This is a post in which I am just thinking out loud (writing your thoughts down is a great way to think out loud and organize your thoughts). The things that I write in this post may also be beneficial for some younger student of theoretical physics (which, if true, will be a bonus for me).
When I was an undergrad, I had to learn everything on my own by reading books. When I say “had to”, I don’t mean it in a way where this is something that I had to do but I didn’t like doing it. I loved it. I couldn’t depend on my university courses because I knew that their quality isn’t top notch and I also wanted to read things much more quickly. Reading books from cover to cover all day gave me meaning of my existence. At that time, it came very easily to me. I just start reading a book on a new subject that I wanted to study and by the time I finished that book, I would know quite a lot about that subject. It all seemed so methodical. Things seemed to connect with each other so nicely.
Then, in my fourth semester of undergrad, I started reading Peskin and Schroeder’s (PS) book on quantum field theory. I loved it too as the results seemed to derive so smoothly from the formalism. However, while reading PS, I felt that reading this book is so different from the previous books on undergraduate physics. In undergraduate physics books, you don’t need to use a pencil and paper (or black/white board) to verify the steps that are done in the reading. They are simple enough that you can do them in your mind. PS forced me to do all the steps that came during the reading.
Due to this thing, my reading speed went really slow. While reading undergraduate books, I used to finish multiple pages, sometimes whole chapters, in a day (I amn’t bragging. Any dedicated student can do this) but when I started reading PS, there were some days where I managed to read only three pages in a day because the intervening steps took my whole day away. I started to panick a bit because I thought that this indicates that I am not good enough for learning QFT. In hindsight, I can say that this wasn’t the case. I was just encountering a graduate level theoretical physics text for the first time (and I didn’t have any significant guiding teacher while reading PS. I had the internet though).
After some weeks of reading PS, I got used to the fact that graduate level textbooks (and research papers too) are like this. They leave a lot of steps and expect you to do them. Now this is the point in a theoretical physics student’s life where a student can either become lazy and don’t bother doing steps at all (and leave steps for “later”) OR that student can take up the challange and verify all the reasoning (or get a mixture of these two mindsets). All of this stuff might be coming off as very trivial to a reader who is a theoretical physicist but I don’t think that this stuff is trivial (we can agree to disagree).
Ok so what did I do? Well, I would say that got a mixture of these two mindsets but leaning towards “taking the challange” side. What I actually mean is that I used to do steps but there were times when I didn’t feel like doing steps and I could follow the reasoning of the text if I “trusted the author” for the steps and do the steps later. In short, sometimes I did get lazy and didn’t do the steps.
What were the consequences of this partial laziness? The sections that I read with doing the steps were so well understood by me that I could even teach them while sleeping (ok this is an exaggeration because I don’t like to do anything else while sleeping) but there were some parts of the book that I read again and again, and because of this rereading, I did understand their idea but I never “felt” that I understood them (I have done the steps for those sections now and now I do feel confident that I understand those sections). Now I appreciate why graduate level textbooks miss alot of steps and ask the graduate students to do those steps. You learn a lot by doing the calculation yourself.
There was another bad consequence of not doing steps. It may seem that the origin of the upcoming problem is something else but at least for me, the cause of the upcoming problem is my occasional laziness of not doing steps. This problem already started when I was studying QFT but it escalated when I started to learn subjects like supersymmetry, conformal field theory, string theory and the relevant maths like algebraic topology etc. Let’s see if I can characterize the problem clearly. The problem is that ‘when I read/heard about some results or some facts, I used to assume that this result/fact is really hard to derive’. In other words, if a result felt hard to derive, I would assume that it is hard to derive and this assumption would refrain me from even trying to see how would one derive this. This problem is something that has created a lot of problems for me. I always feel that I didn’t learn a lot of things that could have learned a long time ago, just because I had a fear that this thing is hard to learn (without even knowing about that thing).
A factor that contributed to my fear was my insistence that if I need to learn something, I will learn it in a systematic manner (because this is how I learned all my undergrad physics, QFT and later, string theory) but this is something that doesn’t always happen when you are in grad school or when you are a researcher in general. Research (which includes learning new stuff for research) is a very nonlinear thing. Everything wont happen in a nice, systematic way.
So, how did I overcome this? or have I overcome this at all? Well, I would say that it is much better now (I do feel laziness sometimes but I think that this is because of my health). So what did I do to overcome this years long problem? One thing that I did is to write more and more. Overleaf (online latex) is my home. I just tried to do the calculations that I thought are hard and I was surprised to learn that a lot of the results that I thought are hard to derive were actually so easy. It was only my fear that kept me from deriving them. I also failed many times which is fine (failure is part of life, specially if your life includes academia).
When I started my Ph.D. I had to take some courses whose content I was already familiar with. However, when I was doing the homeworks of these courses, it felt really good to redo all the known steps that I had done in my undergrad and (I don’t know how but) I think that starting phase of my Ph.D. had a big part to play in my recovery from the problem mentioned above.
I think that some part in my recovery was also played by my advisor. He showed me some of his notes that he wrote in one of his post docs before writing a paper and in these notes, he derived all the steps of a paper that he was using for his research. These notes were written in latex and those notes (+ some other notes that he showed me later) were very inspirational for me in this regard. As a side note, let me tell you that when theoretical physicists write a paper, a lot of them have a lot of unpublished notes (many times the length of the paper) that they wrote while working on this paper. I have seen some examples of it myself.
So here was the end of the story of an aspect of my student/researcher life that was really problematic for me. I hope it was useful for you as well. Thanks.
Hassaan Saleem 