Very broad question on understanding where formulas come from in physics

[HJ Farnsworth]

Greetings everyone,

As we all know, when learning new topics in physics, it is often necessary to learn derivations of abstract formulas. When I go over these derivations, I rarely have trouble understanding them. However, I was curious on people’s opinions as to what degree these derivations should be memorized. It seems ridiculous to attempt to memorize all of them from start to finish, due to the extreme length of many of them – after all, I don’t only want to know where formulas come from, I also want to have the time to learn how to apply formulas.

In many courses that I have taken, though, my professors have explained complex derivations from start to finish. This could be a result of memorization, or just a familiarity with their topic that makes it easy for them to reproduce a derivation on their own.

So everyone, what is your opinion? At what point do you say that you have learned a derivation, and by what method do you go about learning it? Could you reproduce complicated derivations on your own, without any guidance, after learning them by your method?

Thanks for your thoughts.

-HJ Farnsworth

 

[Pengwuino]

I think everyone has trouble with derivations at the start and I think that's perfectly acceptable. I personally have very few if any derivations memorized. I remember one of my professors saying that he didn't have a certain formula memorized and said "why should I? That's why I have books". It's not really important to memorize derivations. It's important to be able to DO the derivation, however! Even if it requires looking up certain properties. You'll never be in a situation where you're asked to derive the completeness of a Hilbert space without any assistance (that was just an example, I've never even seen that done). It's silly. That's not being a physicist.

What really is important is knowing how to do it if need be, even if you have to consult a text for certain properties. It's also important to know the limitations of something, what the beginning stipulations are, and what the motivation is. For example, I've derived the lorentz transformation a few times. Do I remember how? Vaguely. Do I remember what the assumptions are? Sure! Limitations? You bet. The importance? 'Course. Step by step procedure? God no.

 

[Rap]

I agree with Pengwuino, but also, to me, its like reading a novel. Do you need to memorize the entire novel in order to appreciate it? No, but certain lines in the book that really tell you something you didn't know, they might be worth memorizing, as a way of reminding you of some little nugget of truth. If you understand a derivation, then don't memorize it. If there is some part that you don't understand, and then come to understand, remember that part. When I go thru a derivation, my mind goes, blah blah blah, then all of a sudden I see something I didn't know, and then I start my brain recorder.

 

[Nabeshin]

What really is important is knowing how to do it if need be, even if you have to consult a text for certain properties. It's also important to know the limitations of something, what the beginning stipulations are, and what the motivation is. For example, I've derived the lorentz transformation a few times. Do I remember how? Vaguely. Do I remember what the assumptions are? Sure! Limitations? You bet. The importance? 'Course. Step by step procedure? God no.

Truer words have never been spoken! This was phrased perfectly, and is exactly how I feel on the matter as well.

 

[rezeew]

Hello HJ Farnsworth,

Thank you for bringing up this interesting topic. I believe that understanding the derivation of formulas is crucial for truly grasping the concepts and principles of physics. However, I do agree that attempting to memorize every single derivation can be overwhelming and not always necessary.

In my opinion, the most important aspect is to understand the underlying principles and logic behind the derivation. This will not only help in memorizing the formula, but also in applying it to different scenarios. In addition, it is important to practice and solve problems using the formula to solidify your understanding.

As for reproducing complicated derivations on your own, it depends on the individual and their level of understanding. Some may be able to reproduce them after learning them through their preferred method, while others may need guidance or reference materials. It is also important to note that as new research and discoveries are made, formulas may be updated or modified, so it is important to stay updated and continue learning.

Overall, my advice would be to focus on understanding the principles and logic behind derivations rather than just memorizing them. This will not only help in learning how to apply the formulas, but also in developing a deeper understanding of physics as a whole. Thank you for sharing your thoughts and I hope this helps.

Best,