This blog item is to share some ideas about what one must expect while putting their feet into the experience of a doctoral degree. I have wanted to write about this several times in my past 5 years, but I think this is the best time to do it: after submitting my thesis. The beginning of the post is a bit grim and if you want only encouragement, skip to the end.
At the onset, I must clarify that a PhD experience can be as uplifting and utopian as it can be discouraging and difficult; but it is almost always some of both, and most certainly always didactic. Finally, no two PhDs are ever the same — even for scholars working with the same advisor on similar topics. So, take all I say with as much salt you might need — you'll figure out how much : )
"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics."
— David L. Goodstein, States of Matter
The above is an introduction to a popular book on Statistical Mechanics. It is a rather difficult statement to start off a discussion on such a beautiful subject. However, with all its darkness, the lines point blank address a key concern that stalwarts too deep into the subject had faced in the past. Hence, a caution is crucial.
I feel similarly about a PhD. It is a beautiful life experience in many ways. However, not always must beauty lie in happiness and content. When delivered by bitterness, an experience may become beautiful in retrospect, having evolved as a person while progressing through it. In this destructively beautiful way, the experience of a PhD teaches many lessons and skills which are separate from the core of academia. I remember that 5 years ago, when I began my PhD journey, I gave myself the following reasons:
- Love of science and maths that I inherited from my father
- Inspiring professors who got me into research and believed that I was not 'jhaker koi'
- The freedom to work on problems of my choice
- Constructive peer pressure from the many friends and students around me, and the province of West Bengal which always had a strong focus on higher education
- My mother's dream, which eventually also became mine, of me studying at a world class university with scholarship
- I wanted to be a Professor — a really cool one, that students loved
- And finally, because a PhD was more than just any other degree; it was meant to be a life-altering experience
Because of all of this, I was ready to take up something that most people avoid for pragmatic reasons: there is little money in a PhD, finding a stable job takes a long time, you need to keep working beyond regular hours to make your profile better, there are no regular recruitment drives, you need to be and work alone (often in personal life as well), deal with a perpetual imposter syndrome, battle repeated failures, and risk your mental health. We take on all of this with the hope that one day when your experiment actually works or your simulation finally produces a reasonable result, it will be the first time a minute piece of the universe will have been brought from oblivion to the realm of human perception — and that would feel great.
Why did I do the research I did?
Since my undergrad in Aerospace Engineering where I learnt fluid mechanics for the first time, I was amazed by how complex equations (Navier-Stokes + continuity + thermodynamics) could be reduced to simpler versions to capture the underlying physics of a problem. This is where the appreciation for 'reduced-order hydrodynamics' — a part of my thesis title — comes from. I was also inspired by nature more than technology, and wanted to work on modelling physical phenomena using partial differential equations, specifically in astrophysical and geophysical contexts. This was from my exposure to such systems during my masters, when I worked on granular flows on rotating objects mimicking rubble-pile asteroids.
Advanced topics like linear stability analysis, modal solutions, and wave dynamics encapsulated the elegance of mathematical approaches to understanding really complicated systems. To add to the generic mass, momentum, and energy balances, there were other physical phenomena that could be incorporated — magnetism, radiation, chemistry — which made geophysical and astrophysical flows even more exciting. Moreover, fluid dynamics appeared to be a rather neglected part of astrophysical sciences, and there were opportunities to bring the wealth of knowledge in geophysical fluid dynamics to the field.
How did I come about doing this research?
My initial goal was to do oceanography. However, there was no funding in that area. I did want to stick to primarily fluid dynamics, so I chose to work with stars and exoplanets. I said yes to the professor who responded first. I knew less about those topics, but I felt interested especially because the field of 'exoplanets' was relatively new and often sounded extremely cool to my friends and family.
Initially, my entire research plan was stars-focused — probing meridional circulation in stars. We borrowed an atmospheric science framework to better explain and obtain analytical solutions to a relevant time-dependent problem in Sun-like main-sequence stars. The framework would also have applications to certain exoplanets, like tidally locked hot Jupiters, but that was not the primary project. I learnt about stars and struggled a lot with it, coming from a non-Physics background.
While working on the project on stars, I realized that very few people were working on something related in the field. I felt extremely out of place in research, as if I did not belong to the community. The first paper was facing significant backlash from the stellar physics community through rejections. I also had a lot of trouble with the second project, specifically Dedalus simulations where I ran into stability issues. It was not until my 3rd year that I actually found someone at the APS meeting for the Division of Fluid Dynamics — through pure personal effort — with whom I could discuss problems in the code. With all this in the background, I was starved for academic interactions and hit rock bottom. Meanwhile, in the second year of my PhD, ChatGPT was released and my primary supervisor decided to pivot from astrophysics to AI.
To assuage the situation, I requested him to give me a project that I could carry out with the only other group member I had then, who was working on exoplanets. The project, related to magnetic drag on sub-Neptunes, unfortunately did not reach completion. But my personal exploration of the topic led to the formation of a critical component that helped create the second part of my thesis.
Being familiar with Dedalus, I was able to single-handedly adapt a new version of the code that solved shallow water flows on a rotating sphere to simulate planetary atmospheres with a variety of forcing mechanisms — thermal forcing with fixed or moving substellar points resembling tidally locked or asynchronous planets, or convective forcing resembling brown dwarf atmospheres. This opened a huge playground for exploration of dynamical phenomena. I decided to look into other systems, and took that as an opportunity to complete a project from start to finish entirely independently — dreaming of a solo-author work.
In this time, I had also connected with a new professor in the department and was working on observing proposals for high-resolution cross-correlation spectroscopy of ultra-hot Jupiters. She unofficially became my supervisor. Parallely, I also did some work on the physics understanding capacity of LLMs with my earlier supervisor. One of the problems designed did later end up in Humanity's Last Exam, a benchmark for LLMs. Around this time, I had finished writing the first draft of my solo project on variably irradiated asynchronous planets, for which I found interesting climate states under certain resonance conditions. Both my supervisors suggested me to contact another professor for feedback on the work, and this person became the final unofficial supervisor. With his incredibly valuable feedback, I was confident enough to submit my work to a reputed journal. This paper took the least amount of time to get reviewed and accepted.
My PhD thesis now had two prongs, like a tuning fork. The last year was spent writing competitive fellowship proposals and working on the final chapter. I had to find the base that connected the two prongs. For this I turned to the original reason for which I started my PhD: fluid mechanics. Fluid mechanics not only provides the common thread tying both my research sectors, but also represents the nonlinearity of my journey as a PhD student. It was nothing like I imagined, but at the end of it all, I see that this is the work I always wanted to do.
What did I learn?
A PhD trajectory is largely nonlinear. Often we envision something at the beginning, and by the end we seem to have arrived somewhere else. To navigate this period, you would come up with your own ways, much like you'd do in life in general. Yet, it is helpful to know how others have navigated their journey.
- Acceptance: The cards you are dealt and the cards you chose may not take you where you would want to be in the desired amount of time. Accept that.
- Change: Be flexible to make changes. Adjust, adapt. Better late than never. I have had friends change groups as late as their fourth year of PhD and do great later on.
- Persistence: The more time you spend on a problem, the greater the chance you will crack it. Do not let go. However, there is a trade-off: let go if it is too much.
- Do not compare: Comparison is the thief of joy. Do compare with where you were a year ago for a reality check on your progress.
- Independent thinking: The PhD is yours. You do all the work. The role of the supervisor is to supervise. You cannot expect anything from them.
- Collaborate: Find the people you need to get your work done. Advisors, collaborators, graduate students, undergraduates — don't discriminate.
- Do other stuff: Have extracurriculars, a personal life to hold on to when the PhD gets tough. Organise events and do outreach.
- Move on: Do not hold grudges. Maintain a professional attitude.
- Stand up for yourself: Do not shy away from voicing your concerns at possible forums, but make sure to have done work if you want people on your side.
- Nothing beats hard work.
- Diversify avenues: Pursue at least two projects at the same time.
A lot of the above is pretty generic. Nonetheless, it is good to begin. Here I shall also refer to a post that I made 5 years ago about a bunch of survival resources for non-genius students like me who want to do a PhD.
As I have mentioned earlier, a PhD might not be anything that you imagined, and everything you had not — but you will get through it!