George, John, Paul, Ringo, and Fermi
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As soon as the meeting ended, I stepped outside to gather myself in the peaceful open space of our large front yard. There, a cluster of four towering loblolly pines—whimsically named George, John, Paul, and Ringo by me—formed an elegant skyline against the pristine, boundless azure. The fabulous foursome immediately greeted this restless soul with their distinctly soothing scent that was monopolizing the yard’s morning air.
On one of Paul’s upper twigs perched a familiar visitor to our yard, a tufted titmouse with its distinctive pointed crest. It was pouring its small heart out in a vehement song. Perhaps the lonely bird felt envious of or was flat out peeved by the lively chatter of a pair of courting Carolina chickadees, happily munching on sunflower seeds from the tube bird feeder that I had hung on George’s thickest limb.
A bit to the left of Ringo, a young Eastern gray squirrel with a gorgeous bushy tail caught my eyes as it darted nimbly among John’s branches in the mellow morning light. These delightful critters provided me a much-needed diversion, to take my mind off the impending showdown with the ruthless honcho, however brief.
I then sauntered leisurely, past a shorter and stouter pine, over to the backyard, where an Autumn Blaze maple stood in splendor, its broad, oval crown set noticeably amid the sea of green pines. Every year, from mid-October to mid-November, one of my daily rituals was to dash to this tree as soon as I woke up and relish its foliage resplendent in mesmerizing hues, the colors blazing with a fervor that rivaled the vibrancy of Mom’s best hanbok. Resenting anything that might hasten the shedding of those dazzling leaves, I’d give the stink eye to any passing wind or raindrop.
Fortunately, the maple’s beauty wasn’t limited to autumn alone. It would catch my attention in early spring when tender buds sprouting on its bony twigs shyly blushed with a reddish palette; in summer when its branching stems garbed themselves in lush, star-shaped foliage of medium green; and even in the starkness of winter, the season Shakespeare deemed ideal for a sad tale, when a lingering touch of ruddy hue forlornly clung to its denuded branches.
And there was more to the maple than its pretty appearance. The area surrounding the tree provided my personal sanctuary, my own cut of the universe. Under its generous shade, I could lose myself in music, dive into a book, doze off, or just drift into a reverie, my imagination roaming unrestrained until it ran out of castles to build.
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This spot in our yard also became a refuge for my older brother and me during the dog days of summer. When a sweltering Georgia July night threatened to stifle us within the confines of our home, we’d bolt outside, shirts tossed aside, and flop down under the maple. We would then just lie there, chatting until the cool green grass had fully absorbed the heat from our skin. Every now and then, wind would sweep through the backyard, stirring the hearty summer maple leaves and pine needles to perform nocturnal songs and dances that complemented the ambiance of our nighttime outdoor retreat.
If the sky was cloudless, we’d direct our gaze upward at the blackness teeming with tiny white shimmers and marvel, not only at their beauty but also at the realization that observing them was akin to riding a time machine to peer back in time. For instance, Polaris, also called the North Star, is 434 light-years away from Earth. The light we’re currently seeing from that star began its journey to Earth during the time when England was ruled by the first Elizabeth and young Shakespeare was penning The Taming of the Shrew, one of his earliest works. Isaac Newton, the genius who would later revolutionize our understanding of the motions of stars like Polaris, wasn’t even born yet.
On particularly clear and dark nights, Hyung and I would even go galaxy hunting, chasing after the faint outline of the Andromeda galaxy. Our interest in the Milky Way’s distant sibling was sparked by a thought-provoking Japanese anime television series, Galaxy Express 999, with its philosophical, melancholic tale of a boy’s adventures on a spacefaring train bound for Andromeda.
To kick off our cosmic hunt, Hyung and I would first cast our eyes high toward the middle of the night sky. We’d then trace with our fingers as if they were mouse cursors to spot the familiar pattern of stars that formed the keystone in our favorite constellation, Hercules. Next, slightly to its left, the Lyra constellation with its beacon star Vega, one of the brightest fixtures in the summer sky. After pinpointing Vega, our fingers would navigate once again to the upper left until we found the Cassiopeia constellation, its quintet of luminous stars sketching a distinctive “W” pattern on the black canvas.
Tucked near the right-hand half of the W, we’d finally locate our quarry: the faint, fuzzy glimmer of the Andromeda galaxy, the most distant object visible to the naked eye at an inconceivable 2.5 million light-years away. Touching again on how stargazing intertwines with the past, this barely perceptible blur of light had started its epic voyage toward us at a time when our earliest human ancestors, Homo habilis, were just starting to use stone tools. As Hyung and I intensely squinted our eyes to peer at the Andromeda galaxy, we even imagined whether there might be alien beings there who could also gaze at the minuscule hazy patch of our Milky Way in their night skies, wondering whether similar intelligent beings exist here as well.
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One time, we even ventured to estimate the number of places in the Andromeda galaxy that might harbor intelligent life, like we have here on Earth. For this ambitious mental exercise, we used the estimation method proposed by the Italian-American scientist Enrico Fermi. He was a particle physics professor at the University of Chicago in the 1950s, and during his first lecture each semester, this sui generis scientist introduced his students to an unusual approach, later known as the Fermi Question. It helped them estimate answers to problems using only logical reasoning, existing knowledge, and a bit of plausible imagination.
For example, Fermi would randomly ask his students a question that seemed totally unrelated to physics, like challenging them to estimate how many piano tuners were in the city of Chicago. (Back then, it was more common for American families to own pianos than it is today.) For the students who were stumped and didn’t know where to start, Fermi showed them how to quickly approximate a number that wasn’t too far off from the real answer. It probably went something like this:
There are about 3 million people living in Chicago. If we assume an average of four people per family, that gives us roughly 750,000 households (3 million divided by 4). Now, not every family has a piano, but from experience, we can reasonably guess that maybe one in five does. So, that gives us around 150,000 pianos (750,000 divided by 5).
Now, let’s think about the piano tuners: a tuner probably works 50 weeks a year, taking a two-week vacation, and works five days a week. We don’t know exactly how many pianos a tuner services each day, but let’s say about four—that would mean one tuner tunes or fixes about 1,000 pianos a year (50 x 5 x 4).
Since we estimated there are around 150,000 pianos in Chicago, if we divide that by 1,000 (150,000 divided by 1,000), we can estimate that there are about 150 piano tuners in the city.
Of course, Fermi’s approach isn’t perfect, since his estimate is based on assumptions and doesn’t account for certain variables—like the fact that not all 150,000 pianos will need tuning or fixing every year. Still, even though his conclusion might be off by a factor of 1, 2, or even 3, it’s unlikely to be off by a factor of 4 to 10. In other words, it’s pretty improbable that, in the 1950s, there were only 15 to 90 piano tuners in all of Chicago, or as many as 600 to 1,500.
The Fermi Question was really useful when his students needed to get a rough estimate for a difficult question, especially when it involved big numbers, before diving into more advanced formulas and methods for precise calculations. By doing this kind of mental exercise, Fermi emphasized that the process was just as important as the final answer when tackling complex scientific problems.
Also, Fermi probably asked the ‘piano tuner’ question not just to show his students the benefits of logical thinking and imagination, but also to highlight the importance of curiosity and knowledge. After all, being able to come up with simple shortcuts to solve tricky problems and get close to the right answer depends on having a curious mind that’s gathered knowledge from lots of different areas. Plus, the more you know, the more there is to love, and the less you know, the less there is to love.
To estimate the number of places in Andromeda with intelligent alien civilizations, Hyung and I utilized various pieces of information we already knew: the number of stars in Andromeda (around 1 trillion), the structure of our solar system with its 300 planets and moons, the concept of a galactic habitable zone, the Goldilocks zone for planets, random chance, and even the odds of winning a 6/49 lottery (1 in 14 million). After going through a dozen stages of calculations in our heads with these huge numbers, we finally came up with these figures:
- Number of planets and moons – 300 trillion
- Number of habitable planets and moons with complex living organisms – 15 billion
- Number of places that harbor intelligent beings – 37
We knew our estimates might be off by considerable factors, but narrowing down the number from 300 trillion to just 37 somehow made the universe feel a little friendlier and less intimidating. And even if our final number was overly optimistic, we felt confident that, given the sheer number of solar systems in Andromeda, there had to be at least a few places harboring alien civilizations. After all, organic molecules, the building blocks of life, are found throughout our own solar system—in planets, moons, and even asteroids—so why should it be any different in other solar systems across the cosmos?
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As an educator in the present day, I believe that Fermi’s outside-the-box brain exercises are still valuable, even in this age of smartphones and AI. In fact, the world my students live in today is far more complex than it was for me at their age. Consider the massive amounts of qualitative and quantitative data they are bombarded with daily, a volume that will only grow as they face increasingly complicated challenges, like the climate emergency and advances in artificial intelligence, robotics, quantum computing, blockchain technology, nuclear fusion, CRISPR gene editing, and 3D printing.
Human civilization is currently in the midst of a new technological revolution, one as transformative as the Industrial Revolution of the mid to late 19th century. Approaching problems like Fermi to imagine solutions and estimate possible answers—even when exact precision is not possible—is more critical than ever for today’s generation, in any line of work.
And there’s no doubt that curious young people who have cultivated knowledgeable and healthy minds can make more informed and rational decisions in important personal matters as they grow older, enrich their lives, and protect themselves from falling prey to disinformation, fake news, illogical ideas, and demagoguery in today’s age of social media misinformation and extreme racial, nationalistic, and religious ideologies.
With that in mind, I often challenge my students with random guesstimation exercises while teaching, some serious and some silly. But the most fun I ever had with a Fermi guesstimation challenge was in 2019, when I asked a small group of students—refugees from Africa and Asia who had come to Korea with their parents and whom I was volunteering to teach on weekends—to estimate the number of Starbucks in Seoul. They were to follow a logical path, using only basic knowledge, reasonable assumptions, and, if needed, some simple math. The person who came closest to the answer would win a grande green tea Frappuccino from Starbucks. The line of reasoning the eventual winner used was so impressive that it would’ve made Fermi proud if he were alive today:
“Okay, teacher, what I do know for sure about Seoul is that there’s always a Starbucks near a subway station. A lot of these stations are in busy areas, so it makes total sense for the company to put stores there. I’ve also noticed there’s always a Starbucks in big department stores and near E-Mart supermarkets.
“I know there are around 300 subway stations in Seoul because I learned that in school. So, I’ll start by assuming there’s at least one Starbucks near each station.
“But some stations, like the ones in Gangnam and Myeongdong, are always packed with people, so they probably have more than one Starbucks nearby. I know for sure there’s more than one store around Gangnam Station. So, I’m going to guess that at least 30% of the subway stations are in super crowded areas, and each of those probably has at least one extra Starbucks nearby.
“I also know there are 25 districts in Seoul, and I’m guessing there’s at least one big department store and two E-Marts per district, since that’s how it is in mine. Based on my own experience, I’m pretty sure there’s just one Starbucks in each of the 25 department stores and 50 E-Marts.
“There must also be some Starbucks that aren’t near a subway station or big department store, because I saw one like that a few weeks ago. It was in the middle of a quiet, fancy neighborhood, far from busy areas. But since it’s pretty rare to see a Starbucks in a place with no subway or mall nearby, I’ll assume there’s only one of these stores in each of the 25 districts.
“So, here’s my final estimate, teacher: 300 x 1 + 300 x 0.3 + 75 x 1 + 25 x 1 = 490.”
I once read online that there were about 284 Starbucks in Seoul in 2014. Not expecting a huge 75% growth in just five years, I skeptically grabbed my phone to check the Starbucks Korea website and see how many stores there really were in Seoul in 2019. It turned out there were 497. My student was off by just 7 from the actual number.
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I stood still in the backyard’s serenity, gazing at the maple’s canopy draped in achingly beautiful colors, though many leaves were already losing their vibrancy, and inhaling the natural fragrance emanating from the foliage. Autumn, more than any other season, is a feast for both the eyes and the nose. To seek solace once again in the maple’s familiar comforts, I began gathering a heap of fallen leaves in a sunlit spot beneath the tree. I then lay down on the pile, relishing the soft sounds of rustling and crinkling as I settled in. The morning sun kindly blanketed me with a warm photon sheet.
Suddenly, a swift gust of wind jolted the leaves, sending the light-tan desiccated ones clinging for dear life to the maple to rain down on my face. I perversely enjoyed listening to their swan song, for there’s no sound in nature sweeter to my ears than the melody of crisp autumn leaves falling to the earth in droves. Perhaps only the persistent sound of heavy summer rain on a still night comes as a close second.
But as much as I craved to lie on the leaf-strewn bed and continue savoring the visual and olfactory sweetness of the romantic autumn morning, there was an orphaned kitten in my room whose fate hung in the balance. The poor thing needed me to act urgently to secure the necessary votes, all within a fleeting fifty-minute window.
Springing to my feet, I vigorously dusted off my jeans and red UGA football hoodie, then sprinted toward the basement of the house. This spacious area was solely occupied by my older brother, whom I not only regarded as a role model but also trusted as a dependable ally—or so I thought.