Why are Physicists so informal with mathematics?

[symbolipoint]

What is wrong with videos? A video is a medium through which information can be communicated. If I transcribed the contents of the same videos into words, printed them and bound them in the form of a book, suddenly that would have more credibility for you?!

Just because a UCLA physics professor expresses himself on VIDEO, it is unacceptable to you?!

Depends on the video. Depends on the quality; depends on the precision; depends on the faithfulness to concept.

 

[Sassan]

”Common sense” is an utterly useless argument in physics.

Correct. I should have said, "common logical sense" by which I mean LUCIDITY in explanation vs. shoving an equation down someone's throat.

I am sorry it has not been clear that I am approaching this topic from the viewpoint of not physics but physics education. I have an undergraduate degree in physics, another in math, and have been a professor at the university level for the past 45 years in a different field: Computer Information Systems. I am approaching this topic only pedagogically. Physicists can discover their truths, celebrate, and move on. But how do we teach those truths to truth-seekers?

Case in point: There is a video entitled "Why is the speed of light what it is? Maxwell equations visualized". The interesting thing is NOT the video itself but the comments written below it. This is only a small sample . . . . . .

I teach electrical theory at university and I’ve never seen such a brilliantly clear explanation of the Maxwell equations and their consequences - Many Thanks.

I've learned more about electromagnetism and the meaning behind Maxwell's equations in these 13 minutes than in 5 years of studying electrical engineering.

As a former undergrad in physics and grad in oceanography, I wish all educators were required to be at this level of understanding, enthusiasm and preparedness.

Thanks. I learned more in 13 minutes then in a semester of Fields and Waves when I was in college 25 years ago.
If only I was taught physics like Arvin does, oh my lost life! No matter then, I will savour the delightful insights of physics in my remaining late years.

If only I had these videos explaining these concepts 20 years back, maybe I would've been a physicist today.

These same reactions can be found to MANY other pedagogical physics videos in which LUCIDITY is the key. Or the teacher can walk into the classroom, write the Maxwell’s equations on the board, and say, “That’s it. If you don’t understand, you don’t belong. Get out”!

 

[Orodruin]

That sounds more like a teacher-specific problem than a problem of the subject. I have known professors in both physics and math who suffer from this. It is hardly something subject specific.

It should be noted that while Maxwell’s equations were important in the historical development of relativity, the modern view is rather the opposite. The speed of light is named so for historical reasons and the main insight of relativity is the geometry of spacetime and the existence of an invariant speed. That this is the speed appearing in Maxwell’s equations follows unambiguously from EM theory being one of the simplest relativistic field theories that can be written down. It is not so much that the speed of light results from Maxwell’s equations as Maxwell’s equations having to contain it in order to be a self consistent relativistic field theory.

Unfortunately, videos that present things seemingly lucidly can still be wrong or not in line with a modern theoretical viewpoint.

 

[Sassan]

That sounds more like a teacher-specific problem than a problem of the subject. I have known professors in both physics and math who suffer from this. It is hardly something subject specific.

It should be noted that while Maxwell’s equations were important in the historical development of relativity, the modern view is rather the opposite. The speed of light is named so for historical reasons and the main insight of relativity is the geometry of spacetime and the existence of an invariant speed. That this is the speed appearing in Maxwell’s equations follows unambiguously from EM theory being one of the simplest relativistic field theories that can be written down. It is not so much that the speed of light results from Maxwell’s equations as Maxwell’s equations having to contain it in order to be a self consistent relativistic field theory.

Unfortunately, videos that present things seemingly lucidly can still be wrong or not in line with a modern theoretical viewpoint.

Thank you for your explanation. You sound like there is perfect consensus amongst professional physicists who read only peer-reviewed journals, and also that this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner. There is almost a feeling of disdain for clarity and lucidity, never mind that Einstein's own book (The Evolution of Physics) is the very picture of lucidity and clarity.
I hope you agree that even among living professional physicist who read only peer-reviewed journals, there is a lot of deep disagreement on a number of topics.

 

[Orodruin]

You sound like there is perfect consensus amongst professional physicists who read only peer-reviewed journals, and also that this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner.

I believe you are misrepresenting some things here. Outreach is an integral part of doing science.

However, yes, for things such as special relativity and basic electromagnetism there is consensus among physicists on how it works. These theories are over a century old and have been studied in excruciating detail. The issue you are experiencing is more likely arising from the fact that popularising these theories for general consumption presents its own set of issues precisely because they are not as easy to intuit about as perhaps classical mechanics. Speaking in a more popularised setting invariably leads to making analogies and simplifications and many times - nay usually - things are distorted in translation and concessions on accuracy have to be made for the sake of presenting a digestible message.

I hope you agree that even among living professional physicist who read only peer-reviewed journals, there is a lot of deep disagreement on a number of topics.

A number of topics at the very fore front of research, yes. That is the nature of the scientific discourse. However, special relativity and electromagnetism certainly do not belong to these topics.

 

[russ_watters]

and also that this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner.

FYI, some of the people you are discussing this with are in fact teachers.

 

[Sassan]

I believe you are misrepresenting some things here. Outreach is an integral part of doing science.

However, yes, for things such as special relativity and basic electromagnetism there is consensus among physicists on how it works. These theories are over a century old and have been studied in excruciating detail. The issue you are experiencing is more likely arising from the fact that popularising these theories for general consumption presents its own set of issues precisely because they are not as easy to intuit about as perhaps classical mechanics. Speaking in a more popularised setting invariably leads to making analogies and simplifications and many times - nay usually - things are distorted in translation and concessions on accuracy have to be made for the sake of presenting a digestible message.


A number of topics at the very fore front of research, yes. That is the nature of the scientific discourse. However, special relativity and electromagnetism certainly do not belong to these topics.

Maybe this question will clarify my point (which is not about popularizing physics but about teaching it deeply): Regarding the Lorentz factor, do you believe a student learning the Special Theory of Relativity needs to be taught only what the formula for the Lorentz factor is and what role it plays in various phenomena such as time dilation, length contraction, etc., or . . . that student also needs to UNDERSTAND (key word) its mathematical derivation (where the formula came from)? The first is knowing, the second is understanding.

 

[pines-demon]

Maybe this question will clarify my point (which is not about popularizing physics but about teaching it deeply): Regarding the Lorentz factor, do you believe a student learning the Special Theory of Relativity needs to be taught only what the formula for the Lorentz factor is and what role it plays in various phenomena such as time dilation, length contraction, etc., or . . .

No that is not enough.

that student also needs to UNDERSTAND (key word) its mathematical derivation (where the formula came from)?

It depends on what you mean by that. If you mean grab some well thought postulates and derive the Lorentz factor from those postulates then that is not enough.

If you mean, see how the theory explains all the contradicting experiments and how it relates to previously known physics, then yes. However, in physics (in philosophy is a different story), you do not need to think "why" the universe decided the Lorentz factor and not Riemann function, for example.

 

[DaveC426913]

word) its mathematical derivation (where the formula came from)? The first is knowing, the second is understanding.

Can that even be taught?

Doesn't it fall upon the motivated student to ensure he understands it?

 

[Sassan]

No that is not enough.


It depends on what you mean by that. If you mean grab some well thought postulates and derive the Lorentz factor from those postulates then that is not enough.

If you mean, see how the theory explains all the contradicting experiments and how it relates to previously known physics, then yes. However, in physics (in philosophy is a different story), you do not need to think "why" the universe decided the Lorentz factor and not Riemann function, for example.

Neither. I mean deriving the mathematical expression for the Lorentz factor geometrically in one minute using Pythagoras' Theorem.

 

[Frabjous]

but there is so much controversy amongst physicists as to exactly HOW this happens. I have read many accounts of it by folks with physics degrees, but they tend to accuse one another of committing misconceptions, and that only THEY have the correct explanation.

If only I had these videos explaining these concepts 20 years back, maybe I would've been a physicist today.

These same reactions can be found to MANY other pedagogical physics videos in which LUCIDITY is the key.

Your argument is all over the place.

 

[pines-demon]

Neither. I mean deriving the mathematical expression for the Lorentz factor geometrically in one minute using Pythagoras' Theorem.

You say neither, but postulating some triangle and getting the Lorentz factor is one of the options there. However that basically leads to no understanding of anything, just shows that you know how to handle triangles but not when to use them or how it maps to nature.

 

[Sassan]

You say neither, but postulating some triangle and getting the Lorentz factor is one of the options there. However that basically leads to no understanding of anything, just shows that you know how to handle triangles but not when to use them or how it maps to nature.

I never said or implied that in teaching the role of the Lorentz factor in Special Relativity, the ONLY thing that matters is its geometric derivation. What I AM saying is that teaching that simple geometric derivation (in addition to everything else) creates a deeper understanding than just memorizing a formula. That derivation makes one UNDERSTAND the WHY of time dilation in addition to the WHAT and the HOW of it. But if the standard physics education is based on just learning and knowing physics without understanding it (whenever that understanding is possible), and professional physicists advocate this paradigm, who am I to disagree?!

 

[Dale]

this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner. There is almost a feeling of disdain for clarity and lucidity

@Sassan frankly, this is a ridiculous assertion. There are many gifted and respected physics instructors. The fact that not every professional physicist is a good physics instructor does not imply some elite community disdain for others. Good physicists who are gifted instructors are celebrated as much for their scientific achievements as their pedagogical prowess (eg Richard Feynman).

The same thing happens in every single other field of human endeavor. Not all history scholars are gifted history instructors, capable of making the material accessible to others. Are all historians therefore categorically elites with a disdain for clarity and lucidity?

Insert any other academic subject in place of physics or history. This is a nonsense complaint with 0 validity. It is a false generalization.

 

[Sassan]

@Sassan frankly, this is a ridiculous assertion. There are many gifted and respected physics instructors. The fact that not every professional physicist is a good physics instructor does not imply some elite community disdain for others. Good physicists who are gifted instructors are celebrated as much for their scientific achievements as their pedagogical prowess (eg Richard Feynman).

The same thing happens in every single other field of human endeavor. Not all history scholars are gifted history instructors, capable of making the material accessible to others. Are all historians therefore categorically elites with a disdain for clarity and lucidity?

Insert any other academic subject in place of physics or history. This is a nonsense complaint with 0 validity. It is a false generalization.

I made a generalization, and like every other generalization, there are exceptions. I am not commenting on the teaching ability of physicists. I am commenting on the fact that physics instructors (generally) feel their job is to pass on the knowledge they have to their students as opposed to awakening the spirit of discovery and exploration in their students, such as . . . .
"If you wanted to (dis)prove this conjecture, what experiment would YOU perform?"
"From such-and-such (historic) experiment, what other theoretical deduction can you make?"
I am not hallucinating that one of the most convincing, lucid, and imaginative physics textbooks is entitled "Physics for the Inquiring Mind" (Eric Rogers). It does not take Sherlock to deduce from this title that many other physics textbooks are NOT for the inquiring mind. If they were, why would Eric Rogers waste his time writing another one?!?! When you read that book, you UNDERSTAND physics, not just LEARN physics.
If this does not make sense, then I am at the end of the line.

 

[Orodruin]

Regarding the Lorentz factor, do you believe a student learning the Special Theory of Relativity needs to be taught only what the formula for the Lorentz factor is and what role it plays in various phenomena such as time dilation, length contraction, etc., or . . . that student also needs to UNDERSTAND (key word) its mathematical derivation (where the formula came from)? The first is knowing, the second is understanding.

Obviously they need to know how it arises as a result of the spacetime geometry. Students should be kept as far away from possible from time dilation and length contraction as possible because those only act as distractions and apply only to very special cases. You obviously have not been around the relativity forums enough or you would know exactly what is my approach to teaching relativity, which goes deeper into understanding what spacetime is rather than focusing on the flashy stuff more introductory courses would throw in your face.

But if the standard physics education is based on just learning and knowing physics without understanding it (whenever that understanding is possible), and professional physicists advocate this paradigm,

It is not, and they do not. You are simply way off base here.

who am I to disagree?!

First you should inform yourself better about what is the actual state of the field.

 

[Dale]

do you believe a student learning the Special Theory of Relativity needs to be taught only what the formula for the Lorentz factor is and what role it plays in various phenomena such as time dilation, length contraction, etc., or . . . that student also needs to UNDERSTAND (key word) its mathematical derivation (where the formula came from)? The first is knowing, the second is understanding.

I think that you are missing the point in your question. As a physics instructor I can tell you for certain that different students learn things differently. The idea that a solid grounding in the mathematical derivation will generally lead to UNDERSTANDING is incorrect.

Some select students will gain understanding that way. Others will gain understanding through spacetime diagrams. Others will gain it through homework problems. Others will gain it through group work or projects.

A conscientious instructor will try as varied an experience as feasible and will carefully watch and listen to their students and check for understanding.

 

[Orodruin]

I am commenting on the fact that physics instructors (generally) feel their job is to pass on the knowledge they have to their students as opposed to awakening the spirit of discovery and exploration in their students, such as . . . .

Why do you think physics instructors are any different from instructors of other subjects here? I can name a number of math instructors that would fit the bill perfectly. You'll find good and bad instructors in all areas of teaching. Physics is no different and your assertion that it is while calling the entire cadre of practicing physicists elitists is quite frankly extremely insulting.

 

[Sassan]

Obviously they need to know how it arises as a result of the spacetime geometry. Students should be kept as far away from possible from time dilation and length contraction as possible because those only act as distractions and apply only to very special cases. You obviously have not been around the relativity forums enough or you would know exactly what is my approach to teaching relativity, which goes deeper into understanding what spacetime is rather than focusing on the flashy stuff more introductory courses would throw in your face.


It is not, and they do not. You are simply way off base here.


First you should inform yourself better about what is the actual state of the field.

Thank you for your advice, and for the time you took to engage me. We have obviously reached the end of this particular line. However, I have some genuine questions (not in the argument mode) about some stuff that puzzles me. Thank you.

 

[Dale]

I am commenting on the fact that physics instructors (generally) feel their job is to pass on the knowledge they have to their students as opposed to awakening the spirit of discovery and exploration in their students

What is your background? You seem to be completely ignorant about how teaching works.

Most instructors (physics, history, any subject) teach at some educational institution as part of a broader curriculum. Their job literally is to pass on a specified subset of the knowledge they have to their students in a specified time frame. They have to do that because the rest of the instructors will assume that students who passed that class already know that specified material.

A gifted instructor can do that and also convey enthusiasm for a topic. That can be contagious and lead a student to desire further discovery and exploration. Not all instructors are gifted, and not all students desire more.

Again, this is not particular to physics instructors. It applies to all academic fields, and probably most non-academic fields. Your singling out physics for this criticism is unwarranted

 

[Orodruin]

However, I have some genuine questions (not in the argument mode) about some stuff that puzzles me. If you care to help me out, please send an email to <redacted> to open the lines of communication outside of this forum.

I spend a lot of my free time trying to help people understand physics on these forums. For free. I happen to generally believe in the openness of the forums and the idea that anyone that has the knowledge and the time can weigh in rather than pre-solociting replies to unknown questions. If you have subject questions, please direct them to the appropriate subforum here on PF.

 

[Sassan]

What is your background? You seem to be completely ignorant about how teaching works.

Most instructors (physics, history, any subject) teach at some educational institution as part of a broader curriculum. Their job literally is to pass on a specified subset of the knowledge they have to their students in a specified time frame. They have to do that because the rest of the instructors will assume that students who passed that class already know that specified material.

A gifted instructor can do that and also convey enthusiasm for a topic. That can be contagious and lead a student to desire further discovery and exploration. Again, this is not particular to physics instructors. It applies to all academic fields, and probably most non-academic fields.

Yes, I must be ignorant about how teaching works after having taught at the university level since 1979 at three different universities, currently at California State University.

 

[Dale]

Yes, I must be ignorant about how teaching works after having taught at the university level since 1979 at three different universities, currently at California State University.

Then how can you make these ludicrous assertions specifically singling out physics instructors? You should know better

 

[Sassan]

Then how can you make these ludicrous assertions specifically singling out physics instructors? You should know better

This is how: Physics (also chemistry) is different from all other subjects (I have an undergrad degree in physics and another in math, a Masters degree in math, another in philosophy, and a doctorate in Systems Sciences from an Ivy League institution) because it involves understanding nature via experimentation. This poses a dilemma for the physics instructor: Do I teach only the generally acceptable results deduced from those experiments, or do I go further back and encourage students to understand why an experiment was performed, how that experiment was performed, how certain deductions were made from that experiment, and whether the outcome of that experiment is amenable to other conclusions. As the adage goes, are we giving students fish or teaching them HOW to fish? If the reality of physics teaching today is to encourage students to foster the spirit of independent discovery/exploration, then I apologize and we have nothing more to discuss.

 

[Dale]

Physics (also chemistry) is different from all other subjects (I have an undergrad degree in physics and another in math, a Masters degree in math, another in philosophy, and a doctorate in Systems Sciences from an Ivy League institution) because it involves understanding nature via experimentation.

Well that is another false generalization. There is a huge body of experimental work in medicine, psychology, biology, materials science, and many other scientific fields. Physics does not have a monopoly on the scientific method.

This poses a dilemma for the physics instructor …

Again, this is not unique to physics. As someone with your background should know.

If the reality of physics teaching today is to encourage students to foster the spirit of independent discovery/exploration, then I apologize and we have nothing more to discuss.

It is the reality at the graduate level. Again, as you should know.

 

[Sassan]

Well that is another false generalization. There is a huge body of experimental work in medicine, psychology, biology, materials science, and many other scientific fields. Physics does not have a monopoly on the scientific method.

Again, this is not unique to physics. As someone with your background should know.

It is the reality at the graduate level. Again, as you should know.

> experimental work in medicine, psychology, biology, materials science,
Medical education does NOT involve experimentation; I know: I was married to a surgeon.
Psychology involves experimentation but because they use mostly nominal/ordinal/interval (and not ratio) scales of measurement, those experiments have a different (less rigorous) scientific basis than physics
Material science is "essentially" a branch of physics, or is at least based on physics.
And the one you did not mention: Political Science. That is an important field, but today it is not taught AS science.

 

[Orodruin]

Medical education does NOT involve experimentation; I know: I was married to a surgeon.

That’s simply not true. I strongly doubt the let your (former?) spouse into an OR without any previous hands-on knowledge on how to handle it. That is experimentation. The entire subject of medicine rests on the results of countless trials and other experiments. Suggesting otherwise is quite astonishing.

My parents, both medical doctors, used to say they met at a corpse that they had to dissect.

 

[Frabjous]

Do I teach only the generally acceptable results deduced from those experiments, or do I go further back and encourage students to understand why an experiment was performed, how that experiment was performed, how certain deductions were made from that experiment, and whether the outcome of that experiment is amenable to other conclusions.

That’s several history of science courses. It took centuries to get from Newton to Hamilton. Faraday started his career in the 1810’s. Hertz didn’t do his experiments until the 1880’s. Does one need to teach the old quantum mechanics before doing Heisenberg and Schrodinger? These debates took generations. One cannot teach them and get students to state of the art in an acceptable amount of time.

 

[Dale]

Medical education does NOT involve experimentation; I know: I was married to a surgeon.

Another ill informed generalization. Some medical education DOES involve experimentation; I know: I coauthored papers where medical students actually performed and published experiments. This is universal in combined MD PhD programs.

Psychology involves experimentation but because they use mostly nominal/ordinal/interval (and not ratio) scales of measurement, those experiments have a different (less rigorous) scientific basis than physics

How is that for elitism? You want to dismiss the science-ness of an entire branch of science because it isn’t “rigorous” enough for you. I don’t think that the scientific method forbids nominal measurements, so why should you?

Not only is psychology, as a field, highly experimental, but it is also a perfect counterexample to your claim because experiments are central to the education process. Freshman psychology classes are packed full of experiments and even undergraduates perform novel scientific experiments as part of the routine curriculum.

Agriculture is another field where the education curriculum relies heavily on experiments. Both agriculture and psychology are trying to understand very complicated systems, but such complicated systems are in fact part of nature, and scientific experiments are in fact part of their curriculum.

Anyway, I am done here. Your arguments have been sufficiently debunked. Your criticism of physics education is full of false generalizations, and your valid criticisms also apply to many other disciplines.

 

[Sassan]

That’s simply not true. I strongly doubt the let your (former?) spouse into an OR without any previous hands-on knowledge on how to handle it. That is experimentation. The entire subject of medicine rests on the results of countless trials and other experiments. Suggesting otherwise is quite astonishing.

My parents, both medical doctors, used to say they met at a corpse that they had to dissect.

Words must mean different things to us! "Hands-on knowledge" is not experimentation. Dissection is not experimentation; it is demonstration and, at best, exploration. Are medical students told by their professor, "This is the research question, and this is a hypothesis pertaining to that question. Now I want you to set up an experiment to see if you can confirm or falsify that hypothesis"?!
90% of medical training is memorization of terminology and facts; the rest is demonstration, exploration, and analysis. I am talking strictly about medical TRAINING, not the broad interdisciplinary field of medicine.
Being astonished is not an argument.

 

[Sassan]

Another ill informed generalization. Some medical education DOES involve experimentation; I know: I coauthored papers where medical students actually performed and published experiments. This is universal in combined MD PhD programs.

How is that for elitism? You want to dismiss the science-ness of an entire branch of science because it isn’t “rigorous” enough for you. I don’t think that the scientific method forbids nominal measurements, so why should you?

Not only is psychology, as a field, highly experimental, but it is also a perfect counterexample to your claim because experiments are central to the education process. Freshman psychology classes are packed full of experiments and even undergraduates perform novel scientific experiments as part of the routine curriculum.

Agriculture is another field where the education curriculum relies heavily on experiments. Both agriculture and psychology are trying to understand very complicated systems, but such complicated systems are in fact part of nature, and scientific experiments are in fact part of their curriculum.

Anyway, I am done here. Your arguments have been sufficiently debunked. Your criticism of physics education is full of false generalizations, and your valid criticisms apply to all disciplines.

I write "those experiments have a different (less rigorous) scientific basis than physics" and you read that as I "want to dismiss the science-ness of an entire branch of science." So much for communication.

 

[Orodruin]

"This is the research question, and this is a hypothesis pertaining to that question. Now I want you to set up an experiment to see if you can confirm or falsify that hypothesis"?!

Impossible. It may be possible in early stages of physics education, but certainly not in latter stages.

You certainly cannot expect physics students to design an experiment verifying the Higgs mechanism.

And talk about elitism when you claim monopoly on what can and cannot be considered an experiment, dismissing out of hand entire branches of science where for some reason you do not feel experiments are rigorous enough.

 

[pinball1970]

Medical education does NOT involve experimentation;

Medics, students of dentistry and probably the vast majority of life sciences have to complete units on biochemistry, bacteriology, pathology et al, all of which have lab work, experiments which is part of the teaching.

 

[pines-demon]

I never said or implied that in teaching the role of the Lorentz factor in Special Relativity, the ONLY thing that matters is its geometric derivation. What I AM saying is that teaching that simple geometric derivation (in addition to everything else) creates a deeper understanding than just memorizing a formula.

Then this is a weird example, because physics student do learn that.

That derivation makes one UNDERSTAND the WHY of time dilation in addition to the WHAT and the HOW of it.

It does not tell you the WHY, you can remove WHY from physics and everything stays the same.

But if the standard physics education is based on just learning and knowing physics without understanding it (whenever that understanding is possible), and professional physicists advocate this paradigm, who am I to disagree?!

Physicists understand it, what makes you think that they don't? I maybe missed that part.

 

[berkeman]

You sound like there is perfect consensus amongst professional physicists who read only peer-reviewed journals, and also that this elite group feels no need to communicate their knowledge to those at a lower level in a lucid, clear, logical manner. There is almost a feeling of disdain for clarity and lucidity

Despite the efforts of the professional scientists and educators who've been replying to you, you appear quite set in your opinions, and this thread is not going anywhere productive. It is now closed.