I thought I would also add my two cents, though there have been many excellent responses already. I recently defended my PhD in Physics (MIT '18).
First of all - great idea! It is never too late to learn math and physics! In fact, with hard work and commitment, anybody can muster them to a high level.
(1) Reading =/= understanding in math and physics. You understand a topic only if you can solve the problems.
(2) Work through the solved problems you encounter in textbooks carefully.
(3) Most people around me have never read any physics textbook cover to cover. E.g. reading Halliday, Resnick & Walker completely might take you years! Not all topics are equally important. Focus on the important parts.
(4) You need guidance on what is important and what is not. Online courses, college material (especially problem sets!), teaching webpages could be a helpful guide. MIT OCW is an excellent resource, once you are ready for it.
(5) Finding someone to talk to is really useful. You will likely have questions. Cultivating some relationship that allows you to ask questions is invaluable.
(4) College courses in math and physics have a very definitive order. It is really difficult to skip any step along the way. E.g. to understand special relativity, you must first understand classical physics and electrodynamics.
(5) Be prepared that the timescales in physics are long. Often, what turns people off is that they do not get things quickly (e.g. in 15-30 minutes). If you find yourself thinking hours about seemingly simple problems, do not despair! That is normal in physics.
(6) You have to 'soak in' physics. It takes time. Initially, you might feel like you do not make a lot of progress, but the more you know, the quicker it will get. Give yourself time and be patient and persistent.
(7) Often, just writing things down helps a lot with making things stick. It is a way of developing 'muscle memory'. So try and take notes while reading. Copying out solved problems from textbooks is also a good technique.
(8) Counterintuitive: If you get completely stuck, move on! Learning often happens in non-linear ways. If you hit an insurmountable roadblock, just keep going. When you return in a few days/weeks, things will almost certainly be clearer.
> (8) Counterintuitive: If you get completely stuck, move on! Learning often happens in non-linear ways. If you hit an insurmountable roadblock, just keep going. When you return in a few days/weeks, things will almost certainly be clearer.
This is something our education system does a poor job at.
My observation from watching a 3.5-year-old all the time is that bootstrapping most skills (e.g. riding a 2-wheeled scooter, solving simple logic puzzles, drawing, cutting with scissors, building structures out of construction toys) does not require frequent or extensive practice per se, but only practice spaced out in time, combined with a positive emotional outlook. The student can try something with limited success for a little while (maybe 15–30 minutes), go away for a few weeks, come try again and fail again, go away for another few weeks, etc., and after a few months there are sudden leaps in ability as the brain has apparently been churning away at the problem in the background without any obvious deliberate effort in between.
I think we should be organizing education to expose concepts and tools early before people are “ready”, but not putting any particular pressure on repeated failure/struggle, and then trying again intermittently.
Instead we try to organize instruction so that each idea, tool, or method is taught once, with students encountering something new for the first time and being expected to understand it through short-term brute effort and punished if they fail, and then often a concept or idea is subsequently left aside and not revisited.
> being expected to understand it through short-term brute effort
Very true, very true. But I have to give grades.
Sure there are things you can do, like quizzes they take as many times as they want and where you only take the final value. But then people don't complete the work. I can't pass them along to Calc II without knowing 70% of Calc I.
It's a tough question in psychology. I had hoped tech would help with it, but I've not had luck in that direction.
>as the brain has apparently been churning away at the problem in the background without any obvious deliberate effort in between.
This is so fundamental. I picked up a similar concept from a passionate english teacher in 7th grade. He said, after a certain point you've done all that you can do, so let your subconscious work on it, sleep on it and the next day or week you'll find your idea coming together. Paraphrased of course.
Sleep is a very important component of this IMO. It doesn't work as well if you are in poor health and sleep-deprived.
It's like some kind of garbage collection and backend processing happens that we just don't fully understand yet as part of the learning process.
Similarly, I found back in college that concepts processed and stored in short-term memory needed to be "slept on" to fully and solidly store into long-term memory and "stick".
Control the input, carefully imagine and focus on the desired output and your brain will take care of much of the rest. Let it.
An excellent list. Pretty much hits the nail on the head. The only thing I would is this:
Often times, well known phenomena and concepts are NOT explained well specifically because they are well known. Whether it's a lecturer or a YouTube video, lots of sources tend to skimp out on the fundamentals. Having said that, don't let it discourage you. It took me forever to discover what the Uncertainty Principle actually means and how it manifests itself in real life. This is related to point 5) I guess.
A lot of good pieces of advice (especially on problem-solving, timescale, and moving on).
However, some points are IMHO superfluous, for example:
> Not all topics are equally important. Focus on the important parts.
These statements are correct and general, and most people would agree with (even having no idea the topic), but are rarely actionable (or even: make sense for a newcomer). Vide most of the motivational quotations.
In short: hard to disagree. But how the heck a newcomer knows what is important and what is not?
The introduction or author's foreword usually covers that in my experience. They'll say which chapters you can skip, and sometimes lay out a map of the key milestone chapters.
There are plenty of textbooks and lecture notes available online and that article links to most of the popular choices. Make sure to choose correct order of topics to avoid getting stuck!
Wow, thanks for the link! What an incredible resource! It’s really a shame that she had to become famous for being mistreated, rather than for writing such a helpful post as this.
I think it's essential to have a strong grasp of high school mathematics, not just high marks, but actually understand it. Gaps here are very serious. What do you think?
(not parent) Agreed. But I would also say that physics can actually help you a lot with understanding math. I learned both physics and math very organically at high school, going way ahead the curriculum, and to me it was more like a single subject. For a physicist, math is just such an essential tool. I cannot imagine having the understanding of calculus that I have without physics. (But then again that's why I'm not a mathematician.)
I'm not the original commenter but here's my thoughts.
For reference, I studied theoretical physics up to a bachelor level in university. Despite the "theory" focus I still had to do the same amount of lab work as everyone else. I did not enjoy it. I didn't learn much about the concepts from it.
I did however learn about the importance of visualising and representing data, statistics and so on.
We all learn differently I guess - for me lab work was a chore and that mental barrier probably didn't help me learn what the experiments were designed to teach.
Absolutely. How can you claim to model something if you haven't at least looked at the thing with your own eyes, played with it with your (metaphoric) hands?
Experiments teach you, that reality is complicated and models have to be simple, but with judicious choices of assumptions, one can still get accurate and precise prediction out of simple models. I am a theoretical physicist, but I would say the experimental courses I have taken were the most important courses in understanding the limitation of theory.
I disagree. Perhaps in some areas, like electromagnetism or optics, but there are large fields in physics where it's not necessary (statistical mechanics, quantum mechanics, gravity, high-energy physics)
I am not saying that you should to do experiments in every area. Just that experiments in a few areas (usually mechanics/EM/optics/basic QM targeted by undergrad labs) is sufficient to give you the necessary intuition about the limitations of theory in all areas.
Short answer: not every physicist works in a lab. Theoretical & mathematical physics are entirely about working with mathematical models of phenomena that other people observed in a lab. It's enough to understand that any theory is rooted in the experimental, and should be falsifiable by it.
First of all - great idea! It is never too late to learn math and physics! In fact, with hard work and commitment, anybody can muster them to a high level.
(1) Reading =/= understanding in math and physics. You understand a topic only if you can solve the problems.
(2) Work through the solved problems you encounter in textbooks carefully.
(3) Most people around me have never read any physics textbook cover to cover. E.g. reading Halliday, Resnick & Walker completely might take you years! Not all topics are equally important. Focus on the important parts.
(4) You need guidance on what is important and what is not. Online courses, college material (especially problem sets!), teaching webpages could be a helpful guide. MIT OCW is an excellent resource, once you are ready for it.
(5) Finding someone to talk to is really useful. You will likely have questions. Cultivating some relationship that allows you to ask questions is invaluable.
(4) College courses in math and physics have a very definitive order. It is really difficult to skip any step along the way. E.g. to understand special relativity, you must first understand classical physics and electrodynamics.
(5) Be prepared that the timescales in physics are long. Often, what turns people off is that they do not get things quickly (e.g. in 15-30 minutes). If you find yourself thinking hours about seemingly simple problems, do not despair! That is normal in physics.
(6) You have to 'soak in' physics. It takes time. Initially, you might feel like you do not make a lot of progress, but the more you know, the quicker it will get. Give yourself time and be patient and persistent.
(7) Often, just writing things down helps a lot with making things stick. It is a way of developing 'muscle memory'. So try and take notes while reading. Copying out solved problems from textbooks is also a good technique.
(8) Counterintuitive: If you get completely stuck, move on! Learning often happens in non-linear ways. If you hit an insurmountable roadblock, just keep going. When you return in a few days/weeks, things will almost certainly be clearer.