I do not fully understand the process of understanding of a material one reads. Suppose someone reads a chapter from a physics book. How does one make sure that one had really understood what she/he had read? I must confess that at times I read from text and I even feel that I had understood the content but later (may be at the time of exams or solving assignments or when somebody raises a question from that topic), I realize that the feeling was illusory and I feel so stupid. At times I feel that my understanding is incomplete even at basic levels. I am eager to know from experienced people in this forum if there is any method to test whether one had really understood the content of what one had read. I am talking of advanced level physics courses. May be one can also suggest useful skills one can develop for better grasp of items one studies. Thanks.

I have some other related thoughts. Perhaps this is not just a problem with me but with many others, including even researchers. I have seen during one seminar given by an well-known faculty member of an institute, another well-known researcher from audience started asking questions and making comments which revealed lack of understanding of the speaker and he was almost in tears! Not that the speaker was dishonest but this shows that even experts like him can have "illusory" sense of understanding of a topic (not only what he/she had read but done some research work). So may be there is nothing like full understanding of a topic but deeper and deeper understanding of topics. So the question now becomes, how can one attempt to understand a topic deeply and keep going deeper? And for students, how can they be sure their understanding of a topic is good enough?

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    $\begingroup$ Best ways to learn something: 1) Apply it, 2) Teach it. (in that order) $\endgroup$
    – Michael
    Oct 29 '13 at 15:01
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    $\begingroup$ Solve the problems at the end of the chapter $\endgroup$
    – anna v
    Oct 29 '13 at 15:06
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    $\begingroup$ This is an excellent question, I must say. I wonder whether and why this question had not been asked and handled before. It's a general question that should be asked and sought for answer in any field, and a keen one if we want to do well in physics. I may not do a well-round job on answering but at least I'll try to get it started. $\endgroup$
    – Chin Yeh
    Oct 29 '13 at 15:20
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    $\begingroup$ I think this might be off-topic as it's really not specific to physics -- the same could be asked about any material and I think the answers would be the same... We'll see how others feels about the OT-ness, but it is a good question. $\endgroup$
    – tpg2114
    Oct 29 '13 at 15:42
  • $\begingroup$ This YouTube video may help... $\endgroup$ Oct 29 '13 at 16:01

How does one make sure that one had really understood what she/he had read?

This may not be what you're expecting but try to explain it to yourself (or your dog or cat).

If you can't, you got some more work to do. However, I think you'll find that the process of forming and focusing your thoughts into a coherent presentation of the material has the effect of revealing precisely what it is you need to review.

If I recall correctly, there is an anecdote of a famous physicist that would, when stuck on a particular problem, explain the problem to his dog (which would of course, listen attentively!). More often than not, the solution to the problem would become apparent during this process.


This seems prone to invite more debate than one definite answer, but the question is very interesting, so here are my 2 cents:

1.) to get better understanding, close the book/pdf file and try to give a talk about the subject. Use paper/blackboard to help your mind, but do not look into the text. You will find that often you cannot continue without the book.

Most often, this is because the material is not well motivated in our minds, and we cannot understand poorly motivated manipulations; and then most of us, necessarily forget them.

Try to get into the root of the stuff - why is this interesting? What is the author trying to resolve? Does he/she accomplish that? How exactly?

2.) To find out if you really understood (good) text, try to find errors in it. If you can find some and explain how they have arisen, you know you understand the topic at least as well as the author, and maybe even better.


$\ $Excellent question. It's also a general question that should be asked and the answer sought after in any field; it's particularly keen in physics. I hope my answer is only a start in this discussion and could attract our community to offer more well-thought, practical and detailed answers.
$\ $First of all, doing well in exercises and exams is one of the indicators that we have a basic understanding about a subject, but by no means a determining factor.
$\ $Second, ask ourselves or anyone else we can get interested in the subject with lots of questions. Then seek answers.
$\ $Third, take ownership of these questions. The question must have had been asked by the pioneer in this field before and handled pretty well. But that's no matter; we still take ownership of that question.
$\ $Fourth, keep asking more questions from different angles. The initial question that got us hooked to a subject is a route to the destiny. But knowing how to get there is only a start. We have to survey the place, by surveying more. Like the incident OP referred, even an expert in a field can be embarrassed by a question from the audience.
$\ $Fifth, keep at it until we feel the answer coming out so naturally that this should be the answer and there is no other way to it.
$\ $With all this rigmarole, you might ask, can I do the same myself? Mostly no, but I have an excuse: teaching others to do it seems much easier than actual doing.


I think the most important concept here is feedback. My main claim is that

If you truly want to understand something in physics at a deep level, you will ultimately need some form of feedback.

Here's what I mean. Take the story of the researcher almost in tears:

The researcher's superficial understanding was revealed because he received intelligent feedback.

Take your personal concern that you read a textbook and then find out that your understanding was incomplete when doing problems or being asked questions:

Your superficial understanding is revealed by the feedback you get from either not being able to solve a problem, or not being able to explain something.

Consider the following suggestions people have already made in the comments or their answers:

  1. Apply it.
  2. Teach it.
  3. Explain it to yourself or your dog.
  4. Solve problems at the end of the chapter.
  5. Ask lots of questions.

Notice that a common characteristic of all of these is that each provides its own form of feedback about your understanding. Even when you explain something to yourself, you are giving yourself feedback.

Its generally difficult for humans to make progress in their conceptual understanding in isolation. We are creatures that make intellectual progress through a process that includes a lot of mental trial and error. By getting feedback, your brain recognizes where it's in error, then it tries to understand again, and its understanding becomes incrementally better each time.

Incidentally, this is probably the main reason I participate on physics.SE. Its an amazing way to get feedback from lots of people, and this deepens my understanding. Yay!


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