaches and whose methods he adapted. Names that often come up include G Nammalvar, an early pioneer of organic farming in Tamil Nadu; Shripad Dabholkar of Maharashtra (whose book Plenty For All has been a major source of inspiration); Bhaskar Save of Gujarat; and Narayana Reddy of Karnataka (who often visited the Sathy farm to provide guidance; Reddy, in turn, was influenced by Masanobu Fukuoka’s One-Straw Revolution). In investigating the life and work of these farmers, I got the impression that a robust response to the negative effects of the Green Revolution had quickly emerged in India. Today, however, the declining labor supply in agriculture poses a bigger challenge: no one aspires to be in farming anymore, and all over India, there’s been a hollowing out in rural areas as people move to urban centers.

I would often mention the Sathy farm with great pride to my friends in the United States. However, the truth is that I was unaware — and am still unaware — of the basics of farming. Perippa often explained his techniques when I visited, and though I sensed his passion each time, I had not made the effort to follow the details. But this time was different. This time, when he took me around the farm, bent down to pick a handful of topsoil and explained how his goal was to increase the diversity of microorganisms in it; or plucked a plant to illustrate the structure of tap and feeder roots; or described how he was using certain plant species called cover crops to fix much-needed nitrogen in the soil – this time, I tried to learn as much as I could, and there was far greater emotional resonance.

What’s changed in the last few years is my curiosity about the history of life on Earth and how all life is interrelated. At its core, perippa’s organic farming vision was to create a healthy soil environment that allowed symbiotic relationships between plants, fungi, insects, and microorganisms to prosper. These relationships, in which there is a lot of give and take of nutrients, are hundreds of millions of years old. For instance, plants provide carbon to fungi living in their roots; in exchange, the fungi extract nutrients such as phosphorous from the soil, which the plants absorb. In popular culture, evolution is often presented as a competitive struggle for survival and it is to some extent that. But there are also myriad examples of species collaborating in mutually beneficial ways. We are yet to fully fathom the magnitude and complexity of such partnerships.

I’d read about these concepts in books such as Lynn Margulis’s Symbiotic Planet and Merlin Sheldrake’s Entangled Life. The great pleasure of my visit to Sathy was to see them in action. I still don’t understand enough about farming but if I do learn something in the future – that’s a big if, given my academic commitments! – then I’ll view this trip as a true start.

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I took all the pictures above except for the picture of my perimma — that’s from an article in the newspaper The Hindu in which she was interviewed about traditional varieties of rice. (Unfortunately, this article is behind a paywall.)

Revisiting C Rajagopalachari’s Mahabharata

I am reading C Rajagopalachari’s Mahabharata again after more than twenty years. This is the abridged prose version of the epic Sanskrit poem: at 1.8 million words, the longest in the world, with countless retellings and adaptations across millennia. Although the historicity of the Mahabharata is still being worked out, the story is set in North India in the millennia before the common era.

I chose to revisit the Mahabharata to alter my reading habits a bit. I’ve been absorbed with Western books on natural history, biology and science in the last few years. They have helped me look at the world in a completely new light. But I also felt the need to read something with a totally different worldview — at least something outside the bubble of Western science. So, as I flew to Bangalore, India, to be with my parents for a few weeks this winter break, I decided to take the Mahabharata along. My parents are devout Hindus and their 9th story flat is so full of images of the deities they worship and the television they watch is so full of commentaries of old Hindu texts, that the milieu of the Mahabharata fits seamlessly here.

Ninety odd pages in, I am really enjoying it. The stories in the book seem charged with a deeper meaning, now that I am much older than when I first read them. Each chapter features a character, sub-plot or theme, with a clearly defined beginning and end. Yet each chapter also fits into the larger narrative of dynastic conflict and war between two groups of cousins: the Pandavas and Kauravas.

In addition to the primary cast — Bhishma, Kunti, Drona, Duryodhana, Krishna, Arjuna, Bhima, Draupadi: all household names in India — dozens of fleeting characters come and go, playing small but important roles. There are forest sages with yogic powers who can foretell the future and deliver powerful curses (and yet soften their impact if sincere pleas are made). There are celestial deities, demons and monsters who seem quite apart from humans in their special abilities but still remain very human in their desires and foibles. The chain of cause and effect — actions at one time resulting in karmic consequences in another — is a recurring theme throughout. The stories involve exceptional acts of generosity and sacrifice but deceit, long-standing grudges and a yearning for revenge play an equally important role. In fact, it is the vices, which most characters succumb to, that make the Mahabharata so interesting.

One of my favorite stories is of a king named Yayati, an ancestor of the Pandavas and Kauravas. Yayati marries Devyani, the daughter of a famous sage named Sukracharya (Devyani has her own chapter in the book and an equally fascinating story). Without telling Devyani, Yayati secretly also marries Devyani’s attendant, Sarmishta. Devyani is naturally distraught when she finds out. Her furious father Sukracharya curses Yayati with premature old age which takes immediate effect.

Shocked, Yayati begs Sukracharya to remove the curse. Sukracharya says that the curse has to take its course, but relents that if Yayati “can persuade anyone to exchange his youth for your age the exchange will take effect”. Yayati desperately wants his youth back since he is “still haunted by the desire for sensual enjoyment”. He still wants to enjoy the company of women. He turns to his five sons, and this is what he asks them:

“The curse of your grandfather has made me unexpectedly and prematurely old. I have not had the fills of the joys of life… One of you ought to bear the burden of my old age and give his youth in return. He who agrees to this and bestows his youth on me will be the ruler of my kingdom. I desire to enjoy life in the full vigor of youth.”

What an extraordinary request — of course no one wants to give their youth away even if a kingdom is received in return! The first four sons refuse. But, in an astonishing act of selflessness, the youngest son Puru agrees to his father’s request. Moved and delighted, Yayati embraces Puru and immediately finds that his youth is back while Puru has turned old. He tells is son he will “enjoy life for just a while more and then give you back your youth.”

Yayati indulges himself for many years. He spends time with a beautiful woman (an apsara) in an exotic location (Garden of Kubera). But after years and years of trying of fulfill his sexual desires, there’s a key moment when he realizes that repeated gratification has not helped him. He returns to Puru with this realization:

“Dear son, sensual desire is never quenched by indulgence any more than fire is by pouring ghee on it. I had heard and read this, but till now I had not realized it. No object of desire — corn, gold, cattle or women — nothing can ever satisfy the desire of man. We can reach mental peace only by a poise beyond likes and dislikes. Such is the state of Brahman. Take back your youth and rule the kingdom wisely and well.”

Yayati retires to the forest to lead a simple life of austerities. The chapter, thus, ends with a well known teaching of Indian spiritual traditions: that one must develop the wisdom to not run after sense pleasures. The interesting part is that Yayati was quite aware of this, yet simply hearing or reading about it did not compel him to act differently. Only repeated experience — seeking gratification again and again and failing to find anything substantial or lasting — convinced him. Perhaps the true message of Yayati’s story, then, is that there is no short-cut to such realizations, that the path can be long and convoluted.

An interesting footnote: A few days after publishing this post, I was browsing at a bookshop in Bangalore when I stumbled upon a novel by V.S. Khandekar titled Yayati. This chance encounter with Khandekar’s novel — just a few days after publishing this post — belongs to the department of interesting coincidences! (Much like how I saw a slug for the first time in Amherst, a few days after reading Elizabeth Tova-Bailey’s The Sound of a Wild Snail Eating.) It turns out that Yayati is a classic of Marathi literary fiction in which Khandekar re-imagines and elaborates on the story through different first-person narratives.

Some Thoughts on Joyce Carol Oates’ Fiction

I hardly read any fiction these days! Books on science and history have all but taken over. Maybe it’s the terrain that comes with being an academic — too much scholarly, intellectual stuff . The one exception is Joyce Carol Oates: I keep returning to her fiction again and again. In 2017, I read her exceptional short story collection Lovely Dark and Deep. Two recent collections of novellas — Evil Eye and Cardiff by the Sea — have left an even stronger and lasting impression*.

Most stories in these books are about women (students, junior co-workers, younger family members) who find themselves, willingly or unwillingly, drawn into the orbit of influential and successful men (wealthy patriarchs, distinguished poets, famous scientists and professors, or just husbands, sons, fathers, grandfathers). The men are the unequivocal villains of most stories: they are manipulative and sinister, often using their power, either at work or in a family relationship, to coerce or harass the women their lives. Still, Oates endows them with an intriguing complexity**.

Ensnared in relationships with such troublesome men, the women find themselves disoriented and sometimes physically threatened. A sense of foreboding pervades the stories and deepens as the narrative progresses. The suspense comes not from the plots (which tend to be straightforward) but from the psychological portraits of the characters, a slow unveiling of past traumas and sudden shifts in perspective. I am also amazed at the precision with which Oates sketches, in a few quick sentences, details of a coastal landscape, a large centuries-old house, a small New England town, an office building, the dresses and physical appearance of her characters. These details and the often tumultuous inner worlds of her characters blend seamlessly in Oates’ signature narrative style: short, urgent paragraphs interspersed with italicized words and phrases.

Not since The Death of Ivan Ilych and Other Stories — a dazzling collection of Tolstoy’s fiction — have I come across such powerful short stories and novellas.

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* I also read Night. Sleep. Death. The Stars, Oates’ 2020 novel last summer. I wasn’t as taken by it, but some scenes, characters, and passages were as astonishing as the best of her short stories.

** The uncle of the female protagonist in the lead novella of Cardiff by the Sea — a story that does not quite follow the narrative template I’ve outlined above — is the most interesting of the male characters.

A Week in Santiago, Chile

I was in Santiago, Chile recently for the IFORS conference. Two universities — the University of Chile and the Pontifical Catholic University of Chile — jointly hosted the event. There was the usual socializing, dining and fun that happens at conferences. I met colleagues and friends from Latin America, Asia and Europe, and was able to explore the city a bit.

Santiago, home to 7 million Chileans, sprawls along the foothills of the Andes. Majestic, snow-capped mountains loom in the eastern skyline. Smog from the traffic, unable to escape the wall of mountains perhaps, lay suspended in a haze over the high rises. I noticed graffiti everywhere, with no wall or building left blank — this gave the city a somewhat edgy look. Still, when compared to the other Latin American cities I’d visited — Lima, La Paz, Quito, Mexico City — Santiago seemed wealthier.

The conference included a day trip by bus to the towns of Valparaiso and Vina Del Mar along Chile’s rocky coast. The drive took us through small towns, wineries, farms, and hills with cacti, palms, and eucalyptus trees. Our tour guide, Rafael, spoke of Chile’s history during the journey: how the Spanish, after their success in toppling the mighty Incas in the north, arrived in Santiago in 1541, after an arduous crossing of the Atacama Desert. They came looking for gold, a recurring fantasy of Spanish conquests in the Americas. In the decades that followed, they faced fierce resistance from the indigenous Mapuche. Like other Andean countries such as Peru, Ecuador, and Bolivia, Chileans have a mixed Spanish-indigenous ancestry. However, according to Rafael, Chileans are more European and are therefore lighter-skinned. He had the precise numbers for himself: “I am 54% Spanish, 44% Mapuche, and 2-3% African.”

Rafael also spoke of the country’s modern history: the coup d’état against Salvador Allende’s government; the adoption of neoliberal policies by Augusto Pinochet‘s regime; the massive protests of 2019-20 and ongoing turbulence in the country’s politics related to the re-writing of its constitution. In a memorable phrase, Rafael called Chile a ‘bipolar country’, swinging between the extremes of the left and right. Born in 1977, Rafael grew up during Pinochet’s military dictatorship. His father, a construction worker, was once detained by authorities. But his father’s hands were so battered from bricklaying and cement work that the authorities released him. Because of that incident and the detention and disappearance of thousands of other Chileans, Rafael grew up disliking Pinochet. But now he has a more ambiguous view. He feels that had Pinochet not intervened, the situation in Chile might well have been worse.

After the conference, I climbed up the San Cristobal hill and visited the Chilean Pre-Columbian Art Museum. I found some thought-provoking exhibits at the museum. Such as this 7th century pot from Peru’s southern desert region with a painting of three hummingbirds feeding on a flower. Because I’d seen a hummingbird the previous day in Santiago, hovering around and dipping its bill into an orange-petaled flower, I felt an instant connection to the unknown artist (or artists) who had painted a similar scene 1500 years ago. (Though I doubt that three hummingbirds can amicably feed together as depicted!)

And this beautiful, abstract-looking exhibit below is a quipu . The Incas, who commanded a vast Andean empire, used quipus for administrative purposes. Each quipu consists of a primary “inner” cord to which all the radiating secondary strings are attached; each secondary string has a cluster of knots. Variations of this basic arrangement were used to record and convey quantitative data using a base-ten numeric system. Exactly what the logic is, I don’t quite understand; I guess you could think of the quipu as the string or textile version of an abacus. But — as I learned from the appendix of Charles Mann’s 1491: New Revelations of the Americas Before Columbus — some scholars have hypothesized that quipus were not just for storing numbers, they may also have been an unusual kind of writing system that is yet to be deciphered.

Skunk Cabbages And Ferns

Living almost halfway between the equator and the north pole — the 45 degree North line is a few hours drive away from Amherst, in Vermont — has its downsides in the winter. But spring always brings great relief and beauty. And so many changes mark the coming of spring! You can track the arrival of migrating birds, watch turtles sun themselves on exposed logs, or — with the air so thick with pollen — simply enjoy a fit of morning sneezes.

A few days ago, while walking through the Lawrence Swamp conservation area in Amherst, I came across these skunk cabbages (Symplocarpus foetidus). In February and even in March, there was no sign of them. Yet by mid April scores of these low-lying plants carpet the moist, swampy parts of the Massachusetts. Skunk cabbages are named for their pungent odors but I don’t smell anything in their presence. I am always struck, though, by how vividly green they are (at least at this time of the year) and the very particular way in the leaves open up and curl.

Farther up, I found a section of the forest floor completely covered with skunk cabbages. Coiled spirals of ferns — called fiddleheads around here — will slowly begin to unfurl among them, adding to the visual drama. In fact, if you zoom in and look closely, a few tentative fern stalks are there already. For a few weeks in this patch of the forest, the two species will seem conjoined. But by mid summer, the ferns — equally striking in their appearance — will be tall enough to hide the skunk cabbages underneath. So the seasonal rhythms go!

Update, June 21st: This is how the same patch now looks, with the ferns very dominant.