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“Why is it that no one has undertaken the task of cleaning the Augean stables of elementary differential equations? I will hazard an answer: for the same reason why we see so little change anywhere today, whether in society, in politics, or in science“

I see a lot of parallels with the Physics department and I think the reason is much more depressing. Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained.

There is also a certain veneration of the establishment and traditions. I remember on my first day of Classical Mechanics the 50+ year old teacher beamed with pride when he told us he used the same exact textbook when he was in school. As if it was written by the Shakespeare of textbook writing and nobody has managed to surpass it in decades. It' frankly should be an embarrassment

As he observed, other departments will step in an do much better. The best linear algebra class I had was a graduate course in the electrical engineering department

I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on. I really wish textbooks with open licenses would take over and they could be reworked and improved year after year by different people



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.


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.


> Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained.

I have been a on the mathematics faculty, including at some decent places, for almost 20 years. I have never met a single university mathematics teacher who thought this way. To the contrary, we are delighted when someone shows even a spark of interest or aptitude (hopefully both). Granted there are high bars for reaching professional competence, but that's intrinsic to the subject—and there is a welcoming place, in math probably more than in any physical science, for amateurs as well as professionals.

> As he observed, other departments will step in an do much better. The best linear algebra class I had was a graduate course in the electrical engineering department

It's worth noting that this isn't necessarily because EEs are better teachers—although of course in any particular case they might be—but because they can give you a course more focused on your interests. Math departments wind up teaching many courses populated largely, if not entirely, by non-math majors, and we cannot be discipline experts in every field of application in which students might be interested—nor, even if we were, could we simultaneously teach one course in a way that appealed simultaneously and particularly to the diverse applications needed by every student.


I don't think the line of thinking is directly "lets make this painful on purpose" but there is a sense of - everyone has to go through the same gauntlet and some people are just not cut out of math/physics/etc. It's just the way of the world. There is not direct desire to make the experience better/smoother/easier than it was your generation.

I don't know how it is in the Math department, but in Physics there is almost a sort of hazing that goes on, where some subjects are just known for how grueling they are and how you just have to go through it

"To the contrary, we are delighted when someone shows even a spark of interest or aptitude" Not to read too much into it, but this kinda hints at the problem. You're delighted at the students that have passed your IQ test. There is generally very little care given to the 70%+ of students that aren't making the cut. The true horror is how many students are in the class and not getting it. And the teachers are not freaking out

From my university experience (which was a while ago) it was abundantly clear that most students hate their math/physics classes, were bored out of their skulls and the teachers are only interested in the engaged students that are getting it.

What you should be "delighted" by is when you find a new way to explain something that resonates with most of the class


I don't know why you're catching downvotes, I think you're completely right. In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material.

Professors of undergraduates don't seem to think from the undergraduate perspective. Most undergrads have only ever known school, and are just following directions while fumbling their way to their first interview. From that perspective it doesn't make any sense why some classes have to be immensely difficult and high-stakes, and others can be a little easier. From the graduated perspective, you can see "the big well-intentioned lie"--in truth, no field can be condensed into 16 weeks, even if you're studying it and nothing else 14 hours per day. The more difficult a class is, the closer it is to the truth that the class itself is a carefully structured playground, and the real field is more dizzyingly wide and complex than any student can imagine. However, I don't see why this lesson has to be so painful to students.


I mean, have you ever taught a class? Do you know how it feels when we make sure a topic is covered both in class and recitation with plenty of time for questions and the students still stuff it?


No, I've never taught a class, so it's possible that the experience of teaching as a professor would irrevocably change my opinion. However, I have spent a lot of time tutoring math and directing bands and choirs, so I'm familiar with the frustration that comes from explaining concepts and then assigning necessary work with plenty of time to do it and then having people still show up unprepared.

I believe that there is a negative feedback loop in the current model of schooling: unprepared students produce jaded instructors produce unprepared students. The big problem with the current lecture method is that any interruption of the momentum of the course for the students' own personal benefit comes with a social cost, so it's better to just shut up and pretend you know what's going on. Furthermore, many lectures build on themselves, so if you misunderstand a concept at minute 3, by minute 20 you're checked out and by minute 50 you're clock-watching. That's why so many math lectures are silent with the exception of the occasional interjection from a star student.

Combine this with the fact that most students are insufficiently prepared for course material in the first place and you end up with modern STEM college: kids who don't get the material slogging through piles of completion-based assignments and exams and putting in the minimum amount of work to get the degree, after which most get the exact same job they'd have gotten if they'd worked harder anyway. They're almost incentivized against deep examination of any one topic, because all time spent working on one assignment incurs a cost against other assignments, or against leisure.

There are so many issues with the way education works at scale in the first world that going down any pathway would take a thousand words, so I'll sum up by saying that I believe that you have a point, and I also believe that the majority of undergraduates are underprepared, entitled, have underdeveloped work ethics, and lack both the discipline and drive necessary to really get something out of their education. However, I still think that the extreme burn-out classes cause more detriments to higher education than they bring as a whole.


> In my engineering curriculum in some cases the teachers were openly hostile to students that had a hard time understanding the material.

While there's no excuse for it, I think faculty see so much apathy on such a regular basis that sometimes it's easy to mistake sincere struggle for a lack of desire to engage. For precisely that reason, I try very hard to recognize and reward my students who are willing to take the time to work with me, whatever their existing comfort or proficiency level with the subject is, but I know that there are times (probably many more than I'd like to imagine) when I don't rise to that ideal.

> Professors of undergraduates don't seem to think from the undergraduate perspective. … However, I don't see why this … has to be so painful to students.

I think you might underestimate how painful it is to faculty, too! Most of us are in this for the love of our subject, and many are even in it for the love of teaching, and it's painful to have something that's so beautiful and beloved for us be the cause of suffering in others.

Anyway—while I completely agree that it would be better if the learning experience could be the joy it should be, and free of the pain that it often carries, I do wonder if some of this might be intrinsic. There are certain topics that are just difficult, and on their first encounter with which most learners will find themselves lost and confused. But those topics have to be, or are believed to have to be, understood to be successful in the field, so that loss and confusion will have to be felt some time. Isn't it better if that's in the classroom rather than on the job?

> The more difficult a class is, the closer it is to the truth that the class itself is a carefully structured playground, and the real field is more dizzyingly wide and complex than any student can imagine.

This is a beautiful description. I know as a teacher that I try to communicate this to my students, but also that I surely fail much more often than I succeed.


> This is a beautiful description. I know as a teacher that I try to communicate this to my students, but also that I surely fail much more often than I succeed.

Thanks. There's an element of hopelessness in trying to explain the immensity of human knowledge to someone who's lived their entire life captured by mandatory schooling. It's just not an interesting thought to most of them. Their worldview has been so artificially limited that attempts to explain the limitations of their circumstances just appear to be more limitations. "Guys, there are more than six hundred thousand mathematicians working right now in the US, and they're working with concepts first thought of as long ago as 3000 BC and maybe earlier!" "Okay, will that be on the test?"

> Isn't it better if that's in the classroom rather than on the job?

If only we were having this conversation in a bar instead of a text forum. That's a huge question and it's clear you're actually interested in talking about your thoughts on it. It's also a subject that interests me.

When you say:

> But those topics have to be, or are believed to have to be, understood to be successful in the field,

I think that's where the big disconnect comes from. What's the point of school? Is it to know enough to be useful at a job, or to plumb the depths of knowledge? Is it some third thing? Ask any recruiter and they'll tell you the new hires aren't prepared to actually do anything useful, and ask any advisor and they'll tell you the new graduate students aren't prepared to actually do anything useful, so we can at least conclude that there's some kind of disconnect going on. Students spend thousands of hours and hundreds of thousands of dollars doing something that does not actually adequately prepare them for what people want them for.

I have a hundred different ideas about how to address this. One thought I've been mulling over recently is that a redefinition of grades is in order. From essay that we're commenting on:

"My colleague’s error consisted of believing that the more testable the material, the more teachable it is. A wider spread of performance in the problem sets and in the quizzes makes the assignment of grades “more objective.” The course is turned into a game of skill, where manipulative ability outweighs understanding...

In an elementary course in differential equations, students should learn a few basic concepts that they will remember for the rest of their lives, such as the universal occurrence of the exponential function, stability, the relationship between trajectories and integrals of systems, phase plane analysis, the manipulation of the Laplace transform, perhaps even the fascinating relationship between partial fraction decompositions and convolutions via Laplace transforms. Who cares whether the students become skilled at working out tricky problems? What matters is their getting a feeling for the importance of the subject, their coming out of the course with the conviction of the inevitability of differential equations, and with enhanced faith in the power of mathematics. These objectives are better achieved by stretching the students’ minds to the utmost limits of cultural breadth of which they are capable, and by pitching the material at a level that is just a little higher than they can reach."

At the undergraduate/introductory level, the only important question is "what awareness do you have of the breadth of this field, and what mastery do you have over the concepts that most agree are its "most fundamental"? You and I both agree that class is a "playground", and any "grade" is in fact meaningless. Rather than assigning As, Bs, Cs etc. as a percentile of subjective completion of arbitrary problem sets, As-Fs should be assigned at the discretion of the instructor as a holistic assessment of oral and written examination, completion of problems and problem sets, participation in the class, and general wisdom.

Students would of course resist this. They want to be graded on impartial, meaningless criteria. That's how they're taught from third grade, and it's the method that allows for the least possible interaction with the material. The only reason they want these grading criteria is so they can plan to spend as little time as possible on the class. This method of approaching learning simply has to be broken at every level of education. You shouldn't even have a GPA until college.


> At the undergraduate/introductory level, the only important question is "what awareness do you have of the breadth of this field, and what mastery do you have over the concepts that most agree are its "most fundamental"? You and I both agree that class is a "playground", and any "grade" is in fact meaningless. Rather than assigning As, Bs, Cs etc. as a percentile of subjective completion of arbitrary problem sets, As-Fs should be assigned at the discretion of the instructor as a holistic assessment of oral and written examination, completion of problems and problem sets, participation in the class, and general wisdom.

I'm not completely sure I agree that this is the solution—if we're re-inventing grades anyway, then I'd like to do something more radical than using the same old A–F and just interpreting them differently (although, even if given free rein to do whatever I liked, I don't know what I would do!)—but I definitely agree that grades, and the standard approach to them, are the most pernicious part of "education" (in the sense of the current schooling system). If there were any way to get away with it, then I would be happy to—indeed, I would prefer to—have all evaluative exercises be diagnostic and informative, only for the students' benefit, and to assign no grade at all, or an A for everyone; but this seems incompatible with a modern university structure (and anyway is essentially forbidden by university administration).


> You're delighted at the students that have passed your IQ test. There is generally very little care given to the 70%+ of students that aren't making the cut.

That's because happy students are all alike, but every unhappy student is unhappy in their own way. It's just not feasible to care in depth about why any one of the 70%+ is not learning effectively. They're probably missing some prior topic that's effectively a prereq for the class, but that's something that should be addressed by the student themselves.


> What you should be "delighted" by is when you find a new way to explain something that resonates with most of the class

You are right, and I am! I don't think that's incompatible with also being delighted when someone shows interest or aptitude. In fact, the synergy is the best part, when someone shows interest or aptitude because they are willing to put in the work to follow the pathway that I have tried to open up for them.


I don't think it's that at all. The real cause is just some entirely institutionalised academics wrote the textbooks and everyone else is copying it rote as if it's the way of doing everything because that's all they know.

You need people from outside the echo chamber. I found The Open University to be a considerably better education provider on that basis than the red brick I attended quite frankly. The material and tuition is far far far better.

Incidentally your point in Khan Academy is spot on. That's basically OU but the material is miles better and it actually leads to a qualification.

Example free course: https://www.open.edu/openlearn/science-maths-technology/intr...


> "Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained."

So true, in many areas. I know a couple of young people that got destroyed by this kind of meat grinding machinery. Typically applies to every medical studies in France, where many kids (with parents that have the money to pay) are going to Spain, Romania or Belgium to study in a less oppressing environment and better teaching methods.


Khan Academy is excellent for Calculus however their material for Differential Equations is rather minimal since they don't really go into university level material.

Perusing online resources for Differential Equations shows that there doesn't seem to be much agreement on how to define the core subject, and there is no grounding on 'how we got here' to provide a path forward to people just starting out. My experience so far, at least.


Curricula are hard to change for the same reason widely-used apis are hard to change: it’s the downstream dependencies. There’s a shared understanding of what “took undergrad differential equations” means, and breaking from that has a cost. If you teach differently, your students will be at a disadvantage because they won’t know the things futre courses, tests and employers expect them to know. Maybe that will be outweighed by the objectively superior education you’ll have provided with your bold new approach, and maybe not.

Not that we should give up and resign ourselves to outmoded received pedagogy, but these are hard breaking changes and we should set our expectations accordingly.


Otoh biology classes don’t suffer from this as much. Textbooks are routinely updated to reflect new understandings. Professors seem to have a lot of choice with what they cover, often highlighting their own subfield where they can speak more to it. Physics classes in comparison felt like a factory. You’d also pay twice as high a lab fee as any biology or chemistry lab to play with 40 year old brass weights and frictionless cars.


One argument TFA makes is that a lot of the material is not ever subsequently used.


This masochism also applies to classical music (eg violin). Decades of rote before you’re allowed to express your own musical thoughts.


I was going to make a variant of this comment. $FAMOUS_COMPOSER's $REALLY_HARD suite is right there, you can get the sheet music and it clearly says "play this note, then play that one, then stop for a specific duration...and so on". That doesn't $EXPLETIVE mean that if you watch Khan Academy's video on how to play notes[1..n] you can play the music according to the composer's specification.

I think people who are frustrated they can't grok diff eq in a n-week course are likewise deluded. There is such a deeper meaning those symbols on the page, and I suspect there is simply no way to spoon feed it.


There are plenty of alternative teaching methods for instruments. (TBH, I don't even know what you are referring to by "classical music", but yeah, some places can be quite oppressive.)


> Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies. The system acts an an informal IQ test - that maintains the prestige of the departments. If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained.

In a twist of irony anyone could have predicted: this selects for the middle of the bell curve, and not the right-hand tail.

I feel as though there are a set of personality qualities that must not be present in order to achieve anything worthwhile. Wasting time, frivolous activities, and fostering an outsized ego are just a few.


Yeah, the high-capability outliers are used to coast in any subject and may or may not have time to adapt to the laborious requirements before failing.

Also, anybody with "street-smarts" can see the cost-benefit ratio and perceive the benefit is kept much smaller than some other, easier subjects, while the cost is artificially inflated.

What it does select is people that really love the subject. And is at least a little bit smarter than average.


> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on

When the entire video is generated by an AI, that dynamic changes. It's no issue to improve "the script", and have it seamlessly regenerated. We can't be that far away from this capability, and it could have a profound impact on available learning resources.


The problem isn't writing a better text, it's having departments willing to teach it, or to try alternate approaches at all.


The OP referenced the Khan Academy as an attempt to displace the ossified educational institutions we have. But it has its own limitations and challenges, some of which will soon be rendered moot by the coming wave of AI technologies, perhaps giving it the final push it needs to truly take hold.

Can imagine a world where it doesn't matter where or how you get your education, all that matters is that you can have your knowledge verified by an accredited _testing_ institution. This would open education up to a world of creative competition for students, and allow individuals to find a learning paradigm that best works for themselves.


This might work well for knowledge/IC-based attainment. There are still other groups, who are possibly the majority when combined:

Some people are there for "the experience", no matter how much it costs, nor how little benefit it results in. They will still be paying $80k for an experience that qualifies them for nothing, even though they had that qualification already before they started.

Some other people are there for the network, and/or will learn leadership skills in that environment. They can't build/learn those things in an online environment.


Agreed. One size does not fit all. It's just the hope that options like Khan Academy are made truly viable for those who are well served by such options.


You have to have a pretty helpless attitude to blame someone else (teachers) on your inability to learn from a good textbook.

How are you ever going to learn anything truly novel in the world if you always delegate teaching to a teacher?


I shouldn't need to read a 500page textbook to understand a class that a teacher has been 'teaching' for 20 years. He's there to give me an understanding of the subject. I have at least 5 classes each semester which are very technical and difficult, it's impossible for me to read a textbook on each while also reading a 20-30 page lab instruction each night, all written in a technical language which I barely understand. I can try but so many times constant consumption of this literature lead to burnout


"Technical and difficult": there are both important concepts and broad strokes that your teacher should be good at explaining, and important details that should be explored in a textbook because they need good pictures, data, editing etc. more than good explanations.

Taking a longer time than normal to learn a topic and prepare university exams might be a good alternative to burnout; or maybe your lifestyle and/or intellect are incompatible with studying.


The entitlement in your comment is staggering...

Why such a desire to be spoonfed, whining about having to put in the work?


Am I not supposed to expect a quality lecture from a university professor? I have had such a bad experience with certain lecturers, I'm certain what they were saying wasn't incorrect but the way they were speaking made it impossible to follow. It wasn't just me who thought so. I admit I've had learning difficulties my whole life but I believe it is actually impossible to learn all the material from the classes with all the details from books. You can pick a field or two which interest you the most and delve deep into the details. An extremely fundamental topic at my uni is called "introduction to circuit analysis". It was taught by a professor who was so bad at teaching it there was no point in coming to his lectures. You would learn more from watching youtube videos. Everyone was aware of the state of that class. Even our lab professors would mock his teaching style. Now if every class was like this we would be lost. I'll give a recent example of another lecturer who I also consider bad, but fortunately he is teaching an easy subject. First class a kid asks 'what's the difference between a router and a switch'. The professor answers 'a switch works on layer 2 and a router works on layer 3'. In my opinion this is a non answer. Yeah he said the truth but it didn't mean anything. If that student didn't know the difference between a switch and a router then surely he doesn't know about the ISO OSI model. Before you think he probably didn't have time to answer more specifically to make sure he understands. This guy notoriously keeps digressing from the subject. As that classes subject is one I am familiar with I knew the way he taught it was impossible to make sense of because he never answered in a concrete way, everything felt so drawn out and lacking a focal point, it's hard to describe. It took him four hours to go over the ISO OSI model and honestly while I wasn't paying attention to every single word he said. With all the digressions and constant comments about stuff you just couldn't follow his train of thought. On the contrary electromagnetism class was absolutely amazing. It's still a difficult subject, at least for me because I've always been pretty bad at physics but the lad who taught it was brilliant. He made sure we all understood, he started with very basic concepts that everyone knew, just to be certain everyone is on the same page. His presentations were concise, easy to follow with links to read up/watch stuff that you didn't fully get or wanted to learn more about. They had plenty of visualizations with gifs of stuff. It's a pleasure going to his classes. So I think that I should expect the lectures to give me an understanding of a subject. If I had to read a book for every class there wouldn't be enough time in a day for me to catch up.


We call this "University"


no one is there to give you anything

they are there to give you a chance

maybe it is impossible for you to do this, but it’s clearly not impossible for others

that challenge is valuable information

maybe a different area is a better pursuit for you

or maybe a better way to view learning

good luck


You are just wrong. There is a lot more that goes into teaching a subject better than 'generating a better textbook'. There are thousands of hours of work that need to happen to figure out how to make the subject make more sense. It is not a question of 'writing down known result sin a different order'. The subject needs to be reworked in its entirely. Advanced results need to be made elementary. Simple formulations of complex ideas need to be discovered, articulated, and developed into exercises. Out of every available model the best models need to be picked and refined and tested. Etc. And then you have to get everyone on board with the project!

Almost none of the work is 'rewriting the book.'


The video won't be generated by AI, because there will no video.

The mid-game is personalised, conversational, interactive tutoring.

The end-game will be deciding how much humans need to know about any of this, because AI will be far better at 99% of it.

If this seems unlikely, consider that Cauchy, Gauss, Laplace, and so on were all super-elite 0.001%-ers in terms of ability.

No one knows whether AI will eventually have the creative ability to work at their level of insight.

Personalised training could select for prodigies, and - whatever we decide to do with them - we'd have more super-talents than we do now.

Currently a lot of talent is wasted because of political and economic inefficiencies.


> there will no video...

There will likely be video. Visual presentations can be an important part of learning. Perhaps it will be generated JIT, but likely AOT compilation of video will represent a useful savings in processing power. Students can always "put their hand up" to interrupt a presentation for a little one-on-one time with professor AI.


Then you could simply read the script — no need for the video at all.


For those who prefer to read the script, of course. For those who benefit from a much more multimedia presentation, the generated video and associated generated items, will be preferable.


I have a lot of expertise in this domain:

> I had a lot of hope for things like Khan Academy, but the issue is video is not text and it's hard to iterate and improve on.

Not the issue.

> I really wish textbooks with open licenses would take over and they could be reworked and improved year after year by different people

The issue.

There actually isn't even a good open content license, analogous to the GPL-style licenses. Improving on video means having access to the source files. Ditto for interactive activities. Khan Academy is designed to look as open as possible, while withholding just enough and being just mean enough with license to make any sort of reuse a hopeless endeavor.

With the proper piece in place, video is very possible to iterate upon.


>I really wish textbooks with open licenses would take over and they could be reworked and improved year after year by different people

Could anyone explain to me how they think this might work in practice?

I am presently producing an undergrad textbook in quantum theory. I have two motivations: 1. IMO the "qubits first" (ie teach finite-dimensional QM before wave mechanics) approach to introducing the theory is superior (basically only Feynman did it of all the "classic" books) and 2. I'm involved in third world education and I want the book to be freely downloadable.

Now its a lot of work despite having taught the course multiple times and produced comprehensive lecture notes etc. Once its done I am sure I will not have the time to keep updating it, expanding on the problem sets and so on. A former student on the course is helping with the conversion and he will be a co-author, but like me he sees it as a service not at all about producing a product. So I think we're both very open to the idea of such "open license".

Given all that here are the kinds of questions that immediately arise:

- Mechanically how should one make the book available for such re-working? Put the source files on github? (Not something I've ever used, but I know roughly how it works).

- Via what mechanism does someone get to be credited for work they might do on better versions?

- Who decides what is the current "definitive" or "best" version? I will have a separate website for the book so I guess new versions can be announced there. But one way or the other I won't be involved forever.

- QM is fraught with crackpots, people who have whacky ideas on how to explain things and so on. Can they be prevented from "taking over", rewriting large chunks into (what I would view as) nonsense and so on? Note that presumably my name would still be associated with the new versions, so the issue is primarily not lending credence to stuff I fundamentally disagree with, not that they shouldn't be allowed to go do their thing.

- We will make a POD service available for purchasing hardcopies, the (expected to be small) royalties from which would be donated to third world physics/math education. Is there some license that can ensure any subsequent use of the material is also similarly non-profit?

I can see some (though not perfect) analogies with open-source software, so perhaps someone here has useful ideas about this kind of thing already...


> Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable

I have a PhD in particle physics, and I've been a researcher at CERN with colleagues from multiple countries.

And I cannot understand what you are saying there.


> > If you're pigheaded and clever enough to get through the masochistic torture is that their undergrad textbooks then you're probably pretty clever and so the prestige of the degrees is maintained.

> I have a PhD in particle physics, and I've been a researcher at CERN with colleagues from multiple countries. And I cannot understand what you are saying there.

Hrm.


???


For what it's worth, I was a researcher at CERN with colleagues from multiple countries, where I turned down an offer to do a PhD in particle physics :-)

(A foolish career decision in retrospect.)

I think they are saying that if you were clever enough to do physics at that level, you wouldn't understand the problem being discussed. So when you said you don't understand, you gave a live demonstration.

When you emphasised your physics credentials as if to say the above didn't make sense even to a physics-smart and well-credentialed person, that pattern-matched even more strongly with the idea that those who go far through higher education institutes don't relate to the problem so don't tend to work on improvements.


What I meant is that I think I know something about academics in science in general, and in Physics in particular.

Getting my PhD was not easy for me, as it wasn't for the most people I met, because none of us is a so-called genius. Rather, all of us had to put a lot of effort and discipline in order to move on.

And never did we met any artificial obstacles or deliberate difficulties. Physics is hard; it is as hard as many other academic fields. You need focus, you need discipline, and yes, you need passion to be able to keep focus and discipline.

But you will be welcome if you try, and you will receive a lot of help. Maybe you will find out it was not the right choice for you and you will change your target, but you will not be screened out and rejected just because.


> The system acts an an informal IQ test

Undergrad textbooks in Physics may be somewhat challenging. But the graduate texts (at least in theoretical Physics) tend to be MUCH harder, especially if your undergrad degree didn't include several courses of abstract algebra and topology.

Ideally, physicists should have Geometric Algebra (Clifford Algebra) as part of their undergraduate classes. But at least when I went to Uni, there was no space in the undergrad tracks for this level of math.


There is nuance to this.

It's not so much a habit of being deliberately arcane as, in my opinion at least, badly attempting to keep the sense of the sublime that engineering departments often lose touch with.

I went to a pretty shit physics department, but there were glimpses of beauty. The engineering department was more professional, better run, definitely more fun if you like the thrill of actually making something, but as engineers theory is just a means to an end, so I would've been bored on some fundamental level.

Aside:

As a (I suspect) dyslexia diagnosis in-waiting I am a sucker for really good, crisp typesetting. Old books often struggle with that (e.g. particularly curly non-latin characters are almost unreadable for me), but reasoning is timeless.

Landau & Lifshitz is old, ugly, a bit terrifying, and yet timelessly brilliant. Difficult, but in a physically challenging way rather than the more modern, Grecian-thinking, rigour-by-nomenclature style found in modernity.


Makes me think of Jackson's electrodynamics - yit always seemed to me a hazing ritual. I remember a story of someone asking him a question from the book and he basically said "how the hell would I know?"

I enjoyed the book and class myself but it did not make me a better physicist, just a better mathematician


given the current political environment i think we should protect and promote old textbooks as much as possible. they’re lean, devoid of ceremony, makes no assumptions about race/gender/political orientation/socioeconomic status of the students as they work their way through the foundations of the subject. for a modern example of mumble jumble junk, with so much presuppositions about your intelligence, see the rust book[0]. it’s a tough book to study because it wastes so many words saying nothing at all. many people have used it yet rust lifetimes and borrow checker semantics is as arcane and elusive as the holy grail.

[0]: https://doc.rust-lang.org/stable/book/


> Both fields embrace a sort of masochism and active desire to keep knowledge impenetrable b/c it acts as a mechanism to feed out the dummies.

Did you go to a top university? And did you study physics in grad school? I find this statement amusing given how easy the undergrad curriculum was compared to grad school physics.

In my undergrad, physics was challenging only in that you needed a good command of the mathematics. If you had that, the actual instruction (and textbooks) were of average difficulty.

But again, experience may vary from university to university. Certainly I can see professors who could have made it much tougher if they wanted to.

As for the rest of your comments in this thread: Sorry, but to me this is another HN thread where people insist it can be taught better, and teachers are being irresponsible in not finding such approaches, but with very little actual proof that it can be as good as imagined. It's not like you have concrete examples of better pedagogy to pointed out.


Came here to quote the same exact part. The author is hilarious and savage but it seems appropriately. Amazing prose and sad state of affairs


Just out of curiosity, what was that classical mechanics textbook?


Pretty sure it was An Introduction to Mechanics Kleppner, Kolenkow

The book was probably okay-ish, the point is that surely someone could have made some improvements in the past few decades


Doesn’t it use cgs only (I think the new editions finally bit the bullet and switched to mks)


Goldstein?




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