Is learning derivations of formulae always very important?

[Wrichik Basu]

I understand that it is useful to learn and remember the derivations of formulae in most cases. However, I tend to forget the derivations of several formulae, especially those in optics and dynamics.

For a moment, let's forget the examinations. I wish to pursue higher studies in applied physics, if possible either on particle physics, or something related to quantum. What problems can I face in future if I do not remember the derivations, but remember the formulae well?

 

[symbolipoint]

This response is more broadly about derivations using any or much of one's arithmetic or algebra skills. Everyone in the physical sciences, natural sciences, engineering, or any other field which relies on Mathematics absolutely must have skill enough to perform some algebraic derivations. Just as much, a person must be able to take numerical information directly from real or fictional situations and derive his own needed formula.

 

[Orodruin]

This depends on what you mean. If you mean remembering exactly each step of the derivation of a known formula, then no. However, this

What problems can I face in future if I do not remember the derivations, but remember the formulae well?

makes me very concerned. Science is not about being able to plug and chug things into formulae. It is about being able to start from something known and from there being able to synthesise new knowledge. As such, a vital skill is to be able to derive the needed relations based on your input. For example, I do not remember all of the derivations of different relations that are in my book, but give me half an hour and I will most likely be able to reproduce them for you.

The needed skill is to be able to derive the relations, not to memorise the derivation of known relations.

 

[Wrichik Basu]

depends on what you mean. If you mean remembering exactly each step of the derivation of a known formula, then no.

Yes, I was meaning remembering formulae step by step.

However, this makes me very concerned. Science is not about being able to plug and chug things into formulae. It is about being able to start from something known and from there being able to synthesise new knowledge. As such, a vital skill is to be able to derive the needed relations based on your input. For example, I do not remember all of the derivations of different relations that are in my book, but give me half an hour and I will most likely be able to reproduce them for you.

The needed skill is to be able to derive the relations, not to memorise the derivation of known relations.

Skills needed to derive relations are a different story, and is 180° opposite to memorising formulae. I know that plugging values into formulae is only about 0.1% of Science.

My school teachers think that if one memorised derivations and can recall that, then that person knows physics. But I have a different view - formulae are not everything in physics. As you said, if you give me some time, may be I'll be able to derive the formulae. But I cannot always memorise derivations, and that is where the conflict arises. So, I wanted to understand what are opinions of experienced professors, who have faced a world of research.

Thanks for the help.

 

[clope023]

I understand that it is useful to learn and remember the derivations of formulae in most cases. However, I tend to forget the derivations of several formulae, especially those in optics and dynamics.

For a moment, let's forget the examinations. I wish to pursue higher studies in applied physics, if possible either on particle physics, or something related to quantum. What problems can I face in future if I do not remember the derivations, but remember the formulae well?

If you can derive the formulas from first principles, you'll remember them and know how to really use them; if all you do is passively memorize them you won't be able to do as much or be as potentially creative with them.

 

[jtbell]

To put it another way: you should be able to reconstruct a derivation from scratch, given enough time, using your understanding of the fundamental physical principles and your knowledge of mathematical techniques, not simply regurgitate the detailed steps from memory.

Are you still at the introductory (first-year university) level in studying physics? In those courses, most exercises ask you to calculate a numerical value as the answer. In upper-level courses, on the other hand, most exercises ask you to derive an equation as the answer.

 

[haushofer]

I understand that it is useful to learn and remember the derivations of formulae in most cases. However, I tend to forget the derivations of several formulae, especially those in optics and dynamics.

For a moment, let's forget the examinations. I wish to pursue higher studies in applied physics, if possible either on particle physics, or something related to quantum. What problems can I face in future if I do not remember the derivations, but remember the formulae well?

You must learn your own derivations/understanding of topics. Not necessarily the ones by textbooks.

To give an example: I always found textbook derivations of the Coriolis and centrifugal force in classical mechanics quite complicated. Untill I did my PhD involving General Relativity, in which suddenly this Coriolis force became a big deal. I found that you can easily deduce these forces by performing a time-dependent rotation on a geodesic equation in which initially the connection coefficients are zero (this already defines a certain frame of reference). It cleared up a lot of confusion.

You need to develop your own coat rack to put your own understandings if you really want to understand stuff at a deep level.

 

[Joshy]

I think it's alright to use base x height if you want to get the area of a rectangle (basic geometry), but it's probably helpful knowing why it doesn't work well on different shapes and what you could do to get the area otherwise (ie. an integral). I don't think I'd be getting the right answer if I applied base x height to a pentagon shaped object.

I'm still early into my career as an engineer, but I'm quickly seeing the consequences of people who were really good at reciting formulas without understanding it. They heavily rely off of tribal knowledge and luck to move forward, and they act more like technicians rather than engineers or researchers. I cannot remember everything to the last detail neither am I suggesting anything positive about my own skills, but I think it's good to at least see and understand derivations at least once; to understand what assumptions or approximations were made, and why these formulas work or what kind of parameters/conditions invalidate it.

 

[symbolipoint]

To put it another way: you should be able to reconstruct a derivation from scratch, given enough time, using your understanding of the fundamental physical principles and your knowledge of mathematical techniques, not simply regurgitate the detailed steps from memory.

Are you still at the introductory (first-year university) level in studying physics? In those courses, most exercises ask you to calculate a numerical value as the answer. In upper-level courses, on the other hand, most exercises ask you to derive an equation as the answer.

That characterization of beginning university Physics is not correct. Students in Physics 1 - Fundamental Mechanics DO learn right away and throughout, to derive their answers from the needed fundamental equations and mathematical principles.

 

[jtbell]

Students in Physics 1 - Fundamental Mechanics DO learn right away and throughout, to derive their answers from the needed fundamental equations and mathematical principles.

Indeed, but I often felt like Sisyphus, constantly reminding / urging / nagging students to "first do the algebra, then do the arithmetic", i.e. derive an equation that gives the desired final numeric answer, and not plug numbers into one fundamental equation after another, daisy-chain style.

 

[Vanadium 50]

Indeed, but I often felt like Sisyphus, constantly reminding / urging / nagging students to "first do the algebra, then do the arithmetic", i.e. derive an equation that gives the desired final numeric answer, and not plug numbers into one fundamental equation after another, daisy-chain style.

That's easy to fix. Just put in your syllabus that the partial credit stops when the numbers go in.

 

[symbolipoint]

Indeed, but I often felt like Sisyphus, constantly reminding / urging / nagging students to "first do the algebra, then do the arithmetic", i.e. derive an equation that gives the desired final numeric answer, and not plug numbers into one fundamental equation after another, daisy-chain style.

That's easy to fix. Just put in your syllabus that the partial credit stops when the numbers go in.

Exactly! That is, in fact, what many courses (especially in Physics) REQUIRE of the students. No credit given without picking the necessary equations, drawing the representative diagram, and then deriving the answer in symbolic form, before doing the substituting of values.