Author: sk4109

As a transition from education to profession, college is the place where students have gone through lots of changes, and interpersonal relationships are definitely included. For example, let’s say a young and innocent college kid, Bob, has this feeling that although he is always getting to know new people, it is becoming more difficult for him to keep up with existing connections and friends. Of course, he has some “close friends” whom he keeps in touch with every day, but besides that, how close he is to “non-close friends” completely depends on how lucky they are to bump into each other on the way to Ferris Booth.

AbsentWeakStrong-HiRes-Tie-network

Graphic courtesy of Leadership Close Up

In our society, interpersonal relationships can be characterized as weak ties and strong ties. When you have a strong tie with someone, you keep up with him or her frequently and there are ways that you two meet or connect frequently — just think of someone in your housing group. When you have a weak tie with someone, one the other hand, you might still share a lot of common interests with that person, but for some reason you are connecting with him or her less frequently, and the cause of such infrequency could be unintentional — it might be because you two aren’t in the same class, or because you are living in Wien but your friend is living in Harmony and you don’t meet each other.

However, such infrequent connection could also, if not more likely, be caused by human calculation, and therefore we can actually draw a parallel between friendship and the prisoner’s dilemma in game theory. Yes, friendships can indeed be a game.

Let’s suppose we have two friends, Bob and Jim, and they know each other. One of the assumptions that we apply here is that Bob is a friend to Jim because Bob believes Jim will make him happy, and vice versa for Jim (I’m guessing you don’t to be friends with someone who makes you unhappy!). They both want to be very close to each other, but they are also aware that it takes some cost to keep up, for example if they hang out for an hour they lose an hour of study time, and therefore the more they want to connect, the higher the cost they have to pay to sustain a high level of connection.

In economics, we believe all happiness can be quantified, so we can do a simple experiment here to see how the outcome is derived. Suppose both Bob and Jim have two choices: either to connect the other one frequently or not. There is a special case: let’s say Bob chooses to connect with Jim frequently but Jim chooses to connect with Bob less frequently, what does each other gain out of this relationship? Remember since there is a cost of connecting, Jim will be better off choosing to connect frequently, because he is getting the same care and attention from Bob with a smaller cost. But, on the other hand, it will be hurtful, mostly emotionally, for Bob when he sees Jim is not giving him same attention and caring he deserves. We can characterize the situation in the following payoff matrix:

Picture1
If you have taken economic classes you can see what I mean by this matrix, and you know what Bob and Jim will choose to do.  If you are not familiar with economics, the basic idea behind this is that, because Bob knows he will be better off if when Jim contacts him frequently, he contacts Jim less frequently, Bob has an incentive to choose to connect Jim less frequently. But Jim faces the same situation and he will have an incentive to choose to connect less frequently and as a result, they will end up in a weak tie with each other.

It may seem disappointing in the beginning, but such incentives disappear as long as the game of friendship is being played repeatedly for a long time, and for a long time the real benefit of keeping a close relationship will outweigh the advantage of not returning to your friend once, and in such case a strong tie can be sustained. In other words, your relationship ends when you realize that there is an end of it, and upon such calculation from pure reasoning, there is a sentiment of friendship that we cherish.

 

Meet Mathew Pregasen. Mathew is a Columbia junior studying computer science who founded a startup with Anuke Ganegoda (CC ’18), Sahir Jaggi (SEAS ’17) and Rikhav Shah (MIT ’19). Named Parsegon Inc, the company implements a new method of transcribing English descriptions of math into mathematical script. For example, Parsegon’s technology could take a sentence “integral from 0 to 10 in region D of 2x squared + 3x cubed – the square root of x” and convert it into visual, textbook-formatted math.

How did you come up with the idea of Parsegon? What experience made you want to start your own business?

The way it started was pretty accidental. It was first a small project that we had no intention of turning into a company, but as it developed we realized it had more potential. Soon, we started to think of this project in a business context. We did Almaworks, raised some funding, hired some people for the summer, and further developed our business. In the ending, it is a technology project.

How did Almaworks facilitate your business development process?

I think the most beneficial part is that it connects you with incredibly helpful mentors. At first, you might not know too much about design, planning, or the law associated with a startup business, but as long as you get close to a mentor, you will get proper advice on business direction, project development, and especially important legal services.

What’s the current entrepreneurial environment at Columbia like? How does it compare to other schools?

I think in the last two years, there has been some significant changes, where the administration—especially entrepreneurship administration—has been putting a lot of resources into the entrepreneurship community. They raised the amount of provided grants and have organized the Columbia Entrepreneurship Competition for the last four years.  Alongside that, you have clubs like CORE (Columbia Organization of Rising Entrepreneurs) and ADI (Application Development Initiative) that push this culture. I think ultimately the culture should be self-accelerating instead of accessory, but you need to have some initial velocity at the beginning.

 

Mathew Pregasen

Image via Mathew Pregasen

So back to Parsegon. It seems to be designed for people who are not fast at mathematical typing. How do you attract people who are already proficient at mathematical expression in typing packages such as LaTeX?

We are not competing with LaTeX and we don’t expect people to write papers in Parsegon. That being said, we do have a very user-friendly environment that reduces time and difficulty in typing. Parsegon is also educational in the sense that it makes teaching more accessible to students and enables the entire classroom to engage in interactive math.

 

You have been trying to integrate Parsegon into classrooms. What is the feedback from teachers and students?

We primarily focus on high schools, and we’ve been having very strong feedback.

What do you think is the biggest challenge for Parsegon?

I think the greatest challenge for us is to make a technology that provides a number of services for very diverse classroom environments. Some people might not be familiar with computer typing and some do prefer a very traditional and structured typing style, so although we are making it more accessible to people, it is still a big challenge to build the technology that accommodates the needs of everyone and strikes a proper balance between accessibility and formality.

Are there any computer science classes at Columbia that have helped you in this process?

Namely Operating Systems (W4118) with Jason Nieh. I also took a class called Computer Theory with Alfred Aho which was useful for the theoretical angle.

What do you think is the future of Parsegon?

We want to build the best tool for educational practices in the America. We believe that there is a big gap between the technology side of users and the technology provided for educational professionals, and we believe that our implementation will not only complement the traditional learning method, but also improve it. The importance of Parsegon is that it teaches students to understand the language of math. If you can understand the language of math, you usually also understand the theory of math much more coherently. And we believe that is the best way Parsegon could improve the learning process of math on a more cognitive level.

A year is long enough for surprises to happen, especially this past year. People suddenly found out that the world they live in has gone through a course that no one could ever have predicted. One year ago, hardly anyone foresaw the European Union losing its most important player and perhaps in the future losing a second one; hardly anyone could say affirmatively that a billionaire without any political experience could become the president of US. People are shocked, fearful, and puzzled by these facts. We call this series of events a wave of anti-establishment—not only anti-establishing the social system that we have relied on so much, but, more importantly, challenging the ways we look at and interpret the world.

While people are asking, “What is wrong with our world?” it is equally important to be introspective and ask what is “Wrong with my own thinking that causes so much disillusionment with what really happened?” It is not an easy question, and people can have diverse answers for it, but besides the debates of ideology, social norms and political correctness, maybe we can focus on something that is less paid attention to, something that seems to be irrelevant to politics: math.

Throughout human civilization, people have used reason to understand the world, and after thousands of years of development, almost every field of study has become dependent on the use of rationality. Usually, we tend to call such rational tool “model.” People use models to capture the factors of the issue being studied and use logical representations to depict the fundamental laws that govern the behavior of these factors. The most widely used model among people is the mathematical model, where the logical representations are necessarily mathematical expressions. Such a use of math has been adapted in economics, political science, sociology, and even psychology. Investors use math to make investment strategy, economists use math to understand the behavior of economics, politicians use math to predict the patterns of voters, and policymakers use math to structure the best policy for the country.

For a long time, math has successfully captured the behavior of the world and did a pretty good job in assisting people with their applications in the real world, and people have been more and more dependent on math to solve the complex situations they face. But because of these successes, people also ignore the shortcomings of mathematical models in social sciences, and such ignorance could cause problems.

One weakness of math models is that in order to achieve more accurate depiction of the scenario, comprehensiveness is sacrificed. The first thing to do when constructing a math model is to make assumptions and simplify the situation to a bunch of factors that are representable by math expressions. But in this simplification some important factors are tossed away because they cannot be clearly quantitated. One clear example is people’s sentiment, which in some cases dictates the situation, but because it is too hard to be modeled, it is usually left out or excessively simplified. With an absence of sentimental factors, the model can sometimes interpret facts incorrectly.

Another shortcoming of math is not a shortcoming in nature, but could hurt people when they are too dependent on a math model. The nature of math assumes a deterministic model. That is to say, with given conditions and given principles, the outcome can be well defined. Usually the models taught in economic classes and political science classes don’t assume any stochastic scenarios, and they don’t talk about things that are not solvable (otherwise what is the point of studying it?) But neither of the preconditions are always true. Sometimes we cannot grasp the condition correctly due to our limited ability to observe the complete picture, and sometimes we just simply don’t have the correct principles on which this world functions. In either case, model thinking could fail.

The use of math modeling in our daily life is not essentially problematic. It is the overdependence on it that causes some misleading in perceiving the world and interpreting it. If we don’t fully grasp the pros and cons of using mathematical reasoning in social science fields, we will constantly encounter conflicts between our assumptive beliefs and real facts.

 

Recently, a group of Chinese students reported that their room name tags were ripped off during the time of the Chinese New Year. Some students found that their door tags with their names written in Chinese spelling were removed, and such incidents were reported in different residence halls, including East Campus, Furnald, Shapiro and Hartley. The Lion is currently investigating if this is an intentional action of discrimination towards Chinese community.

This has raised concern among Chinese students. A student living in East Campus reported that she lives in a suite where all members are students from China, and their name tags have been ripped off three times since the beginning of this semester.

A number of students affected by such incidents have reported them to Public Safety and Residential Life, who we have also contacted for comment. We’ll update this story as we get more information.

 

Update 2/18/17, 3:48pm: The Deans of CC, SEAS, and GS have responded to the incident. The full email is below:

Dear Undergraduate Students,

It is an unfortunate reality that neither Columbia nor any other university is able to exist untouched by incidents that contradict our institution’s most precious values. The removal of the name tags of Chinese students living in undergraduate residence halls earlier this semester is one of those times, and all of us feel the harm done. Even more troubling is that the vandalism occurred around the celebration of Chinese New Year.

We continue to monitor the ongoing investigation of this incident and to provide support for students directly affected. As always, the investigation will remain confidential while it is being conducted. What we can tell you at this point is that we will continue to apply our rules and act in a manner that aims to deter this type of offensive behavior in the future. If you have any information that could shed light on what happened or those responsible, we urge you to please share it with a staff member in Residential Life or Multicultural Affairs, or to reach out to Cristen Kromm, Dean of Undergraduate Student Life for Columbia College and Columbia Engineering, or to Tom Harford, Dean of Students for the School of General Studies.

It is perhaps commonplace for people to point out after incidents like this that the measure of an institution is found in its response; nonetheless, the observation feels particularly apt in this case, given the two videos produced by Columbia students in recent days, as well as the solidarity event held by the Global Ambassadors Program. These and other poignant expressions serve as a powerful rejection of targeting of any group on our campus, whether identifiable by race, ethnicity, religion, gender identity, or sexual orientation. We applaud those messages; they are a testament to the strong spirit of activism, courage, support, and inclusion that defines our student body.

The collective commitment across our community to learning, expanding knowledge, and public service depends on an equal commitment to welcoming students, faculty, and staff from across the nation and around the world. It is impossible for us to pursue our schools’ missions without the contributions of people with a diversity of backgrounds, perspectives, and experiences. We will continue to frequently reassert this point during a time when the importance of celebrating difference bears reminding. We want to thank all of those who already have made themselves heard.

Sincerely,

Peter J. Awn
Dean
School of General Studies

Mary C. Boyce
Dean of The Fu Foundation School of
Engineering and Applied Science

James J. Valentini
Dean of Columbia College and
Vice President for Undergraduate Education

Several days before the Nobel Prize Committee awarded this year’s Nobel Peace Prize to the current Colombia President Juan Manuel Santos, a referendum took place in Colombia that rejected the peace deal made by Santos and the Revolutionary Armed Forces of Colombia (FARC). This result put the Nobel Prize Committee in an awkward position, as the committee awarded Santos “for his resolute efforts to bring the country’s more than 50-year-long civil war to an end,” yet the millstone on the peace journey was just rejected by Colombia’s population. Though people rejected the peace deal mostly because they were unsatisfied with the conditions set in the peace deal, such as releasing FARC officers who are currently in custody, the rejection still reveals the immaturity of peace in Colombia and poses questions on Santos’ legitimacy of the award.

Besides the awkwardness from the referendum rejection, people also question whether Santos’ contribution is significant enough to receive the Nobel Peace Prize. The conflict between Colombia government and FARC could be traced back to 1960s, when the left-wing revolutionary force was established in the wave of communism in Latin America. The conflict was brutal and inhumane, and claimed the lives of more than twelve percent of Colombia population. However, due to the relieved tension between United States and Latin America countries, as well as the diminishing power of FARC that could no longer stand for more aggression, a peace deal seems to be inevitable to resolve the conflict that both parties could no longer support.

The Nobel Peace Prize endorses those who have “done the most or the best work for fraternity between nations, for the abolition or reduction of standing armies and for the holding and promotion of peace congresses,” yet it has been criticized for being too political. Some critics believe that the reasons for awarding is based on the contemporary significance, which makes the prize lack eternality. Current president Barack Obama has been awarded “for his extraordinary efforts to strengthen international diplomacy and cooperation between peoples” only nine months after his presidency, and it is doubtful how the committee could examine the effectiveness of his international diplomacy in such a short period of time, as the increasing tension in Syria and the rise of ISIS raise more questions of the legitimacy of his award.

A political Nobel Peace Prize does not endorse its original purpose, as it is supposed to endorse some higher stakes that go beyond contemporary politics. It should be more humanitarian, more cosmopolitan, and more inclusive. In terms of this year, the Syrian Civil Defense organization, which was nominated but not awarded, may have been a better choice, as the group continues humanitarian rescues in the most dangerous country with no assistance from other political groups. Getting rid of influences from politics and political norms is hard for the Nobel Peace Prize, but it is necessary to keep the prize’s eternal significance.

Perspectives of a Math Major runs alternate Wednesdays. To contact the author to submit a piece of your own, email submissions@columbialion.com.