At some point around graduation last year, a friend asked me what I had learned in the past four years. I don’t remember what I said at the time, other than that it was surely haphazard and incomplete, but the question kept kicking around in my head. So, a whole year later, as it turns out, here is a perhaps fuller, if necessarily still incomplete, answer to that question.

On abstraction

Being a math major at MIT, I of course learned some math. I see math as the study of abstraction and abstract structure, and I learned plenty about both – especially from the perspective of algebraic topology and related fields, but also as they pertain to other fields of math, physics, and computer science. (It turns out that many of the fields that interest me have abstraction as a core idea.)

I’ve learned that maintaining these abstractions in one’s head is hard. By the time you’re thinking about something like the Steenrod Algebra everything you do relates to reality only through at least five1 layers of abstraction. The value of the abstraction is of course that you don’t have to think about the whole stack most of the time, when you’re just doing some algebraic computation. But to put things together, you have to load it all back into your head, and I learned how hard that is.

We need better ways of thinking about these abstractions, in math but also in physics, computer science, and probably elsewhere, too, because the difficulty of maintaining abstractions prevents us from building better ones that can do more for us. I’ve learned that web development, for instance, is surprisingly time-consuming even for experienced developers; there’s just a lot of code to write for everything one does. We need to be working at a much higher level – not just a slightly more powerful programming language or framework, but something really new. But it’s not at all clear how one gets there without collapsing under the weight of the abstractions. In any case, I digress – something I definitely already knew how to do more than four years ago.

On symmetry

On a more specific note, perhaps the single most interesting vaguely academic thing I learned about probably wasn’t in math classes at all: it was the idea of gauge symmetry in physics. Lie groups keep popping up as motivation everywhere in physics and math, and their particular application in quantum field theory results in a really incredible theory of the universe with surprisingly few arbitrary choices. Gauge symmetry, among other things, caused me to realize what I wish I had known earlier: that the applications of math can be really interesting in their own right.

Even classical field theory, as simplified as it is, is already a beautiful way of thinking about things, and quantum field theory is even better with the added benefit that it appears to actually describe our universe with unparalleled accuracy. Unfortunately it’s at the top of a mountain of physics and math, and even giving a real flavor for it without a lot of background is difficult. But I learned a lot on the parts of that mountain that I climbed.

On knowledge transfer

From my first evening at MIT, I began to learn the MIT oral history – the stories of hackers past, the escapades of student groups, and the origin of dorm traditions. And they are really an oral history2: they come with their heroes’ journeys, their tired tropes, and their cultural wisdom. The four-year memory of undergraduates makes passing on knowledge and values a constant concern for student groups and dorms, and I learned a lot about that.

As chair of MIT ESP and in various other positions, I learned a fair amount about the mechanics of knowledge transfer. I learned that it’s harder than it seems: there are any number of reasons to decide not to pass something on: that it won’t actually be that useful, that it’s just your opinion, that things will change anyway; and there are just as many ways to pass on knowledge that isn’t actually useful. But I also learned that the harder thing, and the arguably more important one, is values transfer. Passing on knowledge is hard, but it’s doable, and it’s not like I’m now completely off the grid if someone has a question. But passing on values is a lot harder, and something at which I wasn’t nearly as successful as I would have liked to be.

ESP certainly continues to care about its core mission, but with other values and other organizations it’s less clear: will ESP continue to fight the battle for student independence, even when it makes some enemies and conflicts with other goals? Will my floor, Bonfire, continue to collectively value leadership in the same way? Will the ASA continue to understand just what it means to say that “it is the highest responsibility of the [ASA] to act in the best interest of the MIT Community and of the Student Activities which it represents”? And is it even right for any of those organizations to carry on my values, as new members come in with their own expectations and ideals?

In the midst of that difficulty, I’ve learned the value of trivial traditions, and of the physical objects we leave behind: the party theme that recurs every year without fail, the furniture and kitchen implements that get passed down over the years, the murals that date back to time immemorial. Perhaps it’s silly, but the fact that the chair that pkoms bequeathed to Bonfire or the fancy printers that I convinced ESP to buy are still around holds some strange measure of meaning to me.

On people

I learned that people are messy, but totally worth it. In political science classes I learned about the ridiculous factors like shark attacks that affect how people vote. But I also learned how in spite of the ignorance of the average American, voters’ choices are often better-informed than one might expect. In learning about all of the ways in which our democracy doesn’t function, what I found most impressive were the ways in which it does function.

I learned a lot about organizations, and about how people function in them – both small organizations like ESP, and large organizations like MIT. As chair of ESP, I learned about the mechanics of managing an organization: running discussions, building consensus, making policy, overseeing people, and so on. And by paying attention to student politics and sitting on various student and faculty committees I learned about how amazingly complicated large organizations can and perhaps need to be.

And I learned a lot about social dynamics and how people interact informally. I learned that small social groups are wonderfully rewarding but also incredibly complicated, that telling someone they’re welcome to join you doesn’t make you welcoming, and that your friends will do stupid things and sometimes that’s okay and sometimes you should join them. I learned about the highs and lows of romantic relationships and about both deep and shallow friendships, all of which I certainly found more of than in high school. What I learned about people was mostly squishy and abstract, but it’s been an absolutely critical part of growing up.

On what it means to care

And, as strange as it is to say as such, I realize that as an undergrad I learned to care. This isn’t to say I hadn’t valued anything before – certainly my family was important to me before, for instance – but in some sense which is difficult to describe I learned how to really, deeply care.

I learned to care about ESP. The best and the worst thing about being in charge of the organization was the amount of ownership and responsibility I felt for it. It was the worst thing because that responsibility translated pretty directly into work, and into constantly thinking about what things meant for ESP. When I screwed up as chair, I noticed, because I could see how it affected this thing I care about. But the other side of that responsibility was that I felt a stake in the success of ESP. I cared about ESP and its students, teachers, and admins, and while I could take direct credit for only a very small part of whatever they collectively did, I was proud to be a part of it. And while the responsibilities of being chair faded as my term as chair ended, I still care a lot about ESP, and I’m still happy whenever it does something awesome, which it turns out is quite often.

I learned to care about the world. In high school if someone asked I would have said that of course I wanted to improve the world, but to be honest I didn’t think much about it – I tried to be a good person when I got an opportunity but didn’t particularly seek them out. Even freshman year when I joined ESP it was in large part because it was fun and it was what my friends were doing. And sometime in the following four years, I discovered I actually cared about the world. I learned that the best place to be at the end of an ESP program is at helpdesk in Lobby 10, to see all of the smiling students, parents, teachers, and admins as they leave more excited about learning than when they arrived. I learned just how many people have vastly fewer opportunities than I, and I learned that that’s something that bothers me. I learned that I want to do something with my life that is useful to the world in whatever small way it can be, and that I hope that everyone who is able to does the same. (And I learned that not everyone is able to do so! And that it’s worth giving people the benefit of the doubt and recognizing that being able to do something about these problems is itself a privilege.) I learned that the world is a pretty shitty place, but that we can make it just a little bit less shitty if we try.

And I learned to care about people. I had had friends before, but the peers I lived with and worked with on problem sets and extracurriculars became incredibly important to me. I learned that if you end up in the hospital in a snowstorm, your friends will trek through any amount of weather to help you get back home. I learned that when you’re still staring at piles of Feynman diagrams at 6am it’s a bit more fun when it’s with friends. And I learned how, and when, and why, to shout “BONFAAR” at the top of my lungs with my floormates. Four years later, I care about those friends in a new way.

On why it all matters

I learned a lot, by experiencing it, about the value of the undergraduate experience. I already knew there was a lot more to it than classes, but I learned how small a part of my education happened in a lecture. I worry that as we can offer the more academic parts of an education more cheaply online, we’ll lose the rest, or worse, we’ll end up with a two-tiered system in which only the privileged get these more important but less quantifiable parts of an education. I don’t think Khan Academy’s mission to offer a free, world-class education for anyone, anywhere will be complete until we can provide that too.3

Thanks among others to MITOC I (re-)discovered a love of hiking. And in doing so, I discovered that one of the reasons I love standing on top of a mountain is that what I see is, in the end, so fleeting – the mountain won’t look the same the next day, nor will I be back then, or perhaps ever. There will be other mountains on other days, but none quite the same, and the pictures won’t measure up, and that makes the moment at the top what it is. At the end of my four years I learned that being an undergrad has the same fleeting beauty – I won’t again be chair of ESP, or live with exactly the same group of people, nor, necessarily, would I want to, and I learned that’s part of what makes it special.

Thanks to Miriam Gershenson for comments on a draft.

1. By my count, a mathematical structure like $$\mathbb{R}^n$$ is an abstraction over anything in reality; point-set topology abstracts those; (co)homology, then cohomology operations add two more; and then the Steenrod Algebra sits on top of all of that.

2. With the exception of a few stories that have been written down, and of course Hack, Punt, Tool.

3. Obligatory disclaimer that my opinions here, and elsewhere on my blog, are my own.