How to Learn Things
My advice
A summary of my accumulated thoughts and links to the best resources on learning things, both methods and media. I'd imagine this advice probably works best for hard-sciences as that is the context in which it was developed1.
Creating Understanding
Creating and maintaining understanding should be the goal of the kind of learning I'm attempting to describe with this list.
Transcription
One of the most useful techniques for picking up highly technical / mathematical fields I have used is re-writing the content. With a pen and paper, by hand. Not the prose word for word, but writing out equations and proofs helps you both check and build understanding, as it makes it more difficult for you to skip over crucial bits.
Transcription works best when you are actively recalling the information, if only for a short time (ie look at the next couple of lines, store in short term memory, and then try to reproduce). This kind of active recall also helps to force engagement.
I usually don't refer back to these types of notes later (my handwriting is far too poor for that), but without doing this I usually find the content goes... in one eye and out the other?
Spaced repetition systems [SRS]
Spaced Repetition is a technique for building long-term understanding by reviewing flashcards at increasing intervals. It leverages the mechanics of memory to give you exponential recall for linearly increasing effort. SRS is super useful for learning stuff you won't use every day but will need to recall at some point in the future (so if you're a programmer, you wouldn't ankify your favourite programming language but you may add that piece of maths you use once every 3 months). I still find the best software tool for doing SRS to be Anki.
Many others have written far better on this topic than I could hope to, so you should go read them to get the lowdown (and you really should, the method is a game changer):
Michael Nielsen's essay, which serves an an excellent introduction to the topic.
SRS is remarkably good at enabling fluid thought in highly technical disciplines..
Andy Matuschak's essay using spaced repetition will help you write better prompts (how meta...).
Be sure to check Alexey Guzey's life-changing tip on how to actually follow your own advice using Anki...
Writing
Often the best way to get to grips with fields which are more vague than hard tech/maths is to write about them. The reason writing is valuable isn’t that it is super ‘correct’ or original or anything like that, it simply needs to be written out so you can reflect - it is often difficult to assess ideas in your own head.
As an added bonus, if others like your writing, you can get leverage on your learning by sharing your insights on a blog (hey!)
I was using Roam Research which is all the rage at the moment, but for some reason I can't use it properly and always fail to backlink, and find it hard to navigate. I've really taken to the beautiful Bear app, though.
See also - Why You Should Start a Blog Right Now, and the million other things on the internet explaining why writing in public is valuable2.
Teaching
For much the same reasons as writing, teaching can really help clarify stuff in your head by forcing you to express it. If you are in a course and have others around you learning the same material, teach them. Doesn't work as well if you are learning on your own, unfortunately.
Sidenote - I often wonder if one of the useful functions teaching performs for graduate students (apart from funding...) is to force them to actually learn all that material they forgot in undergrad by continually revising it, in essence performing a 'poor-man's spaced-repetition' function.
Those exercises at the end of the chapter that you probably want to skip
Yup, you should prolly do them to improve your understanding, but with a few of caveats
Too easy = don't do them, you aren't learning anything
If you only need a high-level overview rather of a topic than a working knowledge, doing them probably isn't needed. In these cases a good strategy can to be picking out the key facts you need and putting them into spaced repetition.
If you are going to be imminently using this knowledge in a project, you will probably learn equivalent skills by doing that and so doing the exercises may be a waste of time.
Practical experience
There is no substitute for practical experience. Having to apply knowledge forces you to internalise it on a level that not even spaced repetition will enable. Plus, in an environment with others working on the same tasks, you will be forced to learn from people who are better versed than you in the same topic and feel social pressure to improve yourself.
Information Ingestion
Notes on publishing formats...
Books
There are probably too many books. It depends what your goal is. If your goal is simply to learn something, so often, reading a blog post is better than reading a book. Even if the book is, of course, much longer. Books embody knowledge, they store knowledge, they certify knowledge. Those are important, I’m not anti-book. But as a means of communicating knowledge, once you’ve read a certain number of key, earthquake, worldview-shattering books, books are way overrated. They’re actually a pretty weak, impotent way of learning new things. --Tyler Cowen
Books in general are pretty overrated as a tool for learning. The amount you retain from most is pretty minimal (do you remember anything from that book you read last year? -- in many cases, the answer will be no...)
My advice? Don’t read books super linearly - skip bits you aren’t interested in. And super don’t feel guilty about this - reading 30% of a book in sections is far better than not reading it at all, especially if you don't have the time or need to go into everything on a topic in detail. Especially for many nontechnical topics (and even for some technical ones) only 30% of a book is worth reading anyways...
Engagement the material is what actually produces lasting understanding, whether that comes from doing exercises or reviewing Anki3. Ankification or doing exercises inherently slows your reading down dramatically, so be strategic in what read, engage with it deeply, and don’t fall for the trap of feeling like you need to read all the things just because PC has a long book list!
Blogs
Blogs are a fantastic source of info especially for non-technical subjects and advice (hey!) They provide a short introduction to a wide breadth of topics that cuts the fat present in many books (just imagine how long this blog would be if I had signed a contract with a publisher). However, blogs often do not have an explicit way for you to understand the material long-term4; for this revert to SRS. When you're just beginning learning highly-technical subjects books are probably better though as they can include neccacary foundational knowledge.
See also: My linked list with some blogs you may like to follow. Marginal Revolution is one great entry point into the blogosphere. Twitter is a great place to find blogs from interesting people too, although it can be expensive.
Lectures
I find watching lectures to absorb content basically completely useless. They are the worst of all worlds - they dont require any active effort from (even less than reading a book without doing exercises), go into less detail, and take up more of your time 5! The two scenario where I find that lectures can be pretty useful is
When you are stuck understanding something and need it explained in a different way.
If you want to get an overview of something, seminars are quite useful (as long as you take notes.)
Papers
...are an awful format for trying to learn stuff, because they have to follow relatively fixed conventions resulting in a ton of irrelevant boilerplate. Reading papers to stay up-to-date in your field is obviously necessary in academic disciplines, but for getting up to the frontier of knowledge, blogs and even lectures provide far less convoluted introductions...
Questions
How do I actually apply the advice in this list?
Make Spaced Repetition a habit, and follow Alexey Guzey's advice on instilling novel thought patterns with Anki to remind yourself to use these techniques. The "habits" deck really works for shaping my thought patterns and habits.
Some more good advice in this LessWrong post.
What should I learn?
IDK because I don't know what field you are in, but a couple of possible strategies:
Try to learn stuff that is fundamental to the field of your core interests (kinda obvious).
Learn things that are immediately practically useful.
Optimize for long-term understanding - learn fundamentals to the greatest extent possible, but don’t get bored by areas of the stack you have no interest in and thus stop learning. * For example in computing, I wish I had learned a lot about lower-level areas of the stack (OS details, assembly, etc) earlier. Even though to do any particular task you don’t need to know this stuff, in the end it is pretty important to be able to incorporate new stuff into your mental model quickly and to ensure the mental model of what you are actually doing at high levels of the stack is correct.
Make sure you have a clear teleology for what you are learning, otherwise at some point you will lose motivation to learn it and stop.
Appendix: Min-maxing marks
That’s all fine and good, but what if I have an upcoming test, I don’t care about the subject, and I just need to {pass, get 80%, whatever} expending as little time and energy as possible…?
How to get decent marks with minimal effort... any instructors reading this, prolly stop here 😌. It's pretty hard to describe this strategy as "learning" (you will not remember anything two weeks after the test) but it serves its purpose.
0. Wait until you actually need the knowledge…
One of the biggest mistakes students make is thinking that they need to ‘keep up’ with content through a semester. This is inefficient, as you will likely then have to go and re-learn the content when the time comes.
The time you need to cover content before a test is shorter than you might think. Milage will vary but for me for finals in undergrad, probably less (<=3 days) now that most things (at least for me) are open book with COVID (so I need not concern yourself with memorizing formulae). You almost certainly don’t need to go to lectures and tutorials, unless you are struggling to understand particular concepts in which case watching the recordings of these can be super helpful.
1. Find out what the minimal amount of knowledge you need is. Find the minimal spanning list of concepts to learn. Anything not on the syllabus need not apply, and if you are learning it you are wasting your time.
2. Read the textbook to load this minimal amount of knowledge in your working memory. Cross out items on the aforementioned list to learn until you're done. Refer to lectures when confused or stuck on a concept. You don’t need to understand every proof in-depth unless it will be on the exam - surface level details only.
3. Find as many past tests as you can and do as many as you are willing to within your time budget. The aim here should be coverage of question types. Start by doing questions at a variety of difficulty levels, but gradually increase the cutoff for minimal difficulty questions (practising easy ones over and over will make you feel good but you won’t learn much).
If there are particularly difficult questions on past tests, make a note with your solutions to these problems so in the test you can refer back to them during the test (assuming you're allowed to).
I find that this practice phase works best when you do it with maniacal focus the day or two before the test to the exclusion of basically all other activities. If you are doing this method you're probably pretty bored by the course anyway, so just try and compress the time into a single block to minimise the pain.
See also: Karpathy’s advice for undergrads.
Also, subjectivity warning: this advice not meant to be prescriptive, but rather descriptive of best practices I have found that may help you… It’s just my opinion, man.
As an aside, it shocks me how rare blogging is in many formal academic disciplines (outside of basically posting a summary of your paper on twitter)… This may be due to the incentive structure of academia (encouraged to keep ideas relatively private to avoid getting scooped). I think this view is probably wrong, and most would on net benefit amount of crystallization of structural insights they would get from writing less formally within their discipline. For great examples of this sort of thing, see An Outsider’s Tour of Reinforcement Learning, or some of Chris Olah’s pieces.
If you don’t believe me, just try doing one of the exercises from that textbook one week after reading it, without having either used spaced repetition to remember the contents or done the problem set previously.
Apart from some such as Stratechery which perform somewhat of a spaced repetition function as you read about similar ideas every day which are frequently.
I take my own medicine on this one- I attend very few lectures at uni - I simply find it impossible to learn through this medium. I think it is simply because they require so little effort to engage with; learning requires this to occur.