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Peaslee debaters win Speaker of the Year and Team of the Year

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Peaslee members Miriam Pierson ’18 and Nate Urban ’18 made debate history last week.

Together, they won Team of the Year, and Pierson took home the Speaker of the Year award.

These awards are given out annually to the top-ranked college debate team and debater, respectively, within the American Parliamentary Debate Association. Pierson and Urban are the first debaters from a liberal arts college to take home the Team of the Year award since 1997. Pierson is the fourth woman ever to win the Speaker of the Year award since its inception in 1984.

Pierson and Urban clinched both of their awards on April 7, at a tournament at Princeton University where they placed third overall.

“It didn’t hit us right in the moment,” Urban said.

Teams advance in the rankings by placing in tournaments. Speakers climb in rank by earning speaker points, which are awarded to individual team members at tournaments. By the time Pierson and Urban traveled to Princeton, it was clear that they would emerge the top-ranked team in the league. The winner of Speaker of the Year was decidedly less obvious.

“That was a very intense, down-to-the-wire type thing,” Pierson said. “There were three kids behind me who were in the running to pass me.”

Only once Pierson was named the top speaker at the Princeton tournament did she realize that she had won Speaker of the Year.

“I was very relieved. It’s really exciting,” she said.

Pierson has been debating for eight years. She originally joined debate in high school as a way to confront her fear of public speaking.

“Some of the most important things I got from debate have nothing to do with competitive success,” Pierson said. “It was really important for me to learn how to speak in front of an audience. I was that person who would not talk in class. I would get nervous when I had to raise my hand. I think it’s been really helpful for that.”

Pierson’s debate career at the college has been historic. In her first year at Swarthmore, she won the Novice of the Year award, which is awarded to the top new debater in the league. Last year, paired with Will Meyer ’17, Pierson won the A.P.D.A. National Championship and was ranked the 11th speaker overall. Urban, who started debating his sophomore year at Swarthmore, finished 16th in the speaker rankings this year.

“In the lore of the debate world, where all these people who debated like 20 years ago get on Facebook and talk about the all-time greats, Miriam is firmly in that discussion,” Urban said. “So from my perspective it has been cool to watch her set a lot of goals and reach them.”

According to Pierson and Urban, this level of success is unusual for a debate team from a small college. A.P.D.A. is often dominated by Ivy League teams, particularly those from Harvard, Yale, and Princeton. In the past 10 years, debaters from these schools have won Team of the Year eight times and Speaker of the Year four times.

“It’s a number of things,” Pierson said of the Ivies’ consistent success. “[Ivy League schools] really heavily recruit the top high school debaters. Neither Nate nor I were top high-school debaters. We both really got much more serious about the activity in college. Nate hadn’t even debated before in his life.”

Pierson also feels that small schools are at a disadvantage when it comes to resources. Though Peaslee is funded by an endowment left by its namesake alum, the team still does not have access to the extensive network of past cases and coaches that Ivies do.  

Despite its material limitations, Pierson and Urban feel that Swarthmore’s unique ethos has also propelled Peaslee toward success.

“I think Swarthmore particularly, as a school, really looks for people who are into this type of discussion and debate as an activity: very academic people,” Pierson said.

They also attribute Peaslee’s success to its inclusive environment.

“Debate teams can get super competitive. I’ve seen teams that have a bad environment where it’s like if someone’s doing well, someone else is really angry at them. It’s just really not been like that on our team, which is super positive,” Pierson said.

However, Pierson notes that within the wider sphere of college debate, women and people of color in particular have often felt excluded. As a successful female debater, Pierson has frequently experienced both overt and coded sexism from fellow debaters.

“When I first got onto the league, there weren’t a lot of women debaters who were doing well…” she said. “There were people who would say things like, ‘Maybe women are less persuasive inherently because their voices aren’t deep enough.’ Someone said something to me about how ‘male voices resonate in your soul, and you can really feel the arguments.’”

However, Pierson feels that debate has recently become somewhat more welcoming. In 2017, Jerusalem Demsas, then a senior at the College of William & Mary, became the first black woman to win Speaker of the Year. 2018 also marks the first time Speaker of the Year has been awarded to women in consecutive years.  

“I think it’s really nice to see the league and just debate, in general, becoming a lot more inclusive of women and also for people of color too,” Pierson said. “I think that’s a really positive thing.”

Peaslee president Annie Abruzzo ’20 feels that Pierson has been a positive inspiration for younger female debaters at Swarthmore.  

“I think this kind of success is really good for recruitment,” Abruzzo said. “Not only for recruitment in general, but also recruitment of women onto the team. Debate is something that has often been de facto super male, so to have … someone you can learn from, who is that successful and also happens to be a woman, is really great.”

Pierson and Urban are seniors, so the Princeton tournament was their final time competing in college debate. Though Peaslee will no longer have Pierson and Urban on the team, their influence will still be felt.

“For the team next year, I think there’s definitely big shoes to fill,” Abruzzo said. “I think most debaters can’t aim for that. [However, Pierson and Urban] have tons of cases they’ve written that we’ve been able to learn from. They’ve been able to teach us or help us write our own cases.”

Pierson and Urban plan to continue to be involved with debate at the college next year, if their work schedules permit.

“One of the cool things about the debate league is that a lot of the judges are recent alumni,” Urban said. “We will still be involved to some extent. I think there’s a pretty good chance one of us coaches the Swarthmore team to some degree.”

Looking forward, Pierson and Urban are confident that the Swarthmore team will continue to be successful next year.

“It’s … a really great group of people,” Pierson said. “They’re very close friends with each other. They’re all pretty nice and supportive … And I think they’re going to be really good.”

A queer uprising at Swarthmore: what does it meme?

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On the chilly evening of March 15, snow lay on the ground from the winter storm that had recently swept across Swarthmore’s campus. Little did we know that there was another storm approaching. No, not with wind, nor sleet nor snow — oh no, nothing could prepare us for this storm, not umbrella nor coat nor boots: a meme storm was coming.

It all started in the humble abode of the Swat Danker Memes Society page on Facebook. This page is a place where over 1,000 Swatties (a surge in members came after aforementioned storm) come together to share relatable memes, sometimes post original content, and just generally have a good time.

However, this was not the case on March 15, at 4:30 pm. No, on this fated day the revelry was displaced by none other than, the discourse. It all started with fairly innocent origins when a member posted a meme that consisted of a bit of an inside joke for the queer community. Some non-queer members of the Swat Danker Memes Society, naturally, were confused about what it all meant, and one reached out to the community for an explanation —no problem here. It is what happens afterwards, however, that struck a nerve within the queer community and caused the page to gradually evolve from comment war to gay meme hellfire.

A member of the queer community rejected this request for explanation. Their declination to explain, however, was not met with the same earnest desire for learning and respect for the queer community that the original question suggested. What happened next was an overwhelming flow of online discourse on the matter of respectability politics, whether the queer community (or any marginalized community for that matter) owes anyone an explanation of their culture and many, many offshoot debates that included everything from misgendering people to US foreign policy. It was a bitter war that ended in deleted comments, screenshots, and even more memes. It was a sight to make any baby boomer stop in their tracks and go “those goddamned millennials.”

But what does it all matter? Can political debates on college meme pages have any significance? I’d first like to start this discussion by expressing my frustration that we even need this “Facebook war” in the first place. I was originally pretty upset that the queer community was just trying to enjoy a meme that was meant for them (and was hilarious, by the way) but it had to devolve into political arguments and discourse. However, at the end of the day, perhaps the conversations held around gender and the queer community were, if anything,  important for the growth of Swarthmore’s communal understanding of how to approach oppressed groups in their safe spaces. I do believe that it is perfectly respectable to ask questions about another’s culture — and that sometimes it may well generate enriching discourse that offers both parties a meaningful experience. However, as we have seen through last week’s online discussions, demanding that members of a community participate in discourse with you at your beck and call, even after they have expressed their desire not to, is where it gets dicey.

At the end of they day, a healthy dose of respect and a good understanding of your place is what is needed when approaching these situations. Sometimes, one needs to step back in an argument and ask themselves “Who am I really helping, and who am I hurting by saying/asking this? Am I simply putting unnecessary stress and pressure on already oppressed groups by saying/asking this? What are my privileges in this situation?” All it takes is a little conscientious thinking — really!

Now on to the gay memes. Yes, the glorious overflow of queer memes the following day, which was a response to the fact that all the arguing pretty much ruined the one posted the day before. This outpour of memes proved to me that we really can have nice things (sheds single tear). It may seem trivial, but I’m super pumped by the unity and hilarity of Swat’s queer community that was shown that day.

People might say that the debates were pseudo-activism and there is no real depth behind anything that occurred that day. However, I would like to disagree, activism starts with raising your voice — in whatever context, whether that be online, or in the newspaper or at a protest. No one is saying that you’re going to single-handedly change the world with a Facebook post, but social change happens after the culmination of several incessant voices who refuse to be silent in every sphere of discourse. That day, the Swat Danker Memes page happened to be one of those spheres. Believe it or not, people can tackle more than one issue at once, and being active on  a Facebook debate doesn’t mean you aren’t engaging in other forms of activism in different areas.

Also, as it relates to the specific act of the proliferation of queer memes one needs to remember that the queer community wasn’t trying to be activists in the first place: we were trying to feel good about ourselves. No one is saying that memes are some shining form of activism that are going to change the world (though that may be up for debate). But in those moments, they made the queer community feel empowered and united. It sure as hell made me feel good after feeling pretty frustrated with the whole thing. Isn’t that what matters?  

Free will does not matter

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Freedom is a big word in our country and all too often the notion is taken for granted. Elsewhere I have written on the need to weigh the implicit negative rights of the historically marginalized against the positive rights of those who are privileged. Now, I would like to consider the so-called ‘will’ behind all of our rights and actions.

Usually, people split into one of two camps, those who believe in free will, that individuals will an action to happen and those who assert hard determinism, that the action was going to happen regardless. This is not to say that people apply the same beliefs on free will to all circumstances. It can vary with the given situation: you have absolute control over some things (e.g. whether or not you wake up on time for class) and other things were simply meant to happen (e.g. that great relationship of yours that is going to last forever).

The problem I have with the free will v.s. hard determinism debate is that the result should not, and cannot, possibly matter. We will never (I assume) be able to discover whether we were pre-destined to do certain things. Is this not why most agree that the plans of God, or the gods, or “the natural order,” are nothing but elusive? Unlike other big unanswerable questions, like “what is the meaning of life,” there is only one practical answer to the question of whether or not free will exists: it does not matter.

If we accept hard determinism, we can no longer be held accountable for their actions since some external force predetermined those actions. How exactly do we punish a murderer if they were destined to commit murder all along? Hard determinism removes the possibility of living a moral life. Because of this, we must always accept that some degree of moral autonomy exists for the average human and we must always take responsibility for our final decisions and actions. Of course, this comes with some exceptions, such as the mentally handicapped who do not choose to have a mental illness, young children who are not in control of their actions, and the senile elderly. On the other hand, to what degree is individual will truly “free?” I would contend that two otherwise identical individuals presented with the same dilemma would not make the same decision due to their different social backgrounds. Simply consider two intellectual high school students who are both presented with two college offers: one to a prestigious school that offers no financial aid and another to a less prestigious school that offers a full ride. Is the decision of the kid whose parents cannot afford to pay full tuition as “free” as the individual whose family is much more financially well off?

So, we must accept that most individuals are somewhat responsible for their actions, but those actions are not fully free. But is this not inherently paradoxical? How do you hold someone accountable for something they did not “freely” do? While talking about the existence of free will seems nonsensical to me, discussing the degree to which an individual’s will is “free” could not be more paramount.

During one of my philosophy classes last semester, we began talking about prostitution. Multiple people (men) in the male-dominated class spoke along the traditional libertarian line that we must respect an individual’s free will to do something, even if that something is morally questionable, so long as it does not harm someone else. I ask why we speak of free will along a binary of free and not free. I ask why we focus on the final decision without talking about the factors that led to that decision. I ask not whether the prostitute freely chose their particular line of work, I ask what kind of conditions resulted in that choice. Only then do we get to talk about the different level of coercion present within society, whether that be the strong influence of parental figures or the socioeconomic conditions manufactured by the patriarchy.

A lot of people say nothing is free. And they are right. There is no such thing as absolute freedom in a coercive society, but the degree to which something is free is something we really can, and should, talk about.

What is Freedom of Speech?

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As a citizen of China, one of the most oppressive regimes in the world, I must say that I am disappointed by my fellow liberals’ indifference toward free speech. My experience tells me that whether or not citizens have the right to free speech is the most important distinction between a democracy and a dictatorship. To give you an idea of what it is like to be a Chinese citizen, for the first 18 years of my life, my typical class schedule included a “Politics and Thoughts” class that taught Communist Party propaganda, a History class that taught alternative history carefully censored and rewritten by the Communist Party, and a literature class that included only authors and articles the Party deemed appropriate. I was required to memorize key speeches and principles invented by Party leaders in order to pass the ideology test, in which if anyone dared to write anything negative about the Communist Party, he or she would automatically get a zero and not graduate.

In China, online forums and social media are carefully monitored so that “counter-revolutionary” comments are promptly removed and perpetrators are punished. Human rights lawyers and activists are routinely jailed in secret locations or sent to “forced labor camps” for their beliefs and activities. It isn’t that life is insufferable for normal people without free speech; the brilliance of censorship is that it makes you think only one kind of view can possibly be right, so you don’t feel the need to protest, dissent, or even think.

In high school, during a summer at Yale, and my first time in the United States, I took a human rights class and a legal philosophy class. For the first time in my life, I read the Universal Declaration of Human Rights, which proclaims that “everyone has the right to freedom of opinion and expression.” I read John Stuart Mill’s “On Liberty” and his belief that everyone should have the absolute right to free speech. I read the landmark Supreme Court case, National Socialist Party of America v. Village of Skokie (1977), in which a Jewish lawyer of the American Civil Liberties Union defended the Nazi Party’s right to march in a predominantly Jewish village. I learned about the Tiananmen Square Massacre, on which information was censored in China and where brave college students fought for democracy. They fought for freedom of speech and thought only to face the crackdown of an illiberal regime stuck in its own ways. I learned that liberalism means tolerance and commitment to our inalienable and indivisible rights, no matter what powerful people say, and I began to proudly call myself a liberal. Imagine my surprise when I discovered that most of my liberal friends at Swarthmore not only advocate violence against those who hold a different view, but also believe that freedom of speech is somehow a “conservative value.”

Most debates about free speech these days are simply confused. The kind of knee jerk reaction that many liberals display toward claims of free speech is largely a response to the hypocrisy of some conservative politicians, who, while arguing that liberals are stifling free speech on campus, are perfectly willing to withhold funding from colleges they deem too “radical.” Free speech as a constitutional right is different from the kind of “campus free speech” for which such conservatives are clamoring. Unfortunately, many liberals fail to draw the distinction and end up losing faith in the doctrine of free speech in general. Even more unfortunate are attempts to equate free speech with oppression or even white supremacy. Without freedom of speech, only those in positions of power can speak.

Freedom of speech as a legal, constitutional, and human right is important because it is the bedrock of democracy. Every attempt to undermine this right risks undermining the foundation of democracy and making the U.S. more like China or Russia. You may think I am being alarmist, but plenty of examples exist where free speech restrictions in other liberal democracies have backfired. After a German comedian accused the Turkish President and Dictator Recep Tayyip Erdoğan of oppressing minorities and having sexual intercourse with farm animal Erdoğan sued the comedian with the support of German Chancellor Angela Merkel, under an old German law. In France, after the terrorist attack in 2015, a Muslim was sentenced to a year in prison for shouting “I’m proud to be Muslim. I don’t like ‘Charlie’ [“Charlie Hebdo,” a far-left French magazine previously attacked for mocking Islam]. They were right to do it.” As Howard Gillman, the Chancellor of UC Irvine, argues, “[d]emocracies are more fragile things than we might like to believe.” Free speech is important partly because it allows political minority groups to voice their opinion without fear of retribution.

The constitutional right to free speech, however, is not absolute. Child pornography, obscenity, fighting words, libel, and incitement, for example, are not protected by the First Amendment. But these exceptions are meant to be exactly that – exceptions. Some have argued that hate speech is not free speech. It is factually incorrect as a descriptive claim, and practically and legally problematic as a prescriptive claim. Since the issue of hate speech matters deeply to many skeptics of free speech, I’d like to set the record straight here. In R.A.V. v. City of St. Paul (1992), a unanimous decision of the Supreme Court declared unconstitutional a law that banned the placement of a burning cross or Nazi swastika on public and private property. The majority reasoned that the law was unconstitutional because it only prohibited particular kinds of fighting words that involve “race, color, creed, religion or gender.” In other words, the law constituted both viewpoint and subject matter discrimination. Even though in Beauharnais v. Illinois (1952) the Supreme Court upheld a similar law because the Court considered speech targeting racial or religious groups to be “group libel,” as constitutional law scholars Kathleen Sullivan and Gerald Gunther explain, most judges no longer believe that Beauharnais is good law.

Should the government be allowed to ban hate speech as many free speech skeptics wish? I do not believe this is a good idea. While it is permissible for the government to prohibit speech that incites imminent violence (see Brandenburg v. Ohio (1969)), or increase penalty for hate crime (see Wisconsin v. Mitchell (1993)), as the Court argues in R.A.V., any specific prohibition on hate speech involves content-based restrictions. If, for the sake of argument, the government is allowed to ban speech based on its content, then who is to stop right-wing politicians from passing laws that prohibit speech, for example, that advocates for the violent overthrow of capitalism or mocks Christianity? As the ACLU argues, “free speech rights are indivisible. Restricting the speech of one group or individual jeopardizes everyone’s rights because the same laws or regulations used to silence bigots can be used to silence you.” Of course, the Court can recognize a hate speech exception to the First Amendment, but as The Economist argues, such an exception will only encourage ideologues to harass those who hold a different view. In India, a psychologist and well-known public intellectual was charged under the country’s hate speech law for making a point about corruption and lower-caste politicians. He has since said that because of the incident, he “will have to be careful now.” Similarly, a hate speech law may allow Trump to sue Clinton if she had instead said Evangelical Christians or white Trump supporters belong to a “basket of deplorables.” I am not arguing that instituting a hate speech exception is constitutionally impossible, but I suspect it will either be too broad so as to amount to censorship, or too narrow so as to be utterly indistinguishable from other exceptions such as fighting words.

Speech on campus, of course, is an entirely different matter. Public colleges are required by the Constitution to provide First Amendment protection for everyone. Private colleges like Swarthmore, on the other hand, should protect the most vulnerable members of their communities, but they should also promote diversity of political opinion and speech that has intellectual value. The decision to allow or disallow certain speech is ultimately a balancing act, but colleges should not, for example, disinvite conservative speakers merely because their viewpoints are unpopular or offensive. (I do not, however, believe Milo Yiannopoulos deserves a platform on campus, because I do not believe his speech has any value at all.) Some, however, have argued that hate speech deserves a place on campus. Gillman and UC Berkeley Chancellor Nicholas Dirks, for example, argue that only by subjecting hate speech to examination can we expose the lie and bigotry that it is. I am sympathetic to such arguments even though I believe the line should be drawn where students might begin to feel unsafe.

There is another issue: do some students, because of their “privileges,” have no right to discuss certain topics or issues? There is a strong case to be made that those who belong to groups that traditionally have less voice should be given more voice to enrich the “marketplace of ideas,” but I think the answer to this question should be no. A friend of mine told me that when his public policy class was discussing whether catcalling should be made a felony, he was told by a female student that his view does not matter because he is not a woman. However, as a low-income and minority student, he knew that such laws disproportionately affect minorities. Regardless of whether his view was correct, he was capable of making a valuable contribution to the discussion. The point is, in the context of campus speech, more speech is almost always better than less.

When mathematical reasoning gets murky

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In a recent piece for the Phoenix, “Why Mathematical Reasoning Should Be a Part of Civic Education,” Zhicheng Fan advocates expanded mathematical education as an antidote to the post-factual political climate into which the U.S. has unfortunately ventured.  The argument, in essence, rests on two assertions: (1) mathematics reinforces the notion of universal truths, leaving “alternative facts” deservedly exposed as the sham that they are, and (2) the precision and logical rigor incumbent on a mathematician trains one to think and act more rationally.  Thus, it appears that by encouraging a broader spectrum of society to study mathematics, we would expect to see a cultural shift toward a greater adherence to logic, truth, and attention to detail.

I absolutely agree that mathematical education should be embraced and enlarged. I particularly support Fan’s suggestions of bringing proofs, both the banal and the beautiful, into the curriculum at an earlier stage and incorporating more math history to contextualize and humanize the material and inspire students. However, I wish to add an additional layer of consideration.  I believe that transferring mathematical reasoning to the “real world” is not so simple as Fan’s quixotic zeal suggests. While the qualities Fan ascribes to mathematical reasoning are indeed staples of the discipline, there is yet another that I have found to be essential though often overlooked: using intuition to guide exploration.  I draw the same conclusion as Fan, that math education should be broadened, and in the same ways he suggests.  However, my premise is a slight variant: I claim that mathematics not only teaches us to write clearly, accurately, and honestly, but also to think creatively, metaphorically, and imprecisely—but in a productive way!

Allow me first to clarify some points for context: (1) Fan invited me to write this response piece, and my goal in doing so is to encourage a continued civil, fruitful discussion where we build on each other’s ideas; (2) Fan is currently my student in Modern Algebra, but I have already learned as much from him, both in that class and in this editorial discussion, as he perhaps has from me as his professor; (3) the other course I am currently teaching is Introduction to Mathematical Thinking, the class Fan recommends toward the end of his article, and I wholeheartedly reaffirm Fan’s suggestion to take it—particularly those of you who might have had a scarring mathematical experience in the past.

Let me begin with the challenges of applying mathematical reasoning to non-mathematical situations.  An example from Fan’s article conveniently illustrates the point.  The mathematical existence of the Weierstrass Function, a graph fluctuating in such an inconceivably dramatic manner that it is impossible to draw, is said to demonstrate that it is “conceptually possible for a car to move without speed at any moment.”  I highly doubt such an occurrence is possible, or that it even makes sense.  Thus, the confidence established by mathematical certainty leads one precipitously off a cliff of plausibility when adapted to a physical setting.  In other words, transferring mathematical fact to the real world leads to what Fan refers to as a “conceptual possibility,” which arguably is none other than our foe, the “alternative fact.”  If such a simple case as interpreting the derivative of a function as the speed of a car is problematic, imagine applying mathematical reasoning and certainty more broadly to the world of beguiling complexity and nuance in which we live. Some believe the 2008 financial crisis was exacerbated by false-confidence resulting from this discrepancy between the precision of mathematical models and the chaotic uncertainty of the real world.  For a fascinating discussion of the over-zealous reliance on mathematical models that our society has in recent years been consumed by, see the recent book “Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy” by Cathy O’Neil.

But hope is not lost. Mathematics is not a useless Platonic realm confined to our imaginations, nor simply a progenitor of pernicious mathematical models.  Mathematics provides the backbone for a great deal of science and technology and has had a tremendous, very real, and often extremely positive impact felt across the planet.  Of course, this includes a positive impact in the classroom as well.

Classroom mathematics can be deceptive. The clean, accurate, polished form with which mathematical facts, or theorems, are presented in textbooks belies their oftentimes controversial histories and messy prior incarnations.  Mathematics continually develops itself by envisioning greater levels of generality and more rigorous foundations and then summoning past knowledge, placing it within modern language and perspective.  In doing so, mathematics acts as a self-cleaning oven, deftly erasing its history of missteps and vagaries while offering a feeling of timelessness and universality.  When the name of a 17th century prodigy comes up in class, for instance, we seldom describe the theorem the way it was stated and viewed at the time of its publication. Instead, with statements that have evolved over centuries, we see only the most recent incarnation.  Thus mathematical ideas percolate through continual modernization, even if the words themselves grow stale.

The mathematical world seamlessly blends irrefutable reality with resplendent fantasy.  When I think about math, I think in terms of metaphor and cartoon simplifications of complex notions.  Details, logic, and precision only enter the thought process at a later stage at which I am ready to probe further the depths of a mathematical thought or to communicate it to others.  Thus, while I agree that math helps train the brain in rigor and truthful properties, what strikes me most about my years of doing mathematics is somewhat the opposite. Rather, math has trained me to embrace the uncertain, to heedlessly leap into vast hinterlands of vague thought while grasping for familiarity, to recognize that creativity arises from uncertainty, and to become cognizant of the difference between an idea and a written or spoken manifestation of it.

Since Fan ended his article with a beautiful theorem demonstrating the enduring elegance of mathematical truths, allow me to end mine with an equally accessible example of a conjecture. That is, a simple statement whose rigorous verification continues to defy the entire mathematical community.

The Collatz Conjecture: Given any positive integer n, divide by two if it is even or multiply by three and add one of it is odd; repeat this procedure and you will eventually end up with the number one.

Try it!  Here is an example for n = 10:

10 —> 5 —> 16 —> 8 —> 4 —> 2 —> 1

Computers have checked unimaginably many values of n yet no general pattern has emerged allowing us to firmly establish this result for the infinitude of possible values.  Mathematics is as much about the unknown as it is about the known, and that’s why I love it.

Why Mathematical Reasoning Should Be a Part of Civic Education

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We now live in a world where reason and truth are under siege on a daily basis. The Economist declares that we have entered an era of “post-truth politics.” Falsehoods are called “alternative facts.” Science is subject to ideological manipulation. On both sides of the aisle, moral relativism and partisan politics have largely replaced commitment to constitutional principles and our inalienable rights. For many conservatives, religious freedom is important only if the religion is Christianity. For many liberals, the core liberal tenet of free speech is now somehow contingent on the identity of the speaker. While people everywhere used to struggle for our indivisible and inalienable human rights, we now like to manipulate these principles to fit our own narratives. I think part of the problem is lack of appreciation; learning about history or politics in oppressive regimes can help. The other part of the problem is inability or unwillingness to reason on both sides. Mathematical reasoning, I argue, provides an antidote to this culture of relative truth.

First, some clarifications on terminology. By relativism, I mean the belief that moral truths are relative to individual perspective, and that universal moral truths do not exist. By mathematical reasoning, I mean the ability to use proofs and rigorous arguments to generate indisputable mathematical knowledge. Mathematical reasoning is different from numeracy in that the latter denotes only the ability to work with numbers and calculate them.

The culture of truth and certainty that is generated by the method of proof in the mathematical world is sorely needed in the political and social sphere. In mathematics, once someone has proven that there are infinitely many prime numbers, no distortion or reframing or political maneuver or “alternative facts” can change that. This does not mean that skepticism has no place in mathematics, or, as political scientist Andrew Hacker apparently believes, that mathematics thrives under oppressive regimes. Basic assumptions in mathematics are often revised in light of evidence that shows a system can generate paradoxical results. For example, our intuitive understanding of sets as collections of objects was discarded after the discovery of the famous Russell’s paradox: the set of all sets that are not members of themselves can neither contain nor not contain itself. All mathematics asks is this: believe what you have a strong argument for, unless reason shows otherwise, in which case you must not believe.

Mathematics also teaches important skills that are transferable to political and social debates. First, mathematics teaches attention to detail. For example, try solving for x: ax = b. If your answer is x = b/a, then you miss the case in which a = b = 0 (which would mean x can be anything), or the case in which a = 0 but b is not 0 (which would mean there is no value x can be for the equation to hold.) Getting into the habit of considering all the “borderline cases” and scenarios can be useful in discussions about technical issues, such as affirmative action or voter ID law. Second, mathematics teaches basic strategies of argumentation. For example, in calculus, to show the claim that continuous functions must be differentiable somewhere is false, mathematicians created a counterexample called the “Weierstrass function.” In essence, it means that it is conceptually possible for a car to move without speed at any moment. One can also use “proof by counterexample” to show that freedom of speech is not absolute. For example, one cannot falsely shout fire in a movie theater. Third, mathematics teaches how to identify assumptions and gaps in arguments. One famous example in mathematics was the proof of Fermat’s Last Theorem: for any integer n greater than 2, there are no three positive integers x, y, and z such that xn + yn = zn. It took mathematicians 358 years to prove this result, but the first version of the proof contained a fatal error that was discovered during peer review. Eventually, the mathematician Andrew Wiles fixed his proof after a year of hard work, just before he was about to give up. The obsession with the rigor of argumentation in mathematics trains students of mathematics to develop a critical eye for arguments in general, as I have personally experienced. Fourth, mathematics teaches problem solving skills that can be particularly useful in policy-making and nonprofit work. The best proofs in mathematics are those that can be written in relatively few lines but are hard to discover. The best policy ideas are usually the same: easy to state, but hard to come by. Finally, mathematics teaches how to write well. Mathematical arguments are often more technical than arguments in other disciplines. Clarity of writing, therefore, becomes key in the discipline. Évariste Galois, one of the most important mathematicians in the 20th century, developed group theory in a paper that was considered “incomprehensible” by some mathematicians. It was only after he rewrote his mathematical manuscripts and published them the day before he died in a duel that his mathematical contributions became well-known.

Learning mathematical reasoning need not be difficult or stressful. Mathematical proofs should not be included in standardized tests such as SAT. Rather, exposure to mathematical reasoning can take the form of exposition and exploration. Teachers can show the most beautiful and famous proofs in different areas of mathematics, and guide students through each step of the proofs. Teachers can also present students with propositions that they can either prove or disprove. Finally, teachers can include tales from history of mathematics to illustrate how mathematical results can have profound philosophical implications. My favorite example is how Kurt Gödel’s and Alan Turing’s results in mathematical logic have shed light on the nature of human mind. Since this article is partly my opinion on educational reform and partly an advertisement for mathematics, I include here one of my favorite proofs in mathematics. If you like this argument or this way of thinking, you should definitely consider taking one of the mathematics classes offered at Swarthmore, such as Introduction to Mathematical Thinking.

Prove that there are infinitely many prime numbers.

Proof: Assume there are only finitely many prime numbers. Let p1, p2, p3, … , pn be all the prime numbers, arranged from the smallest to the largest. Let p = p1×p2×p3×…×pn + 1 (take the product of all the prime numbers and add 1).  Then p is larger than any of the prime numbers, since it is at least larger than or equal to p1 + 1, p2 + 1, … , pn + 1. Therefore, p is not one of the prime numbers, since our list contains all of them. p is thus a composite number, and it must be divisible by one of the prime numbers. However, the remainder of p divided by any of the prime numbers is 1, meaning that p is not divisible by any of the prime numbers. We have a contradiction. The only possibility, then, is that our assumption at the beginning was wrong. Therefore, there are infinitely many prime numbers. Q.E.D.


Revisiting the Social Justice Requirement Debate

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As a former debater, I am keenly aware of how manipulation of language can shape our perception of arguments. It was Aristotle who identified the three modes of persuasion that are still taught and used in academic debate: ethos, pathos, and logos, or appeal to authority, appeal to emotion, and appeal to logic. The first two, used well, can bolster the credibility of strong arguments. Without logos, however, ethos and pathos alone can sometimes be intellectually dishonest and can even backfire. To demonstrate this point, here I revisit last year’s campus debate on the controversial proposal of a social justice requirement.

Here is my view on the SJR: even though familiarity with social justice issues is really important, the SJR does not necessarily promote its stated goals, and, compared to other options, it restricts our freedom of choice with respect to academic decisions. The SJR is a paternalistic requirement because it forces students, for their own benefit, to take courses that they would not take otherwise. I do not deny that learning about important social issues is a compelling interest both for the school and for students. However, as Gilbert Guerra argues in “Why A Social Justice Requirement Isn’t Right for Swarthmore,” social justice is a “politically charged topic,” and graded social justice courses forced on unwilling students could be “tantamount to indoctrination.” Furthermore, initiatives that attempt to encourage students to take social justice-related courses, such as volunteer programs like Chester Youth Courts and Dare 2 Soar, or participate in protests and political campaigns, may have better outcomes since participation would be voluntary. Even posting on Facebook about your favorite professors is better than requiring anyone to take classes with these same professors.

Many counterarguments can be made. For example, one could question whether students have or should have any freedom of choice with academic decisions. Moreover, one could challenge Guerra’s comparison of the SJR with indoctrination or argue that the SJR is a worthwhile last resort to reach “recalcitrant” students who cannot otherwise be motivated to care about social justice. All of these arguments are worth considering. However, my point is this: even those who care about progressive causes can still make reasonable and valid points against “orthodox” views, and their arguments deserve to be considered in a constructive and analytical fashion.

Consider one op-ed, “The Price of Privilege: Swarthmore and the Social Justice Requirement,” published in the Daily Gazette last year. The author, first affirming the importance to “acknowledge one’s privilege,” goes on to assert that opponents of the SJR are only trying to “make life easier and convenient for people;” they are not defending the students’ freedom of choice over their own academic decisions. The author then states to be “insulted by the argument that we should not inconvenience people …I am insulted by the argument that professors will determine grades based on someone’s opinions or only scheme to indoctrinate people … I am insulted by the argument ‘people who are ignorant of X will be resentful and will dislike being informed [of x].’ ”

Insulted how? Either he feels personally offended by these arguments, or he is intellectually insulted by the arguments’ sheer stupidity. However, as I have demonstrated above, arguments against SJR are not necessarily grounded in offensive or prejudicial assumptions. Nor can these arguments against the SJR be so easily dismissed. Sure, if anyone actually claims the SJR is bad solely because it is “inconvenient” or “rude,” then the author may have reason to feel insulted. However, in three sweeping statements that the author is offended by the ideas that the arguments should not inconvenience people, professors will determine grades based on someone’s opinions, and ignorant people will be resentful,  and plenty of platitudes, the author creates a straw man argument to dismiss the core arguments by opponents of SJR. This is done without offering any cogent counterarguments.

The article also employs jargon that can be inaccessible and confusing for many. For example, one paragraph acknowledging that there are “real concerns and critiques of a social justice requirement,” employs terms that are inaccessible and confusing for many, including “cultural appropriation,” “privilege policing,” and monolithic indoctrination.” These terms would have been utterly incomprehensible for me to read when I first came to Swarthmore.

Jargon, when used indiscriminately, can seem intimidating and insincere for many. Especially outside of academic discourse, it is often used as a shortcut that sacrifices clarity, or even meaning, for mere expediency, and, sometimes, an unearned sense of authority. As Fredrik deBoer of Brooklyn College argues, few people who use the phrase “cultural appropriation” know what it means. Consider the following rewrite of a paragraph that conveys more or less the same message:

“Swatties often respect cultural differences and refrain from making stereotypical judgments. We respect history, and we celebrate diversity. But we need more. A social justice requirement does not dictate what to believe or what to do; it gives us the tools to challenge inequality and deprivations of individual freedom in our society.”

Those unfamiliar with jargon would also feel respected and welcomed to join the discussion. I mention this article because it is symptomatic of a somewhat elitist culture that routinely alienates or intimidates dissenters, skeptics, or those with low level of information or knowledge about certain subjects. If I had read this article a year ago, I would not have had the courage to voice my opposition or ask for clarification since, as an international student who did not know how to use these “buzzwords,” I often felt my opinion would somehow be judged inferior (I still do sometimes). Alternatively, I could even have been tricked into agreeing with the author despite the article’s lack of strong arguments, a phenomenon jokingly known as “proof by intimidation” in mathematics.

What is published in the Phoenix or the Daily Gazette, or even a Facebook post, is read by many, both on campus and off campus, who have not made up their mind about a certain issue or who hold a different view. If the tone is derisive, or the argument is hidden behind too much high-sounding jargon and too many empty words, someone who is not used to terms such as “heteronormativity” or “intersectionality” may be discouraged from voicing their own opinion and having it fairly assessed by peers. Alternatively, miscommunication and distortion could cause people to “talk past each other.” Finally and most importantly, weak arguments may be left unchallenged simply because they “sound about right.” These consequences can be especially detrimental in a college setting where free and informed debate is supposed to be celebrated and promoted. We all need to be mindful of our use of language if we believe that honest and equal discussion among peers is important.

Establishing community: is there hope?

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As a Swattie, I think it’s pretty much understood that while students enjoy exciting events on campus. Getting people to attend the event, however, is a challenge in itself. Between the impossible hours of readings and problem sets, campus jobs, and extracurriculars, we rarely have the opportunity to put down our homework, let alone convince ourselves to attend yet another commitment. This makes sense; why would we go to a lecture or study break for an hour when we could devote that time to sleep instead?

While this is accepted as normal, always attending to our own individual needs takes away from our sense of community. It forces us to think too much about ourselves instead of getting to know, or at least appreciate, the other amazing individuals who contribute to Swat. Add our divided opinions about issues like affirmative action, our differences in income or race, and even our diverse interests in academics, and we run the risk of modeling factions rather than a collective whole.

This is an issue at Swat that’s often easy to ignore. Everyone assumes that since we are a college of only about 1600 students, with only one dining hall, and all students collectively drowning in assignments, we must be a tight knit community. However, I think the events of the last few weeks, such as the feelings of the low-income population after the need-based admissions article in the DG and the Jewish members of our community in the aftermath of a series of Swastika-related incidents, have served as examples of how we must make more of an effort to come together in appreciating differences and understanding them, rather than denouncing them.

The college has taken actions to reinstate a sense of community, through collections every Friday and more vigils after tragic events. With the relatively low student turnout, however, we can’t help but ask ourselves: is it even possible to foster a more collective campus? If students are too consumed with academics and don’t have the time to devote to creating an intimate campus culture, what’s the point of trying?

After watching the presidential debate on Monday with hundreds of other Swatties in the Lang Performing Arts Center, I can say that Swarthmore has more of a community than I think many of us have ever known; we must continue to find ways to bring this community together more often. Never in my time at Swarthmore had I felt so connected with everyone, and so proud to be surrounded by a group of people who were so engrossed in the same issues, coming together to engage in the same important cause. In the United States, we are currently experiencing an epidemic of some of the lowest political participation rates in history. Yet on Monday night, I witnessed more civically engaged Swatties voluntarily in one room than I had ever seen. Everyone was glued to the screen, actively listening to each candidate, watching their every move, and waiting to see how they would respond to the issues. Everyone was well aware of the fact that we will all be affected by the issues discussed in the debate, and thus all have a role in the situation and some level of responsibility for the outcome.

But it wasn’t just the fact that everyone was watching and practicing an aspect of participatory democracy that gave me hope for our community. We were all laughing, commenting, and simply appreciating one another’s presence. Each person in the room contributed to a sense of energy and excitement (even a sense of disgust at times), which made the debate that much more interesting and enjoyable. I felt as if I were part of a bigger cause, one that is ambitious, driven, and inspirational; I felt that I was where I was supposed to be.

Of course, this is far from where we need to be in establishing a stronger Swarthmore. Campus Republicans would have felt completely ostracized at the debate, and even outside of political events, conservative students are constantly disparaged for sharing their views. Moreover, this event failed to demonstrate diversity of thought, instead depicting the power of group polarization rather than the excitement we all ought to have felt in being around one another. But it was a symbol of hope. The debate watch party demonstrated that we have the power to create a much more positive energy on campus if we just have a stronger foundation. It showed that Swarthmore is a body of students who care—we just need to find more effective ways of coming together to remind one another of this more often.

Swarthmore is nowhere near as strong of a community as it has the potential to be, but it is a group of amazing, passionate people who want to make a difference. We need to invest more time and resources into bringing everyone together into a family of supportive changemakers.

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