A point that's rightfully emphasized by the author:
> Solving problems is the only way to understand physics. There's no way around it.
This generalizes well to other fields. I don't want to discourage anybody from trying to educate themselves in a difficult field (be it physics or something else), but that's a very common and immediately visible problem with autodidacts. If you haven't worked through enough hard problems you lack the intuition that ties together theory.
That’s a POV I’ve grown to adopt as I got older (like many, perhaps). I used to heavily privilege theory, believing that everything could (and maybe should) be derived from first principles.
Now I place the concrete over everything else; theory is nice when it can illuminate why the practice works. Otherwise, it’s just words.
The most frustrating is when I have friends who have derived their entire understanding of a subject I know as a practitioner (typically something tech/programming related) from watching YouTube videos/listening to podcasts.
Because they’ve heard hours and hours from experts, they have a feeling of deep understanding. But talking to them about this topic is extremely frustrating because their knowledge clearly has never had to be applied to the real world, and is grounded in nothingness, so they misunderstand lots, but they feel like they know what they’re talking about as much as you do.
> That’s a POV I’ve grown to adopt as I got older (like many, perhaps). I used to heavily privilege theory, believing that everything could (and maybe should) be derived from first principles.
> Now I place the concrete over everything else; theory is nice when it can illuminate why the practice works. Otherwise, it’s just words.
That mirrors the trajectory of all humankind, doesn’t it? From lofty Platonic ideals to nitty gritty empiricism and experimentation.
I only became reasonably proficient in physics when I took the summer off between undergrad and graduate school and spent three months, six days a week, ten hours a day, doing nothing but working through four years of undergraduate physics curriculum by solving problems from my textbooks.
I went on to earn a doctorate in biophysics and then began a career developing instrumentation for biomedical research. While I no longer work directly in the field of physics, the physical intuition and reasoning abilities honed by a physics education has allowed me to successfully lead teams consisting of electrical and mechanical engineers, while serving as the liaison to biologists and doctors. I regard a physics education as a modern-day ‘liberal arts’ technical degree.
> Dario Amodei: We have generally found that if we hire someone who is a Physics PhD or something, that they can learn ML and contribute just very quickly in most cases.
Like another commenter, I'm curious what drove you to this. Seems like clearly A Good Idea I Could Have Benefited From, but my attitude was always: I finished the class, whatever I need to learn through application, life will point me toward. Yet I wish I had done something similar to what you did. What gave you the impetus?
> I finished the class, whatever I need to learn through application, life will point me toward.
In math/physics, it often won't. Solving lots of problems serves two particular purposes: To really solidify the concepts in your mind so you won't forget, and ensuring you learn the techniques and not just the knowledge.
For the former, you may find yourself in the position where you find yourself way over your head, and won't know where to start. You usually will not have a single gap, but many. You'll find yourself realizing you'll need to look up material from several textbooks to regain the knowledge you've lost. Once you begin that process, you'll pick up one of your old textbooks and while the physics knowledge may be absorbed, you'll realize you've forgotten much of the math needed to solve such problems. In the unlikely event you'll retain enough to follow the textbook, it is very unlikely you'll know the techniques well enough to solve the real world problem.
And your colleagues will. You'll be alone, and you'll drop out of that group. With physics/math, there often are hard boundaries in these groups. Those who meet the bar are in. Those who don't drop out, because it really sucks being the only person in the group who is struggling with what everyone else considers as basic.
SW engineering has a much more gradual change in skills amongst people, and usually the problems most people work on are fairly learnable in a short amount of time.
Plus, at various times, I’ve had to revisit things I learned years ago and ended up understanding it much better because I could connect it to a swath of things I hadn’t learned the first time I saw the material.
Math and its applications are a contact sport. You don’t truly appreciate it until you try to use it yourself.
This is really interesting perspective -- thanks for sharing it. I think there's something to the idea that some fields are more 'binary' than others -- that if you can't make it past some threshold of _true understanding_ that you will be denied experiences that could push that threshold further. Such a field would warrant a different strategy for learning / mastery than a less binary field.
We were required (by the state I believe) to take a comprehensive test assessing our competency at physics. I struggled with test and was disheartened that four years of strenuous effort would be all for naught. I knew I needed to do something to shore up my understanding of physics if I was going to retain the knowledge decades onwards. The other reason was a simple love for the beauty and underlying simplicity of the subject.
But you will spend the rest of your life arguing with people who insist that there must be a ("quick and dirty") substitute and you're responsible for finding it.
Totally 100% with this. When younger I thought I could read the material and say "Oh, okay that makes sense I understand this." Only to fail miserably when on a test or somewhere I had to apply what I "knew" and realizing I didn't actually know it. I lean strongly toward autodidacticism and learned that if I could solve problems with the technique then I knew it.
My calculus 1 professor gave the advice that the best way to study is to do every problem in the book, then go and get another book and do every problem in that book, and keep doing that until you look at a problem and know exactly every step to do immediately.
There’s certainly fields of math where I’ve seen a twist on the advice. Differential geometry, for example, is a big field with a lot of notation. Different textbooks end up using very different notations and covering non-overlapping sections of the field. Therefore, the advice I got was to not just do the problems, but translate the definitions and theorems into a unified notation that you feel is natural.
That's how I learned probability theory. I studied from one book and solved all problems, then moved to the next, until it became second nature. Probability theory is one of the topics that you will never learn by only reading, it is necessary to develop the necessary intuition.
Which exactly describes the problem with today's culture of people watching a 10 minute youtube clip and then thinking they are experts on the subject matter.
Yes, and I'd take it further. What I'd like to see more of in physics texts is presenting a problem before offering the solution. Too often you get what amounts to a laundry list of techniques and ideas, which are the components to the answers to hard problems, but the student isn't motivated to learn them. If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill. For example, I think calculus is probably better learned after trying to write down some force laws, and perhaps doing some numerical analysis. Then when you learn them you realize those nice closed-form solutions aren't busywork, they are huge labor saving tools that eliminate ad hoc labor intensive analysis.
I would also deemphasize the more mathy parts of calculus - do you really need a deep dive into continuity or the fundamental theorem of calculus? Eventually, yes. But it's just like programming: you're not going to need to understand language theory or ADTs or category theory or lambda calculus to write your first program. Or your second. And, IMHO, you should only reach for this understanding when you realize you need it. Otherwise, it won't integrate well into your toolkit.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this!
I suffer from this. Sure, I'd like to learn physics, but what I don't want to do is learn all of it. Right now. Because what I'd rather learn is what I need to solve the problem I have. It's a silly problem, it's not real world, but it's my problem that I'd like solved.
As I've grabbed my horse and lance and rushed at this windmill from assorted directions, I quickly run into my limitations that prevent the problem being solved. I run into vocabulary problems with the math, the fact that I simply don't have the math to approach the problem (which appears to be some vector calculus -- I think. "No, you idiot, it's XYZ instead", but I don't know enough to know that it's not vector calculus, if, indeed, it isn't). I try to apply basic kinematics to the problem, but I don't know if that's enough. And, finally, it could be all of those things plus, oh, some optimization issues and, also, would you like to be introduced to the several different techniques for computing numeric integration and the differential equation solvers?
"Eeep!"
To quote the film "Addams Family Values":
Wednesday: Pugsley, the baby weighs 10 pounds, the cannonball weighs 20 pounds. Which will hit the stone walkway first?
Pugsley: I'm still on fractions.
So, yea, that's me, I'm Pugsley. It seems I need 2+ years of mechanics, calculus, and differential equations, and, probably, some time with computer based simulation all to chart the course for a spaceship to a planet for a 40 year old role playing game. Of course, I don't know what the, perhaps, abbreviated path I could take through those domains to get to be able to answer my question. That might knock a year off the study, but, unlikely. "Better to have all of the foundation" and all that. Which is true, but I'm kind of after the "reward" part here, not so much the "journey".
I don’t recommend the first book. At least in my edition the typesetting is just odd, which makes it harder to read than it should be. The front matter indicates it was typeset in Mathematica, which probably explains it. The later books in the series don’t suffer from this problem.
The videos that it was essentially transcribed from are great tho.
If it exists, you could probably replace most of the first book with just a really good explanation of the Lagrangian, with lots of examples, I think.
> What I'd like to see more of in physics texts is presenting a problem before offering the solution.
Yes.
> If you present the hard problem first, the student may flail around and realize: I need something to help with this! Now that they know they need it, and why, you can give them the tool that fits the bill.
No.
If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
I never taught at the university level, but with middle and high school math students I taught them to how (re)discover the solutions, rather than teaching them the solutions directly.
As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution -- or tell us to learn it between classes and bring questions back.
> As a practical matter, many of my college classes went too quickly to do anything _but_ teach the solution
My calculus instructor in college was one of those where they'd go through the problem and on step 7 (or whatever) go "Oh, where did we make the error?" where we'd all flail until they pointed us back to step 3 and then had to redo everything all over again. It was, for me, the most maddening way to teach. I was struggling just to get everything copied from the board to experience it by rote, completely unprepared to even process what was going on, much less have to go back and redo everything all over again.
I dropped that class. I always felt it was a mistake not taking calculus in High School. I had a very good relationship with the math teacher there, and we could have done it, to some level, casually between classes. I just didn't take him up on it.
I don't think it breaks trust, if you tell them what's going on. "Hey kids, I'm going to give you a problem that went unsolved until Newton. I don't expect you to find his answer, which I'll teach you later, but I want you to try to solve it your own way."
> If an instructor deliberately gives a student a problem that they know the student _cannot_ solve, then it rightfully destroys trust.
This does not destroy trust, but gives the student an important lesson: we only have the techniques to solve, say, 0.0000001% of the problems. So you have to learn brutally hard for the next many years (or rather decades) to have the minimal qualifications to be able to invent whole new techniques that no person has ever come up in history before to increase this ratio from, say,to 0.000000100000000001% (even this would trigger a whole new aera in the history of science).
>> Solving problems is the only way to understand physics. There's no way around it.
The reason is that you think you understand what you read, but as Richard Feynman said:
> The first principle is that you must not fool yourself, and you are the easiest person to fool.
You think you understand 90% of what you read, but in reality it's probably only 20-30%. By doing the exercises, at the very least you'll know that you don't know that much. And if you then reread the materials a few pages before, you'll realize that you have skimmed (or worse, skipped) some parts because you mistakenly thought you already understood it.
Another tips from my personal experience: When you're reading a textbook, keep asking in your mind questions with the types of "what if" and "how about," which are sometimes not yet explained in the section you're reading. Also, keep associating what you've recently learned with what you've already known (days ago, years ago).
Be curious and validate that you really understand what you think you understand.
Although, I think what you're describing doesn't completely lie on the reader. Oftentimes, the author has plain just not explained things clearly or even remotely well, and the reader has to play a little bit of 20 questions to get to the meat of something. When a book is properly written, then the shared load between the reader and the writer is much more balanced.
In college, I was always the first one out of my friends to “get” a concept, like fast Fourier transforms, anything with signal processing or even coding or any labs we had to do etc so I would spend time teaching them in the library. However I never did any of the exercises, mostly due to laziness and not arrogance. They would get A’s and I would get C’s and D’s.
I emphasize this story to my kids because knowing isn’t important because everyone eventually figure it out. It’s the ones who can do the problems and get good marks that succeed in the end.
I think this shows a lack of self-doubt, which can be deadly. Those problems acted as verification to yourself that you understood the theory and its application. If you truly understood the material, then the problems would be zero effort. However, if you struggled with them it's a signal that you don't know what you think you know.
As someone who had an a similar experience to whom you are replying to, this was definitely not the case. The problems were easy, but were not "zero effort". Even if it takes you only a few minutes to do the steps and show the work per problem, then that could still take you 30-60 minutes to complete the assignment. That was time I'd spend doing things I wanted to do (fun in the short term, a nightmare in the long term).
I think usually the easy problems are just the "burn-in" time to solidify understanding, but there's usually a couple hard problems that take way longer to work through and those will teach you the intuition. Doing simple calculation is different than being forced to conceptualize the entire path from starting information to system to evolution to result.
This is kind of interesting to hear because I was the other way around. I found the best way to understand something was to teach it to others. That way I took what I already understood and was able to see what other people misunderstood, which was often something I'd never expected to be an issue, and add their experience in learning the topic on to what I already knew which expanded my overall understanding.
Then again, in the process of teaching I always found myself teaching people to work problems, which required me to be able to work the problems myself. In a way, it's kind of impressive you managed to avoid doing that.
It used to pose as a difficulty for self leaners because they did not have access to assignments, exams and solutions unless they register for classes.
Nowadays it's a lot easier when there are so many free materials from top school online. And stack exchange and reddit is available almost 24-7 if one ever has a question.
> It used to pose as a difficulty for self leaners because they did not have access to assignments, exams and solutions unless they register for classes.
Many textbooks still employ the deplorable practice of not presenting the answer to all exercises at the end, unfortunately.
It's kind of a tautology though. Physics isn't remotely special in this regard at all, and it doesn't need generalizing from physics. One needs to work through anything to truly learn it: music, sports, gardening, life, writing, etc.
> Solving problems is the only way to understand physics. There's no way around it.
This generalizes well to other fields. I don't want to discourage anybody from trying to educate themselves in a difficult field (be it physics or something else), but that's a very common and immediately visible problem with autodidacts. If you haven't worked through enough hard problems you lack the intuition that ties together theory.