Only with time

This semester, I am teaching a batch of students from the 4th year of our Integrated BS-MS programme. Technically, they are at a level equivalent to first year MSc students. Last week, while discussing properties of the Fourier transform with them, I suggested that in case they forget a certain property or formula, but need it, they should not hesitate to work it out by applying the basic definition of a Fourier transform. "Since there's only a handful of you, you will almost certainly get extra time to finish your quiz or exam," I joked. Before I knew it, I started reflecting loudly on an important change that happens gradually in our lives around their age. Up to a certain point in life, academic success almost exclusively depends on how quickly one can answer questions (correctly) in a time-bound exam. But, as we transition into adult life, success or progress in a career (and other parts of life) depends on how much time we are willing to give to a task at hand. 

I was thinking about what my students would be doing in their fifth year and onwards: working on research projects for their MS thesis and beyond. This would involve learning new topics on their own outside of a structured curriculum, often from research papers which are not easy to read. It would involve spending time on answering a new question for which no hints are given at the end of a textbook. There will be no assurance that the answer will arrive, or about when it will arrive. Any progress will be visible after long days and months of tedious calculations and focused thinking on a topic. One will make mistakes, and correct them time and again. The same holds for other areas of our lives: health, fitness, developing personal relationships or learning new skills. A functional adult life is a direct consequence of how much time we devote to whatever we take up (sometimes by choice and sometimes by compulsion), and how patiently we wait for growth or progress.

Many games that we learn in our childhood, such as arranging jigsaw pieces, building objects out of lego pieces and playing chess train us to be generous with time along with concentration. For that matter, even in the exam-dictated part of our lives, the ability to perform well in restricted timelines comes from long hours, days and months of dedicated, unapologetic practice. Thinking or taking quick action on your feet when time is short comes when you have practiced something for long. For example, while learning to play tennis, the backhand motion takes long to learn for many of us (true at least for me). But, a few months of practice down the line, we don't even think for a second when there is a need to use it. Delivering a decent lecture requires a long preparation time. The shorter the lecture time, the longer you have to spend in organizing the essential ideas in order to communicate them without going over time. As Pascal pointed out, even writing short letters takes time. Almost everything meaningful in life requires time and patience. 

Taking time to do something has multiple aspects. The first is the "woodpecker" aspect: the basic "action" level of spending time on activities. This time is to be devoted, either in short, regular chunks of time, or in long chunks, based on the situation. On a regular basis, we set aside time daily for an activity, preferably during hours when there is minimal chance of being disturbed. When a project is stuck or nearing completion, we dedicate larger chunks of time to it, at the cost of ignoring or postponing some other tasks.  During collaborations, things often get sorted out while the collaborators are visiting each other, as opposed to meeting online. While time-bound, regular online (or offline) meetings ensure progress, a collaboration visit nudges all parties to put aside other activities for a while, and spend long hours thinking about something at a stretch. This often accelerates a project out of a rut, and this is precisely why summer time (when we don't have to worry about teaching schedules) is so valuable for scientists. But, in any case, whether in regular periods or in larger, continuous chunks, the woodpecker aspect is about chipping away at something.

The second is the "washing machine" aspect [1]. This aspect is about putting in the time to go through a process. For example, this involves waiting patiently for an experiment to run its course and yield the results. Situations, where we take action, and wait for the consequences, however long it may take. Those of us who waited for visa appointments in the Covid and post-Covid periods will relate to this. There is nothing we can do while the process is going on, other than regular monitoring and paper-work.  The medical treatment to recover from an illness is part of this category. We go through the course of treatment and wait for healing. To a large extent, the endeavour to get fitter could also be considered as an example here. One makes a (hopefully, sustainable) diet and exercise plan, follows it diligently and waits for as long as it takes for the body to respond. 

Then, there is a third "flower blooming" aspect, one of the most important aspects of any scholarly activity. This aspect is about working with a new idea or method, and waiting for time to shape it into different manifestations and applications. Our duty, which is the equivalent of watering and nurturing a plant, is to actively reflect upon the meaning of the idea by thinking about it, making a regular effort to write and rewrite it, and by finding out its connections with other ideas and problems. We try not to let it go unheeded, as we wait for it to "bloom". As an idea blooms, we revisit, polish, review and reframe it over time. As students, this aspect of time comes into play in our journey of learning. While a course introduces a topic, the learning, understanding and absorption of the content will take much longer than a semester and will be each student's individual journey. Here is the translation of a beautiful Sanskrit verse shared by my colleague, Professor Pavan Kumar: "One fourth from the teacher, one fourth from own intelligence, one fourth from classmates, and one fourth only with time".

[1] Most posts on this blog are written during long linen-wash cycles. 

One day at a time, one step at a time

An experience that most functioning adults face is that of building up a routine with great effort, only to have it come crashing down in the face of an unexpected adversity.  Sometime in the summer of 2024, I found myself in such a situation. A health crisis in my family meant that I had to stay away from IISER for about six weeks.  My family dealt with the crisis wisely by putting together all the support systems and structures.  We all did what was necessary, and somehow managed to keep our work lives going (even if remotely). In my case, that meant regularly corresponding with my students and colleagues, and taking care of other urgent administrative work (such as preparing budgets for conference grants, following up with our grants office, submitting course outlines etc).  But, I soon realized that I was unable to focus on anything that required "deep work": I could not concentrate on my ongoing research projects, and my usual writing routine could not withstand the shock of the situation. One of my collaborative projects was gaining speed at this time, and while I joined all the meetings, it was actually the collaborators who were pulling all the weight during this phase while I started blankly at the screen. 

After the family situation was better, I returned to campus.  Nevertheless, there was a thick fog in the mind, possibly due to the stress of the situation and several weeks of irregular sleep. I was finding it hard to recover despite being back on home ground. Soon, there was another month-long phase of travel, and the writing routine seemed at its lowest ebb.

The redemption came in September in the form of an eight-day-long vacation in Kashmir that I had planned long before the family crisis had erupted. I was to stay for the whole duration in a quiet hill station called Yousmarg, known for its beautiful meadows. While planning the vacation (or more appropriately, the stay-cation), I had hoped to be in a completely relaxed state of mind after a summer of conferences and paper submissions, and to possibly start something afresh. But, it was not to be: the version of me that reached Yousmarg was terribly anxious at falling behind in all her research projects, and was struggling with low attention span. This could not continue.

So, I made a plan: I decided to focus on just one project and devote a few hours every morning to it. I also planned to work on the project for the rest of the day, but the latter part could be more flexible, combined by walking around Yousmarg, reading [1], or taking a nap, based on my mood and energy levels. The strategy was to start small and do a little bit every day.  In fact, I started with proof-reading some parts that had already been written by my collaborators, and promised not to judge myself even if it took me all day to understand some steps of a proof.  The important thing was to make some progress everyday, and regain my attention span in small increments.

It worked! 

The lack of internet at the hotel worked like elixir for someone looking to regain their attention span. I waded through all the project-related material (downloaded before the travel), line by line, step by step. Since I could not type on Overleaf or connect to my collaborators, I made notes and zeroed down on a couple of points that looked troublesome. The walks around the hotel became more pleasant while I thought these points over [2]. 

By the end of my trip, I found myself up-to-speed with all that had happened in the project during the summer, except for a couple of points. This may well have been the first ``vacation" in which I got to relax, while also working without anxiety. Soon after returning to Pune, I resumed my teaching duties (the post-midsem part of a second year course on probability to a large class) and regular meetings with students. At this time, I spoke to a friend who had recently overcome a similar challenge. She had survived a much more difficult situation, and was able to walk me through the different stages of regaining focus. "When the fog lifts, you will know; until then, one has to keep doing whatever we can."

While the ``fog" had still not lifted completely, the sunlight had started to filter in. My energy levels and attention span were both coming back, and the stability of not having to travel for the next three months motivated me to double down on the project. On the morning of the Mahalaya, I made a to-do list of literature search and writing needed to take care of some sections of the paper. The aim, everyday, was to not leave the study table until the task for that day had been completed. By the morning of Vijaya Dashmi, I had completed multiple sections, and had also corrected the points which were troubling me in Yousmarg. 

For those who know what I am talking about, these points had to do with some subtleties in the relationship between the symmetric-power L-functions for Hecke newforms and the Rankin-Selberg L-functions; with the corrections in place, all the subsequent sections had to be modified.  Our project is to find explicit constants in the zero-free regions for modular L-functions, and every estimate has to be noted and incorporated carefully and precisely into the "master" equations.  Soon after Diwali, our team of collaborators resumed our weekly meetings (we are working between three countries and four time zones).  In complete contrast to the summer, I was now eagerly engaged in the meetings, and would enthusiastically look forward to them through the day.  This is when I knew that the fog had lifted completely. We started working on each section, and over the last month, have cleaned up the manuscript and written out the proof of our main theorem. We are now in the final stages of the article, and the month of December will be spent in proof-reading and finalizing the draft. The feeling of showing up well-prepared for every meeting and absorbing all the insights from collaborators to improve one's understanding of the project is priceless. I enjoy working on this project every morning, and it is such a relief to have overcome the writing inertia of the summer months.

The writing routine is back, but with a realization that adversities and shocks can strike unexpectedly. Regaining one's focus requires kindness to oneself and some flexibility in work habits. It requires us to control where we spend our time and energy, but without slipping into victim mode (as my friend wisely pointed out). Above all, it is about taking one step at a time, one day at a time, consistently. If something looks intimidating (as it naturally will, if we are recovering from a situation which took us away from something we were doing regularly), break down the task into small steps, and focus on one step at a time without negative self-talk. Replace "Why I am I so stupid?" with "What exactly is the problem in this step?" Replace "Why am I so slow?" by "What progress have I made since yesterday? What can I do next?" If the next step seems to invite procrastination, break it down into even smaller steps. 

In time, we build things back (we really do, however "low" we start), and at the same time, become non-judgmental observers of our own growth and progress. For those of us who have to write regularly, the progress becomes visible in the form of all the new sections that were typed up. It can be quite revealing to compare the current version of something with what it was a month ago. While you were taking one little step every day (and possibly wondering if this was enough), your draft was growing bigger and more wholesome, the extent of which can be noted a month later.

Starting tomorrow, I will be busy with preparations for a major conference from 09-13 December at IISER Pune.  The rest of the month will be spent in conference travel and time with my family. Will I be able to guard my morning writing routine through all of this? And if there is a crack, can I bounce back to normalcy by taking one step at a time? We will leave these questions for a future blog post.

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[1] I specifically chose the letters and poems of Emily Dickinson because the Sangarmal hotel at Yousmarg, where I stayed, reminded me of her homestead. But, I may have chosen the wrong collection of letters. This particular collection contained many letters in which she is exhorting her friends, in moving language, to reply to her letters and not ignore her. These letters made me very angry with her friends, and may have drained my mental energies a little. 

[2] The walking, however, had other consequences. People in Yousmarg are extremely friendly; the thought of a (female) tourist walking all alone on a cold day is unbearable to them and they will take you to their homes and serve tea. The personal connections made through such interaction are invaluable, and sometimes, one just has to postpone the Math to the privacy of the hotel room and garden :-)