The Magic of Motivation

At some point, while you have been reading articles for classes, attending seminars, teaching and occasionally collecting data, you have progressed into the later years of your PhD.  One day you will realize, “Hey, I’m getting there!” and simultaneously feel “Ugh, so much more to do.”  This is the point in time when your motivation is as necessary as your experimental controls.  Why does this point in time happen so abruptly and how do you keep moving past it?

First, let’s briefly consider why this dichotomy of optimism and frustration occurs.  I think it has to do with the grand scope of a PhD program.  The large, amorphous goal is to develop, execute and communicate a project of to-be-determined size, depth and importance.  What you find at the end may be completely different than what you thought when you started.  And there is no simple roadmap of how to get from Point A to Point B while hitting all the landmarks in between.

From Point A to Point B

Our minds (and hearts) often have difficulty wading through the small details of a big picture. To better allow our brains to get to the end point, we need to set smaller, intermediate goals.  Now you may think, “Goal setting is obviously important for getting my papers written and my   experiments completed, but how does this help my motivation?”   Not only do these intermediate goals enable us to manage the day-to-day, they help us see progress on the messy path to Point B.  This article on mindtools.com has some great tips for goal setting and utilizing these goals as a compass toward your big picture.

Goal setting seems like the practical explanation to the question of how to maintain motivation.  I really appreciated this TIME article’s not-so-logical explanation of productivity loss.   Life is not just logic, and emotions alter our productivity and motivation.  So, what to do when you have an experiment that is just not working, your advisor asking you to do more and the feeling of frustration and fatigue inhibiting every reasonable plan of action? Here are three magical suggestions:

  1. Stay Positive: Whatever is going wrong is temporary and not the end.  If you are relating to this article, it is because you are in the middle of the long journey.  This means you have accomplished A LOT on your way to this point.  Remember all of those experiments that have gone well, those papers that you have really liked, that conference talk that was awesome.
  2. Get Rewarded: Tom and Donna from Parks and Recreation have this one solid with “Treat Yo’self Day.”  You don’t need a reason – you’ll feel happy and much more excited to get back to the grind.
  3. Get Peer Pressure: You care what your friends think, so use them!  Ask them to push you toward that scholarship deadline or paper outline.  Be deadline buddies and set dates to check in on your progress.

There is no one path to a PhD or one solution for staying motivated, so these tips are as good a place to start as any.  Slow days will come and go.  Stick with it.  There is light at the end of the tunnel…

March Mad-Scientist

It’s probably been too long since I wrote when I have trouble remembering my password to submit this post. There have been times during grad school when I could easily blame laziness as an excuse, but the past four weeks have been the most taxing and stressful of my academic career: finalizing my dissertation.

So here I am, writing this, in my possession a fully revised and edited document containing over 31,000 words thinking that while my defense is still ahead of me, do I feel much different than I did before sending my final draft to my committee? Okay, bad example, that e-mail had so many emotions tangled together before hitting that Send button.  Let’s go back an hour earlier to when I packaged my Word document into a .pdf and finally had time to exhale. Breath in……and…..out.

I was surprised at how little I felt. Now, maybe this isn’t the case for other people, but I had this preconceived notion that finishing your dissertation should feel like this monumental moment in your life, the culmination of 4+ years potentially ending in you never being labeled a “student” again.  That all those sleepless nights or worse, nights you slept and dreamt about your dissertation, were going to stand for something and you’d have this sense of pride and accomplishment. For me, nothing.

Through the process of writing, editing, yelling obscenities at Microsoft Word, editing, fixing graphs in Excel, and (still more) editing, I started to see places in my results that opened up not holes, but passages for future and additional work that could show critical information. Information that would allow our whole research group to make stronger conclusions about our respective individual projects and potentially what they could mean for the scientific community. So, despite not feeling any changes, those thoughts made me realize one thing. It was time for me to go and maybe that was THE difference.

The Truest Sentence You Know: How to Get Un-stuck

The greatest frustration of graduate school has to be that, no matter how often I hope it will, the dissertation never writes itself. How convenient that would be! Alas. It’s one thing to feel confident and assured that you know what you’re doing in the archive. You found a seventeenth-century piece of parchment, and you actually managed to decipher a line of chancery hand? Congratulations, and well done you! You’ve earned a slice of cake and sit-down. And while you savor that pastry, it all comes together in your head – chapter titles, concluding paragraphs, clever introductions. You can see it all. Then you sit down to write it. And that’s another thing entirely.

I can’t be the only one who knows this feeling. It’s like that liminal space between waking and dreaming when your limbs don’t quite work. The fear of failure or – worse – mediocrity can be paralyzing. I’ve always fashioned myself a writer, but what if this time…what if this time…

And then I know I need him. I need Ernest Hemingway.

Hem may have led a disastrous personal life, but he knew a thing or two about putting pen to paper. And even he, the (so to speak) consummate professional, had his bad days. But, thankfully, because he was the consummate professional, he soldiered through them, and, lucky for us, he wrote about it. His advice, recounted in A Moveable Feast, was directed at himself as he struggled with a story in his Paris years. But he might have been talking to me too.

“Do not worry. You have always written before and you will write now. All you have to do is write one true sentence. Write the truest sentence that you know.”

By some miracle, it works. It always works. It gives my writing the strength and attitude it needs to be convincing and, if luck is shining on me that day, stylish. Excavating my draft for the core truth I want to convey – in this sentence, this paragraph, this chapter – and being able to communicate it in a simple declarative sentence makes me a powerful writer for a moment.

Because that has to be part of the goal, doesn’t it? I’d like the dissertation to be more than passable, more than good. I’d like it to be stylish. Readable. Art historians like me write about people who created, but we’re creating something too. Shouldn’t we recognize that we are engaging in a creative act and try to act accordingly? Shouldn’t we try to write something worth reading? Something that contributes not only to our field or to the humanities but to humanity? (Did I go too far there?) I don’t flatter myself that I’m the next Simon Schama, Paul Barolsky or John Summerson, whose work I would gleefully read under the shade of an elm tree. But what was the point of doing all this if I’m not going to try?

Hemingway rented a room in the Latin Quarter of Paris – no heat, no toilet, no fun of any kind. When he was stuck, he stared into the fire, peeling an orange until he settled on the truest sentence he knew at that moment. He knew the fear of failure would be there, and he had a strategy for facing it. And Lord knows, he wasn’t alone. A list provided by my good friend and writer Michael Fuchs includes a series of successful writers lamenting their own fear of failure, including himself as he prepares his fifteenth manuscript. And Nora Ephron famously said, “I think the hardest thing about writing is writing.” We all get stuck. What is your strategy for getting un-stuck? In the end, I suppose it all comes down to discipline, whatever your discipline.

Workshop Podcasts Now Available

In response to requests, selected Project AGER workshops will now be recorded, when feasible, and posted on the new “Podcasts” page on this blog.

Two podcasts are now available:  Turning your dissertation into a book or article, presented by Chie Ikeya, Assistant Professor, History Department, 2/12/2014, and Careers in Academe: Issues to Consider, presented by Dean Barbara Bender, GSNB.  They are here.

Communicating science: the elevator speech

In a previous post, I described my experience at a workshop (organized by the Rutgers Graduate School-New Brunswick) on communicating science.  I described the importance of preparing descriptions of your work for a spectrum of likely audiences – having at least some idea of what aspects of your work to emphasize to different audiences and what language or ideas to use are critical.  However, in addition to these more customized versions, having a more generic but highly-polished description of your research that you can recite from memory at any time is probably worth having.  This is often known as the “elevator speech,” since it’s supposed to be something simple and short enough that you can say it during the time you’d spend with a stranger in an elevator.

I’ve had a murky version of this for a while, but it was largely a vague set of examples and analogies I liked to use when describing my research to a friend or family member rather than a well-crafted summary.  But the workshop motivated me to finally develop a better version, so here is my latest attempt:

Every cell in your body contains thousands of different kinds of molecules, stuffed into a very small space and interacting with each other in complex ways.  How does this mess of molecules ultimately do all things that cells do, such as making new cells, extracting energy from food, and transporting nutrients?  And how did the precise interactions of all these molecules develop over millions of years of evolution?  This knowledge is important both for treating human diseases in which these cellular functions go wrong (e.g., runaway cancer cell growth), as well as engineering microorganisms to perform useful jobs, such as synthesizing biofuels with bacteria or making better beer with yeast.  My research uses mathematical models and computational techniques to understand how natural selection changes these molecules and their interactions over time.  We want to use this both to understand how organisms naturally evolved in the past and to predict how they might evolve in the future.

Research in Mathematics

Working in mathematics, I’ve found myself often asked the question “What do you do?” Sometimes the expected response is my “elevator pitch” (the short blurb about my area of expertise). But sometimes the question is more basic: “What is it you do, though? Do you just sit all day and think?”

Thinking [cc]

Now, to a large extent, many people in research spend all day thinking. However, mathematics is not simply the art of staring at a problem until the solution materializes in one’s head. (It’s worth a try, but often solutions do not come from epiphany alone.) I would like to discuss a few of the ways in which research is conducted in mathematics, with emphasis on the parallels and similarities that may exist between mathematics and other fields, perhaps to somewhat debunk that notion there may not be any such similarities.

Nature [cc]

Mathematics research revolves around proving new theorems — mathematical statements that can be deduced from the fundamental axioms of mathematics and from preexisting theorems. Generally, though, the procedure is not to make a big pile of the existing statements and to try to string them together randomly until one forms a coherent deduction that results in something meaningful. That would be pretty rough sailing! Mathematics relies on conjectures, put forth as believed to be true and hopefully proven by someone at some later time. While there are conjectures (e.g. Goldbach’s conjecture) which remain unsolved for long periods of time (sometimes resulting in notoriety), most theorems start out as rough ideas or propositions that are developed with increasing structure and refinement until they are proven. In addition to proving new theorems, other steps forward in research include constructing examples of mathematical structures and verifying theorems by re-proving them in new ways. Computational work is also done to improve theorems in the case that a theorem is quantitative (or sometimes, to prove that a quantitative result is best-possible).

El. J. Comb. logo

Know the literature: As in most fields, the mathematical literature is vast, and perhaps especially in mathematics, it is easily accessible. Increasingly, mathematics journals are available online — not just through the library system, but free for instant download on the Web. Having less concern for the preservation of intellectual property, many editorial boards have shifted to such open/free publication. (Indeed, I myself have a publication in The Electronic Journal of Combinatorics, which is precisely such a journal.) There is also the arXiv (the X is pronounced sort of like χ, the Greek chi), which hosts preprints of papers and other works of mathematics (and many other fields).

Being familiar with the body of literature, both seminal papers and other older works as well as the current cutting-edge work (as it appears first, usually on the arXiv), is an important part of conducting research in mathematics. Jacob Fox came to Rutgers in 2009, when he was at Princeton, to speak at a seminar. He noted during his talk the importance of being familiar with the literature, mentioning in particular how his knowledge of a certain publication helped him and his coauthors solve a problem.

Mathematics [cc]

Crafting and Proving Good Conjectures: One of the more important questions is where to start — if we’re going to prove a statement is true, what is that statement? Generating good conjectures is not a matter of guesswork or divine inspiration, at least not entirely (although the former may have helped from time to time, and the latter is open to some debate at least). Increasingly, experimentation is a common way to generate conjectures. It is also often useful to test conjectures in small, typical, or special cases (where “small,” “typical,” and “special” depend on the problem at hand). Usually a conjecture applies to too many cases to test them all (sometimes, infinitely many cases), so this methodology is often used to verify that the conjecture is sometimes true, but not to verify the conjecture exhaustively. (Conversely, experimentation may lead to a disproof of a conjecture by identifying, constructing, or otherwise elucidating a counterexample.) Experimentation may also help unearth components of the proof of the conjecture at hand.

It is also crucial to have a firm understanding of the big picture in the field where these questions are being asked. There is a substantial amount of context and content that guides someone to the right kinds of conjectures and the proofs of those conjectures. Mathematics is a field in which the objects of study are highly structured, and knowing these structures helps eliminate some of the technical clutter that can obfuscate the underlying truths that one wishes to prove and the bits and pieces that go into proving them. Many proof techniques can be adapted to different situations, so in some sense theorems may be proved by matching a generalized proof to a statement you would like to prove specifically.

Proof [cc]

Building Theories and Solving Problems: Tim Gowers is famously credited for roughly dividing mathematicians into the two categories problem-solvers and theory-builders (or rather, he is credited for noting this division in his oft-quoted The Two Cultures of Mathematics). I won’t discuss this dichotomy, but these two activities characterize much of the research done in mathematics. Proving single, unrelated theorems one-by-one is not usually how research goes. Rather, the enterprise involves longer strands of investigation — a dozen theorems sometimes collapses into a single stronger and better statement after enough exploration and refinement. Meanwhile, single ideas branch into many avenues of investigation. But generally, the aim is not to knock down one theorem, then turn around π radians and start over, but to work on larger-scale investigations. I could make a metaphor about bowling pins or dominoes, but I think the idea is clear. An important aspect here is also collaboration, which is a major element of research for many mathematicians. Working on papers is one part of collaboration, but other important activities include seminars & conferences (as participants and as organizers), expository writing, editorial work, and many other collaborative activities.

Structure [cc]

So the venture is to find good lines of research and establish some clear, path along that line. There are the two approaches. The first is to identify important problems and build up theory to solve them. One famous example is Fermat’s last theorem, which conjectured centuries ago and recently proved by Andrew Wiles. During those centuries, large swaths of mathematics were developed in large part as attempts to prove this conjecture (including Schur’s theorem, one of my personal favorites). This “problem solver” work weaves what might be the leading strands of the theory, loose and rough but pushing outwards farther than neighboring strands. Such work often moves mathematics in innovative or interdisciplinary directions, building bridges between fields of mathematics, and may also connect with work in applied mathematics. The “theory builders” weave strength and cohesion into the fabric (to extend the metaphor). To this end, they focus their research on developing and enriching the theory. They may work to classify all types of a particular structure, for example. Such work includes that of several Rutgers faculty in classifying the finite simple groups. This theory-building reinforces others’ work as they develop and solve conjectures, as it makes the underlying theory more robust.

Images used in this entry are used under fair-use and/or under licensing guidelines set forth by the copyright holder that allow use in this blog, as presented for educational or critical commentary. Images are copyright their respective holders and credit or source is indicated in each caption or in the text of this entry, as applicable. Thanks to Yusra Naqvi for her helpful comments and suggestions.

Randomly Walking through Research

From reading papers, it’s easy to gain the following picture of what the research process looks like: someone starts at point A, a known point in the space of knowledge, then directly proceeds through various arguments and data to one’s conclusion at the previously unknown point B.  However, thinking that research actually works this way based on what you see in a paper is like thinking that Michael Jordan just awoke one day and suddenly starting dunking from the free throw line.

No, MJ almost certainly traveled a long road to get that much air.  The same goes for research.  The real research process more resembles the famous physics concept of a “random walk” (or more colorfully, the “drunkard’s walk”).  In a random walk, some process is imagined as an object, perhaps an inebriated human, taking a step in a random direction at regular time intervals [1].  This idea is used to model everything from chemical reactions to stock markets.

The random walk provides an interesting visualization of the research process as well.  Uri Alon, a scientist at the Weizmann Institute in Israel (whose outstanding set of resources for “Nurturing Scientists” will be a topic for future posts), has described the process as the following [2].  You indeed start out at A, headed for B.  (See figure below.)  But instead of a nice straight route, you embark on an irregular trajectory with many detours, barriers, and delays.  Often you are eventually forced to abandon B altogether: B was already discovered by some Russian guys in the 1970s, or maybe it’s impossible, or perhaps it just can’t be reached if you hope to graduate within the current decade.Image

At this point your random walk enters a limbo state that Uri Alon calls “the cloud”: you know you can’t go to B anymore, but you don’t know where else to go.  Being stuck in the cloud is probably the most difficult part of doing research.  But the key is recognizing this is a natural and inevitable part of the process.  If you persevere, you will leave the cloud by eventually finding a new place to go: point C.  In fact, often C is much more interesting than B would have been anyway — the unexpected almost always is.  Of course, sometimes C also fails to work out, too, in which case you redirect to D, E, F, etc.  (Hopefully you don’t run out of letters!)  The point is that research is less like a direct path from A to B and more like a random walk with an unknown trajectory and an unknown destination.  But after all, it is this journey into the unknown that makes research so exciting and so important.

[1]  Mlodinow L.  (2008)  The Drunkard’s Walk: How Randomness Rules Our Lives.  Pantheon, New York.
[2]  Alon U.  (2009)  “How To Choose a Good Scientific Problem.”  Molecular Cell 35: 726-728