I may have mentioned here before that I don’t really hold my own skill at Physics in high regard. It may be that I’m good at it, but I don’t really know and moreover I don’t feel like it’s a relevant observable anyway. What I do think is important is that I know quite accurately a) my skillset and b) the way I apply it.
One of the important requirements for being good at something is being able to keep in perspective where ones limitations lie and how flexible they are. For me, some of my limitations are very inflexible because they lie in the fundamental way that I think and approach life. My biggest one is that I can’t ever take someone’s word for something that I don’t already intuitively understand, not even if I already know that they’re correct somehow (this is one reason I find lectures difficult). It’s not that I don’t want to; I literally can’t process such things*. This is a problem, because I also don’t find it easy to follow intuitively what people try to tell me in terms of mathematics, even if my mathematical skill is at the appropriate level to understand the technicalities.
You might say that is a killing blow for a Physicist – unable to easily understand and unable to listen to an expert! What kind of maths-based scientist is this? Well, I disagree there, primarily because “just taking someone’s word for it” is pretty much the antithesis of science**.
But as I said, it’s important to know your limitations and find ways to work around them. In my case, work really is the operative word – the only solution is hard and specific work to overcome my personal barrier to understanding. I know that I have to spend a lot of time explicitly deriving an equation in order to understand it – and to understand a whole field takes a lot of hard work and immersion in the subject. To be clear – I can’t simply apply something I don’t properly understand so I could not possibly make progress unless I start more or less from scratch (or that’s how it seems to me).
Luckily, that’s what I’m good at – I like immersing myself in a subject in order to understand it***. The important thing to me is that what I understand intuitively through insight or immersion feel obvious, but anything else looks a lot like voodoo. I was pondering this recently when I started reading papers in earnest in an attempt (ongoing) to understand the broad area of Photonics better. My ultimate aim is for it to be a little closer to intuitive for me.
I decided that the best way to do this was by reading papers on the subject – immersion on the highest level I’ve attempted to date, and well beyond what I think is strictly expected of an undergraduate – but I hit a problem. My own limitations make reading papers quite difficult, since papers are just condensed versions of a lot of work which the authors have done over a long time. Hence, one often has to understand intuitively what’s going on or get lost in the details. That meant that I didn’t have a lot of success understanding things at first.
I found this very disheartening.
However, I was this week reminded of a thing which my personal hero said once, which goes some way to justifying the trouble I have.
During the conference I was staying with my sister in Syracuse. I brought the paper home and said to her, “I can’t understand these things that Lee and Yang are saying. It’s all so complicated.”
Richard Feynman,“The 7 Percent Solution”, Surely You’re Joking Mr Feynman, Vintage Books
This is Feynman, yes the Richard Feynman talking about an analogous problem to the one I often face when reading papers. Namely – he’d spent a long time feeling like he was at the back of the field, finding it very hard to keep up with everyone because he wasn’t at the time understanding intuitively what was going on. If you’ve been paying attention, you’ll notice that’s not exactly far removed from my own situation. Just the knowledge that far better Physicists than I can have such limitations is heartening to read, but the really interesting bit is how his sister responds.
What you should do is imagine you’re a student again and… read every line of it, and check the equations. Then you’ll understand it easily.
She more or less tells him to read it more carefully and figure it out for himself! I find this particularly interesting because this is literally the approach I have to take when I read a paper – I find it very difficult to understand unless I expend a lot of effort on explicitly understanding what’s going on. In that sense, I certainly feel that I deviate somewhat from the best of my peers. Nevertheless, I’m glad to confirm that it’s not such a crippling affliction that I can’t keep extending myself further into a career in research.
So if you’re having trouble reading papers, I’d recommend bearing some important things in mind;
- Papers are meant to be succinct; if they make leaps of logic you don’t intuitively understand, it could be useful to work very carefully through it in the manner described earlier.
- Working it out in your own terms can help a lot; as I’ve read more, I have developed a series of reference ideas that I compare equations, ideas, experiments, etc to. The more you read, the better this develops.
- If you really can’t make head nor tail of a paper, you should save it. Read related papers, perhaps a simpler one or one it references. Read around a bit more and come back to it – often it makes significantly more sense!
- Remember that total immersion (like I have to do) tends to be extremely difficult at first. Do not be disheartened if your first five papers are all incomprehensible. Maybe by the time you get to 50 you can start worrying. I estimate that over the past three weeks I’ve read about 100 pages of papers on various subjects, and I’ve certainly noticed an increase in the speed I’ve been going through them recently.
- Some papers really are incomprehensible. Be they just poorly written, grammatically bizarre, or so chock full of jargon that most reviewers would have difficulty, it’s entirely possible that it’s not just you.
- Finally, papers are often easier understood if you have someone to discuss them with. I suggest you take any opportunity you can to do so.
Another useful technique I’ve been told about very recently is something known as a “paper tree” – more or less a route map of the connections of papers. The idea goes like this; you start out with one paper and you read something where there’s a gap in your knowledge. If you look up the reference given by the author for that section, you can start to fill in that gap (or those gaps) – paper 1 led to paper 2 (and maybe number 3 as well). You might discover still more holes in your knowledge, so look at references for those and follow them to 4 and 5 from paper 2 and then 6 and 7 from paper 3 and so on. Then you might have a diagram like this;
This method can help you keep easy track of why you want to read each paper (although after a while you might well find that you’re reading these things out of sheer curiosity! This happened to me).
One happy moment for me came when I discovered a paper – technically a conference transcript – by Feynman himself. It turns out the jammy sod was one of the first people to start talking about Quantum Computing! (on top of more or less inventing nanotechnology, modern Quantum Electrodynamics, and so on…) Feynman’s unique style was so readable I went through all 22 pages just for fun, and loved every minute of it. That dude is really a source of inspiration for me.
Incidentally, if anyone happens to be reading papers in Photonics in their spare time, send me a tweet or five. Otherwise – good luck! Share your stories and tips in the comments and we can discuss more things to do if you’re having trouble reading a paper.
Finally, I’d like to leave you with this; don’t be too disheartened if you’re having trouble keeping up with a paper. They’re written for some of the most intelligent people in the world, after all, and often what they say is so non-trivial that even the authors struggled with it. Do your best to re-create it all in your own language, and you’ll often find it easier.
What I cannot create, I do not understand.
R. P. Feynman
* – This puts me at a massive disadvantage in debates, since any point I hadn’t already thought of is usually pretty difficult for me to respond to – how can I possibly respond to something I am unable to process without re-deriving it for myself? This has lead to me “losing” a lot of debates because I just can’t produce any counter. It’s a little bit depressing sometimes!
** – Thanks to @TheckPhD for the appropriate phrase there =]
*** – (I could potentially argue that’s the whole reason I got into Physics in the first place – few subjects require more immersion just to get interested in! However, that is somewhat tangential.)
Major thanks to @TheckPhD for his responses to the first draft of this post. Comments constructive and useful as ever, even if it did delay the post!