How to ask a question?

When facing something we don’t understand, we might be troubled by the following scenario: I do not understand what it is. How can I ask sensible questions? Will asking a question make me look not so smart?

In fact, it is quite the opposite way around. As a teacher, I am usually very happy to receive questions during class. Because that means students are acting like educated adults: being responsible for their own learning. Asking questions means you are trying to think. You are not trying to calculate without knowing what you are doing.

Trying to think is essential to internalize a physical concept. The traditional lecture provides the illusion that we should always follow the step-by-step derivation. i.e., From A to B, then from B to C. Eventually, we got the answer to the problem. The process brainwashed us: This is how we finish an exam, and this is also how we make discoveries. The fact is, in fact, opposite to this process. We think first; then, we try to write down equations to describe what we are thinking in precise mathematical language.

So try to ask questions after you do some thinking! Or try to identify the questions that will help you to think.

What kind of questions will be helpful in developing independent thinking? How to be confused in an efficient way?

The old but useful strategy: divide and conquer.

When facing something we don’t understand, we might be troubled by the following scenario: I simply do not understand what it is. I don’t even know where to start.

The first step is: to divide your confusion into smaller pieces. How to divide the problem is also important. The principle is: to identify the logic of confusion.For example, we might be confused by the statement: A and B lead to C. But we don’t know what A is, so we should try to find the definition of A. The definition of A might be the quantity F at zero temperature. We might not understand what F is, but we know what temperature means in principle. So we look up what the description of F. F might be a concept related to the statistics of particles, then we know the issue we are facing is to understand the meaning of the statistics of particles. By iterating this process, we identified lots of unknown knowledge. However, we have a clear picture that, to understand the hazy statement that we started with, we need to understand what we meant by the statistics of particles.

Try to think and discuss with the people about the logic and how you develop the line of thoughts to identify the key question is the statistics of the particles. Then, you can try to relearn the idea of statistics of the particle and see if it helps to understand other relevant ingredients.

Ask yourself: what I am trying to understand?

Is the definition not clear? How to go from the left-hand side to the right-hand side of the equation? You claim A is large, large compared with what? Is it exactly equal or just an approximation? After thinking through what you are trying to ask, try to see if that changes the previous way of thinking and have a fresh start.

Ask yourself: what are the examples that conflicts with the statement you just heard of?

There is a reason that we are confused! It must seem shaky, according to some of our past experiences. For example: when we learn quantum mechanics, we might encounter a description based on wave interpretation. However, what we have in mind might be the phenomena that are related to the particle picture. For example, the energy is quantized. How does it fit with the wave interpretation? A useful way to convey your confusion is: “Prof. X, what you described does not make sense to me. In quantum mechanics, I expect the energy to be quantized. However, the phenomena you described using wave interpretation seem to contradict the quantized energy picture. How to have a consistent picture for both cases?”

Ask yourself: what are the simplest non-trivial examples that can demonstrate your confusion?

If we don’t understand phase transition, we don’t want to start with the phase transition with various different structures.

For example, it is not a good idea to start from the superconductivity to explore the phenomena of phase transitions since we need to understand how electrons form Cooper pairs, how Cooper pairs condensate and develop rigidity, …, etc. and most importantly, how all these relate to zero resistance.

What is the logical minimum set to have the phenomena of phase transition? Discussing with your friends and finding the minimum requirements for a particular concept will help you develop the logical connections of essential concepts for a complex idea. In practice, usually we don’t know what is the simplest non-trivial example. We can start by removing the requirements.

The process will help you learn, and most importantly, one day, you will know the idea in your bone.

Ask yourself: can I have something out of the simple dimensional analysis?

We learn dimensional analysis from the general physics course during the first day of our undergraduate week, but we rarely learn how to use it. There is an interesting book by Migdal [BeuinusovichL18] demonstrating how to use dimensional analysis to proof the Pythagorus’ theorem. You might want to take a look about the neat example. Also, it is interesting to ask: under what condition this proof might fail.