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.

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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.”)

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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!

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.

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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.)

The Wonder of Observing Another Species

When I was down with COVID in mid-September this year, two friends lent me Elisabeth Tova-Bailey’s The Sound of a Wild Snail Eating — a short, beautifully written account of a year in the author’s life. It was just the kind of reading I needed as I recovered. I finished the book a few weeks later at my usual slow — snail-like? — pace, completing a few paragraphs or a few pages each evening.

A viral infection — not COVID, for this was some decades ago — is also the central event in Tova-Bailey’s book. She catches it after a trip to Europe and finds herself in the middle of a debilitating illness that lasts two decades. The virus, she says, “re-wrote the instructions followed within every cell in my body, and in doing so, it rewrote my life, making off with nearly all my plans for the future.” The year that this book documents, Tova-Bailey is largely bed-ridden. Even standing or sitting up for a few minutes is hard.

On a whim, a visiting friend brings a wild snail (Neohelix albolabris) from the woods into her room. The snail makes its home in a pot of violets and in its early days — finding itself suddenly removed from its natural habitat and with nothing else to eat — consumed whatever paper it could find, paper being the only ‘woody’ thing in the room. This is the first of many remarkable details in the book:

The night before, I had propped an envelope containing a letter against the base of the lamp. Now I noticed a mysterious square hole just below the return address. How could a hole — a square hole — appear in an envelope overnight? Then I thought of the snail and its evening activity.

When Tova-Bailey puts some withered blossoms, the “snail investigated the offering with great interest and began to eat one of the blossoms”. Realizing that the snail needs a home that is closer to its woodland habitat, Tova-Bailey arranges for terrarium, a small habitat put together in a large glass bowl consisting of soil, mosses of various kinds, ferns and rotting bark. She feeds the snail with portobello mushrooms. (Check this Vimeo link to see the terrarium and hear a recording of the snail eating.)

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A new version of ‘Thirty Letters in My Name’

From 2005-2018, I used to write a blog called Thirty Letters In My Namethe title, as you might guess, refers to the imposing length of my first (Hari Jagannathan) and last name (Balasubramanian). That blog contained a mixed bag of topics: travel, history, literature, mathematical concepts that I taught in my courses. Many of the themes I explored eventually turned into longer essays for the website 3 Quarks Daily. I haven’t written much since 2018. The break was due to personal circumstances that required me to slow down and retreat for a while.

Now I feel like writing again. This time, I want to work my way through themes that are close to my heart: wonders of the natural world, the history and diversity of life on earth, ecology and environmental conservation. I have no formal training in these areas. What little I’ve learned of the natural world comes from bits and pieces assembled from regular hikes in the mountains, forests, and coasts of the American Northeast, and then reading about them in books.

But I suppose one has to begin somewhere. That’s what I hope to do in this version of Thirty Letters In My Name: start writing and see where it leads. Although I expect many pieces to be nature-focused, my other interests — literary fiction, history, travel, movies, concepts in mathematics and probability — are all likely to make a regular appearance; I will also post edited versions of my previously published 3 Quarks Daily essays. Let’s see how this turns out!

One Foot in Engineering, the Other in the Humanities: Reflections on My Career and Interests

This essay, first published in at 3 Quarks Daily,  is summary of the themes spanning the humanities and sciences that have interested me over two decades.

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I’ve always thought of myself as someone who is more drawn to the humanities than to math or the sciences. This can seem very puzzling to someone who looks at my career details: degrees in engineering and a career in academia in a branch of applied mathematics called operations research. Even I am stumped sometimes – how did I get so deep into a quantitative field when all my life I’ve held that literature (literary fiction in particular), history and travel are far better at revealing something about the human condition than any other pursuit?

Some follow an ambition stubbornly wherever it takes them and whatever the consequences. I did not have that kind of resolve. Growing up in west and central India, I read a lot English and American fiction – Agatha Christie, Alfred Hitchcock, Alistair Maclean – and decided that I must become a writer (English only of course for the mentally colonized, why would I write in Tamil or Hindi?). The ambition was strong enough to have a grip on my thoughts for the next two decades, but never strong enough to counter practical concerns. Like many middle class families, my parents felt I had to get into an engineering or medical college since both offered the promise of financial stability. I simply went along, following what high school friends around me were doing. After toying with majors as diverse as electronics and metallurgy I finally settled on something called production engineering. In 1996, I left home and attended what was then called the Regional Engineering College, twenty kilometers from the south Indian city of Tiruchirappalli: a semi-industrial, semi-rural middle of nowhere kind of campus where teenagers from far flung states of India came and lived in packed hostels for four years.

The ambition to become a writer, meanwhile, bided its time. All you had to do was write one breakthrough novel, something like Arundhati Roy’s The God of Small Things, become famous, then write full time: that was the naïve worldview that sustained me for a long time.

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Early Years in Arizona

Wrote this back in December 2020 for 3 Quarks Daily, to mark two decades since I moved from India to the United States. This piece is about my grad school years at Arizona State University.

In the summer of 2000, after completing my bachelor’s degree in engineering, I had to decide where to go next. I could either take up a job offer at a motorcycle manufacturing plant in south India, or I could, like many of my college friends, head to a university in the United States. Most of my friends had assistantships and tuition waivers. I had been admitted to a couple of state universities but did not have any financial support. Out of a feeling that if I stayed back in India, I’d be ‘left behind’ – whatever that meant: it was only a trick of the mind, left unexamined – I took a risk, and decided to try graduate school at Arizona State University. I hoped that funding would work out somehow.

So in August 2000, I found myself traveling across continents to this powerful country that I knew little about. It was my first ever time outside India and my first ever flight. From Chennai, I flew to Kuala Lumpur, then, after an eight-hour layover which I didn’t mind at all, to Los Angeles and finally, after the worry of a missed connection, to Phoenix, Arizona. The gleaming, modern airports, the meals and the movies, the turbulence and the clouds: it was all very exciting, a glimpse of an elite world that had once seemed inaccessible.

At the Phoenix airport, someone from the Indian Students Association at ASU came to pick me up. After what seemed like a recklessly fast drive – in fact it was normal: it’s just that I’d never experienced a 70-miles-an-hour ride on a highway before – he dropped me off at an apartment shared by three Indian grad students. One of them, my host until I found an apartment, wore a veshti, the wraparound skirt common in south India. He spoke Tamil fluently; he spoke it so well that I could well have been in my home state. I had a nagging suspicion at the time that people might change as soon as they landed in a foreign country – that they might change their attire, even forget their mother tongue. It was reassuring to know that wasn’t true. At the heart of such doubts, I see now, was a fear that I would quickly surrender my Indianness.

I slept well on the couch that first night, and when I woke up next morning, everyone was gone.  There was a massive, just-opened bag of potato chips on the dining table. What better way to experience America on your first morning than digging into a big bag of Lays that grad students, making good use of buy-one-get-one-free, always had in good supply? I had never seen a bag that size! I ate some with guilt, consoling myself that nobody would notice. Not that anyone cared, of course. It was only the first of many ‘big’ things I encountered in those early days: a massive warehouse – a Costco store – where you could pick out things in bulk at cheap prices; gleaming red tomatoes as large as cricket balls (but strangely tasteless); monster trucks with 53-foot long trailers hurtling down the highways and interstates, looming behind small cars until they yielded.

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