Hacker News Reader

Comment by mnl | Hacker News Reader

What's the problem with a good book, age? Baby Rudin's first edition is 70 and the latest one is from 1976. It's still widely used and will be for a while.

Honestly your problem was that you didn't know any Classical Mechanics yet and you were assuming that the volume of recent developments made old books obsolete. Maybe in Biology, in Physics getting to recent developments would mean that you're familiar with Goldstein, Landau's Vol. I... Abraham-Marsden? Arnold? Those are old.

Often newer editions actually worsen textbooks and then only a few contemporary books become references in the long run. It's always been like this, there's tons of great books from the 70s that aren't used today and could definitely do. At least they're not ~1,000 pp. of waffle, which is what you usually get for your first textbook on anything nowadays.

View on HN

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”.

What about these amazing resources from Daniel Murfet at University of Melbourne:

http://therisingsea.org/post/mast30026/

They have videos as well as everything else. I'd love to study them with someone/some group of people one day.

But, you don't need videos if there are carefully-written course notes PDFs.

Try Oxford: https://courses.maths.ox.ac.uk/course/index.php

E.g. two random Analysis-related courses (second more advanced than first)

https://courses.maths.ox.ac.uk/course/view.php?id=65

https://courses.maths.ox.ac.uk/course/view.php?id=4988

And there are tons of others, but with videos is a bit harder.

Berkeley exam papers with solutions: https://tbp.berkeley.edu/courses/math/113/

Fantastic, thanks!

> 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...

> people continue to find new and better ways to explain and illustrate concepts

I strongly disagree. All the best math and CS books I have are old.

New books about old topics tend to be less informed about the context and core ideas that led to their development.

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 mentioned peer learning, collaboration is that.

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.

I had a 1930s edition of a "radio physics" textbook as a child, and because there could be no prior assumptions about exposure or familiarity, it was filled with very complex ideas explained so cohesively and coherently that, well, I could understand.

The author knew that this book was for people who might be as involved in the business of radio as its science or engineering, so they wrote as much about the application across every industry, breaking down the systems to the component level and manufacturers, deployment, and ordering, as they did the design and theory.

I learned how to evaluate a textbook from its structure and style. It certainly wasn't designed for discrete lessons, and the professor would have needed a diverse and practical understanding to teach it effectively.

> complex ideas explained so cohesively

I wonder if the same thing isn't happening with computer science. When I started studying the topic in the late 80's, I was part of the earliest generation that actually did, and everything seemed to be explicitly written with the goal of making sense. Some things (like recursion and pointers) were fundamentally complicated, but they were made as simple as they reasonably could be.

My son is studying computer science in college right now and I look at the way they present the material and it often seems designed to confuse - I'll read it over and then explain it to him the way _I_ was taught it and he'll say, "oh my gosh, why don't they explain it that way?"

I feel like teaching is mostly a one size fits all endeavor, but people learn and think in different ways, just like a processor is optimized for some operations but not others.

Take simple arithmetic like 12x17. Some people do the long form multiplication (carry the one..), some people say it's 12x10+12x7. Some remember 12x12 from times tables and go 12x12+12x5. Some people make it 24x8+12 => 48x4+12 => 50x4-8+12 etc. Some do it on the abacus in their heads.

All valid, though some are slightly more optimal than others. Good teachers empower alternative solutions and try to help people connect what they already know to what they already understand.

As someone who only learned multivariable calculus successfully via independent study of exterior differential forms as a result of off-handed comments from the differential geometry professor who taught my first-year calc course, I wholeheartedly agree.

Oh, and 12×17 = 10×17 + 2×17 = 10×17 + 2×10 + 2×7 = 170 + 20 + 14 = 204.

Do you have any ore information on that book? I would like to dig it up at a local library. Is is this one perhaps? https://archive.org/details/dli.ernet.16412/page/n9/mode/2up

I'd like to know which book it was.

I took Lebesgue integration and some pretty high powered group theory classes in the 1989s and am retaking them now, and I have to say the presentation now is much better. I think having Terrence Tao blog about how stuff really works makes a difference, at least for lower level grad classes. :) and trying to present groups as the widely useful abstractions they are instead of just a cute self contained theory makes a difference.

Interesting to note we haven’t got a text book for these classes just lecture notes and a number of text books recommended if we want additional presentations.

The problem is that there is no good textbook for Classical Mechanics out there. At least not on an introductory level.

It's funny that for the 19th century and the first few decades of the 20th one physicists were so eager to simplify and generalize their knowledge. With the side-effect of learning quite a few surprising things from the work. And yet for almost a century the goal is explicitly the opposite. (It's almost like if Academia is in crisis...)

I learnt a lot of physics from Marion's 2nd edition (not SR there though). An older and completely forgotten fine textbook is W. Hauser's Introduction to the Principles of Mechanics. Then you jump into Goldstein (the 1980 one, again not SR there). It's a good idea to buy any Schaum book from Spiegel about this too, also for vector analysis if you can't take a course on that.

Yeah, in retrospect, I've set myself for failure with that universal claim.

But the proof of failure is instructive :)

While not exactly "introductory" in terms of mathematical prerequisites, Spivak's Mechanics I[1] is an interesting take on the subject, with extensive historical references if you're in to that sort of thing.

[1] https://archive.org/details/physics-for-mathematicians-mecha...

Taylor’s is fairly “introductory” and it’s fantastic. Very well written.

No Bullshit guide to Math and Physics https://minireference.com/

(serious reply, if it's insufficient for a freshman course i propose following up with Feynman https://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp..., any objections?)

The problem is that the pedagogy, as in, the best most effective way to teach people things, should improve massively in 70 years. Whether it actually does, that is another question.

Should it really though? Maybe pedagogy is just hard and we can't expect constant progress.

Pedagogy, like any other field is constantly developing. We are continually learning new and better ways to teach materials and thus I think the continued evolution of teaching materials has the potential to be a good thing (and I've created curriculum for professional learning, for grad school and for bootcamps).

It is true that just because a book in newer it is not necessarily pedagogically better

It is also true that a poor selection of content or understanding by the author could doom a book even with better pedagogy.

All that said, I love the idea of OSS books/exercises for teaching - I don't know if a sufficiently engaged and competent (domain + pedagogy) would evolve around and/all of them, but it'd be a fine experiment to try!

It would also be great training material for LLMs to help them to tutor using more thoughtful metaphors and examples.

I think that researching pedagogy is very difficult, and, like many scientific fields, it is hard to reproduce results found in papers. (I am not an expert in this area -- I am just a former teacher with around 10 years teaching experience.) One of the main things I notice is that standardized test scores are not really improving. I think that high school students today would score about the same as high school students in the 1980's if they were given the same multiple choice tests. This implies to me that the field has not advanced a lot. I do think that LLMs and other computer based teaching could help.

The problem is, like many social sciences, people refuse to apply the scientific method to pedagogy and would rather lean on vibe-based "theories".

Your response does a pretty good job demonstrating the internal challenges universities face. The interest in making a change was motivated by unmet needs, and it's not going away until those needs are met. The only way to deal with people who won't meaningfully engage in the problem solving process is to go around them.

A textbook should be provided for reference. Copying its contents on a blackboard isn't teaching. You still have to design your course. There's goals to meet, you have to evaluate where your students come from and your job is getting them there.

Besides pedagogy, in college you have to respect your students as studying adults and give them a proper bibliography, emphasizing references for independent study if they don't like your lecture notes, nor your approach, nor whatever.

I understand what a university is, I also understand and am qualified in secondary education and it would be incredibly depressing turning colleges into extended high schools because of business models. That would be exploiting students, I never agree with that.

I actually completely agree with everything you wrote. I'm also very familiar with the ongoing battle between education and training.

What I'm talking about is expanding options to meet additional education needs. Since universities are a shared resource, any solution must be carefully designed to preserve the ability to continue providing existing services. That's difficult to achieve, so I understand the obstructionist response.

All I'm saying is that if you position yourself as an obstructionist, don't be surprised when you're treated like one.

I'm very adaptable nowadays. It's just that I think I know which things should work, but I'm not fighting society, particularly not on this.

The thing with giving the public what they want and being too much of a pragmatist is that we've seen it before.

Consider Western universities in the 17th century, they were still there churning out degrees, but modern science, mathematics and technology developed elsewhere.

The old one-size-fits-some approach is as pragmatic as it gets. Society's education needs have grown beyond what the old model can adequately service. We need new solutions that don't cause regressions on the old solutions.

You're right to protect your existing solution against regressions, and there's value in revisiting old topics in the new discussions, but you're not going to constructively contribute much if you're unwilling to engage with why so many people feel the need for something different in the first place.

Reply on news.ycombinator.com