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It All Adds Up

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Mathematics Professor John Schmitt and student Aden Forrow in Warner HallNearly 60 seconds of silence had elapsed since I mentioned to John Schmitt that he must be inordinately proud of the young man sitting to my left. The awkwardness for me began around the, oh, 20-second mark, so my discomfort surely must have been palpable at this point. Schmitt had seemed ready to answer a few times, but each time he stopped. Finally, he said, “Aden’s intellect isn’t my doing. His work ethic isn’t my doing. His thoughtful approach to problem solving isn’t my doing. I’m delighted that he has these opportunities [after graduation], but pride is not something I can claim. Delighted. That’s what I feel.” I exhaled. My fear that I had misspoken was replaced by the revelation that this mathematician wanted to make sure he was precisely understood.

Let’s back up a moment. I was in Schmitt’s Warner Hall office, chatting with him and the aforementioned Aden, full name being Aden Forrow ’13, an exceedingly quiet, very pleasant young man from the Boston area. In a recent talk, Schmitt had referred to Aden as likely “the most mathematically gifted student I have ever taught.” For the past year or so, the two have been investigating a problem within the area of mathematics known as combinatorics. Schmitt explained that in combinatorics “we are given a finite set of objects and a set of rules placed upon the objects, and our two most basic questions are 1) does there exist an arrangement of the objects that satisfies the rules, and 2) if so, how many?” A Sudoku puzzle is a trivial combinatorial problem, Schmitt said. “But what is more interesting,” he added “is discerning the minimum number of clues that can be given while still providing for a valid puzzle.” The conjecture is 17, and recently an Irish mathematician designed a procedure to prove that no 16-clue puzzle could exist. Tricky thing is, it would take a standard desktop computer 300,000 years to complete the computation.

So Schmitt and Aden are trying to solve the problem using a tool known as the Combinatorial Nullstellensatz . . . and that’s pretty much all I will say about this tool. I asked Schmitt to explain it to me, and another silence arose. Aden quietly chuckled. Then, as polite as he could be, Schmitt attempted to tell me about the Combinatorial Nullstellensatz. Let’s just say that we subsequently both agreed that C. N. is not meant to be understood by a general audience. And, frankly, it’s beside the point.

The point, really, of our discussion was not how Aden and Schmitt were attempting to solve this problem, nor was it about whether they would actually solve it at all. (“One never knows how long it will take to solve a math problem, if you can solve it in the first place,” Schmitt would later say.) No, the reason we were talking that afternoon was because it was so unlikely to be having this discussion in the first place.

Before he met Aden, Schmitt had never found the need to provide a student in an enrolled course with his or her own set of problems, problems that were not a part of the course syllabus. But just one or two days into Aden’s participation in Math 247, Graph Theory, Schmitt knew he had to do something different. “He wasn’t challenged by the class. He picked up on subtleties, special cases that I’ve never seen an undergraduate recognize. There have been times when I’ve noticed disparities between talented students and the whole of a class, but this generally happens in introductory courses. Aden was on an entirely different level.”

So Schmitt decided he would seek out a problem for which he and Aden could apply the Combinatorial Nullstellensatz technique. (Using Sudoku came to him at breakfast one morning while he was having his granola.) “And we have been having an ongoing mathematical conversation that each of us has wanted to have. These conversations have been entirely outside of any syllabus; Aden receives no course credit.”

I asked Aden if this matched his recollection.

He thought for about five seconds and then said, “More or less.”

“Aden is very understated,” Schmitt added.

Aden smiled. “One of the things I like about Middlebury is the amount of attention professors give to their teaching and to their students,” he said. Schmitt mentioned that I could very easily be writing a story about Aden’s collaboration with Noah Graham, in the physics department, “but then you would have missed out on capturing my good looks.”

At this, Aden let out a loud, sustained laugh. It was startling, given how quiet he had been. It was a laugh one shares with a peer.

Aden Forrow ’13 will enroll in the mathematics graduate program at MIT next year. If he has an idea for the Sudoku project, he knows who he will call first.   
    

Nordic Coach Andrew Gardner talks NCAAs

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Language, in Depth: Living with Dyslexia

Categories: Midd Blogosphere

bookmaze_WEBThe time that stands out to me, the time when I first realized that I was different, was when I was in the third grade.

At my school, all of the kids in the third grade were asked to read a children’s book to the first graders. This program instilled a very real sense of, I don’t know, superiority, I guess. The age difference between first and third grade isn’t great, but in third grade you can read; it was a differentiator. Reading was imbedded into that sense of identity as a third grader; we were the “big kids,” and we were going to demonstrate it by doing something the first graders couldn’t.

Up until this point, I don’t think I had a full understanding that I couldn’t read like my classmates. I just knew that it was hard, and that was the extent of it. I thought it was like that for everybody. But when it came time for us to choose our books, I remember kids choosing these chapter books, the Magic Tree House series, to show off their reading chops; or maybe they were picking more simple books they had been able to read for a while, books that the first-graders were just learning to read.

So I went that route, picking The Cat in the Hat—except I couldn’t read it. I knew what the story was about because my parents always read to me at bedtime, and I had a pretty good visual memory of the book. I knew how many words there were on a page. The pictures somewhat corresponded with the words, and I could remember the pictures. So up until “reading day” I would have my parents read me that book, and I would try and memorize the story. I would try to remember the words that they were saying.

And then it came time to read the book aloud to the first-graders. And it was right then, when I was sweating, my hands shaking, fumbling for words . . . that’s when I knew. These kids were correcting me. They could read it. And I couldn’t.

That’s when it dawned on me that there was this structure, this hierarchy in the educational world—third-graders should be able to do things that first-graders couldn’t—and I didn’t have a place in it.

I was given the diagnosis in the fourth grade, and it came with such a profound sense of relief. Up until that point, I just felt that I wasn’t smart enough; I couldn’t do what the teachers felt I could do. So getting the diagnosis—that was the ultimate clarification that I was different, but that was good. Suddenly, there was a category that I fit into; I wasn’t alone.

Being diagnosed as dyslexic immediately gave me a sense of what my strengths were and what my weaknesses were. To get these laid out for me was so important because it told me that, OK, there are things I’m going to struggle with, but there are also things that I won’t struggle with. Before, I had no confidence; I just assumed everything would be a struggle.

I was so lucky that my mom was a teacher, because she never had the belief that there were “normal” kids and there were kids who didn’t fit that definition. She sees each kid as an individual learner. The concept that there’s a standard student and there’s a student who needs accommodations is ridiculous because there is no “standard” student. She inherently understood that. Up until my diagnosis, I might have felt alone at school, but never at home.

In high school, I loved studio art, and I think it was expected that because I was dyslexic and because I was good at art, that I’d go to art school. But I saw this as a copout, I saw this as running away from my dyslexia, of conforming to others’ beliefs in what I could or couldn’t do. I had this deep drive to prove to people that I could do academics. I was going to go to a rigorous liberal arts school! And then I was going to be a history major!

When I got here, I felt like Middlebury had taken a risk with me; I was a risky investment. I mean, I knew what I could do, but how could they know for sure? I had bad SAT scores, and I probably spelled some stuff wrong on the application. So I put pressure on myself to prove that kids with learning disabilities, kids who don’t do well on the SATs, can contribute a lot to the community—they can be creators, innovators.

At first I thought that meant excelling in areas I wouldn’t normally excel in and limiting myself to one studio art course a semester—things like that. And I did well. But then I wondered, Why am I not doing what I really want to do? I remember being told that I was going to reach a point in my life when I’d be able to do the things that I wanted to do, that I wouldn’t always have to work so hard to overcome my learning difference.

But there’s no guy standing on the corner saying, “You know that point? It’s happening right now.” You have to come to that realization yourself, and I think this is especially difficult for people with learning differences. When do you shed off that stuff that you have to do?

I think I’ve spent a long time feeling not so great about myself; there are self-esteem issues deeply embedded in working within other people’s expectations. And if you are not doing what you really want to do, not playing to your strengths, then the validation you receive is completely external, and you never feel satisfied.

I’m still working through it. But I’m a studio art major now, though I might minor in history.

Living with dyslexia . . . it’s hard. But from my experience, you have to own it. It’s who I am. It’s always going to be me. Understanding this is essential in order to be happy as a human being.

Language, in Depth: What is the Meaning of “Meaning”?

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Middlebury_Prism-WEBWhat is the meaning of “meaning”?

This apparently recondite question, posed by the philosopher Hilary Putnam in a seminal 1975 paper, actually lies at the core of the branch of linguistics known as semantics. How we answer this question will have important implications for a variety of issues that are currently hotly debated in linguistics, such as whether some concepts are innate, whether different languages create different styles of thought or experience (linguistic determinism), how languages are learned, and so on.  In the second half of the 20th century, the prevalent commonsense view of meaning faced a number of serious challenges, but none was as potentially revolutionary as that raised by Putnam and other similarly minded philosophers of language.

I always begin my Philosophy of Language course by asking students what they take to be “the meaning of ‘meaning,’” and the most common initial response is, in short, that meaning is something in the head. The meaning of a sentence like “It’s six pm in Denver now” is a thought in the mind of the speaker, presumably the thought that right now the time in Denver is six pm; the meaning of a word, for instance “cauliflower,” is the speaker’s concept of that thing. This view is a very commonsensical one for us today, and also one with a long historical pedigree.

The 17th century philosopher John Locke held that a man’s words “stand as marks for the ideas in his own mind, whereby they might be made known to others, and the thoughts of men’s minds be conveyed from one to another.”

But Putnam and other philosophers, such as Saul Kripke, raised deep-seated objections to the idea theory, objections whose implications philosophers and linguists are still trying to unravel. Putnam’s challenge takes the form of a thought experiment involving a make-believe planet called “Twin Earth.”  Imagine, he says, that somewhere in the universe there is a planet that is, with one exception, molecule for molecule identical with Earth. On Twin Earth there are twin trees and twin rocks. There are even doppelgangers of you and me, who speak something that sounds just like English. The only difference between the two planets is that on Twin Earth, the lakes and rivers don’t contain H2O, but a substance with a different chemical formula we can abbreviate XYZ. XYZ is, to the naked eye, indistinguishable from H2O, and Twin Earthians drink it, cook with it, and even call it by the same sound we use, “water.”

But, Putnam asks, what does the Twin Earthian word “water” mean? Clearly, it does not mean water. After all, water is H2O, not XYZ; a substance with a different chemical formula would not be called water. But—and here’s the rub—this difference of meaning would exist even if Person A on Earth and Twin Person A on Twin Earth were exactly identical in terms of what’s “in their heads.” Suppose that it’s the year 1750 (Earth time), and no one on either Earth or Twin Earth has any understanding of chemical composition. Person A and Twin Person A will then share all the same beliefs about their respective liquids:  that it’s clear, odorless, thirst-quenching on a summer’s day, and so on.  But even so, the meaning of Twin Person A’s term “water” cannot be water, for this term refers to XYZ, not H2O.  Person A’s and Twin Person A’s “concepts” of these substances are identical, and yet the meanings of their terms are different. So meanings cannot just be concepts. As Putnam puts it, “Cut the pie any way you like, ‘meaning’ just ain’t in the head!”

Or, at any rate, not wholly in the head. Putnam’s proposal is actually that the meaning of most words includes two components: one that is not in the head, the word’s extension, or the things to which it applies (in the case of water, H2O); and one that is in the head, the word’s “stereotype.” This may seem, to put it mildly, surprising. How could H2O itself be part of the meaning of “water” in 1750, before anyone knew that water was H2O? Putnam’s idea is that “water”, and indeed most words, are actually akin to indexical words like “this,” “that,” and “now,” whose meaning depends on context. What I mean when I say “that” depends on whether I’m pointing to my cat or my car, and if I’m pointing to my cat, what I mean is the cat itself. In a similar way, the meaning of “water” “reaches out” to encompass the actual stuff in the world to which the word refers, even if the speaker doesn’t fully know the nature of that stuff.

Putnam’s view of meaning has sparked a great deal of controversy since it was proposed, but it has had a tremendous influence. What are its implications? What it means for broader questions concerning, for instance, the innateness of language and linguistic determinism, is still very much a subject of debate. However these specific issues are decided, this new perspective has suggested to many a broad reorientation of our way of thinking about the relationship between the mind and the world. The idea theory of meaning, by picturing meaning as something wholly within the speaker’s head, in a sense separates the mind from the world. On Putnam’s view, the meanings we grasp with our minds encompass things outside the mind, which suggests we should think of the mind as fundamentally open to the world, rather than closed in on itself.

For those who accept Putnam’s argument, there is much work to be done in order to understand what exactly this means about the nature of human subjectivity and its relation to the world.

John Spackman is an associate professor of philosophy. He teaches a course at Middlebury titled “Philosophy of Language.”

By All Appearances

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Dwayne-Nash-1WEB

Dwayne Nash ’99 was once part of the legal institution he now seeks to reform.

The morning was like any other. It was late February, and Dwayne Nash ’99 woke in a brownstone on Manhattan Avenue, in New York City’s Precinct 28, where Malcolm X once demanded custody of a black man the police beat nearly to death. That was before the riots, before crack hit hard and the War on Drugs took the dealers and doers to prison, and Harlem became a nice, historical neighborhood with tree-lined streets and rents so high that Nash, a former criminal prosecutor, could hardly afford his own apartment. This morning, like every morning, Nash lay in bed and scrolled through headlines on his iPhone. One caught his eye—a neighborhood watchman had shot and killed an unarmed black kid in Sanford, Florida. Trayvon Martin had looked “suspicious,” the watchman, George Zimmerman, said. Martin was on his way home with an iced tea and a bag of Skittles when Zimmerman called the police. By the time an officer arrived, the young man was dead.

Nash had known his share of murders, but this one particularly rattled him. Zimmerman had claimed he acted in self-defense, and the police let him go. “You have one person standing there with a gun, the other person dead. You have to give the body the benefit of the doubt,” said Nash. Why didn’t they? “I don’t think the police were incompetent. I think they saw no value in Trayvon, in investigating any further. His blackness made his body less important.”

Two weeks later, a reporter for the Chronicle of Higher Education met Nash in a coffee shop in Harlem. Nash, 35, is at first glance modish and circumspect; the reporter took note of his “Burberry tie” and “wing-tipped shoes.” She wanted to know what he thought of the incident. Nash, a doctoral candidate at Northwestern University’s black-studies program, was researching the history of stop-and-frisk, a police tactic popularized in the 1990s by former New York City mayor Rudy Giuliani. His research is part of a growing body of work that equates the criminalization of today’s minorities with the laws that once denied African Americans their basic rights. One-third of all black men in the United States are under the watch of the criminal justice system—in prison, on probation, on parole—the majority charged with drug possession and other nonviolent offenses. Statistically, a white person is more likely to use drugs than an African American. Scholars have known for a long time that the numbers don’t add up and trace the disparity to the 1980s and the War on Drugs, when police raided dense, urban neighborhoods. But Nash’s work traces the problem even further back, to the 1960s, when the Civil Rights Act passed and white Americans grasped at a new kind of racial control.

Nash chose his words carefully to the Chronicle reporter, at once gentle and emphatic: “Whether we are stopped, searched, arrested, or shot, it’s all the same. We’re being read as a threat, criminal, or suspicious at the very least. Instead of Trayvon Martin, it could have been me that was killed. I pray that a gun barrel is not pointed to my face for making an innocent gesture or for being in the wrong place at the wrong time because of my skin color. There was no right place for Trayvon. He was walking home in the rain, doing nothing wrong, and he was read as suspicious.”

This past October, when I met Nash in Chicago, I asked him to reflect again on the incident. George Zimmerman, the watchman who shot Martin, had since been arrested and charged with second-degree murder. Nash was dissatisfied. “There is a long history of viewing the black body with criminal suspicion,” he said. “That memory has been transmitted across generations and time—and across institutions, as well.” In this case, said Nash, the real problem was not Zimmerman, nor even the cops, but Florida’s stand-your-ground law, which gives the benefit of the doubt to anyone who claims they shot another in self-defense. “If you believe that Zimmerman was just one bad apple, just ‘that racist,’ then you miss the point,” he said. “Zimmerman knew that he could draw from the law to protect himself. He knew he had greater rights than Trayvon. He did something wrong, but the legal institution made that possible.”

The Mother Tongue

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navajo2_webLanguage is culture. The Navajo language is Navajo culture. When one changes, so does the other. Many ceremonies and cultural activities peculiar to and associated with the language that my grandparents spoke are now gone.

I will never experience the Navajo associated with that worldview. It is gone forever. But language is alive. When it diminishes in one area, it expands in another. In Navajo, we adopt new words to articulate contemporary concepts and objects like neuro-immunology and computers. We strive to maintain the integrity of tradition while accommodating an ever-changing world.

Although cultures may evolve and languages may change with the times, certain linguistic and cultural associations function as inalienable, immutable forces that keep us Navajos. One such force is the notion of k’e—relationship building that is linguistically and culturally Navajo. Within our clanship system, a 96-year-old grandmother may call me “Daddy.” On Navajo, when I talk about all my children, everyone understands. Off Navajo, I am often asked how many children I have and it is demanded of me to explain how one of my children can be 46 years older than me. I used to try, but now I don’t even bother. My reality in Navajo needs no explanation in English to a non-Navajo worldview.

This peculiar relationship allows our elders to be childlike again. It allows them to be goofy without being ridiculed. They use this opportunity to ask of me as their father things that I cannot provide them. Through these interactions, they teach me how to be a caring and loving father to my own children, passing on lifelong lessons of parenting. At the same time, they would tease my children as brothers and sisters, establishing lasting and valuable relationships. These elders and my children bond together for life, respecting and loving one another as siblings.

In Navajo, we call our biological nieces “mothers.” From birth they are our mothers; our kinship demands that we respect them as matriarchs. Our interactions with them must help them become mothers and leaders of the family. Knowing this, I do my part, misbehaving and allowing them to chastise me for being foolish. In so doing, we begin to train them to become matriarchs.

Video: Rex Lee Jim, on his interest in langauge

They learn quickly. On her first day at school as a kindergartener, my youngest niece was running around when her teacher asked her to stop. When she refused, her teacher said, “I am going to tell your uncle, the school board president.”

“What uncle?” she responded.

“Rex.”

“He’s not my uncle; he’s my son. I tell him what to do!”

The Navajo teacher realized what was going on. “Well, I will tell your ‘mother’ Janice (the ‘aunt’) at the high school.” My niece settled down right away.

The Navajo language allows us to develop intimate and unique relationships, which is the foundation of strong, healthy communities. When we no longer speak the language, what makes us distinct and unique will be gone. We will be speakers of English with brown skins. The Navajo community will no longer be.

Whither Courtly Love

Categories: Midd Blogosphere

CourtlyLove-webWhen I was an English major at Middlebury back in the eighties, courtly love was my cod liver oil: dosages were the mandatory price I paid for the lovely beef stew of Middlemarch and the meringue of Pride and Prejudice. It was key to Chaucer’s Knight’s Tale, in which two suitors duke it out to win the love of fair Emily, and Spenser’s deadly boring Faerie Queene, and even in Shakespeare, my bugaboo was unavoidable: the romantic fealty of courtly love is captured in Sonnet 18 (Shall I compare thee to a summer’s day…), and its vanilla rituals mocked in Much Ado About Nothing and As You Like It. Even when it was the subject of satire, courtly love spawned my biggest, baddest internal eye roll. Once I had my diploma in my 22-year-old hand, I was sure that with respect to the canoodling of knights and ladies, I’d never look back.

But then I wound up writing an entire book about the social and cultural history of heartbreak, and no matter how sturdy my decades-long resistance to courtly love was, ignoring it in my book would have been downright negligent. After all, at least in the beginning stages of the courtly romance formula, heartbreak was codified: a knight attempts to attract a married noble lady’s attention via stolen glances; then he circles said lady like a shark, perhaps by attending court just a little too often; then he declares “I love you,” perhaps from behind a curtain or in a dark corner; the lady replies, “No, no, no! I’m so very married and so very devout!” and focuses on her needlepoint; the knight says he just might die if his lady doesn’t return his love; then the knight moons around court bemoaning how the lady doesn’t love him back.

Only when the knight takes a dramatic risk is the spell of unrequitedness broken: he might get his hot little hands on a ribbon from the lady, tie it to his lance, and proceed to win a jousting tournament (with bonus points for any injuries sustained). Only then might she give in and reward him with kisses and/or sex, and from there they might sneak about for a little clandestine codpiece ’n’ corset action. The nobility of courtly love, of the heartbreak, was in the attenuated longing, and consummation between the lovelorn knight and his lady was theoretically verboten. If the relationship was consummated, the thrill of the chase was replaced by the thrill of evading detection.

No doubt part of the reason why I found courtly love so irksome lay in the fact that it was so at odds with what I was experiencing as a young woman at Middlebury in the eighties—or thought I was experiencing. Among my peers/friends, romance and its close associate, eroticism, were certainly not celebrated. (The terms I recall for sexual encounters were “hooking up,” “muckling,” and most memorably, if repeated encounters were the case, “dealing.”) In my own personal experience, the only thing that sex and romance at Middlebury had in common with courtly love was that it was furtive: the closest thing I had to a relationship in college was a guy I’d hook up with—FOR THREE YEARS!—but we couldn’t hack breakfast together in Proctor, much less meet up to see a Hitchcock movie at Dana Auditorium. It makes sense then that my muckling self, sitting there in the second row of a classroom in Munroe, Faerie Queen open, was perplexed by the idea of an entire subculture devoted to mooning around for love.

But then, nearly 25 years later, I found myself fascinated by the academic debates that have, for decades now, framed discussions about courtly love. What was it exactly? A real phenomenon, a literary device, or a little of both? Among those who believe that knights really did hotly pursue married women, the phenomenon is thought to have been more or less natural adaptation: in a milieu where marriages among the upper classes were arranged and loveless, courtly love was a neat ruse that covered, justified, or perhaps even celebrated adultery. Some who have studied it have gone so far as to suggest that the spread of courtly love across Europe from the 12th century onward marked a sexual revolution in which women radically turned the tables on men. Others are quick to point out that there is really no evidence whatsoever that courtly love existed anywhere but on paper and in song: no legal cases, no chronicles, no correspondence. It has even been suggested that many depictions of courtly love in medieval literature were more or less ironic jokes, just as they were in Shakespeare several hundred years later.

Initially, as I absorbed the fact that courtly love has no smoking gun, I felt vindicated: my 20-year-old self was wise beyond her years. She knew courtly love was bogus. It was as absurd as, in today’s world, a midlevel manager professing undying love for the CEO’s wife, sailing into tough meetings with her Hermes scarf wrapped around his arm, and then crying to the crowd around the water cooler about how she doesn’t love him back.

But the nagging questions about it also got me thinking about love at Middlebury in the eighties—about what was, what wasn’t, and what might have been. Naturally this line of thinking got me rummaging around in what I think of as my Middlebury closet, pushing past my cynicism to the painful box of regrets/box of pain, but it also got me going drawing comparisons between the upper echelons of the medieval world and, yes, Middlebury. Think about it: like a royal court, Middlebury is elite, packed with smart and attractive people; like a court, it is physically isolated from the rest of the world; and like a court, it has its cliques and pecking orders. It is a castle on a hill.

And, like any court, and any small school, Middlebury also had its own culture. What strikes me now is that a key component of that culture was this: love wasn’t cool. “Hooking up” was cool, walks of shame were cool, but unabashed love, as in shouting to the hills that are his also, that you were madly in love? Not so much. Sure, there were the rare couples who were in love and wore their hearts on their Patagonia sleeves, but those were the exception, not the rule. The way I see it, never in the history of man has there been a group of 18–21-year-olds quite so determined to not be in love.

I’m sure this had something to do with the fact that for four years, we were in essence at an endless banquet: you could pick and choose among countless smart, attractive, and more-or-less like-minded individuals to spend your time with. Indeed, you could have a crush in every dining hall to keep you entertained. The rock climber who ate with his friends in the SDUs; the lacrosse player in Proctor who you hooked up with freshman year; the moody poet in Lower Proctor. I also think the collective resistance to love originated in naiveté: little did we know just how precious that time in the castle on the hill was, and weak was our understanding that never again would we share such intimate space with so many interesting people the same age. So the saying goes, youth is wasted on the young.

But I’ve talked to a few close friends from Middlebury about this, and we all agree that there was more to it than that. At Middlebury then, and perhaps now, tribalism was fierce. Perhaps the lack of love at Middlebury also had something to do with fear of crossing social boundaries, of being associated with someone who, even within the coziness of Middlebury, was “other.” Love wasn’t in the air, but following the rules was. And foremost in that pack of rules was this: “Thou shalt not profess undying love.”

I’m in my mid-forties now, and perhaps unduly preoccupied in my research on love by what was, what wasn’t, and what might have been. I regret that I didn’t have the confidence and steeliness to tell the boys I loved—and yes, there were a few—how I felt, and I regret dismissing the ones who were bold, and yes! wise enough to at least hint that they loved me. Love wasn’t in the air, and yet it was all around us. The flickers deserved to be fed.

And as for courtly love, the trappings of adoration, confession, and persistence, and my now-ancient distaste for them? Now I know that the line between scorn and envy is a thin one. Love isn’t just loving, it’s letting oneself be loved.

Meghan Laslocky ’89 is the author of The Little Book of Heartbreak: Love Gone Wrong through the Ages, Plume/Penguin 2013.