Re-Reflection
In 2009, as I was approaching the end of my Phd program, I wrote a blog post titled, Some Thoughts on Grad School. It described lessons I learned during my time at MIT.
Since then, I’ve received many requests to revisit the theme. Now that I’m a professor — albeit a new one — I thought I’d once again reflect publicly on what I did well and what I wish I’d done better.
With this in mind, I want to offer a pair of thoughts on a topic of particular importance to my path as an academic: complexity.
Thought #1: Avoid Complexity When Seeking Problems
Early in my graduate school experience, I had a mentor named Rachid — a well-known distributed algorithm specialist from EPFL. I learned many things from Rachid. For example, I once asked him for advice on a summer internship I was considering. I made different arguments about the value of gaining connections and learning about industry.
“If you want my personal opinion,” he replied, “your time is better spent at MIT, preparing the next STOC/SOSP/JACM paper.”
To put this in context: STOC, SOSP, and JACM are acronyms for some of the most elite conferences and journals in the field of computer science. The lesson Rachid offered — which I’ve since strongly embraced — is that in the end, hard results are all that count.
But the Rachid lesson I want to emphasize here is about the danger of complexity. His approach was to always reduce a problem to its purest, most simple form. This is what leads to true understanding of the mathematical reality underlying the issue, he believed. Once you’re armed with this understanding, you can then, and only then, add back details (and the complexity they require) with confidence.
If you want to see this philosophy in action, take a look at this paper I co-authored with Rachid and another graduate student from MIT. The big picture problem that interested us was messy: how do parties work together to solve problems when their only means of communication is a broadcast channel where a malicious adversary can both jam and spoof messages?
You’ll notice in the paper, however, that we immediately reduce this down to the simplest possible expression of what makes this setting difficult: two players, Alice and Bob, trying to communicate a single bit, while a third player, Collin (the collider), tries to disrupt things.
All of the results in the paper build on our deep understanding of this simple three-player game.
(For what it’s worth, the paper has since been cited around 50 times.)
The problem here is that most graduate students tend toward the opposite of this approach. Their biggest fear is that they’ll propose a result and someone more knowledgeable will look at it, declare it “trivial,” and therefore validate their nagging imposter syndrome. Accordingly, students tend to rush to add technical complexity right away, as if a page full of math validates their ability.
This approach is flawed because it’s hard to make an impact in a technical field without deep understanding, and it’s hard to build deep understand of anything that’s not dead simple to describe. This is why the most respected professors are often those who are most likely to interrupt you and say, “slow down, and explain this to me like I don’t understand anything.”
They don’t want equations, they want insight.
Bottom Line: Hold off complexity as long as possible when studying a problem. It will inevitably enter the scene, but the later the entrance, the more insight you’ll develop.
Thought #2: Seek Complexity in Your Technical Skills
My first thought concerned something I think I do pretty well. My second thought concerns something I didn’t do enough as a graduate student, and that I’m only now, painfully, learning to embrace.
The value of a graduate student (not to mention, an assistant professor), I’ve come to realize, is directly proportional to the quantity and complexity of their technical tool kit. If you study algorithms, for example, the more corners of the literature you’ve mastered, and the more mathematical analysis techniques you’re comfortable with, the more problems you’ll be able to solve. And the more problems you’re able to solve, the more likely that you’ll solve some hard ones — the key currency for an academic career.
This thought doesn’t contradict the first thought (though it might seem to). When tackling a problem, you want to start with its simplest expression. To find a good problem and then make sense of its simplest expression, however, you need the most powerful possible combination of knowledge and skills.
The trickiness here is that mastering new knowledge and learning new technical skills is like learning to play a new instrument: it’s difficult, and frustrating, and takes a long time.
All graduate students are forced to develop a basic tool kit due to the deliberate practice required to pass your courses and contribute to your first publications. The students that thrive, however, don’t stop there; they keep pushing themselves to learn more.
I didn’t do nearly enough of this.
It took me two years to get decent at solving a certain class of problems concerning deterministic distributed algorithms (roughly 2004 – 2006). There was then a two year period where I was satisfied to use only this hammer and go seek nails, no matter how hard they became to find.
The issue I faced was that my field was moving forward. Randomization was where the interesting new work was being done, and my approach was in danger of becoming dated.
It wasn’t until 2008 that I began the dreary effort of teaching myself probability theory. In this early paper, for example, you can see the beginning of the transition: the majority of the results are deterministic, but they draw on a tentative, randomized sub-routine. (This is where, for example, I reintroduced myself to Dr. Chernoff).
The next year I published this paper, which pushed me forward in my learning, but was also a terrible strain. A significant fraction of its results came from the following process:
- I would get stuck because I didn’t know enough probability theory.
- I would go talk with one of my co-authors, who would reply by filling a white board with a bunch of inequalities.
- I would scramble back to my office and try to recreate the argument from scratch, filling in the details, before it slipped my mind.
- I would return to my co-author to discover that I had fouled up my dependencies in some terrible way that would likely involve the intervention of something called a “Martingale.”
This was pretty brutal. But I learned quite a bit.
I am realizing now, however, that my pace was still too slow. For example, I should have shot past independent probabilities and mastered techniques for bounded dependence. This is a natural — though difficult — next step that I avoided for too long.
Over the past year, I’ve been systematically increasing my pace of skill learning (more on this soon), but if I had committed to this mindset with more purpose back in 2006, I’m embarrassed to think about the extraordinary impact on my work it might have had by now.
Bottom Line: Treat your time as a graduate student like a professional musician treats his or her performance repertoire. If you’re not constantly straining yourself to learn more and perform better, you’re in danger of being left behind.
(Photo by Nietnagel)
The seeking complexity over simplicity phenomenon is a real common problem. In addition to what you said another reason I think it appeals to many people because it often creates busywork that leads to an illusion of productivity. Plus while it may be more work in terms of amount of activity required, it’s much easier in terms of challenging oneself and building awareness. A lot of people are less daunted by memorizing a bunch of little rules and than exceptions than mastering the insights needed to boil everything down to a few grand, unifying concepts.
Good post, but I’d like to ask: do you still fully support all of the advice in your original “Some Thoughts on Grad School” post? I re-read it and it is still sound advice. It flies in the face of prevailing sentiment, particularly in certain fields where the cult of the academic martyr holds sway–but that’s precisely why it seems like such good advice.
>Bottom Line: Hold off complexity as long as >possible when studying a problem. It will >inevitably enter the scene, but the later the >entrance, the more insight you’ll develop.
Although this is very important it is equally important to note that in order for the results be useful in real life one has to keep the big picture in mind. Without adding all the complexity details the whole process is mostly wasted.
Would also add that in order to train your skills it is useful to read alot about other subjects – lots of insights how to use or apply the skills you have learned or could learn.
Great post. As usual your insight traslates well to my discipline in the social sciences. I see my doctoral students often choosing topics neglecting the big picture importance of the topic and focusing on the technical contribution.
Tools are important, no doubt. But what do you do if you have had tenure and some of the tools have passed you by? Plus you can still generate publications using old tools, just not maybe in the top journals.
Excellent insight. As a 65 year old student for life, this post resonated with me.
Thank you.
Cal, great post. I’m sure that many successful profs have had these insights and kept it to themselves or a small cadre of colleagues. Thank you for sharing them.
Agreed. Busy work is terribly dangerous because it makes it seem like your accomplishing a lot, but it never really challenges you, so the time is, in many ways, wasted.
I’m not quite sure what you mean by “fully support”, but those general ideas I think are still good ones to keep in mind when strategizing as a grad student.
There’s an art here that I have not yet mastered. You have a deep sense of the real world which leads toward a general problem area that seems useful. Then you distill a clear, crisp problem that you dive deep and really understand. Then you start adding back the details that brings its back to the real world setting that inspired you in the first place.
Go learn em!
Hey Cal,
Sorry if this is the wrong place, but I wanted to ask you if you could set up a create a separate Twitter feed for your blog posts? Kind of like @thisissethsblog using http://www.twitterfeed.com. I know you don’t use Twitter personally but I’ve been trying to use it as an simplified RSS reader.
Thanks.
Right on mate! I’m currently a postdoc in Immunology and I feel the same way. I’ve realized that I don’t really understand anything without first grasping the underlying principles. It’s hard to build upon ideas without first knowing the foundation. Similarly, to answer the big questions, I think it’s also necessary to distill it to its simplest form. I’m also in the process of developing my tool kit, which I think is necessary once I start applying for jobs. Keep up the good writing and good ideas!
Hi Cal,
I have a question that’s somewhat unrelated to your post. I’m an undergrad (a rising junior) and I’ve been doing research in the same (CS) lab for 1.5 years now. I have one coauthorship and hopefully a second one soon. If I stay in the same lab, I’ll almost definitely get to be a first author on a paper in the fall. But I’ve been thinking about switching over to a different lab in the fall instead, to get to know other professors and other areas of CS (the downside being that I wouldn’t readily get to author another paper). I’m about 95% sure I want to go to grad school– strategically, which would be the better choice?
Don’t. As an undergrad doing research your main goal is to a) prove to the grad school world that you can handle high-level research; and b) develop at least one tool to be as sharp as possible so you’ll have something to get started with at grad school.
Exploring topics, figuring out what you want to focus on — these are challenges for after you’ve started and gotten comfortable in a PhD program.
My two cents…
Then who would I ask for solid grad school recommendations, and how do I make an informed decision about what I want to do my PhD in/who I want to work with in grad school?
-Anonymous above
“””over the past year, I’ve been systematically increasing my pace of skill learning (more on this soon), but if I had committed to this mindset with more purpose back in 2006, I’m embarrassed to think about the extraordinary impact on my work it might have had by now. “”” please can you tell us more about this 🙂 Thank you .
@Bo Sun: You can do that yourself with twitterfeed.com, just create a feed with the RSS for this blog
This is why a burning passion is important. Makes you want it all, insatiably. This is the price to pay to excessive cold calculating. You trade risk for mediocrity. Someone has to do it, maybe most of the people must do it. In a sense it stills the smartest choice but like all non valorial passionate choices easily subject to regret.
The two thoughts that got my attention and that I need to work on are these.
1) “Learning something new is difficult, frustrating, and takes a long time.”
2) “Push and constantly strain yourself to learn more and perform better”
It’s time to revamp my goals, plans, and schedule.
Grad school recommendations usually come from a professor (or professors) you did research with and some professor’s whose classes you dominated.
In terms of picking an advisor at a school: don’t drag your feet but also don’t rush. See what their group is publishing, and, importantly, see where the group’s graduates are ending up.
You want to see steady publications on topics that catch your interest and a good success rate in graduate placement.
Oh my. Search the blog for the word “passion” for my thoughts on that particular topic…
Is this advice applicable to non-technical fields of study as well, like law or international relations?
Agree the big picture is important, and I see you are in computer science, but it is hard for me, theoretical chemistry/physics, to see the big picture without the details. I always like to quote Heisenberg who said we can only visualize the microscopic through the equations. From that visualization, eventually the big picture emerges.
Maybe I am just incredibly slow but it takes me a long time to see the big picture, and I think to chose a project believing I have the big picture in mind might be a bit naive. Maybe we need to see the trees before we see the forest.
This is a wee bit off topic but is it possible to apply the superstar techniques mentioned in ‘How to be a High School Superstar’ in college? Would it be too late then?
Cal,
Any opinion on masters in finance vs. MBA programs?
I’m looking at applying to Princeton and LSE next year instead of going to work for 4-5 years and then applying to MBA programs.
Cal, I like this post. I think your two main points transcend grad school and could easily apply to one’s career or personal life. I have a question about your second point. Put more generally, I think your point was “acquire a broad array of skills so that you can help solve a broad array of problems.” It seems to me that this principle contradicts the idea that people are more successful when they specialize, that to gain the maximum amount of career capital we each need to buckle down and master one thing. After all, life is only so long, and time scarcity dictates that each of us needs to balance breadth of skill with depth of skill. Is there in fact a tradeoff between these two principles? Should each of us seek to optimize among them, rather than maximize one or the other? Or am I missing something?
I think your point was “acquire a broad array of skills so that you can help solve a broad array of problems.
Is there in fact a tradeoff between these two principles? Should each of us seek to optimize among them, rather than maximize one or the other? Or am I missing something?
Now that you’re a prof, what criteria do you use in deciding whether or not to accept a new grad student into your lab or bailiwick? Conversely, when new grad students need to find a prof to sponsor or mentor them, how should they go about it?
I really liked your advice in this updated piece. I just wanted to comment on something in the original. You said to ignore people who live in the dorms, and I think I get what you basically meant with regards to avoiding sheltered people, but there can be important mitigating factors.
For instance, LGBT students in most states throughout the country can be legally evicted from private residences solely on the basis of their sexual orientation. Universities, especially public ones, tend to have very strong anti-discrimination rules with a level of enforcement not found outside the walls of dorms. I’m in Arizona and live in my school’s dorms for this exact reason; they can’t evict me for being gay, while any apartment complex could. I love the blog, and didn’t take particular offense to the remark, but I did want to correct the misconception that only sheltered weirdos live in the dorms.
The two thoughts that got my attention and that I need to work on are these.
1) “Learning something new is difficult, frustrating, and takes a long time.”
2) “Push and constantly strain yourself to learn more and perform better”
I have to say you put up a really nice article, very helpful I need.
You say strip back complexity when you solve a problem. But what about abstraction?
I recall that a mathematical problem has two qualities– abstraction and complexity. Initially, to solve a problem, would you make the problem more or less abstract?
I work full time while doing my PhD in computer science in Germany (no classwork only research). On a good week, I am able to squeeze in around 16h for my PhD. My advisor is a very cool and encouraging person, so I don’t have a lot of pressure from that side. I have doubts regarding my ability to finish it. Does somebody walk that way before?! Can you share your thoughts about whether it’s doable or not?
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