You're conflating things. This issue isn't that Classical Mechanics has somehow evolved or changed. It's that people continue to find new and better ways to explain and illustrate concepts. At lest personally I don't know of any field or book where I've felt "Hmm, this is basically perfect and I can't imagine a better way to explain these concepts".
Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? it's really apparent there is a LOT of room for improvement in pedagogy.
As the linked PDF illustrates, most people are teaching along a set formula and sequence of concepts. Good teachers will try to tweak and iterate on these formulas and evolve a better curriculum that sinks in better for students.
Naturally as time goes on, if each author has to start from scratch, then it becomes harder and harder to beat "the best book on BLAH" from the last 100 years. (Though I refuse to believe it's a monumental task to write a better textbook than Rudin)
If you have open copy-left books, then in theory people could start with a Rudin, fork it, tweak it and improve it. 70 years of improvement could yield some amazing forks!
"Often newer editions actually worsen textbooks"
That's typically because they select a random new author to in-effect update their copyright date.. and the new author is rarely of the same caliber as the first
> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos?
I have. I went through Khan Academy, Brilliant and 3Blue1Brown. After spending more than 100s of hours I started getting the feeling that these are all good for elementary level math.
But for any serious math (think real analysis, complex analysis, group theory and beyond), all these platforms did was leave me with a warm fuzzy feeling of having learned something cool but in reality that warm fuzzy feeling was not good enough for solving actual exercises that come in textbooks or really deeply understand the material.
I've given up on these online learning media. Back to textbooks. The difference is like night and day.
Note that 3B1B often warns you that his videos bring perspective for a book/class that you're doing or are already done with. And Khan Academy's focus is for K-12.
If you want anything past Analysis 1 I think you'll find that universities guard their content.
> If you want anything past Analysis 1 I think you'll find that universities guard their content.
Not so; there's an absolutely vast amount of freely available undergraduate mathematics resources available at all levels. Honestly, so much that it makes it confusing to choose and not get distracted by the options -- perhaps AI-mediated distillation could be helpful in the future.
Really? Can you link some for Analysis and beyond?
I wanted to find good analysis video lectures from a real university complete with problem sets, homeworks and their solutions. I couldn’t. I think MIT OCW now has one analysis course like that, but it’s relatively “recent”.
> I think you'll find that universities guard their content.
Hmm. All the way back to when I was in college there was advanced content available from the Open University. You had to be awake at 2am and it was in black and white, but it was there.
I didn't mean to say videos are better - just as far as I can tell that's where the most creative new teaching techniques are on display. I'd definitely prefer they were in the written word. Especially if they were an open collaborative effort. Books are great for flipping back and forth with. You have an "ah-ha" moment and skip back several pages and reread something you misunderstood on a first read-through. It's somehow clunky and takes you out of the flow when you do it in a video.
Critically, you can read/listen to something and come away with the false impression you understand it. Sitting down and doing problem is .. not always fun.. but can be critical for the concepts to sink in. I think this is the main point of what you're saying
I could see in the future it being something like watching a video and then doing a programming exercise
I've given up on these online learning media. Back to textbooks. The difference is like night and day.
Are there people who think this is an "either/or" choice, as opposed to a "use both" thing?? I ask, because it's pretty well established that learning is enhanced by use of multiple media types and it seems self-evident to me that books and videos are complementary.
> it seems self-evident to me that books and videos are complementary
Can't speak for others but for me it is more about efficient utilization of time rather than complementing multiple learning methods.
I've found that time spent in learning math from videos have poor return of investment. That time is better spent re-reading a chapter or that thing that I couldn't fully understand the first time and doing more exercises.
Fair enough. For me personally, I find great value in jumping back and forth between different modalities, where the different presentations reinforce each other. But what works for me may not work for everyone, and vice-versa.
I think you're just parroting things you've heard other people say. 3b1b's videos are universally agreed to be excellent, and it's baffling that you think it is a choice between watching them and using textbook and doing the exercises. Anyone with the intellectual capacity to study that sort of material is not going to have a hard time comprehending that they are intended to be complementary, as Grant Sanderson makes very clear at numerous points.
Hmm - I do wonder if for very particular things in physics their heyday has come and gone? Were there more ridiculously talented inviduals deeply steeped in classical mechanics and discussing amongst themselves in the past? I feel modern physicists move onto high-energy phyics or low-energy physics research pretty early in their careers...
Then you are objectively wrong. Look at Grant Sanderson's explanation of introductory Linear Algebra. Very obviously it adds something good to complement the best paper textbooks on the subject.
There are excellent textbooks on Classical Mechanics, probably because it's a crystal clear subject and you can give a detailed account of the essentials in a single volume without handwaving. Of course everything can be improved, but it also can be muddled. If it works think twice before fixing it. Kind of what happens with Rudin and introductory Real Analysis.
On the other hand, there's for instance Optics where you basically have to condense an encyclopaedia and there's always prettier pictures. Or Thermodynamics, Fluid Mechanics etc that can be taught in different ways depending on the curriculum.
There definitely should be pedagogical considerations in higher education, that's lacking because it's usually an afterthought. And it also should be very clear to people getting into higher education that at some later point pedagogy must end and you have to be capable of working your way through the material.
I think you have the perspective of somehow who's succeeded in Physics. In your typical introductory physics class less than half the students will walk away with a very solid understanding of classical mechanics.
To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement
But sure.. Thermodynamics.. things could be worse :)
Sometimes things are just hard because they're complicated and you need to buckle down and learn your multiplication tables. But at least in my own life experience, the vast majority of the time things are a problem because their poorly explained - often by people that poorly understand it themselves.
Once you truly understand something inside and out - and look back on it - it all generally looks relatively simple. But it takes a special talent to be able to go back and reexplain it from the naiive perspective
> In your typical introductory physics class less than half the students will walk away with a very solid understanding of classical mechanics.
That's probably true.
> To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement
In my view, that's probably false. I don't think the problem is masochism, gatekeeping, and people holding on to old textbooks. I think the problem is that classical mechanics is actually hard, at least for most people. If you come in to beginning classical mechanics wanting to have learned it, rather than wanting to learn it, no textbook can save you. And I think that many people come in that way. They want it out of the way as a prerequisite for something else, rather than really wanting to know it for itself.
> To my mind, if the textbook was actually excellent then that would be 80%+. We're nowhere near there. I think there is LOT of room for improvement
I think you overestimate the capabilities of students entering university (even 20 years ago), and underestimate how poor high schools can be in preparing said students.
I went to a mediocre university. A 50-80% drop out rate was there for both physics and EE - I don't know how it compares to the other engineering. And I did not even consider it challenging. Almost all the classes were a breeze for someone like me who was well prepared going in. At least in that EE department, the teachers were very dedicated to teaching. They would allocate 3-9 hours a week for office hours, and the pace they taught as was slow (probably only covered 70-80% of the material that is covered in a top university).
Students were given lots of chances.
The reasons they drop out are:
- Poor preparation at the high school level
- Poor discipline. A lot of students didn't transition well to independence, and didn't have an authority figure (e.g. parent) controlling their schedule.
- Realizing too late what it means when courses are built on top of other courses. Thus you'd have people getting an A in Calculus I, but almost failing Calculus III because they didn't realize they needed Calculus I beyond the course.
- In high school you can get far with a cursory understanding of the material. At university, you could get a B, or even an A, with that approach for introductory courses, but that approach will start trending towards an F in junior/senior level courses.
Sure, I agree with you that pedagogy can be improved, but I expect that 80% would at best become 60% if all you focus on is pedagogy.
I almost wrote above that, to my knowledge and IMVHO, no one has succeeded at writing a book on Thermodynamics yet. I self-censored because that would be too flippant, wouldn't it? Lmao
I took thermodynamics over 30 years ago. I remember having the feeling of learning a different language using a text book whose explanations also needed translation. I remember the book explained Entropy using chaos theory or randomness and talked about popular philosophy during the 19th century. After a bit of mental torture, I realized by Entropy they really mean Thermodynamic Stability. It is just that heat usually dissipates when materials touch, they were using words like chaos or randomness to describe the process. But their description was vague and poorly conceived.
I think Thermo can only be taught if you have a solid foundation in statistics. And stats... is not really taught in the US? I tried to selfstudy a bit, but the textbook situation with stats make math look amazing. For very intro practical things, there are stuff like John Taylor's book... but past that anything rigorous - I actually have no idea how people learn anything
Why should pedagogy ever end? That's like saying at some point in health care medicine must end and you're responsible for your own treatment. What are the professors for, doing research and abusing their grad students?
The idea is becoming intellectually independent, arriving in the stage of self-pedagogy if you like. Peer learning when there's the chance.
You can't realistically expect that there will always be someone up the ladder to explain things to you. I mean, who explains stuff to the professors if it worked like that?
When you get to university, the lesson is very much that you have to learn things yourself. I found that the more decorated the professor, the worse he was at explaining anything, due to some mixture of being unable to go back to a state of ignorance and being in a seat where his main responsibilities are elsewhere (grant applications!). I'm talking about 1or2-to-one tuition here, done several times a week to kids who did very well in high school.
Yes, you have to shed the expectation that others will teach you, I agree with that. In the end, people slogged through by doing a bunch of reading from various sources. It is maybe the main lesson of university for everyone: you're not in high school anymore, you won't just learn whatever the guy says while talking to you. It's quite the shock if you had actually good teachers at school.
The thing is though, you can still demand good teaching materials. Textbooks have to explain things in the clearest way possible. They shouldn't be confusing, especially considering they end up being the main source for just about everything. In this modern world where there are online lectures and textbooks, there's no reason we can't all have the very best explanations of every relevant concept. Yes, of course as a student you still have to put in the time, but the materials ought to be the very best.
You seem to have a very individualistic notion of education.
Even at the research level we are not independent islands of learning and discovery. People collaborate, some pickup certain concepts better than others and vice versa. So we teach and aid each other.
It seems you're firmly against this notion? Or if not please clarify your position?
I think everyone should be capable of working alone as well, and that has been the general assumption around as far as I've noticed. Of course collaboration is usually way more productive and also unavoidable.
But we were talking about education. Theses are individual for a reason.
> Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? it's really apparent there is a LOT of room for improvement in pedagogy.
There is a study showing that you actually understand material better, if you use the most primitive methods: chalkboard and a lecture. Because you are forced to visualize the material yourself, instead of being presented with a ready-made animation.
It probably makes sense to use visual aids for students that just can't grasp the concept, but I believe this will only help in elementary math.
1. I think the research shows that increasing the cognitive load increases the retention. So in general, when it is harder to learn something, you retain it better.
2. When I struggle with books it is because they do not present the motivation behind what they are doing. Videos and "more popular" articles can both provide the big-picture motivation and overview. Sometimes, you have to construct a motivation for yourself, based on what you read. That's hard. Maybe you even invent something new in order to understand a concept better. This approach is slow, though. It's easier if someone explains to you why a certain concept is "hard" or a point of view from which the concept is "easy".
3. I think students who build on a partial understanding are not going to have a better time with videos. They are in greater need of learning how to learn something than they are of facts, but school does not teach that skill (afaik).
I've suggested to college students that they leave their laptops behind and attend lecture with pen and notebook, and take notes. It makes things a lot more sticky in the mind.
And do the homework problems. You'll never understand the material without doing the problem sets.
Have you looked at for instance Khan Academy's Grant Sanderson (aka 3Blue1Brown) Math videos? it's really apparent there is a LOT of room for improvement in pedagogy.
As the linked PDF illustrates, most people are teaching along a set formula and sequence of concepts. Good teachers will try to tweak and iterate on these formulas and evolve a better curriculum that sinks in better for students.
Naturally as time goes on, if each author has to start from scratch, then it becomes harder and harder to beat "the best book on BLAH" from the last 100 years. (Though I refuse to believe it's a monumental task to write a better textbook than Rudin)
If you have open copy-left books, then in theory people could start with a Rudin, fork it, tweak it and improve it. 70 years of improvement could yield some amazing forks!
"Often newer editions actually worsen textbooks"
That's typically because they select a random new author to in-effect update their copyright date.. and the new author is rarely of the same caliber as the first