Positive externalities, and the freshness of failure

I’m writing this partially because Tom has been bugging me about writing (it has been a while since I’ve published), and because I want to postpone my post about Owl City, mainly because I think it would decrease our subscriptions by 100%.

I was told the other day that a positive externality is essentially where one person does something, and the cost is only placed on the actor.  Apparently a perfect example of this is participation in sections.  The teaching fellow will ask the class a question, and there will be an awkward silence, sometimes lasting up to thirty seconds.  Eventually someone caves and hazards an answer, or the TF gives the answer and moves the section along.

But actually attempting an answer is the positive externality; if your answer is correct, then you and the class benefit, because you’re forced to explain why your answer is correct, and your peers learn from you; if your answer is incorrect, the TF gets a little concerned and takes pains to explain why your answer is not correct.  Here, everyone benefits, but you “suffer the humiliation” of giving the wrong answer.

I’ve always been a little annoyed by these unnecessary silences, and in the past month I’ve tried to answer the questions when I thought I knew the answer, or when it was a binary question I would hazard a guess, just to move along so that we could learn more.  When I was right, there was never an overwhelming sense of satisfaction.  When I was wrong, I have to say it was embarrassing and definitely was not an experience I wanted to repeat.

This is sort of related to the practice of asking questions in lectures and sections.  This is even more frustrating to me, especially when the instructor specifically asks if the students understand what just happened.  Of course people are going to be confused by something when there’s a slew of facts shoveled on them, but for some reason no one wants to be the person to ask for elucidation.

I know I’m not the only person who doesn’t understand everything, because there have been a couple of occasions where friends in my section have thanked me for asking a certain question because they learned something from it.

I think the “smart questions” are the ones that bother me more actually, e.g. “Isn’t angular momentum just a clever trick, or does it have any deeper significance?” or “Do we prefer Lagrangian mechanics to Newtonian mechanics because the former is more beautiful?”  These are the types of questions that people ask to show that they have absorbed the material so completely that they need to show the rest of the class that they’re wondering about the deeper significance of every result.  Of course the less gifted students pick up on this, and often they scramble for these types of questions so that they can prove that they aren’t part of the lowly masses of students trying to just get by.  It’s a cheap trick to gain the professor’s respect, and everyone involved knows it but ignores it.

This is getting a little bitter.  I’m going to throw something in here to lighten the mood a bit.

So I feel like the issue is that for most of my classmate’s lives, they were consistently the best at everything they did, or pretty damn close.  THEN.  We get thrown into this high-powered environment, suddenly you’re on a level playing field with everyone, and you’re just not that special anymore.  For the first time in our lives, failing is an option, and it’s terrifying.  Eventually we realize that it’s very difficult to fail here, but we are still aware that there’s always someone better than us at what we love to do.  Luckily we can hide our grades from our peers so that there isn’t a direct comparison.  I think that the only place left to really compare yourself to others is in your section, where you discuss your insecurities with your schoolwork.  But here, it’s really easy to not have any questions; why would you ask him to go over that last step if you understood it in the first place?  I believe that the practice of not answering or asking questions is a face-saving technique that most Harvard students have adopted.

Like everything else here, the question-problem is wrapped up in the ego.  People don’t want to expose their inadequacies to their peers, so they hide in silence, implying the answer is so obvious it doesn’t deserve a serious consideration (apologies to anyone who this is actually true for; I’m looking at you, Danny.)

I’m guilty of this ego thing as well (or maybe I’m the only one guilty of it…) but I’m trying very hard to overcome it.  By admitting you don’t know something, you can open yourself up to learning it.  But the way sections are treated now makes it difficult to speak up when you really don’t understand something.

I guess I should include as a disclaimer that this mostly applies to my math and physics sections here at Harvard; for all I know people actually contribute to discussions in humanities concentration courses.

That is all, goodnight!

Games

So today I went to the Google Games, an event at the Google Cambridge office involving a bunch of geeky competitive events.

Highlights:

• There was a music-identification round (part of a larger trivia round), during which they rickrolled us and played awesome music like the Firefly theme, Korobeiniki, Do You Wanna Date My Avatar, and Dragostea Din Tei. Unfortunately, I was unable to correctly name Korobeiniki, as I have long held the misconception that it is called Kalinka. (I’ve been disabused of the notion before, but still couldn’t remember the right name.)
• There was a puzzle round; I spent the last half hour or so working through about 70 cases of one puzzle, looking for the one that satisfied certain conditions. At the one-minute-remaining mark, I had three cases left. I managed to eliminate one more of them, and then sent in the other two as answers, feeling sure that I had missed the answer. Instead, one of them was correct! I was both happy and sad.
• I was really excited to play Wii Sports Resort (there were supposed to be rounds in rowing, basketball, skydiving, and swordplay), and I was the only one on the team who’d played before, so we kind of figured I’d do them all. Then they said each person should only do one event, so we decided to be good competitors (they almost definitely wouldn’t've noticed had I done them all), and two other people did the first two events (I wanted to do swordplay). Then time ran short and the last two rounds were canceled. I was and remain severely disappointed.
• We were the highest-ranking Harvard team (the first five spots went to MIT). Success!
• Foosball. Playing with new people was fun. There was a left-handed table there (you shoot left instead of right); interesting, but it was also a really bad table.

Resolutions

Hello, dear Blandfill readers. This is a slightly more serious post, I suppose, so you’re in for a treat!
I’d like to talk a little bit about “resolutions” that I think I’d like to adopt in my life. These are sort of like New Year’s resolutions, but different in two ways. First off, I think that 01 January of every year is a little too arbitrary to be meaningful, and it seems like overall it’s a pretty atrocious way to attempt self-changes (at least statistically speaking: Wikipedia says “Recent research shows that while 52% of participants in a resolution study were confident of success with their goals, only 12% actually achieved their goals.”);  and secondly, it’s common for New Year’s resolutions to be pretty specific: “Work out more”, “lose weight”, “get better grades”, “spend more time with family”,  ”get more sleep”, et cetera, and I’m not super interested in small specific changes.

So, Tom, what the heck are you talking about?

I’ve more or less alluded to this in previous blog posts (such as, in chronological order, pursuit, advance, funny, ‘trospection) but college has really helped me confront myself and my beliefs and such – not so much politically or religiously, but personally and emotionally. Living at home with my family was a sort of painful box for me; not because of anyone in particular’s fault, but because of my overall situation; and though I numbed to the pain and managed to “be good at stuff” to whatever extent university admissions folks think is important, it’s only since I’ve come here, living without my family, with my roommates, in a new community, that I’ve been able at all to address bigger questions.

I’ve been thinking about ways I’d like to change myself, become better, perform self-improvement — whatever the hell you feel like calling it — and the following “pieces of thought” (they happen to be cartoons) struck a chord in my mind.

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interview

I had a phone interview with D.E. Shaw today (I’m applying for a summer internship there). I was kind of afraid I’d get asked about what I wanted to get out of it and where I wanted to be in ten years, which I would’ve had an awkward time answering (that is, arguably, a bad thing in its own right, but never mind). It turned out to be basically fact-based, so that was okay. I talked about the work I did with an astronomy professor last term; the interviewer had me talk about how we processed the data, then asked me some questions about the statistics of it. I remembered the process pretty well, though I guess I wasn’t very clear and had to retry some of it. I remembered the Poisson distribution, but he asked about the conditions for one to be approximated by a normal distribution, which I didn’t really remember. I said it’s acceptable when the expected number of events is at least 20, which turns out to be about right.

After that he asked how to do quickselect, which I answered fairly well, and how to partition an array in place, which was okay, though I didn’t say it very smoothly. Then he asked a pretty simple probability question, which I sort of figured out how to do pretty quickly in kind of a neat way, but it was different from what he was expecting and I didn’t explain it very well, so that kind of fell down. I got the expected method with some prompting, but I really should’ve made it more clear that I actually knew what I was doing. I think he did somewhat recognize what I was saying, at least. Still, I think that was quite a trip-up.

“I will stomp on things to focus my mental energies, or ‘menergies’.”
– T-Rex

Best Dataset Ever

This is an end-of-semester thing that we’ve been looking forward to.  Back in mid-October, I thought it would be fun to record our sleep and wakeup times.  We started on October 14th, and here are the results from calculating hours slept.  I think we have a lot less than the average number of all-nighters for college students.

You can download the dataset (csv format) here.

Note: the hours slept are calculated for the night before, e.g. Sunday values correspond to hours slept Saturday night through Sunday morning.

Summary (hours):

As you can see, Danny, Duncan, and Tom have left-skewed distributions (the mean is less than the median) whereas I’m right-skewed.  I have the highest mean sleep time and the lowest standard deviation.  Tom has the highest standard deviation, and Duncan has the lowest mean sleep time.  Graph:

Days of the week:

We were also curious about our sleep patterns during the week.  Tom was usually very well rested on Tuesdays.  Graph:

Correlation Matrix:

Unsurprisingly, I am not very correlated with the others.  Duncan and Tom have the highest correlation.

My hours:

My variance increased over the semester.  Graph:

Danny:

Thanksgiving break meant a lot of sleep for Danny.  Graph:

Duncan:

I bet you can tell when Duncan had an astronomy lab write-up.  Graph:

Tom:

The wild roller coaster ride that is Tom’s sleep schedule.  Graph:

All of us: